Answer:
P = -2600/3 t + 25600/3
P = -8200/3
Step-by-step explanation:
t is the time in years since 1990, so two points on the line are (5, 4200) and (8, 1600).
Using the points to find the slope:
m = (y₂ − y₁) / (x₂ − x₁)
m = (1600 − 4200) / (8 − 5)
m = -2600/3
Now writing the equation in point-slope form:
P − 4200 = -2600/3 (t − 5)
Converting to slope-intercept form:
P − 4200 = -2600/3 t + 13000/3
P = -2600/3 t + 25600/3
In 2003, t = 13:
P = -2600/3 (13) + 25600/3
P = -8200/3
The linear formula for the moose population is P = -800t + 8200. The moose population predicted by this model for the year 2003 is 2,400.
Explanation:In this question, we are given that in 1995 the moose population was 4200 and by 1998 it was 1600. This change in population mimics a linear relationship. We are asked to find the formula for this line and then predict the moose population in 2003.
We know that 1995 corresponds to t = 5 (since t is the years since 1990) and 1998 corresponds to t = 8. Therefore we can find the slope of the line (m) as (4200- 1600) / (5 - 8) = -800 per year. Since we know that the line crosses the point (5,4200), we can find the y-intercept, denoted as (b), using the formula y = mx + b.
Substitute m = -800, x = 5, and y = 4200 into the equation and solve for b
4200 = -800 * 5 + b
This simplifies to b= 4200 + 4000 = 8200
Therefore, the formula is P = -800t + 8200
To predict the moose population in 2003, simply substitute t = 13 into the formula (since 2003 is 13 years since 1990). Therefore,
P = -800 * 13 + 8200 = 2400
Therefore, the model predicts that the moose population in 2003 would be 2400.
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the sets e and f are given below
E= (-2, -1,3,5,6,7)
F=(-2,2,6)
what is the intersection of e and f
find the union of e and f
write your answers using set notation
Intersection of two sets E and F is set G which contains elements x that are common to set E and set F.
[tex]G=E\cap F=\{x; x\in E\wedge x\in F\}[/tex]
Here G is,
[tex]G=\{-2,6\}[/tex]
Union of two sets E and F is a set H which contains all elements x that occur in set E or set F.
[tex]H=E\cup F=\{x; x\in E\vee x\in F\}[/tex]
Hence,
[tex]H=\{-2,-1,2,3,5,6,7\}[/tex]
Hope this helps.
r3t40
The intersection of sets E and F: E ∩ F = {-2, 6}
The union of sets E and F: E U F = {-2, -1, 2, 3, 5, 6, 7}
A line crosses the coordinates (-3, 5) and (4, -2). What is the slope-intercept form of the equation of this line?
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-5}{4-(-3)}\implies \cfrac{-7}{4+3}\implies \cfrac{-7}{7}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=1[x-(-3)]\implies y-5=1(x+3) \\\\\\ y-5=x + 3\implies y=x+8[/tex]
which of the following statements are true? Please help
Answer:
B and C
Step-by-step explanation:
- The answer in the attached file
Which of the following best describes the relationship between (x-3) and the polynomial x^3 + 4x^2 + 2?
A. (x-3) is not a factor
B. (x-3) is a factor
C. It is impossible to tell whether (x-3) is a factor
Answer:
A) (x-3) is not a factor of x^3+4x^2+2
Step-by-step explanation:
(x-3) is a factor of f(x)=x^3+4x^2+2 if f(3)=0. This is by factor theorem.
So let's check it.
f(x)=x^3+4x^2+2
f(3)=3^3+4(3)^2+2
f(3)=27+4(9)+2
f(3)=27+36+2
f(3)=63+2
f(3)=65
Since f(3) doesn't equal 0, then x-3 is not a factor.
Answer:
A. (x-3) is not a factor
Step-by-step explanation:
You can find if (x-3) is a factor of the polynomial by dividing the polynomial by (x-3) by using long division or synthetic division.
Long division:
x^2+x+3
(x-3)/x^3+4x^2+0x+2
-(x^3-3x^2)
x^2+0x
-(x^2-3x)
3x+2
-(3x-9)
-7
Here you can see that (x-3) is not a factor of the polynomial because when you divide x^3 + 4x^2 + 2 by (x-3), there is a remainder of -7
Synthetic Division (A shortcut version of long division just to see if there is a remainder and if the supposed factor is really a factor) :
3 1 4 0 2
- 3 21 63
1 7 21 65
As seen before (x-3) is not a factor of the polynomial because there is a remainder. If 65 were 0, the (x-3) would be a factor of the polynomial.
What is the average rate of change for this function for the interval from x=3 to x=5?
Answer:
B
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 3, 5 ]
From the table of values
f(b) = f(5) = 32
f(a) = f(3) = 8
Hence
average rate of change = [tex]\frac{32-8}{5-3}[/tex] = [tex]\frac{24}{2}[/tex] = 12
Answer:
The average rate of change is [tex]12[/tex]
Step-by-step explanation:
Given:
Interval; x = 3 to x = 5
We'll represent these by
x1 = 3
x2 = 5
The corresponding y values are:
When x = 3, y = 8
When x = 5, y = 32
This will also be represented
y1 = 8
y2 = 32
Average rate of change is then calculated as follows
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
Where m represent average rate of change
By Substitution, we have
[tex]m = \frac{32 - 8}{5 - 3}[/tex]
[tex]m = \frac{24}{2}[/tex]
[tex]m = 12[/tex]
Hence, the average rate of change is [tex]12[/tex]
Use the recursive formula f(n) = 0.4 . f(n-1) + 12 to determine the 2nd term if f(1) = 4.
A. f(2) = 12.6
B. f(2) = 13.2
C. f(2) = 13.6
D. f(2) = 14.2
Answer:
Assuming you have [tex]f(n)=0.4f(n-1)+12[/tex] with [tex]f(1)=4[/tex], the answer is f(2)=13.6.
Step-by-step explanation:
I think that says [tex]f(n)=0.4f(n-1)+12[/tex] with [tex]f(1)=4[/tex].
Now we want to find [tex]f(2)[/tex] so replace n with 2:
This gives you:
[tex]f(2)=0.4f(2-1)+12[/tex]
[tex]f(2)=0.4f(1)+12[/tex]
[tex]f(2)=0.4(4)+12[/tex]
[tex]f(2)=1.6+12[/tex]
[tex]f(2)=13.6[/tex]
Answer:
13.6 (Answer C)
Step-by-step explanation:
I think you meant f(n) = 0.4 * f(n-1) + 12, where * represents multiplication.
Then f(2) = 0.4 * (4) + 12, or 1.6 + 12, or 13.6.
I could use some help! During the day, Lisa’s dog is tied by rope to a tree in the center of her yard. The scale drawing below shows the area that the dog has to run. If the actual length of the rope is 4 5/6 feet, what is the scale used in the drawing?
Step-by-step explanation:
Considering Lisa's yard is allowing the dog to run around a circumscribed circle with a ray of 4 5/6 feet then the maximum of the area that he could cover is the area of that circle A= 3.14×(4 5/6)^2/2
Not being able to see the drawing, I assume that if the area of the yard has a value below the value described above then the dog would run around the yard untill the rope's fully swirled around the tree or untill Lisa comes home
Use the diagram to find the measure of the given angle.
Given measure of the angle: EAD
Answer:
The measure of the angle EAD is 90°Explanation:
Angles may be named by three letters, each represented a point on each of the angle's ray or by the vertex.
The angle EAD is the angle A (the letter of the center is the vertex).
In this case it is indicated the measure of the angle on the diagram using a small square.
The small square is a conventional symbol to indicate that the angle is 90°, which is named right angle. That determines that the rays, segments or lines meet perpendicularly.
That is one fourth (1/4) of the complete circle (1/4 × 360° = 90°).
