Solve each quadratic equation by completing the square.
6x2 – 28x = - 16

On a scale drawing of a basketball court, 1 inch equals 8 feet the actual area of the basketball court if the scale drawing is 11. 75 inches by 6. 25 inches will be 4,700 square feet.

Given:

To solve the given question we will assume the court is rectangular in shape so we will solve by using formula of Area of rectangle

\(\rm Area \;of\;rectangle\;= l\times b\)

Where, l=length

            b=breadth

According to the given question,

    \(\rm Area = 94\; feet \times 50\; feet\\\\ = 4,700 \;square\; feet.\\\)

Therefore, Area of the basketball court will be 4,700 square feet.

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Answer: The train traveled 199.5 km

Step-by-step explanation:

We know the relationship:

Distance = Time*Speed

We know that the speed of the train was 105km/h

And we know that it leaves at 13:14, and arrives at 15:08.

Then the total amount of time that the train was traveling is:

T = (15 hours and 8 mins) - (13 hours and 14 mins)

= (15 - 13) hours and (8 - 14) mins

=  2 hours and (-6) mins.

We know that one hour has 60 minutes, then this is equal to:

T = 1 hour and 54 minutes.

But because the speed is kilometers per hour, we need to rewrite the 54 minutes in hours.

This can be done as follows:

1 hour = 60 minutes.

Then: 54 minutes = (54/60) hours = 0.9 hours.

Then:

1 hour and 54 minutes = 1.9 hours.

Now we know the speed and the time, then the distance can be calculated as:

Distance = speed*time = 105km/h*(1.9 h) = 199.5 km

The train traveled 199.5 km

Answer:

The train traveled 199.5 km

Step-by-step explanation:

We know the relationship:

Distance = Time*Speed

We know that the speed of the train was 105km/h

And we know that it leaves at 13:14, and arrives at 15:08.

Then the total amount of time that the train was traveling is:

T = (15 hours and 8 mins) - (13 hours and 14 mins)

= (15 - 13) hours and (8 - 14) mins

=  2 hours and (-6) mins.

We know that one hour has 60 minutes, then this is equal to:

T = 1 hour and 54 minutes.

But because the speed is kilometers per hour, we need to rewrite the 54 minutes in hours.

This can be done as follows:

1 hour = 60 minutes.

Then: 54 minutes = (54/60) hours = 0.9 hours.

Then:

1 hour and 54 minutes = 1.9 hours.

Now we know the speed and the time, then the distance can be calculated as:

Distance = speed*time = 105km/h*(1.9 h) = 199.5 km

The train traveled 199.5 km

1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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Answer:

which class you read now

Answer:

see explanation

Step-by-step explanation:

Given

2t - \(\sqrt{2}\) = 3t + \(\sqrt{2}\) ( add \(\sqrt{2}\) to both sides )

2t = 3t + 2\(\sqrt{2}\) ( subtract 3t from both sides )

- t = 2\(\sqrt{2}\) ( multiply both sides by - 1 )

t = - 2\(\sqrt{2}\)

-----------------------------------------------------------

Given

(- x + 2\(\sqrt{3}\) )(- 3x - \(\sqrt{2}\) ) = 0

Equate each factor to zero and solve for x

- x + 2\(\sqrt{3}\) = 0 ( subtract 2\(\sqrt{3}\) from both sides )

- x = - 2\(\sqrt{3}\) ( multiply both sides by - 1 )

x = 2\(\sqrt{3}\)

- 3x - \(\sqrt{2}\) = 0 ( add \(\sqrt{2}\) to both sides )

- 3x = \(\sqrt{2}\) ( divide both sides by - 3 )

x = - \(\frac{\sqrt{2} }{3}\)

Answer:

140

Step-by-step explanation:

∫P=700

∫T=2

∫R=10% after a few calculating you get 140.....the answer is right just sorry for my bad explaining

The orthogonal trajectories of the curve y = 14ax are the curves given by y = -1/(14a) + F, where a is an arbitrary constant and F is a constant of integration.

