Find the axis of symmetry and the vertex of the graph of f(x)=x^2+8x+10

Answer:

6 units

Step-by-step explanation:

We find the distance by subtracting the "ends"

=-4-2= -6 (ignoring the negative)

We get

=6

Answer:

The oil slick area A exhibits exponential growth. Assume time t is measured in days.

dAdt=kA,A0=20,A1=20×3=60

Solve this separable differential equation.

dAdt=kA

∫dAA=∫kdt⟺ln(A)=kt+C

A(t)=A0ekt

Determine the constant k using the initial and first day oil slick area values A0,A1.

A1=A0ek×1 on day one

k=ln(A1A0)=ln(6020)=ln(3)

Substitute the known constant k and A0 into the equation.

A(t)=20eln(3)t

Verify the model A(t) matches the desired oil slick expansion. Does it triple every day?

A(0)=20e0=20

A(1)=20eln(3)1=60=3×20

A(2)=20eln(3)2=180=3×60

A(3)=20eln(3)3=540=3×180

It checks out!

On what day has the oil slick reached 1 hectare? The area is measured in square meters.

1 hectare = 10,000 square meters

10000≤20eln(3)t Solve for t days.

t≥1ln(3)ln(1000020)

t≥5.657 days

Answer

The oil slick reached 1 hectare after about 5+1/2 days.

Step-by-step explanation:

Answer:9/4

Step-by-step explanation:

3/4 + (1/3/1/6) - (1/2)

3/4 + (1/3 ➗ 1/6) - 1/2

3/4 + (1/3 x 6/1) - 1/2

3/4 + ((1x6)/(3x1)) - 1/2

3/4 + (6/3) - 1/2

3/4 + 2 - 1/2

(3+8-2)/4

9/4

Answer:

4x+ 1 = 24 + 1 = 25 m.

Step-by-step explanation:

Given, perimeter = 62 m. Perimeter : 2 (L+W) = 62 m. hence, L+W = 31 m. x = 30/5

Answer:

Step-by-step explanation:

let width be x

length = 2x + 4

2(x + 2x + 4) = 62

6x + 8 = 62

6x = 54

x = 9

length = 2(9) + 4 = 22cm

Answer:

1/2π

Step-by-step explanation:

For khan, you HAVE to put the pi symbol. just type pi and itll work

Answer:

1/2 pi (Sorry i don't have the pi symbol)

Step-by-step explanation:

Answer:

[tex]x \geq 3(y + z)[/tex]

Step-by-step explanation:

I am going to say that:

Mary's amount is x.

Ashley's amount is y.

Oscar's amount is z.

Mary has at least 3 times the amount of cash that ashley and oscar have combined

Ashley's and Oscar's combined amount is y + z.

3 times this amount is 3(y + z).

At least 3 times means that z is equal or greater than 3(y + z).

So

[tex]x \geq 3(y + z)[/tex]

Answer:

Should be the bottom one

Step-by-step explanation:

You can find this by counting. It is the only one with 12 units.

Answer:

Step-by-step explanation:is number 4 i pick it and its correct

Answer:

8 footballs

18 basketballs

36 baseballs

24 softballs

Step-by-step explanation:

Let f = footballs

f = 8

Let b = basketballs

b = 2+2f = 2 +2(8) = 2 +16 = 18

Let B = baseballs

B = 5f -4 = 5(8) -4 = 40-4 = 36

Let s = softballs

s = 6+1/2B = 6+1/2(36) = 6+18 = 24

The total is 86

f+b+B +s = 86

8+18+36+24 = 86

86=86

There are 8 footballs.

Two more than twice the number of footballs are basketballs:

2f + 2 = b

f = number of footballs

b = number of basketballs

In the first statement, there are 8 footballs. So, f = 8

2(8) + 2 = b

16 + 2 = b

18 = b

Therefore, there are 18 basketballs.

Four less than 5 times the number of footballs are baseballs:

5f - 4 = a

f = number of footballs

a = number of baseballs

In the first statement, there are 8 footballs. So, f = 8

5(8) - 4 = a

40 - 4 = a

36 = a

Therefore, there are 36 baseballs.

Six more than half of the baseballs are softballs:

a/2 + 6 = s

a = number of baseballs

s = number of softballs

In the third statement, there are 36 baseballs. So, a = 36

(36)/2 + 6 = s

18 + 6 = s

24 = s

Therefore, there are 24 softballs.

Best of Luck!

Answer:

k = 13The smallest zero or root is x = -10

Step-by-step explanation:

you can write "x^2" to mean "x squared"

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) = x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+10 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line.

Subtract 48-19=29 Correct me if I'm wrong.

That means it's 29 cups.

Answer:

29 cups

Step-by-step explanation:

step 1: since the liquid in the photo is shown to go up to between 18 and 20, it has to be 19 cups.

step 2: so she had 48 cups, right? and she used 19. so we have to subtract 19 from 48.

step 3: 48-19 = 29. she has 29 cups left..

i hope this helps!

Answer:

Step-by-step explanation:

Median of a dataset is the value at the centre of the dataset after rearrangement.

Given the data {8,x , 4,1}, the median of the set will be two values(x and 4). Since we have two values as the median, we will take their average.

Median of the first data set = x+4/2 ...(1)

For the second dataset  {9,y , 5,2}, the median will be y+5/2

Since we are told that the medians of both datasets are equal, we will equate the value of the medians of both datasets as given below;

x+4/2 = y+5/2

cross multiplying;

2(x+4) = 2(y+5)

Dividing both sides by 2 will give;

x+4 = y+5

From the resulting equation;

y-x = 4-5

y-x = -1

(y-x)² = (-1)² = 1

Answer:

110

Step-by-step explanation:

Answer:

137

Step-by-step explanation:

i did this on i-ready :>

Answer:

  f(x) = x^2 -12x +20

Step-by-step explanation:

There are an infinite number of functions with zeros at those values of x. One simple polynomial function with those zeros is ...

  f(x) = (x -10)(x -2) . . . . . each zero contributes a factor

  f(x) = x^2 -12x +20

Answer: 8+2x

Step-by-step explanation:

Hi, Perimeter is the distance around a two-dimensional shape.

To calculate it, we have to add all the side lengths of the figure. The missing side  is the ? side (right side). To obtain it we have to subtract the top right side length (2) to the left side length (12)

So, the expression is equal to:

P = 12+ (x-4) + (x-12) +2 +(12-2)

P = 12+ x - 4 +x -12+2 +10

P = 12-4-12+2+10+x+x

P =8+2x

Answer:

a=10

b=6

Step-by-step explanation:

add 2 to 8, to get a, then subtract 4 from 10 to get b

Answer:

10 and 6

Step-by-step explanation:

Answer: 2.86

Step-by-step explanation:

14+26=40

40/14

Answer:

2.86

Step-by-step explanation:

Answer:

  linear

Step-by-step explanation:

A linear function has a constant rate of change.

_____

The word "common" is usually used to refer to a shared characteristic of two or more entities. It would not ordinarily be used to describe a characteristic of one function. We're not quite sure what you mean by "has a common rate of change."

Answer:

Equation: -2x = -6

Solution: x = 3

Step-by-step explanation:

1. Take a look at the diagram. With two -x on one side and 6 of the -1 on the other, we can see the equation to be -x - x = -1 - 1 - 1 - 1 - 1 - 1

2. However, this is not a proper equation as it is not simplified: - 2x = -6

3. Now that we have the equation, apply simple algebra to recieve x, as such:

-2x = -6 ⇒ x = -6/-2 ⇒ x = 6/2 ⇒ x = 3

Answer:

equation:-2x=-6

solution: x=3

Step-by-step explanation:

-2x=-6

step one : divide -2 from both sides of the equal sign[tex]-2x/-2=-6/-2[/tex]

then boom you got x=3

copy paste this

4x + 6

4(14) + 6 (substituting x = 14)

56 + 6

62

Answer:

Regression equations can help you figure out if your data can be fit to an equation.This is extremely useful if you want to make predictions from your data- either future predictions or indications of past behavior.For example,you might want to know what your savings are going to be worth in the future.There are several types of regression equations,some of the more common include exponential and simoke linear regression.In elementary statistics,the regression equation you are most likely to come across is the linear form.

Answer:

10.5

Step-by-step explanation:

Answer:

Here is the answer:

Step-by-step explanation:

10.5

Correct question is ;

Given the equation of the parabola x² = -36y

The focus of the parabola is:

Answer:

Option C - Focus = (0,-9)

Step-by-step explanation:

The equation of the parabola is:

x² = -36y

Thus, y = - x²/36

Using the vertex form,

y = a(x − h)² + k, to determine the values of a, h, and k.

We will have;

y = (-1/36)(x − 0)² + 0

Thus,

a = - 1/36

h = 0

k = 0

The distance (p) from the vertex to a focus of the parabola is gotten by using the following formula.

p = 1/4a

So, p = 1/(4*(-1/36))

p = - 1/(1/9)

p = -9

Now, The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

Focus is (h, k+p)

Plugging in the relevant values, we have;

Focus = (0, (0 + (-9))

Focus = (0,-9)

The value of the puzzle is 17

The value of the triangle :

Value of Circle :

Value of whole yellow square :

Value of half-yellow square :

Using the above information:

Triangle + Circle + half-square

10 + 5 + 2 = 17

Therefore, the solution to the puzzle is 17

Learn more on puzzles : https://brainly.com/question/31416634

#SPJ6

Answer:

A.

Step-by-step explanation:

Given that Ebony waited for more than 56 minutes, option A summarizes the steps to write the inequality.

First, the term "more than" means greater than which is represented by the inequality symbol, >.

So, let's assume that the inequality variable is x and given that the minute she waited for is more than 56.

Writing this together will give

x > 56.

Hence, from the list of given options, only option A gives the actual representation of the statement; while others are not

Answer:

The answer is A

Step-by-step explanation:

I took the test in edge and got it right! Hope this helps!

Answer:

11/12

Step-by-step explanation:

Find the common denominator.

4 and 3 both go into 12.

4 goes into twelve three times so multiply the denom and the num.

9/4 = 27/12

3 goes into twelve four times.

4/3 = 16/12

Subtract.

27/12-16/12

= 11/12

Answer: 11/12

Step-by-step explanation:

multiply 3 and 4 to get a common denominator.

multiply 3 by 9 and 4 by 4

this gets u 27/12 and 16/12

subtract.

11/12

Answer:

P represents the population in year 0

Step-by-step explanation:

The exponential growth function is f(x) = a (1 + r)^t, where a is the initial

amount (at t = 0), (1 + r) is the factor of growth , r is the rate of growth

in decimal ant is the time of growth

the function C(t) = P(1 + r)^t represents the population of

centerville at year t, where P is the initial population and r is the

rate of increase

If your investment is increased 10% annually, then that means

each year, your total has multiplied itself by 110% (the growth factor

is 1 + 10/100 = 1.1)

(1 + r) is the factor grows each year

C(t) = P(1 + r)^t

C depends on P(starting population) , r(the increasing rate and

t(the time in year)

r is the rate of increase means the percentage of increasing , then

0 < r < 1

r is not less than 0

P is the initial amount when t = 0

P represents the population in year 0

Answer:

P represents the population in year 0

Step-by-step explanation:

Answer:

Probability of getting a sample with 14% rebellious humans or more is 0.0104.

Step-by-step explanation:

We are given that an alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10%.

They abducted a random sample of 400 humans, performed special psychological tests, and found that 14% of the sample are rebellious.

Let p = population proportion rebellious humans

The z score probability distribution for sample proportion is given by;

                             Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat[/tex][tex]\hat p[/tex] = sample proportion rebellious humans = 14%

            n = sample of humans = 400

            p = population proportion rebellious humans = 10%

Now, probability of getting a sample with 14% rebellious humans or more is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 14%)

         P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.14) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.14-0.10}{\sqrt{\frac{0.14(1-0.14)}{400} } }[/tex] ) = P(Z [tex]\geq[/tex] 2.31)

                            = 1 - P(Z < 2.31) = 1 - 0.9896 = 0.0104

The above probability is calculated by looking at the value of x = 2.31 in the z table which has an area of 0.9896.

Hence, the required probability is 0.0104.

Answer:

It's 0.7% (make sure to include the % sign)

Step-by-step explanation:

Khan Academy

Answer:

No

Step-by-step explanation:

Since shape a has 32 squares

And shape b has 42

So b is bigger

Answer:

11.60740741

Step-by-step explanation:

Answer:

11.6074074074

Step-by-step explanation:

Answer:

You will have $2,814.20 after 7 years

Step-by-step explanation:

We are given that You invest $2,000 into a savings account that gets 5% interest compounded yearly.

Principal = $2000

Rate of interest = 5% =0.05

We are supposed to find How much money will you have after 7 years?

Formula : [tex]A = P(1+r)^t[/tex]

A= Amount

P = Principal

t =time

r = rate of interest in decimals

Substitute the values in the formula :

[tex]A = 2000(1+0.05)^7[/tex]

A=2814.20

So, Option A is true

Hence You will have $2,814.20 after 7 years