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3 years ago

Name the binomial you can multiply by (x + 9) to get the product x^2 + 5x- 36

1 answer:

5 0

If you would like to solve (x^2 + 5x - 36) / (x + 9), you can do this using the following steps:

a = ?
(x + 9) * (x + a) = <span>(x^2 + 5x - 36)
x^2 + ax + 9x + 9a = x^2 + 5x - 36
ax + 9x = 5x
a + 9 = 5
a = 5 - 9
a = - 4

The correct result would be x - 4.
</span>

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What is the y-intercept of the line given by the equation y=5x-21

Bess [88]

Answer: C.( 0,-21)

Step-by-step explanation: Use the slope-intercept form to find the slope and y-intercept.

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2 years ago

A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$

Hence, the equation of the parabola is $y=-\frac{1}{4}(x-2)^{2}+9$ .

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2 years ago

Find a general solution of y" + 4y = 0.

klio [65]

Answer:

$y(x)=C_{1}cos2x+C_{2}sin(2x)$

Step-by-step explanation:

It is a linear homogeneous differential equation with constant coefficients:

y" + 4y = 0

Its characteristic equation:

r^2+4=0

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r2=-2i

We use these roots in order to find the general solution:

$y(x)=C_{1}cos2x+C_{2}sin(2x)$

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3 years ago

Express p in terms of q if

Irina-Kira [14]

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2 years ago

Find each measure of the parallelogram

zysi [14]

Answer:

z = 8

x = 5

Step-by-step explanation:

Because it is a parrallelogram 3z - 4 and 2z + 4 is congruent if you make it an equation and equal each other (3z - 4 = 2z + 4) It will be 8

They are also equal to each other so you will do the same thing

4x - 6 = x + 9

x = 5

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2 years ago