Use the rate and the amount of water pumped after 13 minutes to find how much will have been pumped into pool after 14.5 minutes? The unit rate is 24 gal/min so 1.5 minutes after 13 minutes, an additional gallons will be pumped in

For the linear function y = 2/3x + 1 given in this problem, we have that:

a) The slope is of 2/3 and the intercept is of 1.

b) The y-intercept is marked at y = 1 on the y-axis.

c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.

d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

In slope-intercept format, a linear function is defined as follows:

y = mx + b.

For this problem, the function is:

y = 2/3x + b.

Hence:

From the intercept, we know that point (0,1), which has x = 0 and y = 1, is part of the graph of the function.

Considering the concept of the slope, of change in y divided by change in x, we have that:

Hence point (3,3) also belongs to the graph of the given function. Given two points, we can graph a line passing through them, hence the graph is given at the end of the answer, and represents the function y = 2/3x + 1.

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Since 40 x (951-686) can be rewritten as 5x (951-686), the value of 40 x (951-686) is 8 times as value of 5 x (951-685).

A multiplicative comparison compares two expressions so that they are produced when one is multiplied by a certain number.

You must be able to distinguish between the given expressions in order to do that.

So the expression 40 x (951-686) can be rewritten as 5 x (951-686), the value of 40 x (951-686) is 8 times of the expression 5 x (951-685) as we can notice here.

Without engaging in a complicated multiplication process we have to comprehend the two expressions to find the difference between the respective products.

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The area of triangle ABC is 17.5 or 35/2

To solve this, we need to know the base and height of the triangle.

In this case, the base is the side AB, and the height is the side BC

Now we can count the units to get the lenght of the sides:

AB is 7 units long

BC is 5 units long.

Now we can use the formula for the area of a triangle:

Where A is the area, b is the base and h is the height.

Putting the values of b and h:

Then the area is 35/2 or 17.5 square units

The simplified equation is sin(2x) = 2

The trigonometry ratio is given as

2sinxcosx/sin^2x+cos^2x-1= 1

Rewrite the equation of the trigonometry formula properly

So, we have the following equation

2sin(x)cos(x)/sin^2(x)+cos^2(x) -1 = 1

Add 1 to both sides of the equation

So, we have the following equation

2sin(x)cos(x)/sin^2(x)+cos^2(x) = 2

Express 2sin(x)cos(x) as sin(2x)

So, we have the following equation

sin(2x)/sin^2(x)+cos^2(x) = 2

Express sin^2(x)+cos^2(x) as 1

So, we have the following equation

sin(2x)/1 = 2

Multiply both sides by 2

So, we have the following equation

sin(2x) = 2

Hence, the simplified equation of the trigonometry formula is sin(2x) = 2

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Answer:

Hi

Step-by-step explanation: how are you doing

20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.

A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.

First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).

We know that there are 30 total pints of the mixture. Thus:

x+y=30

We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.

For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:

.65x+.90y=30 ×0.7

Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:

65x+90y=2100

Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:

65x+65y=1950

Subtract the second equation from the first equation:

25y=250

y=10

Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).

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Answer:

3/5

Step-by-step explanation:

You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.

Answer:

3/5

Step-by-step explanation:

You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.

We solve as follows:

The solution is 36.

Answer:

24

Step-by-step explanation:

Answer:

$2070

Step-by-step explanation:

→ Find the total cost of 12 months

750 + ( 12 × 110 ) = 2070

what is volume answer the volume is your topic for to day

Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

Step-by-step explanation:

Each value of x corresponds to only one value of y, making the relation a function.

Answer:

Step-by-step explanation:

You want a system of inequalities that will define the area within the triangle with vertices (-2, 1), (1, 7), and (4, -2), including only the left side.

An equation through points (x1, y1) and (x2, y2) can be written as ...

  (y2 -y1)x -(x2 -x1)y = x1·y2 -x2·y1

Removing any common factor from the coefficients, and making sure the leading coefficient is positive will put this in standard form.

For points (-2, 1) and (1, 7), the equation of the line can be ...

  (7 -1)x -(1 -(-2))y = (-2)(7) -(1)(1)

  6x -3y = -15 . . . simplify

  2x -y = -5 . . . . . divide by 3 (shading is right of the solid line)

For points (1, 7) and (4, -2), the equation of the line can be ...

  (-2 -7)x -(4 -1)y = (1)(-2) -(7)(4)

  -9x -3y = -30 . . . simplify

  3x +y = 10 . . . . . . divide by -3 (shading is left of the dashed line)

For points (4, -2) and (-2, 1), the equation of the line can be ...

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

  3x +6y = 0 . . . simplify

  x +2y = 0 . . . . divide by 3 (shading is right of the dashed line)

In each of the above equations, the x-coefficient is positive. This means the equal sign can be replaced with > when shading is right of the line, and with < when shading is left of the line.

There will be an "or equal to" symbol when the line is solid.

This means our inequalities are ...

Answer: 1yd 2ft

Explanation

s we have a subtraction, we have to have the same units. Thus, in order to do so we have to consider that 1 yd = 3ft:

Then, converting 2yf to ft:

Now, we can make the subtraction:

Finally, we can convert 3 ft to one yd:

and we have 2 ft left.

Given:

1 = 1²

1 + 3 = 2²

1 + 3 + 5 = 3²

1 + 3 + 5 + 7 = 4²

1 + 3 + 5 + 7 + 9 = 5²

1 + 3 + 5 + 7 + 9 + 11 = ___

Let's find the answer and determine the pattern.

Here, we have:

1 + 3 = 4

Now, write the sum as a perfect square:

4 = 2²

For the third equation:

1 + 3 + 5 = 9

Now, write the sum as a perfect square:

9 = 3²

This means the result will be the sum written as a perfect square.

Thus, we have:

1 + 3 + 5 + 7 + 9 + 11 = 36

Now, let's write the sum (36) as a perfect square:

36 = 6²

Therefore, we have:

1 + 3 + 5 + 7 + 9 + 11 = 6²

• ANSWER:

6²

Answer:

Solve the inequality & graph the answer. 3)>2 14 A) v> 280: 10 B) v<--: 7 C) v> -34: D) v<-34: 11110 276 278 280 282 284 286 7 O 0 2 ++++++ +0 -40 -38 -36 -34 -32 -30 -40 -38 -36 -34 -32-30

Step-by-step explanation:

Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.

Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.

Proportions, like ratios, use fractional values because they show the quantity of one variable in another.

We state proportions in fractions, decimals, or percentages.

The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli

3/4 pound = 0.75 pound

9/8 cups = 1.125 cups

The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)

1.5 cups = 1½ cups

Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.

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We need to expand the term:

This seems like a colossal task, we would need to multiply (5x-2) 6 times. However, we can use a useful tool that is called the 'Pascal's triangle'

I'll paste an image of it above

We will use it in this way:

Each one of the rows, represent the n in the term:

So, if we have the expression (x+y) we will pay attention to the upper row, if we have (x+y)^2 we will need the second row, and so on.

In our case, we need the 6th row.

Now, usually a term of the form

As we say, look at the 6th row of the triangle, the numbers a, b, c,..., and g are given there!

And we need the term that corresponds to x^2, we need the number e=5!

So, after the expansion, the coefficient of the term x^2 will be equal to 5

Answer:

Step-by-step explanation:

4 x - 5 y + z = 9z = - 27 + 6 x + 8 y3 x

The ratio of blue paint to the total paint in the mixture is 5:8.

Given:

In the figure, there are 10 blocks of blue paint and 6 blocks of red paint.

Total paint in the mixture = 10+6 = 16

Ratio of blue paint to total paint = 10/16 = 5/8

Therefore, the required ratio is 5:8.

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We can see that the value of k is -3, then the line is:

y = -3*x + 4

By finding two points of the line, we can graph the line like in the image you can see below.

Here we have the following linear equation:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above equation so we get the value of k.

-2 = k*2 + 4

Solving this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

So the value of k, the slope of the line, is k = -3.

Then the line is:

y = -3*x + 4

If we evaluate in x = 1, we get:

y = -3*1 + 4 = 1

So, at this point we know that the line passes through points (1, 1) and (2, -2).

Now we can draw these two points on a coordinate axis, and then connect them with a line. That will be the graph of the linear equation.

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Answer:

-1/5 is the slope

Step-by-step explanation:

the equation

y2-y1 over x2-x1

This is an improper fraction since the absolute value of the numerator (1677) is greater than the absolute value of the denominator (203). We can say that this fraction cannot be reduced.

Answer:

1/216

Step-by-step explanation:

[tex] \frac{1}{6} \div 6 \div 6[/tex]

[tex] \frac{1}{6} \div \frac{6}{1} \div \frac{6}{1} [/tex]

[tex] \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} [/tex]

[tex] \frac{1}{216} [/tex]

We have a quadrilateral inscribed in a circle.

The quadrilateral is a trapezoid.

When we have a quadrilateral inscribed in a circle, opposite angles are supplementary.

Then, we can write:

Answer: x = 21.1

Answer:

see explanation

Step-by-step explanation:

(a)

the angles shown are alternate interior angles and are congruent

(c)

since they are congruent , then

27x - 5 = 130 ( add 5 to both sides )

27x = 135 ( divide both sides by 27 )

x = 5

(d)

then

27x - 5 = 27(5) - 5 = 135 - 5 = 130

The linear function passing through the point (2,-9) that is perpendicular to the line y=x+6 is:

y = -x -7.

A linear function is modeled according to the following rule:

y = mx + b.

The coefficients of the linear function are as follows:

When two lines are perpendicular, the multiplication of their slopes is of -1.

For this problem, the line is perpendicular to line y = x + 6, which has slope 1, hence:

m = -1.

Then:

y = -x + b.

When x = 2, y = -9, hence we use this to find the intercept b as follows:

-9 = -2 + b

b = -7.

Hence the rule is:

y = -x -7.

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Answer:

Step-by-step explanation:

The linear equation is 3x+4y=7. The solution to the equation 3x+4y=7 is unique.

Given that,

The linear equation is 3x+4y=7

Any equation with a maximum degree of 1 is said to be linear. No variable in a linear equation, thus, has an exponent greater than 1.The graph of a linear equation is always a straight line.

There are numerous options if x and y are not positive integers (natural numbers), thus it is best if they are.

The x and y are positive integers so it is a unique solution.

Therefore, The solution to the equation 3x+4y=7 is unique.

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An expression for the amount of money (in nickels) in n dollars is 20n nickels.

A nickel is a five-cent coin produced by the United States Mint that is made of a copper-nickel alloy rather than silver. Because 100 cents equal one dollar and one nickel equals five cents, we conclude that 20 nickels are equivalent to one dollar.

To write an expression for the amount of money (in nickels) in n dollars,

Convert the n dollars to nickels.

1 dollar = 20 nickels

So, n dollars = 20n nickels

The required expression for the amount of money (in nickels) in n dollars is 20n nickels.

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Answer: 9 - 5x

Step-by-step explanation:

6 + (3 - 5x) = 6 + 3 - 5x = 9 - 5x