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3 years ago

A field is 53 1/3 yards wide. What is the width of the field in feet?

Mathematics

1 answer:

Umnica [9.8K]3 years ago

5 0

Answer: The width of the field = 160 feet

Step-by-step explanation:

We are given that , A field is $53\dfrac{1}{3}$ yards wide.

That means , The width of the field = $53\dfrac{1}{3}$ yards

Since , the fraction is in mixed for , so first we convert this into improper fraction.

$53\dfrac{1}{3}=\dfrac{3(53)+1}{3}=\dfrac{160}{3}$

Therefore , the width of the field = $\dfrac{160}{3}$ yards

Since 1 yard = 3 feet.

⇒ the width of the field = $\dfrac{160}{3}\times3$ feet

Therefore , the width of the field = 160 feet

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Find all real $x$ that satisfy $$(2^x - 4)^3 (4^x - 2)^3 = (4^x 2^x - 6)^3. $$

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The polynomial-like expression is satisfied by the real value x = 1.

<h3>How to determine the real solution of a polynomial-like expression</h3>

In this question we must apply the concepts of logarithms and algebra properties to solve the entire expression. Initially, we expand the right part of the expression:

$(2^{x}-4)^{3}+(4^{x}-2)^{3} = (4^{x}+2^{x}-6)^{3}$

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$(2^{x}-4)^{3}+(4^{x}-2)^{3} = (2^{x}-4)^{3}+3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2}+(4^{x}-2)^{3}$

$3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2} = 0$

$2^{x}-4 + 4^{x}-2 = 0$

$2^{x}\cdot 2^{x} + 2^{x}-6 = 0$

$u^{2}+u - 6 = 0$

$(u+3)\cdot (u-2) = 0$

Hence, the roots of the pseudopolynomial are $u_{1} = -3$ and $u_{2} = 2$ . Only the second one have a real value of x. Hence, we have the following solution:

$2^{x} = 2$

$x\cdot \log 2 = \log 2$

$x = 1$

The polynomial-like expression is satisfied by the real value x = 1. $\blacksquare$

To learn more on logarithms, we kindly invite to check this verified question: brainly.com/question/24211708

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3 years ago

In the diagram, CE = 12 and BE = 5. Based on the given information, AE = .

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GalinKa [24]

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3 years ago

Given the Arithmetic sequence A1,A2,A3,A4 28, 33, 38, 43 What is the value of A11?

harkovskaia [24]

28,33,38,43

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an = a1 + (n - 1) * d
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Let P be between M and N use the segment addition postulate to solve for X

marta [7]

Step-by-step explanation:

given,

MP = x - 8

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we know,

according to segment addition postulate AB + BC = AC

now,

MP + PN = MN

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→ 4x = 21 + 17

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→ x = 9

therefore, value of x is 9.

hope this answer helps you dear! take care

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3 years ago