Find the sum of each pair of vectors and match it with the magnitude of the resultant vector. PLEASE HELP. Information on the picture
Answers
First of all, let's write this statement in vector form. For the fist vector we have:
Magnitude 3.5 m/s, direction angle 35°:
Let's say this is vector [tex]\vec{A}[/tex], so the magnitude is:
[tex]\left|\vec{A}\right|=3.5m/s[/tex]
And the direction is defined as:
[tex]\theta = 35^{\circ}[/tex]
So the components are:
[tex]Ax=\left|\vec{A}\right| cos\theta \\ \\ Ax=3.5 cos35^{\circ}=2.86m/s \\ \\ \\ Ay=\left|\vec{A}\right| sin\theta \\ \\ Ay=3.5 sin35^{\circ}=2m/s[/tex]
So vector [tex]\vec{A}[/tex] is:
[tex]\vec{A}=2.86i+2j[/tex]
For the second vector:
Magnitude 4 m/s, direction angle 150°:
Let's say this is vector [tex]\vec{B}[/tex], so the magnitude is:
[tex]\left|\vec{B}\right|=4m/s[/tex]
And the direction is defined as:
[tex]\theta = 150^{\circ}[/tex]
So the components are:
[tex]Bx=\left|\vec{B}\right| cos\theta \\ \\ Bx=4 cos150^{\circ}=-2\sqrt{3}m/s \\ \\ \\ By=\left|\vec{B}\right| sin\theta \\ \\ By=4 sin150^{\circ}=2m/s[/tex]
So vector [tex]\vec{B}[/tex] is:
[tex]\vec{B}=-2\sqrt{3}i+2j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=\vec{A}+\vec{B}=(2.86i+2j)+(-2\sqrt{3}i+2j) \\ \\ \boxed{\vec{R}=-0.60i+4j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{Rx^2+Ry^2} \\ \\ Rx=Ax+Bx \\ \\ Ry=Ay+By \\ \\ \\ \left|\vec{R}\right|=\sqrt{(-0.6^2)+(4)^2} \\ \\ \boxed{\left|\vec{R}\right|=4.05m/s}[/tex]
2. Magnitude 4.5 m/s, direction angle 55°, magnitude 3 m/s, direction angle 135°.Matches to 5.83 m/sMagnitude 4.5 m/s, direction angle 55°:
Let's say this is vector [tex]\vec{C}[/tex], so the magnitude is:
[tex]\left|\vec{C}\right|=4.5m/s[/tex]
And the direction is defined as:
[tex]\theta = 55^{\circ}[/tex]
So the components are:
[tex]Cx=\left|\vec{C}\right| cos\theta \\ \\ Cx=4.5 cos55^{\circ}=2.58m/s \\ \\ \\ Cy=\left|\vec{C}\right| sin\theta \\ \\ Cy=4.5 sin55^{\circ}=3.68m/s[/tex]
So vector [tex]\vec{C}[/tex] is:
[tex]\vec{C}=2.58i+3.68j[/tex]
For the second vector:
Magnitude 3 m/s, direction angle 135°:
Let's say this is vector [tex]\vec{D}[/tex], so the magnitude is:
[tex]\left|\vec{D}\right|=3m/s[/tex]
And the direction is defined as:
[tex]\theta = 135^{\circ}[/tex]
So the components are:
[tex]Dx=\left|\vec{D}\right| cos\theta \\ \\ Dx=3 cos135^{\circ}=-\frac{3\sqrt{2}}{2} \\ \\ \\ Dy=\left|\vec{D}\right| sin\theta \\ \\ Dy=3 sin135^{\circ}=\frac{3\sqrt{2}}{2}[/tex]
So vector [tex]\vec{D}[/tex] is:
[tex]\vec{D}=-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=\vec{C}+\vec{D}=(2.58i+3.68j)+(-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j) \\ \\ \boxed{\vec{R}=0.46i+5.80j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(0.46)^2+(5.8)^2} \\ \\ \boxed{\left|\vec{R}\right|=5.83m/s}[/tex]
3. Magnitude 3 m/s, direction angle 70°, magnitude 3 m/s, direction angle 135°.Matches to 3.32 m/sMagnitude 4.5 m/s, direction angle 55°:
This is vector [tex]\vec{E}[/tex], so the magnitude is:
[tex]\left|\vec{E}\right|=3m/s[/tex]
Direction:
[tex]\theta = 70{\circ}[/tex]
Components:
[tex]Ex=\left|\vec{E}\right| cos\theta \\ \\ Ex=3 cos70^{\circ}=1.02m/s \\ \\ \\ Ey=\left|\vec{E}\right| sin\theta \\ \\ Ey=3 sin70^{\circ}=2.82m/s[/tex]
