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Ray Of Light [21]
3 years ago
12

Pam and her grandma are planning to make a quilt together. The quilt will be made out of fabric squares that measure 6 inches on

each side. The quilt will have 3 more squares along its longer edge than it will have along its shorter edge.
If there are x fabric squares along the quilt's shorter edge, find an expression for f(x), the length of the quilt's shorter edge in inches.
f(x)=
6x
Next, find an expression for g(x), the length of the quilt's longer edge in inches.
g(x)=
Which function can you use to find the area of the quilt in square inches?
Mathematics
1 answer:
san4es73 [151]3 years ago
6 0

Answer:

There are x squares on the shorter side, each square measures 6 inches.

<u>The length of the shorter side is:</u>

  • f(x) = x*6 = 6x

<u>The length of the longer side is:</u>

  • g(x) = (x + 3)*6 = 6x + 18

<u>The area of the quilt is:</u>

  • A = 6x(6x + 18) = 36x² + 108x

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3 years ago
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Natalie has 300 cookies for a bake sale. She makes 8 more batches with 12 cookies in each batch. She sells 6 bags of cookies wit
vitfil [10]

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Step-by-step explanation:

6 0
2 years ago
Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the inter
hoa [83]

Answer:

0.20 and 0.36

Step-by-step explanation:

y(t) = 2 sin (4π t) + 5 cos (4π t)

We wish to convert this to:

y = A sin(ωt + φ)

We know that ω = 4π.  We also know the following:

5 = A sin φ

2 = A cos φ

Divide the first equation by the second equation:

5/2 = tan φ

φ = tan⁻¹(5/2)

Now, square the two equations and add them together.

5² + 2² = (A sin φ)² + (A cos φ)²

29 = A²

A = √29

The equation of the wave is therefore:

y = √29 sin(4π t + tan⁻¹(5/2))

The maximum negative position is -√29.  And half of that is -½√29.

-½√29 = √29 sin(4π t + tan⁻¹(5/2))

-½ = sin(4π t + tan⁻¹(5/2))

7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)

7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π

t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24

Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.

t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24

t ≈ 0.20 or 0.36

5 0
3 years ago
Which choices are equivalent to the exponential expression below? check all that apply. (2/3)^3
rosijanka [135]

Answer:

B. (2/3) x (2/3) x (2/3)

C. 8/27

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Step-by-step explanation:

You need to know the following property

\LARGE \left(\frac{a}{b} \right)^c = \frac{a^c}{b^c}

Exponent also means you're multiplying the same number for an 'n' number of times.

For example, 2^3 = 2 * 2 * 2

we multiply it by itself 3 times since 3 is the exponent.

x^y

x is the base, y is the exponent

we read it as x to the power of y

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4 0
3 years ago
Help asap!! interpret the meaning of the expression
Triss [41]

Answer:

D

Step-by-step explanation:

This is exponential growth, and to my understanding, the format goes:

<em>initial amount (percent growth/ decay)^time</em>

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<em>percent decay = (1 - decimal percent) </em>

Your equation:

1500(1.02)^t

Using the above format, 1500 appears to be the initial amount, which increases by 2% per annum.

i think

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3 years ago
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