Write the equation of the parabola that has the vertex at point
(−2, 5.5) and passes through the point (−2.5, 2.5).

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Answer:

The dimensions of the lid are 8mm by 19mm.

w = 8

l = 19

Step-by-step explanation:

[tex]l=w+11\\l\times w=152[/tex]

where l is length and w is width. This can be solved as a system of equations.

[tex]l\times w=152\\(w+11)\times w=152\\w(w+11)=152\\w^2+11w=152\\w^2+11w-152=0[/tex]

At this point, it gets a little tough. I might be unnecessarily overcomplicating things, but this is the only way I see to solve the problem.

=================== Skip down below if you don't care about factoring

You need to factor the newly created trinomial.

[tex]ax^2+bx+c[/tex]

With a trinomial in this form, you need to find 2 numbers that add together to make b and multiply together to make ac.

Here, we need 2 numbers that add to 11 and multiply to -152. First, factor 152:

1, 152

2, 76

4, 38

8, 19

Then the reverse of all of those is true too, of course:

19, 8

38, 4

etc

In our case, we're looking for -152, so one of our factors will be negative. We're also looking for factors that add up to 11. Looking at these factors, you can see that 19 - 8 = 11, so our factors are 19 and -8.

Finally, you can use those to factor our trinomial. Split up the middle number (11w) into two:

[tex]w^2+11w-152=0\\w^2-8w+19w-152=0[/tex]

And now, you can factor by grouping:

[tex]w^2-8w+19w-152=0\\w(w-8)+19(w-8)=0\\(w+19)(w-8)=0[/tex]

===================

Now that the number is factored, you can finally find w:

[tex](w+19)(w-8)=0[/tex]

Here, you can see that the equation will be true when w = -19 or w = 8. Those are our solutions, but we can't have a negative distance, so it's just

[tex]w=8[/tex]

Going all the way back to the top, now you can use the width to find the length.

[tex]l=w+11\\l=8+11\\l=19[/tex]

That one was much easier.

The dimensions of the lid are 8mm by 19mm.

Finally, check that with both of the original equations to make sure it's correct.

[tex]l=w+11\\19=8+11\\19=19\\\\l\times w=152\\19\times8=152\\152=152[/tex]

Answer:

C. 9

Step-by-step explanation:

K(3)=3*3=9........................

Answer:

[tex]q\le \:12[/tex]

Step-by-step explanation:

Solving

[tex]\mathrm{Switch\:sides}[/tex]  (Not a required step)

[tex]q+3\le \:15[/tex]

[tex]\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}[/tex]

[tex]q+3-3\le \:15-3\\=q\le \:12[/tex]

[tex]\bold{q\le \:12}[/tex]

Graphing

Answer:

[tex]f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5} [/tex]

The answer would be C and F

Answer: 1 & -5

Step-by-step explanation

Answer:

11

Step-by-step explanation:

11*2=22

29-7 =22

Answer:

11

Step-by-step explanation:

Let x be your number

Is means equals

2x = 29-7

2x= 22

2x/2 = 22/2

x =11

Answer:

H=2  r=1

Step-by-step explanation:

P= 2h+4r + πr = π+8

h= π+8- πr -4r/2

(pls give brainliest if helps!)

Answer:

a+b)(a-b)

(Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

1 plus 2x (276-5y) + 69= A.

A function is an expression that defines a relationship between an independent variable and a dependent variable.

The number of bacteria colonies after 2 hours is 220.

It is an expression that defines a relationship between an independent variable and a dependent variable.

We have,

P(t) = 4t² + 27t + 150

Where t = time

P(t) = population of a slowly growing bacteria colony after a particular time

The growth rate after 2 hours:

P(2) = 4 x (2)² + 27 x 2 + 150

P (2) = 16 + 54 + 150

P (2) = 220

Thus the number of bacteria colonies after 2 hours is 220.

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The distance traveled by Raven in 1 hour at the given rate is 4.0 miles.

The given parameters:

The speed of Raven motion is calculated as follows;

[tex]V = \frac{Distance}{Time} \\\\V = Distance\ \times \ \frac{1}{Time} \\\\V = 2\frac{2}{5} \ miles \ \ \times \ \ \frac{1}{3/5 \ hr} \\\\V = \frac{12}{5} \ miles \ \ \times \ \ \frac{5}{3 hr} \\\\V = 4 \ mph[/tex]

The distance traveled by Raven in 1 hour at the given rate is calculated as follows;

[tex]D = 4 \times 1\\\\D = 4 \ miles[/tex]

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Answer:

12195508,42

Step-by-step explanation:

An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.

Therefore,

Assume that each year has 52 weeks: then compounding occurs.

n = 52 × 80n

times and the rate for each compounding is

[tex]$i=\frac{5.8 \%}{52}=\frac{0.058}{52}$[/tex]

If the original deposit amount is

PV

then the future value

FV

is equal to

[tex]$$F V=P V \cdot(1+i)^n=P V \cdot\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}$$[/tex]

We know the future value (which is given as $ 102,393.44), so calculating the present value is simple:

[tex]P V=F \frac{V}{(1+i)^n}=\frac{\$ 102,393.44}{\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}}[/tex]

The simplest way to compute this is to use a calculator:

[tex]$P V \approx \$ 991.45 .$$[/tex]

We can simplify this expression with great precision just for fun. It is well known that

[tex]$\left(1+\frac{1}{n}\right)^n \rightarrow e$[/tex]

which easily implies that

[tex]$\left(1+\frac{a}{n}\right)^n \rightarrow e^a$[/tex]

Here,

[tex]$$\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}=\left(\left(1+\frac{0.058}{52}\right)^{52}\right)^{80} \approx\left(e^{0.058}\right)^{80}=e^{0.058 .80}=e^{4.64}[/tex]

That is, [tex]P V \approx F V e^{-4.64}$.[/tex]

Hence, An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.

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Answer:

1/4

Step-by-step explanation:

Sample space = 12

Prob of sum = 8 is:

[2,6], [3,5]. [4,4]

That is 3/12 = 1/4

Using the exponential function, it is found that:

The exponential function is:

[tex]y(x) = 30078(1.003)^x[/tex]

Hence, considering today as an starting point, the function is:

[tex]y(x) = 30078(1.003)^{x + 260}[/tex]

One week from now, we have y(1), hence:

[tex]y(1) = 30078(1.003)^{1 + 260} = 65734.37[/tex]

One week from today, the stock is predicted to close at $65,734.37.

One month from now, we have y(4), hence:

[tex]y(4) = 30078(1.003)^{4 + 260} = 66327.75[/tex]

One month from today, the stock is predicted to close at $66,327.75.

One year from now, we have y(52), hence:

[tex]y(52) = 30078(1.003)^{52 + 260} = 76584.35[/tex]

One year from today, the stock is predicted to close at $76,584.35.

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Answer:

One week from today, the stock is predicted to close at $65,734.37.

One month from today, the stock is predicted to close at $66,327.75.

One year from today, the stock is predicted to close at $76,584.35.

Step-by-step explanation:

Answer:

75 m, 96 m

Step-by-step explanation:

a. Area = length x width

7050 = 94 x width

7050/94 = w

75 m is width

b. perimeter = 2L + 2W

356 = 2L + 2(82)

356 = 2L + 164

192 = 2L

96 m = L

4 3/4 = 19/4

133/(19/4) = 133(4/19) = 1197/19 = 63 mph

Answer: The answer is 8.91.

Answer : 8.91

Step - by - step explanation :

Sometimes if a question is to big for you - it's best to start off small . . .

4.60 + 3.28 = 7.88

7.88 + 1.03 = 8.91

Answer:

3y

Step-by-step explanation:

(-9x+7y)-(-9x+5y)

Distribute the negative(-)

-9x+7y+9x-5y

-9 and 9 cancel each other

3y

The simplest terms of the given expression  (-9x + 7y) - (-9x + 5y) will be 2y.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

(-9x + 7y) - (-9x + 5y)

Open the bracket

-9x + 7y + 9x - 5y

Combined likely terms together

-9x + 9x + 7y - 5y

0 + 2y = 2y

Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".

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Answer:

Step-by-step explanation

RHS = cos 105° + cos 15°

         = cos (90° + 15°) + cos (90° – 75°)  

         = – sin 15° + sin 75°

         = sin 75° – sin 15°

          = LHS

Answer:

Step-by-step explanation:

sin75-sin15

=sin (90-15)-(-cos (90+15))

=cos 15+cos 105

Answer:

0

the answer is 0........

Keep the denominators the same and subtract the numerators. So for example in your example:

7/8 - 3/8

Leave the 8 alone. Subtract 3 from 7.

7 - 3 = 4

So answer is:

4/8

Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2

Answer:

Step-by-step explanation:

Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.

  15x +30y = 1725 . . . . . total liters of use

  x + y = 75 . . . . . . . . . total hours of use

The second equation lets us write an expression for y:

  y = 75 -x

This can be substituted into the first equation to give ...

  15x +30(75 -x) = 1725

  -15x + 2250 = 1725 . . . . . . simplify

  -15x = -525 . . . . . . . . . . . subtract 2250

  x = 35 . . . . . . . . . . . . . . divide by -15

  y = 75 -35 = 40

The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.

Answer:

7/12 or 8/12 are both good options

Step-by-step explanation:

nvr mind, its 7/12 only

Answer:

Interest rate

Step-by-step explanation:

The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.

Answer:

8 short sleeve shirts

Step-by-step explanation:

Subtract the total amount of of shirts by the number of shirts with long sleeves to find your answer.

Here is ur answer of your question

Step-by-step explanation:

→ 8 + 4 = 2(x -1)

→ 12 = 2x - 2

→ 2x - 2 = 12

→ 2x = 12 + 2 = 14

→ x = 14/2 = 7

→ x = 7

hence, option D (7) is correct.

Hope this answer helps you dear ! take care

Answer:

try 6.93 for answer on equilqteral triangle

Answer:

(0,-2)

Step-by-step explanation: