Multiply using the distributive property

1. A MAP SCALE READS 1CM:5KM. IF A DISTANCE ON THE MAP MEASURES 7CM, THE ACTUAL DISTANCE WILL BE?. 2. A SCHOOL DINING HALL IS 35

Agata [3.3K]

Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. $42^\circ$

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map = 7 cm

Actual distance = Measurement of map $\times 5$

Actual distance = 7 $\times 5$ = 35 km

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Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

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Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to $\frac{1}{5}$ cm on scale

30m is equivalent to $\frac{1}{5} \times 30$ = 6 cm on scale

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Solution 4.

Angle of elevation of A from B = $42^\circ$

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = $42^\circ$

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Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, $\angle B = 42^\circ$

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

$sin\theta = \dfrac{Perpendicular}{Hypotenuse}$

OR

$sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m$

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So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. $42^\circ$

5. 16.73 m

7 0

3 years ago

Snow+snow+snow=30 Snow+stick+stick=20 Stick+2glass+2glass=9 Stick+1glass+snow=?

KengaRu [80]

Stick =5
1 glass =1
snow=10
5+1+10= 16

8 0

3 years ago

Read 2 more answers

As a laboratory assistant, you measure chemicals using the metric system. For your current research, you need to measure out 45

sergiy2304 [10]

Answer: 1.587 ounces of sodium chloride

Step-by-step explanation:

We know that 1 ounce is equivalent to 28.35 gr.

So we use this as a conversion factor to find the equivalent amount of sodium chloride in ounces.

If we need 45 grams of sodium chloride then this equals to:

$45\ g* \frac{1\ ounces}{28.35\ gr} = 1.587\ ounces$

Finally you need 1.587 ounces of sodium chloride

5 0

3 years ago

Read 2 more answers

Can someone help me find the area of this triangle please

Minchanka [31]

12 $x^{4}$ $y^{7}$

area = $\frac{1}{2}$ × base × height

= $\frac{1}{2}$ x 3xy² × 8x³ $y^{5}$ = 12 $x^{(1 + 3)}$ $y^{(2 + 5)}$

= 12 $x^{4}$ $y^{7}$

5 0

4 years ago

Read 2 more answers

If you are good at determining sequences please help! (Show work)

ziro4ka [17]

Answer:

-62.5008

Step-by-step explanation:

the pattern here is dividing by -5, so just continue dividing by -5 starting on -3 and continuing 4 more times. record each number and then add them together using a calculator. you will get -62.5008

Please mark brainliest :)

8 0

3 years ago