At a sale this week, a sofa is being sold for $272. This is a 36% discount from the original price. What is the original price?

Answer:

C

Step-by-step explanation:

2x -15 +3x -5 = 180

5x -20 = 180

5x = 180+20 = 200

x = 200/5 = 40

3x -5 = 3(40)-5 = 120-5 = 115

2x -15 = 2(40) - 15 = 80-15 = 65

[tex]h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} [/tex]

[tex]y = a{(x - h)}^{2} + k [/tex]

Where the a-term determines how wide, narrow, upward or downward the graph is.

The h-term determines the horizontal shift of graph. (x-axis)

The k-term determines the vertical shift of graph. (y-axis)

The vertex of graph is at (h,k). We can find the vertex by using the given formulas.

From the equation, the coefficients are:

[tex] \begin{cases} a = - 1 \\ b = 12 \\ c = - 31 \end{cases}[/tex]

Substitute these values in the formulas.

Find the value of h

[tex]h = - \frac{12}{2( - 1)} \\ h = - \frac{12}{ - 2} \\ h = - \frac{ - 6}{1} \longrightarrow - ( - 6) = 6 \\ h = 6[/tex]

Hence, the value of h is 6.

Find the value of k

[tex]k = \frac{4( - 1)( - 31) - {(12)}^{2} }{4( - 1)} \\ k = \frac{124 - 144}{ - 4} \\ k = \frac{ - 20}{ - 4} \longrightarrow \frac{5}{1} = 5 \\ k = 5[/tex]

Hence, the value of k is 5. Then we substitute both value of h and k in the vertex form

[tex]y = a {(x - h)}^{2} + k \\ y = - 1 {(x - 6)}^{2} + 5 \\ y = - {(x - 6)}^{2} + 5[/tex]

Since the vertex is at (h,k). Therefore the value of h is 6 and k is 5. Therefore:

[tex] \large{(h, k)=(6, 5)}[/tex]

(6,5) is the vertex.

Answer:

x=-3

Step-by-step explanation:

Because its straight, on the x-axis, and on -3.

===========================================================

Explanation:

This green line goes through -3 on the x axis. Every point on this line has the same x coordinate and that x coordinate is x = -3. For instance, the two points (-3,5) and (-3,2) are on this green line. The equation of this line is x = -3 to indicate that x must be -3, but y can be anything you want. So that's why the y term doesn't even show up here. We cannot write the equation into slope intercept form. The slope of any vertical line is undefined.

Answer: 18 units long

Step-by-step explanation:

In the diagram, it looks like line segment AW is 6 units long and WB is 12 units long. Because of parts-whole postulate (the whole is equal to the sum of its parts), you can add AW and WB's lengths together. 6 + 12 = 18, so the length of line segment AB is 18 units long.

Answer:

b=-5

Step-by-step explanation:

Divide by -9 to eliminate the -9 on -9b

(Since -9b is the same thing as -9 times b we can use the inverse of multiplication which is division to eliminate the -9 from b but we need to do it on both sides to make it balance)

-9b/-9=45/-9

b=-5

Answer:

1:2

Step-by-step explanation:

The ratio of the number of sides of a square to the number of edges of a cube is- A)1:2.

Answer:

Step-by-step explanation:

It's with c or d I am confused with those two

Answer:

1:4

Step-by-step explanation:

Quilt A covers 4 squares. Quilt B covers 16 squares.

4/16 = 1/4

So, the ratio of A to B is 1:4.

Answer:

A.1:4

Step-by-step explanation:

pls, tell me if wrong have a good night/day <3

3x+5x+1=17

x=2

y=5•2+1

y=1

(x, y)=(2, 11)

3x+2(4x+5)=43

x=3

y=4•3+5

y=17

(x, y)=(3, 17)

I think I did it right and I hope I helped you

68

Outliers are numbers that don't fit in with the rest of them..

Answer:

9ft

Step-by-step explanation:

The top of a ladder is placed against the side of a house. The ladder is 15ft long and the wall is 12ft high. How far from the wall will the base of the ladder be positioned if the top of the ladder meets the top of the wall.

We solve this question using Pythagoras Theorem

c² = a² + b²

Height of the wall = Opposite side = b = 12ft

Length of the ladder = Hypotenuse = c = 15ft

Distance between the wall and the base of the Ladder = Adjacent = a

Hence:

15² = a² + 12²

a² = 15² - 12²

a = √15² - 12²

a = √81

a = 9 ft

Therefore, the wall will be 9ft from the base of the ladder , if the top of the ladder meets the top of the wall

Answer:

$45

Step-by-step explanation:

Pls mark me brainliest

Answer:

the slope is 3/4x

Step-by-step explanation:

if you need it in slope intercept form too its y=3/4x-1

Answer:

b

i did this before xD

Answer:

A)

45% of customers were not satisfied with the graphics.

B)

22,500 people are expected to not be satisfied with the graphics.

6,500 people are expected to have no opinion.

C)

The majority of people are unsatisfied with the graphics.

Step-by-step explanation:

The company polled 1,000 out of the 50,000 people who had purchased the program.

42% was satisfied with the graphics.

And 13% had no opinion.

Part A)

When totaled, those satisfied, unsatisfied, and with no opinion should be 100%.

Since 42% are satisfied and 13% have no opinion, this leaves 100 - 42 - 13 or 45%.

So, 45% of customers were not satisfied with the graphics.

Part B)

Since 45% of the polled were unsatisfied with the graphics, 45% of the total 50,000 can also be expected to not be satisfied.

45% of 50,000 is 0.45(50000) = 22500.

So, 22,500 people are expected to not be satisfied with the graphics.

Likewise, 13% had no opinion.

So, 13% of 50,000 is 0.13(50000) = 6500.

6,500 out of the current 50,000 customers are expected to have no opinion with the graphics.

Part C)

Since the majority of people are unsatisfied with the graphics (45% > 42%), it is reasonable to create a new version with improved graphics.

The answers are in the photo. Hope this helps! ;)

Answer:

C?

I hope this helps, if not C than A- i get them mixed at times- Sorry

Step-by-step explanation:

♥ Hey Grey Here! ♥

Answer:I think its 2×-3

Step-by-step explanation:Hope it helps kiddo

Answer:

29 miles

Step-by-step explanation:

116 divided by 4

Answer: 29 mph

Hope this helps :)

The pressure exerted by the block can be obtained as 60 N/m².

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

Since, the pressure is obtained as the ratio of Force to area.

It can be worked out using the following operation as,

Pressure = Force ÷ Area

⇒ 120 ÷ 2 = 60 N/m².

Hence, the pressure can be obtained as 60 N/m².

To know more about arithmetic operation click on,

https://brainly.com/question/25834626

#SPJ2

Answer:

120

Step-by-step explanation:

3 feet in a yard

36÷3=12

12×10=120

Answer:

funny

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

8/8-3/8=5/8

Answer:

 \bold{\text{Slope (m)}=\dfrac{1}{4}}Slope (m)=41

Step-by-step explanation:

A linear equation is of the form: y = mx + b   where

m is the slope

b is the y-intercept (where it crosses the y-axis)

x + 4y = 16

     4y = -x + 16

       y = -\dfrac{1}{4}x+\dfrac{16}{4}y=−41x+416

       y=-\dfrac{1}{4}x+4y=−41x+4

The y-intercept (b) = 4

Next, find the slope given point (4, 5) and b = 4

\begin{gathered}y=mx+b\\\\5=m(4)+4\\\\1=4m\\\\\dfrac{1}{4}=m\\\\\\\\\large\boxed{Slope (m)=\dfrac{1}{4}}\end{gathered}y=mx+b5=m(4)+41=4m41=mSlope(m)=41

the answer is 90

50 ×2 = 100

100 - 10 = 90