79+(-42 divide 6)- -24 the answer is 96 show me how u got it

Answers

Answer 1

79+(-42/6)-(-24)

first use -42 divide by 6

79 + (-7) - (-24)

then open all the parentheses

79 - 7 + 24

and use 79 minus 7

72 +24

add them together

96

That's how to get it.

Answer 2

Answer:

Step-by-step explanation:

79+(-42 divide 6)- -24

The first step is division

79+(-7)- -24

Then we add and subtract from left to right

72 --24

72+24

96


Related Questions

Celia simplified the expression - 4x{1-3)-(2x+2). She checked her work by letting X-5 in both expressions. Her work for the
original expression is shown below.

Answers

Answer: I think it is the last one

Step-by-step explanation: if you work it out, it equally 6x-2

Answer:

6x-2

Step-by-step explanation:

[tex]- 4x(1-3)-(2x+2)[/tex]

When x=5 the value of the expression is 28

Now we check with each expression given in the options

Plug in 5 for x in each option

[tex]-6x-1=-6(5)-1=-30-1= -31[/tex]

[tex]-6x+2=-6(5)+2=-30+2= -28[/tex]

[tex]6x+1=6(5)+1=30+1= 31[/tex]

[tex]6x-2=6(5)-2=30-2=28[/tex]

So 6x-2 gives us 28 when x=5

A window is in the shape of a kite. Caleb wants to apply a layer of plastic film on the top half of the window so that the glass appears crackled. What are the dimensions of the layer of film he will apply?

9 inches in width and 7 inches in height
9 inches in width and 14 inches in height
18 inches in width and 7 inches in height
18 inches in width and 14 inches in height

Answers

Answer:

18 inches in width and 7 inches in height

Using kite, the dimensions of the layer of film the Caleb will apply is 18 inches in width and and 7 inches in height.

What is Kite?

A Kite is "quadrilateral with two distinct pairs of congruent consecutive sides".

What is relationship between kite and quadrilateral?

If a kite is quadrilateral, then "its diagonal are perpendicular and exactly one diagonal each other".

According to the question,

A window is in the shape kite has an height of 14 inches and a width of 18 inches. Caleb wants to apply a layer of plastic film on the top half of the kite shape window. The window has dimensions of width 18 inches and 14 inches of height.

In order to the find new dimensions to apply a layer of plastic film on the top half of the kite shape window only if we divide the height by two then we get new dimensions on the top half of the kite shape window.

= [tex]\frac{14}{2}[/tex]

=7 inches

Hence, new dimensions to apply a layer of plastic film on the top half of the kite shape window is 18 inches in width and and 7 inches in height.

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Kathy runs 16 miles a week. If she continues to run at this rate how many miles will she run a year​

Answers

Answer:

Remember, 1 is the multiplicative identity.  That means that we can multiply a value by 1 and not change the value, only change the units.

For example:  If we have 3 dozen eggs, how many eggs do we have?

             3 dozen

          (3 dozen)*(12 eggs / 1 dozen) = 36 eggs    (dozen cancels out, leaving only eggs)

In this problem:

   (16 miles / 1 week)

   (16 miles / 1 week)*(52 weeks / 1 year)       (weeks cancel out, leaving miles/year)

   832 miles/year

Note: with either 365 (or 366) days in a year, there are 365/7 = 52.14 weeks in a year, but we'll use 52 because the problem gave miles/week.

Step-by-step explanation:

quadratic function (f)x=2x^2+8x-7

Answers

Answer:

See attached images

Step-by-step explanation:

The expression of your question is

f(x) = 2x^2+8x-7

A full analysis of the function is shown in the images below

Which of the following must be true for an expression to be a difference of
two squares?

(((a. all variables are raised to an even power

b. there are only two terms

c. both terms have negative coefficients)))


Answers:
O A. a and
O B. a, b, and c
OC. b and
O D. a and b

Answers

Answer:

D

Step-by-step explanation:

A difference of squares is represented in general as

a² - b²

Both variables have an even power (2) → a

There are only two terms → b

(a) Find an angle between 0° and 360° that is coterminal with – 120°.

(b) Find an angle between 0 and 2π that is coterminal with 15π/4

Give exact values for your answers.​

Answers

Answer:

a)  [tex]240\degree[/tex]

b) [tex]\frac{15\pi}{4}[/tex]

Step-by-step explanation:

Coterminal angles have the same terminal sides in standard position.

a) To find an angle between [tex]0\degree[/tex] and [tex]360\degree[/tex], that is coterminal with [tex]-120\degree[/tex], we keep adding multiples of [tex]360\degree[/tex] until we get an angle within the specified range.

 [tex]-120\degree \implies -120\degree +360\degree=240\degree[/tex].

In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.

b) This time we want to find an that coterminal with [tex]\frac{15\pi}{4}[/tex] radians.

We keep subtracting multiples of [tex]2\pi[/tex] until we get an angle measure within the specified range.

[tex]\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}[/tex]

Lin took 75 boxes of carrots and 80 boxes of potatoes to the market. She sold 68 boxes of carrots and 71 boxes of potatoes. How many boxes of vegetable did she take home?

5. Write and solve the arithmetic problem for each step.



?
Answer the question below. Type your response in the space provided.

How many boxes of carrots are left?
How many boxes of Potatoes are left?
How many boxes altogehter are left?


Answers

Answer: 7 boxes of carrots, 9 boxes of potatoes, 18 boxes total

Step-by-step explanation:

75 -68=7 boxes of carrots

80-71=9 boxes of potatoes

For this case we have:

x: Represents the number of carrot boxes

y: Represents the number of boxes of potatoes

Initially we have:

[tex]x = 75\\y = 80[/tex]

If you sold 68 boxes of carrot we have:

[tex]x = 75-68 = 7[/tex]

If you sold 71 boxes of potatoes, we have:

[tex]y = 80-71 = 9[/tex]

The number of boxes I take home is given by:[tex]x + y = 7 + 9 = 16[/tex]

ANswer:

7 boxes of carrots left

There are 9 boxes of potatoes left

A total of 16 boxes remain

The surface temperature averages at 15 degrees Celsius and increases 25 degrees Celsius with each kilometer of depth. Let one variable be the distance away from the surface and the other variable be the temperature. Now write an equation that models the relationship between the variables. I choose the variable, d for distance and t for temperature.

Answers

Answer:

15+25d=t

Step-by-step explanation:

the initial value is 15 it increases(+) by 25 to each kilometer(distance=d) of depth.

Final answer:

The equation that models the relationship between distance d in kilometers and temperature t in degrees Celsius is t = 25d + 15. This means that for each kilometer increase in depth, the temperature increases by 25 degrees Celsius in addition to the initial 15 degrees Celsius surface temperature.

Explanation:

The relationship between the variables, distance (d) and temperature (t), is described as a linear function. Given that the surface temperature is 15 degrees Celsius and it increases by 25 degrees Celsius with every kilometer, the mathematical model is expressed as:

t = 25d + 15

In this equation, t represents the temperature and d is the distance from the surface in kilometers. This implies that for every kilometer increase in depth, the temperature increases by 25 degrees Celsius on top of the initial 15 degrees Celsius surface temperature.

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what is measure of cgf?​

Answers

Answer:

[tex]<CGF = 130[/tex]

Step-by-step explanation:

A triangle adds up to 180.

180 - 50 = 130

Since both of the missing angles are congruent each of the missing angles is 65 degrees.

130/2 = 65

As per the exterior angle theorem, the measure of the exterior angle is determined by the sum of the opposite interior angles.

65 + 65 = 130

So, the measure of [tex]<CGF = 130[/tex]

Find the greatest common factor: 24y8 + 6y6

Answers

For this case we must find the GCF of the following expression:

[tex]24y ^ 8 + 6y ^ 6[/tex]

By definition, the largest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. We find the factors of each number:

24: 1,2,3,4,6,8,12,24

6: 1,2,3,6

Thus, the GCF of both numbers is 6

The GCF of the expression is: [tex]6y ^ 6[/tex]

Answer:

[tex]6y ^ 6[/tex]

What is the value of f(4)in the function below? F(x)=1/4•2^x

Answers

Answer:

f(4) = 4

Step-by-step explanation:

F(x)=1/4•2^x

Let x = 4

F(4)=1/4•2^4

      = 1/4 * 2^4

      = 1/4 *16

      = 4

Answer: f(4) = 4

Step-by-step explanation:

f(x) = 1/4 . 2^x

To find f(4) we simply replace x by 4 in the above equation;

f(4) =1/4 . 2^4

f(4) = 1/4 . 16

f(4) = 16/4

f(4) = 4

Therefore f(4) is equal to 4

Helppppp me immmm stuckkkkk

Answers

Answer:D

Step-by-step explanation: 4y-3x=4    -2x-8y=8

                                        4(-.5)-3(-2)=4    -2(-2)-8(-.5)=8

Work this problem from here

4*-.5= -2

-3*-2=6

6+-2=4

so this is a true statement

-2*-2=4

-8*-.5=4

4+4= 8

so this statement is also true

Find the coordinates of the focus and equation of the directrix for the parabola given by
y2 = −4x.

The general formula for this parabola is y2 = 4px.

Therefore, the value of p is _____

The coordinates of the focus are ______

The equation of the directrix is ______

Answers

Answer:

The answers to your three problem question are shown

1) the value of p is

p = -1

2) The coordinates of the focus are

Focus =  (-1,0)

3) The equation of the directrix is

Directrix

x = 1

Step-by-step explanation:

The general equation for this parabola is

y^2 = 4px

Problem 1

Find the value of p.

We are told that the equation of the problem is

y^2 = -4x

And the general formula is

y^2 = 4px

From there, we can deduce that

p = -1, because

y^2 = 4(-1)x = -4x

This means that p = -1

Problem 2

Find the focus

To find the focus we can see the equations attached below for the focus, vertex and directrix.

In these case, the equations still apply, even though the variable is inverted, we just need to adjust it

y^2 = -4x =>

x = (-1/4)*y^2

x = a*y^2 + b*y +c

Focus

((4ac -b^2  + 1)/4a, -b/2a)

But, b = 0 and c = 0

=>

(1/4a,0) = (1/4(-1/4),0) = (-1,0)

Focus =  (-1,0)

Problem 3

Find the directrix

The equation is

x = c - (b^2 + 1).4a

But, b = 0 and c = 0

x = -4*a

x = -4* (-1/4) = 1

x = 1

Directrix

x = 1

Answer: P is -1

Focus is (-1,0)

Directrix is X= 1

there are only blue cubes, yellow cubes and green cubes in a bag there are
three times as many blue cubes as yellow cubes
and five times as many green cubes as blue cubes
sarah takes a random cube from the bag
what is the probability sarah takes out a yellow cube?
give your answer in its simplest form

Answers

Answer:   [tex]\bold{\dfrac{1}{19}}[/tex]

Step-by-step explanation:

Let x represent the quantity of yellow cubes

Yellow: x

Blue: three times yellow --> 3x

Green: five times blue --> 5(3x) = 15x

Yellow + Blue + Green = Total cubes

    x      +   3x  +    15x   =       19x

[tex]Probability=\dfrac{yellow}{total}=\dfrac{x}{19x}=\large\boxed{\dfrac{1}{19}}[/tex]

The probability of Sarah taking out a yellow cube from the bag is 0.7 or 5/7.

What is probability?

The fraction of favorable outcomes of an event to the total number of outcomes of the event is said to be the probability. The fraction can also be written in the simplest form.

P(E)= n(E)/n(S) where E -event, n(E) - favorable outcomes and n(S) is the total outcomes.

Calculation:

It is given that a bag contains blue cubes, yellow cubes, and green cubes.

Consider the number of blue cubes = n

So, the number of yellow cubes = 3 times as many as blue cubes

                                                     = 3n

Then, 5 times as many as green cubes = blue cubes

⇒ number of green cubes = n/5

Then the total number of cubes in the bag

= n + 3n + n/5

⇒ [5n + 15n + n]/5

⇒ 21n/5

Then the probability of taking out a yellow cube = (possible outcomes of a yellow cube)/(total number of cubes)

⇒ [tex]\frac{(3n)}{(21n/5)}[/tex]

⇒ 15n/21n

⇒ 5/7

∴ The probability of taking out a yellow cube = 5/7 = 0.7.

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If
[tex]f(x) = \frac{(3 + x)}{x - 3} [/tex]
what is
[tex]f(a + 2)[/tex]
?

a)
[tex] \frac{3 + f(a + 2)}{f(a) - 1} [/tex]
b)
[tex] \frac{(5 + a)}{(a - 1)} [/tex]
c)
[tex] \frac{(3 + a)}{(a - 3)} + 2[/tex]

Answers

Answer:

Option B: [tex]\frac{5+a}{a-1}[/tex]

Step-by-step explanation:

Given function is:

[tex]f(x) = \frac{3+x}{x-3}[/tex]

In order to find f(a+2), we have to put a=2 in place of x in the function

So,

[tex]f(a+2) = \frac{3 + (a+2)}{(a+2)-3}\\ =\frac{3+a+2}{a+2-3}\\ = \frac{5+a}{a-1}[/tex]

Hence, we can see that option b is correct ..

9(x-2) + 3(5-2x) = 2

Answers

9x -18 + 15 -6x = 2
3x -3= 2
3x= 5
X= 5/3

Hope this helps!

First you must distribute the numbers outside the parentheses to the numbers inside the parentheses

Let's start with the first one:

9(x-2) + 3(5-2x) = 2

9(x - 2)  

9*x + 9*-2

9x + (-18)

9x - 18

so...

9x - 18 +  3(5-2x) = 2

Now on to the second set of parentheses:

9x - 18 + 3(5-2x) = 2

3(5 - 2x)

3*5 + 3*-2x

15 + (-6x)

15 - 6x

so...

9x - 18 + 15 - 6x = 2

Now you must combine like terms. This means the numbers with the same variables must be combined...

First set of like terms:

9x - 18 + 15 - 6x = 2

9x + (-6x)

3x

so...

3x - 18 + 15 = 2

Second set of like terms:

3x - 18 + 15 = 2

-18 + 15

-3

so...

3x - 3 = 2

Now bring -3 to the right side by adding 3 to both sides (what you do on one side you must do to the other). Since -3 is being negative on the left side, addition (the opposite of negative/subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

3x + (- 3 + 3) = 2 + 3

3x + 0 =5

3x = 5

Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.

3x/3 = 5/3

x = [tex]\frac{5}{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Find the distance between the given points.

R(0, 0) and S(6, 8)

Distance =

2√7
√(22)
10

Answers

Answer:

The correct answer is last option  

10

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here  (x1, y1) = R(0, 0)  and (x2, y2)  = S(6, 8)

Distance, RS = √[(x2 - x1)² + (y2 - y1)²]

 = √[(6 - 0)² + (8 - 0)²]

 = √[6² + 8²]

 = √[36 + 64]

 = √100

 = 10

Therefore the correct answer is last option  10

A comedian knows eleven jokes. One joke is​ old, one joke is​ new, and the other jokes are somewhere between. If the order in which these jokes are told makes a difference in terms of how they are​ received, how many ways can they be delivered if the old joke is told first and the new joke is told​ last?

Answers

Answer: I believe nine

Step-by-step explanation: If one and 11 stay in the same place then it would start as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. then it would be 1, 10, 2, 3, 4, 5, 6, 7, 8, 9, 11. then 1, 9, 10, 2, 3, 4, 5, 6, 7, 8,11 and so one.

Why is causation so much more difficult to prove than correlation?

Answers

The more changes in a system, the harder it is to establish causation

Convert the mixed numbers into improper fractions. Convert the improper fraction to mixed Numbers.

Answers

Answer:

13. 23/4

14. 13/2

15. 6 and 1/2

16. 2 and 7/12

Answer:

13. 23/4

14. 13/2

15. [tex]6\frac{1}{2}[/tex]

16. [tex]2 \frac{7}{12}[/tex]

Step-by-step explanation:

13) 5×4=20

    20+3=23

    [tex]\frac{23}{4}[/tex]

14) 2×6=12

     12+1=13

     [tex]\frac{13}{2}[/tex]

15 an 16 divide

the graph represents f(x)=[x]+3. what is f(-2.2)?

Answers

Answer:

f(-2.2) = 1

Step-by-step explanation:

There is a horizontal blue line with equation y = 1 between x = -3 and x = -2.  Thus, f(-2.2) = 1.

Answer:

f(-2.2) = 1

Step-by-step explanation:

There is a horizontal blue line with equation y = 1 between x = -3 and x = -2. Thus, f(-2.2) = 1.

I need to know this answer please!

Answers

Answer:

3*5=15

15 is your answer

ANSWER

15 square units.

EXPLANATION

Each box is 1 square units.

When we count the number of boxes we obtain 15 boxes.

This implies that the area of the rectangle is 15 square units.

Alternatively, we can observe that:

The rectangle is a 3 by 5 rectangle.

So the area is

[tex]3 \times 5 = 15 \: units \: square[/tex]

The rectangle is 15 units square.

What is the value of a in the equation a = 2 + 3a + 10?

Answers

Answer:

a= -6

Step-by-step explanation:

Given

a=2+3a+10

In order to find the value of a, we have to isolate a on a single side of the equation

So,

subtracting 3a from both sides

a-3a = 2+10+3a-3a

=>a-3a=12

=> -2a = 12

Dividing both sides by -2

=> -2a/-2 = 12/-2

=> a = -6

The value of a in the given equation is -6 ..

Evaluate sin(arccos(-4/
[tex]evaluate \: sin(arccos( - \frac{4}{ \sqrt{25))[/tex]

Answers

Answer:

sin(arccos(-4/√25)) = 0.6

Step-by-step explanation:

The expression you want to evaluate is

sin(arccos(-4/√25))

= sin(arccos(-4/5))

We place this expression into a calculator and get the result

arccos(-4/5) = 2.498 rads = 143.1°

then

sin(143.1°) = 3/5

sin(143.1°) = 0.6

sin(arccos(-4/√25)) = 0.6

Write the following phrase as an expression.
half of n

Answers

Translating the half to symbols would be 1/2. Therefore, your answer is 1/2(n)

Hope this helps!

Answer:

1/2n

Step-by-step explanation:

half of n

of means multiply

1/2 * n

n/2

Plzzz HELP (3 QUESTIONS!!)

6) Which of the following numbers is written in standard notation for 1.31x10^-5?

a) 11,310
b) -11,310
c) .01131
d) .00001131

7) Select the expression written in scientific notation that is equivalent to 4.8 x 10^5-9.7 x 10^4.

a) -4.83x10^9
b) 480,000-97,000
c) 3.83x10^5
d) 0.000048 – 0.00097

8) Select the expression that is equivalent to (4 x 10^3)(5x10^7).

a) 4.5 x 10^3+7
b) (4+5) (10^3+10^7)
c) 4.5 x 10^3x7
d) ( 4 x 5) (10^3+10^7)


Answers

Answer:

6: d, 7: b and c, 8: a

Step-by-step explanation:

6) The answer is (d).

We have,

0.00001131 =1.131×0.00001

= 1.131/100000

= 1.131×10^-5.

So, this is correct answer.

7) This question have two answers (b) and (c), both are correct.

(b) 480000-97000

= 4.8x100000-9.7x10000

=4.8x10^5-9.7x10^4

(c) 4.8x10^5-9.7x10^4

= 4.8x10^5-0.97x10^5

= (4.8-0.97) x10^5

=3.83x10^5

8)(a)

(4 x 10^3)(5x10^7).

= 4x5x10³x10^7

= 4x5x10^(3+7).

e shown below.
(93)10 - 930​

Answers

Answer:

0

Step-by-step explanation:

(93)10 - 930=

930 - 930=

0

The passing yards for the top 5 quarterbacks in the country are 3,832, 3,779, 3,655, 3,642, and 3,579. Find the variance and standard deviation. Round to the nearest hundredth.
(EXPLAIN WORK)

Answers

Answer:

variance = 8,732.24

standar deviation = 93.45

Explanation:

In order to calculate the variance and standard deviation of a set of data, you first must calculate the mean.

Mean = average = μ = ∑ values / (number of data)

Hence, the mean of our data set is:

mean = μ = [ 3,832 + 3,779 + 3,655 + 3,642 + 3,579] / 5 = 18,487 / 5 = 3,697.4

Now you can calcuate the variance using the formula.

For a data set (which is all your population and not a sample) the formula is:

Variance = ∑ (value - μ)² / (number of data)

That is:

Variance = [ (3,832 - 3,697.4)² + (3,779 - 3,697.4)² + (3,655 - 3,697.4)² + (3,642 - 3,697.4)² + (3,579 - 3,697.4)² ] / 5

Variance = 8,732.24 (rounded to the nearest hundreth)

The standard deviation, S.D., is the square root of the variance:

[tex]S.D.=\sqrt{8,732.24}=93.45[/tex] (rounded to the nearest hundresth)

Answer:

Variance = 8732.24 and standard deviation = 93.45

Step-by-step explanation:

We have to calculate the variance and standard deviation of the data set

3,832, 3,779, 3,655, 3,642, 3,579

First we calculate the mean of the data

Mean = [tex]\frac{(3,832+3,779+3,655+3,642+3,579)}{5}[/tex]

         = [tex]\frac{18487}{5}[/tex]

         = 3697.4

Now we calculate the variance by subtracting the mean from value of data set and square it.

3832 - 3697.4 = 134.6² =  18,117.16

3779 - 3697.4 = 81.6² = 6,658.56

3655 - 3697.4 = -42.4² = 1,797.76

3642 - 3697.4 = -55.4 = 3069.16

3579 - 3697.4 = -118.4 = 14,018.56

Add up the squared result and take the mean

=  [tex]\frac{(18117.16+6658.56+1797.76+3069.16+14018.56)}{5}[/tex]

=  [tex]\frac{43661.2}{5}[/tex]

Variance = 8732.24

To calculate standard deviation, we take the square root of the variance = [tex]\sqrt{8732.24}[/tex]

Standard deviation = 93.44645526 ≈ 93.45

Variance = 8732.24 and standard deviation = 93.45

Which of the following vectors are orthogonal to (2,1)? Check all that apply.
A. (1,-2)
B. (-3,6)
C. (1,2)
D. (-2,-3)

Answers

Answer:

A. (1,-2)

B. (-3,6)

Step-by-step explanation:

we know that

If two vectors are orthogonal, then the dot product ( or scalar product) of the vectors is equal to zero

so

Let

a (x1,y1)  and b(x2,y2)

The dot product is equal to

a.b=(x1*x2+y1*y2)

Verify each case

case A) (2,1) with (1,-2)

(2,1).(1,-2)=(2)*(1)+(1)(-2)=2-2=0

therefore

(1,-2) is orthogonal to the given vector

case B) (2,1) with (-3,6)

(2,1).(-3,6)=(2)*(-3)+(1)(6)=-6+6=0

therefore

(-3,6) is orthogonal to the given vector

case C) (2,1) with (1,2)

(2,1).(1,2)=(2)*(1)+(1)(2)=2+2=4

therefore

(1,2) is not orthogonal to the given vector

case D) (2,1) with (-2,3)

(2,1).(-2,3)=(2)*(-2)+(1)(3)=-4+3=-1

therefore

(-2,3) is not orthogonal to the given vector

Answer: B, D, E

On EDGE

Step-by-step explanation:

Dana kicks a soccer ball. The table shows the height of the soccer ball with respect to the time, in seconds, after the ball was kicked.

Time | Height
(Seconds) | (Feet)
~~~~~~~~~~~~~~~
0.5 21
1 34
1.5 39
2 36
2.5 25
3 6

Which Graph best displays the relationship shown in the table?

(i just need confirmation that its C)

Answers

Answer: It is!!!!!!!!

Answer:

The correct option is C.

Step-by-step explanation:

The standard form of a parabola is

[tex]y=ax^2+bx+c[/tex]

The table of values represents the coordinate pairs of the parabola. It means the graph of the parabola must be passes through these coordinate pairs.

From the given table it is clear that the parabola passes through the points (0.5,21), (1,34) and (1.5,39).

[tex]21=a(0.5)^2+b(0.5)+c[/tex]

[tex]21=0.25a+0.5b+c[/tex]             .... (1)

[tex]34=a(1)^2+b(1)+c[/tex]

[tex]34=a+b+c[/tex]                      .... (2)

[tex]39=x(1.5)^2+y(1.5)+z[/tex]

[tex]39=2.15a+1.5b+c[/tex]            .... (3)

On solving (1), (2) and (3), we get

[tex]a=-16, b=50,c=0[/tex]

The equation of parabola is

[tex]y=-16x^2+50x+0[/tex]

[tex]y=-16x^2+50x[/tex]

The graph of parabola is shown below. It is same as graph in option C.

Therefore the correct option is C.

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