Give the vertex form and factored form of f(x)=x^2-12x+35.

What specific information does
each form provide?

Answer: [tex]P=2000(1.04)^t[/tex].

Step-by-step explanation:

It is given that,

Initial population of a town = 2000

Growth rate = 4% = 0.04 per year

The exponential growth function for population is

[tex]P=P_0(1+r)^t[/tex]

where, [tex]P_0[/tex] is initial population, r is growth rate and t is number of years.

Substitute [tex]P_0=2000,r=0.04[/tex] in the above equation.

[tex]P=2000(1+0.04)^t[/tex]

[tex]P=2000(1.04)^t[/tex]

Therefore, the required equation is [tex]P=2000(1.04)^t[/tex], where P is population after t years.

Answer:

It's image

Step-by-step explanation:

Refraction of light and particles

Answer:

infinite solutions

Step-by-step explanation:

-3f + 3f = 0

0=0

This is always true so there are infinite solutions

Answer:

All Real Numbers (infinite Solutions)

Step-by-step explanation:

When you cancel out the -3f and the +3f you get [tex]0=0[/tex] and since that is true you get all real numbers

Hope this helps

Answer:

2.975 gallons a week

Step-by-step explanation:

It wants u to cross and multiply so what i would do is put both of them together and multiply across and when u get the answers that u multiply u then divide to see what was the lowest and what the greatest ratio was so for me i would gi with a

Answer:

35.2

Step-by-step explanation:

Answer:

In the 8% option , $5,000 should be invested

In the 12% option, $15,000 should be invested

Step-by-step explanation:

Let’s start with the total return.

Since the total return expected is 11%, the amount expected to be returned will be;

11/100 * 20,000 = $2,200

Now, let the amount invested at 8% interest be $x while the amount invested at 12% interest be $y

Mathematically;

x + y = 20,000 ••••••(i)

Now let’s work with the interest part;

On the 8% part, amount of interest expected is 8/100 * x

on the 12% part, amount of interest expected is 12/100 * x

8% of $x + 12% of $y = 2,200

Writing this fully mathematically, we have;

(8/100 * x) + (12/100 * y) = 2,200

8x/100 + 12y/100 = 2,200

Multiply through by 100

8x + 12y = 220,000 ••••••(ii)

Now we have two equations to solve simultaneously;

x + y = 20,000

8x + 12y = 220,000

From i, x = 20,000-y

Substitute this into ii

8(20,000-y) + 12y = 220,000

160,000-8y + 12y = 220,000

4y = 220,000 - 160,000

4y = 60,000

y = 60,000/4

y = $15,000

x = 20,000 -y

x = 20,000 - 15,000

x = $5,000

Hey there! I'm happy to help!

If something is 11 less, we are subtracting 11.

-11

We have 11 less than seven times a number x.

7x-11

The word is means equals.

7x-11=-4

Now we need to isolate the x. We add 11 to both sides.

7x=7

We divide both sides by 7.

x=1.

Have a wonderful day! :D

Answer:

74°F

Step-by-step explanation:

In order to find the average of a certain amount of numbers, you add those numbers together and divide by how many numbers there are. In this case, you would reverse that method to find the last number. We know that there were four readings, and we have three of them and the average. Multiply the average (84.75) by the number of readings (4), and you get the sum of all the readings (339). Then you subtract each of the readings that you already know to isolate the last reading. 339 - 112 (first reading) = 227, 227 - 68 (second reading) = 159, and 159 - 85 (fourth reading) = 74. Therefore, the third reading must be 74.

Answer:

n = 18

Step-by-step explanation:

[tex] \frac{6}{5} = \frac{n}{15} [/tex]

Cross multiply and simplify

[tex]6 \times 15 = 5 \times n \\ 90 = 5n[/tex]

Divide both sides of the equation by 5

[tex] \frac{90}{5} = \frac{5n}{5} [/tex]

Simplify : Cross cancel common factor: 5

[tex]18 = n \\ n = 18[/tex]

Answer:

n=18

Step-by-step explanation:

hope this helps.

plzzz brainliest

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(3, 5.25) and (3, –8.75)

The distance between them is

[tex]d = \sqrt{ ({3 - 3})^{2} + ({5.25 + 8.75})^{2} } \\ = \sqrt{ {0}^{2} + {14}^{2} } \\ = \sqrt{196} \: \: \: \: \: \: \: \: \: \: \\ = 14 \: \: \: \: \: \: [/tex]

We have the final answer as

Hope this helps you

Answer:

0.60714285714

Answer:

B. No the input is not feasible

because you cannot rent 6,5 movies  :p

Answer:

No, the input is not feasible.

Step-by-step explanation:

I took the test, and got it right, the other dudes logic is sound as well.

Answer:

2500

Step-by-step explanation:

$10 times 52 is $520 a day so multiply 520 times 5 and you get $2600 so round that and it is $2500

Answer:

z = 8

Step-by-step explanation:

We divide 6 on both sides ^^

Answer:

The mantle is the #2 the crust is #1 the outer core is #3 the inner core is #4

Hoped I helped

Answer:

A

Step-by-step explanation:

Answer:

  $1769.06

Step-by-step explanation:

The sum of Mia's three highest salaries is ...

  $92,000 +94,800 +96,250 = $283,050

so the average is ...

  $283,050/3 = $94,350

Her pension is then ...

  0.01875 × $94,350 = $1769.06

_____

Additional comment

This is equivalent to the total of those salaries, divided by 160.

  T/3 × 0.01875 = T × (0.01875/3) = T × 0.00625 = T/160

Sometimes, there are simpler ways to calculate things like this.

Answer:

The answer is B

Step-by-step explanation:

The answer is B because if you divide 4 into 24 it will equal 6, therefore the answer is B because it is 1/6

Answer:

1/10

Step-by-step explanation:

The value of 2 in 1,703,298 is 200.

The value of 2 in 3,932,574 is 2,000.

2,000 divided by 200 is 10.

Therefore, the 2 in 1,703,298 has 1/10 the value of the 2 in 3,932,574.

Answer:

1 tenth or 10%

Step-by-step explanation:

The 2 in the first number is in the hundreds place (200) but the 2 in the second number is thousands place(2000)

200/2000=0.1 or 10%

Hope this helps! Plz award Brainliest : )

Answer:

[tex] \boxed{\sf Height \ of \ parallelogram \ (h) = 8.4 \ cm} [/tex]

Given:

Area of parallelogram (A) = 31.5 cm²

Base of parallelogram (b) = 3.75 cm

To Find:

Height of parallelogram (h)

Step-by-step explanation:

Area of parallelogram (A) = Base (b) × Height (h)

31.5 = 3.75 × h

h × 3.75 = 31.5

h = [tex] \sf \dfrac{31.5}{3.75} [/tex]

h = 8.4 cm

The height of the parallelogram is 8.4cm with a base of 3.75cm and an area of 31.5 sq cm.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

Given, The area of the parallelogram is 31.5 sq cm and the base is 3.75 cm.

We know the area of a parallelogram is base×height.

∴ h×3.75 = 31.5.

h = (31.5/3.75) cm.

h = 8.4 cm.

learn more about parallelograms here :

https://brainly.com/question/1563728

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Answer:

The equation of the line is:

[tex]y = -4\,x +16[/tex]

Step-by-step explanation:

A line perpendicular to the given one is going to have a slope equal to the opposite of the reciprocal of 1/4. That is the slope of the new line will be "-4".

Now we write the point-slope form for a line using the info provided of slope -4 and point (5, -4):

[tex]y-y_0=m\,(x-x_0)\\y - (-4) = -4 \,(x-5)\\y+4 = -4\,x +20\\y = -4\,x +16[/tex]

Answer:

y = -4x + 16

Step-by-step explanation:

For questions like this, I would first find the slope of the line that we are trying to find the equation for. To do this, I would use the line y = 1/4x - 2 and find the slope of a line that would be perpendicular to it. Taking the negative reciprocal of the slope of y = 1/4x - 2 will do just that.

By looking at the equation y = 1/4x - 2, we can see that the slope of the line is 1/4. The negative reciprocal of 1/4 would be -4, which would be the slope of the line whose equation we are trying to find.

Since we have a point on the line, and we now have the slope of the line, we can now make an equation for the line in point-slope form:

y + 4 = -4(x - 5)

Now while this is an equation for the line, lets try to get it into slope-intercept form:

y + 4 = -4(x - 5)

Distribute the -4 on the right side of the equation.

y + 4 = -4x + 20

Subtract 4 from both sides.

y = -4x + 16

And now we have the equation of the line in slope-intercept form.

I hope you find my answer helpful.

Step-by-step explanation:

12/32 in simplest form

First both have the table of 4 in common

3/8

Then we cannot divide it further so this is the simplest form

Answer:

18.75/ hour

Step-by-step explanation:

Simply divide 150 by 8.

Answer:

yellow :)

Step-by-step explanation:

Answer:

The region in the x-y plane is the set of points

[tex]R=\{(x,y)\mid0\le x\le 1,x^2\le y\le\sqrt x\}[/tex]

The height of the solid falls between the x-y plane (for which z = 0) and the equation of the plane, z = 3x + 2y.

So the volume is

[tex]\displaystyle\int_0^1\int_{x^2}^{\sqrt x}\int_0^{3x+2y}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^1\int_{x^2}^{\sqrt x}(3x+2y)\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^1(3x^{3/2}+x-3x^3-x^4)\,\mathrm dx[/tex]

[tex]=\displaystyle\frac65+\frac12-\frac34-\frac15=\boxed{\dfrac34}[/tex]

Answer:

3/5

Step-by-step explanation: