SV is an angle bisector of ∠RST. If m∠RSV = (3x + 7)° and m∠RST = (8x − 12)°, find x. Select each definition, postulate, or theorem you will use. A Angle Addition Postulate B Linear Pair Theorem C definition of midpoint D definition of angle bisector The solution is x = .

QUESTION POSTED AT 05/12/2019 - 04:02 PM

Answered by admin AT 05/12/2019 - 04:02 PM

∠RSV=(3x + 7)°
∠RST = (8x − 12)°
∠RSV=∠VST=1/2∠RST


(3x + 7)°+(3x + 7)°= (8x − 12)°
3x+7+3x+7=8x-12
3x+3x-8=-12-7-7
-2x=-2
x=-2/(-2)
x=1

А. Angle Addition Postulate
х=1





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Related questions

Find the quotient. (6x 2 + 23x + 20) ÷ (5 + 2x) 3x - 4 3x + 4 3x +19

\frac{6x^{2} + 23x + 20}{2x + 5} = \frac{6x^{2} + 15x + 8x + 20}{2x + 5} = \frac{3x(2x) + 3x(5) + 4(2x) + 4(5)}{2x + 5} = \frac{3x(2x + 5) + 4(2x + 5)}{2x + 5} = \frac{(3x + 4)(2x + 5)}{2x + 5} = 3x + 4

The answer is B.

ANSWERED AT 18/01/2020 - 01:13 PM


QUESTION POSTED AT 18/01/2020 - 01:13 PM

If 75 pairs of jeans are sold, what is the company’s profit?

Revenue: 2x² + 17x - 175
Cost: 2x² - 3x - 125
Profit: 20x - 50

Profit = Revenue - Cost
Profit = 2x² + 17x - 175 - (2x² - 3x - 125)
Profit = 2x² - 2x² + 17x + 3x - 175 + 125
Profit = 20x - 50

x = 75

profit = 20(75) - 50
profit = 1500 - 50
profit = 1450

ANSWERED AT 18/01/2020 - 01:13 PM


QUESTION POSTED AT 18/01/2020 - 01:13 PM

If 75 pairs of jeans are sold, what is the company’s profit?

What exactly is the question? With out a price of the jeans, the answer is probably 75x. X as in the price of the Jeans.

ANSWERED AT 18/01/2020 - 01:13 PM


QUESTION POSTED AT 18/01/2020 - 01:13 PM

If a cylinder’s radius and height are each shrunk down to a third of the original size, what would be the formula to find the modified surface area?

We let

r1 = the original radius of the cylinder

r2 = the new radius of the cylinder

h1 = the original height of the cylinder

h2 = the new height of the cylinder

SA = surface are of the cylinder

 

the radius and the height are shrunk down to a third of their value therefore

 

r2 = r1/3

h2 = h1/3

 SA = 2(PI)r^2 + 2(PI)rh

SA = 2(PI)[(r1^2)/9] +2(PI)(r1/3)(h1/3)

 

Simplifying

SA = [2(PI)r]/9 * (r1 + h1)

ANSWERED AT 18/01/2020 - 01:12 PM


QUESTION POSTED AT 18/01/2020 - 01:12 PM

A triangle ABC with vertices A (6, 8), B (6, 12), and C (10, 12) is rotated 90 degrees What are the coordinates of B'?

I think it would be (2,8)

ANSWERED AT 18/01/2020 - 01:12 PM


QUESTION POSTED AT 18/01/2020 - 01:12 PM

A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 12 inches. If the lizard is 8 inches from a point of tangency, find the direct distance between the lizard and the cactus (x). If necessary, round to the hundredths place.

Answer:

10 in

Step-by-step explanation:

We are given that

Diameter of cactus=d=12 in

Radius of cactus=\frac{d}{2}=\frac{12}{2}=6 in

Distance of lizard from point of tangency=8 in

We have to find the direct distance between lizard and cactus.

In triangle OAB,

OA=6 in

AB=8 in

Pythagorous theorem: (Hypotenuse)^2=(base)^2+(perpendicular\;side)^2

Using pythagorous theorem

OB^2=(6)^2+(8)^2=100

OB=\sqrt{100}=10 in

Hence, the direct distance of lizard from cactus=10 in

ANSWERED AT 18/01/2020 - 01:11 PM


QUESTION POSTED AT 18/01/2020 - 01:11 PM

The Wilson Manufacturing Company uses a machine to stamp out parts for lawn mowers. On average, the machine will produce 7 defective parts for each 1,000 made. Using a direct variation formula, determine the number of defective parts that would be expected if the machine produced 7,000 parts.

Answer: 49

Step-by-step explanation:

The direct variation formula for two quantities x and y is given by :-

y=kx, where k is constant.

Let x be the number of parts produced by machine and y be the number of defective parts produced .

For x = 1,000 and y=7 , we have

7=k(1000)\\\\\Rightarrow\ k=\dfrac{7}{1000}

Now, for x =7 ,000, the value of y will be :-

y=\dfrac{7}{1000}\times7000=49

Hence, the the number of defective parts that would be expected if the machine produced 7,000 parts = 49

ANSWERED AT 18/01/2020 - 01:10 PM


QUESTION POSTED AT 18/01/2020 - 01:10 PM

Which of the following is the rational exponent expression of fifth root of 7 n?

The rational exponent expression would be (7n)^1/5

ANSWERED AT 18/01/2020 - 01:09 PM


QUESTION POSTED AT 18/01/2020 - 01:09 PM

How does this model demonstrate the Pythagorean Theorem? Three squares whose corners touch so that the respective edges form a triangle. The smallest square has a side labeled six and is made up of thirty-six smaller squares. The largest square has a side labeled ten and is made up of one hundred smaller squares. The third square has a side labeled eight and is made up of sixty-four smaller squares. A. The sum of the lengths of the shortest and the longest sides is equal to twice the length of the middle side. So double the length of the longer leg of any right triangle is equal to the sum of the shorter leg and the hypotenuse. B. The sum of the area of the two smaller squares is equal to the area of the larger square. So the sum of the lengths of the two legs of any right triangle squared is equal to the length of the hypotenuse squared. C. The sum of the area of the smallest and the largest squares is equal to the area of the middle square. So the sum of the lengths of the shorter leg and the hypotenuse of any right triangle squared is equal to the length of the middle leg squared. D. The length of the longest side minus two equals the length of the middle side. The length of the middle side minus two equals the length of the shortest side. So the length of the short leg of any right triangle is equal to the length of the middle leg minus 2, and the length of the hypotenuse is equal to the length of the middle leg plus 2.

"  B is your best choice but it is very badly stated. this gives an Example of the Pythagorean theorem. it does Not demonstrate it. B is written incorrectly, it should say "sum of squares of the lengths of the legs" Not "sum of the lengths of the two legs of any right angle squared"

ANSWERED AT 18/01/2020 - 01:07 PM


QUESTION POSTED AT 18/01/2020 - 01:07 PM

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129. If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?

Time (weeks) 0     1     2      3      4    5      6      7     8 
Weight (lb) 150 144 143 141 140 137 137 132 129

Change in time (weeks) =      5 - 0      =   5    = -0.3846 
Change in weight (lbs)       137 -150      -13

The average rate of change of weight with respect to time over the first five weeks of the program is -0.3846. It is a negative sign because the weight is decreasing.

ANSWERED AT 18/01/2020 - 01:04 PM


QUESTION POSTED AT 18/01/2020 - 01:04 PM

Janie uses a reflecting tool to reflect Point B onto Point A. Which of the following statements are true about the line of reflection? 1. Reflection line is perpendicular to AB 2. Reflection line does not bisect AB. 3. Reflection line passes through the midpoint of BA. 4. Reflection line forms two equal angles with segment AB.

You can understand the concept of reflection by imagining a lake. Suppose a mountain is reflected on the lake across an imaginary horizontal line in the ground. This line is the Line of Symmetry. So, in this problem we need to solve four items. Therefore:


1. Reflection line is perpendicular to AB


This is true. To reflect Point B onto Point A, we need to take a Line of Symmetry perpendicular to the segment AB as illustrated in Figure 1. This line is the one in red and the blue square indicates that the red line and the segment AB are perpendicular.  


2. Reflection line does not bisect AB


This is false. Instead, the line in red bisect the segment AB, that is, it divides the segment into two equal parts as indicated in Figure 2. The x in blue represents the point at which the red line bisects the segment.


3.  Reflection line passes through the midpoint of BA.


This is true. Given that the red line divide the segment into two equal parts, then the point at which the red line bisects the segment is also called the midpoint (M) as indicated in Figure 3.


4. Reflection line forms two equal angles with segment AB.


This is true. As you can see in Figure 4, the two blue angles are equal and the two green angles are equal. So, reflection line forms two equal angles with segment AB. In fact, each of these angles measures 90 degrees. Accordingly, all these four angles are equal.

ANSWERED AT 18/01/2020 - 01:03 PM


QUESTION POSTED AT 18/01/2020 - 01:03 PM

Which of the following equations is written in standard form? A. 2.5x+3y=12 B. -10x-3y=1 C. 2x+3y=12 D. 5x+5y=10

C. 2x+3y=12 is written in standard form

ANSWERED AT 18/01/2020 - 01:02 PM


QUESTION POSTED AT 18/01/2020 - 01:02 PM

How many sides can two congruent angles share

8 i think the answer

ANSWERED AT 18/01/2020 - 01:01 PM


QUESTION POSTED AT 18/01/2020 - 01:01 PM

Which of the following equations is in slope-intercept form? A. 2y = 3x – 1 B. x = 3y – 1 C. y = –3x D. 9x = 2

C is in slope intercept form

ANSWERED AT 18/01/2020 - 12:59 PM


QUESTION POSTED AT 18/01/2020 - 12:59 PM

Brine is a solution of salt and water. If a tub contains 50 gallons of a 5% solution of brine, how much water must evaporate to change it to an 8% solution?

Let x = amt of water evaporated :.05(50) = .08(50-x) 2.5 = 4 - .08x .08x = 4 - 2.5 .08x = 1.5 x = 18.75 lb of water evaporated : ; Check; amt of salt remains the same, only the percentage is different, right? .05(50) = .08(50-18.75) .05(50) = .08(31.25) 2.5 = 2.5

ANSWERED AT 18/01/2020 - 12:59 PM


QUESTION POSTED AT 18/01/2020 - 12:59 PM

The function f(x) is shown on the graph. What is f(0)? 12 only 2 and 3 only –2, –1, 1, and 2 only –2, –1, 1, 2 and 12

Answer: 12 only

Step-by-step explanation:

The given graph is representing the function f(x).

To find the value of f(0), we need to check the position of curve at x=0.

It implies we need to check the position of curve on y-axis.

We can see there is only one point where function curve is intersection the y-axis such that at x=0 .i.e. y=12

Hence, from the given graph the value of f(0)=12 only.

ANSWERED AT 18/01/2020 - 12:58 PM


QUESTION POSTED AT 18/01/2020 - 12:58 PM

Henry wants to avoid interest capitalization on his $7,800 unsubsidized Stafford loan. Henry will graduate in four years, and the loan has a duration of ten years. The loan has an interest rate of 5.6%, compounded monthly. How much must Henry pay every month to avoid interest capitalization?

Interest capitalization means adding the interest to the principal balance. To avoid that you need to keep the balance at or below $7800. Let's assume Henry wants to pay the minimum amount necessary to avoid interest capitalization. Then, since it compounds monthly at an APR of 5.6%, each month a certain amount is added to the balance. That amount should be the yearly interest rate divided among the months in the year. Multiply that number by the principal to see how much interest accrues at the end of each month. That's what Henry needs to pay.

ANSWERED AT 18/01/2020 - 12:57 PM


QUESTION POSTED AT 18/01/2020 - 12:57 PM

Which statements about the system are true? Check all that apply. y = x – 4 3y – x = –7 The system has one solution. The system consists of parallel lines. Both lines have the same slope. Both lines have the same y–intercept. The equations represent the same line. The lines intersect.

Answer and explanation:

Given : Equations y=x-4 and 3y-x=-7

To find : Which statements about the system are true? Check all that apply.

Solution :

First we solve the system of equations,

y=x-4  .....(1)

3y-x=-7  ......(2)

Substitute y from (1) in (2),

3(x-4)-x=-7

3x-12-x=-7

2x=5

x=\frac{5}{2}

Substitute the value of x in (1),

y=\frac{5}{2}-4

y=\frac{5-8}{2}

y=\frac{-3}{2}

1) The system has one solution i.e. (\frac{5}{2},-\frac{3}{2})

2) The system has solution which means it is not parallel lines.

