Answer:
If want just the approximated solutions in the interval from 0 to 360:
199.47
340.53
90
270
If you want all the approximated solutions:
199.47+360k
340.53+360k
90+360k
270+360k
Step-by-step explanation:
2 cos(x)+3 sin(2x)=0
First step: Use double angle identity for sin(2x). That is, use, sin(2x)=2sin(x)cos(x).
2 cos(x)+3*2sin(x)cos(x)=0
2 cos(x)+ 6sin(x)cos(x)=0
Factor the 2cos(x) out, like so:
2cos(x)[ 1 + 3 sin(x)]=0
In order for this product to be zero, we must find when both factors are 0.
2cos(x)=0 or 1+3sin(x)=0
Let's do 2cos(x)=0 first.
2cos(x)=0
Divide both sides by 2:
cos(x)=0
So the x-coordinate is 0 on the unit at x=90 deg and x=270 deg (in the first rotation).
Let's do 1+3sin(x)=0.
1+3sin(x)=0
Subtract 1 on both sides:
3sin(x)=-1
Divide both sides by 3:
sin(x)=-1/3
Unfortunately this is not on the unit circle so I'm just going to take sin^-1 or arsin on both sides (this is the same thing sin^-1 or arsin).
x=arcsin(-1/3)=-19.47 degrees
So that means -(-19.47)+180 is also a solution so 19.47+180=199.47 .
And that 360+-19.47 is another so 360+-19.47=340.53 .
So the solutions for [0,360] are
199.47
340.53
90
270
If you want all the solutions just add +360*k to each line where k is an integer.
A square has an area is 49yd^2 what is the side length of each side
Answer:
The side length is 7 yds
Step-by-step explanation:
We know the formula for area of a square is
A = s^2 where s is the side length
49 = s^2
Take the square root of each side
sqrt(49) = sqrt(s^2)
7 =s
The side length is 7 yds
Final answer:
To find the side length of a square given its area, calculate the square root of the area. In this case, the side length of the square is 7 yards.
Explanation:
A square has an area of 49yd². To find the side length of each side, you need to take the square root of the area. In this case, the side length of each side would be 7 yards.
Select the graph of the solution. Click until the correct graph appears. {x | x < 4} ∩ {x | x > -2
Answer:
So the solution is -2<x<4 with it's graph is
O~~~~~~O
------(-2)--------(4)-----------
Step-by-step explanation:
The intersection symbol means it has to be included in both sets.
We have that x<4 and x>-2.
If we graph this, where do we see both shadings:
~~~~~~~~~~~~~~~0 x<4
O~~~~~~~~~~~~~~~~~ x>-2
-------(-2)-------------(4)------------
Both shadings happen between -2 and 4 (and not outside that area).
So the solution is -2<x<4
It's graph is
O~~~~~~O
------(-2)--------(4)-----------
Disclaimer:
I didn't see any equal signs in your problem.
You know the [tex]\ge[/tex] or the [tex]\le[/tex] so we didn't have any closed dots.
The graph is, °←--------------------→°
-2____0_________4
What is intersection?
The intersection of two sets is the set of all those elements which are common to both of the sets.
Here, given that, {x | x < 4} ∩ {x | x > -2}
It indicates that, x is less than 4, i.e. x= 3,2,1,0,-1,-2,-3,......
Again, x is greater than -2, i.e. x = -1,0,1,2,3,4,....................
Now, as it is intersection of this two sets
So, we have, x= -1,0,1,2,3.
Hence, the required graph is,
°←------------------------------------→°
_(-2)__________0____________4_____
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When you multiply a function by -1 what is the effect on its graph
Answer:
Please see attached image.
Step-by-step explanation:
When you multiply a function by -1 you are basically reflecting the values of the function over the x-axis.
The values that were negative become positive and the positive values become negative.
Please, take a look at the attached graph below, where there are examples with two functions.
What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem?
