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34kurt
3 years ago
10

Help ASAP What is the solution to this equation? (1/4)^x+1 =32

Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

Answer:

B.  \displaystyle \frac{-7}{2}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Exponential Rule [Powering]:                                                                           \displaystyle (b^m)^n = b^{m \cdot n}
  • Exponential Rule [Rewrite]:                                                                              \displaystyle b^{-m} = \frac{1}{b^m}<u> </u>

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle \bigg( \frac{1}{4} \bigg)^{x + 1} = 32<em />

<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Rewrite:                                                                                                             \displaystyle \bigg( \frac{1}{2^2} \bigg)^{x + 1} = 2^5
  2. Exponential Rule [Rewrite]:                                                                              \displaystyle (2^{-2})^{x + 1} = 2^5
  3. Exponential Rule [Powering]:                                                                          \displaystyle 2^{-2(x + 1)} = 2^5
  4. Set:                                                                                                                    \displaystyle -2(x + 1)} = 5
  5. [Division Property of Equality] Divide -2 on both sides:                                \displaystyle x + 1 = \frac{-5}{2}
  6. [Subtraction Property of Equality] Subtract -1 on both sides:                        \displaystyle x = \frac{-7}{2}
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Based on the calculations, the depth of tent is equal to 12 feet.

<h3>How to calculate the depth of the tent?</h3>

Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):

  • Triangle ABC is an isosceles triangle (AB = AC).
  • The front and back of the triangle are identical triangles.
  • Side AD is perpendicular side BC.
  • CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.

Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:

AC² = AD² + DC²

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AD² = 5² - 3²

AD² = 25 - 9

AD² = 16

AD = √16

AD = 4 feet.

Also, we would determine the area of the triangle (ABC):

Area = 1/2 × b × h

<u>Where:</u>

  • b is the base area.
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Substituting the given parameters into the formula, we have;

Area = 1/2 × 6 × 4

Area = 12 feet².

Depth of tent = 3 × height of ADC

Depth of tent = 3 × 4

Depth of tent = 12 feet.

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7 0
10 months ago
Mr. Granville needs some plywood that is about three over four-inch thick. Which plywood is closest to three over four-inch thic
Makovka662 [10]

Answer:

The plywood that is closest to three over four-inch thick is thirteen over sixteen inches thick

Step-by-step explanation:

we have

3/4 in

Verify each value

case A) 13/16 in

we know that

3/4 in=12/16 in ----> multiply by (4/4)

Find the difference

13/16-12/16=1/16 in

case B) 11/32 in

we know that

3/4 in=24/32 in ----> multiply by (8/8)

Find the difference

24/32-11/32==13/32 in

case C) 1/2 in

we know that

1/2 in=2/4 in ----> multiply by (2/2)

Find the difference

3/4-2/4=1/4 in

case D) 3/8 in

we know that

3/4 in=6/8 in ----> multiply by (2/2)

Find the difference

6/8-3/8=3/8 in

<em>Compare the values of the difference and find the less value</em>

we have

case A) 1/16=2/32 in

case B) 13/32 in

case C) 1/4=8/32 in

case D) 3/8=12/32 in

The less value is case A) 2/32 in

therefore

The plywood that is closest to three over four-inch thick is thirteen over sixteen inches thick

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Answer this thanks!!!!
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Answer:

B

Step-by-step explanation:

$65×6%=$3.90

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m I right

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Riley solved and equation as shown in the table
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She made the mistake in step 4

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