This question has two parts. Use the information to answer Part A and Part B.

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

-------------------

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

-------------------

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

-------------------

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 = $42^\circ$

-------------------

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

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

============

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

Simplify. (2 x 108) + (4 * 103) Give the answer in scientific notation

lions [1.4K]

Answer:

628

Step-by-step explanation:

216+412 = 628

First you get rid of the brackets by solving what's in them. Then you just add up the numbers and BOOM. The equation is solved. :-)

6 0

3 years ago

Please solve and show all work thanks

mars1129 [50]

Answer:

The smallest of the two consecutive integers is 10 or less.

Step-by-step explanation:

Let x represent the smallest of the even integers in the sequence.

Then the sum of two consecutive even integers is ...

x + (x +2) = 2x +2

And half the sum of the next two consecutive even integers is ...

(1/2)((x +4) + (x +6)) = x + 5

The relationship between these values is ...

2x +2 ≤ 7 + (x +5)

Subtracting x+2 gives ...

x ≤ 10

The least of the two consecutive even integers is at most 10.

5 0

3 years ago

Michael is taking a 500 mile road trip if he is 48% of the way there how many miles has he driven

Natalka [10]

Answer:

Step-by-step explanation:

500× 48 %=240 miles

8 0

3 years ago

There were 200 people who voted at the town council meeting. Of these people, 40% voted for building a new basketball court in t

Nezavi [6.7K]

120 people
40% of 200 is 80
200-80=120
so 120 people voted against the basketball court

3 0

3 years ago

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