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The area of a photograph is 35 square inches. Its length is two inches longer than its width. Find the length and width of

devlian [24]

Answer:

length is 7 inches and the width is 5 inches

Step-by-step explanation:

Hello, I think I can help you with this

the area of a rectangle is given by:

$(equation1)Area=length * width\\$

Step 1

According to the question data,the length is two inches longer than its width.which means that you can take the width and add 2 inches to obtain the length, in mathematical terms

(equation 2)Width + 2 inches = length

Step 2

Now, put equation 2 into equation 1

$Area=length * width\\Area=(width + 2 )*width\\Area=width^{2}+2widht\\Let\ width=w$

Step 3

replace and solve for w

Let

A=35

$A=35\\Area=w^{2} +2w\\35=w^{2} +2w\\w^{2} +2w-35=0\\use\ quadratic\ formula\ to\ solve\\if\\ax^{2} +bx+c=0\\x=\frac{-b +- \sqrt[2]{b^{2}4ac } }{2a}\\ +- means\ there\ are\ 2\ solutions, we\ will\ take\ the\ positive\ one, because\ it\ is\ a\ distance.\\Now, replacing\\a=1,b=2,c=35\\\\w=\frac{-2 + \sqrt[2]{2^{2}-4*1*-35 } }{2*1}\\w=\frac{-2 + \sqrt[2]{4+140} }{2}\\w=\frac{-2+\sqrt{144} }{2} \\w=\frac{-2+12}{2}\\w=\frac{10}{2}\\w=5$

so, the width is 5 inches,

replacing this value in equation 2

Width + 2 inches = length

5 in +2 in =length

7 in = length

so , the length is 7 inches

Have a good day.

4 0

3 years ago

In the following exercises, simplify each expression.

jasenka [17]

Answer:

The answer would be 8.3*10^7.

Step-by-step explanation:

This is because the beginning factor in scientific notation (in this case it is 8.3) must be no less than one, and no more than ten. Once we figured that out, we simply count the number of decimal points from 3 to the final 0. Try it yourself. You will discover that the resulting answer is 7 decimal movements. Now, since we are using scientific notation, we will want to multiply by ten to the power of the number of decimal movements (in this case it is 7.) And that's all! The answer is 8.3*10^7. I hope this helped (:

8 0

2 years ago

An industrial psychologist consulting with Lara music stores knows that the average number of complaints management receives eac

xeze [42]

Answer:

Step-by-step explanation:

H0 : μ ≥ 6

H1 : μ < 6

Test statistic :

n = 20

Sample Mean, x = 3

σ = 1.5

Test statistic = (x - μ) ÷ σ/sqrt(n)

Test statistic = (3 - 6) ÷ 1.5/sqrt(20)

Test statistic = - 3 / 0.3354101

Test statistic = −8.944271

Since, sample size is < 30 ;

Obtaining the Critical value using the from T;

Tcritical at 0.05, df = 19 = - 1.729

Tstatistic < Tcritical

−8.944271 < - 1.729

Hence, we reject the Null:

We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

3 0

3 years ago

Can you help me please

adoni [48]

Answer:

The answers are:

2u = <10,2>
-3u = <-18,-6>
u+v = <11,3>
3u-4v = <-9,-5>

Step-by-step explanation:

Given vectors are:

u = <5,1>

v = <6,2>

The vectors are given in the form of ordered pairs, the operations can be applied on the coordinates of ordered pairs

Now,

$2u = 2(5,1) = (10,2)$

$-3v = -3(6,2) = (-18,-6)$

Now we have to add two vectors

In order to add two vectors, their respective coordinates are added:

So,

$u+v = (5,1) + (6,2)\\= (5+6, 1+2)\\=(11,3)$

And

$3u-4v = 3(5,1) - 4(6,2)\\= (15,3) - (24,8)\\= (15-24, 3-8)\\=(-9, -5)$

Hence,

The answers are:

2u = <10,2>
-3u = <-18,-6>
u+v = <11,3>
3u-4v = <-9,-5>

3 0

3 years ago

Y = 10 is a solution for 7(x + 9) = 132

12345 [234]

Answer:

its close 9.45

Step-by-step explanation:

7(x+9)=132

7x+63=132

7x=132-63

7x=69

x=69/7

x=9.45

8 0

3 years ago

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