13. The number of pictures your printer
can print are shown in the table. Find
the rate in pictures per minute.
Minutes 2 4 6
8
Pictures 16 32 48 64
15.
16

The unit price of one gallon of paint is going to be $35.96.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that 1/4 gallon of paint costs $8.99 so for 1 gallon we will have to multiply both the paint amount and the money which buys it to 4 which will conclude that 1 gallon costs $8.99 × 4 is equal to $35.96. So, 1 gallon of paint will cost $35.96.

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The value of a variable from one equation is substituted in the other equation when using the substitution method.

The graphic approach and the algebraic method are the two main categories into which simultaneous linear equations can be solved. One of the categories of the algebraic approach is the substitution method. The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Steps for Substitution method:

Therefore in the Substitution method, The value of a variable from one equation is substituted in the other equation.

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Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.

What is a function ?

Function can be defined as a relation , which relates an input to output is called as function.

In Mathematics, an extraneous solution (or spurious solution) is an solution, consisting of that to an equation, that emerges from the procedure of solving the hassle but isn't always a legitimate strategy to the problem.[1] A missing solution is an answer that is a valid strategy to the hassle,

however disappeared all through the process of solving the problem. each are frequently the consequence of acting operations that are not invertible for a few or all values of the variables, which prevents the chain of logical implications inside the proof from being bidirectional.

Hence , The Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.

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Answer:

I'm not sure what equation is needed here. Could you share the table?

Either way, you can take the number of students there are and multiply that to the number of chaperones needed per group of 12- basically see how many groups of 12 you can fit in the overall group of students

The graph of the function f(x) = 2x² + 2x - 2 is plotted and attached

The graphs of the function is plotted by making a table of value for a number of the x values and the corresponding y values as done below

Using the function the table is created as f(x) = 2x² + 2x - 2

For x = -4, y =  2 * (-4)² + 2 * (-4) - 2 =  22

For x = -2, y =  2 * (--2)² + 2 * (-2) - 2 =  4

For x = 0, y =  2 * (0)² + 2 * (0) - 2 =  -2

For x = 2, y =  2 * (2)² + 2 * (2) - 2 =  10

For x = 4, y =  2 * (4)² + 2 * (4) - 2 =  38

The table of values

x     y

-4   22

-2   4

0    -2

2     10

4    38

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The polynomial 4 2x3 is a degree 3 polynomial, also known as a cubic polynomial.

Polynomial is an expression consisting of variables, constants, and coefficients. It is an algebraic expression that can contain exponents, fractions, multiplication, addition, and subtraction. Polynomials are used to model many real-world situations, such as the volume of a cylinder or the area of a triangle. The degree of the polynomial is determined by the highest exponent of the variables in the expression. Polynomials can be divided, factored, and manipulated using the rules of algebra.

It consists of three terms and its general form is

ax³ m + bx² + cx + d, where a, b, c, and d are constants

and x is the variable. In this case,

a = 4, b = 2, c = 0 and d = 0,

so the polynomial is 4x³ + 2x².

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Answer:

Step-by-step explanation:

the first equation we konw x=-2y-1,

then -2y-1=y+5

so, y = -2, x=3

Answer:

y = -2

x = 3

Step-by-step explanation:

y + 5 + 2y = -1 (substitute)

3y + 5 = -1        (Simplify)

3y = -6            (Get rid of 5)

y = -2                 (Divide)

x = -2 + 5         (plug in y)

x = 3                 (simplify)

hope this helps :)

Answer: Hypotenuse

Step-by-step explanation:

The Hypotenuse is known as the longest side of a triangle.

The value of YZ = 2 units.

The Latin words "col" and "linear" are combined to form the word "colinear." "Col" stands for "together," and "Linear" is a line. Collinear points are hence points that are situated along a single line. Numerous instances of collinearity can be observed in daily life, such as a line of pupils standing together.

Given X, Y, and Z are collinear. Y is between X and Z.

so XY + YZ = XZ

given XY = 12 units and XZ = 14 units

XY + YZ = XZ

12 + YZ = 14

YZ = 14 - 12

YZ = 2 units

Hence measure of YZ is 2 units.

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The sum of all the positive two-digit integers where one of the digits is three times the other is 630.

To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.

For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.

For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.

The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.

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The transformation of the function is given by reflection along y axis and a translation of 5 units up

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the transformation be represented as A

Now , the equation will be

Let the triangle be represented as ΔODG

Now , the coordinates of ΔODG is

O = O ( -1 , -2 )

D = D ( -5 , -3 )

G = G ( -2 , -4 )

Now , the transformed triangle is ΔACT

The coordinates of ΔACT is

A = A ( 1 , 3 )

C = C ( 5 , 2 )

T = T ( 2 , 1 )

Now , on reflecting the triangle ΔODG along y axis , we get

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse

So , the coordinates of triangle O'D'G' , we get

O' = O' ( 1 , -2 )

D' = D' ( 5 , -3 )

G = G' ( 2 , -4 )

Now , translating the triangle ΔO'D'G' up by 5 units , we get

The y coordinate of the triangle gets incremented by 5

So ,

A = O' ( 1 , -2 + 5 )

C = C ( 5 , -3 + 5 )

T = T ( 2 , -4 + 5 )

And , the coordinates of the triangle ΔACT is

A = A ( 1 , 3 )

C = C ( 5 , 2 )

T = T ( 2 , 1 )

Hence , the transformation is reflection along y axis and followed by translation of 5 units up

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The length of the arc of the sectored watered is 27.9 feets

length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference

The length of an arc is given by :

L = theta/360 × 2πr

where tetha is the angle substends

r is the radius

Here the radius is the length at which water is sprayed = 20 ft

tetha = 80°

therefore l = 80/360 × 2×3.14 × 20

L = 29feets

Therefore the length of the arc formed by the water is 27.9 feets

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On solving the provided question we can say that  by linear equation number of, Red Balls = 6x 18; Blue Balls = 3;  Yellow Balls = 6

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

A bag contains 27 balls

• The ratio of red to blue to yellow balls is 6:1:2

To Find : The number of red,blue and yellow balls present in the bag

Let us take the variable as 'x' to represent the number of balls in the bag

When we Put the values in a equation,

6X+X+2x = 27

9x = 27

x = 3

Hence the number of,

Red Balls = 6x 18

Blue Balls = 3

Yellow Balls = 6

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The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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A linear, negative relationship is the type of relationship which is shown in graph of Time vs. Position of Battery Operated Car .

A linear equation is an algebraic expression such as y=mx+b. The slope is m, and the y-intercept is B. A "linear equation in two variables" is the term used to describe the previous sentence, which has variables named y and x. Two different variables can be found in bivariate linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

The area's 46-16 opposed to 14 is different from the area's 18 and T in a different way. The place is there. It isn't linearly getting farther apart. The lee is actually growing as a result.

Option B, the slanting upwards, is what we're going to go with. Since it will be linear, it isn't option C. It is untrue that the speaking has not been constant over the distance. Because it is a D-option, this increase-decrease is untrue. Option B is the best choice. Absolutely.

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Answer:

1 bucket

Step-by-step explanation:

3/4 buckets = 3/4 hours

multiply both sides by 4/3 to get one hour

(4/3) * (3/4) buckets = (4/3) * (3/4) hours

1 bucket = 1 hour

Answer:

One way to use positive feelings from a situation towards future motivation is to focus on the positive aspects of the experience and try to replicate them in the future. For example, if you had a particularly enjoyable and successful project at work, you might try to identify the specific factors that contributed to your success and seek out similar opportunities in the future. This approach can help you to build on your strengths and experiences and maintain a positive and motivated outlook. Additionally, setting specific goals for yourself and tracking your progress can help to keep you motivated and on track towards future success.

The required inequality to represent the above data regarding Valentina is x > 3.

Valentina uses more than 36 ounces of dough 12 cinnamon rolls made by Valentina of weight ounces of dough represented by x ,then required inequality is given by 12x > 36.

Number of cinnamon rolls made by Valentina = 12

Weight of all 12 cinnamon rolls are equal

x represents the ounces of dough used by Valentina to make cinnamon roll.

Ounces of dough used by Valentina is more than 36.

Required inequality to represent the above data is given by:

12x > 36

Divide by 12 form both the sides we get,

12x /12 > 36/12

x > 3

The inequality is x > 3.

