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Dafna11 [192]
2 years ago
15

Question 4 options:

Mathematics
1 answer:
andrew11 [14]2 years ago
4 0

I. The value of x is equal to 8.

II. The dimensions of the rectangle are 13 and 5 inches respectively.

<u>Given the following data:</u>

  • Area of a rectangle = 65 square inches.
  • Length of rectangle = x + 5 inches
  • Width of rectangle = x - 3 inches

To find the value of x, and the dimensions of the rectangle:

Mathematically, the area of a rectangle is given by the formula:

A = LW

Substituting the values, we have:

65 = (x+5)(x-3)\\\\65=x^2-3x+5x-15\\\\65=x^2+2x-15-65\\\\x^2 +2x-80=0\\\\x^2 +10x-8x-80=0\\\\x(x+10)-8(x+10)=0\\\\(x-8)(x+10)=0

x = 8 or x = -10

<u>For the</u><u> length:</u>

when x = 8

Length = 8 +5

Length = 13 inches.

<u>For the</u><u> width:</u>

when x = 8

Length = 8 -3

Length = 5 inches.

Find more information: brainly.com/question/11037225

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Zolol [24]

The equation 5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0 is a quadratic equation

The value of x is 8 or 1

<h3>How to determine the value of x?</h3>

The equation is given as:

5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0

Rewrite as:

-5/x - 2 + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0

Take the  LCM

[-5(x + 2) + (x -5)(x- 2)]\[x^2 - 4 + [3x + 8]/[x^2 - 4] = 0

Expand

[-5x - 10 + x^2 - 7x + 10]/[x^2 - 4] + [3x + 8]/[x^2 - 4] = 0

Evaluate the like terms

[x^2 - 12x]/[x^2 - 4] + [3x + 8]/[x^2 - 4 = 0

Multiply through by x^2 - 4

x^2 - 12x+ 3x + 8 = 0

Evaluate the like terms

x^2 -9x + 8 = 0

Expand

x^2 -x - 8x + 8 = 0

Factorize

x(x -1) - 8(x - 1) = 0

Factor out x - 1

(x -8)(x - 1) = 0

Solve for x

x = 8 or x = 1

Hence, the value of x is 8 or 1

Read more about equations at:

brainly.com/question/2972832

8 0
2 years ago
Which answer represents the series in sigma notation? −3+(−1)+1+3+5 A:∑j=15(2j−5)
insens350 [35]

Answer:

A:∑j=15(2j−5)

Step-by-step explanation:

a = -3

d = -1 - (-3) = -1 + 3 = 2

j-th term: a + (j-1)d

-3 + (j - 1)(2)

-3 + 2j - 2

2j - 5

8 0
3 years ago
What is 218.4 rounded to the nearest whole number
kati45 [8]

Answer:

It's 218, since 4 rounds below 5.

Step-by-step explanation: Please brainliest!

5 0
2 years ago
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How do i find the derivative of<br><img src="https://tex.z-dn.net/?f=9%20%5Cdiv%20%20%5Csqrt%7Bx%7D%20" id="TexFormula1" title="
Alekssandra [29.7K]
Possible derivation:
d/dx(3)
The derivative of 3 is zero:
Answer: = 0
4 0
3 years ago
NEED HELP ASAP PLEASE
timurjin [86]

If the unknown value is x, then x = \frac{14}{4} × 6 = 21.

Explanation:

  • Since it is a double number line with a ratio, all the ratios of one number line to the other will remain equal for all the values along both the number lines. Assume the unknown value to be x.
  • The ratio of the number on the first number line to the corresponding number on the second number line is calculated to be;                                  \frac{7}{2} = \frac{14}{4} = \frac{x}{6} = \frac{28}{8} = \frac{35}{10} = 3.5. So \frac{x}{6} = 3.5, x = 3.5 × 6 = 21.
  • We can also calculate x by the following method. As ratios are equal we can directly substitute the value to another ration.                                                      So \frac{14}{4} = \frac{x}{6}, x = \frac{14}{4} × 6 = \frac{84}{4} = 21.

3 0
3 years ago
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