To find the orthogonal trajectories of the curve y = 14ax, we need to find a family of curves that intersect the given curve at right angles. The differential equation for the orthogonal trajectories can be derived by taking the negative reciprocal of the derivative of the given curve.

Differentiating y = 14ax with respect to x, we get dy/dx = 14a. Taking the negative reciprocal, we have -dx/dy = 1/(14a). Rearranging the equation, we get dx/dy = -1/(14a).

This is a first-order linear differential equation, which can be solved by separating variables and integrating. Integrating both sides, we have ∫ dx = ∫ -1/(14a) dy. This simplifies to x = -y/(14a) + C, where C is the constant of integration.

To eliminate the constant of integration, we can express it as another function of y. Let C = F, where F is a constant. Rearranging the equation, we get x = -y/(14a) + F. This equation represents the family of curves that are orthogonal to the given curve y = 14ax.

The orthogonal trajectories of the curve y = 14ax are given by the equation y = -1/(14a) + F, where a is an arbitrary constant and F is a constant of integration. These curves intersect the given curve at right angles.

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Based on the information in the graph, we can infer that at first the amount of money decreased radically and then began to rise steadily in a low amount.

To read the graph we must identify the data represented by each of the axes of the plane. In this case the y axis represents the amount of money and the x axis represents time. So the ratio is the amount of money over a given time.

To read the graph we must take into account the line that represents the relationship. It must be taken into account that the horizontal variations refer to the time that increases without variations. The data that can have variations is the amount of money that, as we can see, begins with a pronounced decrease and later increases slowly.

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Answer:

116 square cm

Step-by-step explanation:

Find the area of each shape

7*10=70

4*4=16

1/2(15)*4=30

70+16+30=116

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

I believe it's 9

Step-by-step explanation:

Answer:

9²

Step-by-step explanation:

9²

We have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

To prove that there exists a value of x such that tan(x) = x for each whole number n, we can use the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a continuous function takes on two different values at two different points in an interval, then it must also take on every value between those two points at some point within the interval.

In this case, we consider the function f(x) = tan(x) - x. We want to show that there exists a value of x in the [(2n-1)π/2, (2n+1)π/2] where f(x) = 0, which means tan(x) = x.

First, we note that f(x) is continuous within the given interval since both tan(x) and x are continuous functions.

Next, we evaluate f((2n-1)π/2) and f((2n+1)π/2):
f((2n-1)π/2) = tan((2n-1)π/2) - (2n-1)π/2 = -∞ - (2n-1)π/2 < 0
f((2n+1)π/2) = tan((2n+1)π/2) - (2n+1)π/2 = ∞ - (2n+1)π/2 > 0

Since f((2n-1)π/2) < 0 and f((2n+1)π/2) > 0, by the Intermediate Value Theorem, there must exist a value of x in the integral  [(2n-1)π/2, (2n+1)π/2] such that f(x) = 0. This means there exists an x such that tan(x) = x for each whole number n.

Therefore, we have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

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Answer:

first one

Step-by-step explanation:

the sum of (9k-4) =3542

so it will be the first one because

28((5+248)/2)=3542

Answer:

a

Step-by-step explanation:

cuz i milk da cows homie, all fo my edge brothas, no cap on jaw, j keepin it real fo yall homies

Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

The percentage that will decrease on the moon is: 83.5%

The weight of a 200-pound person on the moon is 33 pounds, which represents a decrease in weight by 200 - 33 = 167 pounds. To find the percentage decrease in weight, we need to divide the decrease in weight by the original weight and multiply by 100.

Using the formula: Percentage decrease = (Decrease in weight / Original weight) * 100

Percentage decrease = (167 / 200) * 100 = 83.5%.

Therefore, the person's weight decreased by 83.5%, from 200 pounds on Earth to 33 pounds on the moon. This decrease in weight is due to the weaker gravitational pull on the moon compared to Earth.

It's important to note that the weight of an object is determined by its mass and the gravitational force acting on it, and weight is not the same as mass. An object's mass remains constant, regardless of its location, but its weight can change based on the strength of the gravitational force acting on it. On the moon, the gravitational force is weaker than on Earth, which results in a decrease in weight for objects on its surface.

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Answer:

above sea level

Step-by-step explanation:

The angle subtended at the center of the arc is 102⁰

Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.  If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.

Lenght of arc = A/360 *2пr

A = angle at center = ?

п = 22/7 r = radius = 840 feet

⇒1500 = A/360  2 *22/7 * 840

1500 = 36960A/2520

3780000= 36960A

making A the subject we have

3780000/36960 = A

A = 102.27

A= 102⁰

The angle is 102⁰

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Answer:

ूेऐेुेुलौयकौइकौलएेःरःरइौईौकौथटइिौइिौइोौकइेईौकेञौञे

Answer:

i will see if i can figure it out

gl dude

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ok ill try to find it and answer it

Answer: 1. [-8, 8]

2. [-27, 27]

Step-by-step explanation:

1. |X|≤8

x≤8 or x>=-8

-8<=x<=8 ==> [-8, 8]

2. |X|≤27

x≤27 or x>=-27

-27<=x<=27 ==> [-27, 27]

The properties used by Elizabeth to solve equation are mentioned in option A,D,E and F.

These characteristics make it possible to modify equations while maintaining their consistency, which eventually aids in identifying the variable and the equation's solution.

In given steps to the solution of equation,

\(\frac{3(x-2)}{4} -5= -8\)

\(\frac{3(x-2)}{4}= -3\)        (Addition property of equality)

\({3(x-2)}= -12\)   (Multiplication property of equality)

\(3x-6=-12\)      (Distributive property)

\(3x=-6\)

\(x=-2\)               ( Division property of equality)

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Solution:

Given the triangle ABC with the points below

And it's dilation, triangle A'B'C, with points

To find the scale factor of dilation, the formula is

Scale factor = Dimension of the new shape ÷ Dimension of the original shape, i.e.

Taking point A and A',

Substituting their dimensions into the scale factor formula

Hence, the scale factor is 2

The inequality for number of hours Aman worked

90.9 hour < h < 127.27 hour

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Amar travel expenses will cost between $1,800 and $2,400 total.

He has $300 In savings, and he earns $16.50 per hour at his job.

let the number of hours be represented by h.

So, 300 + 16.5h = 1800

16.5h = 1500

h = 90.9

and, if the expense exceeds to $2400

300 + 16.5h = 2400

16.5h =  2100

h = 127.27

Thus, the inequality is

90.9 hour < h < 127.27 hour

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Answer: D. as a total number of family member increases the amount of money that the family spends on food increases

Step-by-step explanation:

i.e. independent variable acts like a cause to effect the dependent variable.

This can be seen only in Option D. as it is very obvious that increase in family member will increase the cost of food.

Hence, there is direct effect of number of people on food's cost.

Rest of options represents correlation but not causation .

Hence, the correction option is D.

Answer:

A scale factor exists because any two circles are similar. You can use the radii to determine the scale factor.

Step-by-step explanation:

The ratio between the radii is 31 so the scale factor is 31=3. The circumference of the smaller circle is C=2π(1)=2π.

Answer:

it would be “>”, 100% guaranteed.

Answer:

answer is >

Step-by-step explanation:

hope this is helpful

Answer:

Step-by-step explanation:

To find what the ratio would be, we need to know what to multiply 5 & 3 by so that when we add them, we get 80. Let's assume the number we multiply by is x:

5x + 3x = 80

8x = 80

x = 80 / 8

x = 10

Now, we multiply 5 by 10 and 3 by 10

= 50:30

Your ratio would be 50:30

Double check: 50 + 30 = 80