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2 years ago

Solve each equation by factoring. (x – 7)(2x - 3) = 0

Mathematics

1 answer:

Orlov [11]2 years ago

5 0

Answer:

x = 7 and 3/2

Step-by-step explanation:

We can say:

x - 7 = 0 and 2x - 3 = 0

Lets solve for x - 7 = 0 first:

Add 7 to each side of "="

=> x = 7

Now lets solve for 2x - 3 = 0

First add 3 to each side of "="

=> 2x = 3

Now divide each side by 2

=> x = 3/2

Hope this helps!

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Answer:

Your answer is C) 1.92

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3 years ago

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If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

4 0

3 years ago

Find the surface area of the composite figure.

zhuklara [117]

Answer:

438.97 cm²

Step-by-step explanation:

To find the surface area, we break up the figure into two pieces(blue and yellow) and then add them together.

SA = 2(w · l + h · l + h · w)

2 · (6 · 16 + 4 · 16 + 4 · 6)

368 cm²

70.97 cm² + 368 cm²

438.97 cm²

5 0

2 years ago

Simplify: (2x – 3)2 4x2 + 9 4x2 – 12x + 9 4x2 – 12x + 6 4x2 – 6

Alexxandr [17]

Answer:

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Step-by-step explanation:

we have

$(2x-3)^2$

we know that

$(a-b)^2=a^2-2ab+b^2$

In this problem

$a=2x\\b=3$

substitute in the formula

$(2x-3)^2=(2x)^2-2(2x)(3)+(3)^2$

$(2x-3)^2=4x^2-12x+9$

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