(7.5.C) Similarity Problems

Answer:

The answer is D. II 1 > -2 and III -2< 1 Hopefully this is helpful!

Step-by-step explanation:

Answer:

[tex]x^{4}-17x^{2} +16[/tex] = (x -1)(x + 1)(x - 4)(x + 4)

Step-by-step explanation:

At first, let us find the first two factors of [tex]x^{4}-17x^{2} +16[/tex]

∵ The sign of the last term is positive

∴ The middle signs of the two factors are the same

∵ The sign of the middle term is negative

∴ The middle signs of the two factors are negative

∵ [tex]x^{4}[/tex] = x² × x² ⇒ first terms of the two factors

∵ 16 = -1 × -16 ⇒ second terms of the two factors

∵ x²(-1) + x²(-16) = -x² + -16x² = -17x² ⇒ the value of the middle term

∴ (x² - 1) and (x² - 16) are the factors of [tex]x^{4}-17x^{2} +16[/tex]

Now let us factorize each factor

→ The factors of the binomial a² - b² (difference of two squares) are

   (a - b) and (a + b)

∵ x² - 1 is the difference of two squares

∴ Its factors are (x - 1) and (x + 1)

∵ x² - 16 is the difference of two squares

∴ Its factors are (x - 4) and (x + 4)

∵ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of (x² - 1) and (x² - 16)

∵ (x² - 1) and (x² - 16) are the factors of [tex]x^{4}-17x^{2} +16[/tex]

∴ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of [tex]x^{4}-17x^{2} +16[/tex]

∴  [tex]x^{4}-17x^{2} +16[/tex] = (x -1)(x + 1)(x - 4)(x + 4)

Factoring an expression involves rewriting the expression in simpler forms

The factorized expression is (x - 4)(x + 4)(x - 1)(x + 1)

The expression is given as:

[tex]\mathbf{x^4 - 17x^2 + 16}[/tex]

Express 17 as 1 + 16

[tex]\mathbf{x^4 - 17x^2 + 16 = x^4 - x^2 - 16x^2 + 16}[/tex]

Factorize

[tex]\mathbf{x^4 - 17x^2 + 16 = x^2(x^2 - 1) - 16(x^2 - 1)}[/tex]

Factor out x^2 - 1

[tex]\mathbf{x^4 - 17x^2 + 16 =(x^2 - 16)(x^2 - 1)}[/tex]

Express 16 as 4^2, and 1 as 1^2

[tex]\mathbf{x^4 - 17x^2 + 16 =(x^2 - 4^2)(x^2 - 1^2)}[/tex]

Apply difference of two squares

[tex]\mathbf{x^4 - 17x^2 + 16 =(x - 4)(x + 4)(x - 1)(x + 1)}[/tex]

Hence, the factorized expression is (x - 4)(x + 4)(x - 1)(x + 1)

Read more about factoring expressions at:

https://brainly.com/question/19386208

The value of the 6 in Kiera's number is 10x greater than the 6 in Chloe's number

Answer: 4.

Step-by-step explanation: 2 + 2 is 4.

Answer:

what are the equations

Step-by-step explanation:

Answer:

D. (142886, 196914).

Step-by-step explanation:

To solve for this question, we would use t score instead of z score. The reason is because, our sample size is small.

The formula for Confidence Interval =

C.I = Mean ± t score × standard deviation/√n

n = 5 samples

Degrees of freedom = n - 1 = 5 - 1 = 4

The t score for a 95% confidence interval with degrees of freedom 5 is : 2.776

Hence,

Confidence Interval =

169,900 ± 2.776 × 21,756/√5

169,900 ± 2.776 × 9.7295789837

169, 900 ± 27009.311259

Confidence Interval

169,900 - 27009

= 142886

169, 900 + 27009.311259

= 196914

Hence, the confidence interval = (142886, 196914)

Option D is the correct answer

Using the t-distribution, it is found that the 95% confidence interval for the average price of a home of this size in Newberry is of (142886, 196914), given by option D.

In this problem, we have the standard deviation for the sample, thus, the t-distribution is used to solve this question.

First, we find the number of degrees of freedom, which is the sample size subtracted by 1, so df = 5 - 1 = 4.

Then, we find the critical value for the 95% confidence interval with 4 df, which looking at the t-table or using a calculator is given by t = 2.7765.

The margin of error is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

In this case:

[tex]M = 2.7765\frac{21756}{\sqrt{5}} = 27014[/tex]

The confidence interval is:

[tex]\overline{x} \pm M[/tex]

Then

[tex]\overline{x} - M = 169900 - 27014 = 142,886[/tex].

[tex]\overline{x} + M = 169900 + 27014 = 196,914[/tex].

Thus, the correct option is D. (142886, 196914).

A similar problem is given at https://brainly.com/question/15180581

Answer:

slope of fig 1st(m)= 1/4

y-intercept of 1st fig=-1

slope of fig 2= -1

y-intercept of 2nd fig=2

Step-by-step explanation:

Answer:

area of triangle is

[tex]\frac{1}{2} * b*h\\\\\frac{1}{2} *6*8\\\\6*4=24[/tex]

Answer:

3.6

Step-by-step explanation:

30 of 12% =3.6

hope this helped

Answer:

3.6

Step-by-step explanation:

Answer:

Two.

Step-by-step explanation:

200 + 10 + 6 = 216

216 divided by 100 is 2.16

Therefore there are two hundreds in 200 + 10 + 6

Answer:

the ask a question about the question isnt working

Step-by-step explanation:

but can you zoom in its really glitchy and blurred from far away

Yeah I would also need it zoomed in please.

Answer:

48 cups

Step-by-step explanation:

Answer: 48

Step-by-step explanation:

Usually, I would do the four cups in one gallon thing. This time, I don't need to because we already know how many cups there are in one gallon. Just multiply 16 by 3 to find how many cups.

= 16 x 3

= 48

Answer:

The answer would be 536 cones.

Step-by-step explanation:

You have to subtract 164 from 700.

700-164=536.

Answer:

The answer is 2.5 minutes per lap.

Step-by-step explanation:

Divide the number of minutes by the amount of laps:

25/10 = 2.5

To check your answer, multiply 2.5 my the amount of laps.

2.5 x 10 = 25

I hope this helped you! If it did, please consider rating, pressing thanks, and/or giving my answer 'Brainliest.' Have a wonderful day. :)

Answer:

40 seconds per lap

Step-by-step explanation:

10 divided by 25 is 0.4

So im pretty sure the anser is 40 secounds

Sorry if im wrong- im not that great at math eaither I just used a calculator.

Answer:

23.8

Step-by-step explanation:

2(5.2) + 2(6.7) = 23.8

Answer:

23.8 ...............

Step-by-step explanation:

I asked my alexa.

Answer:

The standard deviation increases, it's mean, medium and mode, if you put them in order and then go through and get your middle number it'll be 81.

If a score of 50 is added to the data set,

The standard deviation increases.

The range increases.​

"It is the average of all elements of the data set."

"It is the middle number in a sorted list of numbers."

[tex]SD=\sqrt{\frac{\sum{(x-M)^{2}} }{N} }[/tex]

where, SD is the population standard deviation

N : the size of the population

x : each value from the data

M : the mean of the data

range = maximum value - minimum value

For given situation,

Consider the original set of test scores: 71, 75, 80, 81, 81, 84, 89, 93

N = 8

range R = 93 - 71

⇒ R = 22

Mean M = (71 + 75 + 80 + 81 + 81 + 84 + 89 + 93)/8

⇒ M = 654/8

⇒ M = 81.75

Now, we find the median K

First we sort given data set: 71, 75, 80, 81, 81, 84, 89, 93

The middle numbers are 81 and 81

So, the median is the average of 81, 81

So, K = 81

Now, we calculate the standard deviation.

[tex]SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(89-81.75)^{2}+(93-81.75)^{2}] }{8} }[/tex]

⇒ SD = 6.61

Consider, the set of test scores with 50 added to the data set.

N = 9

range R = 93 - 50

⇒ R = 43

Mean M =  (71 + 75 + 80 + 81 + 50 + 81 + 84 + 89 + 93)/9

⇒ M = 704/9

⇒ M = 78.22

Now, we find the median K

First we sort given data set: 50, 71, 75, 80, 81, 81, 84, 89, 93

The middle number is 81.

So, the median is K = 81

Now, we calculate the standard deviation.

[tex]SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(50-81.75)^{2}+(93-81.75)^{2}] }{9} }[/tex]

⇒ SD = 11.76

So, we can observe that if a score of 50 is added to the data set, the correct statements are:

The standard deviation increases.

The range increases.​

Learn more about mean, standard deviation, median, range here:

https://brainly.com/question/17998130

#SPJ2

Answer:

100 people

Step-by-step explanation:

Population Of People=115Percentagencrease=15%

The New Population corresponds to 115%

(That is 100+15)

We want to find the population that corresponds to 100% that is the original population.

Therefore Original Population;

[tex] \frac{100}{115}\times {115}{} [/tex]

[tex]100 \: people[/tex]

Answer:

13:7

Step-by-step explanation:

20 - 7 = 13 girls

Girls  Boys

13        7

Answer:

it would be 7:20 im pretty sure

Step-by-step explanation:

Answer:

73.72 units²

Step-by-step explanation:

Area of the shaded region = Area if the rectangle - area of the semicircle

Area of the rectangle = length*width

Length = 10 units

Width = 8 units

Area of rectangle = 10*8 = 80 units²

Area of semicircle = ½(πr²)

radius (r) = 8/2 = 4 units

π = 3.14

Area of semicircle = ½(3.14*4) = 3.14*2 = 6.28 units²

Area of the shaded region = 80 - 6.28 = 73.72 units²

Answer: 54.88

Step-by-step explanation:​

The shape shown is a circle that overlaps a rectangle. The shaded region is a rectangle with half a circle cut out. To find the area of the shaded region, we can find the area of the rectangle and the area of the overlapping semi-circle and subtract them. The rectangle has a height of 10. The width of the rectangle is the diameter of the circle, 8. First, find the area of the rectangle:

AAA=length×width=10⋅8=80

To find the area of the circle, we need to find the radius. The radius is one half the diameter, therefore r=4. Use the value of r to solve for the area:

AAA=πr2=3.14⋅(42)=50.24

Now we can subtract half the area of the circle from the area of the rectangle:

Area of rectangle−Area of half circle=Area shaded region

80−50.242

A=54.88

So the area of the shaded region is 54.88.

Answer:

im pretty sure thats a trench ;_;

Step-by-step explanation:

Answer:

4x-7

Step-by-step explanation:

Answer:

the first one is 21 and the second one is 11

Step-by-step explanation:

I am not 100 percent sure

Answer:

450 miles per hour

Step-by-step explanation:

Kelly flies at a distance of 2,100 miles

The time taken for the trip is 4 2/3 hours

Therefore the rate of speed can be calculated as follows

= 2,100 ÷ 4 2/3

= 2,100 ÷ 14/3

= 2100 × 3/14

= 150 × 3

= 450 miles per hour

Answer:

450

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

multiply 6 for the numerators and denominaters

Answer:

Yes they are proportional

Step-by-step explanation:

May I please have brainliest?

Answer:

0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don't (starting at 1 instead).

Answer:

0 is a rational, whole, integer and real number.