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3 years ago

What are the areas of each shape

Mathematics

1 answer:

Snezhnost [94]3 years ago

3 0

Answer:

Hi since area is measured in square units, all you have to do here is count the squares within those shapes.

Step-by-step explanation:

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Simplify the expression: –3(–7 + 3z)

aleksandrvk [35]

Hey there! I'm happy to help!

We want to multiply each term inside the parentheses by the number on the outside.

-3(-7)=21

-3(3z)=-9z

Therefore, our expression is 21-9z.

Now you know how to use the distributive property! Have a wonderful day! :D

5 0

3 years ago

A statue is mounted on top of a 21 foot hill. From the base of the hill to where you are standing is 57feet and the statue subte

AleksandrR [38]

Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

PQ = 57 feet = Distance between you and the base of the hill

SR= h=height of the statue

$\angle SPR$ =Angle subtended by the statue to where you are standing.

$\angle x=\angle RPQ$ = which is unknown.

Let us begin solving now. The first step is to find the angle $\angle x$ which can be found by using the following trigonometric ratio in $\Delta PQR$ :

$tan(x)=\frac{RQ}{PQ} =\frac{21}{57}$

Which gives $\angle x$ to be:

$\angle x=tan^{-1}(\frac{21}{57})\approx20.22^{0}$

Now, we know that $\angle x$ and $\angle SPR$ can be added to give us the complete angle $\angle SPQ$ in the right triangle $\Delta SPQ$ .

We can again use the tan trigonometric ratio in $\Delta SPQ$ to solve for the height of the statue, h.

This can be done as:

$tan(\angle SPQ)=\frac{SQ}{PQ}$

$tan(7.1^0+20.22^0)=\frac{SR+RQ}{PQ}$

$tan(27.32^0)=\frac{h+21}{57}$

$\therefore h+21=57tan(27.32^0)$

$h\approx8.45 ft$

Thus, the height of the statue is approximately, 8.45 feet.

3 0

3 years ago

The ratio of two numbers is 6 : 8. The sum of the numbers is 28. What are the two numbers?

Otrada [13]

Answer:

12 and 16 or 12:16

6 x 2 = 12

8 x 2 =16

12 + 16 = 28

Step-by-step explanation:

5 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a

8090 [49]

Answer:

C. 14 metres cubed

Step-by-step explanation:

The volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius, while the volume of a cylinder is denoted by: $V=\pi r^2h$ , where r is the radius and h is the height.

Here, we know that the sphere and cylinder have the same radius and height. However, the "height" of the sphere is technically just the diameter, which is twice the radius. So, h = 2r. We know the volume of the cylinder is 21, so:

$V=\pi r^2h=\pi r^2*2r=2\pi r^3$