8 times the sum of a and b

Answer:

Step-by-step explanation:

The function is f(x)=x^2 + ax + b

Derivate the function:

● f'(x)= 2x + a

Solve the equation f'(x)=0 to find a

The minimum is at (3,9)

Replace x with 9

● 0 = 2×3 + a

● 0 = 6 + a

● a = -6

So the value of a is -6

Hence the equation is x^2 -6x+b

We have a khown point at (3,9)

● 9 = 3^2 -6×3 +b

● 9 = 9 -18 + b

● 9 = -9 +b

● b = 18

So the equation is x^2-6x+18

Verify by graphing the function.

The vetex is (3,9) and it is a minimum so the equation is right

Answer:

Surface area of a cone = 461.58 In²

Step-by-step explanation:

Surface area of a cone = πrl + or

Surface area of a cone = πr(r+l)

Where r = radius

Radius= diameter/2

Radius=14/2

Radius= 7 inch

And l slant height= 14 inch

Surface area of a cone = πr(r+l)

Surface area of a cone = π*7(7+14)

Surface area of a cone = 7π(21)

Surface area of a cone = 147π

Surface area of a cone = 461.58 In²

Answer:

[tex]x=70[/tex]

Step-by-step explanation:

If we know that the LCM of 10, 14 and x will be 70, that means x has to be a factor of 70.

First, let's find the multiples of 10 and 14 until they equal 70.

[tex]10: 10,20,30,40,50,60,70[/tex]

[tex]14:14,28,42,56,70[/tex]

Since we're asking for the greatest value of x, that means that x has to be smaller or equal to than 70 but still large enough to be the greatest.

Hey, isn't 70 a factor of 70? The remainder gets to 1 which is a whole number, so 70 is a multiple of 70.

So, [tex]x = 70[/tex].

Hope this helped!

Answer:

x = 35

Step-by-step explanation:

70 factored is 2 x 5 x 7

x  = 35

Answer:

Step-by-step explanation:

7x - 21 + 12 - 3x = -8

4x - 9 = -8

4x = 1

x = 1/4

Answer:

x= 0.25, or x=1/4

Step-by-step explanation:

First, use the distributive property and multiply 7 within the parenthesis:

7x -21

Next, use the distributive property again, and multiply 3 within the parenthesis:

12 -3x

Combine Like terms: 7x - 21 + 12 - 3x

4x - 9

Add 9 to both sides: 4x - 9 = -8

-8 + 9 = 1

Divide 4 by both sides: 4x = 1

1 / 4 = .25 or 1/4

Answer:

The height of the flag pole is approximately 19 feet and 2 inches.

Step-by-step explanation:

Let suppose that length of the shadow of the object is directly proportional to its height. Hence:

[tex]l \propto h[/tex]

[tex]l = k\cdot h[/tex]

Where:

[tex]h[/tex] - Height of the object, measured in inches.

[tex]l[/tex] - Shadow length of the object, measured in inches.

[tex]k[/tex] - Proportionality constant, dimensionless.

Now, let is find the value of the proportionality constant: ([tex]h = 5\,\frac{1}{4} \,ft[/tex] and [tex]l = 2\,ft\,\,10\,\frac{1}{2}\,in[/tex])

[tex]h = \frac{21}{4}\,ft[/tex]

[tex]h = \left(\frac{21}{4}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)[/tex]

[tex]h = 63\,in[/tex]

[tex]l = (2\,ft)\cdot \left(12\,\frac{in}{ft} \right) + \frac{21}{2}\,in[/tex]

[tex]l = 24\,in + \frac{21}{2}\,in[/tex]

[tex]l = \frac{48}{2}\,in+\frac{21}{2}\,in[/tex]

[tex]l = \frac{69}{2}\,in[/tex]

Then,

[tex]k = \frac{l}{h}[/tex]

[tex]k = \frac{\frac{69}{2}\,in }{63\,in}[/tex]

[tex]k = \frac{69}{126}[/tex]

[tex]k = \frac{23}{42}[/tex]

The equation is represented by [tex]l = \frac{23}{42}\cdot h[/tex]. If [tex]l = 10\,\frac{1}{2}\,ft[/tex], then:

[tex]l = \frac{21}{2}\,ft[/tex]

[tex]l = \left(\frac{21}{2}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)[/tex]

[tex]l = 126\,in[/tex]

The height of the flag pole is: ([tex]l = 126\,in[/tex], [tex]k = \frac{23}{42}[/tex])

[tex]h = \frac{l}{k}[/tex]

[tex]h = \frac{126\,in}{\frac{23}{42} }[/tex]

[tex]h = \frac{5292}{23}\,in[/tex]

[tex]h = 230\,\frac{2}{23}\,in[/tex]

[tex]h = \frac{115}{6}\,ft\,\frac{2}{23}\,in[/tex]

[tex]h = 19\,\frac{1}{6}\,ft \,\frac{2}{23}\,in[/tex]

[tex]h = 19\,ft\,\,2\,\frac{2}{23}\,in[/tex]

[tex]h = 19\,ft\,\,2\,in[/tex]

The height of the flag pole is approximately 19 feet and 2 inches.

Answer:

12 mangoes

Step-by-step explanation:

Two types of boxes contains mangoes

The larger box contain 4 mangoes than the number of mangoes that is present in 8 smaller box

Each of the box have a total of 100 mangoes

Let y represent the number of mangoes that is present in the smaller box

Therefore, the number of mangoes in the smaller box can be calculated as follows

8y + 4= 100

Collect the like terms

8y= 100-4

8y= 96

Divide both sides by the coefficient of y which is 8

8y/8= 96/8

y= 12

Hence the number of mangoes that is present in the smaller box is 12

Answer:

A.

Step-by-step explanation:

I used a graphing calculator to check

Answer:

A

f(x)=(x+2)/(x+1)

Answer:

a = x

b = 5

Step-by-step explanation:

for the polynomial x² + 10x + 25, b = 5 and a = x.

In the polynomial x² + 10x + 25, we can observe that the first term, x², is the square of x, and the last term, 25, is the square of 5. This suggests that the polynomial follows the perfect square trinomial identity.

The middle term, 10x, can be rewritten as 2ab, where a represents x and b represents a term that when squared equals the last term, 25.

In this case, b = 5, because 5² = 25.

To find a, we can take the square root of the first term, x². The square root of x² is x, so a = x.

Therefore, for the polynomial x² + 10x + 25, b = 5 and a = x.

Learn more about trinomial identity here

https://brainly.com/question/17033454

#SPJ2

Answer:75

Step-by-step explanation:54+21

Answer:

15 bicycles, 6 skateboards

Step-by-step explanation:

We are looking for the number of skateboards and the number of bicycles. Those two numbers are our unknowns.

We define variables for those two numbers.

Let s = number of skateboards.

Let b = number of bicycles.

A skateboard has 4 wheels. s number of skateboards have 4s wheels.

A bicycle has 2 wheels. b bicycles have 2b wheels.

The total number of wheels is 4s + 2b.

The total number of wheels is 54, so our first equation is

4s + 2b = 54

The total number of skateboards and bicycles combined is s + b.

We are told the total number of skateboards and bicycles combined is 21.

The second equation is

s + b = 21

We have a system of two equations in two unknowns.

4s + 2b = 54

s + b = 21

We can solve it by the elimination method.

Rewrite the first equation below.

Multiply both sides of the second equation by 2 and write it below that. Then add the equations.

          4s + 2b = 54

(+)      -2s - 2b = -42

-----------------------------

          2s         = 12

s = 6

There are 6 skateboards.

Now we substitute 6 for s in the second original equation and solve for b.

s + b = 21

6 + b = 21

b = 15

There are 15 bicycles.

Answer: 15 bicycles, 6 skateboards

Answer:

6x

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

Answer:

m=48

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

m = 48

▹ Step-by-Step Explanation

Rewrite:

m/8 = 6

Use the inverse operation:

8 * 6 = 48

m = 48

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

8

Step-by-step explanation:

In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.

The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:

[tex]56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3[/tex]·[tex]7[/tex]

[tex]72=(24)(3)=8(3)(3)=2^3[/tex]·[tex]3^2[/tex]

Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the [tex]2^3[/tex].

Thus, [tex]2^3=8[/tex] is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.

Answer: Yes, Substitution property is the correct option.

Step-by-step explanation:

Given: m∠A+m∠B =70° ...(i),  m∠X=m∠A

Then, substitute m∠X for m∠A in (i) , we get

m∠X+m∠B =70°

So, the correct option is "Substitution property"

Answer:

40°

Step-by-step explanation:

The circumference of a circle is equal to 360°

The arc AB is 180°, the arc AC is given as 100° so the arc CB is 80° and since <A is an inscribed angle it is equal to the half of the arc it sees

80 ÷ 2 = 40

Answer:

C!

Step-by-step explanation:

Answer:

The correct option is;

D. 65% to 74%

Step-by-step explanation:

The accuracy of a forecast given based on a percentage or proportion or likelihood is determined by the based on the prevalence of the forecast in a similar proportion over the range of data points in which the forecast is made

Therefore, if it actually rained on 70% of those days for which the forecast was made, the forecast can be said to be very accurate.

Which is to say that the forecast of 70% chance of rain can be considered very accurate if it rained on 65 to 74% of those days which is in the range of the forecasted 70%.

Answer:

I hope it helps.

The solutions in photo ^_^

6:40 or 6 hour 40 minutes,

if you go back(subtract) 1 hour and 40 minutes

i.e. 6hours 40 minutes- 1 hour 40 minutes

subtract minutes from minutes and hours from hours,

5:00

note that here the minutes value is not negative so it was not a problem, what If it was 6:40-1:50?

Answer:

[tex]\huge\boxed{77}[/tex]

Step-by-step explanation:

The number can be divisible by 7.

The multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77,84 and so on

Finding the factors for all of the multiples of 7:

7 => 1,7   [Not 4 factors]

14 => 1,2,7,14    [4 factors but Sum = 24]

21 => 1,3,7,21   [4 factors but Sum = 32]

28 => 1, 2, 4, 7, 14, 28    [Not 4]

35 => 1,5,7,35   [4 factors but Sum = 48]

42 => 1, 2, 3, 6, 7, 14, 21, 42     [Not 4]

49 => 1,7,49   [Not 4]

56 => 1, 2, 4, 7, 8, 14, 28, 56       [Not 4]

63 => 1, 3, 7, 9, 21, 63     [Not 4]

70 => 1, 2, 5, 7, 10, 14, 35, 70    [Not 4]

77 => 1, 7, 11, 77     [4 factors and Sum = 96]

Answer:

77

Step-by-step explanation:

The first factor is 1

Since it is divisible by 7, 7 will also be one of its factors.

Therefore the four factors are

1, 7, x, y

When x and y are integers

Using the following law...

The product of factors of a number in the same position (left or right) (increasing or decreasing order) is equal to the number

Counting from left

y is the first factor

x is the second factor

Counting from the right

1 is the first factor

7 is the second factor

Applying the last

y×1=x×7

y = 7x

the sum of the factors is 96

1+7+x+7x = 96

8x+8=96

8x = 88

x= 11

Hence the number is

7x = 7(11)

=77

Answer:

5 -3 = 2

3-5 = -2

Step-by-step explanation:

In this question, we want to examine the validity of the statement by the use of an example.

Firstly, we need to understand the meaning of the fact that they are ‘closed’

By saying these numbers are closed under this arithmetic operation i.e subtraction, we directly mean that they obey the closure property.

Now, to obey the closure property means that if we move either way i.e by switching the numbers and performing the same arithmetic operation of subtraction, we are supposed to get same answer.

What this means in terms of examples is as follows;

Consider two positive numbers, 5 and 3

Now we know that 5-3 = 2

To check if the closure property is obeyed, switch the place of the numbers.

This means we would have;

3-5 = -2

We can see that both results are not the same. We can then conclude that the arithmetic operation of subtraction is not closed or does not obey the closure property for positive numbers.

Answer:

4/20

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

The probability of landing on tails for any fair coin is [tex]\frac{1}{2}[/tex], or 50%. It doesn't matter how many times you've landed on heads/tails before, it always remains at [tex]\frac{1}{2}[/tex].

Hope this helped!

Answer:

2/3

Step-by-step explanation:

Hey there!

Well in the equation,

y = 2/3x - 3

the slope is 2/3 because the equation shows 2/3x and wherever the x is in slope intercept that the slope.

Hope this helps :)

Answer:

-3x + y = 8.

3y = 9x.

Step-by-step explanation:

To find the slope of the lines we convert to slope-intercept form, which is

y = mx + c   (m is the slope.)

The slope of y = 3x + 5 is therefore 3.

Parallel lines have the same slope.

Finding the slope of the given lines:

-3x + y = 8

y = 3x + 8  - slope is 3 so this is parallel to  y = 3x + 5.

3y = 9x

Divide through by 3:

y = 3x  - so this is also parallel to 3x + 5.

y = -jx  The slope is -j so it is not parallel.

16x + 2y = 12

2y = -16x + 12

y = -8x + 6  - Not parallel.

Answer:

B, C, A.

Step-by-step explanation:

A = C + 3A = C + 3

A = C + 3

A = C + 3A

C + 3A = C + 3

3A = 3

A = 1

A = C + 3

1 = C + 3

C + 3 = 1

C = -2

B = 2C

B = 2(-2)

B = -4.

So, from least to greatest, B = -4, C = -2, and A = 1.

Hope this helps!

Answer: 180x5y2

Hope this helps!

Answer:

[tex]180x^5y^2[/tex]

Step-by-step explanation:

[tex]5x^3y^4(6xy^-^1)^2\\5x^3y^4(6^2x^2y^-^1^(^2^))\\5x^3y^4(36x^2y^-^2)\\180x^5y^2[/tex]

Answer:

[tex]Net\ Change = \$13997.53[/tex]

Step-by-step explanation:

Given

[tex]Debt = \$15,234.68[/tex]

[tex]Monthly\ Payment= \$247.43[/tex]

[tex]Duration = 5\ months[/tex]

Required

Determine the net change

First, we need to determine the total repaid amount;

[tex]Amount = Monthly\ Payment * Duration[/tex]

Substitute values for Monthly Payment and Duration

[tex]Amount = \$247.43 * 5[/tex]

[tex]Amount = \$1237.15[/tex]

The net change is the difference between the loan amount and the repaid amount

[tex]Net\ Change = Loan\ Amount - Repaid\ Amount[/tex]

[tex]Net\ Change = \$15,234.68 - \$1237.15[/tex]

[tex]Net\ Change = \$13997.53[/tex]

Hence, the net change over the period of 5 months is $13997.53

Answer: Quiana's initial loan amount is -15, 234.68. This is the total amount of money she must pay back to the lender.

Answer:

two games must be won by the team

Step-by-step explanation:

Let the no. of games played by x, since  team

does not lose any more games.

Then total game won = 6+x

total game lost = 4

win: loss = 6+x : 4

given ratio of win and loss = 2:1

6+x : 4 = 2: 1

6+x = 8

=> x = 8-6 = 2

Thus, two games must be won by the team

then total win will be = 6+2 = 8

and loss = 4

ration of win : loss = 8:4 = 2:1

Answer: The frog fell asleep for 4 nights.

Step-by-step explanation: First, he climbs up 3m every night. there are 16 nights before he gets to 29m. He has not climbed up for the 16th day so 15*3= 45. 45-29= 16. 16/4=4. The frog slept for 4 nights.

Answer:

Step-by-step explanation:

[tex]Midpoint = (3,-2)\\1st \: endpoint = (1,6)\\2nd \: endpoint = ?\\\\\\Let \: (1,6) \:be \:x_1y_1\\Let\:(3,-2)\: be\:x\:and\:y\\\\x=(x_1+x_2)/2\\y=\frac{(y_1+y_2)}{2} \\\\3 =\frac{1+x_2}{2} \\\\3\times 2 =1+x_2\\\\6 = 1+x_2\\6-1=x_2\\\\x_2 =5\\\\y=\frac{(y_1+y_2)}{2} \\-2 = \frac{6+y_2}{2}\\\\ -2 \times 2= 6+y_2\\\\-4 = 6+y_2\\\\-4-6=y_2\\\\y_2 = -10\\\\Answer = (5 ,-10)[/tex]

Answer:

b

Step-by-step explanation:

In general

Given

y = f(x) then y = f(Cx) is a horizontal stretch/ compression in the x- direction

• If C > 1 then compression

• If 0 < C < 1 then stretch

Consider corresponding points on the 2 graphs

(2, 2 ) → (4, 2 )

(4, - 2 ) → (8, - 2 )

Indicating a stretch in the x- direction.

y = f([tex]\frac{x}{2}[/tex] ) with C = [tex]\frac{1}{2}[/tex] , that is 0 < C < 1

stretches the graph in the x- direction by a factor of 2

Thus

y = f([tex]\frac{x}{2}[/tex] ) → b