Graph y≤2x+3

One mirror is to be in the shape of a triangle whose height is 6 feet less than twice the base of the mirror. If the mirror has

Vlad1618 [11]

Answer:

Base of the mirror is 12 feet and height of the mirror is 18 feet.

Step-by-step explanation:

Given:

Area of the triangular mirror = 108 sq ft.

Let base (b) of the mirror be x.

Now given:

height is 6 feet less than twice the base of the mirror

So we can say that;

Height (h) = $2x-6$

We need to find the base and height of the mirror.

Solution:

Now we know that mirror is in triangular shape so we will apply area of triangle formula to find base and height.

Now Area of triangle is half times base times height.

framing in equation form we get;

$108=\frac{1}{2} \times x \times(2x-6)\\\\108=\frac{1}{2}\times x \times 2(x-3)\\\\108=x(x-3)\\\\108=x^2-3x\\\\x^2-3x-108=0$

Now we will find the roots of x by factorizing the equation we get;

$x^2-12x+9x-108=0\\\\x(x-12)+9(x-12)=0\\\\(x-12)(x+9)=0$

Now we will solve for 2 values of x we get;

$x-12=0\\\\x=12\ ft\\\\Also;\\\\x+9=0\\\\x=-9\ ft$

Now we get 2 values of 'x' one positive and one negative.

Since x is base of the triangle which cannot be negative.

so we will discard the negative value.

Hence;

base of triangle = 12 ft

Height of the triangle = $2x-6=2\times12-6 =24-6 =18\ ft$

Hence Base of the mirror is 12 feet and height of the mirror is 18 feet.

7 0

3 years ago

What is the mean absolute deviation of 42 31 1 1 2 4 5 6 7 3

FromTheMoon [43]

The mean absolute deviation is 10.52.

<h3>What is the mean absolute deviation?</h3>

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It is a measure of variation of a data set.

MAD =1/n ∑ l x - m(x) l

Where:

n = total numbers in the data set

x = number

m(x) - median

The first step is to determine the mean of the data set: (42 + 31 + 1 + 1 + 2 4+ 5 + 6 + 7 + 3) / 10 = 10.2

Find the absolute value of the difference between the number and the mean. Add the result | (42 - 10.2) + (31 - 10.2) + (1 _ 10.2) + (1 - 10.2) + (2 - 10.2) + (4 - 10.2) + (5 - 10.2) + (6 - 10.2) + (7 - 10.2) + (3 - 10.2) = 105.2

Divide the sum by the total number in the dataset = 105.2 / 10 = 10.52

To learn more about mean absolute deviation, please check: brainly.com/question/27365177

#SPJ1

5 0

1 year ago

A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the se

Zolol [24]

Answer:

Expected value: 3/7

Change landing on purple to -1.5

Step-by-step explanation:

Expected value

=3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7

Fair game: Expected value = 0

Change the value of 0 to -1.5

7 0

2 years ago

A TV's regular price is $349. It is on

Nata [24]

Answer:

rounded is $207.66

Step-by-step explanation:

you start by doing 349(0.30) which would be 104.7

349-104.7=244.3

next you do 244.3(.15)=36.645

244.3-36.645= $207.655

4 0

2 years ago

Read 2 more answers

n a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2472 subjects randomly selecte

Leona [35]

Answer:

0.3876<p<0.4389

Step-by-step explanation:

-Given $n=2472, \ x=1022 , \ CI=0.99$

-We calculate the proportion of surveys returned:

$\hat p=\frac{1022}{2472}\\\\=0.4134$

For a 99% confidence interval:

$z_{\alpha/2}=2.576$

#The margin of error is calculated as;

$ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255$

The confidence interval are then:

$CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389]$

Hence, the confidence interval is 0.3876<p<0.4389

5 0

3 years ago