A rectangle was rotated 270° about the origin. The image is shown. Which points are vertices of the pre-image? Check all that apply.

Answer:

1) 2(x-1)^2

2)  y=2(x-1)^2

Step-by-step explanation:

The 1st one is a statement in the terms of x, and the 2nd on is in the slope intercept(graphing) format

Answer:

Divide by 7 or multiply by 1/7

Step-by-step explanation:

7x = 12

Divide each side by 7

7x/7 = 12/7

x = 12/7

We could also multiply each side by 1/7

7x * 1/7 = 12*1/7

x = 12/7

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same: [tex] \\8x^{9}[/tex]

Step-by-step explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]

[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]

[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]

[tex] \\8x^{9}[/tex]

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]

[tex] \\ (2*x^{5-2})^{3}[/tex]

[tex] \\ (2*x^{3})^{3}[/tex]

[tex] \\ (2^{3}*x^{3*3})[/tex]

[tex] \\ (8*x^{9})[/tex]

or [tex] \\ 8x^{9}[/tex].

Answer:

Every decade, the number of species decays by a factor of 0.0834.

Step-by-step explanation:

Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:

[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]

Every decade, the number of species decays by a factor of 0.0834.

Answer:

28% subtracted

Step-by-step explanation:

khan

Answer:

a² + 2ab + b² + ac + bc

Step-by-step explanation:

(a + b + c) * (a + b) = aa + ab + ac + ba + bb + bc

= a² + 2ab + b² + ac + bc

The trick you use here is called the distributive property.

Answer:

[tex]a^2+b^2+2ab+ac+bc[/tex]

Step-by-step explanation:

[tex](a+b+c(a+b)=\\a^2+ab+ac+ab+b^2+bc=\\a^2+b^2+ab+ab+ac+bc=\\a^2+b^2+2ab+ac+bc[/tex]

Answer:

2

Step-by-step explanation:

A corresponding angle is in the same position on another parallel line

1 and 2 are both above the parallel line and  to the left of the transversal

1 and 2 are corresponding angles

Answer: Angle 2

Step-by-step explanation:

Corresponding Angles are angles that take up the same spot at independent vertices, with the same transversal.  Both angle 1 and 2 are the top left angles of their vertex.

Hope it helps <3

Answer:

[tex]\boxed{\sf \ \ \ x = 1 \ \ , \ \ y = 1 \ \ \ }[/tex]

Step-by-step explanation:

hello

we can multiply by 10 both parts of the equations so this is equivalent to

(1) 15x + 8y = 23

(2) 3x - 2y = 1

and we are asked to use the method of substitution

from (2) we can write 3x = 2y + 1

and we substitute 3x in (1) as 15x = 5*3x it comes

5*(2y+1) + 8y = 23

<=> 10y + 5 + 8y = 23

<=> 18y + 5 = 23  let's subtract 5

<=> 18y = 23 - 5 = 18  let's divide by 18

<=> y  =  1

and finally replace y in 3x = 2y + 1

3x = 2*1 + 1 = 3 <=> x = 1 (divide by 3)

so the solution is x = 1, y = 1

hope this helps

Answer:

(1,1)

Step-by-step explanation:

1.5x + 0.8y = 2.3

0.3x − 0.2y = 0.1

I'm going to multiply both of these equations by 10, so we can work with whole numbers.

15x+8y=23

3x-2y=1

We can simplify one of the equations to isolate a variable.

I'm going to isolate y in equation 2.

3x-2y=1

Subtract 3x from both sides.

-2y=-3x+1

Divide both sides by -2.

y=1.5x-0.5

Plug 1.5x-0.5 into the first equation for y.

15x+8(1.5x-0.5)=23

Distribute.

15x+12x-4=23

Combine like terms.

27x-4=23

Add 4 to both sides.

27x=27

Divide both sides by 27.

x=1

Plug that back into original equation to find y.

15(1)+8y=23

15+8y=23

Subtract 15 from both sides.

8y=8

Divide both sides by 8.

y=1

The solution to the system is (1,1).

Answer:

2

Step-by-step explanation:

We already have the zeros, so we can write the cubic polynomial in this general form:

[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]

Where:

[tex]x_1 = 5[/tex]

[tex]x_2 = 5i[/tex]

[tex]x_3 = -5i[/tex]

So we have that:

[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]

[tex]y = a(x -5)(x^2 + 25)[/tex]

To find the value of the leading coefficient 'a', we can use the point (1, -208) given:

[tex]-208 = a(1 -5)(1 + 25)[/tex]

[tex]-208 = a(-4)(26)[/tex]

[tex]a = -208 / (-104) = 2[/tex]

So the leading coefficient is 2.

Answer:

0.158655253931 or 15.8%

Step-by-step explanation:

Answer:

60,480 is the correct answer.

Step-by-step explanation:

First of all, let us have a look at the formula of factorial of a number 'n':

[tex]n! = n \times (n-1) \times (n-2) \times ...... \times 1[/tex]

i.e. multiply n with (n-1) then by (n-2) upto 1.

Keep on subtracting 1 from the number and keep on multiplying until we reach to 1.

So, [tex]9![/tex] can be written as: [tex]9 \times 8 \times 7 \times ...... \times 1[/tex]

Similarly [tex]3![/tex] can be written as: [tex]3 \times 2 \times 1[/tex]

Re-writing [tex]9 ![/tex] :

[tex]9 \times 8 \times 7 \times ...... 3 \times 2 \times 1\\\Rightarrow 9 \times 8 \times 7 \times ...... 3 ![/tex]

Now, the expression to be evaluated:

[tex]\dfrac{9!}{3!} = \dfrac{9 \times 8 \times 7 \times ..... \times 3!}{3!}\\\Rightarrow 9 \times 8 \times 7 \times 6 \times 5 \times 4\\\Rightarrow 60480[/tex]

Answer:

60480

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

I used Desmos

We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).

For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.

So, for the first function:

[tex]f(x) = (1/5)*|x - 15|[/tex]

The y-intercept is:

[tex]f(0) =  (1/5)*|0 - 15| = 15/5 = 3[/tex]

For the second function:

[tex]g(x) = (x - 2)^2[/tex]

The y-intercept is:

[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]

Then we can see that g(x) has a greater y-intercept than f(x).

If you want to learn more about y-intercepts:

https://brainly.com/question/1884491

#SPJ2

Answer:

Option C

Step-by-step explanation:

The datasets is incomplete. Here is the correct question.

The data represents the number of minutes dan spent on his homework each night 30, 35, 35, 45, 46, 46 52, 55, 57. Which box plot correctly represents the data

The question lacks the required option. Find the options in the diagram below:

To get the correct box plot to represent the data, we need to calculate the lower quartile, median and the upper quartile of the data.

Since our data is already in increasing order of magnitude we can go ahead and calculate this parameters.

To get the lower quartile, we will find Q1 first.

Q1 = N+1/4 th value.

This means we have to locate the N+1/4 the value.

N is the total number present in the dataset = 9

Q1 = 9+1/4 = 10/4

Q1 = 2.5th value

This equivalent is the third value in the dataset.

Hence, our lower quartile is 35

Median is the middle value after rearrangement.

Based on the datasets, the value at the middle is 46 by inspection.

For the upper quartile Q3,

Q3 = 3(N+1)/4 th value

Q3 = 3(9+1)/4

Q3 = 30/4

Q3 = 7.5th value

The upper quartile is the 8th value in the dataset i.e 55

Based on the box plots, the only box that correctly plots this values [35, 46 and 55] is the third option.

Answer:

A

Step-by-step explanation:

edg2020

Answer:

First blank is 4, second blank is 0

Step-by-step explanation:

divide it :)

Answer:

Yellow box #1=0

Yellow box #1=4

Step-by-step explanation:

Answer:

The total number of ways the researcher can select  5 women and 5 men for a study is 7,56,756.

Step-by-step explanation:

The complete question is:

From a group of 10 women and 15 men, a researcher wants to randomly select  5 women and 5 men for a study in how many ways can the study group be selected?

