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3 years ago

Select the assumption necessary to start an indirect proof of the statement. If 3a+7 < 28, then a<7.

1 answer:

7 0

When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.

In our case we assume a is not smaller than 7, that is we assume a≥7.

a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:

3a+7≥28,

which is a contradiction because 3a+7 is smaller than 28.

So our assumption is wrong, which means the opposite of it is correct.

Answer: assume a≥7

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A rectangular prism has a top face with an area of 20 ft2 and a height of 5 ft. What is the volume of this rectangular prism? Th

kkurt [141]

Answer:

the volume of the rectangular prism is 100 ft³

Step-by-step explanation:

Given;

area of top face of a rectangular prism, A = 20 ft²

height of the rectangular prism, h = 5 ft

Volume of the rectangular prism = Area of top face x height of the rectangular prism

Volume of the rectangular prism = A x h

Volume of the rectangular prism = 20 ft² x 5 ft

= 100 ft³

Therefore, the volume of the rectangular prism is 100 ft³

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3 years ago

Delta Math:<br> Finding Angles (Level 1) 1/5<br> Full explanation please<br> will give brainlist

olga nikolaevna [1]

Answer:

$m\angle FGC =101\degree$

Step-by-step explanation:

$m\angle CBF = 46\degree$ (Given)

$m\angle FIG = 55\degree$ (Given)

$m\angle IFG = m\angle CBF$ (Corresponding angles)

$\implies m\angle IFG = 46\degree$

$m\angle FGC =m\angle IFG+ m\angle FIG$

(By exterior angle theorem)

$m\angle FGC =46\degree+ 55\degree$

$m\angle FGC =101\degree$

4 0

2 years ago

1 + tanx / 1 + cotx =2

Lera25 [3.4K]

Answer:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 + cot(x) + tan(x) = 2

Multiply both sides of 1 + cot(x) + tan(x) = 2 by tan(x):

1 + tan(x) + tan^2(x) = 2 tan(x)

Subtract 2 tan(x) from both sides:

1 - tan(x) + tan^2(x) = 0

Subtract 1 from both sides:

tan^2(x) - tan(x) = -1

Add 1/4 to both sides:

1/4 - tan(x) + tan^2(x) = -3/4

Write the left hand side as a square:

(tan(x) - 1/2)^2 = -3/4

Take the square root of both sides:

tan(x) - 1/2 = (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

tan(x) = 1/2 + (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Take the inverse tangent of both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) = 1/2 - (i sqrt(3))/2

Take the inverse tangent of both sides:

Answer: x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

4 0

3 years ago

How many solutions douse -5x-8=+8

larisa [96]

Answer: One solution

Step-by-step explanation:

Given

-5x-8=8

Add 8 on both sides

-5x-8+8=8+8

-5x=16

Divide -5 on both sides

-5x/-5=16/-5

x=-3.2

Therefore, it has one solution

Hope this helps!! :)

Please let me know if you have any questions

8 0

3 years ago

X+2y=6 <br> SHOW ALL OF YOUR WORK!

Alika [10]

Answer:

x+2y=6

Subtract 2y from both sides.

x=6−2y

Step-by-step explanation:

x=6-2y

3 0

3 years ago

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