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Alik [6]
3 years ago
14

A rectangle has a width of 2.5. When the length of this rectangle is decreased by 5 inches, the new area of the rectangle is 17.

5.
Part A: Write an equation to represent this situation, where x represents the original length of the rectangle.
Part B: Find the original length of the rectangle.
Mathematics
1 answer:
kati45 [8]3 years ago
7 0
<h3><u>Part A: An equation to represent this situation, where x represents the original length of the rectangle is:</u></h3>

17.5 = (x-5) \times 2.5

<h3><u>Part B: Original length of the rectangle is 12 inches</u></h3>

<em><u>Solution:</u></em>

Given that,

A rectangle has a width of 2.5

Therefore,

width = 2.5 inches

Let "x" be the original length of the rectangle

When the length of this rectangle is decreased by 5 inches

Therefore,

New length = x - 5

The new area of the rectangle is 17.5 square inches

Therefore,

<em><u>The area of rectangle is given as:</u></em>

Area = length \times width

17.5 = (x-5) \times 2.5\\\\17.5 = 2.5x - 12.5\\\\2.5x = 17.5 + 12.5\\\\2.5x = 30\\\\x = 12

Thus original length of the rectangle is 12 inches

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Triangles J K L and M N R are shown.
Free_Kalibri [48]

The correct answer is option B which is we need ∠L ≅  ∠R to prove congruency.

<h3>What is congruency?</h3>

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.

Here we are given that

KL = NR

JL = MR

Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.

So for the triangles to be congruent by SAS, angle L must be congruent to angle R.

∠L=∠R

Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

Learn more about congruency at

brainly.com/question/14418374

#SPJ1

4 0
2 years ago
Posttest
PtichkaEL [24]

Answer:

a) y=2x+4 b) 2 c) 6 d) Sorry, you'll have to do that buy it's not too difficult! ^u^

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

1a) Well, if you add the y to both sides, you would get y=2x+4

1b) Since the main form is y=mx+b with m being the slope, the slope in y=2x+4 must be 2

1c) 6, because if x is 1, 2(1)+4=6

1d) I'm afraid you'll have to do that, just substitute in different numbers for x

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

Please, please give brainliest, it would be greatly appreciated, I only need one more before I advance, thanks!

5 0
2 years ago
May i have help with this
Leya [2.2K]

Answer: D. 7^11

Step-by-step explanation:

For exponents with the same base, we just add the exponents and keep the same base. 7 is the same base; therefore 5+6=11 which means the answer is 7^11

3 0
2 years ago
A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you
hram777 [196]

Answer:

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom   n  - 1     df = 22 - 1     df = 21

As the question mentions " different " that means,  a two-tail test

At 0,01 significance level     α  = 0,01       α/2  =  0,005

and t(c)  = 2,831

Test Hypothesis

Null Hypothesis                      H₀          μ  =  μ₀

Alternative hypothesis           Hₐ          μ  ≠  μ₀

To calculate t(s)

t(s)  =  (  μ  -  μ₀ ) /σ/√n

t(s)  =  (  433,50 - 385 ) / 86,92 / √22

t(s)  =  2,6171

Comparing   t(c)   and t(s)

t(s) < t(c)

Then  t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim

6 0
3 years ago
The cost of 15 gallons of gasoline is $48 which equation shows this in function notation
Lynna [10]
Are there different choices for the answer? You did not list any equations to choose from
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