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VMariaS [17]
3 years ago
10

ALGEBRAIC PROOF!!!! PLS HELP!!! The area of a rectangular blanket is 20 square feet. The blanket's length is (2x + 1) ft and the

blanket's width is 2x ft. find the dimensions of the blanket. provide justification for each step.
Mathematics
1 answer:
Fynjy0 [20]3 years ago
7 0

Answer:

Length: 5 ft; width: 4 ft.

Step-by-step explanation:

A = LW     formula for area of rectangle

(2x + 1)(2x) = 20      substitute length, width, and area into formula

4x² + 2x - 20 = 0      use the distributive property to multiply out left side

2x² + x - 10 = 0         divide both sides of equation by 2

(2x + 5)(x - 2) = 0        factor out trinomial

2x + 5 = 0  or  x - 2 = 0        use zero product rule to solve for x

2x = -5  or x = 2       subtract 5 from both sides; add 2 to both sides

x = -5/2  or  x = 2

We discard x = -5/2 since it would give negative length and width, and the length and width cannot be negative.

Length: 2x + 1 = 2(2) + 1 = 5

Width: 2x = 2(2) = 4

Length: 5 ft; width: 4 ft.

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What is the length of the the midsegment of a trapezoid with bases of length 14 and 24​?
krek1111 [17]

Step-by-step explanation:

Length \: of \: midsegment \\  =  \frac{1}{2}  \times sum \: of \: lengths \: of \: bases \\  \\  = \frac{1}{2}  \times(14 + 24) \\  \\  = \frac{1}{2}  \times38 \\  \\  = 19  \: units

6 0
3 years ago
Read 2 more answers
I need help plz percent equations the question is blank% of 16 = 12
ch4aika [34]

Answer:

16 x 0,75

(0,75 = 3/4) so you could take 3 x 16 = 48 and then take 48/4 and the answer should be 12 but the percent is 75%

5 0
3 years ago
5. A baseball card sold for ​$241 in 1975 and was sold again in 1988 for $405. Assume that the growth in the value V of the​ col
Tju [1.3M]

The exponential growth rate of the baseball card given its price in 1975 and 1988 is 4.07%.

<h3>What is the exponential growth rate?</h3>

The exponential growth rate is the rate of increase in the value of an asset with the passage of time.

Exponential equations have the form ab^{x}

Growth rate = (future value / present value)^(1 / number of years)

(405 / 241)^(1/13) = 4.07%

To learn more about exponential functions, please check: brainly.com/question/26331578

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5 0
2 years ago
A graduate student majoring in linguistics is interested in studying the number of students in her college who are bilingual. Of
Eddi Din [679]

Answer:

48.41% probability that 17 or fewer of them are bilingual.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 50, p = \frac{466}{1320} = 0.3530

So

\mu = E(X) = np = 50*0.3530 = 17.65

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.3530*0.6470} = 3.38

Probability that 17 or fewer of them are bilingual.

Using continuity correction, this is P(X \leq 17 + 0.5) = P(X \leq 17.5), which is the pvalue of Z when X = 17.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{17.5 - 17.65}{3.38}

Z = -0.04

Z = -0.04 has a pvalue of 0.4841

48.41% probability that 17 or fewer of them are bilingual.

8 0
4 years ago
Solve for x <br> 4(x+7)=5x+8
wel

Step-by-step explanation:

4x+28=5x+8

x=20

.............

8 0
3 years ago
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