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3 years ago

Se the given length and area of a rectangle to express the width algebraically.

1 answer:

7 0

Factor the area polynomial into (2x - 1) and (x + 5)

length is (x + 5) and area is found by multiplying length and width, so the width is (2x - 1) as it's the other factor of the area polynomial after factoring

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Which of the following ordered pairs are solutions to the system of equations below?

Masja [62]

The ordered pair (-1, 6) is the solution to the system of equations.

Step-by-step explanation:

Given equations are;

3x+2y=9 Eqn 1

y=4x+10 Eqn 2

Putting value of y from Eqn 2 in Eqn 1

$3x+2(4x+10)=9\\3x+8x+20=9\\11x=9-20\\11x=-11$

Dividing both sides by 11

$\frac{11x}{11}=\frac{-11}{11}\\x=-1$

Putting x=-1 in Eqn 2

$y=4(-1)+10\\y=-4+10\\y=6$

Solution: (-1, 6)

The ordered pair (-1, 6) is the solution to the system of equations.

8 0

3 years ago

Rewrite the slope intercept equation of the line y = 2x + 5 in standard form. A) 2x - y = -5 B) 2x + y = 5 C) -2x - y = -5 D) 2x

Alina [70]

Answer: OPTION A.

Step-by-step explanation:

The Standard form of the Equation of a line is the following:

$Ax + By = C$

Where "A", "B" and "C" are integers ( $A>0$ )

Given the equation of the line in Slope-Intercept form:

$y = 2x + 5$

You can follow these steps is order to rewrite it in Standard form:

1. Subtract 5 from both sides of the equation:

$y-(5) = 2x + 5-(5)\\\\y-5=2x$

2. Subtract "y" from both sides of the equation:

$y-5-(y)=2x-(y)\\\\-5=2x-y$

Therefore, the equation of the given line in Standard form is:

$2x-y=-5$

8 0

3 years ago

Can someone explain me how to find square root by prime factorization ?

liubo4ka [24]

Answer:

<h2><u>STEPS</u></h2>

Step I: Obtain the given number.
Step II: Resolve the given number into prime factors by successive division.
Step III: Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
Step IV: Take one factor from each pair.
Step V: Find the product of factors obtained in step IV.
Step VI: The product obtained in step V is the required square root.

<h2><u>Example </u></h2>

<u> Find the square root of 324</u>

324 = 2 x 162
= 2 x 2 x 81
= 2 x 2 x 3 x 27
= 2 x 2 x 3 x 3 x 9
= 2 x 2 x 3 x 3 x 3 x 3
∴ √324 = √( 2 x 2 x 3 x 3 x 3 x 3 )
√324 = 2 x 3 x 3
√324 = 18

5 0

4 years ago

HELLPPPP ITS DUE TODAYYY!!!

Schach [20]

Fraction- 3/10
decimal- 0.30
percent- 30%

8 0

3 years ago

Read 2 more answers

Which are the x-intercept and y-intercept of the line drawn through the points A and B?

ladessa [460]

First you have to figure out what the equation of the line is. Let's use the slope formula to find the slope, and then one of the points to find the y-intercept. We'll put the line's equation in y=mx+b form.

$slope = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} } \\ slope = m \\ m = \frac{5 - 1}{-7 - 1} \\ m = \frac{4}{-8} \\ m = - \frac{1}{2}$

Now, we'll use that slope in y=mx+b form with one of the coordinates in order to find what b (which is also the y-intercept) equals
$y = - \frac{1}{2}x + b \\ 1 = 1(- \frac{1}{2}) + b \\ 1 = - \frac{1}{2} + b \\ 1 \frac{1}{2} = b$

therefore your y-intercept is equal to 1.5. In order to find the x-intercept we'll take our new equation $y = - \frac{1}{2} + 1 \frac{1}{2}$ and make y = 0, because the line intersects with the x-axis when y is equal to zero.

$y = - \frac{1}{2}x + 1 \frac{1}{2} \\ 0 = - \frac{1}{2}x + 1 \frac{1}{2} \\ -1 \frac{1}{2} = - \frac{1}{2}x \\ x = 3$

therefore, your x-intercept is 3 and your y-intercept is 1.5

6 0

3 years ago