12.2 Apples and Oranges
At the corner produce market, apples cost $1 each and oranges cost $2 each.
1. Find the cost of:
a. 6 apples and 3 oranges
b. 4 apples and 4 oranges
c. 5 apples and 4 oranges
8 apples and 2 oranges
Unit 3: Linear Relationships
Lesson 12: Solutions to Linear Equations
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The character Hannah is sent back in time to the Holocaust in Jane Yolen's book "The Devil's Arithmetic," where the Nazis tattoo a number on her arm.

The guy who tattooed Hannah's arm begs her not to forget the number because it serves as a powerful reminder of the significance of remembering and never forgetting the past and acts as a permanent reminder of the crimes done during the Holocaust. Hannah must remember the number since it is also a way of tracking and identifying people within the concentration camp.

Hannah is questioned about her name by the prisoner who is in charge of tattooing the ladies. That person is Chaya Abramowicz, she responds. She is wearing his daughter's outfit, he informs her. She had the same name, Chaya. He advises her to live for all the Chayas in the world and to never forget her prisoner number.

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The volume of the prism in this problem is given as follows:

C. 9/16 cubic feet.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

For this problem, two of the dimensions are formed by three cubes, hence their measures are:

3 x 1/4 = 3/4 foot.

The remaining dimensions is composed by four cubes, hence the measures are:

4 x 1/4 = 1 foot.

Hence the volume is given as follows:

V = 1 x 3/4 x 3/4

V = 9/16 cubic feet.

The problem is given by the image presented at the end of the answer.

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The possible equation of the sequence is f(x) = -2x + 5

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

Sequence type = arithmetic

Also, we have the following features

slope = negative

y-intercept = positive

A linear equation (or an arithmetic sequence) can be represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the given features, we can use the following assumed values

m = -2

c = 5

So, the sequence is

f(x) = -2x + 5

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They will be equal at the same altitude at x= 48 seconds

Assume the question is when the planes will be at the same altitude.

A is 2184+30.25x, where x is the number of seconds.

The aircraft B is 75.75x

They will be equal at the same altitude if

75.75x=2184+30.25x

Collecting like terms and making x the subject of the relation

75.75x -30.25x = 2184

45.5x = 2184

Making x the subject

x = 2184/45.5

x=48 seconds

The two airplanes  will be at the same altitude at 48 seconds

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Answer:

x = -1

Step-by-step explanation:
y-0.8x=0.5

5y-2.5-4x

Get y by itself.
y = 1.3

Put 1.3 into the second equation

5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1

I hope this was able to help you :D

The correct statement relative to the polynomial function is given as follows:

A. p(1)= 4

B. p(x)= (x^2 + 5x + 2) +4/x-1

The polynomial function for this problem is given as follows:

p(x) = x^3+4x^2-3x+2

Dividing the polynomial function by x - 1, the quotient and the remainder are given as follows:

Meaning that:

Hence the correct options are given by option A and option B.

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The surface area of the rectangular prism is  182m²

It is important to note that the surface area of a rectangular prism is expressed as;

Surface area = 2(wl + hw + hl)

Where;

Now, from the diagram show, we have the values as;

Length = 3

Height = 7

Width = 7

Substitute the values into the formula

Surface area = 2(7×3 + 7×3 + 7 ×7)

multiply the values

Surface area = 2(21 + 21 + 49)

expand the bracket

Surface = 182m²

Thus, the value is 182m²

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Answer:

So, the question is asking how many pounds are there in 48 shipments if ever 12 shipments are 3 pounds, so what you want to do is so how many times 12 will go into 48 and then multiply that by 3!

48/12 = 4

4 * 3 = 12

The total 48 shipments weigh 12 pounds!

Step-by-step explanation:

Hope it helps! =D

Answer:

The weight of one pack of sardines is 3 pounds / 12 packs = 0.25 pounds/pack

So the weight of 48 packs of sardines is 0.25 pounds/pack * 48 packs = 12 pounds.

A graph which shows the relationship given in the table is: B. graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 56 through the point 1 comma 54.

In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 56

In conclusion, we can reasonably infer and logically deduce that the y-intercept is equal to (0, 56).

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Answer:

YOUR WELCOME THE ANSWER IS

Step-by-step explanation:

B (-:{

Answer:

8

Step-by-step explanation:

42/7 =

6..

Since +6 more to 42 = 48 =

42+6=

48.

Just add 1 more month =

7+1=

8

Need more explanation I am happy to help :)

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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A  Linear Function best explains the relationship between the return and time.

What is the scatter plot?

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.

It is given that this scatter plot was created using daily stock market returns.

To determine which type of function fits the data of the graph best see the points of the graphs.

The scatter plot is not forming a parabola or curved graph so it can be a quadratic function.

The scattered in such a form that only a straight line can be the best fit for the scatter plot.

Therefore, a linear function is the best representation.

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You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.

Linear regression is a statistical method that is used to study the relationship between two continuous variables, often referred to as the independent variable (x) and the dependent variable (y). The goal of linear regression is to find the best-fitting line that describes the relationship between these two variables. The best-fitting line is known as the regression line, and it is represented by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept.

To find the linear regression equation, we need to use the least squares method to find the line of best fit that describes the relationship between the homework grade (x) and the test grade (y). The equation of the line is in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m) and y-intercept (b) we can use the following formulas:

m = (n(Σxy) - (Σx)(Σy)) / (n(Σx²) - (Σx)²)

b = (Σy - m(Σx)) / n

where n is the number of data points, Σx and Σy are the sum of x and y values, Σxy is the sum of the product of x and y values, and Σx² is the sum of the squares of x values.

Given the data points, we can use this information to calculate the slope and y-intercept, and write the linear regression equation.

Given the linear regression equation of the form y = mx + b

You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.

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The number of counters Rick has is equal to 12 counters.

The number of counters Tony has is equal to 1:1.5.

The value of p is 1.5.

In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let R represent the number of counters Rick has.

Let S represent the number of counters Selma has.

Let O represent the number of counters Tony has.

Let T represent total number of counters.

Translating the word problem into an algebraic equation, we have;

S = 2R     .....equation 1.

O = 2R - 6    ......equation 2.

T = R + S + O   ......equation 3.

Substituting equation 1 and equation 2 into equation 3, we have:

T = R + S + O

54 = R + 2R + 2R - 6

54 = 5R - 6

5R = 54 + 6

5R = 60

R = 60/5

R = 12 counters.

For Tony, the number of counters is given by:

O = 2R - 6

O = 2(12) - 6

O = 24 - 6

O = 18 counters.

In ratio form, we have:

O = 1:P

O = 1:(18/12)

O = 1:1.5

The number of counters Rick has is equal to 12 counters.

The number of counters Tony has is equal to 1:1.5.

The value of p is 1.5.

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Answer:

The answer in intercept form will be

[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]

Answer:

$16.8

Step-by-step explanation:

u got to trust me

Answer: $16.8

im sure its this it has to be

The number of ways to answer the questions is given as follows:

15,625.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, there are six questions, each with five possible options, hence the number of ways to answer the questions is calculated as follows:

5^6 = 15,625 ways.

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Substitution is a method for solving systems of equations that involves solving for one variable in one equation and then substituting that value into the other equation.

Here's how we can use substitution to solve the system of equations:

5x+y=9

10x−7y=−18

Solve one equation for one variable, for example:

y = 9 - 5x

Substitute this expression of y into the other equation:

10x - 7(9 - 5x) = -18

Solve the equation resulting from the substitution

10x - 63 + 35x = -18

45x = 45

x = 1

Substitute this value of x back into one of the original equations to find the value of y.

5(1) + y = 9

y = 4

So the solution is (x,y) = (1,4)

You can check this solution by substituting it back into both original equations.

Answer: 1.2 miles

You can find the answer by using the pythagorean theorem.

a^2 + b^2 = c^2.

(5000)^2 + (4000)^2 = c^2

25 million +16 million = c^2

41 million = c^2

Take the square root of both sides in order to get the value of C.

C = about 6,403 feet.

1 mile = 5280 feet

6403/5280 = 1.2

Buddy would walk about 1.2 miles

The value of distance after calculating are  AB = 4 ft and BC = 16 ft.

What is ratio?

A ratio is a comparison between two numbers or quantities. It is typically expressed as a fraction, with the first number being divided by the second number. Ratios are often used to compare values or to express a portion of a whole.

It is given in the question, that Ladd is rearranging his living room furniture. He wants his couch to sit along the 20-ft wall.

To find the length of AB and BC we need to relate them using the equations.

AB + BC = 20 ft (from the diagram) ----------- (Equation 1)

∵ AB : BC = 1 : 4

⇒ 4AB = BC

Substituting,  BC = 4AB into equation 1.

AB + 4AB = 20 ft

5AB = 20 ft

AB = 4 ft

Plugging AB = 4 ft into equation 1.

4 + BC = 20

BC = 20 ft - 4 ft

BC = 16 ft

Thus, the value of sides AB = 4 ft and BC = 16 ft , and here AB and BC are in ratio 1:4.

