Find the area of the shape

Logan is a land surveyor. He wants to determine d, the distance across a lake that cannot be directly measured. He draws this di

Mice21 [21]

Answer:

The first option (5.7km)

Step-by-step explanation:

Since we have a right angle triangle and we know two of its sides we can easily find out the thirds side (the value of d) by using the Pathagoras Theorem. In our case 7 and d are our legs and the hypotenuse is equal to 9, so...

(Based on the Pathagoras Theorem)

$c^{2} = a^{2} + b^{2}$

$9^{2} = 7^{2} + d^{2}$

$d^{2} = 9^{2} - 7^{2} \\d^{2} = 81 - 49\\d^{2} = 32\\d = \sqrt{32}\\$

d ≈ 5.7km

There for aproximate distance across the lake is equal to 5.7km

7 0

3 years ago

Read 2 more answers

Explain the difference between qualitative and quantitative data. Choose the correct answer below. A. Quantitative data are coll

Leona [35]

The correct answer is F. Quantitative data are numerical in nature, while qualitative data are categorical in nature.

Explanation:

In research and all the different fields that apply to it, the word "data" refers to information, values or knowledge that can be used to understand a specific situation or phenomenon. Additionally, data can be of two different types quantitative and qualitative, these differ in their nature, the phenomenons they described and the way they should be analyzed. Indeed quantitative data refers mainly to numerical data or information about quantities such as statistics that are especially useful in mathematics, science and similar that focus on numbers. On the other hand, qualitative data refers to data based on categories or qualities and because of this qualitative data is used in humanistic research, although both types of data can be combined to study a phenomenon. Considering this, the key difference between both types of data is "Quantitative data are numerical in nature, while qualitative data are categorical in nature".

3 0

3 years ago

Alana is making circular picture frames. She needs to put a ribbon along the border of each one. Use what you know about pi and

ki77a [65]

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7 0

3 years ago

Solve linear equations -4(b+3)-12=2b-16+5b

daser333 [38]

Answer:

$Exact form:b=-\frac{8}{11}\\Decimal form: b=-0.72727272727272727272$

Step-by-step explanation:

$-4(b+3)-12=2b-16+5b$

$-4b-12-12=2b+5b$

$-4b-24=7b-16$

$-4b=7b+8$

3 0

3 years ago

Read 2 more answers

Help. Solving Multi Step Ratio Problems!

Romashka-Z-Leto [24]

Answer:

Part 1) $30\ coupons$

Part 2) $12\ sandwiches$

Part 3) $60\ push-ups$

Part 4) $96\ minutes$

Part 5) $\$95$

Part 6) $1\frac{7}{8}\ cups\ of\ pretzel$

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

so

Using proportion

Find out the number of salads you could buy to get $10 in coupons

$\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons$

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

so

$\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches$

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does 15 push-ups

so

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

$\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups$

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

$1\ h=60\ min$

$\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes$

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

$\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25$

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

so

For every mug that Janet sells, she earns 2($5)=$10

using proportion

$\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70$

step 3

Adds the amount earned by Aly plus the amount earned by Janet

$25+70=\$95$

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

$1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix$

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

$\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel$

Convert to mixed number

$\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel$

6 0

3 years ago