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2 years ago

Help ! solve the following system of equations -9x+2y=-13 2x-9y=20

Mathematics

1 answer:

Stella [2.4K]2 years ago

5 0

Answer: x = 1, y = -2

Step-by-step explanation:

-9x+2y=-13

x= 13/9 + 2/9y

2x-9y=20

2(13/9+2/9y)-9y=20

Substitute y with -2.

x= 13/9+2/9(-2)

After solving you'll see that 1 is a possible solution for x.

Check your answer

-9x+2y=-13

-9x1+2(-2) = -13

2x-9y=20

2x1-9(-2) = 20

-13 = -13

20 = 20

Therefore, x=1 and y=-2

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Answer:

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Step-by-step explanation:

8) a) x = 8.

10) c) x = 3

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2 years ago

A scuba diver descends in the water at a rate of 23 1/2

Makovka662 [10]

The scuba diver's position relative to sea level after the 4.6 minutes is 5.1 ft.

Given:

A scuba diver descends in the water at a rate of 23 1/2 feet per minute for 2.6 minutes.

A scuba diver ascends at a rate of 28 feet per minute for 2 minutes after seeing a big fish.

To find :

The scuba diver's position relative to sea level after the 4.6 minutes.

Solution:

Rate of a scuba diver descending in the water for 2.6 minutes = $R _1$

$R_1= 23\frac{1}{2}ft/min=\frac{47}{2} ft/min$

Distance covered by a scuba diver in 2.6 minutes = $d_1$

$d_1=R_1\times 2.6min=\frac{47}{2} ft/min\times 2.6 min=61.1 ft$

Rate of a scuba diver ascending for 2 minutes = $R _2$

$R_2= 28ft/min$

Distance covered by a scuba diver in 2 minutes = $d_2$

$d_2=R_2\times 2min=28 ft/min\times 2 =56 ft$

The position of scuba diver after 4.6 minutes relative to sea level:

$d_1-d_2=61.1 ft-56 ft=5.1ft$

The scuba diver's position relative to sea level after the 4.6 minutes is 5.1ft.

Learn more about ascending rate and descending rate here:

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3 0

2 years ago

I need help asap please

rjkz [21]

Answer:

$x = -\frac{3}{2}$ or $x = 1$

Step-by-step explanation:

Using the zero product property, first step is to set the given equation, $2x^2 + x - 1 = 2$ , to zero. Then factorise the left side.

Thus,

$2x^2 + x - 1 = 2$

Subtract 2 from both sides

$2x^2 + x - 1 - 2 = 2 - 2$

$2x^2 + x - 3 = 0$

Factorise the left side

$2x^2 + 3x - 2x - 3 = 0$

$x(2x + 3) - 1(2x + 3) = 0$

$(x - 1)(2x + 3) = 0$

Find the solution

$x - 1 = 0$

$2x + 3 = 0$

$x = 1$

$2x + 3 = 0$

$2x = -3$

$x = -\frac{3}{2}$

The answer is: $x = 1$ or $x = -\frac{3}{2}$

3 0

3 years ago

What is the are of a hexagon with a radius of 5 inches?

xxTIMURxx [149]

The area of a hexagon with a radius of 5 inches is 86.603.

6 0

3 years ago

Half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories 1/4 of a pepperoni pizza plus a who

yulyashka [42]

Answer:

Correct choice is D (In a whole pepperoni pizza are 660 calories, in in a whole ham and pineapple pizza are 580 calories).

Step-by-step explanation:

Let x calories be the number of calories a whole pepperoni pizza contains and y calories be the number of calories a whole ham and pineapple pizza contains.

1. If half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories, then

$\dfrac{1}{2}x+\dfrac{3}{4}y=765.$

2. If 1/4 of a pepperoni pizza plus a whole ham and pineapple pizza contains 745 calories. then

$\dfrac{1}{4}x+y=745.$

3. Multiply each equation by 4 and get a system of two equations:

$\left\{\begin{array}{l}2x+3y=3060\\x+4y=2980\end{array}\right.$

From the second equation $x=2980-4y$ , then

$2(2980-4y)+3y=3060,\\ \\5960-8y+3y=3060,\\ \\-8y+3y=3060-5960,\\ \\-5y=-2900,\\ \\y=580.$

Then

$x=2980-4\cdot 580=2980-2320=660.$

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3 years ago