Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ(x) = 2x2 + 4x – 16 C ƒ(x) = x2 – 2x – 8 D ƒ(x) = 2x2 – 4x – 16

Answer:

see below

Step-by-step explanation:

First we need to find the slope

m = ( y2-y1)/ ( x2-x1)

   = (60-64)/( 10-0)

   = -6/10

   = -2/5

The y intercept is (0,64)

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = -2/5 x + 64  where y is in the thousands of feet

m = -2/5 * 1000 = -400 ft / minute

The height decreases since the sign is negative

The height decreases 400 ft per minute

The y intercept is (0,64)

64 is in the thousands of ft

64*1000 = 64,000 ft

When it starts, it is at 64,000 ft

The descent starts at a cruising altitude of 64,000 ft

Answer:

Question 1: the angle of y is the same as 49 degrees.

So, y = 49 degrees.

y + x = straight line

=> Straight line = 180 degrees

=> 49 + x = 180

=> 49 - 49 + x = 180 - 49

=> x = 131

Answer to Question 1:

x = 131 degrees

y = 49 degrees

Question 2: Angle x is  the same as 119 degrees

x + y = straight line

=> Straight line = 180 degrees

=> 119 + y = 180

=> 119 - 119 + y = 180 - 119

=> y = 61

y + z = straight line

=> Straight line = 180 degrees

=> 61 + z = 180

=> 61 - 61 + z = 180 - 61

=> z = 119

Answer to Question 2:

x = 119 degrees

y = 61 degrees

z = 119 degrees

Answer:

Step-by-step explanation:

Let the missing number be 'x'

⇒[tex] \mathsf{15 + 9 = x(5 + 3)}[/tex]

Distribute x through the parentheses

⇒[tex] \mathsf{15 + 9 = 5x + 3x}[/tex]

Swap the sides of the equation

⇒[tex] \mathsf{5x + 3x = 15 + 9}[/tex]

Add the numbers

⇒[tex] \mathsf{5x + 3x = 24}[/tex]

Collect like terms

⇒[tex] \mathsf{8x = 24}[/tex]

Divide both sides of the equation by 8

⇒[tex] \mathsf{ \frac{8x}{8} = \frac{24}{8} }[/tex]

Calculate

⇒[tex] \mathsf{x = 3}[/tex]

Hope I helped!

Best regards!

Answer:

The price for 4 people is 52 dollars.

4 × (5.75 + 7.25) = 52

The total cost including drink and popcorn is $52 according to a given condition.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Cost of movie ticket =  $7.25/person

Cost of popcorn and drink =  $5.75/person

Total cost per person = 5.75 + 7.25 = $13

Now,

Number of people = 4

So,

4(5.75 + 7.25) = 4(13) = $52

Hence "The total cost including drink and popcorn is $52 according to a given condition".

For more about the equation,

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Answer:

[tex]\large \boxed{\mathrm{-3w + 5(2w + 1)}}[/tex]

Step-by-step explanation:

-2w + 3 + 5w - 2

Combine like terms.

3w + 1

-3w + 5(2w + 1)

Expand brackets.

-3w + 10w + 5

Combine like terms.

7w + 5

Answer:

The answer is C.

-3w +5(2w +1)

Step-by-step explanation:

Answer: a = 9, b = 48, c = -1

Step-by-step explanation:

"a" represents the points you receive if an Ace is picked.  It is given that you get 9 points ----> a = 9

"b" represents the number of cards that are Not an Ace.  4 cards in the deck are Aces so 52 - 4 = 48 cards are Not an Ace -----> b = 48

"c" represents the points you receive if Not an Ace is picked.  It is given that you lose 1 point ----> c = -1

Answer:

Here is the rest of the page

Step-by-step explanation:

Answer:

36.53 cm²

Step-by-step explanation:

Picture this repeated four times to make a circle.  The circle would have a radius of 8. [tex]\pi[/tex]r² would give us 201.06.  One quarter of that would be 50.265.

The area of the square is length times width, or 8X8=64.  

64-50.265=13.735.  That would be ONE of the non shaded sections of the square.  If you take that away twice, the leftover part would be the shaded area.

64-13.735-13.735=36.53 cm²

Hello There!!

I'm not a 100% sure this right.

Step-by-step explanation:

f(x)=ax2+bx+c for which f(1)=0, f(-2)=6 and f(2)=-14

0 = a +b +c

6 =4a -2b +c

-14=4a+2b +c

subtract third equation from second to get

20 = -4b and so b=-5

first equation is now 5 = a+c

second is now -4=4a+c

subtract to get -9=3a and so a=-3

equation one now is 0=-3-5+c or c=8 Hope This Helps!!

Step-by-step explanation:

for finding the weight of 12 boxes multiply 12 with the weight of first box and then you will get your answer. Tell me the answer which you found and if it will be correct I will say ok if not I will give you the correct answer

The Answer is:

B.) Plan B

The right plan for Him is Plan B which is; Raise the price by 10 percent each week until the price reaches $8.00.

We have Bagel Emporium sells a dozen bagels for $5.00.

A plan should be kind of an arrange that is done as a parts of any given idea or layout.

We conclude that the right plan result in the price of the bagels reaching  $8.00.  fastest is Plan B that is Raise the price by 10 percent each week until the price reaches $8.00 as it doubles the rate as the percentage is increased.

The correct plan is B.

Learn more about plan from;

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Step-by-step explanation:

f(x) = x² - 5x - 9

To solve both expressions first find f( -4) and f(5)

For f(- 4)

Substitute the value of x that's - 4 into the expression

That's

f(-4) = (-4)² - 5(-4) - 9

= 16 + 20 - 9

= 36 - 9

For f(-5)

Substitute 5 into f (x)

That's

f(5) = 5² - 5(5) - 9

= 25 - 25 - 9

Hope this helps you

Answer:

height of the candle after 6 hours= 18.6 centimeters

Step-by-step explanation:

the function gives a line with a slope of −0.4.

the height of the candle after 11 hours is 16.6 centimeters.

after 6 hours, the height will be

But slope= y2-y1/x2-x1

Y2 is the unknown

Y1 = 16.6

X1= 11 hours

X2= 6 hours

y2-y1/x2-x1= -0.4

(Y2-16.6)/(6-11)= -0.4

(Y2-16.6)/(-5)= -0.4

(Y2-16.6)= -5( -0.4)

(Y2-16.6)= 2

Y2 = 2+16.6

Y2 = 18.6 centimeters

height of the candle after 6 hours= 18.6 centimeters

Answer:

infinite number of solutions

Step-by-step explanation:

A dependent system is where the two equations are the same line has has an infinite number of solutions

Answer:

[tex]\boxed{\sf D) \ an\ infinite \ number \ of \ solutions}[/tex]

Step-by-step explanation:

A dependent system of equations has an infinite number of solutions.

When you graph the system of equations, both the equations represent the same line and have an infinite number of solutions.

Answer:

F = 585844 N

Step-by-step explanation:

Given that:

A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface.

The objective of this question is to express the hydrostatic force against one side of the plate as an integral and evaluate it.

To start with the equation of a circle:  a² + b² = r²

The equation of  circle with radius r = 7 can be expressed as:

a² + b² = 7²

a² + b² = 49

b² = 49 - a²

b = [tex]\sqrt{49 -a}[/tex]

NOW;

The integral of the hydrostatic force with a semicircular plate with radius 7 m and the top is 3 m above the surface can be calculated as follows:

[tex]\mathtt{F = 2 \rho g \int \limits^7_3 (a -3) \sqrt{49 -y^2} \ \ da}[/tex]

[tex]\mathtt{F = 2 \rho g \begin {pmatrix}\dfrac{\sqrt{49 -a^2} \ (2a^2-9a - 98)-(441 \times sin^{-1} (\dfrac{a}{3})) }{6} \end{pmatrix}}[/tex]

where;

density of water is 1000 kg/m3

and acceleration due to gravity is 9.8 m/s

Solving the integral; we have:

F = 2 ×  1000 kg/m³ × 9.8 m/s × (29.89)

F = 585844 N

given: [tex] Ac=\frac{vt2}r \quad vt=2 \quad r=2[/tex]

$\therefore Ac=\frac{(2)2}{2}=2$

Answer:

0.801

Step-by-step explanation:

Answer:

0.801

Step-by-step explanation:

801/1000 = 0.801

Answer:

0.000014

Step-by-step explanation:

The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:

City X's Population by Age

0-24 years old 33%

25-44 years old 22%

45-64 years old 21%

65 or older 24%

In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:

P(A and B) = P(A) * P(B)

probability that the first 2 are 65 or older

Let A be the event that the first 2 are 65 or older

The probability of 65 or older 24% i.e. 0.24

So the probability that first 2 are 65 or older is:

0.24(select resident 1) * 0.24(select resident 2)

P(A) = 0.24 * 0.24

       = 0.0576

P(A) = 0.0576

probability that the next 3 are 25-44 years old

Let B be the event that the next 3 are 25-44 years old

25-44 years old 22%  i.e. 0.22

So the probability that the next 3 are 25-44 years old is:

0.22 * 0.22* 0.22

P(B) = 0.22 * 0.22 * 0.22

      = 0.010648

P(B) = 0.010648

probability that next 2 are 24 or younger

Let C be the event that the next 2 are 24 or younger

0-24 years old 33% i.e. 0.33

So the probability that the next 2 are 24 or younger is:

0.33 * 0.33

P(C) = 0.33 * 0.33

       = 0.1089

P(C) = 0.1089

probability that last is 45-64 years old

Let D be the event that last is 45-64 years old

45-64 years old 21%  i.e. 0.21

So the probability that last is 45-64 years old is:

0.21

P(D) = 0.21

So probability of these independent events is computed as:

P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)

                                        = 0.0576 * 0.010648  * 0.1089  * 0.21

                                        = 0.000014

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Answer:

x = -19

Step-by-step explanation:

13x + 14 = 12x - 5

subtract 12x from both sides

x + 14 = -5

subtract 14 from both sides

x = -19

Answer:

x= -19

Step-by-step explanation:

13x+14=12x−5

Subtract 12x from both sides.

13x+14−12x=−5

Combine 13x and −12x to get x.

x+14=−5

Subtract 14 from both sides.

x=−5−14

Subtract 14 from −5 to get −19

x=−19

The line cuts the X axis at [tex]x=3[/tex] and is parallel to the Y axis.

Thus the equation of the line is $\boxed{x=3}$

Answer:

The equation of the line is x = 3.

Step-by-step explanation:

When a line is parallel to the y-axis, its gradient will be undefined. There is no y-intercept and the line touches x-axis so the equation is x = 3.

Answer:

x = 6

Step-by-step explanation:

∠ DBC + ∠ ABC = ∠ ABD , substitute values

5x - 4 + 8x - 3 = 79

13x + 1 = 79 ( subtract 1 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

Answer:

The answer is 18 feet

Step-by-step explanation:

To find the diameter of a circle given it's radius we use the formula

diameter = radius × 2

From the question

radius = 8

So the diameter is

Hope this helps you

Answer:

18

Step-by-step explanation:

Hey there!

Well radius is half the diameter so,

D = r*2

Plug in 9

D = 9*2

D = 18

Hope this helps :)

Answer:

C

Step-by-step explanation:

So we already know that:

[tex]2^x=30[/tex]

And we want to find the value of:

[tex]2^{x+3}[/tex]

So, what you want to do here is to separate the exponents. Recall the properties of exponents, where:

[tex]x^2\cdot x^3=x^{2+3}=x^5[/tex]

We can do the reverse of this. In other words:

[tex]2^{x+3}=2^x\cdot 2^3[/tex]

If we multiply it back together, we can check that this statement is true.

Thus, go back to the original equation and multiply both sides by 2^3:

[tex]2^x(2^3)=30(2^3)\\[/tex]

Combine the left and multiply out the right. 2^3 is 8:

[tex]2^{x+3}=30(8)\\2^{x+3}=240[/tex]

The answer is C.

Answer:

the answer is c

Step-by-step explanation:

Answer:

7.88 or 7.9

Step-by-step explanation:

To find the mean, we need to do:

=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9

=> 71/9

=> 7.88 or 7.9

I divided the sum of all numbers by 9 because we added 9 numbers.

Answer:

Three fractions that are equivalent to [tex]\frac{3}{11}[/tex] are: [tex]\frac{6}{22}[/tex], [tex]\frac{24}{88}[/tex] and [tex]\frac{144}{528}[/tex].

Step-by-step explanation:

Equivalent fractions are set of fractions in which when simplified, they have the same answer.

Given: [tex]\frac{3}{11}[/tex]

i. multiply the numerator and denominator of [tex]\frac{3}{11}[/tex] by 2,

          = [tex]\frac{3*2}{11*2}[/tex] = [tex]\frac{6}{22}[/tex]

i. multiply both the numerator and denominator of [tex]\frac{6}{22}[/tex] by 4,

          = [tex]\frac{6*4}{22*4}[/tex]= [tex]\frac{24}{88}[/tex]

ii. multiply the numerator and denominator of [tex]\frac{24}{88}[/tex] by 6,

          = [tex]\frac{24*6}{88*6}[/tex] = [tex]\frac{144}{528}[/tex]

So that;

             [tex]\frac{3}{11}[/tex] = [tex]\frac{6}{22}[/tex] = [tex]\frac{24}{88}[/tex] = [tex]\frac{144}{528}[/tex].

Three fractions that are equivalent to [tex]\frac{3}{11}[/tex] are: [tex]\frac{6}{22}[/tex], [tex]\frac{24}{88}[/tex] and [tex]\frac{144}{528}[/tex].

Step-by-step explanation:

C = Amount (A) - Principal (P)

Where

C is the compound interest

To find the amount we use the formula

[tex]A = P ({1 + \frac{r}{100} })^{n} [/tex]

where

P is the principal

r is the rate

n is the period / time

From the question

P = Rs 12, 000

r = 5%

n = 3 years

Substitute the values into the above formula

That's

[tex]A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} [/tex]

We have the answer as

Compound interest = 13891.50 - 12000

Hope this helps you

Answer: [tex]\dfrac{8}{\pi}[/tex] .

Step-by-step explanation:

We know that the rate of change of function f(x) from x=a to x= b is given by :-

[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given points on graph  :  (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4).

The rate of change from x = 0 to x = pi over 2 will be :-

[tex]\dfrac{0-(-4)}{\dfrac{\pi}{2}-0}=\dfrac{4}{\dfrac{\pi}{2}}[/tex]     [By using points (0, -4) and (pi over 2, 0) ]

[tex]=\dfrac{8}{\pi}[/tex]

Hence, the rate of change from x = 0 to x = pi over 2 is [tex]\dfrac{8}{\pi}[/tex] .

Answer:

x = 3

Step-by-step explanation:

-40 = -8 (x + 2)

-8 (x + 2) = -40   --- divide both sides by - 8

-8 (x + 2)           -40

--------------   =   ----------

      -8                  -8

x + 2 = 5    --- subtract 2 from both sides

x + 2 - 2 = 5 - 2   then simplify

x = 3

Answer:

x=3

Step-by-step explanation:

First, write out the equation as you have been given it:

[tex]-40=-8(x+2)[/tex]

Then distribute the -8 to the terms inside the parenthesis:

[tex]-40=-8x-16[/tex]

Next, add 16 to both sides:

[tex]-40+16=-8x-16+16\\-24=-8x[/tex]

Finally, divide both sides by -8:

[tex]\frac{-24}{-8}=\frac{-8x}{-8}\\3=x[/tex]

Therefore, x=3.

Answer:

Z-score = 1.5

Step-by-step explanation:

Z-score = (x-mean)/standard deviation

= (90-75)/10

= 1.5

Answer:

[tex]B' = (-96,-24)[/tex]

Step-by-step explanation:

Given

[tex]A(0,6)[/tex]

[tex]B(-8,-2)[/tex]

[tex]C(8,-2)[/tex]

Required

Determine the coordinates of B' if dilated by a scale factor of 12

The new coordinates of a dilated coordinates can be calculated using the following formula;

New Coordinates = Old Coordinates * Scale Factor

So;

[tex]B' = B * 12[/tex]

Substitute (-8,-2) for B

[tex]B' = (-8,-2) * 12[/tex]

Open Bracket

[tex]B' = (-8 * 12,-2 * 12)[/tex]

[tex]B' = (-96,-24)[/tex]

Hence the coordinates of B' is [tex]B' = (-96,-24)[/tex]

Answer:

Bit late but the answer is (-4,-1)

Step-by-step explanation:

Took the test in k12