Complete the square of the quadratic equation x^2 - 2x - 35 = 0. What is the vertex of the equation?
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Answer:

The mean absolute deviation is: 7.44

Step-by-step explanation:

Given

[tex]Scores: 98, 78, 84, 75, 91[/tex]

Required

The mean absolute deviation

First, calculate the mean

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{98+78+84+75+91}{5}[/tex]

[tex]\bar x = \frac{426}{5}[/tex]

[tex]\bar x = 85.2[/tex]

The mean absolute deviation (M) is:

[tex]M = \frac{1}{n}\sum|x - \bar x|[/tex]

So, we have:

[tex]M = \frac{1}{5}(|98 - 85.2|+|78 - 85.2|+|84 - 85.2|+|75 - 85.2|+|91 - 85.2|)[/tex]

[tex]M = \frac{1}{5}(|12.8|+|-7.2|+|-1.2|+|-10.2|+|5.8|)[/tex]

Remove absolute brackets

[tex]M = \frac{1}{5}(12.8+7.2+1.2+10.2+5.8)[/tex]

[tex]M = \frac{1}{5}*37.2[/tex]

[tex]M = 7.44[/tex]

Answer:

1/3=33 1/3%

Step-by-step explanation:

Since there is 3 balls.

Answer:

Step-by-step explanation:

volume of cone v=1/3πr²h

volume of cylinder V=πr²h

V=3v

volume of cylinder=3×222=666 cubic cm.

Answer:

x = 30/7

Step-by-step explanation:

2/3x = − 1/2x + 5

multiply by 6 to clear the fractions

4x = -3x + 30

add 3x to both sides

7x = 30

Divide both sides by 7

x = 30/7

Answer:

Monthly payment = 241.925

Step-by-step explanation:

Effective interest rate is the actual interest paid at the end of the year AFTER compounding.  Most credit cards charge x% ("APR", annual percentage rate)annually.  Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.

Here, effective (annual) interest rate is 8%.  We need the monthly rate, i.

(1+i)^12 = 1.08

Solving, we have i = 0.6434% monthly approximately

To balance the deposits and withdrawals, we note that the last withdrawal is the beginning of year 19, and the last deposit is the last month of year 18.  We therefore conclude that the "future values" fall on the same day, and that they are equal.

We consider the annual deposits D (accumulated at the end of the year, and annual withdrawals W are in separate accounts.  By the end of the operations, one will balance the other (they are equal).

We will need the following formula to calculate future value F given the periodic amount, A, interest rate per period, i, and the number of periods.

F(A,i,n) = A*((1+i)^n-1)/i

Step 1:

calculate the future value of the withdrawals

A = W = 25000 (annual withdrawal)

i = 8% (effective annual interest)

n = 4 years (beginning of 16,17,18,and 19th years)

F(A,i,n) = A*((1+i)^n-1)/i

= 25000( (1+0.08)^4 - 1)/(0.08)

= 112652.80

This is also the total deposit after eighteen years.

Step 2:

calculate the future value of the annual deposits D

A = D (total of annual deposits)

i = 8% (effective annual interest)

n = 18 years

Future value of deposits

F(A,i,n) = A*((1+i)^n-1)/i

= D( (1+0.08)^18 -1 ) / 0.08

= 37.45024373981167D

Since this must equal the total withdrawal, we equate the two to calculate D.

37.45024373981167D=112652.80

and solve for D

D = 112652.80 / 37.45024373981167

= $3008.0659

Step 3

Calculate monthly deposit, X

Effective interest rate is the actual interest paid at the end of the year AFTER compounding.  Most credit cards charge x% ("APR", annual percentage rate)annually.  Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.

Here, effective (annual) interest rate is 8%.  We need the monthly rate, i.

(1+i)^12 = 1.08

The actual monthly interest rate is therefore

i = 1.08^(1/12)-1

Over a 12 month period, (one year), the monthly amount X to accumulate an annual amount D (=$3008.0659) is therefore given by

D = X*((1+i)^n-1)/i

3008.0659 = X*(1.08-1)/(1.08^(1/12)-1)

or the monthly amount

X = $3008.0659 / ( 1.08^(1/12)-1)

= 241.925 per month.

=

Given:

The equation is:

[tex]\sqrt{x+7}+5=x[/tex]

To find:

Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.

Solution:

We have,

[tex]\sqrt{x+7}+5=x[/tex]

Subtract 5 from both sides.

[tex]\sqrt{x+7}=x-5[/tex]

Taking square on both sides, we get

[tex]x+7=(x-5)^2[/tex]

[tex]x+7=x^2-10x+25[/tex]

[tex]0=x^2-10x+25-x-7[/tex]

[tex]0=x^2-11x+18[/tex]

Splitting the middle term, we get

[tex]x^2-2x-9x+18=0[/tex]

[tex]x(x-2)-9(x-2)=0[/tex]

[tex](x-2)(x-9)=0[/tex]

[tex]x=2,9[/tex]

Now, substitute [tex]x=2[/tex] in the given equation.

[tex]\sqrt{2+7}+5=2[/tex]

[tex]\sqrt{9}+5=2[/tex]

[tex]3+5=2[/tex]

[tex]8=2[/tex]

This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.

Substitute [tex]x=9[/tex] in the given equation.

[tex]\sqrt{9+7}+5=9[/tex]

[tex]\sqrt{16}+5=9[/tex]

[tex]4+5=9[/tex]

[tex]9=9[/tex]

This statement is true. So, 9 is a solution of given equation.

Therefore, 2 is an extraneous solution and 9 is a solution of given equation.

Answer:

B. $1650

Step-by-step explanation:

the middle share = 3/(2+3+5) × $5500

= 3/10 × $5500 = $1650

Answer:

c

Step-by-step explanation:

Answer:

x is greater than or equal to 3

So it is the first answer.

A. Zero

They're parallel so they will never intersect therefore: no solutions :]

Answer: In attached

Step-by-step explanation:

Use the given functions to set up and simplify

Attachment has your answer.

I’m not good at typing functions on this app so this image is all I could give.

Answer:

there you go..........

Step-by-step explanation:

x' = ⅓ x => x = 3x'

f'(x) = 7(3x')+1

= 21x' + 1

so g(x) = 21x + 1

Answer:

h = 24.25 feet

Step-by-step explanation:

Xavier shoots a basketball in which the height, in feet, is modeled by the equation.

[tex]h(t) = -4t^2+10t +18[/tex] ....(1)

For maximum height,

Put dh/dt=0

So,

[tex]\dfrac{dh}{dt}=\dfrac{d}{dt}(-4t^2+10t +18)\\\\=-8t+10[/tex]

So,

-8t = -10

t =1.25s

Put t = 1.25 s in equation (1)

[tex]h(t) = -4(1.25)^2+10(1.25) +18\\\\=24.25\ feet[/tex]

So, the maximum height of the basketball is equal to 24.25 feet.

Answer:

Step-by-step explanation:

Using the pythagorean theorem, a^2+b^2=c^2

32/2=16, 20 would be the hypotenuse, so it would be 20^2-16^2=a^2 because we want to find the middle line. 400-256=144. sqrt(144) = 12.

Then since it is an isosceles triangle, we can simply do 12*16=192

The answer for 7 is 192ft^2

For #8, the answer is short leg * sqrt(3) = long leg

On another note, you can find the hypotenuse of a 30-60-90 triangle by doubling the shortest leg

Answer:

13π m

Step-by-step explanation:

circumference of a circle = 2πr

=2*π*6.5

=13π m

Answer:

13[tex]\pi[/tex] m

Step-by-step explanation:

The formula for circumference is 2r[tex]\pi[/tex], so...

2r[tex]\pi[/tex]

2(6.5)[tex]\pi[/tex]

=13[tex]\pi[/tex]

Answer:

Step-by-step explanation:

angle 2 is 75 degree because angle 2 and 75 dgeree are corresponding angles corresponding angles are always equal.

angle 1 + angle 2 = 180 degree (being linear pair)

angle 1 = 180 - 75

angle 1 = 105 degree

∠1 = 105° and ∠2 = 75°

"These are the lines in the same plane that are at equal distance from each other and never meet."

"It is a line that passes through two lines in the same plane at two distinct points."

"The angles which are formed in matching corners or corresponding corners with the transversal when the transversal intersects two parallel lines."

For given question,

Line c and line d are parallel lines.

These parallel lines are intersected by a transversal.

We can observe that ∠2 and the angle that measures 75° are corresponding angles.

We know that the corresponding angles are congruent.

⇒ ∠2 = 75°

Also, the sum of all angles on either side of the line is 180°

⇒ ∠1 + ∠2 = 180°

⇒ ∠1 + 75° = 180°

⇒ ∠1 = 105°

Therefore, ∠1 = 105° and ∠2 = 75°

Learn more about parallel lines and transversal here:

https://brainly.com/question/17432060

#SPJ3

Answer:

y minus 9 = negative 2 (x + 1)

Step-by-step explanation:

i put it onto desnos graphing calculater and thats what i got

Answer:

A

Step-by-step explanation:

bannana

Answer:

ok so for g times h you would have to foil it and then you would multiply it by f of X

Answer:

5

just took the test

Answer:

Step-by-step explanation:

its 5

Answer:

184 m²

Step-by-step explanation:

Surface Area = 2(10*2) + 2(10*6) + 2(2*6)

Surface Area = 2(20 + 60 + 12)

Surface Area = 2(92)

Surface Area = 184 m²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

20:1

Step-by-step explanation:

every 20 dollar she spends she save 1 dollar

Answer:

Not possible to answer.

Answer:

It depends if there is tax or not, if there isn't she can buy 8 of them.

Step-by-step explanation:

$17 is the total so we need to see how many $2 fit in $17.

8×2=16, and 16 is the closest number we can get to.

Answer:

i hatee maths thank u

Step-by-step explanation:

Answer:

1/3, the information with the blouses is there to distract you

Answer:

For 5 the yellow square stays the same, while the blue adds 2 each time.

5. 1(2x) something like that.

6. 3 is 6 4 is 7 5 is 8

I have gotten too old for this, my bad somethings just dont make sense anymore.

Answer:

5.

a. 2 blue blocks added

b. 2 blue blocks are added on the top blue blocks

c.y = 2x +3

6.

a.

1,4

2,5

3,6

4,7

5,8

b. starting off with 4 triangles and ending with a bottom triangle a triangle is added first from the top, then the bottom for each increase (increment)

c. y = x+4

Step-by-step explanation:

all the answers are up

Answer:

16

Step-by-step explanation:

4+8/2*(6-3) = 4+8/2*3 = 4+4*3 = 4+12 =16

Answer:

18

Step-by-step explanation:

4+8 /2 *(6-3)

=4+8/2 * 3

=(4+8)*3/2

=12*3/2

=36/2

=18

Answer: hello your question has some missing data attached below is the missing data

answer:

The second scatter plot

Step-by-step explanation:

The scatter plot that matched the data is the second scatter plot while the first scatter plot wrongly represents the data because values of the Iron not present in the data is also represented in the scatter plot and also some values present in the data table is also missing in the First scatter plot

Answer:

Hello, I am currently doing the same assignment and the brothers scatter plot would be wrong.

Step-by-step explanation:

If you do not believe me then check and see how the table says the iron used were 2, 3, 4, 5, 6, 7, 8, and 9 but in the brothers scatter plot it is shown to have the irons down as 1, 2, 3, 4, 5, 6, 7, and 8.

(in other words the other person who answered is correct)