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Complete question

Valentina is baking jumbo cinnamon rolls for a family breakfast. She uses all the dough she made to form 12 cinnamon rolls of equal weight. The recipe usually makes 36 ounces of dough, but Valentina made more dough than that so she can have larger cinnamon rolls. Let x represent how many ounces of dough Valentina uses for each cinnamon roll. Which inequality describes the problem?

Given line in point-slope form:

Point-slope form is:

We know that to graph a line it is enough two have two points.

One of the points is (x₁, y₁) = (1, - 3).

Find one more point, when x = 3:

The point is (3, 1).

Plot and connect these two points to get the line.

The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

What is an equation?

An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:

expression_1 = expression_2

The given equation is √2x – 1- x = −8.

[tex]2x=x^2-14x+49[/tex]

[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]

Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

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Answer:

1:11

Step-by-step explanation:

We know

There are 25 tables that seat 4 people

First, we find the total number of tables by taking

25 + 30 = 55 tables

Then we find the ratio of tables that seat 4 people to the total number of tables by

5 / 55 = 1/11 = 1:11

So, the ratio is 1:11

By unitary method 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Students traverse a total area of 40 yards by 40 yards, or 1600 yards.

24 kids covered an area of 8 ft x 8 ft, or (8 ft x 1 yd/3 ft)2 = [(8/3) yard]2 = (64/9) yd.

The number of students present is calculated by multiplying the number of students per yard, or 24 students/(64/9) yd2, by the area that students cover.

Therefore: 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

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On solving the provided question, we got to know that he fraction  can bake 200/57 loaves or 3 29/57 loafs.

Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or

1 by 8

13 1/3 divided by 3 4/5

Let's first convert these mixed numbers to incorrect fractions.

13  1/3 =  13(3) + 1 = 39 + 1 = 40/3

3 4/5 = 3(5) + 4= 19/5

Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.

40/3 x 5/19 = 200/57

he can bake 200/57 loaves or 3 29/57 loafs.

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Answer:

625

Step-by-step explanation:

1.25.625

125 = 5³

625 = 5⁴

prime factor 5 , number 125 is 3 number 625 is 4 LCM is 4

LCM = 5⁴

so the LCM is 625

There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the  the value of c such that P(X ≥ c) = 0.20 is 279.44

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,

Given that Mean (μ) = 266

and Standard deviation(σ) = 16

The z-score is the value decreased by the mean divided by the standard deviation:

z = (x−μ)/σ = (240−266)/16

≈−1.63

Determine the corresponding probability using the normal probability table in the appendix:

P (X ≥ 240)

= 1 - P (X < 240)

= 1 - P(Z < -1.63)

= 1 - 0.0516

=0.9484

(a) There is a chance of about 94.84% that the pregnancy last at least 240 days

(b) P (X ≥ 240) = 0.9484

(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.

The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04

thus, the z-value is z=0.84.

x = μ+zσ = 266+0.84*(16 )

=279.44

The  the value of c such that P(X ≥ c) = 0.20 is 279.44

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There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the  the value of c such that P(X ≥ c) = 0.20 is 279.44

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,

Given that Mean (μ) = 266

and Standard deviation(σ) = 16

The z-score is the value decreased by the mean divided by the standard deviation:

z = (x−μ)/σ = (240−266)/16

≈−1.63

Determine the corresponding probability using the normal probability table in the appendix:

P (X ≥ 240)

= 1 - P (X < 240)

= 1 - P(Z < -1.63)

= 1 - 0.0516

=0.9484

(a) There is a chance of about 94.84% that the pregnancy last at least 240 days

(b) P (X ≥ 240) = 0.9484

(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.

The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04

thus, the z-value is z=0.84.

x = μ+zσ = 266+0.84*(16 )

=279.44

The  the value of c such that P(X ≥ c) = 0.20 is 279.44

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Step-by-step explanation:

6(8x+5)

Use the distributive property to multiply 6 by 8x+5.

48x+30

Hope it Helps!

Answer:

If Samuel drives a compact car, he would need to buy 243.75 gallons of gas per year. If he drives a pickup truck, he would need to buy 250.25 gallons of gas per year. So he would need to buy 6.5 more gallons of gas per year if he drives a pickup truck compared to a compact car.

Step-by-step explanation: