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bixtya [17]
3 years ago
10

If x^2+y^2=14 annd xy=5 find the value of (1/2x+1/2y)^2

Mathematics
1 answer:
Leviafan [203]3 years ago
4 0

Answer:

<h2>              7</h2>

Step-by-step explanation:

 \left(\frac12x+\frac12y\right)^2=\\\\=\left[\frac12(x+y)\right]^2=\\\\=\left(\frac12\right)^2\left(x+y\right)^2=\\\\=\frac14\left(x+y\right)^2=\\\\=\frac14(x^2+2xy+y^2)=\\\\=\frac14(x^2+y^2+2xy)=\\\\=\frac14(14+2\cdot5)=\\\\=\frac14\cdot28=\\\\=7                          

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max2010maxim [7]

GIVEN

1) Females outnumber males by 3 to 2.

2) There are 1770 people in the city.

SOLUTION

Let the number of males be x and the number of females y. Therefore, the total number of people can be written to be:

x+y=1770\text{   -----------(1)}

If there are 3 females for every 2 males, we have that:

\begin{gathered} \frac{y}{3}=\frac{x}{2} \\ \therefore \\ x=\frac{2y}{3}\text{   ----------(2)} \end{gathered}

We can substitute equation (2) into equation (1) and solve for y:

\begin{gathered} \frac{2}{3}y+y=1770 \\ \frac{2y+3y}{3}=1770 \\ 5y=1770\times3 \\ 5y=5310 \end{gathered}

Dividing both sides by 5, we have

y=1062

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1 year ago
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)
lutik1710 [3]

so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).

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so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?

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2 years ago
Which expression is equivalent to (3b + 2r) + (4b + r)?
Mice21 [21]

(3b + 2r) + (4b + r)

3b+4b +2r+r

7b +3r

Choice B


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3 years ago
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Rudik [331]
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