Writing equation in slope from, y=mx+c

y=x-4 where m=1 and c=-4

3y-x=-7 where m=\frac{1}{3} and c=-4

3) Both lines have different slopes.

4) Both lines have the same y-intercept.

5) The equations represent the different lines.

6) The lines intersect at (\frac{5}{2},-\frac{3}{2})

ANSWERED AT 18/01/2020 - 12:54 PM


QUESTION POSTED AT 18/01/2020 - 12:54 PM

A pair of inline skates, regularly priced at $180, is now on sale at a 30% discount. What is the sale price of the skates?

So you divide it by 10 to get $18 (10%)
Then you do 18*3 = 54 (This is 30%)
Then you minus this from $180: 180-54= $126

ANSWERED AT 18/01/2020 - 12:54 PM


QUESTION POSTED AT 18/01/2020 - 12:54 PM

Part A: The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

16x2−4x−4x+1=4x(4x−1)−1(4x−1)=(4x−1)(4x−1)=(4x−1)2 Length of each side=4x-1

ANSWERED AT 18/01/2020 - 12:54 PM


QUESTION POSTED AT 18/01/2020 - 12:54 PM

Find the GCF of the following literal terms. m^7 n^4 p^3 and mn^12 p^5

Do you have the 4th problem typed correctly? The two given numbers have no factor (other than 1) in common (i.e., they are relatively prime) so the GCF is 1. 

48 = 2^4 * 3 

Therefore, GCF of 16a^4 b^4 + 32a^3 b^5 - 48a^2 b^6 is 16a^2 b^4, so 
16a^4 b^4 + 32a^3 b^5 - 48a^2 b^6 = (16a^2 b^4)(a^2 + 2ab - 3b^2) = (16a

ANSWERED AT 18/01/2020 - 12:53 PM


QUESTION POSTED AT 18/01/2020 - 12:53 PM

What is the solution of the equation 3y-5y+10=36 ( A) -13 (b) 4.5 (C) 13 (D) 2

3y-5y+10=36

combine like terms

-2y+10=36

subtract 10 from both sides

-2y = 26

divide both sides by -2

y = - 13

so the answer is a

ANSWERED AT 18/01/2020 - 12:52 PM


QUESTION POSTED AT 18/01/2020 - 12:52 PM

Let C be between D and E. Use the segment addition postulate to solve for m. DC = 6m − 21 CE = 7m − 18 DE = 65 a. –3 c. 13 b. 5 d. 8

D-C-E

DC = 6m - 21
CE = 7m - 18
DE = 65

DC + CE = DE
6m - 21 + 7m - 18 = 65
13m - 39 = 65
13m = 65 + 39
13m = 104
m = 104/13
m = 8

DC = 6m - 21 = 6(8) - 21 = 48 - 21 = 27
CE = 7m - 18 = 7(8) - 18 = 56 - 18 = 38

ANSWERED AT 18/01/2020 - 12:52 PM


QUESTION POSTED AT 18/01/2020 - 12:52 PM

If mAC=178 degrees, and mBC=42 degrees, what is m angle BDC?

The measurement of angle BDC is 44 degrees. This can be computed by subtracting 178 degrees from 180 degrees which is 2 degrees. Then using the given mBC which is 42 degrees add this to the 2 degrees which came from the difference computed above. Then it will give us the answer of 44 degrees.

ANSWERED AT 18/01/2020 - 12:51 PM


QUESTION POSTED AT 18/01/2020 - 12:51 PM

Find the value of y when x equals -11, 5x+6y=-37

5(-11)+6y=-37
-55+6y=-37
6y=18
y=3

ANSWERED AT 18/01/2020 - 12:51 PM


QUESTION POSTED AT 18/01/2020 - 12:51 PM

Fiona bought some socks that cost $4.95 for each pair and some belts that cost $6.55 each. Fiona spent $27.95 in all. Let a represent the number of pairs of socks purchased and b the number of belts purchased

The question lacks the total number of socks and belts altogether. Thsi value is necessary so that we can create another equation to solve the unknowns.

if assumed that a = b, the answer, a = b = 2.43 will not make sense since you cannot buy 43% of a pair of socks. Completely define the conditions so that the answer can be obtained. 

by trial and error, 3 pair of socks and 2 belts would be a sensible answer

ANSWERED AT 18/01/2020 - 12:51 PM


QUESTION POSTED AT 18/01/2020 - 12:51 PM