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3 years ago

Solve the system of equations by the substitution method.

Mathematics

1 answer:

pickupchik [31]3 years ago

6 0

Answer:

x =

$- \frac{ 1}{7}$

y =

$\frac{61}{7}$

Step-by-step explanation:

Since both expressions 2x+9 and 9x+10 are equal to y, set them equal to each other forming an equation in x

2x+9 = 9x+10

Now, solve the equation:

2x-9x = 10-9

-7x = 1

x =

$- \frac{1}{7}$

Then, substitute the given value of x in any of the two equations given, let's take y = 2x+9

y = 2×(-1/7)+9

y =

$\frac{61}{7}$

That's it! I hope that this explanation was helpful ;)

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A rectangular prism shaped toy box is 52 centimeters long. The perimeter of one side of the box is 90 centimeters. The height of

Archy [21]

Answer:

The volume of the toy box is 25688 cubic centimetres

Step-by-step explanation:

The 6 faces of a rectangular prism are rectangles, each two opposite faces are equal in dimensions, its dimensions are L, W, H, so two faces has dimensions L , W, two faces L , H and two faces W , H

The formula of the volume of it is V = L × W × H

∵ The toy box is shaped a rectangular prism

∵ The toy box is 52 cm long

∴ H = 52 cm

∵ The perimeter of one side is 90

- Perimeter of any rectangle is twice the sum of its dimensions

∴ Twice the sum of two dimensions of the side = 90 cm

- Divide it by 2 to find the sum of the two dimensions

∴ The sum of two dimensions = 90 ÷ 2 = 45 cm

The sum of two dimensions is less than the height of the box, that means 45 is the sum of the other two dimensions L and W

∵ L + W = 45

∵ The height of the box is is twice as long as it’s width

∴ H = 2 W

∵ H = 52 cm

∴ 52 = 2 W

- Divide both sides by 2

∴ 26 = W

∴ W = 26 cm

Substitute the value of W in the equation of the sum of the two dimensions to find L

∵ L + 26 = 45

- Subtract 26 from both sides

∴ L = 19 cm

∵ V = L × W × H

∴ V = 19 × 26 × 52

∴ V = 25688 cm³

The volume of the toy box is 25688 cubic centimetres

7 0

3 years ago

Triangle DNO has vertices at D(5, 8), N(– 3, 10), and O(– 3, 6). If vertex D is translated 4 units to the right, the best name f

prisoha [69]

Using distance between two points to find the lengths of the edges of the triangle, the correct option is:

b. Isosceles

The distance between two points, $(x_1,y_1)$ and $(x_2,y_2)$ , is given by:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Vertex D is translated 4 units to the right is (9,8).

The lengths of the edges are:

$DN = \sqrt{(9 - (-3))^2 + (8 - 10)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}$

$DO = \sqrt{(9 - (-3))^2 + (8 - 6)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}$

$NO = \sqrt{(-3 - (-3))^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = 4$

<u>Two edges of the same length</u>, hence, it is an isosceles triangle, given by option b.

You can learn more about distance between two points at brainly.com/question/18345417

6 0

2 years ago

Rewrite with only sin x and cos x. (3 points) cos 2x + sin x

ArbitrLikvidat [17]

Answer:

I think its option 2

7 0

3 years ago

First one right gets BRAINLIEST!!<br><br> If f(x)=x²+2x-3 and g(x)=x²-9, find (f/g) 4 and (f+g)(4)

Rasek [7]

Answer:

3 and 28

Step-by-step explanation:

note ( $\frac{f}{g}$ )(x ) = $\frac{f(x)}{g(x)}$

$\frac{f(x)}{g(x)}$

= $\frac{x^2+2x-3}{x^2-9}$ and

( $\frac{f}{g}$ )(4) = $\frac{4^2+2(4)-3}{4^2-9}$ = $\frac{16+8-3}{16-9}$ = $\frac{21}{7}$ = 3

-------------------------------------------------------

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= x² + 2x - 3 + x² - 9 = 2x² + 2x - 12 and

(f + g)(4) = 2(4)² + 2(4) - 12 = 2(16) + 8 - 12 = 32 + 8 - 12 = 28

6 0

3 years ago

Complete the number sentence:

rewona [7]

D divide by 1000… you are shifting the decimal 3 places (there are 3 zeros in 1000) you are dividing because the number is getting smaller.

7 0

2 years ago

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