Use the distributive property to write an equivalent expression. 2(3x+10)

Estimate the area of Alberta in square miles. Show your reasoning

ella [17]

Answer: About $278,250\ mi^2$

Step-by-step explanation:

The missing figure is attached.

Notice in the first picture that Alberta has a complex shape.

You can calculate the area of a complex shape by decomposing it into polygons whose areas can be calculated easily.

Observe the second picture. Notice that it can be descompose into two polygons: A trapezoid and a rectangle.

The area of the trapezoid can be calcualted with the formula:

$A_t=\frac{h}{2}(B+b)$

Where "h" is the height, "B" is the long base and "b" is short base.

And the area of the rectangle can be found with the formula:

$A_r=lw$

Wkere "l" is the lenght and "w" is the width.

Then, the apprximate area of Alberta is:

$A=\frac{h}{2}(B+b)+lw$

Substituting vallues, you get:

$A=(\frac{(410\ mi-180\ mi)}{2})(760\ mi+470\ mi)+(180\ mi)(760\ im)\\\\A=141,450\ mi^2+136,800\ mi^2\\\\A=278,250\ mi^2$

Therefore, the area of of Alberta is about $278,250\ mi^2$ .

5 0

3 years ago

Which of the three following graphs display the same data? i. a bar graph titled county voter turnout (thousands) has year on th

ivann1987 [24]

The graphs that display the same data are a. I and II

<h3>What is Data Representation?</h3>

This refers to the different ways in which a set of data are displayed in a certain place such as a bar graph, frequency table, line graph, etc.

Hence, we can see that from the evaluation of the data, there is the use of the same data in I and II as the bar and line graphs contain the same country voter turnout.

Read more about bar graphs here:

brainly.com/question/25718527

#SPJ4

5 0

2 years ago

PLEASE HELP NEED ASAP!

Scrat [10]

Answer:

what grade is this

Step-by-step explanation:

4 0

3 years ago

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor

Dahasolnce [82]

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

<u>Solution:</u>

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is $\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }$

If they work together they can do the entire prospectus in five hours

$\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}$

On cross-multiplication we get,

$\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}$

$\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}$

On cross multiplication ,we get

$\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}$

<em><u>using quadratic formula:-</u></em>

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$x=\frac{12 \pm \sqrt{144-40}}{2}$

$\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}$

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

3 0

3 years ago

Pls explain How do do all of these and say answers

lyudmila [28]

Answer:

QUESTION ONE-

Cross multiply:

5 * 15 = 12 * y

Simplifying

5 * 15 = 12 * y

Multiply 5 * 15

75 = 12 * y

Solving

75 = 12y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-12y' to each side of the equation.

75 + -12y = 12y + -12y

Combine like terms: 12y + -12y = 0

75 + -12y = 0

Add '-75' to each side of the equation.

75 + -75 + -12y = 0 + -75

Combine like terms: 75 + -75 = 0

0 + -12y = 0 + -75

-12y = 0 + -75

Combine like terms: 0 + -75 = -75

-12y = -75

Divide each side by '-12'.

y = 6.25

Simplifying

y = 6.25

QUESTION TWO-

Cross multiply:

8 * w = 20 * 6

Simplifying

8 * w = 20 * 6

Multiply 20 * 6

8w = 120

Solving

8w = 120

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Divide each side by '8'.

w = 15

Simplifying

w = 15

QUESTION 3-

Cross multiply:

s + 1 * 8 = 4 * 4

Simplifying

s + 1 * 8 = 4 * 4

Reorder the terms:

1 + s * 8 = 4 * 4

Reorder the terms for easier multiplication:

8 * 1 + s = 4 * 4

1 * 8 + s * 8 = 4 * 4

8 + 8s = 4 * 4

Multiply 4 * 4

8 + 8s = 16

Solving

8 + 8s = 16

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + 8s = 16 + -8

Combine like terms: 8 + -8 = 0

0 + 8s = 16 + -8

8s = 16 + -8

Combine like terms: 16 + -8 = 8

8s = 8

Divide each side by '8'.

s = 1

Simplifying

s = 1

Step-by-step explanation:

6 0

3 years ago

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