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skad [1K]
3 years ago
15

What is the value of x that makes the perimeters equivalent?

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
5 0

Answer:

x=5

Step-by-step explanation:

First you want to simplify each shape's perimeter formula.

In this case, we'll call the rectangle A and the triangle B.

1) Address the information (L=Length, W=Width)

A= 2L+2W

B= 2L + W

(Now you add in the information)

A= [2(3x-3) + 2(x-3)]

B= [2(2x-1) +2x]

2) Start to Solve (start by multiplying the 2s by the parentheses)

A=6x-6 +2x-6

B= 4x-2 +2x

3) Combine Like Terms

A= (6x+2x) + (-6 +-6) -> 8x-12

B= (4x+2x) -2 -> 6x-2

4) Now that you've simplified, set both areas as equals to Solve for x

8x-12=6x-2

5) Combine Like Terms. Start by subtracting 6x over. (You subtract to cancel out the positive 6x on the one side, so you can bring it over as a negative)

8x-12=-2

-6x

2x-12=-2

6) Combine Like Terms. Add 12 to both sides (to cancel out the one side's 12)

2x=-2

+12

7) Solve for x.

<u>2x</u>=<u>10</u>

2. 2

x=5

If unsure of answers, you can also plug your answer into the formula to see if your answer was correct. In this case, both shapes have a perimeter of <u>28</u>.

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A researcher wishes to estimate the average blood alcohol concentration​ (BAC) for drivers involved in fatal accidents who are f
Mnenie [13.5K]

Answer:

A 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .

Step-by-step explanation:

We are given that a researcher randomly selects records from 60 such drivers in 2009 and determines the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 ​g/dL.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                               P.Q.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~   t_n_-_1

where, \bar X = sample mean BAC = 0.16 g/dL

            s = sample standard deviation = 0.080 ​g/dL

            n = sample of drivers = 60

            \mu = population mean BAC in fatal crashes

<em>Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>

So, a 90% confidence interval for the population mean, \mu is;

P(-1.672 < t_5_9 < 1.672) = 0.90  {As the critical value of t at 59 degrees of

                                              freedom are -1.672 & 1.672 with P = 5%}    P(-1.672 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 1.672) = 0.90

P( -1.672 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 1.672 \times {\frac{s}{\sqrt{n} } } ) = 0.90

P( \bar X-1.672 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+1.672 \times {\frac{s}{\sqrt{n} } } ) = 0.90

<u>90% confidence interval for</u> \mu = [ \bar X-1.672 \times {\frac{s}{\sqrt{n} } } , \bar X+1.672 \times {\frac{s}{\sqrt{n} } } ]

                                       = [ 0.16-1.672 \times {\frac{0.08}{\sqrt{60} } } , 0.16+1.672 \times {\frac{0.08}{\sqrt{60} } } ]

                                       = [0.143, 0.177]

Therefore, a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .

7 0
3 years ago
Urgent help needed algebra 2
g100num [7]

The solution of the given equation 4(3x - 4) - 7( 2x + 3) = 3 is -20.

<h3>What is a linear equation?</h3>

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

4(3x - 4) - 7( 2x + 3) = 3

To solve;

4(3x - 4) - 7( 2x + 3) = 3

Solve the parentheses using the distributive property;

12x - 16 - 14x - 21 = 3

we need to get the like terms together;

12x - 14x -16 - 21 = 3

-2x - 37 = 3

Add 37 both sides, we get;

-2x = 40

Divide both sides by -2

x = -20

Hence, the solution of the given equation is -20.

Learn more about linear equations;

brainly.com/question/10413253

#SPJ1

4 0
1 year ago
What is the truth value of the following statement? If a number is divisible by 3, then it is odd. True or False?
Verizon [17]

Answer:Not true

Step-by-step explanation:12 is divisible by 3, and 12 is even.

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1.304×10^7 in standerd form
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1.304*10^7 

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The answer to this question would be marked as true
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