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3 years ago

Expand and simplify 9a+3(8-2a).

Mathematics

2 answers:

Zina [86]3 years ago

8 0

9a + 24 - 6a
3a + 24
In bold is your answer

Marianna [84]3 years ago

7 0

3a+24
hope this helps!!!

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The endpoint is the ___ of the angle

Phoenix [80]

Hey there!

ANSWER: <u>vertex</u>

<h2>EXPLANATION:</h2>

Fill in the blank:

The endpoint is the <u>vertex</u> of the angle.

This is your answer because an angle is formed by two rays which are the sides of an angle and they have an endpoint called the vertex.

Hope this helps!

$-TestedHyperr$

6 0

3 years ago

Read 2 more answers

Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear

AlladinOne [14]

Answer:

$x=\frac{83}{50}$

Step-by-step explanation:

we know that

If the three points are collinear

then

$m_A_B=m_A_C$

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope AB

we have

$A(1,\frac{2}{3}),B(x,-\frac{4}{5})$

substitute in the formula

$m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}$

$m_A_B=\frac{\frac{-12-10}{15}}{x-1}$

$m_A_B=-\frac{22}{15(x-1)}$

step 2

Find the slope AC

we have

$A(1,\frac{2}{3}),C(-\frac{1}{2},4)$

substitute in the formula

$m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}$

$m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}$

$m_A_C=-\frac{20}{9}$

step 3

Equate the slopes

$m_A_B=m_A_C$

$-\frac{22}{15(x-1)}=-\frac{20}{9}$

solve for x

$15(x-1)20=22(9)$

$300x-300=198$

$300x=198+300$

$300x=498$

$x=\frac{498}{300}$

simplify

$x=\frac{83}{50}$

8 0

3 years ago

You roll a 6 sided cube, what is the probability of rolling a multiple of 2 or a number greater than 3?

vova2212 [387]

The probability of rolling a multiple 2 or a number greater than 3 is 1/3

7 0

2 years ago

Read 2 more answers

A carpenter is building a bookcase of height h, length 2h, and width w. The bookcase has two shelves. The plywood to be used for

tresset_1 [31]

Answer:

3h² + 35hw ;

a = 3 ; b = 2 ; c = 35

Step-by-step explanation:

Given that :

Dimension of bookcase :

Height = h ; Length = 2h ; width = w

Area of backside :

Height * length

h * 2h = 2h²

Cos of back material = $1.5 per ft²

Cost = 1.5 * 2h²

Cost = 3h²

Top and bottom :

Length * width

2h * w

Side area = 3 * h * w

Total area : Top + bottom +. Side

Total area : 2hw + 2hw + 3hw = 7hw

Pine = $5 per sq foot

Total cost = $5 * 7hw

= $35hw

Entire cost, C

3h² + 35hw

From the format :

ah^b + chw,

a = 3 ; b = 2 ; c = 35

6 0

3 years ago

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

Katyanochek1 [597]

Answer: $(0.367,\ 0.473)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ is the sample proportion, n is the sample size , $z_{\alpha/2}$ is the critical z-value.

Given : Significance level : $\alpha:1-0.99=0.01$

Sample size : n= 85

Critical value : $z_{\alpha/2}=2.576$

Sample proportion: $\hat{p}=\dfrac{36}{85}\approx0.42$

Now, the 99% confidence level will be :

$\hat{p}\pmz_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.42\pm(2.576)\sqrt{\dfrac{0.42(1-0.42)}{85}}\\\\\approx0.42\pm0.053\\\\=(0.42-0.053,\ 0.42+0.053)=(0.367,\ 0.473)$

Hence, the 99% confidence interval estimate of the true proportion of families who own at least one DVD player is $(0.367,\ 0.473)$

3 0

2 years ago