5. Which of the following statements are true? Select all that apply

Geometry help needed!

salantis [7]

Answer:

AC Midpoint (2,0)-

CB Midpoint (5,-4)

midlength is 5

Step-by-step explanation:

midpoint formula $(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})$

A(2,4) C(2,-4)

$\frac{2+2}{2} =\frac{4}{2}=2\\\frac{4-4}{2} =\frac{0}{2} =0$

(2,0)

C(2,-4) B(8,-4)

$\frac{8+2}{2} =\frac{10}{2} =5$

$\frac{-4-4}{2} =\frac{-8}{2} =-4$ midpoint is (5,-4)

Distance between the 2 midpoints is the midsegment

(2,0) and (5,-4)

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

$d=\sqrt{(5-2)^{2} +(-4-0)^{2} } \\d=\sqrt{3^{2} +(-4^{2})\\ } \\d=\sqrt{x} 9+16\\d=\sqrt{25} \\d=5$

3 0

3 years ago

Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Then she donates $2 to clean wate

borishaifa [10]

We have been given that Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Also, she donates $2 to clean water projects per tax return she files.

Further we know that Sterre charged $7,245 and made a donation of $1,242 this year for the tax returns she filed.

Let x be the number of free income tax returns and y be the number of $35 income tax returns.

Therefore, we can set up:

$0\times x+35\times y=7245\Rightarrow 35y=7245\Rightarrow y=\frac{7245}{35}=207$

Since she donates $2 for each return that she files, therefore, we can set up:

$2(x+y)=1242\Rightarrow x+y=621\Rightarrow x+207=621\Rightarrow x=414$

Therefore,

Sterre filed 414 tax returns for free and filed 207 tax returns for $35.

7 0

3 years ago

And could someone please help me with this one please

Goshia [24]

Answer:

C

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (5, 2), thus

y = a(x - 5)² + 2

To find a substitute (4, - 3) into the equation

- 3 = a + 2 ⇒ a = - 3 - 2 = - 5

y = - 5(x - 5)² + 2 ← in vertex form

Expand (x - 5)² and distribute by - 5

y = - 5(x² - 10x + 25) + 2

= - 5x² + 50x - 125 + 2

= - 5x² + 50x - 123 ← in standard form

8 0

3 years ago

2s+10-7s-8+3s-7<br> syplifying expression fyi

Solnce55 [7]

Answer:

-1+5z, -25+20y, 4d+14, 2n-2, 40k+8, 8b+5, -9+22p

Step-by-step explanation:

1) -4+7z+3-2z

-1+5z

2) 15+4(5y-10)

15+20y-40

-25+20y

3) 2d+17-3-2d+4d

4d+14

4) 12n-8-2n+10-4

2n-2

5) 8(2k+1+3k)

16k+8+24k

40k+8

5) 4(2b+2)-3

8b+8-3

8b+5

6) -4+8p-6p-5+20p

-9+22p

7 0

3 years ago

If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year, what is the probability that a wo

nordsb [41]

Answer: 0.01708

Step-by-step explanation:

Given : If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year.

i.e. the probability that house damaged buy fire in a year : $p=\dfrac{15}{1000}=0.015$

The formula for binomial distribution is given by :-

$^{n}C_xp^x(1-p)^{n-x}$

Now, the probability that a woman who owns 14 houses will have fire damage in 2 of them in a year (put n=14 and x=2), we get

$^{14}C_2(0.015)^2(1-0.015)^{14-2}\\\\=\dfrac{14!}{2!(14-2)!}(0.015)^2(0.985)^{12}\\\\=0.0170788520518\approx0.01708$

Hence, the required probability = 0.01708

4 0

3 years ago