If P = (-1,-1), find the image
of P under the following rotation.
90° counterclockwise about the origin
([?], [])
Enter the number that belongs in
the green box.

9514 1404 393

Answer:

  (b)  the correct table is marked

Step-by-step explanation:

Direct variation is characterized by the ratio of y to x being a constant for all values in the table. That constant is the constant of proportionality. For the values in the second table (marked), the ratio is ...

  y/x = 8/6 = 12/9 = 16/12 = 4/3

The constant of proportionality is 4/3.

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

MARK AS BRAINLIEST!!!

The results based on the information provided in the question will be as follows:

a) By using the analysis of variance (ANOVA) table,

MSE= 440.1/10 = 44.01

F = 2717.9/44.01 =61.756

b) To interpret the slope of regression model,

the slope represents that for each $1000 increase in the income of a family on an average sale price increase by 2184.3

c) To calculate the value of coefficient of determination and its interpretation,

0.712 and the lowest that coefficient of determination is 0 and highest is 1. Thus, here the coefficient is high.

d) By using regression equation,

Price = 11.8+2.18×income

Predicted value = (-11.8+2.18×20)×1000 = 31800

e) To compute, 95% confidence slope

= 2.1843/2.228×0.278 = 1.565;2.804

f) The linear relationship between income and price,

All the intervals above have a value of more than 0 therefore we can conclude that the slope is significant. Thus, we have sufficient evidence that at 0.05 level of significance the linear relationship between income and price is inter related.

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Note that the full question is:

The National Association of Home Builders ranks the most and least affordable housing markets based on the proportion of homes that a family earning the median income in that market could afford to buy. Data containing the median income $1000s) and the median sale price($1000s) for a sample of 12 honsing markets appearing on the list of most affordable markets were subjected to a simple linear regression analysis. The following results were obtained. The regression equation is price-11.8 +2.18 income Predictor Coef StDev Constant11.80 12.84 income 2.1843 0.2780 S 6.634 Analysis of Variance Source Regression 1 2717.9 2717 DF SS MS F P Residuni Eror 10 440. Total 1 3158.0 a. Using the snalysis of variance table, find MSE b. Interpret the slope of the regression model. the valus ul and interpret it d. Using the estimated regression equation, the value ofy ifx-$20,000 e. Compute 95% confidence al for the slope 43-1+2.2280T g. At the 0.05 level of significunce, is there evidence of a linear relationship between income and price

The expression of the statement that is given above can be written as follows: 262144y³ + 27.

To determine how to express the given statement the following should be carried out.

When a number is said to be cubed, it means that the number should be times by itself three consecutive times.

That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,

= 64×64×64(y)³ + 3×3×3

= 262144y³ + 27.

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Answer:

Step-by-step explanation:

\(6748_9 = 6 *(9^3) + 7 * 9^2 + 4 * 9^1 + 8 * 9 ^ 0 = 4994_{10}\)

Hence, on base 10, the next whole number is 4995 and if we convert back to base 9, we will have

\(6* 9^3 + 7*9^2 + 5*9*1 = 4374 + 576+45 = 4995_{10}\)

Therefore, the number on base 9 will be 6750

The next number on base 9 is 6750.

Whole numbers are all the natural numbers and zero.

The number 6748₉ in the ten base system is

6748₉ = 6 * (9³) + 7 *9²+4*(9)¹+8*9⁰ = 4994₁₀

On base 10 system the next number will be 4995

4995 = 4374+576+45 = 6*9³+7*9²+5*9*1

Therefore, the next number on base 9 is 6750.

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Answer:

My guess would be D

Step-by-step explanation:

Step-by-step explanation:

The volume of a cube is similar to that of a rectangular prism, the volume equals the length times width times height, however because it’s a cube all the measurements are the same, in this case 7 inches. So volume equals 7^3, thus equaling 343 inches cubed. Hope this helps!

9514 1404 393

Answer:

  3 feet per second

Step-by-step explanation:

If the time is multiplied by 2, the inverse relationship tells you the speed is multiplied by 1/2.

  (1/2)(6 ft/s) = 3 ft/s

The swimmer's average speed is 3 ft/s.

The coordinates of the image are -2P

From the question, we have the following parameters that can be used in our computation:

Ry = -2(P)

To calculate the coordinate of the image, we simply open the bracket

So, we have

Ry = -2(P)

Solving further, the equation can be represented as

Ry = -2 * P

Evaluate the product

So, we have the following representation

Ry = -2P

Hence, the image has an coordinate or ordered pair of -2P

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Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Answer:

$96.00

Step-by-step explanation:

if the bill is $80 an there was a 20% tip, that would mean that the tip was $16, and 80 + 16 = 96. the total bill is $96.00

The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.

To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.

(sin 2x) / (1 + cos 2x)

(2sin x × cos x) / (1 + (cos²x - sin²x))

(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)

We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:

(2sin x × cos x) / (1 + 2sin x × cos x)

(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)

((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)

(2sin x - 4sin²x) / (1/cos²x - 4sin²x)

Since tan x = sin x / cos x, we can rewrite the expression:

(2tan x - 4tan²x) / (sec²x - 4tan²x)

(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)

(2tan x - 4tan²x) / (1 - 3tan²x)

2tan x × (1 - 2tan²x) / (1 - 3tan²x)

tan x

So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.

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Answer:

to find the average rate of change for this function, you have to examine the formula of the average rate of change: (y2-y1)/(x2-x1).  

having that said, you can now plug in the values by solving the equation for x= -4 and x= 2:  

g(-4) = 50

g(2) = 14

so, average rate of change becomes: (14-50)/(2-(-4)) = 36/6 = 6.  

hope that helps!

Step-by-step explanation:

brainliest?

The different coordinates after respective rotation are:

1) A'(2, 0)

2) A'(0, -2)

3) A'(-2, 0)

There are different methods of transformation such as:

Translation

Rotation

Dilation

Reflection

Now, the coordinate of the given point A is: A(0, 2)

1) The rule for rotation of 90 degrees clockwise is:

(x, y) →(y,-x)

Thus, we have:

A'(2, 0)

2) The rule for rotation of 180 degrees is:

(x, y) → (-x,-y)

Thus, we have:

A'(0, -2)

3) The rule for rotation of 180 degrees is:

(x, y) → (-y,x)

Thus, we have:

A'(-2, 0)

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Answer:

√5 is the answer

Answer:

14/15

Step-by-step explanation:

Answer:

I'm not very sure how I even got the answer, but the answer is 14/15

Answer:

25(p+2q)

Step-by-step explanation:

The GCF is 25, so factor out 25 and you have 25 (p + 2q)

Answer:

check below

Step-by-step explanation:

2x + 3y = -21

3y = -21 - 2x

3y = - 2x -21

divide both sides by 3

y = -\(\frac{2}{3}\)x - 7

a. The teacher can expect the batteries to last at least 92.09 days  on minimum average.

b. The teacher will need to spend at most $49.92 on batteries for calculators over the year.

What is minimum average day?

a. The margin of error of ‡9% means that we can be 95% confident that the true average number of days the batteries will last is within 9% of the sample average. To find the minimum average number of days a teacher can expect to have the batteries last in her classroom, we subtract the margin of error from the sample average:

Minimum average = 101 - (0.09)(101) = 92.09 days (rounded to two decimal places)

Therefore, the teacher can expect the batteries to last at least 92.09 days on average.

What is spend ?

b. The total number of batteries required for the 24 TI-84 calculators is:

24 calculators x 4 batteries per calculator = 96 batteries

The total cost of the batteries will be:

96 batteries x $0.52 per battery = $49.92 (rounded to two decimal places)

Therefore, the teacher will need to spend at most $49.92 on batteries for calculators over the year, assuming all batteries need to be replaced.

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Answer:

11 buses

Step-by-step explanation:

Answer:

6^4 * 6^3

Step-by-step explanation:

The simplified expression as a single logarithm is:

log\([(x+4)^3(x-7)^2 / (x-2)^5] + log(x^2)\)

Let's start by using the power rule of logarithms, which states that \(log(base b)(x^a) = a \times log(base b)(x).\)

Using this rule, we can rewrite the expression as follows:

3log(x+4) + 2log(x-7) - 5log(x-2) + log(\(x^2\))

= log\((x+4)^3 + log(x-7)^2 - log(x-2)^5 + log(x^2)\)

Next, let's apply the product rule of logarithms, which states that log(base b)(xy) = log(base b)(x) + log(base b)(y).

Using this rule, we can combine the logarithms:

= log\([(x+4)^3(x-7)^2] - log[(x-2)^5] + log(x^2)\)

Finally, we can apply the quotient rule of logarithms, which states that log(base b)(x/y) = log(base b)(x) - log(base b)(y).

Applying the quotient rule, we can simplify further:

= log\([(x+4)^3(x-7)^2 / (x-2)^5] + log(x^2)\)

Thus, the simplified expression as a single logarithm is:

log\([(x+4)^3(x-7)^2 / (x-2)^5] + log(x^2)\)

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The domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

A function is composite when the co- domain of the first mapping is the domain of the second mapping

Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:

a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13

(f + g)(-2) = 4 + 8 - 2 + 13

(f + g)(-2) = 23

b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13

(f - g)(-2) = 4 + 8 + 2 - 13

(f - g) (-2) = 1

c). f(x) - g(x) = x² - 4x - x - 13

f(x) - g(x) = x² - 5x - 13

Therefore, the domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

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Answer:

Step-by-step explanation:

A grandma wants to divide her 11 dollars in her 8 grandsons, How much will take everyone?

11/8 =1.375

So every grandson has 1 dollar and 37 pennies

The value of a in the equation 60°a = [? ]° is dependent on the value of [? ].

To solve for a in the equation 60°a = [? ]°, we need to isolate a on one side of the equation. We can do this by dividing both sides of the equation by 60°:

60°a / 60° = [? ]° / 60°

This simplifies to:

a = [? ]° / 60°

Since we don't have the value of [? ]°, we cannot determine the exact value of a. However, we can simplify the expression by canceling out the ° units:

a = [? ] / 60

Therefore, the value of a is dependent on the value of [? ].

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Answer:

3/4(n)+1

3/4(8)+1=

6+1=7

3/4(12)+1=

9+1=10

3/4(14)+1=

10.5+1=11.5

3/4(20)+1=

15+1=16

I hope this helps:

Answer:

x = log(3) (8)

or log 8 base 3

Step-by-step explanation:

some number^x = another number

some number = base (the lower case number)

another number = the big number next to it.

put log infront in these situations.

Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

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Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

Define measurement?

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Answer:

9.42

Step-by-step explanation: