Use the vertex to find the general form equation on the quadratic function

The two points on the line to graph the function is (3, 4/3) and (-6, 10/3).

A line is a one-dimensional, straight shape that can go on forever in both directions. It is made up of an infinite number of points that are organized in a straight line.

We are unable to offer two points on the line for graphing in the absence of a line or function.

We consider the function is, [tex]f(x) = 2 - \frac{2}{9} x[/tex]

To graph the function [tex]f(x) = 2 - \frac{2}{9} x[/tex] , we can choose any two values of x, plug them into the equation to find the corresponding values of y, and then plot the points (x, y) on the coordinate plane. Here are two possible sets of points we can use:

Set 1:

Let x = 0:

f(0) = 2 - (2/9)(0) = 2

Therefore, one point on the line is (0, 2).

Let x = 9:

f(9) = 2 - (2/9)(9) = 0

and another point on the line is (9, 0).

Now, we can plot these two points on the coordinate plane and draw a straight line passing through them to graph the function [tex]f(x) = 2 - \frac{2}{9} x[/tex]

Set 2:

Let x = 3:

f(3) = 2 - (2/9)(3) = 2 - (2/3) = 4/3

So one point on the line is (3, 4/3).

Let x = -6:

f(-6) = 2 - (2/9)(-6) = 2 + (4/3) = 10/3

So another point on the line is (-6, 10/3).

Now, we can plot these two points on the coordinate plane and draw a straight line passing through them to graph the function [tex]f(x) = 2 - \frac{2}{9} x[/tex]

Therefore, the two points on the line to graph the function is (3, 4/3) and (-6, 10/3).

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the answer is in the photo

A. The inverse of the function f(x) = 3 / (7x + 1) is g(x) = (3 - x)/7x

B. The inverse function is verified, such that f(g(x)) = x

The inverse of the function is solved as follows

f(x) = 3 / (7x + 1)

let f(x) = y, so that y = 3 / (7x + 1)

writing the equation by isolating x

y (7x + 1) = 3

7x + 1 = 3/y

7x = 3/y - 1

7x = (3 - y)/y

x = (3 - y)/7y

interchanging the variables

y = (3 - x)/7x

hence g(x) = (3 - x)/7x

solving for f(g(x)), to verify

f(g(x)) = 3 / (7((3 - x)/7x) + 1)

f(g(x)) = 3 / ((3 - x)/x) + 1)

f(g(x)) = 3 / ((3 - x + x)/x)

f(g(x)) = 3 / 3/x

f(g(x)) = (3 / 3) * x

f(g(x)) = x

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Answer: To find the length of the other side of the rectangle, we can use the formula for the area of a rectangle, which is:

area = length x width

We know that the area is 2314 square miles and one side is 26 miles. Let's plug these values into the formula and solve for the other side:

2314 = 26 x width

Divide both sides by 26:

width = 2314/26

Simplify:

width = 89

Therefore, the other side of the rectangle is 89 miles.

Step-by-step explanation:

Answer:

The total surface area of the triangular prism is 556 square units.

Step-by-step explanation:

The given 3D figure is a triangular prism.

The formula to find the total surface area of a triangular prism is:

[tex]\boxed{\textsf{Total Surface Area}= \sf 2 A_B+(a+b+c)h}[/tex]

where:

Therefore, the surface area of a triangular prism is the sum of the area of two congruent triangular bases and three rectangles.

The area of a triangle can be calculated by halving the product of the length of its base and height.  

The base of the triangles is 17 units and the height is 8 units.

Therefore, the area of each triangular base is:

[tex]\begin{aligned}\implies \sf Area\;of\;triangular\;base\;(A_B)&=\sf\dfrac{1}{2} \cdot17 \cdot8\\&=\sf 68\;square\;units\end{aligned}[/tex]

Therefore, the values to substitute into the total surface area formula are:

[tex]\begin{aligned}\implies \textsf{Total Surface Area}&= \sf 2 A_B+(a+b+c)h\\&= \sf 2 (68)+(11+14+17)10\\&=\sf 2 \left(68\right)+(42)10\\&=\sf 136+420\\&=\sf 556 \; square\;units\end{aligned}[/tex]

Therefore, the total surface area of the given triangular prism is 556 square units.

Answer:

The value of t that satisfies the equation and makes triangle ABC an isosceles triangle is 9 cm.

Step-by-step explanation:

Since triangle ABC is an isosceles triangle, we know that the lengths of AB and AC are equal. Using the lengths given in the diagram, we can set up an equation:

AB = AC

4t - 7 = 2t + 11

Now we can solve for t:

4t - 7 = 2t + 11

2t = 18

t = 9

Therefore, the value of t that satisfies the equation and makes triangle ABC an isosceles triangle is 9 cm.

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

Answer:

The slope of the line is 60.

Step-by-step explanation:

We are given a table of values, and h and c are substitutes from x and y. Judging by this, if we know the formula [tex]\frac{y2-y1}{x2-x1}[/tex] then we can evaluate the slope, we just have to take two of the coordinate points from the table.

Lets take (3,205) and (6,385) and plug it into the formula

[tex]\frac{385-205}{6-3}[/tex]

Evaluate

[tex]\frac{180}{3}[/tex]

Simplify the fraction

[tex]\frac{60}{1}=60[/tex]

The slope of the line is 60.

By answering the above question, we may state that Hence, neither expressions French nor German are spoken by nearly 97.7% of the world's population.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

In the image you included, a pie chart illustrating the distribution of the global languages spoken by the entire population can be seen.

We need to figure out what portion of the world's population does not speak either French or German in order to respond to your query.

Around 1.2% of the world's population speaks French, according to the pie chart, and 1.1% speaks German, according to the same data.

Hence, it is possible to determine the proportion of people on Earth who do not speak either French or German as follows:

German: 1.1%; French: 1.2%; 100% = 97.7%

Hence, neither French nor German are spoken by nearly 97.7% of the world's population.

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Answer:

  63.0°

Step-by-step explanation:

You want the measure of an angle in a right triangle with hypotenuse 11 and adjacent side 5.

The cosine relation is ...

  Cos = Adjacent/Hypotenuse

  cos(x) = 5/11

Then the angle is found using the inverse cosine function:

  x = arccos(5/11) ≈ 63.0°

The value of x is about 63.0°.

__

Additional comment

The calculator's angle mode needs to be set to "degrees."

We can identify the data values with a frequency of 2 on the line plot, which are 3/16, 5/8, and 1/2.

A line plot is a visual representation of data that shows the frequency of values in a dataset. In the given line plot, we need to identify the data values that have a frequency of 2.

Firstly, we have a data value of 3/16 that has a frequency of 2. This means that the value 3/16 appears twice in the dataset.

Next, we have a data value of 5/8 that also has a frequency of 2. This means that the value 5/8 appears twice in the dataset.

Lastly, we have a data value of 1/2 that has a frequency of 2. This means that the value 1/2 appears twice in the dataset.

Therefore, the data values that have a frequency of 2 on the given line plot are 3/16, 5/8, and 1/2.

In addition to these, we have some other data values on the line plot. The data value of 4 appears only once, and the data values of 12 and 78 are not present on the line plot. Hence, we cannot determine their frequency from the given information.

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The y-coordinate value of Point C if the area of ABC is 9 units squared is: 5 or -1

Point A is at (x, 2) and B is at (x + 6, 2). Since AB must lie on the line y=2  and be 6 units long. Point C is on the line x = -3 . So let C be at (-3, y).

Since ΔABC is a right angle, then point C must have the same x-coordinate as point A. Therefore, A(-3, 2) and B(2, 2).

The area of ΔABC is 9. So,

9 = 1/2 (b)(h)

where b is the base and h is the height.

so b = 6 and h = AC

Solving this for AC gives

9 = 1/2 (6)(AC)

18/6 = AC

3 = AC

Point C must lie 3 units above point A or 3 units below the point A. If it lies 3 units above, then it has a y-coordinate of 2 + 3 = 5.

If it lies 3 units below, it has a y-coordinate 2 - 3 = -1.

Therefore, y-coordinate is 5 or -1.

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The value of y is 5 when x = -31/3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

Thus, from the given question, we can see that:

The value of y is -3 when x = -17/5.

The value of y is 0 when x = 1/2.

The equation that represents this relationship is y = (2x - 1) / (x + 6).

However, the value of y cannot be 2 for any value of x that satisfies this equation.

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Answer:

The volume is 10 × 20 × 12 = 2,400 square inches.

Mean is the average. Add the minutes together and divide by 10.

[tex]80 \div10 = 8[/tex]

The answer is C

Hence, x=-2 and y=4 are the answers to the system of equations.

For the purpose of connecting algebra and geometry with the aid of line and curve graphs, coordinate geometry is necessary. Finding points on a plane is a crucial component of mathematics. It also has a number of uses in other scientific fields such dimensional geometry, calculus, and trigonometry. Use y=-2x in place of x in the first equation:

5x - 9(-2x) = -46

Simplify and find x's value:

5x + 18x = -46

23x = -46

x = -2

We can use the second equation to get y now that we know the value of x:

y = -2x = -2(-2) = 4

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The town with the greatest average rainfall was Milton; the average rainfall in Southport was 0.75 inches more than in Fairview, and the actual rainfall in Fairview was 4.15 inches.

To identify this only observe the table and identify the highest value, in this case, the highest value is 4. 20 in average for Milton.

4.09 - 3.35 = 0.75 inches

3.35 (information registered) + 0.8 = 4.15 inches

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The sides of the triangle in order from shortest to longest are b < a < c

In triangle ABC, the side opposite angle A is denoted by a,

To determine the order of the sides from shortest to longest, we need to use the triangle inequality theorem which implies that

The side opposite the largest angle is the largest side and vice versa

So, we have

b from B = 38 degrees

a from A = 54 degrees

c from C = 88 degrees

Therefore, the order of the sides from shortest to longest is: b < a < c

In other words, the side opposite angle B is the shortest, followed by the side opposite angle A, and the side opposite angle C is the longest.

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1/2cm in the scale drawing represents one foot on the actual building.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). When both the original dimensions and the new dimensions are known, the scale factor may be determined. The following is a basic formula to determine a figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.

Here, we have

Given: The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high.

we have to find how many centimeters in the scale drawing represent one foot on the actual building.

The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter.

Hence, 1/2cm in the scale drawing represents one foot on the actual building.

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Function is continuous across its domain is B.

The domain of a function is the set of numbers that can go into a given function. In other words, it is the set of x-values that you can put into any given equation. The set of possible y-values is called the range. If you want to know how to find the domain of a function in a variety of situations,

If a real function f is given by a formula, it may be not defined for some values of the variable. In this case, it is a partial function, and the set of real numbers on which the formula can be evaluated to a real number is called the natural domain or domain of definition of [tex]f[/tex].

The function f(x) = 0.52 is a constant function, and constant functions are always continuous across their domain.

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The given expression is divisible by 6 without calculating

A number can be divided if it divides evenly (leaving no remainder) into another integer. For instance, 2 divides 34 equally, making 34 divisible by 2. 34 is not divided by 3, though, because doing so would leave us with a remainder.

We can prove that [tex]$5^7 + 5^6$[/tex] is divisible by 6 using modular arithmetic.

First, we can rewrite the expression as [tex]$5^6(5+1)$[/tex], which simplifies to [tex]$5^6 \cdot 6$[/tex].

Since 5 is not divisible by 2, we can use the fact that [tex]$a \equiv b \pmod{m}$[/tex] implies [tex]$ac \equiv bc \pmod{m}$[/tex] for any integer c to simplify our expression to [tex]$(-1)^6 \cdot 6$[/tex], or simply [tex]6 (since $5 \equiv -1 \pmod{6}$)[/tex].

Therefore, [tex]$5^7 + 5^6$[/tex] is divisible by 6.

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The distance travelled in the first 14 seconds would then be 3.57 x 14 = 49.98 metres.the acceleration would be 7.14 - 3.57 = 3.57 metres per second squared.

Distance is the numerical measurement of how far apart two objects are. It is measured in units such as kilometers, meters, miles, feet, inches, and more. Distance can be calculated in one, two, or three dimensions. Distance is a key factor in many real-world applications, such as navigation, transport, and communication. Distance can also be used to describe relationships, such as the connection between two people.

A)To work out the distance travelled on a cycle in the first 14 seconds, we must first determine the velocity of the cycle. This can be done by dividing the distance travelled by the time taken. For example, if the cycle travelled 50 metres in 14 seconds, the velocity would be 50 / 14 = 3.57 metres per second. The distance travelled in the first 14 seconds would then be 3.57 x 14 = 49.98 metres.

B) To work out the acceleration speed in the first 4 seconds, we must first determine the change in velocity over the period of time. We can do this by subtracting the initial velocity from the final velocity. For example, if the cycle started at a velocity of 3.57 metres per second, and increased to 7.14 metres per second after 4 seconds, the acceleration would be 7.14 - 3.57 = 3.57 metres per second squared.

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complete question with diagram is

Question A) Work out the distance travelled on a cycle in the first 14 seconds. Q B) Work out thr acceleration speed in the first 4 seconds.

diagram shows trapezium in graph with velocity at y axiz and time at x axis

the length of blue rectangle 2 to the width of green rectangle 6 is: 2/6 = 0.33 (rounded to two decimal places)

How to find the length of blue rectangle?

To find the length of blue rectangle 2 in relation to the length of green rectangle 4, we need to divide the length of blue rectangle 2 by the length of green rectangle 4.

So, the length of blue rectangle 2 to the length of green rectangle 4 is:

2/4 = 0.5

To find the length of blue rectangle 2 in relation to the width of green rectangle 6, we need to divide the length of blue rectangle 2 by the width of green rectangle 6.

So, the length of blue rectangle 2 to the width of green rectangle 6 is:

2/6 = 0.33 (rounded to two decimal places)

Note that the ratio of the length of blue rectangle 2 to the length of green rectangle 4 is different from the ratio of the length of blue rectangle 2 to the width of green rectangle 6.

A rectangle is a two-dimensional shape that has four sides and four right angles. It is a type of quadrilateral, which means a four-sided polygon.