So:
[tex]\vec{E}=1.02i+2.82j[/tex]
For the second vector:
Magnitude 5 m/s, direction angle 210°:
[tex]\vec{F}[/tex]:
[tex]\left|\vec{F}\right|=5m/s[/tex]
Direction:
[tex]\theta = 210^{\circ}[/tex]
Components:
[tex]Fx=5 cos210^{\circ}=-\frac{5\sqrt{3}}{2} \\ \\ \\ Ey=5 sin210^{\circ}=-\frac{5}{2}[/tex]
Then:
[tex]\vec{F}=-\frac{5\sqrt{3}}{2} i-\frac{5}{2}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=(1.02i+2.82j)+(-\frac{5\sqrt{3}}{2}i-\frac{5}{2}j) \\ \\ \boxed{\vec{R}=-3.31i+0.32j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(-3.31)^2+(0.32)^2} \\ \\ \boxed{\left|\vec{R}\right|=3.32m/s}[/tex]
4. Magnitude 6 m/s, direction angle 120°, magnitude 2 m/s, direction angle 140°.Matches to 5.29 m/sMagnitude 6 m/s, direction angle 120°:
[tex]\left|\vec{W}\right|=6m/s[/tex]
Direction:
[tex]\theta = 120^{\circ}[/tex]
Components:
[tex]Wx=6 cos120^{\circ}=-3m/s \\ \\ \\ Wy=6 sin120^{\circ}=3\sqrt{3}m/s[/tex]
So:
[tex]\vec{W}=-3i+3\sqrt{3}j[/tex]
For the second vector:
Magnitude 2 m/s, direction angle 240°:
[tex]\vec{Z}[/tex]:
[tex]\left|\vec{Z}\right|=2m/s[/tex]
Direction:
[tex]\theta = 240^{\circ}[/tex]
Components:
[tex]Zx=2 cos240^{\circ}=-1 \\ \\ \\ Zy=2 sin240^{\circ}=-\sqrt{3}[/tex]
Then:
[tex]\vec{Z}=-i-\sqrt{3}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=(-3i+3\sqrt{3}j)+(-i-\sqrt{3}j) \\ \\ \boxed{\vec{R}=-4i+2\sqrt{3}j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(-4)^2+(2\sqrt{3})^2} \\ \\ \boxed{\left|\vec{R}\right|=5.29m/s}[/tex]
Related Questions
Which equation can be used to solve for b?
8 Ft
b = (8)tan(30°)
b=tan(30°)
b = (8)sin(30)
b =8/ sin(30)
Answers
Answer:
Answer is
b = (8)tan(30°) - first choice
Step-by-step explanation:
Steps:
tan 30=b/8
b= 8tan30°
Option (a) is correct, b = (8)tan(30°) is the equation which can be used to solve for b
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles
In a right angle triangle the three sides are represented by the letters a, b and c .
a represents the side adjacent with given angle .
b represents the side opposite to the given angle.
c represents the hypotenuse of the triangle .
Check the attached image for clear picture of the right angle triangle with angle 30 degrees .
Using the trigonometric ratio we can write the ratio as
b/a = tan 30
Multiplying both sides by a , we get
b= a tan 30
since a=8 so
b =8 tan (30)
Hence, b = (8)tan(30°) is the equation which can be used to solve for b
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What is the slope of the function (-2,8) (-1,2)(0,-4)(1,-10)(2,-16)
Answers
Answer:
-6
Step-by-step explanation:
To find the slope, plug any two of your points into the slope formula.
I'll use your first two; (-2, 8) and (-1, 2).
[tex]\frac{y2-y1}{x2-x1}[/tex]
Your y1 term is 8, your y2 term is 2.
Your x1 term is -2, your x2 term is -1.
[tex]\frac{2-8}{-1-(-2)} \\\\\frac{-6}{-1+2} \\\\\frac{-6}{1} \\\\-6[/tex]
Your slope is -6.
Answer:
The slope is [tex]\huge \boxed{-6}[/tex].
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\displaystyle \frac{2-8}{(-1)-(-2)}=\frac{-6}{1}=-6[/tex]
Therefore, the slope is -6, and the correct answer is -6.
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?
