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irinina [24]
2 years ago
13

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial.

Mathematics
1 answer:
Anna007 [38]2 years ago
7 0

The correct expression is (a) n = 100; (x + 10)^2

<h3>How to determine the value of n?</h3>

The expression is given as:

x^2 + 20x + n

Take the coefficient of x

k = 20

Divide by 2

k/2= 10

Square both sides

(k/2)^2 = 100

The above value represents the value of n

i.e.

n = 100

So, we have:

x^2 + 20x + 100

Expand

x^2 + 10x + 10x + 100

Factorize

x(x + 10) + 10(x + 10)

Factor out x + 10

(x + 10)^2

Hence, the correct expression is (a) n = 100; (x + 10)^2

Read more about trinomial at:

brainly.com/question/1538726

#SPJ1

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If (−4, 11) and (−6, 5) are the endpoints of a diameter of a circle, what is the equation of the circle?
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Answer:

A. (x+5)^2+(y-8)^2=100

Step-by-step explanation:

1. The standard form of the equation of a circle is (x-h)^{2} + (y-k)^2=r^2

2. To find the center we require the  midpoint   of the  2 given points

center =[\frac{1}{2}(-4-6),\frac{1}{2}(11+5)]

=(-5,8)

3. The radius is the distance from the centre to either of  the 2 given points calculate the radius using the  distance formula

d= \sqrt{(x_{2}+x_{1})^{2} +(y_{2}-y_{1})^{2}

let (x_{1},y_{1})= (-5,8) \\ and (x_2,y_2)=(-4,11)

r=\sqrt{(-4+5)^2+(11-8)^2} =\sqrt{81+9}=10

--> (x-(-5)^2+(y-8)^2=10^2

--> (x+5)^2+(y-8)^2=100

4 0
3 years ago
Read 2 more answers
What is the equation of this line in point-slope form AND slope intercept form <br><br> please help
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Point slope form: y-3=-3/5(x+2)
Slope intercept form: y=-3/5x+9/5
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2 years ago
Let Y be a random variable with a density function given by
Neporo4naja [7]

From the given density function we find the distribution function,

F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y

(a)

F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)

\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1

\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}

(b)

F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y

\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2

\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}

(c)

F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})

\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3

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5 0
3 years ago
Sylvia ran 3km 290m in the morning then she ran some more in the evening if she ran a total of 10km how far did Sylvia run in th
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Answer:

She ran 6.71km in the evening

Step-by-step explanation:

3km 290m = 3.29km

10 - 3.29 = 6.71km

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How would you read this inequality? Answer in a sentence. x&lt;21
Lubov Fominskaja [6]

Answer:

x is less than twenty one

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