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3 years ago

Solve this system of linear equations. Separate the x- and y-values with a comma. -7x + 2y = -8 -16x + 9y = 26

1 answer:

8 0

(4,10).
1. There are three ways to solve this: elimination, substitution, graphing.
2. I chose elimination, so I had to get one negative variable and one positive variable of the same value (for example, 18 and -18)

-7x+2y=-8
-16x+9y=26
I chose to get 2y and 9y to equal -18y and 18y.
So, multiply the first equation by -9. Multiply the second by 2.
63x-18y=72
-32x+18y=52
the 18s cross each other out. So you're left with
63x=72
-32x=52. Add them.
31x=124, divide both sides by 31, and you'll get 4.
x=4
Plug your answer for x into one of the equations. Let's use the first one.
-7(4)+2y=-8
-28+2y=-8. add 28 to both sides.
2y=20, divide both sides by 2.
y=10.
This makes your answer (4,10)

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Solve The Equation 4x×9y=7 4x-9y=9

hoa [83]

Answer:

$\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}$

$4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}$

8 0

2 years ago

A concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The following data represent the strengt

ss7ja [257]

Answer:

Mean = 3640

Mode = 4100

Median = 3830.

Step-by-step explanation:

We are given the following data in the question:

Strength of casts (in psi):

3970,4100,3100,3200,2950,3830,4100,4050,3460

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observation}}{\text{Total number of observations}}$

$\displaystyle\frac{3970+4100+3100+ 3200+ 2950+ 3830+4100+ 4050+ 3460}{9} = \displaystyle\frac{32760} {9} = 3640$

Mode is the entry with most frequency. Thus, for the given sample mode = 4100.

Median

Since n = 9 is odd,

Formula:

$Median = \displaystyle\frac{n+1}{2}th~term$

Data in ascending order:

2950,3100,3200,3460,3830,3970,4050,4100,4100

Median = 5th term = 3830.

7 0

3 years ago

Graph the circle x2 + y2 + 10x + 6y + 18 = 0.

Minchanka [31]

Answer:

see below for a graph

Step-by-step explanation:

Completing the square for x and y terms can help you put this in the standard form.

(x^2 +10x) +(y^2 +6y) = -18

(x^2 +10x +25) +(y^2 +6x +9) = -18 +25 +9 . . . . add square of half linear coefficient

(x +5)^2 +(y +3)^2 = 16 . . . . . . . circle centered at (-5, -3) with radius 4

7 0

2 years ago

Read 2 more answers

a 12-ft-long ladder is leaning against a building. the ladder makes a 45 degree angle with the building. how far up the building

zhuklara [117]

12 cos45degree=8.486 ft

6 0

2 years ago

What is the middle integer?

Elanso [62]

Answer:

-56

Step-by-step explanation:

Hello!

Let's create an equation to figure out what the middle integer really is.

Creating an equation:

n + (n + 1) + (n + 2) = -168 (This is true because we must account for the consecutive integers part.)

Simplifying:

3n + 3 = -168

Subtracting:

3n = -171

Dividing:

n = -57

Now, we plug-and-chug:

-57, -56, -54 (this is because we accounted for adding positive one.)

Thus, the middle integer is $\boxed{-56}$ .

Check:

We can see if we are correct by adding up -57, -56, -54.

(-57) + (-56) + (-54) = -168

So we are correct!

Hope this helps!

7 0

2 years ago