0.1
1/2
1
10
Answers
If an image of a triangle is congruent to the pre-image, the scale factor of the dilation is 1
How to determine the scale factorFrom the question, we understand that the images are congruent
This means that, the shape is not dilated.
Instead, the shape is translated, reflected or rotated.
When a shape is not dilated, the scale factor is 1
Hence, the scale factor of the dilation is 1
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true or false? tan( pi/2 -x)=cotx
Answers
Answer:
True.
Step-by-step explanation:
Let's use the picture I made.
I used degrees instead...
tan(90-x)= b/a . I did opposite over adjacent for the angle labeled 90-x which is that angle's measurement.
cot(x)=b/a . I did adjacent over opposite for the angle labeled 90 which is that angle's measurement.
Now this is also known as a co-function identity.
[tex]\tan(\frac{\pi}{2}-x)[/tex]
Rewrite using quotient identity for tangent
[tex]\frac{\sin(\frac{\pi}{2}-x)}{\cos(\frac{\pi}{2}-x)}[/tex]
Rewrite using difference identities for sine and cosine
[tex]\frac{\sin(\frac{\pi}{2})\cos(x)-\sin(x)\cos(\frac{\pi}{2})}{\cos(\frac{\pi}{2})\cos(x)+\sin(\frac{\pi}{2})\sin(x)}[/tex]
sin(pi/2)=1 while cos(pi/2)=0
[tex]\frac{1 \cdot \cos(x)-\sin(x) \cdot 0}{0 \cdot \cos(x)+1 \cdot \sin(x)}[/tex]
Do a little basic algebra
[tex]\frac{\cos(x)-0}{0+\sin(x)}[/tex]
More simplification
[tex]\frac{\cos(x)}{\sin(x)}[/tex]
This is quotient identity for cotangent
[tex]\cot(x)[/tex]
Answer:
True
Step-by-step explanation:
tan( pi/2 -x)
We know that tan (a-b) = sin (a-b) / cos (a-b)
tan (pi/2 -x) = sin (pi/2 -x)
--------------
cos (pi/2 -x)
We know that
sin (a-b) = sin(a) cos(b) - cos(a) sin(b)
and cos (a-b) = sin(a) sin(b) + cos(a) cos(b)
tan (pi/2 -x) = sin (pi/2) cos (x) - cos (pi/2) sin (x)
----------------------------------------------
sin(pi/2) sin(x) + cos(pi/2) cos(x)
We know sin (pi/2)=1
cos (pi/2) = 0
tan (pi/2 -x) = 1 cos (x) - 0 sin (x)
----------------------------------------------
1 sin(x) +0 cos(x)
tan (pi/2 -x) = cos (x)
------------------
1 sin(x)
We know cos(x)/ sin (x) = cot(x)
tan (pi/2 -x) = cot(x)
What is the following product 3 square root 16 x7 times3 square root 12 x9
Answers
Answer:
[tex]4x^5\sqrt[3]{3x}[/tex]
Step-by-step explanation:
The product will be written as:
[tex]\sqrt[3]{16x^7}*\sqrt[3]{12x^9}[/tex]
As both the radicals have same root 3 so,
[tex]= \sqrt[3]{16x^7 * 12x^9}[/tex]
The powers of x will be added as the base is same
[tex]=\sqrt[3]{16*12 * x^{(7+9)}}\\=\sqrt[3]{192x^{16}}\\[/tex]
We have to break the terms so that the powers can be written as a multiple of 3
[tex]=\sqrt[3]{64*3*x^{15}*x}\\ =\sqrt[3]{(4^3)*3*(x^{3*5})*x}\\ Applying\ cube\ root\\= 4x^5\sqrt[3]{3x}[/tex]
What is the relationship between the graphs of y = 2x and y = 2-x?
Answers
Both of these are linear equations with different y-intercepts and different slopes.
Let's analyze the lines:
y = 2x:
This is a linear equation with a slope of 2 and a y-intercept at the origin (0,0). This means that for every unit increase in x, y increases by 2. The graph is a straight line that passes through the origin.
y = 2 - x:
This is also a linear equation, but with a slope of -1 and a y-intercept at (0,2). This means that for every unit increase in x, y decreases by 1. The graph is a straight line that intersects the y-axis at the point (0,2).
Now, let's consider their relationship:
Both equations are linear, so their graphs are straight lines.
The slope of the first line (y = 2x) is positive (2), indicating a upward-sloping line.The slope of the second line (y = 2 - x) is negative (-1), indicating a downward-sloping line.Therefore, the graphs of these two equations are lines with different slopes. The line represented by y = 2x slopes upwards, while the line represented by y = 2 - x slopes downwards.
Write the ordered pair that represents MP. Then find the magnitude of MP.
M(-19,4), P(4,0)
a. (23– 4): 1545 units
c. (23; - 4): 545 units
b. (-15, 4): 1545 units
d. • (-15, 4): 545 units
Answers
Answer:
(23,-4):[tex]\sqrt{545}[/tex] units
Step-by-step explanation:
We are given that M(-19,4)and P(4,0)
We have to find the ordered pair that represents MP and find the magnitude of MP.
MP=P-M
MP=(4,0)-(-19,4)=(4+19,0-4)
MP=(23,-4)
Magnitude of MP=[tex]\sqrt{(23)^2+(-4)^2}[/tex]
Magnitude of MP=[tex]\sqrt{529+16}[/tex]
Magnitude of MP=[tex]\sqrt{545}[/tex] units
Hence, .option c is true.
Answer:c.(23,-4):[tex]\sqrt{545}[/tex] units
Answer:
A 2021
Step-by-step explanation:
what is 1 1/5 * 2 2/5 - 3/5 because I don't understand lol
Answers
Answer:
2 and 7/25
Step-by-step explanation:
Trust me dude.
let's firstly convert the mixed fractions to improper fractions, also recall PEMDAS, multiplication is done before any additions or subtractions.
[tex]\bf \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}}~\hfill \stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{\cfrac{6}{5}\cdot \cfrac{12}{5}-\cfrac{3}{5}}\implies \cfrac{6\cdot 12}{5\cdot 5}-\cfrac{3}{5}\implies \cfrac{72}{25}-\cfrac{3}{5}\implies \stackrel{\textit{using the LCD of 25}}{\cfrac{(1)72~~-~~(5)3}{25}} \\\\\\ \cfrac{72-15}{25}\implies \cfrac{57}{25}\implies 2\frac{7}{25}[/tex]
4. What is the volume of a cube measuring 5 cm on each side?
Answers
Answer:
the volume of a cube by 5cm is going to be a 5x6=30
Which describes the combined variation in the formula h=2A/b
Answers
The formula h=2A/b indicates a combined variation. As the values of A and B change, the value of H also changes accordingly. Understanding its concept helps in solving related problems.
Explanation:The formula h=2A/b is a representation of combined variation. Combined variation, or joint variation, occurs when a quantity varies directly with the product of two or more other quantities. In other words, as the values of A and B change, the value of h will also adjust accordingly. Let's break it down:
When A increases, H also increases if B is kept constant. When B increases, H decreases if A is kept constant. The value of '2' is the constant of variation here, indicating that H is twice the result of A divided by B.
By understanding the concept of combined variation, solving problems involving such formula will become much easier.
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The equation h=2A/b represents combined variation where h varies directly with area (A) and inversely with width (b). The formula indicates how changing one variable affects another in the context of proportional relationships. The mention of molecular cohesion and size pertains to a different scientific context and is not directly related to this mathematical formula.
The formula h=2A/b describes a scenario of combined variation, where h varies directly as the area A and inversely as the width b. Direct variation means that as one variable increases, the other variable increases as well, while inverse variation indicates that as one variable increases, the other decreases. In this case, if the area doubles, h will also double if b remains constant, and if b is halved, h will double, assuming A stays constant.
The provided information about the parameter a describing inter-molecular cohesion and the parameter b describing the effect of molecular size seems to be associated with a completely different context, likely a scientific or chemical formula, rather than the combined variation formula presented in the question. This formula might be relevant to the Born-Oppenheimer surfaces as depicted in Figure 3.1c, which describes a chemical interaction.
Find the value of C in the picture
Answers
Answer:
The measure of arc c is 86°
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
86°=(1/2)[arc c+arc a]
see the attached figure with letters to better understand the problem
In this problem
Triangles ABO and CDO are congruent by SSS postulate theorem
∠AOB=∠COD
∠AOB=arc a -----> by central angle
∠COD=arc c -----> by central angle
therefore
The measure of arc a is congruent with the measure of arc c
arc a=arc c
so
86°=(1/2)[2arc c]
86°=[arc c]
arc c=86°
PLS HELP, math is my weakest subject and my teachers made it worse.
Answers
Answer:
The correct answer to this problem is the final option, angle BTA is congruent to angle ATC.
Step-by-step explanation:
To solve this problem, we first have to unpack the meaning of the given information. First, let's remember that CPCTC means that corresponding parts of congruent triangles are congruent. This means that the same parts of two different triangles that are stated to be congruent (the same) are thus also congruent (the same).
In this case, triangle BAT and triangle CAT are stated to be congruent. This means that line segment BA and CA are congruent, angles BAT and CAT are congruent, and more because of CPCTC (explained above).
The correct answer to this problem is the final option, angle BTA is congruent to angle ATC. We can figure this out simply by looking at the triangle names. Angle ATC is the same as angle CTA (the letters are just in reverse order). From the congruence statement, we can tell that BTA and CTA are congruent angles due to the fact that triangle BAT and CAT are congruent using CPCTC. Looking at the figure, this makes sense because these two angles appear to be the same measure.
Also, we can eliminate the other answer choices, since they are not corresponding parts of the two triangles (the line segments and angles do not represent two congruent pieces of the triangle - they are not matched up correctly).
Hope this helps!
What is the mean of the data set?
108, 305. 252, 113, 191
Answers
Answer:
193.8
Step-by-step explanation:
The 'mean' of a set is the set's average.
To find the average, add the terms together and divide by the number of terms.
[tex]108+305+252+113+191\\413+252+113+191\\665+113+191\\778+191\\969[/tex]
Divide by your number of terms (5).
[tex]\frac{969}{5} =193.8[/tex]
Answer:
193.8
Step-by-step explanation:
You add up all of the numers and get 969. Then you have to divide by the amount of numbers there are so divide by 5 and get 193.8
Find the length of the median from the vertex B of ∆ABC whose vertices are A(1, -1), B(0, 4) and C(-5, 3)
Answers
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
The median from B intersects the midpoint of AC
Find the midpoint using the midpoint formula
midpoint = [ 0.5(1 - 5), 0.5(- 1 + 3) ] = (- 2, 1 )
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = - 2, 1 ) and (x₂, y₂ ) = (0, 4 )
d = [tex]\sqrt{(0+2)^2+(4-1)^2}[/tex]
= [tex]\sqrt{2^2+3^2}[/tex]
= [tex]\sqrt{4+9}[/tex] = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to 1 dec. place )
What is sin -1(1/2) if the terminal side of 0 is located in quadrant 1.
Answers
Answer:
30
Step-by-step explanation:
[tex]\sin^{-1}(\theta)[/tex] is going to output a number in between [tex]\frac{-\pi}{2}[/tex] and [tex]\frac{\pi}{2}[/tex].
Luckily you are looking for [tex]\theta[/tex] in the 1st quadrant which is contained in the given interval above, so the answer just comes down to what the calculator returns from entering [tex]\sin^{-1}(\frac{1}{2})[/tex] in your calculator.
You may also use the unit circle. sine value refers to the y-coordinate on there.
So you are looking for when the y-coordinate is 1/2 in the fist quadrant which is at 30 degrees.
Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies
Answers
Answer: 6
Step-by-step explanation: 8 times 3/4 equals to 6.
Answer:
6 teaspoons
Step-by-step explanation:
Number of teaspoon in 1 batch = 3/4
Number of teaspoon in 8 batches = ?
We know the quantity of teaspoon of vanilla for one batch. To find the quantity for 8 batches we will simply multiply the quantity of teaspoon of vanilla for one batch by 8
=3/4 * 8
=3*2
=6
Therefore 6 teaspoons will be needed....
x is 4 less than a number . What expression represents the value of x?
Answers
The expression will be x=y-4
What is less than expression?The less than expression implies that one number x is lower than another number b by some constant d i.e. it implies that b is greater than a. If we subtract a from b it will give the constant d.
Here, given that,
x is 4 lesser than a number,
let's assume that number is y
from the above, it is clear that As y is greater than x, if we subtract 4 from y we will get x.
so the expression can be written as
y-x=4
⇒x=y-4
Therefore The expression will be x=y-4.
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The expression 'x is 4 less than a number' can be represented algebraically by the equation 'x = n - 4', where n is the unknown number.
Explanation:If you're asked to represent a situation involving x as an algebraic expression, you should analyze all the provided facts. According to the question, x is 4 less than a certain number. This situation can be represented by the expression x = n - 4, where n is the number being referred to. In this expression, we made sure to account for the fact that x is 4 less than this number, so we subtract 4 from n to find the value of x.
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im sorry if this is annoying but this is the last time
estimate
590 divided 3.21
2
20
200
2000
THANK YOU SO MUCH HAVW A GOOD DAY!
Answers
Answer:
The answer is 183.
When you estimate that it is 200.
So the answer is (C) 200
Step-by-step explanation:
The explanation is shown in the picture.
The answer is 183.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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Which point would map onto itself after a reflection across the line y= -x
A) -4,-4
B) -4,0
C) 0,-4
D) 4,-4
Answers
Answer:
d
Step-by-step explanation:
Answer:
D. (4, -4).
Step-by-step explanation:
y = -x is a line that has a negative slope of -1 ( rising to the left) and passing through the origin. It makes an angle of 45 degrees with the x-axis.
So, for example the point ( 0,1 )will map onto( -1 , 0).
Any point which maps on to itself across this line will have to lie on the line.
If x = 4 y = -x = -4.
2. Does the point (2, 3) lie on the graph of y = 3x - 4 ? Explain. (2 points)
Answers
Answer:
Step-by-step explanation:
because :
when : x = 2 y = 3(2)-4 =6-4 =2 non 3
What is the length of one leg of the triangle?
9 cm
972 cm
18 cm
18/7 cm
Answers
Answer:
9(sqrt)2 (B)
Step-by-step explanation:
1. 18(sqrt)2/2=12.727
2. 9(sqrt)2=12.727
3. 12.727=12.727
They match! So the final answer is B
Hope this helps :)
your question is incomplete. please read below to find the missing content.
A. 9 cm
B. 9[tex]\sqrt{2}[/tex] cm
C. 18 cm
D. 18[tex]\sqrt{2}[/tex] cm
The answer is option B. 9[tex]\sqrt{2}[/tex] cm
What are trigonometry ratios?Trigonometric ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.various ratios are:-sin=perpendicular/hypoteneusecos=base/hypotenusetan=perpendicular/base (tan30°)=5/bcot=base/perpendicularsec=hypotenuse/basecosec= hypotenuse/perpendicular
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios.
Calculations:-
given length=18 cm (hypoteneuse)
angle = 45°
⇒sin 45°=perpendicular/hypoteneuse
⇒1/[tex]\sqrt{2}[/tex]=perpendicular/hypoteneuse
⇒perpendicular =1/[tex]\sqrt{2}[/tex]*hypoteneuse
⇒perpendicular = 18/[tex]\sqrt{2}[/tex] = 12.727
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Consider the quadratic function f(x)=x^2−5x−6.
Determine the following: (enter all numerical answers as integers, fractions, or decimals):
The smallest x-intercept is x=____ .
The largest x-intercept is x=____ .
The y-intercept is y=_____ .
The vertex is ( ___ , ___ ).
The line of symmetry has the equation _____.
Answers
Answer:
Part 1) The smallest x-intercept is x=-1
Part 2) The largest x-intercept is x=6
Part 3) The y-intercept is y=-6
Part 4) The vertex is the point (2.5,-12.25)
Part 5) The equation of the line of symmetry is x=2.5
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-5x-6[/tex]
step 1
Find the x-intercepts
we know that
The x-intercept is the value of x when the value of the function is equal to zero
so
equate the function to zero
[tex]x^{2}-5x-6=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}-5x-6=0[/tex]
so
[tex]a=1\\b=-5\\c=-6[/tex]
substitute in the formula
[tex]x=\frac{-(-5)(+/-)\sqrt{-5^{2}-4(1)(-6)}} {2(1)}[/tex]
[tex]x=\frac{5(+/-)\sqrt{49}} {2}[/tex]
[tex]x=\frac{5(+/-)7} {2}[/tex]
[tex]x=\frac{5(+)7} {2}=6[/tex]
[tex]x=\frac{5(-)7} {2}=-1[/tex]
therefore
The x-intercepts are
x=-1 and x=6
The smallest x-intercept is x=-1
The largest x-intercept is x=6
step 2
Find the y-intercept
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]f(0)=(0)^{2}-5(0)-6[/tex]
[tex]f(0)=-6[/tex]
therefore
The y-intercept is y=-6
step 3
Find the vertex
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]f(x)=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex
Convert the function into vertex form
[tex]f(x)=x^{2}-5x-6[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+6=(x^{2}-5x)[/tex]
Complete the square, Remember to balance the equation by adding the same constants to each side
[tex]f(x)+6+2.5^{2}=(x^{2}-5x+2.5^{2})[/tex]
[tex]f(x)+12.25=(x^{2}-5x+6.25)[/tex]
Rewrite as perfect squares
[tex]f(x)+12.25=(x-2.5)^{2}[/tex]
[tex]f(x)=(x-2.5)^{2}-12.25[/tex]
The vertex is the point (2.5,-12.25)
step 4
Find the equation of the line of symmetry
we know that
In a vertical parabola the equation of the line of symmetry is equal to the x-coordinate of the vertex
we have
vertex (2.5,-12.25)
The x-coordinate of the vertex is 2.5
therefore
The equation of the line of symmetry is x=2.5
Evaluate in 5.
A.) 0.62
B.) 0.70
C.) 1.61
D.) 1.95
Answers
Answer:
option C) 1.61Step-by-step explanation:
The question is to evaluate the natural logarithm of 5. Natural logarithms are logarithms with base e.
e is the irrational number equal to 2.71828182845904523536028747 ... (being irrational the decimals do not end and do not have a repetition period).
Logarithms are evaluated using tables or scientific calculators.
ln (5) = 1.6094379... it is also an irrational number, so it has infinite decimals with no repetition period.
So, rounding to two decimal numbers, ln (5) = 1.61, which is the option C).
Answer:c
Step-by-step explanation:test
***URGENT*** ***50 POINTS***
If you do answer, please provide an explanation because I want to know how to solve these problems for the future and not just have the answer without an explanation.
Answers
Answer:
27) 18 < P ≤ 18 + 6√2 ⇒ answer D
28) The sum of the degree measures these angles is 1080° ⇒ answer B
29) 3E minutes before A ⇒ answer B
30) The difference between the greatest possible values is 0 ⇒ answer E
31) r divided by s = 1/3 ⇒ answer A
Step-by-step explanation:
* Lets explain each problem
27)
∵ BE is a quarter circle
∵ The radius of the circle is 6
∵ Point c is on the arc BE
∴ The distance from D to C = 6 ⇒ not depends on the position of c
because DC is a radius in the quarter circle BE
- In Δ BDE
∵ m∠ D = 90°
∵ DB = DE = 6 ⇒ radii of the quarter circle
- By using Pythagoras Theorem
∴ BE = √ (6² + 6²) = √(36 + 36) = √72 = 6√2
- The perimeter of the quadrilateral ABCD is the sum of the sides
∵ AB = 6 , AD = 6 , CD = 6
- Point C can move from B to E
∴ The length of side BC can b greater than 0(it can not be 0
because the quadrilateral has 4 sides
∴ The length of BC can not exceed the length of BE because the last
position of point C to be on the arc BE is point E
∴ The length of BC ⇒ 0 < BC ≤ 6√2
equal 6√2
∵ P is the perimeter of the quadrilateral ABCD
∴ P = 6 + 6 + 6 + (0 < BC ≤ 6√)
∴ P = 18 + (0 < BC ≤ 6√)
- Add 18 to 0 and 18 to 6√2
∴ 18 < P ≤ 18 + 6√2
28)
- In the figure we have a quadrilateral
- All the arrows represent the exterior angles of the figures
- Use the fact that:
The sum of all angles around a points is 360°
∵ There are 4 vertices (points) on the quadrilateral
∴ The sum of the all angles around the 4 vertices = 4 × 360 = 1440°
- Use the fact that:
The sum of the interior angles of any quadrilateral is 360°
∵ The sum of the angles represented by the arrows is the difference
between the sum of all angles around the 4 vertices and the sum
of the interior angles of the quadrilateral
∴ The sum of these angles = 1440° - 360° = 1080°
* The sum of the degree measures these angles is 1080°
29)
- In any watch the short arrow-hand represents the hours and the long
arrow-hand represents the minutes
- The numbers of the hours in the watch from 1 to 12
- The number of minutes between each two hours is 5 minutes, then
at 1 o'clock the minutes number is 5 , at 6 o'clock the number of
minutes is 30 , at 9 o'clock the number of minutes is 45 , so we can
find the number of minutes at any number of hour by multiply the
number of hour by 5
∵ The number of hours have been replaced by letters
∵ The time on the watch is 45 minutes after 12 o'clock OR
15 minutes before 1 o'clock
∵ The short arrow-hand pointed between L and A
∵ L is the replacing of 12 o'clock and A is the replacing of 1 o'clock
∵ The long arrow-hand pointed at I
∵ I is the replacing of 9 o'clock
∵ The hour number 9 means 5 × 9 = 45 minutes
∴ The hour hand I has 5I minutes
∴ The time in letter is 5I minutes after L
- This answer is not in the choices
- But the answer of 3E minutes before A means:
∵ E is the replacing of 5 o'clock
∴ 3E = 3 × 5 = 15 minutes
∵ A is the replacing of 1 o'clock
∴ 3E minutes before A means 15 minutes before 1 o'clok
* The answer is ⇒ 3E minutes before A
30)
∵ r² = 9
∴ r = ± √9 = ± 3
∴ r has two values -3 and 3
∵ s² = 25
∴ s = ± √25 = ± 5
∴ s has two values -5 and 5
- To find the greatest value of s - r put s greatest and r smallest
∵ The greatest value of s is 5
∵ The smallest value of r is -3
∴ The greatest value of s - r = 5 - (-3) = 5 + 3 = 8
- To find the greatest value of r - s put r greatest and s smallest
∵ The greatest value of r is 3
∵ The smallest value of s is -5
∴ The greatest value of r - s = 3 - (-5) = 3 + 5 = 8
∴ The difference between the greatest possible values of s - r
and r - s = 8 - 8 = 0
* The difference between the greatest possible values is 0
31)
- There are 27 cubes each of side length r
- The 27 cubes are arranged to form on single large cube of side
length s
∵ The volume of any cube is V = L³ , where L is the length of its side
∵ The large cube formed from the 27 small cubes
∴ The volume of the large cube = the volume of the 27 small cubes
∵ The side of the small cube is r
∴ The volume of the small cube is r³
∵ The side of the large cube is s
∴ The volume of the large cube is s³
∴ s³ = 27 r³
- Divide both sides by s³ and 27
∴ s³/(27 s³) = (27 r³)/(27 s³)
∴ 1/27 = r³/s³
- Take ∛ for both sides
∴ ∛(r³/s³) = ∛(1/27)
- The cube root canceled by the power 3 and the cube root of
1/27 is 1/3
∴ r/s = 1/3
* r divided by s = 1/3
what is 145% as a decimal
Answers
Answer:
1.45
Step-by-step explanation:
Percent is the same as putting the number over 100. In this case that would be 145/100 which as a decimal is 1.45.
Answer: is 1.45
Step-by-step explanation:
first you would take 145 percent and divide it by 100 then the answer would be 1.45 or 145/100=1.45
hope this helps
classify the following triangle. Check ALL that APPLY
Answers
Answer:
scalene and obtuse all sides are different and bigger than 90 degree angle
Select the correct answer.
What is the simplest form of this binomial expression?
a^4 − b^4
Answers
Answer:
B
Step-by-step explanation:
If C is the correct answer and if the final result is multiplied out, where does the minus sign in a^4 - b^4 come from? All pluses don't make a minus. A is incorrect.
If D is correct, then a^2 - b^2 should be further factored producing a different kind of answer, like (a + b)^2(c-d)^2 which is not the same as a^4 - b^4. So D is not correct.
The first step in factoring a^4 - b^4 is (a^2 + b^2)(a^2 - b^2) A doesn't lead you anywhere. A is incorrect. The answer must be B.
a^4 - b^4 = (a^2 - b^2)(a^2 + b^2) The first term factors.
a4 - b^4 = (a + b)(a - b) (a^2 +b^2)
Answer:
Step-by-step explanation: THE ANSWER IS B
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located x2 +6x +8= 0
Answers
Answer:
x= -4 and x=-2
Step-by-step explanation:
Using a graphing calculator (See picture attached) we find that the solution to the equation are the x-values at which the graph of the function intercepts the x-axis. It ocurrs at x= -4 and x=-2.
Given that exact roots were found, there's no need to state the consecutive integers between which the roots are located.
If f(x)=x/2-2and g(x)=2x^2+x-3 find (f+g) (x)
Answers
Answer:
C 2x^2 + 3/2x -5
Step-by-step explanation:
f(x)=x/2-2
g(x)=2x^2+x-3
(f+g) (x)=x/2-2+2x^2+x-3
Combine like terms
2x^2 + 3/2x -5
Please answer this correctly
Answers
Answer:
1/3
Step-by-step explanation:
If there are 12 sections and Lia paints 8, then Kira paints 4.
The fraction that represents how much Kira has painted of the wall is
4/12.
4/12 can be reduced.
4 and 12 have a common factor of 4 so we will divide top and bottom of 4/12 by 4 giving us 1/3.