May I please get help with this. I need help with finding the original and final points on the figure and also finding out where I should put my reflection?

In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:

Comparing with the given equation, we have a = -5, b = -270 and c = -520.

Now, let's calculate the x-coordinate of the vertex using the formula below:

Using this value of x in the equation, we can find the y-coordinate of the vertex:

Therefore the vertex is located at (-27, 3125).

Complete the  following Division

Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively

What is Division?

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

1) 96

Divisor = 8

96 / 8

= 12

Quotient = 12

2) 55

Divisor = 5

55 / 5

= 11

Quotient = 11

3) 84

Divisor = 6

84 / 6

= 14

Quotient = 14

4) 63

Divisor = 3

63 / 3

= 21

Quotient = 21

Hence , Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively

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The zeros of a quadratic function are the points where the graph cuts the x axis.

If one zero is - 3, it means that

x = - 3

x + 3 = 0

Thus, one of the factors is (x + 3)

If another zero is - 13, it means that

x = - 13

x + 13 = 0

Thus, one of the factors is (x + 13)

Thus, the quadratic function would be

(x + 3)(x + 13)

We would open the brackets by multiplyingeach term inside one bracket by each term inside the other. Thus, we have

x * x + x * 13 + 3 * x + 3 * 13

x^2 + 13x + 3x + 39

x^2 + 16x + 39

Thus, the quadratic function is

f(x) = x^2 + 16x + 39

To find:

The area of the training field.

Solution:

The training field is made of two semicircles and a rectangle.

The length and width of the rectangle is 96 m and 64 m. So, the area of the rectangle is:

The diameter of the semicircle is 64 m. SO, the radius of the semicircle is 32 m.

The area of two semicircles is:

So, the area of the training field is:

Thus, the area of the training field is 9359.36 m^2.

The volume of a cylinder is calculated using the formula:

where r is the radius of the cylinder and h is the height.

From the question, we have the following parameters:

Therefore, we c n calculae tehe volume of a cylinder to be:

For four cylinders, the combined volume will be:

The volume i 481 .82 cubic inches.

Answer

Explanation

Given

To find the derivative, we have to apply the chain rule:

Considering that in our case,

and n = 3, then:

Simplifying:

Finally, we have to replace 1 in each x in f'(x) to find f'(1):

Answer:

0.135% or 0.00135

Explanation:

• The population mean height = 68 inches

• The population standard deviation = 4 inches

• Sample Size, n = 36

First, find the sample standard deviation:

Next, for X=70, find the z-score:

Since we are looking for the probability that their average height is more than 70 inches, we need to find:

• P(X>70)=P(z>3)

Using the z-score table:

The probability that their average height is more than 70 inches is 0.135%.

We were given a principal to invest ($14,000) in a timespan of 2 years, and we need to choose between applying it on an account that is compounded montlhy at a rate of 6%, and one that is compounded continuously at a rate of 5.88%. To solve this problem, we need to calculate the final amount on both situations, and compare them.

The expression used to calculate the amount compounded monthly is shown below:

Where A is the final amount, P is the invested principal, r is the interest rate and t is the elapsed time.

The expression used to calculate the amount compounded continuously is shown below:

Where A is the final amount, P is the invested principal, r is the interest rate, t is the elapsed time, and "e" is the euler's number.

With the two expressions we can calculated the final amount on both situations, this is done below:

The first account, that is compounded monthly yields a return of $15780.24, while the second one that is compounded continuously yields a return of $15747.12, therefore the first account is the one that yield the larger amount in 2 years.

The most appropriate choice for equation of line in slope intercept form will be given by

x + 2y = -16 is the required equation of line

What is equation of line in slope intercept form?

Equation of line in slope intercept form is given by y = mx + c

Where, m is the slope of the line and c is the y intercept of the line

The distance from the origin to the point where the line cuts the x axis is called x intercept

The distance from the origin to the point where the line cuts the y axis is called y intercept

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

[tex]m=tan\theta[/tex]

If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

The line passes through (0, -8) and (-2, -7)

Slope =

[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]

The line passes through (0, -8)

Equation of line

[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]

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Solution:

Using a graph plotter,

The correct answer that satisfies the graph is OPTION C.

We have the following: system of equations:

A: 3c=d-8

B: c=4d+8

To eliminate variable d first, if we want to use elimination method, we need to have variable d in both equations with the same coefficient but with different signs.

As in equation B, the coefficient of d is 4, then we need to have in equation A a coefficient of -4 for variable d.

Then the answer is we need to multiply equation A by -4.

the company's profit in 2015 was $89,600,000 (89.6 million dollars)

43%

Profit in 2011 = $128 million

Profit in 2015 decreased by 30%

% decrease = (old price - new price)/old price

old price = Profit in 2011 , new price = Profit in 2015

30% = (128,000,000 - new price)/128000000

Hence, the company's profit in 2015 was $89,600,000 (89.6 million dollars)

Percentage increase = (new price - old price)/old price

new price = 128million dollars , old price = 89.6 million dollars

% increase = [(128 - 89.6)in millions/(89.6) in millions] × 100

% increase = 38.4/89.6 × 100

% increase = 0.43 × 100

% increase = 43%

Hence, the label's profit must increase by 43% from its 2015 value to reach $128 million within the next two years

Answer:

Step-by-step explanation:

A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.

So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.

Given the graph of the function:

The graph will be shifted 3 units and to the right 2 units

So, the new vertex will be the point ( 2, 3 )

The new function will be:

So, we will adjust the slider on the following values:

Problem: Find 8 3/4 ÷ 1 2/7. Write the answer in the simplest form.​

Solution:

this is equivalent to:

Now, we do cross multiplication:

then, the correct answer would be:

Okay, here we have this:

Considering that the range of a function is the complete set of all possible resulting values of the dependent variable (y), we can see in the graph of the function that:

The values of the variable "y" go from -1 to plus infinity, this mean that the range is:

-1≤y<∞

Finally we obtain that the correct option is the first option.

In order to determine the mass of the car, you first calculate the acceleration of the car, by using the following formula:

where:

v2: final speed of the car = 2.8 m/s

v1: initial speed of the car = 1 m/s

Δt: time interval = 12 s

You replace the previoues values into th formula for the acceleration:

Next, you the Newton's second law to find the mass of the car. You proceed as follow;

where:

m: mass of the car = ?

a: acceleration of the car = 0.15m/s²

F: force exerted on the car by the man = 127.5N

You solve for m in the formula for F, and you replace the values of the other parameters to obtain m, just as follow:

Hence, the mass of the car is 850kg

Answer:

Step-by-step explanation:

30 will be the expressions that are equivalent to 9 divided by 0.3.

In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in maths are those that hold true even when they appear to be distinct. However, both forms provide the same outcome when the values are entered into the formula.

An expression is equivalent even when both sides are multiplied or divided with the same non-zero value.

The expression 9 divided by 0.3 can be written as 9/0.3

The expression that will be equivalent will be determined as:

= 9/0.3

= 90/3

= 30

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Answer:

1330.81 square feet

Explanation:

In the circle, there are two unshaded sectors with central angles 26° and 90°.

The sum of the central angles = 360°.

Therefore, the sum of the central angle of the shaded sectors will be:

The area of a sector is calculated using the formula:

Substitute the values into the formula:

The area of the shaded sector is 1330.81 square feet (rounded to the hundredth place).

Let's say that the vertex is the following red point:

Then, its reflection across y-axis would be the blue point:

If we observe the coordinates, we will have that:

(5, 3) is transformed into (-5, 3). This is going to happen no matter the coordinate:

Answer:

Step-by-step explanation:

Hello there. To solve this question, we have to remember some properties about polar curves and determining maximum and minimum values.

In this case, we have the function in terms of the angle θ:

We want to determine its minimum and maximum values on the closed interval:

We graph the function as follows:

Notice on the interval, it has a maximum value of 0.