NL ≅ MP
NK ≅ MQ
N ≅ M
L ≅ P
Answer:
L ≅ P
Step-by-step explanation:
To prove congruence through ASA, we need the measures of two angles that are adjacent to a given side. If we are given that two angles are congruent to other angles in another triangle respectively and both of those angles are adjacent to one side (in which each side of each triangle is congruent) then the triangles are congruent through ASA.
To prove congruence using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal. The additional information needed is that angle NM is congruent.
Explanation:To prove that the triangles are congruent using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal.
Given that NL ≅ MP and NK ≅ MQ, we can conclude that the corresponding sides are congruent.Since N ≅ M and L ≅ P, we know that the corresponding angles are congruent.However, to fully prove congruence using ASA, we need to show that the included angle, angle NM, is congruent.Therefore, the additional information needed is that angle NM is congruent.Learn more about ASA congruence theorem here:https://brainly.com/question/13671709
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Which expression is equivalent to (-9x^-1 y^-9)/(-15x^5 y^-3)? assume x =/ 0 y =/ 0
Answer:
The answer is 3/5x^6y^6
Step-by-step explanation:
The given expression is:
-9x^-1 y^-9/-15x^5 y^-3
It can be written as:
= -9/-15 * x^-1/x^5 * y^-9/y^-3
As we know that [x^m/x^n = x^m-n]
= 3/5 * x^-1-5 * y^-9+3
= 3/5 * x^-6 * y^-6
= 3/5 * 1/x^6 * 1/y^6
= 3/5x^6y^6
The answer is 3/5x^6y^6....
The expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
Evaluating an expressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
(-9x^-1 y^-9)/(-15x^5 y^-3)
This can be written as
[tex](-9x^{-1}y^{-9} )\div (-15x^{5}y^{-3})[/tex]
[tex](-9\times \frac{1}{x} \times \frac{1}{y^{9} } )\div (-15 \times x^{5} \times \frac{1}{y^{3} } )[/tex]
[tex](\frac{-9}{xy^{9} } )\div (\frac{-15x^{5} }{y^{3} } )[/tex]
This becomes
[tex](\frac{-9}{xy^{9} } )\times (\frac{y^{3} }{-15x^{5} } )[/tex]
[tex]\frac{-9}{-15 } \times \frac{y^{3} }{xy^{9}\times x^{5} }[/tex]
[tex]\frac{3}{5 } \times \frac{1 }{y^{6}\times x^{6} }[/tex]
= [tex]\frac{3}{5x^{6}y^{6} }[/tex]
= [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
Hence, the expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
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Please help I need it so bad
Answer:
y ≤ 3x - 2 and 4x + y ≥2
Step-by-step explanation:
We can easily solve this problem by using a plotting tool or any graphing calculator.
We test each case, until we arrive to the correct option
Case 1
y ≤ 3x - 2 and 4x + y ≥2
Correct Option.
Please see attached image for graph
In the figure below, triangle ABC is similar to triangle PQR, as shown below:
what is the length of side PQ?
A) 18
B) 4
C) 32
D) 6
Answer:
So, Option A is correct.
Step-by-step explanation:
If the triangles are similar, then the sides are proportional
If triangle ABC is similar to triangle PQR
then sides
AB/PQ = BC/QR = AC/PR
We need to find PQ
We are given AB = 6, BC =8 and QR=24
AB/PQ = BC/QR
Putting values:
6/PQ = 8/24
Cross multiplying:
6*24 = 8*PQ
144/8 = PQ
=> PQ = 18
So, Option A is correct.
Answer: Option A
[tex]PQ=18[/tex]
Step-by-step explanation:
Two triangles are similar if the length of their sides is proportional.
In this case we have the triangle ∆ABC and ∆PQR so for the sides of the triangles they are proportional it must be fulfilled that:
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
In this case we know that:
[tex]BC=8[/tex]
[tex]QR=24[/tex]
[tex]AB=6[/tex]
Therefore
[tex]\frac{BC}{QR}=\frac{AB}{PQ}[/tex]
[tex]\frac{8}{24}=\frac{6}{PQ}[/tex]
[tex]PQ=6*\frac{24}{8}[/tex]
[tex]PQ=18[/tex]
Solve 3x+5y=30 for y
Answer:
y = [tex]\frac{30-3x}{5}[/tex]
Step-by-step explanation:
Given
3x + 5y = 30
Isolate the term in y by subtracting 3x from both sides
5y = 30 - 3x ( divide both sides by 5 )
y = [tex]\frac{30-3x}{5}[/tex]
Answer:
[tex]y=\frac{-3}{5}x+6[/tex]
Step-by-step explanation:
3x+5y=30 is the given equation.
We are asked to isolate y.
The term that contains y is 5y. I'm going to first isolate 5y.
To isolate 5y we see that we have +3x with it. To undo addition of 3x we will need to subtract 3x on both sides.
3x+5y=30
-3x -3x
5y=-3x+30
We now have 5y by itself. There is actually one step left to get the y by itself.
The last step is undo this multiplication between 5 and y.
To undo multiplication you divide.
So we will be dividing 5 on both sides. This gives us:
3x+5y=30
-3x -3x
5y=-3x+30
-- ---------
5 5
So the whole reason we did that is because 5y/5 is just y. I'm going to separate that fraction on the right hand side. This gives me:
y=-3/5 x + 30/5
I'm going to simplify the 30/5 to 6.
y=-3/5 x +6
Evaluate the function at the indicated values if possible. If an indicated value is not in the domain, say so.
f left parenthesis x right parenthesis equals StartFraction x plus 7 Over x squared minus 9 EndFraction
; f left parenthesis negative 7 right parenthesis, f left parenthesis 2 right parenthesis, f left parenthesis 3 right parenthesis
Answer:
f(-7)=0.
f(2)=-9/5.
f(3) doesn't exist because 3 isn't in the domain of the function.
Step-by-step explanation:
[tex]f(x)=\frac{x+7}{x^2-9}[/tex] is the given function.
We are asked to find:
[tex]f(-7)[/tex]
[tex]f(2)[/tex]
[tex]f(3)[/tex].
f(-7) means to replace x in the expression called f with -7:
Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=-7[/tex]
[tex]\frac{(-7)+7}{(-7)^2-9}[/tex]
[tex]\frac{0}{49-9}[/tex]
[tex]\frac{0}{40}[/tex]
[tex]0[/tex]
So f(-7)=0.
f(2) means to replace x in the expression called f with 2:
Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=2[/tex]
[tex]\frac{2+7}{2^2-9}[/tex]
[tex]\frac{9}{4-9}[/tex]
[tex]\frac{9}{-5}[/tex]
[tex]\frac{-9}{5}[/tex]
So f(2)=-9/5
f(3) means to replace x in the expression called f with 3:
Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=3[/tex]
[tex]\frac{3+7}{3^2-9}[/tex]
[tex]\frac{10}{9-9}[/tex]
[tex]\frac{10}{0}[/tex]
Division by 0 is not allowed so 3 is not in the domain of our function.
what dose 24/15 equals to?
Answer: 1.6 or 8/5
Step-by-step explanation: If you want to simplify it, the answer would be 8/5 because each number can be divided by 3. If you need the decimal, it would be 1.6.
Step-by-step explanation:
[tex]\dfrac{24}{15}=\dfrac{24:3}{15:3}=\dfrac{8}{5}\\\\\\\dfrac{8}{5}=\dfrac{5+3}{5}=1\dfrac{3}{5}\\\\\\1\dfrac{3}{5}=1\dfrac{3\cdot2}{5\cdot2}=1\dfrac{6}{10}=1.6[/tex]
What are the zeros of f(x) = x2 + x - 20?