Solution:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

 [tex]{n\choose k}=\frac{n!}{k!\cdot (n-k)!}[/tex]

The number of women in the group: [tex]n_{w}=10[/tex].

The number of women the researcher selects for the study, [tex]k_{w}=5[/tex]

Compute the total number of ways to select 5 women from 10 as follows:

[tex]{n_{w}\choose k_{w}}=\frac{n_{w}!}{k_{w}!\cdot (n_{w}-k_{w})!}=\frac{10!}{5!\cdot (10-5)!}=\frac{10!}{5!\times 5!}=252[/tex]

The number of men in the group: [tex]n_{m}=15[/tex].

The number of men the researcher selects for the study, [tex]k_{m}=5[/tex]

Compute the total number of ways to select 5 men from 15 as follows:

[tex]{n_{m}\choose k_{m}}=\frac{n_{m}!}{k_{m}!\cdot (n_{m}-k_{m})!}=\frac{15!}{5!\cdot (15-5)!}=\frac{15!}{5!\times 10!}=3003[/tex]

Compute the total number of ways the researcher can select  5 women and 5 men for a study as follows:

[tex]{n_{w}\choose k_{w}}\times {n_{m}\choose k_{m}}=252\times 3003=756756[/tex]

Thus, the total number of ways the researcher can select  5 women and 5 men for a study is 7,56,756.

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = average daily cost to rent a car in Los Angeles

x2 = average daily cost to rent a car in Las Vegas

s1 = sample standard deviation for Los Angeles

s2 = sample standard deviation for Las Vegas

n1 = number of sampled cars in Los Angeles

n2 = number of sampled cars in Las Vegas

Degree of freedom = (n1 - ) + (n2 - 1) = (40 - 1) + (40 - 1) = 38

For a 95% confidence interval, the t score from the t distribution table is 2.024

From the information given,

x1 = 102.24

s1 = 5.98

n1 = 40

x2 = 97.35

s2 = 4.21

n2 = 40

x1 - x2 = 102.24 - 97.35 = 4.89

Margin of error = z√(s1²/n1 + s2²/n2) = 2.024√(5.98²/40 + 4.21²/40) = 2.024√1.3371125

= 2.34

The 95% confidence interval is 4.89 ± 2.34

Hypothesis testing

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean average daily cost to rent a car in Los Angeles and μ2 be the the mean average daily cost to rent a car in Las Vegas

The random variable is μ1 - μ2 = difference in the mean average daily cost to rent a car in Los Angeles and the mean average daily cost to rent a car in Las Vegas

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 0

This is a two tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (102.24 - 97.35)/√(5.98²/40 + 4.21²/40)

t = 4.23

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [5.98²/40 + 4.21²/40]²/[(1/40 - 1)(5.98²/40)² + (1/40 - 1)(4.21²/40)²] = 1.78786983766/0.02552804373

df = 70

We would determine the probability value from the t test calculator. It becomes

p value = 0.00007

Since alpha, 0.05 > than the p value, 0.00007, then we would reject the null hypothesis. Therefore, at 5% significance level, there is sufficient evidence to conclude that there is a significant difference in the rates between the two cities.

Answer:

Step-by-step explanation:

Hey there! :)

Answer:

A. 23.

Step-by-step explanation:

Given:

5 + 2(x + 7)² for x = -4

Substitute in -4 for x in the equation:

5 + 2((-4) + 7)²

5 + 2(3)²

5 + 2(9)

5 + 18 = 23.

Therefore, the correct answer is A. 23.

Answer:

23

Step-by-step explanation:

5 + 2(x + 7)^2

Let x =-4

5 + 2 ( -4+7)^2

Parentheses first

5 +2 (3)^2

5+ 2*9

Multiply

5+18

add

23

Answer: Car-maker C1

Explanation:

The minimum value is visually shown as the tip of the left whisker. For car-maker C1, the min value is 12. For car-maker C2, the min value is 10, which we can see is less than C1's value. So that's why C1 is the answer.

Answer:

Total bill = $70.80

Step-by-step explanation:

$60 × 0.18 = $10.80

$60 + $10.80 = $70.80

Hope this helps! :)

Answer:

$70.8

Step-by-step explanation:

Since it is 18 percent tax,we need to find 18% of 60$.In order to do that we need to do 60/1 mutiplied by 18/100 and doing the math 18% of 60 =10.8

Now we have to add 60+10.8=$70.8

Thank you and I hope all you have an amazing day.Hope this helps you.Thank you.

Answer:

4x

Step-by-step explanation:

The Taylor series of a function f(x) about a value x = a is given by f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ... where the terms in f prime f'(a) represent the derivatives of x valued at a.

For the given function, f(x) = 4x and a = -2

So, f(a) = f(-2) = 4(-2) = -8

f'(a) = f'(-2) = 4

All the higher derivatives of f(x) evaluated at a are equal to zero. That is f''(a) = f'"(a) =...= 0

Substituting the values of a = -2, f(a) = f(-2) = -8 and f'(-2) = 4 into the Taylor series, we have

f(x) = f(-2) + f'(-2)(x - (-2))/1! + f''(-2)(x - (-2))²/2! + f'''(-2)(x - (-2))³/3! +...

= -8 + 4(x + 2)/1! + (0)(x + 2)²/2! + (0)(x + 2)³/3! +...

= -8 + 4(x + 2) + 0 + 0

= -8 + 4x + 8

= 4x

Answer: 49/9

Step-by-step explanation: 42/9 + 7/9 = 49/9

Make first fraction into improper fraction with the same common dominator as 7/9 and add them both

Hope this helps:)

Answer:

49/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean score of Mrs. Smith's students and μ2 be the mean score of Mrs. Jones students.

The random variable is μ1 - μ2 = difference in the mean score of Mrs. Smith's students and the mean score of Mrs. Jones students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

From the information given,

μ1 = 78

μ2 = 85

s1 = 10

s2 = 15

n1 = 30

n2 = 25

df = [10²/30 + 15²/25]²/[(1/30 - 1)(10²/30)² + (1/25 - 1)(15²/25)²] = 152.11/3.37883141762

df = 45

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (78 - 85)/√(10²/30 + 15²/25)

t = - 1.99

d) Confidence interval = μ1 - μ2 ± z√(s1²/n1 + s2²/n2)

Where z is the t test score for the confidence level. Since alpha = 0.1, confidence level = 1 - alpha = 1 - 0.1 = 0.9. From the t distribution table, test score at df of 45 = 1.301

z√(s1²/n1 + s2²/n2) = 1.301√(10²/30 + 15²/25) = 4.57

Confidence interval = (78 - 85) ± 4.57

Confidence interval = - 7 ± 4.57

e) we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.

1 - α/2 = 1 - 0.1/2 = 1 - 0.05 = 0.95

The critical value is 1.679 on the right tail and - 1.679 on the left tail

Since - 1.99 < - 1.679, it is not in the rejection regions. Therefore, we would fail to reject the null hypothesis. Therefore, at 10% significance level, there is insufficient evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

Answer:

d

Step-by-step explanation:

The table shows the result of the statement given below.

A data table is a range of cells in which you can change values in some of the cells and come up with different answers to a problem.

here, we have,

Given that,

the chef at a school cafeteria asked 100 male and 100 female students whether they like peas.

42 of the males said they like peas. 64 of the females said they dislike peas.

The number of males who like peas=42 and the number of males who dislikes peas=58.

The number of females who like peas=36 and the number of females who dislikes peas=64.

The table shows the result of the statement given below.

To learn more about the data table visit:

brainly.com/question/17084863.

#SPJ7

Answer:  see proof below

Step-by-step explanation:

Proof by exhaustion means to input several numbers that satisfy the claim and if they all prove to be true then you have proven the claim.