We can determine its minimum value using derivatives, as follows:

Setting it equal to zero, we obtain

Taking its second derivative, we obtain

And notice that when calculating it on this point, we get

A positive value, hence it is a minimum point of the function.

Its minimum value is then given by

Of course we cannot determine that 0 is a maximum value of this function using derivatives because it is a local maxima on a certain interval, and derivatives can only gives us this value when the slope of the tangent line is equal to zero.

The composition of the function, (g o h)(0) = 0.

To find the composition of a function, first, find the value of the inner function by plugging in the given value of x. The output of the inner function would now be used as the input to evaluate the outer function.

We are given the following:

g(x) = 5x

h(x) = √x

To find the composition of the function, (g o h)(0), first, find h(0). To find h(0), substitute x = 0 into the inner function, h(x) = √x:

h(0) = √0

h(0) = 0

Find (g o h)(0) by substituting x = 0 into g(x) = 5x:

(g o h)(0) = 5(0)

(g o h)(0) = 0

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The distance between the parallel lines is [tex]\frac{3}{5}}[/tex].

The given parallel lines are

[tex]y= $-$3x+4\\y= $-$3x+1[/tex]

We have to find the distance between the given parallel lines.

The formula is used to solve the distance between two parallel lines [tex]ax+by+c_{1}=0[/tex] and [tex]ax+by+c_{2}=0[/tex] is

[tex]d=|c_{2} $-$c_{1}|\frac{1}{\sqrt{a^{2}+b^{2}}}[/tex]

The first given line is [tex]y= $-$3x+4[/tex]

We can write that line as [tex]3x$-$y $-$4=0[/tex]

The second given line is [tex]y= $-$3x+1[/tex]

We can write that line as [tex]3x$-$y $-$1=0[/tex]

Comparing the both given parallel lines with the standard equation of line.

After comparing we get

[tex]a=3, b= $-$1, c_{1}= $-$4, c_{2}= $-$1[/tex]

Putting the value in the formula

[tex]d=|(-1) -(-4)|\frac{1}{\sqrt{(3)^{2}+(-4)^{2}}}\\d=|-1+4|\frac{1}{\sqrt{9+16}}\\d=|3|\frac{1}{\sqrt{25}}\\d=\frac{3}{5}}[/tex]

Hence, the distance between the parallel lines is [tex]\frac{3}{5}}[/tex].

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The percentage of people satisfied with car is 50.

What is percentage?
A number or ratio which can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it. There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of something, we mean that it is 50% of everything. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his exam.

To find the percentage We divide 1550 by 3100 and then multiply by 100

We get

[tex]\frac{1550}{3100}*100\\=50[/tex]

Hence the percentage of people satisfied with the car is 50%

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A direct variation between two variables "x" and "y" is given by the following formula:

y = kx

We can rewrite the given expression 8y-7x=0 to get an equation of the form y = kx like this:

8y - 7x = 0

8y - 7x + 7x = 0 + 7x

8y = 7x

8y/8 = 7x/8

y = 7/8x

The number that is being multiplied by x should be the constant of variation k, then in this case, the constant of variation equals 7/8

As shown at the graph, we need to find x and y

The angles (x+1) and (2y+1) are vertical

so, x + 1 = 2y + 1

so,

x = 2y eq.(1)

And the sum of the angles (x+1) , (3x + 4y) and (71 - 3y) are 180

So,

(x+1) + (3x + 4y) + (71-3y) = 180

x + 1 + 3x + 4y + 71 - 3y = 180

4x + y = 180 - 1 - 71

4x + y = 108

Substitute with x from eq (1) with 2y

4 * 2y + y = 108

8y + y = 108

9y = 108

y = 108/9 = 12

x = 2y = 2 * 12 = 24

So, x = 24 and y = 12

The x-intercepts are the points where a curve intercepts the x-axis.

From the picture of the problem, we see that the curve intercepts the x-axis in two points:

Answer

The x-intercepts are at:

• x = -6 at (-6,0)

• x = -2 at (-2,0)