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xxMikexx [17]
3 years ago
10

 LOOK BELOW FOR PICTURE The first Pentagon is dilated to form the second pentagon.

Mathematics
2 answers:
Serggg [28]3 years ago
7 0
The answer is B because 4 x 1.25 is 5
Svetradugi [14.3K]3 years ago
3 0

The first pentagon is dilated to form second pentagon as shown in the given figure.

We have to find the scale factor.

A scale factor is a number which scales, or multiplies, some quantity. The ratio of any two corresponding lengths in two similar geometric figures is also called a scale factor.

Therefore, Scale factor = \frac{5}{4}

= 1.25

And we can observe,, 4 \times 1.25 = 5

Therefore, 5 is the scale factor.

You might be interested in
In ΔPQR, what is the m∠Q?.
charle [14.2K]

The sum of the 3 inside angles of a triangle needs to equal 180:

11x-5 + 6x + 5 + c = 180

Combine like terms:

18x = 180

Divide both sides by 18:

X = 10

Solve for Q:

11x -5= 11(10) -5 = 110-5 = 105 degrees

7 0
3 years ago
Read 2 more answers
Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t
Anika [276]

Answer:

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c

Step-by-step explanation:

Given

\int\limits {\frac{x}{x^4 + 16}} \, dx

Required

Solve

Let

u = \frac{x^2}{4}

Differentiate

du = 2 * \frac{x^{2-1}}{4}\ dx

du = 2 * \frac{x}{4}\ dx

du = \frac{x}{2}\ dx

Make dx the subject

dx = \frac{2}{x}\ du

The given integral becomes:

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du

Recall that: u = \frac{x^2}{4}

Make x^2 the subject

x^2= 4u

Square both sides

x^4= (4u)^2

x^4= 16u^2

Substitute 16u^2 for x^4 in \int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du

Simplify

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du

In standard integration

\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)

So, the expression becomes:

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)

Recall that: u = \frac{x^2}{4}

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c

4 0
3 years ago
Y+5=-(x+5) in standard form
swat32

1. y+5=-x-5

2. y=-x-5-5

3.y=-x-10

4. y=x-10

_______________________

1. distribute negative sign

2. move the constant to the right and change the sign

3. -5-5 equals -10, bring everything down

4. change the sign of the x to positive, the equation is in standard form

5 0
3 years ago
This is due soon help
cricket20 [7]
50 miles = 1 hour
50 x 1 = 50

a. 50 miles x 2 hours = 100 miles
b. 50 miles x 4.3 hours = 215 miles
c. Converting minutes to hours, it would make 20 minutes become 0.333 hours.
50 x 0.333 = 16.65 miles
6 0
3 years ago
Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin
NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)  

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

2) Confidence interval

Assuming that \bar X =5.5 and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=1086-1=1085

Since the Confidence is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that t_{\alpha/2}=2.33

Now we have everything in order to replace into formula (1):

5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139    

5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861

So on this case the 95% confidence interval would be given by (5.139;5.861)    We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

5 0
3 years ago
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