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A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?

Answers

Answer 1

Answer:

The dimensions increased by 4 feet.

What is the area of the rectangle?

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given;

Dimensions of rectangle = 12 + x and 14 + x

The area of the rectangle= (12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x =4

Hence, The dimensions increased by 4 feet.

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Answer 2

Answer:

Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

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Can someone help me translate this into a mathematical notation One fourth of three times a number is five

Answers

Answer:

3x/4 = 5

Step-by-step explanation:

72. Which best describes the polynomial -5x^3?Third degree binomial

First degree trinomial

Third degree monomial

Third degree binomial

Answers

-5x^3?

This is a third degree monomial

It has one term so it is a monomial

the exponent is to the power of 3 so it is third degree

Answer:

Third degree monomial.

Step-by-step explanation:

because it only has one number and is to the third degree

The image of a parabolic lens is traced onto a graph. The function f(x) = 1/4 (x+8)(x-4) represents the image. Atwhich points does the image cross the x-axis?

O (-8, 0) and (4,0)
(8,0) and (-4, 0)
O (2, 0) and (-1,0)
O (-2, 0) and (1, 0)

Answers

The image of the parabolic lens crosses the x axis at the points

(-8, 0) and (4, 0)

How to find the points where the image cross x axis

To find the points where the graph of the function crosses the x axis we need to find the values of x that make f(x) equal to zero

hence we have that

f(x) = 1/4 (x + 8) (x - 4)

0 = 1/4 (x + 8) (x - 4)

x + 8 = 0

x = -8

x - 4 = 0

x = 4

hence we can say that the image of the parabolic lens crosses the x axis at the points (-8, 0) and (4, 0)

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If college tuition last year was $3300 and this year tuition has increased to $3564 what is the percent of increase?

Answers

college tuition and fees have increased 1,120 ... reports that the rate of increase in college costs has been “four times ... tuition at four-year public universities had increased by 15 percent between 2008 and 2010. ... “But if the costs keep on rising, especially at a time when family ...

how much 45% acid solution should be mixed with a 30% acid solution to make 450 ml of a 40% acid solution?

Answers

We do as follows:

let x = amount of 45% solution
y = amount of 30% solution

overall balance => x + y = 450
acid balance => .45x + .30y = .40(450)

Solving simultaneously, we will have:

x = 300 mL
y = 150 mL

This is assuming that partial molar properties does not affect the volume greatly. Hope this answers the question. Have a nice day.

The average starting salary of this year's vocational school graduates is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Answers

Answer:

Minimum: $25,200

Maximum: $44,800

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

$Z = (X - \mu)/(\sigma)$

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.

In this question:

$\mu = 35000, \sigma = 5000$