Justify Step 3 of this Proof

Answer::

:i

Step-by-step explanation:

.

The equation of the parabola is (x - 6)² = 6(y + 5.5).

Given that, a focus at (6,-4) and a directrix at y= -7.

We need to find the equation for a parabola.

Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).

The standard form of the equation of the parabola is  (x - h)² = 4p(y - k), where

The vertex of the parabola is (h , k)

The focus is (h, k + p)

The directrix is at y = k - p  

∵ The focus of the parabola is at (6, -4)

The coordinates of the focus are (h, k + p)

∴ h = 6

∴ k + p = -4 ⇒ (1)

∵ The directrix of the parabola is at y = -7

The directrix is at y = k - p

∴ k - p = -7 ⇒ (2)

Solve the system of equations to find k and p

Add equations (1) and (2) to eliminate p

∴ 2k = -11

Divide both sides

∴ k = -5.5

Substitute the value of k in equation (1) to find p

∵ -5.5 + p = -4

Add 5.5. to both sides

∴ p = 1.5

∵ The form of the equation is (x - h)² = 4p(y - k)

Substitute the values of h, k, and p in the form

∴ (x - 6)² = 4(1.5)(y - -5.5)

∴ (x - 6)² = 6(y + 5.5)

Therefore, the equation of the parabola is (x - 6)² = 6(y + 5.5).

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Your question is incomplete, probably the complete question/missing part is:

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

Random assignment means participants have an equal chance of being in the control group or in the experimental group.

Assignment refers to putting people into experimental or control group. In this, the Random assignment involves dividing the participants into two groups through randomization. That is, selection is on random. Tis method provides equal chance for the participants to be in the experimental or control group.

This kind of assignment will be unbiased and the participants in two groups does not differ in any way. So random assignment makes the experiment and control group equivalent. Also this makes the experimental study more accurate, acceptable and scientific too.

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Answer:

7

Step-by-step explanation:

hope this works :)

consecutive numbers means 2 numbers next to eachother like 8 and 9 or 3 and 4

product means basically the result of numbers multiplying together, e.g. the product of 8×9 = 72

so if you use trial and error you will find 6 × 7 = 42 and since mav is older she must be 7 years old

Answer:

mav is 7

Step-by-step explanation:

let justin's age be n then mav is n + 1 and the product is

n(n + 1) = 42

n² + n = 42 ( subtract 42 from both sides )

n² + n - 42 = 0 ← in standard form

(n + 7)(n - 6) = 0 ← in factored form

equate both factors to zero and solve for n

n + 7 = 0 ⇒ n = - 7

n - 6 = 0 ⇒ n = 6

since n > 0 then n = 6

mav is n + 1 = 6 + 1 = 7

The required solution of the given expression is 7x-24.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.

Given:

The given expression is

[tex](x-3)(x+8)+(2x-x^{2} )[/tex]

According to given question we have

By the expansion theorem we have

The expression is

[tex](x-3)(x+8)+(2x-x^2)\\\\=x^{2} +8x-3x-24+2x-x^{2} \\\\=7x-24[/tex]

Therefore, the required solution of the given expression is 7x-24.

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Answer:

x = -7

Let the first integer be x.

Given the next two integers are consecutive, it would be: x+1, x+2

The problem states: "4 more than the smaller number plus twice the 3rd number is 7 less than the 2nd number."

Translating English to Algebra, you'll get:

(x + 4) + 2(x + 2) + 7 = x + 1

x + 4 + 2x + 4 + 7 = x + 1

3x + 15 = x + 1

2x = -14

x = -7

That would be the third option.

It is false that 5x and 3y are like terms. They can not be combined together through addition.

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Answer:

2n² + n

Step-by-step explanation:

Given sequence:

3, 10, 21, 36, ...

Work out the first differences between terms:

[tex]3 \underset{+7}{\longrightarrow} 10 \underset{+11}{\longrightarrow} 21 \underset{+15}{\longrightarrow} 36[/tex]

As the first differences are not the same, work out the second differences.

[tex]7 \underset{+4}{\longrightarrow} 11 \underset{+4}{\longrightarrow} 15[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of n² is always half of the second difference. Therefore, as the second difference is 4, the coefficient of n² is 2.

To work out the nth term of the sequence, write out the numbers in the sequence 2n² and compare with the given sequence:

[tex]\begin{array}{|l|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4 \\\cline{1-5} 2n^2 & 2 & 8 & 18 & 32\\\cline{1-5} \sf Operation & +1 & +2& +3& +4\\\cline{1-5} \sf Sequence & 3 & 10 & 21 & 36\\\cline{1-5}\end{array}[/tex]

Therefore, we need to add n to 2n² to match the sequence.

Therefore, the nth term of this sequence is 2n² + n.

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Answer:

-8 - (-4) = - 8 + 4

Because negative times a negative is positive

Answer:

12.857 aa 35 +12.222 as 25

Answer:

26 weeks (6 months)

Step-by-step explanation:

$35x + $45y = $1000

I don't know how to show the work but it would take 26 weeks to reach $1,040. That's exactly 6 months, so half a year.

The ratio of the patterned circles to plain circles is 6 : 7.

We are given the four arrays of the circles.

In the first array, we have only 1 plain circle.

In the second array, we have 4 patterned circles and 1 plain circle.

In the third array, we have 1 patterned circle and 4 plain circles.

In the fourth array, we have only 1 plain circle.

So, total patterned circles = 5 + 1

Total patterned circles = 6

Total plain circles = 1 + 1 + 4 + 1

Total plain circles = 7

Ratio of patterned circles to plain circles will be given as:

6 : 7

Therefore, we get that, ratio of the patterned circles to plain circles is 6 : 7.

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Answer:

32 or +-8 depending on question

Step-by-step explanation:

If question is 2x = 64, then x= 32

If question is x^2 = 64, then x= +-8

The conversion of 7/18 into a decimal number using long division would be 7/18 = 0.39

In this question, we have been given a fraction.

We need to convert given fraction into a decimal number using long division.

Given fraction: 7/ 18

Consider the long division of 18 ÷ 7

      0.388

    _________

18 )  7

    -  0

   __________

       70

     - 54

   __________

       160

     - 144

   __________

       160

     - 144

   ___________

       16...

This means, the 7/18 = 0.3888...

If we round the number 0.3888...  to two decimal places then it would be, 0.39

Therefore, the conversion of 7/18 into a decimal number using long division would be 7/18 = 0.39

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Answer: sin(60°)= [tex]\frac{\sqrt{3}} 2[/tex] and cos(60°)=[tex]\frac{1} 2[/tex]

Step-by-step explanation:

sine means opposite/hypothenus (SOH)

opposite=[tex]\frac{\sqrt{3}} 2[/tex] and hypothenus is 1

sin(60°) = [tex]\frac{\sqrt{3}} 2[/tex] ÷ [tex]\frac{1} 1[/tex]

              =  [tex]\frac{\sqrt{3}} 2[/tex] × [tex]\frac{1} 1[/tex]

              =  [tex]\frac{\sqrt{3}} 2[/tex]

cosine means adjacent/hypothenus (CAH)

adjacent= [tex]\frac{1} 2[/tex] and hypothenus is 1

cos(60°) =  [tex]\frac{1} 2\\[/tex] ÷ [tex]\frac{1} 1[/tex]

              =  [tex]\frac{1} 2[/tex] × [tex]\frac{1} 1[/tex]

              =  [tex]\frac{1} 2[/tex]

Answer:

The graph is provided in the image

The statement which is true to the values of 7.055 and 70.55 are true is:

70.55 is 10 times 7.055. is true.

Given, the values are 7.055 and 70.55

statement A.

7.055 is 10 of 70.55

= 70.55×1/10

= 705.5

⇒ 705.5 ≠ 7.055

Statement B.

7.055 is 100 of 70.55.

= 70.55×1/100

= 0.7055

⇒ 0.7055 ≠ 7.055

Statement C.

70.55 is 10 times 7.055.

= 10 × 7.055

= 70.55

⇒ 70.55 = 70.55

hence true.

Statement D.

70.55 is 100 times 7.055.

= 100 × 7.055

= 705.5

⇒ 705.5 ≠ 70.55

Statement E.

7.055 is 10 times 70.55.

= 10 × 70.55.

= 705.5

⇒ 705.5 ≠ 70.55

hence the correct option is 70.55 is 10 times 7.055.

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The expression for r is n(4t-v) and the expression for the width is (P-2l)/2

This is a way of representing a variable with another variable.

Given the expression below:

r/n + t = 4v

Making r the subject

r/n = 4v - t

r =. n(4t-v)

Hence the expression for r is n(4t-v)

For the expression

P = 2l + 2w

P - 2l = 2w

2w = P - 2l

w = (P-2l)/2

Hence the expression for the width is (P-2l)/2

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Answer-

The cost of one tetra is $2.5 and one rainbow fish is $8.5

Explanation

Let the cost one tetra be 'x';

Cost of rainbow fish = x + 6;

According to question;

8x + 2(x + 6) = 37;

10x = 25

x = $2.5;

the amount or equivalent paid or charged for something : price

The average cost of a university training has gone up dramatically.

the outlay or expenditure (as of attempt or sacrifice) made to acquire an item

He executed repute, but at the fee of dropping numerous buddies.

loss or penalty incurred specially in gaining some thing

the price of lives during war

three

costs plural : charges incurred in a judicial process

particularly : those given by the law or the courtroom to the triumphing party in opposition to the dropping birthday party

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Answer: what are the options tho?

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer number 3

is the answer

Answer:from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Car drive 31.4 miles/gallon

for 358 miles, Leah needs 358/31.4 =~ 11.40 gallons

since it cost $2.18 / gallon, it will cost Leah 2.18 * 11.4 = $24.85

The total number of people in the food court eating pizza, burritos, and hamburgers is 113 (Approximate) or (Whole number)

People eating hamburger P(h) =0.38

People eating burritos P(b) = 0.31

Number of people eating pizza = 35

    Let's suppose the total number of people is 1

So,

    By adding the total number of people eating hamburgers and burritos                                          

                                                           = 0.38+0.31

                                                            = 0.69

    The ratio of the total number of people eating pizza = 1.00 - 0.69

                                                                                            = 0.31

   So total number of people eating pizza = 0.31 = 35

   By solving :

              1 = 35 / 0.31

                = (35*100)/31

                = 3500/31

                 = 112.9 (we have to write it down in the nearest whole number)

Here we writing the approximate value of 112.9 = 113 (Approximate)

Hence, the total number of people in the food court in the nearest whole number is 113

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in that function x would be -2

The new percentage of broth to solution 25/60 is 41.67

Broth, also known as bouillon is a savory liquid made of water in which meat, fish or vegetables have been simmered for a short period of time .It can be eaten alone, but it is most commonly used to prepare other dishes, such as soups.

Commercially prepared liquid broths are available, typically chicken, beef, fish, and vegetable varieties. Dehydrated broth in the form of bouillon cubes were commercialized beginning in the early 20th century.

Broths have been used as a nutrition source for the sick in Great Britain since at least the early 1700s, such as for dysentery patients

Let,

60 represents the 100% of the broth to solution

25 represents the x percentage of the broth to solution

Now,

Solving for the 25 which represents the x percentage of the broth to solution.

25/100 = x/100*

25/60 = x/100*x

25(100) = 60x

x = 2500/60

x = 41.67

Therefore,

25 represents the 41.67 percentage of the broth to solution.

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Answer:

a) 25/60=x/100

Step-by-step explanation:

y=47,916.666 dollar after 25 years

librarian salary =25000 dollar in 2000

librarian salary=30500 dollar in 2006

in 6 years increment is 30500 - 25000= 5500dollar

in one year increment is 5500/6= 916.666

m= 916.666 each year

b= 25000

y=mx+b

y=916.666*25+25000      given x=25

y=47,916.666 dollar after 25 years

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