If ( t+ 5)/(t - 5) = 10, what is the value of t ?A) 45 / 11B) 5C) 11/2D) 55/9

Mathematics

1 answer:

love history [14]1 year ago

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The value of t is (D) 55/9.

<h3>What is an equation?</h3>

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.
The word equation and its cognates in other languages may have subtly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

To find the value of t:

Given -

(t+5)/(t-5) = 10
t+5 = 10(t-5)
t+5 = 10t - 50
10t - t = 5 + 55
9t = 55
t = 55/9

Therefore, the value of t is (D) 55/9.

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I NEED THE ANSWER RIGHT NOW PLEASE!!!

strojnjashka [21]

Answer:

Second : 1/6 x + 47

Third : 1 2/3 x + 35 - 1 1/2 x + 12

Fourth : 5 (1/3x) + (5) (7) - (3) (1/2x) + (3) (4)

Step-by-step explanation:

I would start by expanding the expression, showing each step. Then, simplify by collecting like terms.

To expand, you multiply the term outside of the brackets by each term inside the brackets.

5(1/3x + 7) - 3(1/2x - 4)

= 5(1/3x) + (5)(7) - (3)(1/2x) + (3)(4) Showing how to expand

= 5/3x + 35 - 3/2x + 12 Simplified above step by multiplying

= 5/3x - 3/2x + 47 Collected like terms (35 + 12 = 47)

= 10/6x - 9/6x + 47 Change fractions to the common denominator 6

= $\frac{10-9}{6}x$ + 47 Combine fractions with common denominator

= 1/6x + 47 Fully expanded

See which options match the steps I took to expand the original expression.

The second step is the same as option 4.

The last step is the same as option 2.

I bolded those steps that are the same.

Some options use mixed fractions (whole numbers and fractions).

From the third step, I will convert the improper fractions to mixed fractions.

5/3x + 35 - 3/2x + 12

= 1 2/3x + 35 - 1 1/2x + 12

This is the same as option 3.

$\frac{5}{3}x = 1\frac{2}{3}x$ On the left side, 5 goes into 3 ONE time. The ONE becomes the whole number. After 5 goes into 3, there is 2 left, which becomes the numerator.

$\frac{3}{2}x = 1\frac{1}{2}x$ On the left side, 3 goes into 2 ONE time. The ONE becomes the whole number. The remainder is 1, which becomes the numerator.