The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (4, 6) and top of the bulb is at (4, 3)?

(x – 4)2 = –12(y – 6)
(x – 4)2 = –24(y – 6)
(x + 4)2 = 12(y + 6)
(x + 4)2 = 24(y + 6)

Answer:

Since the final answer has a factor of 4, it is a multiple of 4.

Step-by-step explanation:

Let the smaller even number be 2n.

The next greater even number is 2n + 2.

(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.

First, determine the midpoints of each side:

Side AB

M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)

M₁(x, y) = (- 1.5, 0) + (0, 3)

M₁(x, y) = (- 1.5, 3)

Side BC

M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)

M₂(x, y) = (0, 3) + (2, 3)

M₂(x, y) = (2, 6)

Side AC

M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)

M₃(x, y) = (- 1.5, 0) + (2, 3)

M₃(x, y) = (0.5, 3)

Second, determine the slope of the perpendicular bisectors:

Side AB

m = (6 - 0) / [0 - (- 3)]

m = 2

m' = - 1 / m

m' = - 1 / 2

Side BC

m = (6 - 6) / (4 - 0)

m = 0

m' = - 1 / m

m' = NaN  (Vertical line)

Side AC

m = [4 - (-3)] / (6 - 0)

m = 7 / 6

m' = - 1 / (7 / 6)

m' = - 6 / 7

Third, derive the equations of the bisectors:

Side AB

b = 3 - (- 1 / 2) · (- 1.5)

b = 9 / 4

y = - (1 / 2) · x + 9 / 4

Side BC

x = 2

Side AC

b = 3 - (- 6 / 7) · (0.5)

b = 24 / 7

y = - (6 / 7) · x + 24 / 7

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

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Answer:

x=−2+2y/5

Step-by-step explanation:

Add 2y to both sides of the equation.5x=−10+2y

Divide each term in 5x=−10+2y by 5 and simplify.

Divide each term in 5x=−10+2y by 55x5=−105+2y5Simplify the left side

. Cancel the common factor of 5

Cancel the common factor.5x5=−105+2y5Divide x by1.x=−105+y5

Simplify the right side.

Divide

−10 by 5

Answer:

y = 2x - 3

Step-by-step explanation:

1) Find the slope

The slope of any function, if given the coordinates of at least two of the points it crosses, is given by the formula  [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

We are given the points (4, 5) and (-1, -5), therefore, we can substitute their values:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-1)} = \frac{10}5 = 2[/tex]

2) Find the line's equation
We can find the line's equation by substituting one of the given points and the slope we just found into the formula [tex]y - y_1 = m(x - x_1)[/tex]:

[tex]y - 5 = 2(x - 4) \\ \to y - 5 = 2x - 8 \\ \to y = 2x - 3[/tex]

Answer: 2x - 3.

Step-by-step explanation: I took the test.

Answer:

in 1 year Allan would save 120 dollars, this is because, 10x12=120

Step-by-step explanation:

to find out what he would save I 2 years just multiply 120 by 2, 120x2=240, and for 3 years multiply 120 by 3, and so on.

Answer: The answer to this equation is 53.91

45% of 315 = 141.75

When you are using a % number convert it into a decimal ( 45% would be 0.45 or 55% would be 0.55 ). After you convert it into a decimal you can multiply it by the number ( Here it would be 315 )

0.45 x 315 = 141.75

Answer:

141.75

Step-by-step explanation:

To do this question, first, we can write 45% as 45/100.

Now, we have to multiply.

45/100x315

=141.75

Hope that helped!

:D

Answer:

(b) Draw the image of

ΔDEF

∆DEF

Step-by-step explanation:

Answer:

x = 85

Step-by-step explanation:

the exterior angles of a polygon sum to 360°

note the exterior angle at P = 180° - 90° = 90°

sum the 4 exterior angles and equate to 360

x + 72 + 113 + 90 = 360

x + 275 = 360 ( subtract 275 from both sides )

x = 85

Answer:

-170 2/3

Step-by-step explanation:

Divide both sides by 3 to get p by itself

p = -512/3

Simplify

- 170 2/3

Answer:

p=−8

Step-by-step explanation:

Let's solve your equation step-by-step.

[tex] \rightarrow \sf \: p {}^{3} =−512[/tex]

Step 1: Take cube root.

[tex] \sf p={(−512) }^{ ( \frac{1}{3} )}[/tex]

[tex] \sf \: p=−8[/tex]

Answer:

You showed the right work and got the right answer!

x = 6

Step-by-step explanation:

Since B is in the middle of A and C, AB + BC = AC

So,

2x - 11 + 8 = x + 3

x - 3 = 3

x = 6

The term "length" is used to describe an object's size or the separation between two points. Lindsey must buy 4 feet of the board for the ramp itself.

The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.

Distance exists estimated in length. The length contain the dimension of distance in the International System of Quantities. The majority of measurement systems select a base unit for length from which all other units exists derived. The meter serves as the foundational unit of length in the International System of Units.

A rectangle, for instance, has length and width as its dimensions.

1/x = 15°

x = 1/sin 15°

simplifying the above equation, we get

x = 3.9ft

x ≈ 4 ft

Therefore, the value of x ≈ 4 ft.

Lindsey must buy 4 feet of the board for the ramp itself.

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Answer:

70

Step-by-step explanation:

21 is 30 % so multiply 21 by 3 which is 63 and then divide 21 by 3 which is 7 and add the 7 to 63

The profession that is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016 is B. sound engineer technician.

The increase in percentage for orthodontist will be:

= (10214 - 9206) / 9206 × 100

= 1008 / 9206 × 100

= 10.95%

The increase in percentage for sound engineer will be:

= (17864 - 16125) / 16125 × 100

= 1739/16125 × 100

= 10.79%

The increase in percentage for police officer will be:

= (719041 - 648982) / 719041 × 100

= 70059/719041 × 100

= 9.74%

The increase in percentage for editor will be:

= (124135 - 122273)/124135 × 100

= 1862/124135 × 100

= 1.5%

Therefore, the sound engineer has the greatest percentage increase.

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Answer:

sound engineer

Step-by-step explanation:

The next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].

According to the given question.

We have a sequence 3, 6, 12, 24, 48, ..

Since, the first term of the sequence is 3.

The second term of the sequence is 6.

The third term of the sequence is 12.

Here, we can say that the next term is twice the previous term.

So, the next two terms of the given sequence, i.e.

Sixth term = 48 × 2 = 96

Seventh term  = 96 × 192

Therefore, the formula for the nth term of the sequence is given by

[tex]T_{n+1} = 2T_{n}[/tex].

Hence, the next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].

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The value of the factorial expression is 99/10

The expression is given as

98!/100! x 10

The above expression implies that we multiply 10 by the quotient of 98! and 100!

This can be done directly using a calculator, and it can be solved step by step

The step by step procedure is as follows

Expand the denominator

98!/100! x 10 = 98!/100 * 99 * 98! x 10

Evaluate the quotient

98!/100! x 10 = 1/100 * 99 x 10

This gives

98!/100! x 10 = 1/10 * 99

Evaluate the product

98!/100! x 10 = 99/10

Hence, the value of the factorial expression is 99/10

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Answer:

Step-by-step explanation:

-24

Answer:

Final Cost of 3 pounds: 7.25

Final cost of p pounds: 3.50p

Step-by-step explanation:

3.50p - 3.25 = ?

3.50(3) - 3.25 = ?

10.50 - 3.25 = $7.25

Write an expression of the cost to buy at least one pound of chicken.

3.50p

I hope this helps!

The 25th percentile of the data is represented by the 0 to 1 hour range.

48 speakers, or around 25% of the total of 192 speakers, are present.

According to the graph, 60 presenters gave presentations that lasted between 0 and 1 hours.

This means that 48 is between0 and1.

A score that compares a certain score to the scores of the other group members is known as a percentile. It shows the percentage of scores that a particular score outperformed.

A person's performance is gauged by using the percentile calculation to compare it to others. A student's test score is compared to that of other applicants using the percentile approach.

Therefore, the 0 to 1 hour period contains the data's 25th percentile.

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Answer:

Infinite solutions, regardless of the value of n.

Step-by-step explanation:

[tex]5\left(n-2\right)=5n-10\\5\left(n-2\right)\\5n-5\cdot \:2\\5n-10\\5n-10=5n-10\\5n - 10+10=5n-10 + 10\\5n = 5n\\5n-5n=5n-5n\\0=0\\\mathrm{\:for\:n = \infty,-\infty}[/tex]

Answer:

14x cannot be simplified any further.

Answer:

No, 14x can not be further simplified.

Step-by-step explanation:

I hope this helps.

The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 467) and (10, 647)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (647 - 467)/(10 - 2)

Evaluate

Rate = 22.5

This means that the rate of change is $22.5

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 22.5

So, we have

y = 22.5(x - x1) + y1

Using one of the points, we have

y = 22.5(x - 6) + 467

Set x = 0

So, we have

y = 22.5(0 - 6) + 467

Evaluate

y = 332

Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

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The markup percent of the water blaster in the store is 30%

The store sells a water blaster for $26
They bought it for $20

New price is $26

Original price is $20

The markup percent can be calculated as follows

26-20/20 × 100

= 6/20 × 100

= 0.3 × 100

= 30%

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Answer:

one way to name the symbol is our and another way to name the symbol is rco

The other root of the given quadratic equation is a = ± 3/√2.

Given that, x=2 and x²+ax+12=0.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

Now, put x=2 in x²+ax+12=0 and find the value of a.

That is, 2²+2a+12=0

⇒4+12+2a=0

⇒16+2a=0

⇒2a=-16

⇒a=-8

So, the value of a is -8.

Put (0, 6) and (4, 6) in the function y=2x²+bx+c and find the value of b and c.

That is, 6=2(0)²+b(0)+c

⇒ c=6

6=2(4)²+b(4)+c

⇒ 6 = 32+4b+c

⇒ -26 = 4b + 6

⇒ 4b = -32

⇒ b = -8

So, the value of b is -8 and the value of c is 6.

Put x=a (root) in the equation 2x + x/a -9 = 0 and find the other root.

That is, 2a²+a/a -9 = 0

⇒ 2a² - 9 = 0

⇒ a²=9/2

⇒ a = ± 3/√2

Therefore, the other root of the given quadratic equation is a = ± 3/√2.

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The 100–meter backstroke swimming times of the 8 swimmers during the semifinal and the finals of the Olympic games gives;

First part;

The center of the semifinal round is approximately 57.3625

The variability in the semifinal round is 0.0998

Second part;

The center of the final round is approximately 57.0125

The variability in the final round is 0.3336

The times of the swimmers in the semifinal round are;

56.7, 57.2, 57.3, 57.3, 57.4, 57.5, 57.7, 57.8

The central value is given by the mean of the data, is found as follows;

(56.7+57.2+57.3+57.3+57.4+57.5+57.7+57.8)/8 = 57.3625

The variability is given by the standard deviation which is found by the formula;

[tex] \sigma = \sqrt{ \frac{ x_{i} - \mu}{n} } [/tex]

Where;

[tex]x _{i} = the \: ith \: value[/tex]

[tex] \mu = the \: mean[/tex]

The standard deviation found using the given values above and an online tool is presented as follows;

[tex] \sigma = \sqrt{ \frac{ x_{i} - 57.3625}{8} \approx 0.316 } [/tex]

Second part;

In the final, we have the following values from the dot plot;

56, 56.6, 56.6, 57, 57.1, 57.2, 57.7, 57.9

From the above values, using an online calculator, the center, which is taken as the mean is 57.0125

The variance for the final, [tex] \sigma^2 [/tex] ≈ 0.3336

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Refer to the image attached.

Parametric equation uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used.

Now,

In order to plot the graphs of the given parametric equations, we will be sketching a table, in which, the values of the equations will be found at various values of the parameter.

=> Refer to the table in the image attached.

For the values so found of the parametric equations for the respective parameter, a graph will be plotted for both the equations:

Refer to the graph in the image attached.

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The eighth term of the given geometric sequence is: 0.00183.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: -30, 7.5, -1.875, ....

Here, [tex]\frac{7.5}{-30}=\frac{-1.875}{7.5}=-0.25[/tex]

That is, the given geometric sequence has a₁ = -30 and r = -0.25

The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, [tex]a_8=(-30)(-0.25)^7[/tex] ≈ 0.00183

Hence, The eighth term of the given geometric sequence is: 0.00183.

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