How do you find the horizontal asymptote and Y intercept?

Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.

Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k

y = a(x-h)^2 + k

Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get

7 = a(-2 - h)^2 + k

It passing through (1, 10), we can substitute the values of x and y in the equation and get

10 = a(1 - h)^2 + k

It passing through (2,27), we can substitute the values of x and y in the equation and get

27 = a(2 - h)^2 + k

Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k

Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.

Step-by-step explanation:

A book cost $2.00.

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.

Given the no of books purchased by

Alana =4

Petra =2

Angus = 16

So, the total price of 4 books of Alana =$4

Total price for Petra = $2

Total price of Alana and Petra =4x+2x

=6x

Total price for Angus = 16x

But given Angus received a discount  of $15

So price post discount = 16x- 15

According to the question

16x-15 = 6x +5

Adding 15 both sides

16x +15-15 = 6x + 5+15

16x= 6x+20

Subtracting 6x both sides

16x - 6x = 6x - 6x + 20

10x = 20

i.e x=2

Cost of one book = $2

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Answer:

x = 24

. So, first number = 7 * 24 = 168. and second number = 4 * 24 = 96. Therefore the numbers are 168 and 96.

Answer:

42 and 24

Step-by-step explanation:

The numbers in ratio 7 : 4 = 7x : 4x ( x is a multiplier ) , then

7x - 4x = 18 ( difference of 2 numbers is 18 )

3x = 18 ( divide both sides by 3 )

x = 6

Then

7x = 7 × 6 = 42

4x = 4 × 6 = 24

The numbers are 42 and 24

Answer:

This is a prism since both sides are the same triangle,

Lets find the area of the triangle first then multiply it by the width which is 16.

20.5(base or height) x 13.3(height or base) = 272.65

272.65 divided by 2 ( x 1/2) = 136.325 is your area, now we multiply by the width.

136.325 x 16 = 2,181.2 mm3 is your volume.

Whenever coming across these types of volumes we must first find a shape and find its area then multiply it by the figure's height.

Formula area of a triangle:

B(base) x H(height) x 1/2(basically just dividing by 2)

Answer:  

a = 1.5  

VW = 9 ft  

Step-by-step explanation:  

Since the tangent lines connect both circles, we know that the line VU and VX are congruent (equal). Thus, we can set them equal to each other and solve for a:

a + 4 = a² + 0.25                            Set equal  

a² - a = 3.75                                    Isolate a values  

a² - a + 0.25 = 3.75 + 0.25            Complete the square  

(a + 0.5)² = 4                                  Factor  

a + 0.5 = 2                                     Simplify  

a = 1.5

Now we need to calculate VW, but thats easy because its equal to TV, and since we know a, we can just plug it in:

((1.5) + 7.5) ft  

9 ft

Answer:

1:Exponents are not involved..try this 34% 1/2 + ==% 98) ::*37 21 /) ( ^ 11 56/77

2:make a little close parenthesis and make a little = and % x2 RX then multiply it 9 by 9

3:477/^54*(7632)**% 87÷32×(76*09×23) 2/8=97

4:9a/(92 28 ^^_× (32

Step-by-step explanation:

HOPE IT HELPS!!

Answer:

The Volume of a Sphere is equal to 2 times the volume of a cone.

Step-by-step explanation:

The volume of a sphere: 4/3 π r^3

The volume of a cone: 1/3 π r^2 h  

r is the radius

h is the height

In this case, the height can be replaced by the 2r or the diameter, since it would correspond exactly to the height of the sphere of radius r.

So then,

sphere       and    cone

4/3 π r^3             1/3 π r^2 h  

                           1/3 π r^2 * 2r

                           2/3 π r^3    

Ratio sphere : cone

4/3: 2/3

2:1

Therefore the volume of the sphere is twice that of the cone or equal to twice the volume of the cone

Answer:

m+g[tex]\leq[/tex]40

12m + 14g[tex]\geq[/tex]250

Step-by-step explanation:

Jordan is paid $12 per hour for mowing lawns and $14 per hour for planting gardens.

Let m represents the number of hours mowing lawns and g represents the number of hours planting gardens.

He can work a maximum of 40 hours per week, and would like to earn at least $250 this week.

Then, the system of the inequality becomes

m+g[tex]\leq[/tex]40

12m + 14g[tex]\geq[/tex]250

Answer: 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]C=\pi D[/tex]

[tex]79.5=\pi D\\[/tex]

divide by [tex]\pi[/tex]

D = 25.30

radius = [tex]\frac{d}{2}[/tex]

[tex]\frac{25.30}{2} =12.65[/tex]

Answer:

r approx 12.7

d approx 25

Step-by-step explanation:

Answer:

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

D)

hope this helped

Step-by-step explanation:

The scale model door of 2.4 inches is 9.3 ft tall in the actual building.

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape.

By multiplying the numerator of one fraction by the denominator of another and the first term's denominator by the numerator of another, we can do cross multiplication.

Given that:

16 inches = 62 ft

2.4 inches = x ft

To calculate the actual value cross multiply the values:

[tex]x= \frac{(62)(2.4)}{16} \\\\x= 9.3 ft[/tex]

Hence, the actual door is 9.3 ft tall.

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Answer:

25

Step-by-step explanation:

they are alternative exterior angles meaning they are equal.so you can solve by doing

7x-40=5x+10

isolate the terms by adding like terms. ( add 40 from the left side of the equation to the right.)

so it would look like this.

7x=5x+10+40. (the 40 was negative on the left side so you have to do the inverse to move it) do the same with the 5x.

now you have

2x=50. divide 50 by 2 to get your final answer .

Answer:

-10

Step-by-step explanation:

Answer: =10

Step-by-step explanation: Hope this help :D

(-5)(-4)/-3+5

=20/-3+5

=20/2

=10

When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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Answer:

0.2

Step-by-step explanation:

Answer:

0.2 es mayor.

Step-by-step explanation:

0.2>0.08

Answer:

231 and 52.8

Step-by-step explanation:

Given that

Hamza decided the price of the item would be increased by 10 percent

We need to find out the price that normally at 210 pounds and the price that normally at 48 pounds

So,

The price that normally at 210 pounds is

= 210 + 210 × 10%

= 210 +  21

= 231

And, the price that normally at 48

= 48 + 48 × 10%

= 48 + 4.8

= 52.8

Answer:

50 inches

Step-by-step explanation:

Hi there!

[tex]P=2l+2w[/tex] where l is the length of the rectangle and w is the width of the rectangle

Plug in the length (15 inches) and width (10 inches)

[tex]P=2(15)+2(10)\\P=30+20\\P=50[/tex]

Therefore, the perimeter of the frame is 50 inches.

I hope this helps!

The object will hit the ground after 5.01 seconds.

When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,

h= -16t^2+ (80.1)t

When the object hit the ground, the height of the object h would be zero.

To find: time (t) when h = 0

Substitute h = 0 in given equation.

h = -16t^2+ (80.1)t

0 = -16t^2+ (80.1)t

16t^2 -  (80.1)t = 0

t (16t - 80.1) = 0

t = 0  or  16t - 80.1 = 0

t = 0   OR   t = (80.1)/16

t = 0 OR t = 5.01

Therefore, it will hit the ground after 5.01 seconds.

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Answer:

11.25

Step-by-step explanation:

It says if the teams were equal, so divide 45/4 to get 11.25

Answer:

Step-by-step explanation:

11 students on each team

1 student is left out

11x4 = 44

Answer: The tree is 27 feet tall.

Step-by-step explanation:

Here's what we know:

6/10 = x/45 (a 6 foot object creating a 10 shadow is equivalent to something else making a 45 shadow)

We need to isolate x. Multiply both sides by 45:

6*45/10 = x

We can factor out a 2:

3*45/5 = x

We can also factor out a 5:

3*9/1 = x

27 = x

The tree is 27 feet tall.

Answer:

hurry

Step-by-step explanation:

The length is 11.5 cm.

The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

Given: diagonal = 20 cm

In ABC,

AC² = BC² + AB²

AC²= x² + x²

AC²= 2x²

AC= √2 x

IN ACF,

AF² = AC² +CF²

20²=  2x² + x²

400= 3x²

400/3= x²

x= 11.5

hence, length is 11.5 cm.

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Answer:

12

Step-by-step explanation: i think

2nd

Step-by-step explanation:

8/9 to the second power equals to 64/81. Hope this helps!

Answer:

Hi  

x = exponent  

64 = 8·8 = 8^2

81 = 9·9 = 9^2

64/81 = 8^2/9^2 = (8/9)^2

(8/9)^2 = (8/9)^x

x = 2

Step-by-step explanation:

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Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.

Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.

Here, we have,

Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.

Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.

Therefore, option B is the correct option.

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Answer:

Yes and  E

Step-by-step explanation:

Enlargements of the picture or reductions of the image are both types of dilations.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.

Even in the enlarged picture, parallel and perpendicular lines are still discernible.

A dilated image's side's midway matches the pre-exactly. image's

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The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

The given expression:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

To find the formula for K

The formula for K is obtained by making K the subject of the formula as shown below:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

subtract 32 from LHS.

[tex]F-32 = \frac{9}{5} (K-273)[/tex]

multiply 5 with LHS

[tex]5(F-32) = 9(K-273)[/tex]

Take numerator 9 to LHS

[tex]\frac{5}{9}(F-32) = K-273[/tex]

take -273 from RHS to LHS

[tex]\frac{5}{9}(F-32) + 273 = K[/tex]

Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

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