Help on this worksheet please

The quadratic equation with x-intercepts of x = -3 and x = 2, with an intercept of y = -6, is given as follows:

y = x² + x - 6.

A quadratic equation with roots x* and x** is defined as follows:

y = a(x - x*)(x - x**).

In which a is the leading coefficient.

Considering the x-intercepts, the roots of the function are given as follows:

x* = -3, x** = 2.

Hence:

y = a(x + 3)(x - 2)

y = a(x² + x - 6).

The y-intercept is of y = -6, meaning that when x = 0, y = -6, hence the leading coefficient a is given as follows:

-6a = -6

6a = 6

a = 6/6

a = 1.

Hence the function is defined as follows:

y = x² + x - 6.

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The given system of equation have no solutions.

A linear equation is one whose variables all have degree 1.

An inconsistent pair of linear equations is a system of linear equations that cannot be solved. By comparing the coefficients of the equations in a system of linear equations, we can determine whether the system of equations has no solution. We can also infer this from the graph.

The given equations are:

y = 7x + 13

-21x + 3y = 39

Substitute the value of y from equation 1 to equation 2:

-21x + 3(7x + 13) = 39

-21x + 21x + 39 = 39

0

Hence, the given system of equation have no solutions.

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The number 46,000 expressed in scientific notation is 4.6 * 10^4

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

The total area of Pennsylvania is about 46,000 square miles

This means that

Area = 46,000 square miles

So, we have

Area = 4.6 * 10000 square miles

Express 10000 as 10^4

Area = 4.6 * 10^4 square miles

Hence, the expression is 4.6 * 10^4 square miles

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The index forms are solved to give:

17. 5x

18. 3x^2

19. 4

20. 2

Index forms are described as mathematical forms of writing numbers that are too small or too large in more convenient ways.

From the information given, we have that;

[tex]\sqrt{\frac{100x^6}{4x^4} }[/tex]

Find the square root

10x³/2x²

Divide the values

5x

[tex]\sqrt{\frac{81x^8}{9x^4} }[/tex]

Find the square root

9x⁴/3x²

Divide the values

3x²

[tex]\sqrt{\frac{64x^9}{4x^7} }[/tex]

Find the square root

8/2√x⁹/x⁷

4

[tex]\sqrt{\frac{24x^5}{6x^3} }[/tex]

√4x²

Find the square root

2

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a. Quinton expect to make 45 $ from tutoring each month b. he will save 405 $ in 4 month. the number -75 represent the amount deducted.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets,, and grouping can all be represented by mathematical symbol.

We are given that Quinton started his own tutoring business and is tracking the amount of money he makes using the function;

f(m) = 120m - 75,

where m represents the number of months he has been tutoring.

a. for one month

m = 1

f(1) = 120(1) - 75,

f(1) = 120 - 75 = 45

b. for 4 month

m = 4

f(4) = 120(4) - 75,

f(4) = 480 - 75 = 405

c. The number -75 represent the amount deducted in this context.

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Formula a = (v = 2 * pi * r / t)

Formula b = (v2 = g * m_central / r)

The scenario in context to formula a and formula b is given below:

Formula a = (v = 2 * pi * r / t)

It is used to calculate the velocity (v) of a circular object moving with a constant speed around a circle of radius (r) in time (t).

Example scenario: if you want to find the velocity of a moving object in a circular path, use formula a.

Suppose you want to find the velocity of a car moving in a circular path on a race track. The radius of the track is "r" and the time taken for the car to complete one lap is "t".

Using the equation (v = 2 * pi * r / t), we can calculate the velocity as follows:

Let's say the radius of the track is 100 meters and the time taken for the car to complete one lap is 60 seconds. Then, the velocity can be calculated as follows:

v = 2 * pi * (100 m) / (60 s)

v = 31.42 m/s

So, the velocity of the car moving in a circular path on the race track is 31.42 m/s.

Formula b = (v2 = g * m_central / r)

It is used to calculate the velocity squared (v^2) of an object moving under the influence of a central force (g * m_central) and is related to the radius (r) of its orbit.

Example scenario: If you want to find the velocity squared of an object under the influence of a central force, use formula b.

Suppose you want to find the velocity squared of a planet moving in a circular orbit around a star (a central force). The mass of the star is "m_central" and the distance of the planet from the star is "r".

Using the equation (v²  = g * m_central / r), we can calculate the velocity squared as follows:

v² = (6.67 x 10^-11 N m² /kg² ) * (m_central) / (r)

Let's say the mass of the star is 2 x 10^30 kg and the distance of the planet from the star is 1.5 x 10^11 m.

Then, the velocity squared can be calculated as follows:

v²  = (6.67 x 10^-11 N m² /kg² ) * (2 x 10^30 kg) / (1.5 x 10^11 m)

v²  = 2.22 x 10^20 m² /s²

So, the velocity squared of the planet moving in a circular orbit around the star is 2.22 x 10^20 m² /s² .

At, last we can say if you want to find the velocity of a moving object in a circular path, use formula a. If you want to find the velocity squared of an object under the influence of a central force, use formula b.

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Answer: B) 37.68

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Plugging in the given radius of 6 centimeters, we get:

C = 2πr

C = 2π(6)

C ≈ 37.68

Answer: 165%

Step-by-step explanation:

1 whole =100% 13/20=65%

100+65=165

Using the conversion formula of converting temperatures from Celsius to Fahrenheit, we get 36.6°C is 98.68°F.

Temperature is often measured using two different scales: Celsius (°C) and Fahrenheit (°F). To convert a temperature in Celsius to Fahrenheit, we use the formula °F = (°C × 9/5) + 32. In this formula, we first multiply the temperature in Celsius by 9/5 (which is equivalent to multiplying it by 1.8), and then add 32 to the result.

So for example, to convert 36.6 degrees Celsius to Fahrenheit, we plug in 36.6 for °C, and get:

°F = (36.6 × 9/5) + 32

°F = 98.68

Therefore, 36.6 degrees Celsius is equivalent to 98.68 degrees Fahrenheit. This conversion is useful for comparing temperature measurements between different regions, where different temperature scales are commonly used.

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(-2, -4) and (2, 4) is the solution to the given system of simultaneous equation

Given the system of equation

f(x) = x^2 + 2x - 4

g(x) = -2x^2 + 2x + 8

When solving graphically, the point of intersection of both curves on an xy plane is the solution to the system of equation.

According to the graph attached, the solution to the system of equation is (-2, -4) and (2, 4).

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Answer: B

Step-by-step explanation: I took the test

Answer:

Step-by-step explanation:

[tex]\frac{6}{3}[/tex]  =  [tex]\frac{2}{1}[/tex]

Answer:

Step-by-step explanation:

Answer:

-2{x+2y=-4}

2x+3y=1

-2x-4y=8

3y-4y=9

-y=9

y=-9

the value of x is

x+2(-9)=-4

x-18=-4

x=14

therefore { 14,-9}

Answer:

Step-by-step explanation:

Answer:

(1) A

(2)C

(3)B C

Step-by-step explanation:

(1)B. base=5x17=85

  C.(5x4.3)/2+3x(5x17)=10.75+255=265.75

(2) A is wrong

   B. surface area=2x(3.5x8)+2x(3.5x16)+2x(8x16)=56+112+256=424[tex]cm^{2}[/tex]

(3) A. base=(15x8)/2=60[tex]mm^{2}[/tex]

   B. 17x6+8x6+15x6=240[tex]mm^{2}[/tex]

   C. 240+2x60=360[tex]mm^{2}[/tex]

Answer: B  is the answer

Step-by-step explanation:

The area of the shaded portion of the diagram is 218 mm².

The area of the shaded portion of the diagram can be found by subtracting the area of the triangle XYZ from the the area of the circle.

Area of triangle XYZ = 1/2 * YZ * XY

YZ = 16 mm, XZ = 2 * 10 = 20 mm (XZ is the diameter of the circle)

XY = √(20²-16²) = 12 mm      (Pythagoras' theorem)

Area of triangle XYZ = 1/2 * 16 * 12 = 96 mm²

Area of circle = πr²

Area of circle = 3.14 * 10² = 314 mm²

area of the shaded portion = area of circle - Area of triangle XYZ

area of the shaded portion = 314 - 96 = 218 mm²

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Complete Question

The image of the question is attached

Answer:

b-15=16

31

Step-by-step explanation:

Because if your sister is 16 and your brother is that age minus 15 that is her sister's age which means      his age (variable); minus how much older: equals her age

The inequality that shows how much can be added to the regular size for a drink that costs under $4.00 is given as follows:

2.25 + 0.25n < 4.

The drink costs $2.25, plus each of the n additionals cost $0.25, hence the total cost is given as follows:

T(n) = 2.25 + 0.25n.

For a cost under $4, the cost must be less than $4, hence the inequality is given as follows:

2.25 + 0.25n < 4.

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Answer: 26

Step-by-step explanation: if each ride costs $.50 each, and admission costs $7, you multiply .50 by 26 and get 13. After you then add $13 and $7 and that equals $20. $13 dollars Jerold can spend

The angle Θ has these possible values:

The cosine of the angle is given as follows:

cosΘ=-1/2.

The angle on the first quadrant with a cosine of 1/2 is given as follows:

60º.

The cosine is negative on the second and on the third quadrant, hence the equivalent angles are given as follows:

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Cosine is negative, we know that angle C is obtuse. Therefore, the triangle with sides 9, 15, and 19 is an obtuse triangle.

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

To determine whether a triangle with sides 9, 15, and 19 is acute or obtuse, we can use the Law of Cosines, which relates the sides and angles of a triangle:

c^2 = a^2 + b^2 - 2ab*cos(C)

where a, b, and c are the side lengths, and C is the angle opposite side c.

In this case, we have:

a = 9, b = 15, c = 19

Using the Law of Cosines, we can solve for the cosine of angle C:

cos(C) = (a^2 + b^2 - c^2) / 2ab

cos(C) = (9^2 + 15^2 - 19^2) / (2915)

cos(C) = -0.283

Since, cosine is negative, we know that angle C is obtuse. Therefore, the triangle with sides 9, 15, and 19 is an obtuse triangle.

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Answer:

14.76

Step-by-step explanation:

Circumference = 2πr

Substitue the values into the formula

2(3.14) (2.35)=

Multiply pi by the radius

2(7.379)= 14.758

Round the answer to the hundreths place

14.76

Answer:y=-x/-+8

Step-by-step explanation:

The height of the ladder is 19.939 feet

First, we need to know the six trigonometric identities. They are;

From the information given, we have that;

Then

sin θ = opposte/hypotenuse

Substitute the values, we get;

sin 65 = h/22

Find the value

0.9063 = h/22

cross multiply

h = 19.939 feet

Hence, the value is 19.939 feet

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Answer:

Yes.

Step-by-step explanation:

We need to make sure that we match up the right sides before checking for proportionality.

From the picture, we can see that SRT pairs with MLN.

It's easier to see if you draw a diagram of MLN on paper with the same orientation as SRT.

Were you to do this, you would see that as SR lies on the left side of SRT, so does MLN lie on the left side of ML.

Also, both ST of SRT and MN of MLN lie on the right side and RT of SRT and LN of MLN are the base.

Thus, the proportions are

[tex]\frac{SR}{ML}=\frac{ST}{MN}=\frac{RT}{LN} \\\\\\\frac{3.61}{5.415}=\frac{2}{3} \\\\\frac{9.71}{14.564}=\frac{2}{3}\\ \\ \frac{11.97}{17.955}=\frac{2}{3}[/tex]

Since all the ratios simplify to 2/3 and are equal, the sides are proportional.

An expression to represent the perimeter is P = 2m + 2(m² + 11m + 28)/m

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

We are given that;

The expression m² + 11m + 28

Now,

Let's assume that the length of the rectangle is "m" and the width is "n".

The formula for the area of a rectangle is A = l × w. We are given that the area of the rectangle is m² + 11m + 28, so we can write:

A = m² + 11m + 28

Substituting the formula for the area, we get:

m² + 11m + 28 = m × n

We can rearrange this equation to solve for n:

n = (m² + 11m + 28) / m

The perimeter of a rectangle is given by the formula P = 2(l + w). Substituting the values of l and w, we get:

P = 2(m + n)

Substituting the value of n, we get:

P = 2(m + (m² + 11m + 28) / m)

P = 2m + 2(m² + 11m + 28) / m

Therefore, by the given area of rectangle perimeter will be 2m + 2(m² + 11m + 28) / m

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Answer:

Step-by-step explanation: the value is 633.202 ft

In statistics, a predictor variable is an independent variable that is used to predict or explain the outcome of a dependent variable.

Predictor variables are often used in regression analysis, where the goal is to model the relationship between one or more predictor variables and a response variable. Predictor variables can take on different forms, including categorical (e.g., gender, race) and continuous (e.g., age, income). The choice of predictor variables depends on the research question and the underlying theory or knowledge about the phenomenon being studied. For example, in a study investigating the relationship between physical activity and body weight, physical activity might be the predictor variable and body weight the outcome variable. The study might collect data on physical activity levels (e.g., minutes per day of moderate-to-vigorous physical activity) and body weight (e.g., BMI) from a sample of participants, and then use regression analysis to model the relationship between these variables. In regression analysis, predictor variables are typically entered into the model as explanatory variables or covariates, along with other relevant factors such as demographic or environmental variables. The goal is to identify the predictor variables that are most strongly associated with the outcome variable and to determine the direction and magnitude of the relationship. By understanding the role of predictor variables, we can gain insight into the factors that influence or predict the outcomes of interest in a given study.

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The equation of the linear function is y = -1/2x - 6

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

The graph

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

y = mx - 6

From the graph, we have

A unit increment in x gives an decrement of 1/2 in y

This means that

m = -1/2

So, we have

y = -1/2x - 6

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Step-by-step explanation:

Hello, So use the function p, to find the output

[tex]p(3) = - (3 - 4) {}^{2} + 10 = - 39[/tex]

[tex]p(5) = - (5 - 4) {}^{2} + 10 = 9[/tex]

Since p(4)>p(5) and p(3), p(4) is the maximum.

Also p is written in vertex form which is

[tex]a(x - h) {}^{2} + k[/tex]

Since a is negative, we will have a maximum vertex.

The answer is

Oriya has reasoned the vertex is a maximum because p(4) is the highest points compared to points near it such as p(3) and p(5).