Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (x, y) -- (-x, -y)
O (x, y) - (-y, -x)

The product of the ages 2 years from today is 924

Let the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;

xyz = 1716

If the product of their ages last year is 1320, then;

(x-1)(y-1)(z-1) = 1320

Two years ago, the product of their ages will be;

(x-2)(y-2)(z-2) = 1320- (1716-1320)

(x-2)(y-2)(z-2) = 1320-396

(x-2)(y-2)(z-2) =924

Hence the product of the ages 2 years from today is 924

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Answer:

11  units

Step-by-step explanation:

We first need to solve for x

3x -28 +3x -30 + x = 33  Combine the x's

7x - 28 -30 = 33  Combine -28 and -30

7x - 58 = 33  Add 58 to both sides

7x = 91  Divide both sides by 7

x = 13  Now plug 13 into the expression for DE

3x - 28

3(13) - 28

39 -28

11

Answer:

the answer to the question is 1

Answer:

-26 Is the correct answer

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Let x = # of boxes of felt-tip pens.

(x)(3.44)+(4x)(4.41) = 63.24

21.08x = 63.24

x = 3

Because x = 3, the man bought 3 boxes of felt-tip pens and 12 boxes of ballpoint pens.

The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of hamburger sold and y represent the number of cheeseburgers sold, hence:

x + y = 460    (1)

Also:

y = 3x       (2)

From both equations:

x = 115, y = 345

The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.

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The solution of the inequalities is (0.375, 4.25)

The system of inequalities is given as:

3y > 2x + 12

2x + y ≤ 5

Next, we plot the inequalities on a graph (see attachment)

From the graph, both inequalities intersect at

(x, y) = (0.375, 4.25)

This represents the solution of the inequalities

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Answer:

38

Step-by-step explanation:

I'll say that Sana's age is A, Rabia's age is B, and Saleem's age is C.

A + B + C = 47

Three years ago, everyone was three years younger, so we can write the expression as:

(A-3) + (B-3) + (C-3) = x

x is the total age three years ago.

The above equation is the same thing as:

A + B + C - 9 = x

Since we know that A + B + C is 47, we use that number instead.

47 - 9 = x

38 = x

So three years ago, their total age was 38 years old.

The ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)

The function is given as:

y = x^2 + 1

the ordered pairs are the x and y values of the function

So, we stet x = 0, 1, 2, 3 and 4

y = 0^2 + 1 = 1

y = 1^2 + 1 = 2

y = 2^2 + 1 = 5

y = 3^2 + 1 = 10

y = 4^2 + 1 = 17

Hence, the ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)

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Answer:I beleive the answer is c-3600

Step-by-step explanation:

90$ a month for 48 months=4320

Plus the interest rate of 8.33  so 4320x0.833=3598.56

Then you have to round up from 3598.56 to the nearest 100 dollars, so it would be 3600.

Answer:

16

Step-by-step explanation:

4 , 8 , 12 , 16 , 20 , ....................... ans goes on

It will take 21 days before there is another day on which he does both.

The lowest common multiple (LCM) of two or more numbers is the lowest possible number which is completely divisible by all the given numbers.

Given,

John goes for a jog every third day and every Saturday he goes to the gym.

That means he goes to the gym on every seventh day, and goes for a jog every third day.

Therefore, he goes for both on the days which are LCM of 3 and 7.

But, LCM of 3 and 7 is 21.

Hence, he goes for both in every 21 days.

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Answer: D.

Step-by-step explanation: First you find the common factor, which is 5x³y. Then you write in parenthesis what's left over from each term. So  the answer should look like: 5x³y(-3x⁵-4z+9).

We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.  

Let x = number of gallons of 3% milk

Thus;

336 - x = number of gallons of 7% milk

Therefore;

0.03x + 0.07(336 - x) = 0.06(336)

0.03x + 23.52 - 0.07x = 20.16

-0.04x = -3.36

x = 84 gallons

We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.  

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Answer: 5.83

Step-by-step explanation:

[tex]\sqrt{(2-5)^2 + (1-6)^2}=\sqrt{34} \approx 5.83[/tex]

Answer:

  $47.28

Step-by-step explanation:

The total cost is found by adding the costs of the components.

There is one daisy, at $0.85 each.

There are to carnations at $0.50 each, for a total of 2×$0.50 = $1.00.

The is 6 inches of ribbon. That amount is 1/2 foot, so its cost is ...

  (1/2 ft)×$0.24/ft) = $0.12.

The total cost of the components of one corsage is ...

  daisy cost + carnation cost + ribbon cost = $0.85 +1.00 +0.12 = $1.97

There are 24 corsages, so their total cost will be 24 times this amount, or ...

  24 × $1.97 = $47.28

The total cost of the 24 corsages is $47.28. All the costs of the components required for making a corsage are added to get the total cost of the corsage.

It is given that,

The components and their costs:

The cost of each daise = $0.85

The cost of each carnation = $0.50

The cost of the ribbon per foot = $0.24 (1 foot = 12 inches)

The components for making one single corsage:

One yellow daisy + two pink carnations + 6 inches of ribbon = 1 corsage

Then, calculating the price for one single corsage,

1 × $0.85 + 2 × $0.50 + (1/2) × $0.24 = cost of 1 corsage

⇒ $0.85 + $1 + $0.12

⇒ $1.97

For 24 corsages, the total cost = 24 × $1.97 = $47.28

Therefore, the total cost of the 24 corsages is $47.28.

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Answer: The smallest angle is 35°

Step-by-step explanation:

1 angle: 2x

smallest angle: x

third angle: 2x + 5

all angles in a triangle add up to 180 degrees. Therefore,

2x+x+2x+5 = 180

5x+5=180

5x+5(-5)=180(-5)

5x = 175

5x/5 = 175/5

x = 35

The smallest angle is 35°

By subtracting decimals, how much farther she ran on Saturday than on Sunday is determined as: 1.078 kilometers.

When subtracting decimals, the number value is taken into consideration.

Distance ran by Keisha on Saturday = 3.218 kilometers.

Distance ran by Keisha on Sunday = 2.41 kilometers.

Subtract both decimals to determine how much farther she run on Saturday than on Sunday.

3.218 - 2.14 = 1.078 kilometers.

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The standard numbers are obtained from the given numbers as follows;

The standard form of numbers is obtained by expressing the number completely and not using powers of 10

The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;

Number → Standard form

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The expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

From the question, we are to write an expression for each of the given statement

a. the sum of 6 and z

That is,

6 + z

b. the difference between 20 and x

That is,

20 - x

c. 8 less than the quotient of x divided by 6

That is,

x/6 - 8

d. x increased by 5 divided by 4

That is,

x + 5/4

Hence, the expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

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Answer:

71.4% ( i think)

Step-by-step explanation:

If we translate 1 in 1.4 using what is described, it turns into (1/1.4)

Putting this into a calculator, we get 0.714286. Translated into a percent, that becomes 71.4286%

The probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.

When the odds are given as "1 in 1.4," it means that there is 1 chance of success (having a law degree) for every 1.4 chances of failure (not having a law degree).

To find the probability that a member of the Senate (selected randomly) has a law degree, you can use the formula:

Probability = 1 / (1 + Odds)

In this case, the odds are 1 in 1.4, so the probability is:

Probability = 1 / (1 + 1.4) ≈ 1 / 2.4 ≈ 0.4167

So, the probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.

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Answer:

(+22x^2+16x+11)/(2x)

The equation of the perpendicular line is y = -2x + 4

The line equation is given as:

2x = 4y - 8

Make y the subject

4y = 2x +8

Divide by 4

y = 0.5x + 2

The slope of the above equation is

m = 0.5

The slopes of perpendicular lines are opposite reciprocals.

This means that, the slope of the perpendicular line is:

n = -1/m

This gives

n = -1/0.5

n = -2

The equation is then calculated as:

y = n(x - x1) + y1

This gives

y = -2(x - 1) + 2

Expand

y = -2x + 2 + 2

Evaluate

y = -2x + 4

Hence, the equation of the perpendicular line is y = -2x + 4

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The resale value of the car after four years is $4820

The given parameters are:

initial value, a = $27,000

Rate, r = 35%

The value of the car each year is represented as:

Value = a *(1 - r)^t

So, we have:

Value = 27000 *(1 - 35%)^t

After four years, we have:

Value = 27000 *(1 - 35%)^4

Evaluate

Value = 4820

Hence, the resale value of the car after four years is $4820

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A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.

-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.

Cardinalities of A and B

It is given that,

A = {n : -14 < n < -5, n ∈ Z}  ............ (1)

B = {h, i, s, x, z} ......... (2)

Thus, from (1),

A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)

Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,

n(A) = 8

n(B) =5

Reason Behind True or False

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Answer:

(4,-1) (4,0) (4,1)

Step-by-step explanation:

If you graph this, it will be a straight vertical line.  No matter what y is, x will always be 4.

The difference between the functions give:

(f - g)(1) = f(1) - g(1) = -3

For two functions f(x) and g(x), the difference is defined as:

(f - g)(x) = f(x) - g(x).

Then:

(f - g)(1) = f(1) - g(1)

By looking at the given tables, we know that:

f(1) = -2

g(1) = 1

Replacing that we get:

(f - g)(1) = f(1) - g(1) = -2 - 1 = -3

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Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

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If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.

Let's say that each person works at a rate R.

8 people can mow the lawn in 6 hours, then we can write:

(8*R)*6 hours = 1 lawn.

Solving for R:

R = (1/48 lawns per hour).

If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:

(5*R)*T = 1 lawn.

Replacing the value of R:

(5/48 lawns per hour)*T = 1 lawn.

Then we have:

T = (48/5) hours.

We can rewrite that as:

T = (45/5 + 3/5) hours

T = 9 + 3/5 hours.

Then we conclude that the correct option is B.

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Answer: x / 5 = 16

x = 80