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Annette [7]
3 years ago
5

The perimeter of a rectangle is 42 inches. If the width of the rectangle is 6 inches, what is the length?

Mathematics
2 answers:
Andrews [41]3 years ago
4 0

Answer:

B. 15 inches.

Step-by-step explanation:

A rectangle shares two pairs of congruent opposite sides.

Perimeter = 42

Let:

the length of the rectangle = <em>l</em>

the width of the rectangle = <em>w</em> = 6

Perimeter = <em>l </em>+ <em>l </em>+ <em>w</em> + <em>w</em>

Plug in 42 for perimeter &  6 for w in the equation:

42 = <em> l </em> + <em> l</em> + 6 + 6

Combine like terms:

42 = (<em> l </em> + <em> l </em>) + (6 + 6)

42 = 2<em>l</em> + 12

Next, isolate the variable, <em>l</em>. Do the opposite of PEMDAS.  First, subtract 12 from both sides:

42 (-12) = 2<em>l</em> + 12 (-12)

42 - 12 = 2<em>l</em>

30 = 2<em>l</em>

Next, divide 2 from both sides:

(30)/2 = (2<em>l</em>)/2

<em>l</em> = 30/2

<em>l</em> = 15

B. 15 inches is the length of the rectangle.

Check:

<em>l </em>+ <em>l</em> + <em>w </em>+ <em>w </em>= 42

15 + 15 + 6 + 6 = 42

30 + 12 = 42

42 = 42 (True).

~

Stella [2.4K]3 years ago
3 0

Answer:

b.15 inches

Step-by-step explanation:

subtract 12 (2 6inch sides) from the perimeter

get 30 and divide by 2 to get 2 sides

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Before you get started, take this readiness quiz.

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Evaluate Algebraic Expressions

In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Example 2.3.1: evaluate

Evaluate x+7 when

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Solution

To evaluate, substitute 3 for x in the expression, and then simplify.

x+7

Substitute.

3+7

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To evaluate, substitute 12 for x in the expression, and then simplify.

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When x=12, the expression x+7 has a value of 19. Notice that we got different results for parts (a) and (b) even though we started with the same expression. This is because the values used for x were different. When we evaluate an expression, the value varies depending on the value used for the variable.

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exercise 2.3.2

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Example 2.3.2

Evaluate 9x−2, when

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Remember ab means a times b, so 9x means 9 times x.

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Evaluate: 8x−3, when

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Evaluate: 4y−4, when

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Example 2.3.5: evaluate

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Answer

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Example 2.3.6: evaluate

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3 years ago
Which statement best completes the sentence below? If the measure of /_4 is 70^o, then the measure of /_8 is _________________.
Alex_Xolod [135]

Answer:

As given, measure of angle 4 is 70°

Then what would be the measure of ∠8.

Following cases comes into consideration  

1. If ∠4 and ∠8 are supplementary angles i.e lie on same side of Transversal, then

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⇒70°+∠8=180°  [∠4=70°]

⇒∠8=180°-70°

⇒∠8=110°

<u>2nd possibility</u>

But if these two angles i.e ∠4 and ∠8 forms a linear pair.Then

⇒ ∠4 + ∠8=180°

⇒70°+∠8=180°  [∠4=70°]

⇒∠8=180°-70°

⇒∠8=110°

<u>3rd possibility</u>

If ∠4 and ∠8 are alternate exterior angles.

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<u>4th possibility</u>

If If ∠4 and ∠8 are corresponding angles.

then, ∠4 = ∠8=70°

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8 0
3 years ago
You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod
lorasvet [3.4K]

Answer:

a. y=830*(0.87)^x

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

13\%=\frac{13}{100}=0.13

Upon substituting our given values in exponential decay function we will get

y=830*(1-0.13)^x

y=830*(0.87)^x

Therefore, the exponential model y=830*(0.87)^x represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

y=830*(0.87)^2

y=830*0.7569

y=628.227\approx 628.23

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be \frac{830}{2}=415.

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

415=830*(0.87)^x

Upon dividing both sides of our equation by 830 we will get,

\frac{415}{830}=\frac{830*(0.87)^x}{830}

0.5=0.87^x

Let us take natural log of both sides of our equation.

ln(0.5)=ln(0.87^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.5)=x*ln(0.87)

\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}

\frac{ln(0.5)}{ln(0.87)}=x

\frac{-0.6931471805599}{-0.139262067}=x

x=4.977286\approx 4.98

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

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