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Solving Systems of Linear and Quadratic Equations: Mastery Test
Select the correct responses in the table.
The relationship between two numbers is described below, where x represents the first number and y represents the second number.
The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the
first number multiplied by 7.
Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
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Equations
y² +16=x
x² = y +16
1-4y=7x
(2x)² = y + 16
7y-1 = 4x
4y-1 =7x
Reset
(1,15)
(2,-12)
(4,-7)
Next
Solutions
(5,9)
(8,48)
(9,3)

Answer:

2400 mm^2.

Step-by-step explanation:

The ratio of their areas = ratio of the squares of their sides.

So x / 7350 = 40^2 / 70^2   where x is area of smaller hexagon.

x = 7350 * 40^2 / 70^2

= 2400 mm^2.

The area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.

The areas of two similar figures are in the ratio which is equal to the square of the ratio of their corresponding sides.

If we have two figures A and B, and they are similar, then we can say that:

(Area of A)/(Area of B) = {(Side of A)/(Side of B)}².

In the question, we are informed that the two hexagons are similar in shape.

We are asked to find the area of the smaller hexagon, given the larger hexagon has an area of 7350 mm².

As the two hexagons are similar, we can show that:

(Area of the smaller hexagon)/(Area of the larger hexagon) = {(Side of the smaller hexagon)/(Side of the larger hexagon)}².

The side of the smaller hexagon is given to be 40mm, whereas the corresponding side of the larger hexagon is given to be 70 mm.

Thus, we can show that:

(Area of the smaller hexagon)/7350 = {40/70}²,

or, Area of the smaller hexagon = (16/49)*7350 = 16*150 mm² = 2400 mm².

Thus, the area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.

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Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, [tex]\sin{2\theta}[/tex] is always positive.

It is given by:

[tex]\sin{2\theta} = 2\sin{\theta}\cos{\theta}[/tex]

In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and [tex]\sin{2\theta}[/tex] is always positive.

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The correlation coefficient r between the two data sets is 0.33

From the table of values, we make use of the following representations:

Using the above representations, we can now plot our data values in the Excel software

From the Excel application, we have the following summary:

X Values

∑ = 424

Mean = 21.2

∑(X - Mx)2 = SSx = 101.2

Y Values

∑ = 151.8

Mean = 7.59

∑(Y - My)2 = SSy = 8.238

X and Y Combined

N = 20

∑(X - Mx)(Y - My) = 9.54

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

r = 9.54 / √((101.2)(8.238))

Evaluate

r = 0.3304

Approximate

r = 0.33

Hence, the correlation coefficient r between the two data sets is 0.33

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The maximum height of the ball after its third bounce is equal to 3.568 feet.

In this question we are aware that the maximum height reached by the ball decreases linearly after each bounce. To determine that height, we must take advantage of the recursive formula described in statement:

n = 0

a₀ = 10 ft

n = 1

a₁ = 0.85 · 10 - 1

a₁ = 8.5 - 1

a₁ = 7.5 ft

n = 2

a₂ = 0.85 · 7.5 - 1

a₂ = 5.375 ft

n = 3

a₃ = 0.85 · 5.375 - 1

a₃ = 3.568 ft

The maximum height of the ball after its third bounce is equal to 3.568 feet.

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The first one is 10 feet.
The second one is 6.141 feet.

Step-by-step explanation: Edge 2023

The MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average. Option 4

Standard deviation can be defined as a statistic tool that measures the dispersion of a dataset in relation to its mean and is calculated as the square root of the available variance of the set.

It is calculated as the square root of the given variance.

Thus, the MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average.

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Answer:

.0228

Step-by-step explanation:

44 is two standard deviations below the mean   z-score = -2

look up z-score = -2 in z-score table

= .0228        or    2.28 %

Answer:

0.025

Step-by-step explanation:

Answer:

3.Tan(45)=n/2

1=n/2

n=2

Cos(45)=2/m

1/√2=2/m

m=2√2

5.Sin(60)=x/14

√3/2=x/14

14√3/2=x

x=7√3

Cos(60)=y/14

1/2=y/14

y=7

y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. This can be obtained by using the formula for finding the equation of the line.

Equation of a line can be determined using the formula,

y = mx + c

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

m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

Here in this question draw the line passing through cleaners and perpendicular to Planet Drive.

The point where x = 0 is (0, 4)

This means that y - intercept is 4

By considering two points on the line we can find the slope of the equation,

Consider the points (8, 4) and (16, 4)

m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

m = (4 - 4)/(16 - 8) = 0/8 = 0

So we got that,

Putting in the equation of line we get,

y = mx + c

⇒ y = (0)x + 4 ⇒ y = 4

Hence y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. Determine the equation of the line that represents Saturn Avenue. Show your work. Draw and label Saturn Avenue on the coordinate plane.

The correct answer is FV = $11,323.38  

What is compound interest explain?

FV = PV x [1 + R]^N, where FV=Future Value, PV=Present Value, R=Interest rate per period, N=Number of periods.

FV = 9,000 x [1 + 0.047]^5

FV = 9,000 x 1.047^5

FV = 9,000 x 1.258152857750007

FV = $11,323.38

Therefore , the answer is $11,323.38.

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Answer:

y = [tex]-\frac{4x-5}{2}[/tex]

Step-by-step explanation:

Step 1: Switch sides

5 - 2y = 4x

Step 2: Subtract 5 from both sides

5 - 2y - 5 = 4x - 5

Step 3: Simplify

-2y = 4x - 5

Step 4: Divide both sides by -2

[tex]\frac{-2y}{-2} = \frac{4x}{-2} - \frac{5}{-2}[/tex]

Step 5: Simplify

y = [tex]-\frac{4x-5}{2}[/tex]

Answer:

Step-by-step explanation:

floating point

Answer:

π/4 − x

Step-by-step explanation:

I hope its correct

The coordinate pair that represents the volume and cost of the extra-large size is (24, 8).

A coordinate plane is a plane that can be used to represent the position of a point. The plane consists of x-axes and y-axes. The position of a point is referenced from the origin.

The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)

Since the volume of the extra-large size will have three times the volume of the small size, hence:

Volume of extra-large size = 8 * 3 = 24

The cost of an extra large is twice as much as the small size, hence:

Cost of extra large = 4 * 2 = 8

A coordinate plane is a graphing and outline machine for factors and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants inside the coordinate plane. The point at which these strains join is known as the starting place (0, zero).

Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. a few children can be taught to keep in mind this with the phrase 'along the hall, up the stairs, that means that they must observe the x-axis first after which the y.

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Answer:

The answer is A) He has the side lengths in the wrong place in the cosine ratio.

Answer:

A. He has the side lengths in the wrong place in the cosine ratio.

Step-by-step explanation:

got it right on edge23

Answer: x = 2

Step-by-step explanation:

3x - 5 = 1

add 5 to both sides

3x - 5 (+5) = 1 (+5)

3x = 6

divide by 3 on both sides

3x/3 = 6/3

x = 2

The linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4

Linear function are functions that has a leading degree of 1. The equation of a linear function is expressed as y = mx + b

where

m is the slope

b is the intercept

Given the coordinates (-5, -3) and (0, -4)

Slope = -4+3/0+5
Slope = -1/5

The y-intercept of the line will be -4

Determine the equation

y = -1/5x-4

Hence the linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4

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The faster train overtake the slower on 5 p.m.

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time.

Let the number of hours after 1pm at which faster train will overtake slower train be x.

At overtaking point,

Distance travelled by slower train = Distance travelled by faster train

Given :

On equating distances we get

40 x ( x + 20) = 60 x (x)

40x + 80 = 60x

20x = 80

x = 4.

∴The faster train overtake the slower on 1 + 4 = 5 p.m.

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Answer: -3/2

Step-by-step explanation:

we could use the two points (2,3) and (0,4) from the graph

y2-y1/x2-x1

= 0-3/4-2

= -3/2

Answer:

(x+6), (y+9)

Step-by-step explanation:

The x coordinate of J goes from -7 to -1, so it is translated x+6

The y coordinate of j goes from -8 to 1, which is a difference of 9, so it's translated y + 9

Answer:

[tex](9*10^{9})( 6*10^{8})[/tex] or 9.6×10^8

Step-by-step explanation:

The answer is written above.

Hope this helps!

Answer:

9.6 * 10^8  km.

Step-by-step explanation:

960,000,000

= 9.6 * 10^8  km.

The value of the exponent = number of digits after the 9, which = 8.

The solution to the system of equations is x = 3 and y = 10

The system is given as:

2x-2y=-14

3x-y=-1

Multiply (1) by 1 and (2) by 2

So, we have:

1(2x-2y=-14)

2(3x-y=-1 )

This gives

2x - 2y=-14

6x - 2y=-2

Subtract the equations

-4x = -12

Divide by -4

x = 3

Substitute x = 3 in 3x-y=-1

3(3)-y=-1

Evaluate

9 - y = -1

Solve for y

y = 10

Hence, the solution to the system of equations is x = 3 and y = 10

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Verbal scale uses a representative fraction to describe the ratio between the map and the real world is a "true" statement.

A verbal scale is also known as a "word statement" or a "scale expression," and it is one of the possibilities for entering "scale text" in the ArcGIS software.

It is presented as a relationship between map distance and ground distance that is stated in common units that both parties can agree upon.

Uses of the verbal scale:

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The complete question is-

Verbal scale uses a representative fraction to describe the ratio between the map and the real world.(True/False).

−3/7×14/15×7/12×(−30/35)

=(−3/7×14/15)×(7/12×−30/35)

On further calculation, we get

=−2/5×−1/2

We get,

=1/5.

Property 1:

If a/b is a rational number and m is a non-zero integer then a/b =(a*m)/(b*m). In other words, we can say that the rational number remains unaltered if we multiply both the numerator and denominator with the same integer. Ex: 2/3 = 2*2/3*2 = 4/6, 2*3/3*3 = 6/9, 2*4/3*4 = 8/12.

Math Properties

Commutative Property.

Associative Property.

Distributive Property.

Identity Property.

Inverse Property.

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Answer:

[tex]\sf Sin \ S = \dfrac{2}{9}[/tex]

Step-by-step explanation:

 [tex]\sf \boxed{\bf Sin \ S = \dfrac{opposite \ side \ of \ \angle S}{hypotenuse}}[/tex]

             [tex]\sf = \dfrac{RQ}{SQ}\\\\= \dfrac{2}{9}[/tex]

Loc and Reza together will finish the entire mowing process on the lawn at 1:14 p.m.

Loc mow the total area in 20 mins.

So, his pace is 1 lawn / 20 minutes or 1/20th of a lawn each minute.

Reza's pace is 1 lawn / 30 minutes, or 1/30th of a lawn each minute because he can mow the grass in that amount of time.

Reza joins Loc after he has been mowing for 5 minutes. He can mow 1/20th of the grass in these 5 minutes, which is 5/20th of the lawn =1/4th lawn

There is currently just

1-1/4=3/4 of the lawn left to complete.

We may construct the following equation by assuming that they mow together for x mins:

1/20x + 1/30x = 3/4 [amount done by Loc + Reza = total amount]

⇒(3x+2x)/60x = 3/4

⇒5x/60 = 3/4

⇒x/12= 3/4

⇒4x=36

⇒x= 9 mins

So, when they collaborate, they can complete the lawn in 9 minutes.

Hence, Loc mows alone for 9+5 mins = 14 mins

Therefore, it is concluded that starting at 1 p.m they finish the mowing at 1:14 p.m.

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Answer:

Increases from points 0x,-6y to 2x,-3y.

Step-by-step explanation:

Answer:

The equation should be 2.5x+1.8=59.3

Step-by-step explanation:

The number of miles in the taxi ride is 10

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Dalvin took a taxi from his house to the house. The taxi company charged a pick-up fee of $4.80;

The fare per mile is $2

The total fare was $30.80, not including the tip;

Let the number of mile is x

Total fare = pick up fee + fee per mile

30.80 = 4.80 + 2x

2x = 26

x = 13

Therefore, the number of miles by algebra Dalvin took a taxi will be 13

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Rotation is a transformation where an object is rotated about a fixed point.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation, reflection and rotation are rigid transformations because they preserve the shape and size of the figure.

Rotation is a transformation where an object is rotated about a fixed point.

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Answer:  18

Step-by-step explanation:

Angles of a quadrilateral add to 360 degrees, so

[tex]100+100+70+5x=360\\\\270+5x=360\\\\5x=90\\\\x=18[/tex]