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a. The length of the arc is 6.28cm

b. The area of the sector is 25.12cm²

The arc of a circle is defined as the part or segment of the circumference of a circle. A sector is the space bounded by the arc and the radii of the circle. The smaller area is known as the minor sector and the bigger area is known as the major sector.

The length of an arc = tetha /360 ×2πr

= 45/360 × 2×3.14× 8

= 2×3.142 = 6.28cm

The area of a sector = tetha / 360 × πr²

= 45/360 × 3.14 × 8× 8

= 3.14× 8

= 25.12 cm²

Therefore, the length of the arc is 6.28cm and the area of the sector is 25.12cm²

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The value of x is 14.28 units, this is determined using the trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the sides and angles of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Consider the smaller triangle:

Sin (30) = Opposite side ÷ Hypotenuse

0.5 = Opposite side ÷ 10

Opposite side = 5

Consider the bigger triangle:

Sin (22) = Opposite side ÷ Hypotenuse

0.37 = 5 ÷ x

x = 5 / 0.35

x = 14.28

Hence, the value of x is 14.28 units, this is determined using the trigonometric identities.

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Answer:

¿Qué quieres comer?

Step-by-step explanation:

Terra is correct. In order for a relationship to be a function, each input value must result in only one input.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

We know that for a function each input value must result in a unique output value. Terra claims this statement, and hence she is correct.

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Answer:

see below

Step-by-step explanation:

7. (4-4). K =0

d+12-8/4+5 = d+12-2+5 =d+15

The value of x in the figure shown above is equal to 4.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

By critically observing the image of this geometric figure, we can reasonably infer and logically deduce that it is a type of quadrilateral with both pairs of opposite sides being parallel to each other and the opposite angles (vertical angles) are equal and congruent:

Side length A = Side length B

4 + 6 = 6 + x

10 = 6 + x

By collecting like terms, we have the following:

x = 10 - 6

x = 4 units.

In conclusion, the value of x is equal to 4 units.

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Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.

What is axis ?

An axis is a line about which a body rotates or a system oscillates. In mathematics and physics, an axis is often represented as a straight line that serves as a reference point for the measurement of coordinates.

The correct answers are :

(a) The distance from the point (3, 9, -7) to the xy-plane is the distance from the point to the z-axis, which is 7, since the xy-plane is at z = 0

(b) The distance from the point (3, 9, -7) to the yz-plane is the distance from the point to the x-axis, which is 3, since the yz-plane is at x = 0

(c) The distance from the point (3, 9, -7) to the xz-plane is the distance from the point to the y-axis, which is 9, since the xz-plane is at y = 0

(d) The distance from the point (3, 9, -7) to the x-axis is the distance from the point to the x-axis, which is 0, since the point is already on the x-axis

(e) The distance from the point (3, 9, -7) to the y-axis is the distance from the point to the y-axis, which is 0, since the point is already on the y-axis

(f) The distance from the point (3, 9, -7) to the z-axis is the distance from the point to the z-axis, which is 0, since the point is already on the z-axis

Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.

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The quotient from the synthetic division (9a^4-31a^3-21a^2+6a-13)/(a-4) is 9a⁴ - 22a³ - a² + 5a - 8/a -4

Synthetic division can be defined as a mathematical method of dividing a polynomial by a  binomial x - c

Such that, c is a constant.

The steps to take in synthetic division;

Given the polynomial;

(9a^4-31a^3-21a^2+6a-13)/(a-4)

[tex]\sqrt[a -4]{9a^4 -31a^3 +6a -13}[/tex]

c of divisor x-c

                4         coefficients of dividend

                           9     -31     -21      6     -13

                          _____9__-22__-1___ 5_______

                          9       -22     -1      5       -8

The quotient is the;

9a⁴ - 22a³ - a² + 5a - 8/a-4

Hence, the expression is  9a⁴ - 22a³ - a² + 5a - 8/a-4

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Total number sixth graders were surveyed is 600.

"percent" is Latin for "out of 100," so 5 % is literally 5 out of 100

Now--if it were 5 kids with birds, you would know that there were 100 total kids. But it's 30 kids, which is way more than 5; so your total number of kids is going to be way more than 100.

So what you need to do here is figure that "30 sixth graders own birds

i.e. 30 is 5% of some number."

How many times bigger than 5 is 30? (6 times, because 5 x 6 = 30, or you can think of it as 30 divided by 6 = 5)

So if you had to do 5 TIMES 6 to get to 30, you have to do 100 TIMES 6 to get the total number sixth graders were surveyed.

What's 100 x 6?

= 600.

So your total number sixth graders were surveyed is 600.

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