Answer:
x = - 5, x = 4
Step-by-step explanation:
Given
f(x) = x² + x - 20
To find the zeros equate f(x) to zero, that is
x² + x - 20 = 0
Consider the factors of the constant term ( - 20) which sum to give the coefficient of the x- term ( + 1)
The factors are + 5 and - 4, since
5 × - 4 = - 20 and + 5 - 4 = + 1, hence
(x + 5)x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 4 = 0 ⇒ x = 4
Answer:
The zeroes are {-5, 4}.
Step-by-step explanation:
f(x) = x^2 + x - 20 = 0
To factor this function we need 2 numbers whose sum is + 1 ( x = 1x) and whose product is -20. They are 5 and - 4 so we have:
(x + 5)(x - 4) = 0
x + 5 = 0 gives x = -5
and x - 4 = 0 gives x = 4.
A number is divided by 4, and then the quotient is added to 17. The result is 25. Find the number.
[tex]\bf \stackrel{\textit{number divided by 4}}{(x\div 4)}\qquad \stackrel{\textit{then added to 17}}{+17}\qquad \stackrel{\textit{the result is}}{=}\qquad 25\implies \cfrac{x}{4}+17=25 \\\\\\ \cfrac{x}{4}=25-17\implies \cfrac{x}{4}=8\implies x=(4)8\implies x=32[/tex]
16. When Laura finishes cooking, her oven
temperature is 400°F. If her oven cools at a rate of
3.25°F per minute, how many minutes will it take
for her oven to reach 75°F? Enter your response in
the gridded area.
DW
Answer:
Her oven will cool to 75°F in 100 minutes, or 1 hour 40 minutes.
Step-by-step explanation:
Let T(t) represent the oven temperature, and t the time in minutes.
Then:
T(t) = 400°F - (3.25°F/min)t
Find the time, t, at which T(t) will = 75°F:
400°F - (3.25°F/min)t = 75°F
Subtracting 75°F from both sides, we get:
(3.25°F/min)t = 325°F.
Dividing both sides by (3.25°F/min) yields:
t = 100 minutes.
Her oven will cool to 75°F in 100 minutes, or 1 hour 40 minutes.
It will take 100 minutes for Laura's oven to cool down from 400°F to 75°F at a cooling rate of 3.25°F per minute.
The temperature must drop from 400°F to 75°F, so the temperature difference: 400°F - 75°F = 325°F.
325°F / 3.25°F per minute = 100 minutes.
What is a requirement of supplementary angles?
Supplementary angles are 2 angles that have the sum of 180 degrees. Therefore, the requirement of supplementary angles is to have the 2 angles to equal 180 degrees.
Hope this helps!
Answer:
the sum of angles must be 180 degrees
Step-by-step explanation:
The definition of supplementary angles is
"Two angles are supplementary angles if their sum is 180 degrees".
For example, if x and y are supplementary angles then
x + y = 180
Therefore, we can conclude that the requirement of supplementary angles is " the sum of angles must be 180 degrees".
This net can be folded to form a cube with a side length of 20 units.
Answer:
Step-by-step explanation:
A cube has 6 faces and faces are square in shape. Thus to find the surface area of a cube, first we will find the area of one face. To find the area of a face we will simply multiply the side length twice.
20*20=400
Thus the area of one face = 400 units square.
Now to find the surface area of a cube we will simply multiply the area of one face by the number of total faces of a cube.
400*6 = 2400
Therefore the net folded to form a cube has a surface area of 2400 units square....
If the distance between point R(a,a,a) and point J(6,-2,0) is 10, then the value of a could be?
Answer:
Step-by-step explanation:
√(6-a)^2+(-2-a)^2+(0-a)^2 = 10
36-12a+a^2+4+4a+a^2+a^2 =100
3a^2 -8a -60=0
(3a+10)(a-6)=0
a= -3/10 or 6
The speed of sound is about 3.4 × 102 meters per second. Mark is performing a science experiment and he needs to know how far sound travels in 3 × 1010 seconds. If Mark uses a calculator to solve this problem, how will the calculator show the answer?