In a rectangle, the opposite sides are parallel and have equal length. This makes it different from a square, which is also a rectangle but has four equal sides.

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Answer:

1. C

2. B

Step-by-step explanation:

A. A(-2,5) => A' (-2 + 2, 5) or A' (0,5)

B. A(-2,5) => A' (- -2, 5) or A' (2,5)

[tex]\cfrac{31\pi }{4}\implies \cfrac{8\pi +8\pi +8\pi +4\pi +3\pi }{4}\implies 2\pi +2\pi +2\pi +\pi +\cfrac{3\pi }{4}[/tex]

so the angle θ  is really 3 revolutions plus π and then a little bit more, Check the picture below for the red reference angle.

Reflection across the y-axis is the transformation used to the polygon ABCD.

A polygon is closed geometric shape that is made up of straight line segments connected end to end. It is  two-dimensional shape that has three or more sides, angles, and vertices.

In a polygon, sides do not cross each other and  vertices are points where two sides meet.

1)  The type of transformation shown in the image is a Horizontal translation, because the second polygon A'B'C'D' is moved horizontally to the right of the original polygon ABCD while maintaining its size and shape.

2) 90° clockwise rotation

3)  90° counterclockwise rotation.

4)  Reflection across the x-axis.

5)  Reflection across the y-axis.

6)  Reflection across the y-axis

7)  the correct answer is 180° clockwise rotation.

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Complete question -

Answer:

Step-by-step explanation:

the problem that would have to be plugged into the calculator would be as following

Answer: -4/5

Step-by-step explanation: To find the coefficient of y in the equation 3y² - ⅘y + 6 = 0, we need to identify the term in the equation that contains y and then extract the coefficient.

In this equation, the term that contains y is -⅘y. The coefficient of y is the number that is multiplied by y in this term, which is -⅘.

Therefore, the coefficient of y in the equation 3y² - ⅘y + 6 = 0 is -⅘.

The sample sizes for the two universities need to be identical in order for their sampling distributions to have about the same standard deviation.

A sampling distribution is a probability distribution that specifies how a statistic—like the mean or standard deviation—behaves when it is generated from population-based samples of a specific size. It is crucial to statistical inference because it makes it easier to calculate the likelihood of receiving specific sample statistics from a population and to draw conclusions about the characteristics of the population from the sample data. The population factors and sample size both have an impact on the form, centre, and spread of a sampling distribution.

The size of the sample for the sampling distributions is given as:

n1 = (s1 / s2) * n2

where n1 and n2 are the sample sizes for College A and College B respectively.

We may assume that the variances of the two populations are identical as we want the sampling distributions to have about the same standard deviation. As a result, we may make the formula as follows by setting s1 = s2:

n1 = n2

We may draw the conclusion that the sample sizes for the two universities need to be identical in order for their sampling distributions to have about the same standard deviation.

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Answer:

The pilot was scheduled to depart at 4:00 p.m.

Her departure has been delayed by 16 minutes.

Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan.

We want to create an equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination.

First, let's represent the time of her original flight as x, in minutes. This means that her original flight plan would have taken x minutes to arrive at her destination.

However, with the new flight plan approved by air traffic control, she will arrive four times faster than she calculated in her original flight plan. This means that her new flight plan will take x/4 minutes to arrive at her destination.

Now, we need to take into account the 16-minute delay in her departure. This means that she will depart at 4:16 p.m. instead of 4:00 p.m., and therefore arrive at her destination x/4 minutes after 4:16 p.m.

So the equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination is:

Number of minutes after 4:00 p.m. = 16 + x/4

Note that this equation assumes that her flight time is the only factor affecting her arrival time, and does not take into account any other delays or factors that may affect her flight.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's start by defining some variables to represent the amount invested in the CD and the mutual fund. Let:

C = amount invested in the CD

M = amount invested in the mutual fund

From the problem statement, we know that:

C + M = 60,000 (the total investment amount is $60,000)

C >= 2M (twice as much should be invested in CDs as in the mutual fund)

M >= 8,000 (the mutual fund requires a minimum investment of $8,000)

We can use these constraints to write the objective function that we want to maximize, which is the total return on investment:

R = 0.08C + 0.07M

To solve this problem, we can use the following steps:

Substitute C = 2M into the first equation to get:

3M = 60,000

M = 20,000

Since M >= 8,000, we can invest the minimum required amount in the mutual fund and put the rest in the CD:

M = 8,000

C = 60,000 - M = 52,000

Calculate the total return on investment:

R = 0.08C + 0.07M = 0.08(52,000) + 0.07(8,000) = 4,960 + 560 = 5,520

Therefore, the investor should invest $52,000 in the CD and $8,000 in the mutual fund to maximize the return, and the maximum return is $5,520.