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3 years ago

Which is the correct first step in solving the equation shown? 33 - 2x = 31

Mathematics

2 answers:

Lelu [443]3 years ago

8 0

Answer:

Subtract 33 from each side

Step-by-step explanation:

33-2x=31

Subtract 33 from each side

33-33-2x = 31-33

-2x = -2

Yakvenalex [24]3 years ago

3 0

Answer:

Subtract 33 from both sides.

Step-by-step explanation:

Remember that when you are solving for x, to always do the opposite of PEMDAS. Note that anything you do should be on the side of where the variable is, but that because of the equal sign, you must do your operation on the other side as well.

In this case, the first step is to subtract 33 from both sides:

33 (-33) - 2x = 31 (-33)

-2x = 31 - 33

Next, you are to simplify:

-2x = (31 - 33)

-2x = (-2)

-2x = -2

Then, divide -2 from both sides to fully isolate the variable, x. Remember to always fully isolate the variable, and bring the negative sign as well:

(-2x)/-2 = (-2)/-2

x = -2/-2

x = 1

x = 1 is your answer.

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Given the function f, find

Alex73 [517]

Answer:

Step-by-step explanation:

f(x) =2x - 7

f( - 3) = 2( - 3) - 7 = - 13

f(3) = 2(3) - 7 = - 1

f(a) = 2a - 7

- f(a) = - (2a - 7) = 7 - 2a

f(a + h) = 2(a + h) - 7 = 2a + 2h - 7

8 0

3 years ago

Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal

Phantasy [73]

Answer:

Part A

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the given values we get;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

$a = R \cdot cos \left(\dfrac{\pi}{n} \right)$

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the values gives;

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore, we get;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

5 0

3 years ago

what is the value of c when the value of the expression 2(3–5c) is 1 less than the value of the expression 4(1–c)?

Gre4nikov [31]

The answer in fraction form is c = 1/2

The answer in decimal form is c = 0.5

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

Explanation:

Saying "A is 1 less than B" means A = B-1. So whatever B is, subtract 1 from it and you get the value of A.

Replace A with the expression 2(3-5c). Replace B with 4(1-c)

We go from this

A = B - 1

to this

2(3-5c) = 4(1-c) - 1

----------

Let's isolate c

2(3-5c) = 4(1-c) - 1

2(3)+2(-5c) = 4(1)+4(-c) - 1

6-10c = 4 - 4c - 1

6-10c = 3 - 4c

6-3 = -4c+10c

3 = 6c

6c = 3

c = 3/6

c = 1/2

c = 0.5

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Step-by-step explanation:

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