Answer:
[tex]1.02 \times 10^{13}[/tex]
Step-by-step explanation:
Speed of the sound = [tex]3.4 \times 10^{2}[/tex] meters per second
Time to calculate the distance traveled = [tex]3 \times 10^{10}[/tex] seconds
Since,
Distance = Speed x Time
Using the values we get:
[tex]Distance=3.4 \times 10^{2} \times 3 \times 10^{10}\\\\ = 3.4 \times 3 \times 10^{(2+10)}\\\\ = 10.2 \times 10^{12}[/tex]
Since the calculators show the final answer is scientific notation, the above answer in scientific notation would be:
Distance = [tex]1.02 \times 10^{13}[/tex]
Answer:
1.02 E 13
Step-by-step explanation:
The Answer is 1.02 E 13 because E means "time 10 to the power of". So 1.02 E 13 is basically just 1.02 time 10 to the power of 13.
How do I go about solving this?
Answer:
Option B is correct.
Step-by-step explanation:
we are given [tex]f(x) = \frac{x}{2}-3[/tex]
and [tex]g(x) = 3x^2+x-6[/tex]
We need to find (f+g)(x)
We just need to add f(x) and g(x)
(f+g)x = f(x) + g(x)
[tex](f+g)(x)=(\frac{x}{2}-3)+(3x^2+x-6)\\(f+g)(x)=\frac{x}{2}-3+3x^2+x-6\\(f+g)(x)=3x^2+\frac{x}{2}+x-3-6\\(f+g)(x)=3x^2+\frac{3x}{2}-9\\[/tex]
So, Option B is correct.
For this case we have the following functions:
[tex]f (x) = \frac {x} {2} -3\\g (x) = 3x ^ 2 + x-6[/tex]
We must find [tex](f + g) (x).[/tex] By definition, we have to:
[tex](f + g) (x) = f (x) + g (x)[/tex]
So:
[tex](f + g) (x) = \frac {x} {2} -3+ (3x ^ 2 + x-6)\\(f + g) (x) = \frac {x} {2} -3 + 3x ^ 2 + x-6\\(f + g) (x) = + 3x ^ 2 + x + \frac {x} {2} -3-6\\(f + g) (x) = + 3x ^ 2 + \frac {2x + x} {2} -9\\(f + g) (x) = + 3x ^ 2 + \frac {3x} {2} -9[/tex]
Answer:
Option B
One package of blueberries costs $3. How
many packages of blueberries can you buy
for $9?
Answer:
3 packages
Step-by-step explanation:
To find how many packages you can buy for $9, you have to divide 9 by 3.
Since each package costs $3.
So, 9/3 = 3
So you can buy 3 packages of blueberries.
Answer:
3 packages
Step-by-step explanation:
Since you can buy a package for $3, and you only have $9, how many $3 can you fit? Only 3. In conclusion, you can only buy 3 packages.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that
J measures 60°.
J measures 30°.
I measures 60°.
I measures 30°.
Answer:
I measures 60° ⇒ 3rd answer
Step-by-step explanation:
* Look to the attached figure
- To prove that the two triangles are similar by SAS we must to
find two proportional pairs of corresponding side and the measure
of the including angles between them are equal
- The given is:
m∠ F = 60°
EF = 40 , FG = 20
HI = 20 , IJ = 10
- To prove that the Δ EFG is similar to Δ HIJ we must to prove
# EF/ HI = FG/IJ ⇒ two pairs of sides proportion
# m∠ F = m∠ I ⇒ including angles equal
∵ EF = 40 and HI = 20
∴ EF/HI = 40/20 = 2
∵ FG = 20 and IJ = 10
∴ FG/IJ = 20/10 = 2
∵ EF/HI = FG/IJ = 2
∴ The two pairs of sides are proportion
∵ ∠ F is the including angle between EF and FG
∵ ∠ I is the including angle between HI and IJ
∴ m∠ F must equal m∠ I
∵ m∠ F = 60° ⇒ given
∴ m∠ I = 60°
* I measures 60°
To prove triangles are similar by the SAS similarity theorem when dealing with equilateral triangles, the angle between the proportional sides needs to be congruent. In this context, showing that the angle measures 30° would be necessary if one angle is already known to be 60°. Thus, either angle I or J should be proven to measure 30°, depending on which is between the proportional sides.
Explanation:To prove that triangles are similar by the SAS similarity theorem, two conditions must be met: corresponding sides are in proportion, and the angles between those sides are congruent. In the context of proving triangle similarity with equilateral triangles, by using a bisector, we can form a smaller triangle whose hypotenuse is twice as long as one of its sides. Consequently, as the sides preserve this ratio, the angles approach 30° and 60°. Therefore, if we must prove that a triangle in a given figure is similar through the SAS similarity criterion, and we have a side-angle-side situation where one angle is already known to be 60°, the angle we would need to prove congruent would reasonably be 30°.
This conclusion is supported by the nature of equilateral triangles, where bisecting the angle will give us angles of 30° and 60°. Additionally, the similarity of triangles is further backed by the congruency of angles and the proportionality of sides, as mentioned in other contexts within the provided information. Therefore, based on the given context and the properties of equilateral triangles, we would aim to prove that angle I or angle J (whichever is between the proportional sides) measures 30°.
Which of the following best describes a parabola?
O
A. The set of all points in a plane that are equidistant from a single
point and a single line
O
B. The set of all points in a plane that are equidistant from two points
O
C. The set of all points in a plane at a given distance from a given
point
O
D. The set of all points in a plane that are equidistant from two points
and a single line
Answer:
A
Step-by-step explanation:
The definition of a parabola.
Any point on the parabola (x, y) is equidistant from a point ( the focus ) and a line ( the directrix ).
Parabola is best describe by:
The set of all points in a plane that are equidistant from a single point and a single line What is parabola?"Parabola is defined as the set of all the points in a plane that are equidistant from a fixed point known as focus and a fixed line called directrix."
According to the question,
A. The set of all points in a plane that are equidistant from a single
point and a single line.
Equidistant from a single point called focus.Equidistant from a single line known as directrix.It represents the parabola.
Option(A) is the correct answer.
B. The set of all points in a plane that are equidistant from two points.
It represents the line.
Option (B) is not the correct answer.
C. The set of all points in a plane at a given distance from a given
point.
Given point is center of the circle.It represents the circle.
Option (C) is not the correct answer.
D. The set of all points in a plane that are equidistant from two points
and a single line.
It represents the perpendicular bisector.
Option (D) is not the correct answer.
Hence, Option(A) is the correct answer.
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y = 3/5x + 1, 5y = 3x - 2, 10x - 6y = -4
is it perpendicular, parallel, neither
Answer:
[tex]y=\frac{3}{5} x+1[/tex] and [tex]5y=3x-2[/tex] are parallel.
[tex]10x-6y=-4[/tex] is neither parallel nor perpendicular.
Step-by-step explanation:
First, you have to simplify each equation in terms of y.
[tex]y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4[/tex]
Your first equation is already in terms of x, so simplify your second equation.
[tex]5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}[/tex]
Now you can simplify your third equation.
[tex]10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}[/tex]
These are your three equations in terms of y:
[tex]y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}[/tex]
Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.
Two parallel lines will have the exact same slope.
Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of [tex]-\frac{1}{2}[/tex], as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.
Your first two equations have the same slope and are therefore parallel.
Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.
The first and the second lines are parallel as they both have a slope of 3/5. None of the lines is perpendicular to the others.
Explanation:In geometry and algebra, lines can be either parallel, perpendicular, or neither. To determine this, we need to look at the slope of each line. The slope of a line is the value of 'm' in the equation of the line, y = mx + c.
The equations you have provided are:
y = (3/5)x + 1, slope = 3/55y = 3x - 2, rearrange to y = (3/5)x - 2/5, slope = 3/510x - 6y = -4, rearrange to y = (5/3)x + 2/3, slope = 5/3When two lines have the same slope, they are parallel. When two lines have slopes that are negative reciprocals of each other (meaning their product is -1), they are perpendicular. In this case, the first and the second line are parallel (both have a slope of 3/5), and none of these lines is perpendicular to the others.
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Find the value of X in the picture please
Answer:
The measure of arc x is 70°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
and
The inscribed angle is half that of the arc it comprises.
so
The arc that comprises the inscribed angle of 15 degrees is equal to
15(2)=30 degrees
The outer angle of 20 degrees is equal to
20°=(1/2)[x-30°]
40°=[x-30°]
x=40°+30°=70°
A quadrilateral PQRS is inscribed in a circle, A quadrilateral PQRS is inscribed in a circle. The measure of angle PQR is 85 degrees. What is the measure of arc PQR?
Answer:
Measure of arc PQR is 190°
Step-by-step explanation:
First have a sketch of the quadrilateral PQRS inside a circle
You should notice that the intercepted angle is ∠PSR
You should remember that the intercepted arc PQR is twice the intercepted angle ∠PSR
Find the intercepted angle ∠PSR
Remember that in a quadrilateral opposite angles add up to 180°
Hence;
∠PQR+∠PSR=180°
85 + ∠PSR=180°
∠PSR=180°-85°=95°
Find arc PQR
Arc PQR =2×∠PSR
Arc PQR=2×95°
=190°
What is the amplitude, period, and phase shift of f(x) = −3 sin(4x − π) − 5?
Amplitude = −3; period = 2π; phase shift: x equals pi over four
Amplitude = 3; period = pi over two; phase shift: x equals pi over four
Amplitude = −3; period = 2π; phase shift: x equals negative pi over four
Amplitude = 3; period = pi over two; phase shift: x equals negative pi over four
Answer:
2nd choice.
Step-by-step explanation:
Let's compare the following:
[tex]f(x)=a\sin(b(x-c))+d[/tex] to
[tex]f(x)=-3\sin(4x-\pi))-5[/tex].
They are almost in the same form.
The amplitude is |a|, so it isn't going to be negative.
The period is [tex]\frac{2\pi}{|b|}[/tex].
The phase shift is [tex]c[/tex].
If c is positive it has been shifted right c units.
If c is negative it has been shifted left c units.
d is the vertical shift.
If d is negative, it has been moved down d units.
If d is positive, it has been moved up d units.
So we already know two things:
The amplitude is |a|=|-3|=3.
The vertical shift is d=-5 which means it was moved down 5 units from the parent function.
Now let's find the others.
I'm going to factor out 4 from [tex]4x-\pi[/tex].
Like this:
[tex]4(x-\frac{\pi}{4})[/tex]
Now if you compare this to [tex]b(x-c)[/tex]
then b=4 so the period is [tex]\frac{2\pi}{4}=\frac{\pi}{2}[/tex].
Also in place of c you see [tex]\frac{\pi}{4}[/tex] which means the phase shift is [tex]\frac{\pi}{4}[/tex].
The second choice is what we are looking for.
Answer: Second Option
Amplitude = 3; period = pi over two; phase shift: x equals pi over four
Step-by-step explanation:
By definition the sinusoidal function has the following form:
[tex]f(x) = asin(bx - c) +k[/tex]
Where
[tex]| a |[/tex] is the Amplitude of the function
[tex]\frac{2\pi}{b}[/tex] is the period of the function
[tex]-\frac{c}{b}[/tex] is the phase shift
In this case the function is:
[tex]f(x) = -3 sin(4x - \pi) - 5[/tex]
Therefore
[tex]Amplitude=|a|=3[/tex]
[tex]Period =\frac{2\pi}{b} = \frac{2\pi}{4}=\frac{\pi}{2}[/tex]
[tex]phase\ shift = -\frac{(-\pi)}{4}=\frac{\pi}{4}[/tex]
if the coefficient of determination for a data set containing 9 points is 1, how many of the data points must lie on the regression line for the data set.
Answer: 9 points
Step-by-step explanation:
The coefficient of determination is a number between 0 and 1 used to measure the level of precision with which the regression model created fits the data. A measure of [tex]R ^ 2 = 1[/tex] means that the model explains the entire variation between the two variables without error.
Therefore, in this case if [tex]R ^ 2 =1[/tex] means that the 9 points are on the line
Answer:
9 points
Step-by-step explanation:
Price of a jeep dropped from 27000 to 22900. What was the percent decrease in price nearest hundredth percent?
Answer:
(27,000 - 22,900)/27,000 = 0.1519 or 15.19% decrease in price.
Step-by-step explanation:
For this case, we propose a rule for three:
27,000 -----------> 100%
22,900 -----------> x
Where "x" represents the percentage associated with 22,900.
[tex]x = \frac {22,900 * 100} {27,000}\\x = 84.8148148148[/tex]
Now we look for the percentage of decrease:
100% -84.8148148148% = 15.1851851852%
Rounding off we have:
15.19%
Answer:
15.19%
What is the yintercept of the line given by the equation below?
y= 8x+7
Answer:
7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 8x + 7 ← is in slope- intercept form
with y- intercept c = 7
1. If the surface area of a square pyramid is 2225 yards squared. The base of the pyramid has a length of 25 yards. What is the height of the slant on one of the lateral faces?
2. The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.
Answer:
1) 32
2) 8 yards
Step-by-step explanation:
1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:
[tex]LA=2225-25^2=1600[/tex]
The lateral surface area is 4 times the area of one the congruent triangles.
[tex]LA=4\cdot \frac{1}{2}\cdot 25\cdot x[/tex]
[tex]\implies 1600=50x[/tex]
[tex]\implies \frac{1600}{50}=\frac{50x}{50}[/tex]
[tex]32=x[/tex]
Therefore the height of the slant surface is 32 yards
2) The surface area of a cone is [tex]S.A =\pi r^2+\pi r l[/tex], where l is the slant height.
We substitute the surface area S.A=151.58 and [tex]\pi=3.14,r=4[/tex] to obtain:
[tex]151.58=3.14\cdot 4^2+3.14\cdot 4 l[/tex]
[tex]151.58=50.24+12.56l[/tex]
[tex]101.34=12.56l[/tex]
[tex]\frac{101.34}{12.56}=l[/tex]
l=8.06
To the nearest whole number, the slant height is 8 yards
find the domain for the function f(x)=sqrt x^2-x+6
Answer:
The domain is {x : x ∈ R} or (-∞ , ∞)
Step-by-step explanation:
* Lets explain how to find the domain
- The domain of the function is the values of x which make the
function defined
- The quantity under the square root must be ≥ 0 because there is
no square root for negative value
* Lets solve the problem
∵ f(x) = √(x² - x + 6)
∴ The value of (x² - x + 6) must be greater than or equal zero because
there is no square root for negative value
- Graph the function to know which values of x make the quantity
under the root is negative that means the values of x which make
the graph under the x-axis
∵ The graph doesn't intersect the x-axis at any point
∵ All the graph is above the x-axis
∴ There is no value of x make f(x) < 0
∴ x can be any real number
∴ The domain of f(x) is all real numbers
∴ The domain is {x : x ∈ R} or (-∞ , ∞)