For the first one the answer are

Mathematics

1 answer:

BigorU [14]3 years ago

4 0

Answer:

1. add 1/2x to both sides

a. you want to combine the like terms. in this case, it is the x variable.

you are left with 7/6x = 5

2. multiply by 6/7

a. the reciprocal of 7/6 will cancel out the values

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A cone has a volume of 5 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

DENIUS [597]

The answer is 15 in³.

The volume of the cone is:
$V_1= \pi r_1 ^{2} \frac{h_1}{3} = \frac{ \pi r_1^{2} h_1}{3}$
where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone

The volume of the cylinder is:
$V_2= \pi r_2h_2^{2}$
where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone

Since <span>the cone fits exactly inside of the cylinder, they have the same radius and the height:
r</span>₁ = r₂
h₁ = h₂

Also:
V₁ = 5

Now, let's write two volume formulas together:
$V_1= \frac{ \pi r^{2} h}{3}$
<span> $V_2= \pi rh^{2}$ </span>

We can include V₂ into V₁:
$V_1= \frac{V_2}{3}$

⇒ $V_2=3*V_1$
$V_2=3*5 in^{3}$
$V_2=15 in^{3}$

5 0

3 years ago

A company logo is shaped like an equilateral triangle with 2-in.-long sides. What is the height of the logo? Round to the neares

deff fn [24]

Answer:

B. 1.7 in

Step-by-step explanation:

Divide the triangle into 2 congruent right angle triangles

With hypotenuse: 2

Base: 2/2 = 1

Using pythagoras theorem

2² = 1² + h²