Each student wrote a two-step equation. Peter wrote the equation 5x − 4 = 16, and Andres wrote the equation 20x − 16 = 64. The teacher looked at their equations and asked them to compare them. Complete the description of one way in which the equations are similar.


To get Andres' equation, you can multiply every number in Peter's equation by what?

After solving the equation using the function rule the values of y are [tex]9,3,-3,-9[/tex].

A function rule is an equation that describes a relationship between two variables, where one is a dependent variable, and the other is an independent variable. Function rules are used to determine the value of the dependent variable for any given value of the independent variable. Function rules can be written as a formula, a graph, or a table of values. Function rules are often used in mathematics, physics, and other sciences to describe the behavior of a system or process.

Given: Function  [tex]y=-3x-3[/tex]

When we have a function, we just have to replace the x by the numbers on the table, in this case [tex]-4,-2,0,2[/tex].

Substituting the values of x we get,

y = -3 (-4) - 3 ⇒ 12 - 3 = 9

y = -3 (-2) - 3 ⇒ 6 - 3 = 3

y = -3 (0) - 3 ⇒ 0 - 3 = -3

y = -3 (2) - 3 ⇒ -6 - 3 = -9

Hence, the values of y are [tex]9,3,-3,-9[/tex].

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From all the given statements, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.

What is an area of a triangle?

The area of a  triangle is half the product of the base of the triangle and the height of the triangle.

Area = 1/2 * base * height

As given the Area of both the big squares of figure 1 and figure 2 are equal because the side of both the squares is equal, therefore, (a+b).

figure 1,

Big square = (a+b)²,

figure 2,

Big square = (a+b)²,

Also, the sides of the 4 triangles are also the same giving the same area for all 8 triangles from Figures 1 and 2.

Figure 1,

area for 1 triangle = ab/2

area for 4 triangle =  4*(ab/2)

area for white square = big square area - 4 triangles area

                                    = (a+b)² - 4*(ab/2)

Figure 2,

area for 1 triangle = ab/2

area for 4 triangle =  4*(ab/2)

area for white square = big square area - 4 triangles area

                                    = (a+b)² - 4*(ab/2)

Hence, the given statement, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.

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Answer:

[tex]x=64, y=72[/tex]

Step-by-step explanation:

Using the angle sum of a triangle, [tex]x=180-57-59=64[/tex].

Thus, the left hand triangle has angles of 42°, 64° (using vertical angles), and y°. It follows that [tex]y=180-42-64=74[/tex].

Answer:

x = 3; y = -1

Step-by-step explanation:

2x - 3y = 9

x = 4 + y

Since the second equation is already solved for x, use the substitution method. Substitute 4 + y for x in the first equation and solve for y.

2x - 3y = 9

2(4 + y) - 3y = 9

8 + 2y - 3y = 9

-y = 1

y = -1

Now substitute -1 for y in the second original equation, and solve for x.

x = 4 + y

x = 4 + (-1)

x = 3

Answer: x = 3; y = -1

Answer: 55

Step-by-step explanation:

7x+13=9x+1

-1           -1

7x+12=9x

-7x       -7x

12=2x

12/2=6

x=6

7*6+13=55

9*6+1=55

Answer:

-6.5y - 1.1x

Step-by-step explanation:

Rearrange the problem to where like terms are closer together:

11.7y+5.2y + 1.2x + x - 3.3x

Simplify by adding the like terms and your final answer will be -6.5y -1.1x

d

it's because it is 1 event

To find the distance from the blimp to the stadium, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of depression to the stadium, the altitude of the blimp, and the distance from the blimp to the stadium to form a right triangle.

We can then use the tangent function to find the distance from the blimp to the stadium as follows:

tan(7°) = opposite/adjacent

opposite = tan(7°) * adjacent

opposite = tan(7°) * 400 m

opposite = 0.1214 * 400 m

opposite = 48.56 m

To convert this distance from meters to kilometers, we can divide the distance in meters by 1000, as follows:

Distance in kilometers = 48.56 m / 1000

Distance in kilometers = 0.0486 km

Therefore, the distance from the blimp to the stadium is approximately 0.0486 km.

Answer:

Q: How much are 5 small greeting cards?

A: $6

Q: How much are 4 large greeting cards?

A:$17

How much is it altogether? $23.

Step-by-step explanation:

Small greeting card cost: $1.20

Large greeting card cost: $4.25

Let's solve how much it would cost to get 5 small greeting cards.

5 (1.20)=6

So $6 for 5 small greeting cards

Let's solve how much it would cost for 4 large greeting cards

4 (4.25)= 17

So $17 for 4 large greeting cards.

I hope this helps!!! I didn't understand the question completely, so hopefully I added everything that you needed.

The required number of seconds would it take to travel the the length of the building is 91.

The equation for speed is basic like distance partitioned by time. You take the distance voyaged (for instance 3 meters) and gap it when (three seconds) to get the speed (one meter each second) Thus, we can characterize Speed as the pace of progress of position of an article toward any path.

We have,

length of the building = 455 meter

speed of elevator = 5 m/s

We know,

speed = distance/time

5 = 455/time

Time = 455/5

Time = 91 seconds.

Thus,time take to travel the the length of the building is 91 seconds.

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The length of the other wall is 3 meters, according to the declaration made.

Pythagoras' Theorem states that within a right-angled triangle, any square on the hypotenuse side is precisely equal to the sum of something like the squares on the other two sides. The Perpendicular, Base, as well as Hypotenuse are the names of the three sides of this triangle. The hypotenuse throughout this example is the longest side since it is located across from the 90° angle.

The Pythagorean theorem, Pythagorean tuning, all five elements solids, ancient Theory and Proportions, understanding sphericity of the Earth, as well as the identification of the morning and evening luminaries and Venus are only a few of the the mathematical and scientific discoveries that Pythagoras gets attributed with in antiquity.

According to Pythagoras theorem

[tex]c^2=a^2+b^2[/tex]

diagonal (c)= 5 m

length of one wall (a) = 4m

length of other wall (b)= ?

[tex]5^2=4^2+b^2\\25=16+b^2\\b^2=25-16\\b^2=9\\b=3[/tex]

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The values of the variables x, y, z in the parallelogram are x=31, y=153, z=96.

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides. Both the congruence of opposite sides and the congruence of opposite angles require the Euclidean parallel postulate, or one of its equivalent formulations, and neither condition can be proved without it.

The values of the three supplied variables x, y, and z in the parallelogram are given to us.

Let's abbreviate the parallelogram, which is depicted in the attached image, ABCD.

Here,

m∠CAB = 31°,  m∠ABC =96°.

Since CD and AB are parallel, AC is a transversal now. So,

m∠CAB =m∠ACD

m∠ACD=31°

x=31

From the ΔABC we have,

m∠ABC +m∠ACB+m∠BAC=180°

96°+Y+31°=180°

y+127°=180°

y=153°

y=153

And also we know that the measure of opposite angles in a parallelogram are always equal.

So, m∠ADC=m∠ABC

z=96°

z=96

Therefore, the required values of x, y, z are 31, 153, 96.

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The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.

The amount of water vapor in the air as compared to the maximum amount that it can contain at a certain temperature is known as relative humidity. It is computed as a percentage by dividing the actual amount of water vapor in the air by the maximum amount of water vapor the air can contain at the same temperature, then multiplying the result by 100. For instance, if the air can hold 10 grams of water vapor at a certain temperature and there are only 5 grams of water vapor present, the relative humidity would be 50%. High relative humidity can be uncomfortable and promote the development of mold and other microorganisms.

How to solve?

The mean is (60+78+70+84+81+80+85+60+88+75)/10 = 76.8

The standard deviation is sqrt(((60-76.8)^2+(78-76.8)^2+(70-76.8)^2+(84-76.8)^2+(81-76.8)^2+(80-76.8)^2+(85-76.8)^2+(60-76.8)^2+(88-76.8)^2+(75-76.8)^2)/10) = 6.9

Cp = (85-65)/(66.9) = 0.56

Cpk = min((85-76.8)/(36.9), (76.8-65)/(36.9)) = min(0.86, 0.71) = 0.71

The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.

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Answer:

Part a
[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]

[tex]y = \boxed{70}x[/tex]

Part b.
The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute

Step-by-step explanation:

Q6

Part a

The slope-intercept form of an equation is y = mx + b

where m is the slope and b the y-intercept ie the value of y when x is 0

Here we see when x = 0, y = 0 so the value of b is 0 and the equation is simply

y = mx

To compute m, all we have to do is take 2 points on the graph, find the difference in y values(called rise) and divide by the difference in x values(called run)

This would be [tex]\dfrac{y2-y1}{x2-x1}[/tex]

We are given y2 as 280(on the numerator). The corresponding x2 value from the graph is 4

We are given x1(on the denominator) as 2. The corresponding y1 value is 140 from the graph

So just fill in the missing values to get

[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]

The above simplifies to 70

So the equation is

[tex]y = \boxed{70}x[/tex]

Part b
The interpretation is:

The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute

Answer: x = 1.3125

Step-by-step explanation:

−4.75+0.8x=−3.7

First, add 4.75 to both sides

0.8x = 1.05

Then divide by 0.8 on both sides

x = 1.3125

Answer:

x = 1.3125

Step-by-step explanation:

Answer:

Answer down below!

Step-by-step explanation:

Once you multiply 0.85 * 18340 you get

15589

the name of the line is both XY and YX

The total jewels that are inside the box will be 14160.

It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since one diamond in the safe deposit box is worth 12,000 if each of the other jewels are worth 2,160. The total jewels that are inside the box will be:

= 12000 + 2160

= 14160

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The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15

What is a Matrix?

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object

A+B = B+A  Commutative Law of Addition.

A+B+C = A +(B+C) = (A+B)+C  Associative law of addition.

ABC = A(BC) = (AB)C  Associative law of multiplication.

A(B+C) = AB + AC  Distributive law of matrix algebra.

R(A+B) = RA + RB

Given data ,

Let the Matrix be A

Now , the given matrices are

[tex]2\left[\begin{array}{ccc}w&2\\5&z\\\end{array}\right] + 3\left[\begin{array}{ccc}2&x\\-2&-6\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]

On simplifying the matrices , we get

[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] + \left[\begin{array}{ccc}6&2x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]

Now , from the distributive law of matrices ,

2w + 6 = 16   be equation (1)

4 + 2x = 28   be equation (2)

10 - 6 = 4y     be equation (3)

2z - 18 = 12    be equation (4)

So on simplifying the equation , we get

2w + 6 = 16   be equation (1)

Subtracting 6 on both sides , we get

2w = 10

Divide by 2 on both sides , we get

w = 5

So on simplifying the equation , we get

4 + 2x = 28   be equation (2)

Subtracting 4 on both sides , we get

2x = 24

Divide by 2 on both sides , we get

x = 12

So on simplifying the equation , we get

10 - 6 = 4y     be equation (3)

4y = 4

Divide by 4 on both sides , we get

y = 1

So on simplifying the equation , we get

2z - 18 = 12    be equation (4)

Adding 18 on both sides , we get

2z = 30

Divide by 2 on both sides , we get

z = 15

Therefore , the values are w = 5 , x = 12 , y = 1 and z = 15

Hence , The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15

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Answer:

53 if rounding to nearest 10

53.38 if not

Step-by-step explanation:

It's pretty simple actually, let's put vocabulary though

π = pie

r = radius C = circumference

ok now the formula for circumference is,

C = 2πr

because they gave you the radius, it is very simple

plug it in.

C = 2(3.14)(8.5)

3.14 x 2 = 6.28

8.5 x 6.28 = 53.38

if you're rounding to the nearest 10 it will be 53.

welcome:)

Answer:

y = 2/3x + 3

Step-by-step explanation:

(-1,-1) (3,5)

5+1/3+1

6/4

2/3

y = 2/3x + b

5 = (2/3)(3) + b

5 = 2 + b

b = 3

y = 2/3x + 3

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The x-coordinate of the point is 9.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line y = (2/3)x - 6 ______(1)

Now,

The line passes through a point (x, 0).

(x, 0) = (x, y) ______(2)

Now,

Putting (2) in (1) we get,

0 = (2/3)x - 6

6 = (2/3)x

x = 6 x 3 / 2

x = 9

Thus,

The x-coordinate of the point is 9.

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Graphing this equation x³ - 3x² - 4 = 1/(x - 1) + 5 we get one solution of approximately x = 0.91 and another one x = 3.689.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, An equation of degree 3 which is,

x³ - 3x² - 4 = 1/(x - 1) + 5.

Now by graphing this equation we get one solution of approximately x =

0.91 and another one x = 3.689.

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Let x represent the number of people coming on the trip.

The 3-day ticket rate per person plus the total rental cost is 299 + 872.50 = $<<299+872.50=1171.50>>1171.50.

The total amount paid per person for the trip, assuming Marissa and Mykuria are able to get enough friends to come on the trip so that the vacation rental house will be at maximum capacity, is 361.25. This can be represented as an expression as follows:

(299 + 872.50)/x = 361.25

This equation can be rearranged to solve for the value of x, which represents the number of people coming on the trip.

Axillary is 3 skulls.The remainder goes to the appendix.

The bones could potentially represent up to 22 different people.This is due to the possibility that each bone comes from a different person.

There were only 3 skulls, leading some to first believe there would only be 3 persons. However, there were 4 right femurs, indicating that there is a missing skull to correspond with one of the right femurs.

In light of this, you can only conclude, until further proof, that each bone belongs to a different person.

Axillary =3 skulls.

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The absolute value of a correlation coefficient is the strength of the relationship between two variables.

Hence, the answer is (a) the strength of the relationship between two variables.

Correlation coefficients helps to determine the degree of  the relationship between two variables. It lies in a range of -1 to 1.

A positive correlation coefficient implies a positive relationship between the variables and a negative correlation coefficient implies an inverse relationship between the two variables. There is no linear link between the two variables if the correlation coefficient is zero.

--The question is incomplete, the correct question is as follows--

"14. The absolute value of a correlation coefficient is: a. The strength of the relationship between two variables. b. The direction of the relationship between two variables. c. The reliability of the relationship between two variables. d. The validity of the relationship between two variables."

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The equation represents a circle that has a diameter of 12 units will be x² + (y - 3)² = 36. Hence, option A is correct.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the provided information in the question,

Use the equation of a circle,

(x -a)² + (y - b)² = r²

Here, a and b represent the center of the circle and r is the radius of the circle.

A center can be anywhere along the y-axis if it is (0, 3).

(x -0)² + (y - 3)² = 6²

x² + (y - 3)² = 36

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Answer: y=2x - 1

Step-by-step explanation:

The point slope form equation is y=mx + b

m is the slope, to find slope we need to find the rise/run

We see that the y increase by 2 and x increase by 1, so the slope is 2.

The y-intercept is at (0,-1), so the b is -1

So we have the equation y=2x - 1