Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result.
Vertex:
(−4, −1);
Point:
(−2, 4)

Answer:a=275 b =525

Step-by-step explanation:

Hi there, here's your answer:

Given:

a and b are integers

a + b = 800 ....(i)

b = a + 250

Putting value of b in (i)

a + (a + 250) = 800

2a + 250 = 800

2a = 800 - 250

Or

2a = 550

Therefore, a = [tex]\frac{550}{2}[/tex] = 275

Since b is 250 greater than a,

b = 250 + 275 = 525

Hope it helps!

Answer:

Below

Step-by-step explanation:

Here is a sample:

If the tax rate at this restaurant is 9. 5% and some other person’s sales tax is $1. 61 then their subtotal is $18.56

Here, some other person’s sales tax is $1. 61

Let us assume that for the amount of 'p' dollars, the sales tax is  is $1. 61

Here, the tax rate at this restaurant is 9. 5%

This means, 9.5 percent of m dollars is $1.61

Using percentage formula,

m × (9.5 / 100) = 1.61

m × 9.5 = 1.61 × 100

m × 9.5 = 161

m = 16.95 dollars

So, their subtotal would be,

m + sales tax

= 16.95 + 1.61

= 18.56 dollars

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The complete question is:

The tax rate at this restaurant is 9. 5%. Some other person’s sales tax is $1. 61. How much was their subtotal?

Answer:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

If the slope of the line is 6 and the y-intercept is -4, the equation of the line is y = 6x - 4. This equation describes a line with a slope of 6 that intercepts the y-axis at the point (0, -4).

The next three terms are:

0.9072,  0.54432,  0.326592

So, the sequence is:

7, 4. 2, 2. 52, 1. 512, 0.9072,  0.54432,  0.326592

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. a n= a 1 r n – 1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.

The sequence is:

7, 4. 2, 2. 52, 1. 512,.

We have to find the next three terms.

To find r divide the 2nd term by the first:

4.2/7 = 0.6

To check if this is the same ratio for each number divide it by the ratio to get the number before it:

2.52/4.2 = 0.6

1.512/ 2.52 = 0.6

To find the next three terms multiply the last number by the ratio then repeat

(1.512)(0.6) = 0.9072

(0.9072)(0.6) = 0.54432

(0.54432)(0.6) = 0.326592

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Three- Dimensional figures- Cube and Cylinder

Let a be the length of sides of cube and r and h be the radius and height of cylinder respectively.

Cube -  All sides are of same dimensions.

             Let a be the length of the dimensions

             The top, bottom and side view are squares each of length a units.

             The diagonal view is basically a three dimensional right angled   triangle.

Cylinder- h be the length/ height of cylinder and r be the radius of the cylinder.

The top view of cylinder is basically a circle of radius.

The side view is basically curved surface of the cylinder of length h.

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The total area formed by the two congruent trapezoids in this problem is given as follows:

48 m².

The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.

For the two congruent trapezoids in this problem, the parameters are given as follows:

Considering that there are two trapezoids, teh total area is given as follows:

A = 2 x 1/2 x (3 + 9) x 4

A = 12 x 4

A = 48 m².

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Answer:

1 - cos² 15° - cos² 75° can be simplified as follows:

Using the identity cos² x = 1 - sin² x, we can write the expression as:

1 - (1 - sin² 15°) - (1 - sin² 75°)

= sin² 15° + sin² 75° - 1

Using the identity sin 2x = 2sin x cos x, we can write sin 15° and sin 75° in terms of sin 30° and sin 45°:

sin 15° = sin (30° - 15°) = (1/2) * sin 30°

sin 75° = sin (45° + 30°) = sin 45° + sin 30°

Substituting these values in the above expression, we get:

sin² 15° + sin² 75° = (1/4) * sin² 30° + sin² 45° + sin 30° * sin 45°

= (1/4) * (2 * (1/2)²) + (2 * (1/2) * (1/2)) + (1/2) * (1/2)

= (1/4) + 1/2 + 1/4 = 1

So, 1 - cos² 15° - cos² 75° = sin² 15° + sin² 75° - 1 = 1 - 1 = 0.

Step-by-step explanation:

The domain and the range of function f are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function.

The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the values outside the domain are:

x² - 3x - 18 = 0.

(x - 6)(x + 3) = 0

Hence:

Hence the domain is:

(-∞, -3) U (-3, 6) U (6, ∞).

The range of a function is the set that contains all the output values that can be assumed by the function.