By using the dagram, the measure of the given angle include the following:
m∠EAD = 90°
In Mathematics and Euclidean Geometry, a right angle is a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees.
Generally speaking, a perpendicular bisector can be used to bisect or divide a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection;
In this context, we can logically deduce that segment AE is the perpendicular bisector of diameter ED in circle A. Therefore, the measure of angle EAD must be 90 degrees;
m∠EAD = 90°
Help what answer choice is this?
Answer:
Option A
Step-by-step explanation:
The domain must be
[a,∞)
That means that x must have as an argument a square root, because, it cannot take negative arguments for real numbers (a>0)
√(x-a)
x-a≥0
x ≥ a
The only possible option is
Option A.
Please take a look at the attached graph
According to the rules of NCAA volleyball, there must be exactly 6 players on the court at all times and each player has a unique designated position on the court. How many different starting position configurations are possible for the 6 starting players of a volleyball team that follows this rule?
Answer:
720
Step-by-step explanation:
permutation formula=
n!/(n-r)!
There are 720 different starting position configurations possible for the 6 starting players of a volleyball team that follows the rule.
We have
To determine the number of different starting position configurations for a volleyball team with 6 players, we can use the concept of permutations.
Since each player has a unique designated position on the court, we can think of this as arranging 6 distinct objects (the players) in 6 distinct positions (the court positions).
The number of possible arrangements can be calculated using the formula for permutations, denoted as "n P r," which represents the number of ways to select and arrange r objects from a set of n objects.
In this case, we want to arrange 6 players in 6 positions, so we can calculate 6 P 6:
6 P 6 = 6!
Using the formula for factorial:
6! = 6 * 5 * 4 * 3 * 2 * 1
= 720
Therefore,
There are 720 different starting position configurations possible for the 6 starting players of a volleyball team that follows the rule of having exactly 6 players on the court, each with a unique designated position.
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Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?
[tex]\huge{\boxed{(x-2, y+4)}}[/tex]
[tex]x_1 \bf{-2} =x_2[/tex]
[tex]y_1 \bf{+4} =y_2[/tex]
This means that the answer is the subtract [tex]2[/tex] from the [tex]x[/tex] and add [tex]4[/tex] to the [tex]y[/tex], which is represented as [tex]\boxed{(x-2, y+4)}[/tex]
Also, thank you for posting your first question, and welcome to the community! If you have any questions, don’t hesitate to reach out to me!
The translation that maps (3,-4) to its image (1,0) is given by:
(x, y) ⇒ (x - 2, y + 4)
Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Translation is the movement of a point either up, down, left or right.
If a point A(x, y) is moved a units left and b units up, the new point is at A'(x - a, y + b).
The translation that maps (3,-4) to its image (1,0) is given by:
(x, y) ⇒ (x - 2, y + 4)
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when you divide an even number by an even number, is the resut always an even number
Answer:
false
Step-by-step explanation:
if you do 4/4 it is 1 which is odd
Answer:
No, the result is not always even.
Step-by-step explanation:
No, this is not necessary.
There is no general rule that states that an even number divided by another even number will always be an even number.
Few example are:
[tex]\frac{6}{2}=3[/tex]
[tex]\frac{10}{2}=5[/tex]
[tex]\frac{60}{4}=15[/tex]
What is the solution to the following system of equations?
X – 3y = 6
2x + 2y = 4
A.y=-1
B.x=3
C.y=3
D.x=-1
Answer:
x = 3, y = -1 ⇒ ABStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-3y=6&\text{multiply both sides by (-2)}\\2x+2y=4\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-2x+6y=-12\\2x+2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad8y=-8\qquad\text{divide both sides by 8}\\.\qquad\qquad y=-1\\\\\text{Put the value of y to the first equation:}\\\\x-3(-1)=6\\x+3=6\qquad\text{subtract 3 from both sides}\\x=3[/tex]
Answer: y = -1 and x = 3
Step-by-step explanation:
x - 3y = 6 --------(1)
2x + 2y = 4 -------(2)
we multiply (1) by 2
2x - 6y = 12 --------(3)
(3) - (1)
-8y = 8
y = -1
Putting y = -1 into equation (1)
x - 3 (-1) = 6
x + 3 =6
collect the like term
x = 6 - 3
x = 3
Therefore x= 3 and y = -1
Given the Arithmetic series A1+A2+A3+A4 13 + 18 + 23 + 28 + . . . + 113 What is the value of sum?
Answer:
The value of sum is 1323
Step-by-step explanation:
First of all we will find the value of n:
The value of n can be determined by the following formula:
an = a1 + (n - 1)d
where an= 113
a1= 13
d=5
Difference between the values = d=5
Now put the values n the formula:
113=13+(n-1)5
113=13+5n-5
Solve the like terms:
113=8+5n
Move constant to the L.H.S
113-8=5n
105=5n
Divide both sides by 5
21=n
Now put these values in the formula to find the sum:
Sn = n/2(a1 + an)
S21=21/2(13+113)
S21=21/2(126)
S21=21(63)
S21=1323
The value of sum is 1323....
booker has a bag of marbles.there are 10 marbles 6 yellow marbles and 4 red marbles .book 4 teacher reaches into the bag without looking and picks a marble.what is the probability that he picks a red marbles
Answer: 40% or 2/5
Step-by-step explanation:
10 total marbles
6 yellow
4 red
Probability of blindly picking a red marble is 4/10 or 2/5 which can be written as 40%
The probability of picking a red marble from a bag containing 10 marbles, where 4 are red, is 4 out of 10 or 0.4.
The question asks about the probability of picking a red marble from a bag containing 6 yellow marbles and 4 red marbles, totaling 10 marbles. To calculate the probability, you divide the number of favorable outcomes (picking a red marble) by the number of possible outcomes (total marbles). In this case, the probability of picking a red marble is 4 out of 10, which can be simplified to 2 out of 5 or 0.4.
How to solve the inequality to -2(k+3) < -2k - 7
[tex]-2(k+3) < -2k - 7\\-2k-6<-2k-7\\-6<-7\\k\in\emptyset[/tex]
Answer:
No solutions
Step-by-step explanation:
-2(k+3) < -2k - 7
Distribute the -2
-2k-6 < -2k - 7
Add 2k to each side
-2k+2k-6 < -2k+2k - 7
-6 < -7
This is always false, so the inequality is never true
There are no solutions
Which equation is the inverse of y = 9x2 - 4?
Answer:
9÷2+4
Step-by-step explanation:
Answer:
[tex]h(x)=+-\sqrt{\frac{x+4}{9} }[/tex]
Step-by-step explanation:
Hello
I think I can help you with this
Let
[tex]y = 9x^{2}-4\\h(x)=y^{-1}[/tex]
to find the inverse of y([tex]y^{-1}[/tex])
Step 1
switch x and y
[tex]y = 9x^{2}-4\\\\x= 9y^{2}-4[/tex]
Step 2
Now solve the equation for y (isolating y)
[tex]x= 9y^{2}-4\\Add\ 4\ to\ both\ sides\\x+4= 9y^{2}-4+4\\x+4=9y^{2}\\divide\ each\ side\ by\ 9\\\frac{x+4}{9} =\frac{9y^{2}}{9}\\\\x+4=y^{2} \\[/tex]
[tex]h(x)=+-\sqrt{\frac{x+4}{9} }[/tex]
Have a great day
Between which two integers does √11 lie?
A.2 and 3
B.3 and 4
C.5 and 6
D.10 and 12
Answer:
B. 3 and 4
Step-by-step explanation:
In order to find the numbers between which √11 lies, let us first guess the nearest perfect squares to √11. These are 9 and 16. Where 9 comes just before 11 and 16 comes just after 11. Now we have to write all three of them in ascending order.
