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2 years ago

What is the result of substituting for y in the bottom equation?

Mathematics

1 answer:

zhenek [66]2 years ago

6 0

Answer:

(A) $x + 3= x^2 + 2x-4$

Step-by-step explanation:

Given the equations:

$y = x + 3\\y= x^2 + 2x-4$

Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.

Substitution of y into $y=x^2 + 2x-4$ gives us:

$x + 3= x^2 + 2x-4$

The correct option is A.

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Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original pri

grigory [225]

Answer:27 pieces were sold at the original price.

63 pieces were sold at the new price

Step-by-step explanation:

Let x represent the number of pieces of pottery that was sold at the original price.

Let y represent the number of pieces of pottery that was sold at the new price.

They sold some of their pottery at the original price of $9.50 for each piece. This means that the amount that they got from selling x pieces of pottery at the original price would be 9.5x

They later decreased the price of each piece by $2. This means that the new price was 9.5 - 2 = $7.5

This means that the amount that they got from selling x pieces of pottery at the new price would be 7.5y

If they sold all 90 pieces and took in $729, then the equations are

x + y = 90

9.5x + 7.5y = 729 - - - - - - - - - -1

Substituting x = 90 - y into equation 1, it becomes

9.5(90 - y) + 7.5y = 729

855 - 9.5y + 7.5y = 729

- 9.5y + 7.5y = 729 - 855

- 2y = - 126

y = - 126/- 2 = 63

Substituting y = 63 into x = 90 - y, it becomes

x = 90 - 63 = 27

6 0

2 years ago

Malik's arts and crafts shop have a bolt of crimson velvet 32 meters long. A customer came in during the morning and bought 120

Eva8 [605]

Answer: 3200-1520=1680 cm

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2 years ago

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Find the area of the following circle. (Round answer to the nearest whole number.) Circumference = 280 cm. (Hint: Find r from C

Marrrta [24]

Find r :
C=2πr
280=2(3.14)r
r=280/2(3.14)
r=44.6cm

find area :
A=πr²
A=3.14(44.6)²
A=6246 cm²

Answer : 4)6,246

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2 years ago

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Help please.<br><br> Find x.

Degger [83]

You have to use the Geometric Mean for triangles to find x. Our form will look like this: $\frac{2}{x} = \frac{x}{6+2}$ which simplifies to $\frac{2}{x} = \frac{x}{8}$ . Cross multiply to get $x^{2} =16$ . Therfore, x = 4. Usually when we take the square root of a number we will end up with both the principle (positive) root and the negative one as well. But since the 2 things in math that will never EVER be negative are time and distance/length, we will not consider the -4. x = 4

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2 years ago

You are given rectangle ABCD on the grid shown and are told that the figure is to be dilated from the origin, but you are not to

Alenkinab [10]

Answer:

The new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)

Step-by-step explanation:

The rectangle ABCD on the grid shown is attached below.

From the grid, it is clear that the coordinates of point D are (-4, -4)

i.e. D(-4, -4)

As we are told that the figure is to be dilated from the origin.

A dilation tends to stretch or shrink the original figure, depending upon scale factor.

If scale factor > 1, then the image gets enlarged

If the scale factor < 1, the image gets reduction

When we dilate a figure from the origin by any scale factor, the new coordinates of the image can be obtained by multiplying the scale factor with the coordinates of the original object/figure.

As the the coordinates of point D are (-4, -4). If we dilate the figure by a scale factor of 1/2, the new new coordinates of point D would be:

P(x, y) → P'(1/2x, 1/2y)

D(-4, -4) → D'(-4/2, -4/2) or D'(-2, -2)

Therefore, the new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)

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2 years ago