The x - 6 term can be canceled, hence the output value that the function will never assume is of:

1/(6 + 3) = 1/9.

And also y = 0, as it would assume a value of zero at x = 6 but the denominator would also be zero.

Hence the range is of:

(-∞, 0) U (0, 1/9) U (1/9, ∞).

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After the hole is cut, 248  square feet of blue feet of blue surface remain.

What is the surface area of the given cube?

The formula for surface area is equal to six times of square of the length of the sides of the cube. It is represented by 6a², where a is the side length of the cube. It is basically the total surface area.

We have given,

the cube of side length 6 ft,

the shape of a 2-by-4-by-6-foot rectangular prism is cut out of the cube,

to find: After the hole is cut, how many square feet of blue feet of blue surface remain?

area of an original cube is:

= 8 * 6 * 6

= 288 ft²

the area of the cube, after the hole, is cut.

remaining area = original cube area - 2 * 4 *4

= 288 -  32 ft²

= 248 ft²

Hence, After the hole is cut, 248  square feet of blue feet of blue surface remain.

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Answer:

x [tex]\geq[/tex] 7

Explanation:

4x + 5 [tex]\geq[/tex] 33

4x + 5-5 [tex]\geq[/tex] 33 - 5

4x [tex]\geq[/tex] 28

[tex]\frac{4x}{4} \geq \frac{28}{4}[/tex]

x [tex]\geq[/tex] 7

HOPE IT HELPED, PLEASE MARK BRAINLIEST, THANK AND RATE!

With examples

in the photo

Answer:

C. [tex]40.6m^{2}[/tex]

Step-by-step explanation:

=  [tex]\frac{1}{2}[/tex] x ( 11 + 3 ) x 5.8

= [tex]\frac{1}{2}[/tex] x 7 x 5.8 =

[tex]40.6m^{2}[/tex]

Comparing the articles I, II, and III of the constitution, in the descending order of length and detail, the articles are ranked as I, II, and III. Article I is the longest.

Article I of the constitution created the legislative branch, article II of the constitution created an executive branch, and article III of the constitution created a judicial constitution. Article I is the longest and more detailed part of the constitution as the powers and the duties of the legislative branch are much more varied than the executive branch. Additionally, the legislative branch is composed of more individuals than the executive branch.

Article 1 is the longest as founding fathers believed that a legislative branch is very important in a government that represents the citizens. Article 3 is the shortest part of the constitution as the founding fathers did not expect the judiciary to play a large role.

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To find the missing coordinates of the points A and B, you can use the equation c -3/7x + 3 = y. Plugging in the given x-coordinates for A and B, you can solve for their y-coordinates.

A: x = -2, y = -3 B: x = 9, y = 6

To find the slope of the line, you can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates for A and B, you can calculate the slope as m = (6 - (-3))/(9 - (-2)) = 9/11.

To further explore the topic, you can look into how to graph equations in slope-intercept form, as well as how to find equations of parallel and perpendicular lines. You can also learn how to use the equation of a line to calculate distances between points, and how to calculate the midpoint of a line segment.

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Answer:The appropriate number in the cage for the first equation is:

(5²)³ = 5³

The evaluation for log₃9 is:

log₃9 = 2

Step-by-step explanation:

The factor of its radius reduced is 3. The result is obtained by comparing the spherical volumes.

The volume of a spherical can be calculated by

V = 4/3 πr³

Where

A spherical balloon has volume v and radius r. Its volume is reduced by a factor of 27.0.

Find the factor of its radius reduced!

The factor of its volume is

V₁/V₂ = 27

We use the formula for spherical volume to find r₁/r₂.

V₁/V₂ = (4/3 πr₁³)/(4/3 πr₂³)

27 = (r₁/r₂)³

r₁/r₂ = ∛27

r₁/r₂ = 3

Hence, the radius is reduced by a factor of 3.

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The number of units produced does not affect net operating income when using absorption costing.

All production expenses, including direct materials, direct labour, and both variable and fixed overhead costs, are included in the cost of each unit produced in absorption costing. This means that as more units are manufactured, the total manufacturing cost is distributed over a greater number of units, resulting in a reduced cost per unit.

Variable costing, on the other hand, includes only variable production expenses, such as direct materials, direct labor, and variable overhead costs, in the cost of each unit produced. Fixed manufacturing overhead costs are considered period expenses and are not included in the product cost.

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Yes, we can make the rectangle has sides of length n and n, and all four vertices have the same color

A rectangle is a two-dimensional shape with four sides, two of which are parallel and equal in length, and the other two sides are also parallel and equal in length.

In this case, the objects are the points in the plane with integer coordinates, and the available spaces are the six colors.

Since there are an infinite number of points with integer coordinates and only six colors, it follows that there must be a color that appears at the vertices of a rectangle.

In other words, we can color the points in a manner such that there will be a rectangle in which all four vertices are the same color. This is because, if we divide the points into six different regions, there must be at least one region that contains more points than the others.

When we look for a rectangle, we look for two points in this region that are the farthest apart from each other. The rectangle that connects these two points will have all four vertices the same color.

In conclusion, we can make the statement stronger by limiting the size of the purported monochromatic rectangle.

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The height of ball which is droped from 2m and rises to 75% after third bounce is equals to the 0.843 meters.

If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m

In second bounce, height is 1.5 m × 75%

= 1.5 m×0.75 = 1.12 m

In third bounce, 1.12 m× 75%

= 1.12 m×0.75 = 0.843 m

The height the ball reaches on its third bounce is 0.843 m.

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Complete question :

A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the third bounce be?

Answer:

x = -6

Step-by-step explanation:

                   x + 4 = -2

Subtract 4 from both sides,

                x + 4 - 4 = -2 - 4

                         x = -6

                     [tex]\boxed{\bf x = -6}[/tex]

Check: Substitute x = -6 in the LHS of the equation,

      LHS = x +4

              = -6 + 4

              = -2 = RHS

Answer:

2.4 lb

Step-by-step explanation:

We know

Alicia paid 1.32 for a bag of pinto beans

The beans cost .55 per lb

How much did the bag of pinto beans weigh?

1.32 / .55 = 2.4 lb

So, the bag of pinto beans weighs 2.4 lb.

Answer: A

Step-by-step explanation: I just did 3.14x4

Answer:

Step-by-step explanation:

Area of a circle = πr²

r = radius and it is half of the diameter.

Diameter = 4 so radius = 2

Area = 3.14 (2)²

Area = 3.14(4)

Area = 12.56 yd²

Choice A

After 7 years, the balance of the savings account will be $1069.39.

An account balance is the amount of money in a financial repository at any particular time, such as a savings or checking account. The account balance is always the net amount after all debits and credits are subtracted.

The formula to calculate the balance after t years is A = P(1 + r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.

In this case, P = 700.00, r = 0.07, n = 1 (since the interest is compounded annually), and t = 7. Plugging these values into the formula, we get:

A = 700.00 * (1 + 0.07/1)^(1 * 7)

A = 700.00 * (1.07)^7

A = 700.00 * 1.527674

A = $1069.39

So, after 7 years, the balance of the savings account will be $1069.39.

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Answer:

Step-by-step explanation:

-1.15

Answer:

-1.15

The answer is -1.15

The number of ways coach can select students to compete in the race are 1820.

The selections are another name for combinations. The choice of items from a predetermined group of items corresponds to combinations. We don't want to organize anything here. We are going to choose them. We use the notation nCr to indicate how many distinct r-selections or combinations there are among a set of n objects. A combination is distinct from an arrangement or a permutation. No matter how the objects are arranged, combinations are produced by choosing some or all of them.

Given;

There are 16 students on your track team with  4 runners who run different parts of the race.

Now, n=16 and r=4;

nCr = 16C4

=16*15*14*13/4*3*2*1

=4*5*7*13

=1820

Therefore, by combination there are 1820 ways.

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We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.

x = 6, XZ = 18

To solve for x, we can use the formula for the midpoint of a segment, which is (x + z)/2.

Plugging in the given values, we get (x + 13)/2 = 6.

Simplifying, we get x = 6.

To solve for XZ, we can simply plug in the given value for x, which is 6.

Therefore, XZ = 3(6) = 18.

Given three values related to a line segment, XZ, XT, and TZ, we can solve for both the value of x and the length of XZ. To do this, we can use the formula for the midpoint of a segment, which is (x + z)/2. Plugging in the given values for XT and TZ, we can solve for x, which comes out to be 6. We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.

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The detail that best supports the inference that the auto manufacturing industry supports green solutions is -

"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

Given is a graph as shown in the image attached.

We can write -

{ 1 } -

f{g(x)} = (x - 2)² - 2(x - 2) - 3

{ 2 } -

g{f(x)} = (x² - 2x - 3) - 2

Therefore, we can calculate f{g(x)} and g{f{x}) as -

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Answer:

Answer:

The answer is a ( 1 5/6 )

Step-by-step explanation:

.................