√9 , √11 , √16
also
√9= 3 and √16 = 4
and
√9 < √11 < √16
3 < √11 < 4
hence we can see that √11 must lies between 3 and 4
Answer:
B.3 and 4
Step-by-step explanation:
3x3=9
4x4=16
so, 11 goes between 3 and 4
I just gave myself a bad rating because I did not want you guys to get the answer wrong because I posted an answer that was wrong and forgot that I could edit so now that I fixed it is a safe answer
Which of the diagrams below represents the statement “if it is a tree, then it has leaves”
Answer:
Fig A
Step-by-step explanation:
in fig A, we can see that the subset that represents "trees", lies inside the subset that "has leaves". Hence in figure A, we can say that "All trees have leaves" or "if it is a tree, it has leaves"
in fig B however, we see that "has leaves" is inside of "trees", this means that the area in-between "has leaves" and "tree" represents the subset that there are trees without leaves. This is in contradiction to the statement "if it is a tree, it has leaves", hence this is not the answer.
Answer
A
Step-by-step explanation:
hope this helps :)
If f(x) = 4* + 12x and g(x) = 5x - 1, find (f + g)(x).
Answer:
[tex]\large\boxed{(f+g)(x)=4^x+17x-1}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=4^x+12x,\ g(x)=5x-1\\\\(f+g)(x)=(4^x+12x)+(5x-1)=4^x+17x-1[/tex]
Me ajuda ai por favor tenho que entregar amanhã
a) (2a - b)² = (4a² - 4ab + b²)
b) (10m - n²)² = (100m² - 20mn² + n⁴)
c) (4x - 4²) = (16x² - 8x + 4⁴)
d)[tex] {( \frac{1}{3} x - y) }^{2} = ({ \frac{1}{9}x }^{2} - \frac{2}{3} xy + {y}^{2} )[/tex]
e)
[tex](0.25 - a) ^{2} = (0.25^{2} - (2)(0.25)a + {a}^{2} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ( \frac{1}{16} - \frac{1}{2} a + {a}^{2} )[/tex]
f)
[tex] {( \frac{2x}{3} - \frac{1}{2} )}^{2} = ( \frac{4 {x}^{2} }{9} - \frac{2x}{3} + \frac{1}{4} )[/tex]
Divide x5 + 15x+ + 54x3 – 25x2– 75x – 34 by x + 8.
Answer:
Quotient: x^4+7x^3-2x^2-9x-3
Remainder: -10
Step-by-step explanation:
x5 + 15x+ + 54x3 – 25x2– 75x – 34 by x + 8.
Since the exponents are arranged in descending order so, 15x^4
x^5 + 15x^4+ + 54x^3 – 25x^2– 75x – 34 by x + 8
The division is shown in figure attached.
Quotient: x^4+7x^3-2x^2-9x-3
Remainder: -10
Which rule describes composition of transformations that maps ABC to A"B"C"?
I don’t understand how they got the answer. I need a good explanation please.
The correct rule that describes the composition of transformations mapping AABC to AA"B"C" is:
- Ro. 900 ◦ T-6, -2(x, y)
Here's a step-by-step explanation:
1. "Ro. 900" stands for a 900 degrees counterclockwise rotation.
2. "T-6, -2" represents a translation of 6 units to the left and 2 units down.
3. When these transformations are applied in sequence to the original figure AABC, you first rotate it 900 degrees counterclockwise and then translate it 6 units to the left and 2 units down, resulting in the figure AA"B"C".
This rule combines rotation and translation to map AABC to AA"B"C". This composition of transformations is what leads to the desired outcome.
The complete question is : Which rule describes composition of transformations that maps ABC to A"B"C"?
Find four integers whose sum is 400 such that the first integer is equal to twice the second integer, three times the third integer and four time the fourth integer.
Answer:
a=192
b=96
c=64
d=48
Step-by-step explanation:
So we have [tex]a+b+c+d=400[/tex] where [tex]a,b,c,[/tex] and [tex]d[/tex] are integers.
We also have [tex]a=2b[/tex]and [tex]a=3c[/tex]and [tex]a=4d.[/tex]
[tex]a=2b[/tex] means [tex]a/2=b[/tex]
[tex]a=3c[/tex] means [tex]a/3=c[/tex]
[tex]a=4d[/tex] means [tex]a/4=d[/tex]
Let's plug those in:
[tex]a+b+c+d=400[/tex]
[tex]a+\frac{a}{2}+\frac{a}{3}+\frac{a}{4}=400[/tex]
Multiply both sides by 4(3)=12 to clear the fractions:
[tex]12a+6a+4a+3a=4800[/tex]
Combine like terms:
[tex]25a=4800[/tex]
Divide both sides by 25:
[tex]a=\frac{4800}{25}[/tex]
Simplify:
[tex]a=192[/tex].
Let's go back and find [tex]b,c,d[/tex] now.
b is half of a so half of 192 is 96 which means b=96
c is a third of a so a third of 192 is 64 which means c=64
d is a fourth of a so a fourth of 192 is 48 which means d=48
So
a=192
b=96
c=64
d=48
Answer:
a=192
b=96
c=64
d=48
Step-by-step explanation:
hope this helps
QUICK! 75 POINTS !!Select all that are part of the solution set of csc(x) > 1 and over 0 ≤ x ≤ 2π.
Answer:
[tex]\frac{\pi}{4}[/tex]
[tex]\frac{5\pi}{6}[/tex]
Step-by-step explanation:
The answer uses the unit circle and that sine and cosecant are reciprocals.
The first choice doesn't even fit the criteria that [tex]x[/tex] is between [tex]0[/tex] and [tex]2\pi[/tex] (inclusive of both endpoints) because of the [tex]x=\frac{-7\pi}{6}[/tex].
Let's check the second choice.
[tex]\csc(\frac{\pi}{4})=\frac{2}{\sqrt{2}} \text{ since } \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}[/tex].
[tex]\csc(\frac{\pi}{4})>1 \text{ since } \frac{2}{\sqrt{2}}>1[/tex]
[tex]\csc(\frac{\pi}{2})=1 \text{ since } \sin(\frac{\pi}{2})=1[/tex] which means [tex]\csc(\frac{\pi}{2})=1[/tex] which is not greater than 1.
So we can eliminate second choice.
Let's look at the third.
[tex]\csc(\frac{5\pi}{6})=2 \text{ since } \sin(\frac{5\pi}{6})=\frac{1}{2}[/tex] which means [tex]\csc(\frac{5\pi}{6})>1[/tex].
[tex]\csc(\pi)[/tex] isn't defined because [tex]\sin(\pi)=0[/tex].
So we are eliminating 3rd choice now.
Let's look at the fourth choice.
[tex]\csc(\frac{7\pi}{6})=-2 \text{ since } \sin(\frac{7\pi}{6})=\frac{-1}{2}[/tex] which means [tex]\csc(\frac{7\pi}{6})<1[/tex] and not greater than 1.
I was looking at the rows as if they were choices.
Let me break up my choices.
So we said [tex]x=-\frac{7\pi}{6}[/tex] doesn't work because it is not included in the inequality [tex]0\le x \le 2\pi[/tex].
How about [tex]x=0[/tex]? This leads to [tex]\csc(0)[/tex] which doesn't exist because [tex]\sin(0)=0[/tex].
So neither of the first two choices on the first row.
Let's look at the second row again.
We said [tex]\frac{\pi}{4}[/tex] worked but not [tex]\frac{\pi}{2}[/tex]
Let's look at the choices on the third row.
We said [tex]\frac{5\pi}{6}[/tex] worked but not [tex]x=\pi[/tex]
Let's look at at the last choice.
We said it gave something less than 1 so this choice doesn't work.
Answer:x=pi/4 and x=5pi/6
Step-by-step explanation:
on edge just did it
carlos cut 5/12 of a yard of cloth into 5 pieces of equal length . what was the length. of each piece of cloth ?
Answer:
The length of each piece of cloth =1/12 yard
Step-by-step explanation:
Number of pieces = 5
Carlos cut 5/12 of a yard of cloth
Length of each piece = ?
To find the length of each piece simply divide 5/12 by 5.
Length of each piece of cloth = 5/12/5
Length of each piece of cloth =5/12 * 1/5
Length of each piece of cloth=1/12
Therefore the length of each piece of cloth =1/12 yard....
Answer:
the answer is a
Step-by-step explanation:
In △ABC, m∠A=57°, m∠B=37°, and a=11. Find c to the nearest tenth.
Answer:
c = 13.1
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The sine rule is:
# [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
* Lets solve the problem
- In Δ ABC
∵ m∠A = 57°
∵ m∠B = 37°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 57° + 37° + m∠C = 180°
∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides
∴ m∠C = 86°
- Lets use the sine rule to find c
∵ a = 11 and m∠A = 57°
∵ m∠C = 86°
∵ [tex]\frac{sin(57)}{11}=\frac{sin(86)}{c}[/tex]
- By using cross multiplication
∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)
∴ [tex]c=\frac{11(sin86)}{sin57}=13.1[/tex]
* c = 13.1
In △ABC,a=13, b=21, and c=27. Find m∠A.
A. 18.4
B. 31.5
C. 28.0
D. 103.0
Answer:
Option C (28.0°)
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the three sides are given and one unknown angle has to be calculated. Therefore, cosine rule will be used. The cosine rule is:
a^2 = b^2 + c^2 - 2*b*c*cos(A°).
The question specifies that a=13, b=21, and c=27. Plugging in the values:
13^2 = 21^2 + 27^2 - 2(21)(27)*cos(A°).
Simplifying gives:
-1001 = -1134*cos(A°)
Isolating cos(A°) gives:
cos(A°) = 0.88271604938
Taking cosine inverse on the both sides gives:
A° = arccos(0.88271604938). Therefore, using a calculator, A° = 28.0 (correct to one decimal place).
This means that the Option C is the correct choice!!!
For this case we have that by definition, the cosine theorem states that:
[tex]a ^ 2 = b ^ 2 + c ^ 2-2bc * Cos (A)[/tex]
According to the data we have:
[tex]a = 13\\b = 21\\c = 27[/tex]
Substituting we have:
[tex]13 ^ 2 = 21 ^ 2 + 27 ^ 2-2 (21) (27) * Cos (A)\\169 = 441 + 729-1134 * Cos (A)\\169 = 1170-1134 * Cos (A)\\169-1170 = -1134 * Cos (A)\\-1001 = -1134 * Cos (A)\\Cos (A) = \frac {1001} {1134}\\Cos (A) = 0.8827\\A = arc cos (0.8827)\\A = 28.03[/tex]
Answer:
Option C
The accounting department at Nagata Glass reimbursed Abba Jay for traveling to two sales presentations in New Orleans this month. He drove a total of 610 miles to and from the city. The company will pay him $0.32 per mile. His other travel expenses included $6.50 in tolls, and $260.40 per night for two nights in a hotel. The costs of his meals are listed in the table. What were his total expenses for the two trips?
It's a fill in the blank question.
Prove that the diagonals of a rectangle bisect each other.
The midpoint of AC is _____
Answer:
(a,b)
Step-by-step explanation:
simply we find the midpoint of AC and the midpoint of Bd by dividing over 2
Answer:
We choose D.
Step-by-step explanation:
Let the midpoint is O
We will use Angle-SIde-Angle principle to prove that the diagonals of a rectangle bisect each other.
Have a look at the two triangles: AOB and DOC, they are congruent because:
AB = DC ∠OAB = ∠DCO because they are alternate angles∠OBA = ∠CDO because they are alternate anglesSo we can conclude that: OB = OB when two triangles: AOB and DOC are congruent.
Similar, apply for the two triangles: AOD and BOC are congruent so we have OA = OC .
=> It proves that the point O simultaneously is the midpoint and intersection point for the diagonals.
=> The midpoint of AC is ([tex]\frac{2a+ 0}{2}[/tex] , [tex]\frac{0 + 2b}{2}[/tex] ) = (a, b), we choose D.