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3 years ago

Is (7,-2) a solution to the equation x - 4y = 15? Please show work to help me understand.

Mathematics

1 answer:

grin007 [14]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

x - 4y = 15

Substitute the point into the equation and see if the equation is true

7 -4(-2) = 15

7+8 = 15

15 =15

This is true so the point is a solution to the equation

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56.7 should be the right answer

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3 years ago

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What is the solution of

kobusy [5.1K]

Answer:

Third option: x=0 and x=16

Step-by-step explanation:

$\sqrt{2x+4}-\sqrt{x}=2$

Isolating √(2x+4): Addind √x both sides of the equation:

$\sqrt{2x+4}-\sqrt{x}+\sqrt{x}=2+\sqrt{x}\\ \sqrt{2x+4}=2+\sqrt{x}$

Squaring both sides of the equation:

$(\sqrt{2x+4})^{2}=(2+\sqrt{x})^{2}$

Simplifying on the left side, and applying on the right side the formula:

$(a+b)^{2}=a^{2}+2ab+b^{2}; a=2, b=\sqrt{x}$

$2x+4=(2)^{2}+2(2)(\sqrt{x})+(\sqrt{x})^{2}\\ 2x+4=4+4\sqrt{x}+x$

Isolating the term with √x on the right side of the equation: Subtracting 4 and x from both sides of the equation:

$2x+4-4-x=4+4\sqrt{x}+x-4-x\\ x=4\sqrt{x}$

Squaring both sides of the equation:

$(x)^{2}=(4\sqrt{x})^{2}\\ x^{2}=(4)^{2}(\sqrt{x})^{2}\\ x^{2}=16 x$

This is a quadratic equation. Equaling to zero: Subtract 16x from both sides of the equation:

$x^{2}-16x=16x-16x\\ x^{2}-16x=0$

Factoring: Common factor x:

x (x-16)=0

Two solutions:

1) x=0

2) x-16=0

Solving for x: Adding 16 both sides of the equation:

x-16+16=0+16

x=16

Let's prove the solutions in the orignal equation:

1) x=0:

$\sqrt{2x+4}-\sqrt{x}=2\\ \sqrt{2(0)+4}-\sqrt{0}=2\\ \sqrt{0+4}-0=2\\ \sqrt{4}=2\\ 2=2$

x=0 is a solution

2) x=16

$\sqrt{2x+4}-\sqrt{x}=2\\ \sqrt{2(16)+4}-\sqrt{16}=2\\ \sqrt{32+4}-4=2\\ \sqrt{36}-4=2\\ 6-4=2\\ 2=2$

x=16 is a solution

Then the solutions are x=0 and x=16

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3 years ago

Find the distance between the two points shown on the number line.

noname [10]

Answer:

2.6

Step-by-step explanation:

i just counted

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3 years ago

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Write 9/7 as a mixed number. Give your answer in its simplest form.

HACTEHA [7]

Answer:

1 2/7 ........................................

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An agent for a residential real estate company in a sub-urb located outside of Washington, DC, has the business objec-tive of de

devlian [24]

Answer:

Check the explanation

Step-by-step explanation:

Scatter plot

x---square feet

y---rent

SolutionA:

Kindly check the attached image below:

THERE EXISTS A WEAK POSITIVE RELATIONSHIP BETWEEN SQUARE FEET AND RENT .

AS SQUARE FEET INCREASES RENT INCREASES

SolutionB:

Rent=0.4932(squarefeet)+992.99

slope=m=0.4932

Y intercept=992.99

SolutionC:

Interpretation of slope:

slope =m=change in rent/change in square foot

For a unit increase in square feet rent increases by 0.4932

Interpretation of y intercept:

when square feet=0 rent is 992.99

Solutiond:

when squarefeet=800

Rent=0.4932(squarefeet)+992.99

=Rent=0.4932(800)+992.99

=1387.55

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3 years ago