Claim: (2x³ + 3x² + x)/(6) ∈ Z (integer)

Let's choose x = {1, 2, 3, 4)

Case 1: x = 1

2(1)³ + 3(1)² + (1) = 12

12/6 = 2

2 ∈ Z [tex]\checkmark[/tex]

Case 2: x = 2

2(2)³ + 3(2)² + (2) = 30

30/6 = 5

5 ∈ Z [tex]\checkmark[/tex]

Case 3: x = 3

2(3)³ + 3(3)² + (3) = 84

84/6 = 14

14 ∈ Z [tex]\checkmark[/tex]

Case 4: x = 4

2(4)³ + 3(4)² + (4) = 180

180/6 = 30

30 ∈ Z [tex]\checkmark[/tex]

Since each case was shown to be true we have proven the claim is true by exhaustion.

Answer:

The large sample size 'n' = 384.16

Step-by-step explanation:

Explanation:-

Given Margin of error = 4

Given Population standard deviation(σ)  = 40

The margin of error is determined by

[tex]M.E = Z_{0.05} \frac{S.D}{\sqrt{n} }[/tex]

[tex]4 = 1.96 \frac{40}{\sqrt{n} }[/tex]

Cross multiplication , we get

[tex]\sqrt{n} = \frac{40 X 1.96}{4}[/tex]

√ n = 19.6

squaring on both sides , we get

n = 384.16

Final answer:-

The large sample size 'n' = 384.16

Answer:

The single discount rate equavalent is a discount of 40%.

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

Discount of 20%:

20% decrease:

1 - (20/100) = 1 - 0.2 = 0.8

Discount of 25%:

1 - (25/100) = 1 - 0.25 = 0.75

Series of discounts(20% and 25%):

0.8*0.75 = 0.6

1 - 0.6 = 0.4

The single discount rate equavalent is a discount of 40%.

Answer:

a. 55 cars

b. 25 cars

Step-by-step explanation:

Let's call the number of cars with stereo systems N(ss), with air conditioners N(ac) and with sun roofs N(sr).

So we have that:

N(ss) = 30

N(ac) = 30

N(sr) = 40

N(ss and ac and sr) = 15

N(at least two) = 30

a.

To find how many cars have at least one option (N(at least one) or N(ss or ac or sr)), we have:

N(ss or ac or sr) = N(ss) + N(ac) + N(sr) - N(ss and ac) - N(ss and sr) - N(ac and sr) + N(ss and ac and sr)

N(ss or ac or sr) = 30 + 30 + 40 - (N(at least two) + 2*N(ss and ac and sr)) + 15

N(ss or ac or sr) = 30 + 30 + 40 - (30 + 2*15) + 15 = 55

b.

The number of cars that have only one option is:

N(only one) = N(at least one) - N(at least two)

N(only one) = 55 - 30 = 25

Answer:

Option A

Step-by-step explanation:

Given function is,

f(x) = x² + 3x + 5

We have to find the value of f(a + h) so we will substitute (a + h) in place of x, and simplify the expression.

f(a + h) = (a + h)² + 3(a + h) + 5

           = a² + 2ah + h² + 3(a + h) + 5 [(a + b)² = a² + 2ab + b²]

           = a² + 2ah + h² + 3a + 3h + 5

Therefore, Option A will be the answer.

Answer:

x=1/2, y=5

Step-by-step explanation:

This can be solved using substitution!

Hope this helped!

Answer:

{x,y}={ 1/2, 5)

Step-by-step explanation:

[1]    8x + 7y = 39

[2]    4x - 14y = -68

Solve equation [2] for the variable  x

 [2]    4x = 14y - 68

 [2]    x = 7y/2 - 17

// Plug this in for variable  x  in equation [1]

  [1]    8•(7y/2-17) + 7y = 39

  [1]    35y = 175

// Solve equation [1] for the variable  y

  [1]    35y = 175

  [1]    y = 5

// By now we know this much :

   x = 7y/2-17

   y = 5

// Use the  y  value to solve for  x

   x = (7/2)(5)-17 = 1/2

Answer:

C - 3 (negative 64 divided by 8) + 25 =1

Step-by-step explanation:

Answer:

C is correct answer

Step-by-step explanation: