On a hot day, a football team drank an entire 50-gallon cooler of water and half as much again. How much water did they drink?


Jada has 12 library books checked out and Han has one third less than that. How many books does Han have checked out?

The segment XY is a tangent to circle Z.

What is tangent to a circle?

Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle.

To check the segment YX is tangent to circle z, first we have to check that the triangle formed XYZ is right angle triangle or not.

If the triangle XYZ is a right triangle, then we have

XY² +XZ² = YZ²

3.6² +2.7² = (1.8 +2.7)²

 12.96 +7.29 = 20.25            it's true.

Therefore, the segment XY is a tangent to circle Z.

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The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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Answer:

Perimeter o the rectangle = 16x - 2

Step-by-step explanation:

Perimeter of a rectangle = 2(long+ wide)

Then:

Perimeter = 2((6x-4)+(2x+3))

Perimeter = 2(6x+ 2x + 3 - 4)

Perimeter = 2(8x - 1)

Perimeter = 2*8x + 2*-1

Perimeter = 16x - 2

Answer:

6 represents the number of people among which the balls and jacks will be split.

4 represents the number of balls.

10 represents the number of jacks.

Step-by-step explanation:

This is the PLATO answer, hope it helps :)

Answer:

6

Step-by-step explanation:

The quantity of cells that will be in the culture on the 8 day assuming the number of cells is growing at an exponential rate would be = 128,000 cells.

An exponential rate of growth is defined as the increase in the population of an object under study over a period of time.

The number of cells the scientist started with = 1,000 cells

The number of cells in 4th day = 64,000

Therefore the rate of growth of cells per day;

= 64000/4

= 16,000

Therefore on the 8th day, the number of cells would be = 8×16000 = 128,000 cells.

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The series appears to be     166, 199, 232, 265, 298, 331

With examples, define sequence?

A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.

                                      In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.

The last number of the common difference must end in 3

And this must be a 2 digit number

So....the first number must end in 6

The the 4th number must be 265

So..... the 5th number  must end in 8

And the last digit  of the last term must end in  1  [ and begin with 3 ]

Putting all this together  we have that

265  + 2d  =  331

2d  = 66   ⇒  d = 33

So  the first term must be  265 - 3 (66)  =  166

the series appears to be     166, 199, 232, 265, 298, 331

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Answer:

its A

Step-by-step explanation:

took the quiz

Answer:

f(x) has a greater slope.

Step-by-step explanation:

The slope of the image line

= difference in y coordinates / difference in x coordinates

= (7-3) / (3-2)

= 4.

The  slope of f(x) = 6x + 1 is  6.

The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

What is mean by straight line?

A straight line is a combination of endless points joined on both sides of the point.

Given that;

The function, f(x) = 6x + 1

And the function g(x) is a linear function which passes through the points (2 , 3) and (3, 7).

Since, The slope 'm' of any straight line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

And, m = d/dx (f(x))

So, The slope of function f (x) will be;

f(x) = 6x + 1

M = d/dx (f(x))

M = d/dx (6x + 1)

M = 6

And, Slope of linear function which passes through the points (2 , 3) and (3, 7) is;

m = (7 - 3) / (3 - 2)

m = 4/1

m = 4

Thus, The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

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a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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Probability of choosing a math book is 3/5

Probability of choosing an English book is 2/5

Probability of choosing either a math or an English book is 1.

To find the probabilities, we need to determine the total number of possible outcomes and the number of favorable outcomes for each scenario.

Probability of choosing a math book:

Out of the total collection of 6 math books and 4 English books, the number of math books is 6. The total number of books in the collection is 10. Therefore, the probability of choosing a math book is given by:

Probability of choosing a math book = Number of math books / Total number of books

= 6 / 10

= 3/5

Probability of choosing an English book:

Out of the total collection of 6 math books and 4 English books, the number of English books is 4. The total number of books in the collection is still 10. Therefore, the probability of choosing an English book is given by:

Probability of choosing an English book = Number of English books / Total number of books

= 4 / 10

= 2/5

Probability of choosing either a math or an English book:

To find this probability, we add the probabilities of choosing a math book and choosing an English book since these two events are mutually exclusive (a book cannot be both a math book and an English book). Therefore:

Probability of choosing either a math or an English book = Probability of choosing a math book + Probability of choosing an English book

= 3/5 + 2/5

= 5/5

= 1

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Answer:

A is spanned by vector.

Step-by-step explanation:

The null space of matrix is set of all solutions to matrix. The linearly independent vectors forms subset which are spanned and forms the null space. The null space of vector can be found by reducing its echelon. The non zero rows formed are the null spaces of matrix.

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

The height = 18 inches

Step-by-step explanation:

The volume = area of the base × height

Area of the base = 40.5 inches²

The volume = 729 inches³

729 = 40.5 × height

Height = 729 ÷ 40.5 = 18 inches

the answer is 6the answer is 600 words

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

$192

Step-by-step explanation:

Bill: $160.00

Tip: 20%

To figure out 10%, you need to move the decimal point over to the left one place: $16.00

10%: $16.00

16 times 2= $32.00

160.00+32.00= $192.00

Answer:

7 9/10

Step-by-step explanation:

First, we need to add 4 2/3 and 5 2/5.

We should begin with converting the fractions into improper fractions.

4 2/3 + 5 2/5= 14/3 + 27/5

Now, we find the common denominator

= 70/15 + 71/15

We can add:

= 141/15

And simplify. 

= 9 2/5

Finally, we subtract 1 1/2 from 9 2/5

Your answer is 7 9/10. Hope this helps!

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Answer:

The answer is 7 9/10

Step-by-step explanation:

it is 7 9/10 because you do 4 2/3 plus 5 2/5 minus 1 1/2 which equals 7 9/10

Answer

A(-10, 9), A'(-4, 9)

B(-4, 2), B'(-10, 2)

C(-7, 9), C'(-7, -4)

Example 3:

A(-3, 5), A'(3, 5)

B(-3, 0), B'(3, 0)

C(-3, 5), C'(-3, -10)

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Let the no. of students be x

total cost = y

Then the first equation will be

8x + 20 = y

And the second equation will be

3x + 40 = y

A system of two equations where each equation models the total cost y to take x students on each field trip is;

8x + 20 = y

3x + 40 = y

The total cost y is 48 to take x = 4 students on each field trip.

In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables.

A science teacher is planning a field trip to either the aquarium or the science center.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

The science center charges $3 per student and has a class lab fee of $40.

Let the total cost y to take x students on each field trip.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

8x + 20 = y

The science center charges $3 per student and has a class lab fee of $40.

3x + 40 = y

On solving both the equation

Substitute the value of y in the equation 2

3x + 40 = y

3x + 40 = 8x+20

8x - 3x = 40-20

5x = 20

x = 20/5

x = 4

Substitute the value of x in the equation 1

3x + 40 = y

2(4) + 40 =y

8 + 40 = y

y = 48

Hence, the total cost y is 48 to take x = 4 students on each field trip.

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bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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You can't turn this into an equation because there is nothing that states something is equal to each other. You can turn it into an expression though.

(60÷6​) + b

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Answer:140.1

Step-by-step explanation:

Answer:

140.1

Step-by-step explanation:

Answer:

x = 2     y = -12

Step-by-step explanation:

x+ y = -10

2 + y = -10

      y = -10 -2 = -12

A registered investment account, or RRSP, enables you to put money aside for retirement while delaying taxes on investment gains.

An annuity is a financial product that provides regular payments over a specified period of time in exchange for a lump sum of money. It's often used as a retirement income source and comes in different types such as fixed, variable, immediate, and deferred annuities. It's important to understand the terms, fees, and charges before purchasing an annuity.

Registered Retirement Savings Plan is the full form of RRSP.

In Canada, both workers and independent contractors can save and invest during their retirement through Registered Retirement Savings Plans (RRSP).

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Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.