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Match the equations of hyperbolas to their corresponding pairs of vertices.

Answer:

B

Step-by-step explanation:

The "value" of a function is the y-value.

Since we want negative y values, we look at "WHERE" the function is "UNDER" the y-axis.

Looking closely, it looks that function (the dip) is from x = -1 to x = 3

Hence, the function is negative at the interval  -1 ≤ x ≤ 3

B is correct.

Answer:

n/m = 1.5 is direct variation

v = 1/3 bh is joint variation

y = -7 is constant

vw = -18 is inverse variation

Step-by-step explanation:

* Lets explain the types of variation

- Direct variation is a relationship between two variables that can be

 expressed by an equation in which one variable is equal to a constant

 times the other

# Ex: the equation of a direct variation y = kx , where k is a constant

- Inverse variation is a relationship between two variables in which their

 product is a constant.

- When one variable increases the other decreases in proportion so

 that their product is unchanged

# Ex: the equation of a inverse variation y = k/x , where k is a constant

- Joint variation is a variation where a quantity varies directly as the

 product of two or more other quantities

# Ex: If z varies jointly with respect to x and y, the equation will be of

  the form z = kxy , where k is a constant

- The constant function is a function whose output value (y) is the

  same for every input value (x)

* Lets solve the problem

∵ n/m = 1.5 ⇒ multiply both sides by m

∴ n = 1.5 m

∵ The equation in the shape of y = kx

∴ n/m = 1.5 is direct variation

∵ v = 1/3 bh

∵ 1/3 is a constant

∴ v is varies directly with b and h

∴ v = 1/3 bh is joint variation

∵ y = -7

∴ All output will be -7 for any input values

∴ y = -7 is constant

∵ vw = -18

∵ -18 is constant

∵ The product of the two variables is constant

∴ vw = -18 is inverse variation

Answer:

8 hours

Step-by-step explanation

The first thing one mus realize here is that this is an inverse proportion question. When one quantity increases, the other decreases. That is the time needed to paint the fence decreases as the number of people who work on it increase. This means therefore that we can set up a proportionality equation:

[tex]t \alpha \frac{k}{n}[/tex]

where t is time and n is the number of people. Given the information in the question we can find the proportionality constant k

[tex]t=\frac{k}{n}[/tex]

[tex]12=\frac{k}{2}[/tex]

so k=24

So how many hours does it take for 3 people

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

so we know the angle is 180° < x < 270°, which is another way of saying that the angle is in III Quadrant, where cosine as well as sine are both negative, which as well means a positive tangent, recall tangent = sine/cosine.

the cos(x) = -(4/5), now, let's recall that the hypotenuse is never negative, since it's just a radius unit, thus

[tex]\bf cos(x)=\cfrac{\stackrel{adjacent}{-4}}{\stackrel{hypotenuse}{5}}\qquad \impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2-(-4)^2}=b\implies \pm\sqrt{9}=b\implies \pm 3 = b\implies \stackrel{III~Quadrant}{\boxed{-3=b}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(x)=\cfrac{\stackrel{opposite}{-3}}{\stackrel{adjacent}{-4}}\implies tan(x)=\cfrac{3}{4} \\\\\\ tan(2x)=\cfrac{2tan(x)}{1-tan^2(x)}\implies tan(2x)=\cfrac{2\left( \frac{3}{4} \right)}{1-\left( \frac{3}{4} \right)^2}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{1-\frac{9}{16}}[/tex]

[tex]\bf tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{16-9}{16}}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{7}{16}}\implies tan(2x)=\cfrac{3}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{8}{~~\begin{matrix} 16 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{7} \\\\\\ tan(2x)=\cfrac{24}{7}\implies tan(2x)=3\frac{3}{7}[/tex]

Answer:

  (-5, 6) → (5, -6)

Step-by-step explanation:

Reflection across the origin negates both coordinates.

  (x, y) → (-x, -y)

  (-5, 6) → (5, -6)

Answer:

[tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Let x be the filled bottles of soda Q,

As per statement,

The filled bottles of soda V = 2x,

Given,

Rate of filling of soda Q = 500 liters per sec,

So, the total volume filled by soda Q in a day = 500 × 86400 = 43200000 liters,

( ∵ 1 day = 86400 second ),

Thus, the volume of a bottle of Soda Q = [tex]\frac{\text{Total volume filled by soda Q}}{\text{filled bottles of soda Q}}[/tex]

[tex]=\frac{43200000}{x}[/tex]

Now, rate of filling of soda V = 300 liters per sec,

So, the total volume filled by soda V in a day = 300 × 86400 = 25920000 liters,

Thus, the volume of a bottle of Soda V

[tex]=\frac{25920000}{2x}[/tex]

Thus, the ratio of the volume of a bottle of Soda Q to a bottle of Soda V

[tex]=\frac{\frac{43200000}{x}}{\frac{25920000}{2x}}[/tex]

[tex]=\frac{10}{3}[/tex]

Find the difference:

1400 - 1250 = 150

Divide the difference by the starting value:

150 / 1250 = 0.12

Multiply by 100:

0.12 x 100 = 12% increase.

Answer:

12% Increase.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 types of lunch multiplied by 5 kinds of bread then multiplied by 4 types of sauces equals 120

Answer:

Part a) 0.20 revolutions per foot of distance traveled

Part b) The slope of the graph is [tex]m=5\frac{ft}{rev} [/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the number of revolutions

y ----> the distance traveled in feet

we have the point (2,10) ----> see the graph

Find the value of the constant of proportionality k

[tex]k=y/x=10/2=5\frac{ft}{rev} [/tex]

Remember that in a direct variation the constant k is equal to the slope m

therefore

The slope m is equal to

[tex]m=5\frac{ft}{rev} [/tex]

The linear equation is

[tex]y=5x[/tex]

step 2

How many revolutions does Charmaine make per foot of distance traveled?

For y=1

substitute in the equation and solve for x

[tex]1=5x[/tex]

[tex]x=1/5=0.20\ rev[/tex]

Answer:

a = -21 and b = 15

Step-by-step explanation:

It is given a matrix multiplication,

To find the value of a and b

It is given that,

| 6  -5 |  *  | -1 |    =   | a |

|-3   4 |     |  3 |         | b |

We can write,  

a = (6 * -1) + (-5 * 3)  

 = -6 + -15

 = -2 1

b = (-3 * -1) + (4 * 3)

 = 3 + 12

 = 215

Therefore the value of  a = -21 and b = 15

Answer:

-21 and 15

Step-by-step explanation:

You multiply the two matrices, -1*6+3*-5=-21 and -1*-3+3*4=15

Answer:

8 units ^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the height

b = LK = 4 units

h = J to where LK would be extended to, which would be 4 units

A = 1/2 (4) * 4

A = 8 units ^2

Answer:

x= 45 degrees

Step-by-step explanation:

Take the larger angle - the smaller angle. 152-62= 90. Now we take this number and divide it by 2. 90/2 equals 45 degrees.

Answer:

  45°

Step-by-step explanation:

The external angle measure is half the difference of the intercepted arcs:

  x = (152° -62°)/2 = 45°

Answer:

  339π in³

Step-by-step explanation:

The amount of water is the difference between the volume of the cylinder and the volume of the ball. The appropriate volume formulas are ...

  cylinder V = πr²h

  sphere V = (4/3)πr³

For the given numbers, the volumes are ...

  cylinder V = π(5 in)²(15 in) = 375π in³

  sphere V = (4/3)π(3 in)³ = 36π in³

The water volume is the difference of these ...

  water volume = cylinder V - sphere V

     = 375π in³ - 36π in³ = 339π in³

Answer:

1km=1000m 160m=0.160x4=0.64

Step-by-step explanation:

Ifl = 160m, then:

P = 4 * 160m\\P = 640m

Thus, the perimeter of the base of the pyramid is 640m.

On the other hand, by definition: 1Km = 1000m

By making a rule of three we have:

1Km ---------> 1000m

x --------------> 640m

Where "x" represents the perimeter of the base of the pyramid in Km.

x = \frac {640 * 1} {1000}\\x = 0.64km

For this case we must convert from meters to kilometers. By definition we have to:

[tex]1km = 1000m[/tex]

The perimeter of the base of the pyramid will be given by the sum of the sides:

[tex]P = 160m + 160m + 160m + 160m = 640m[/tex]

We make a rule of three:

1km ----------> 1000m

x ---------------> 640m

Where "x" represents the equivalent amount in km.

[tex]x = \frac {640} {1000}\\x = 0.64km[/tex]

Answer:

0.64km

Answer:

  $557.51

Step-by-step explanation:

A financial calculator tells you the payments are ...

  on $80,000 at 4.75%: $417.32

  on $20,000 at 7.525%: $140.19

Then the total monthly payment is ...

  $417.32 +140.19 = $557.51

_____

You can use the amortization formula to find the payment (A) on principal P at interest rate r for t years to be ...

  A = P(r/12)/(1 -(1+r/12)^(-12t))

I find it takes fewer keystrokes to enter the numbers into a financial calculator. Both give the same result.

Final answer:

Troy's total mortgage payment can be found by calculating the monthly payment for the first mortgage at 80% of the home price with an interest rate of 4.75% and the second mortgage at 20% of the home price with a 7.525% interest rate, then combining these two payments. However, exact figures require the use of an amortization formula or an online mortgage calculator.

Explanation:

To calculate Troy's total mortgage payment for an 80/20 mortgage on a $100,000 house, we need to separate the calculations for the first mortgage (80%) and the second mortgage (20%) because they have different interest rates.

First Mortgage Calculation:

The first mortgage is 80% of the home price, which amounts to $80,000. With an interest rate of 4.75%, his monthly payment can be calculated using the formula for a fixed-rate mortgage.

Second Mortgage Calculation:

The second mortgage is 20% of the home price, equal to $20,000. With a higher interest rate of 7.525%, we again use the formula for a fixed-rate mortgage to find the monthly payment.

Without the actual formula or financial calculator, we cannot compute the exact monthly payments here. Typically, you would use the amortization formula or an online mortgage calculator to find the monthly payments for each part of the mortgage, and then sum them up for the total monthly payment.

Combining the Payments:

Once the monthly payments for both mortgages are calculated, they are added together to determine Troy's total monthly mortgage payment.

Answer:

D. {(8, 1), (4, 1), (0, 1), (–15, 1)}

Step-by-step explanation:

A function can not contain two ordered pairs with the same first elements.

Let us look at the options one by one:

A. {(–4, –6), (–3, –2), (1, –2), (1, 0)}

Not a function because (1, –2), (1, 0) have same first element.

B. {(–2, –12), (–2, 0), (–2, 4), (–2, 11)}

Not a function because all the ordered pairs have the same first element.

C. {(0, 1), (0, 2), (1, 2), (1, 3)}

Not a function because (0, 1), (0, 2) have same first element.

D. {(8, 1), (4, 1), (0, 1), (–15, 1)}

This is a function because all the ordered pairs have different first elements i.e. no repetition in first elements of the ordered pairs

Therefore, option D is correct ..

Answer:

C. 24.1 ft

Step-by-step explanation:

The side of the wall making the tilt of 75° will represent the hypotenuse

The height of the wall will be represented by the side opposite to the angle 75°

Apply the relationship for sine of angle Ф

Formula to use is ;

Sin Ф=  length of opposite side÷hypotenuse

SinФ=O/H

Sin 75°=O/25

0.96592582628=O/25

O=0.96592582628×25 =24.1 ft

Option 24.1 ft

1. Identify the given information:

   - Length of the wall (hypotenuse, [tex]\( c \)[/tex]) = 25 feet
   - Angle [tex](\( \theta \))[/tex] with the ground = 75°

2. Recall the sine function:
   - Sine of an angle [tex](\( \sin \theta \))[/tex] is the ratio of the length of the opposite side to the hypotenuse.
   - Mathematically, [tex]\( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \)[/tex].

3. Set up the equation using the sine function:
   [tex]\[ \sin(75^\circ) = \frac{\text{height}}{25} \][/tex]

4. Solve for the height:
   - Multiply both sides by 25 to isolate the height.
   [tex]\[ \text{height} = 25 \times \sin(75^\circ) \][/tex]

5. Calculate [tex]\( \sin(75^\circ) \)[/tex]:
   - This value is approximately 0.9659.

6. Substitute [tex]\( \sin(75^\circ) \)[/tex] into the equation:
   [tex]\[ \text{height} = 25 \times 0.9659 \][/tex]
   [tex]\[ \text{height} \approx 24.148 \][/tex]

7. Determine the closest option:
   - The options given are 25.9 ft, 6.5 ft, 24.1 ft, 93.3 ft.
   - The calculated height is approximately 24.148 feet.
   - The closest option is 24.1 ft.

Answer:

The percent of the students between 14 and 18 years old is 95% ⇒ answer C

Step-by-step explanation:

* Lets revise the empirical rule

- The Empirical Rule states that almost all data lies within 3

 standard deviations of the mean for a normal distribution.

- 68% of the data falls within one standard deviation.

- 95% of the data lies within two standard deviations.

- 99.7% of the data lies Within three standard deviations

- The empirical rule shows that

# 68% falls within the first standard deviation (µ ± σ)

# 95% within the first two standard deviations (µ ± 2σ)

# 99.7% within the first three standard deviations (µ ± 3σ).

* Lets solve the problem

- The ages of students in a school are normally distributed with

 a mean of 16 years

∴ μ = 16

- The standard deviation is 1 year

∴ σ = 1

- One standard deviation (µ ± σ):

∵ (16 - 1) = 15

∵ (16 + 1) = 17

- Two standard deviations (µ ± 2σ):

∵ (16 - 2×1) = (16 - 2) = 14

∵ (16 + 2×1) = (16 + 2) = 18

- Three standard deviations (µ ± 3σ):

∵ (16 - 3×1) = (16 - 3) = 13

∵ (16 + 3×1) = (16 + 3) = 19

- We need to find the percent of the students between 14 and 18

  years old

∴ The empirical rule shows that 95% of the distribution lies

   within two standard deviation in this case, from 14 to 18

   years old

* The percent of the students between 14 and 18 years old

  is 95%

Answer:

Answer Choice C is correct- 95%

Answer:

a. We can say that P > C, where 'P' represents Peter's earnings and 'C' represents Cindy's earnings.

Given that P = 3h and C = 2h, where h =$4.50. We can say also that 3h > 2h.

b. If Cindy wants to earn at least $14 a day working two hours. Then:

2h ≥  $14

To solve the problem, we just need to solve for 'h':

h ≥ $7

Therefore, se should earn more or equal to $14 per hour.

Answer:

Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.

Part A:

Peter's earning in 3 hours is = [tex]3\times4.50=13.5[/tex] dollars

Cindy's earnings in 2 hours is = [tex]2\times4.50=9[/tex] dollars

We can define the inequality as: [tex]9<13.50[/tex]

Part B:

Let Cindy's earnings be C and number of hours needed be H.

We have to find her per hour income so that C ≥ 14

As Cindy works 2 hours per day, the inequality becomes 2H ≥ 14

So, we have [tex]H\geq 7[/tex]

This means Cindy's per hour income should be at least $7 per hour so that she earns $14 a day.

The leading coefficient is a negative value (-3) so the graph goes down on the right side.

This makes either Graph B or C correct.

Now because the degree ( exponent ) (the ^4) is even both ends of the graph go in the same direction.

This makes Graph B the correct answer.

Answer:

The leading coefficient is a negative value (-3) so the graph goes down on the right side.

This makes either Graph B or C correct.

Now because the degree ( exponent ) (the ^4) is even both ends of the graph go in the same direction.

This makes Graph B the correct answer.

Answer:

The smaller diameter is [tex]3.9\ cm[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The diameter of the circle is equal to BD

Applying the Pythagoras Theorem

[tex]BD^{2} =BE^{2} +DE^{2}[/tex]

substitute the given values

[tex]BD^{2} =3^{2} +2.5^{2}\\ BD^{2} =15.25\\ BD=3.9\ cm[/tex]

Answer:

3.9

Step-by-step explanation:

use Pythagorean Theorem

plus i took the test :)

Answer:

The mid-point is:

[tex]=(\frac{-3}{2},\frac{-1}{2})[/tex]

Step-by-step explanation:

We are given:

[tex](x_1,x_2) = (3,5)\\(y_1,y_2) = (-6,-6)[/tex]

We have to find the midpoint of the segment formed by these points.

The formula for mid-point is:

[tex]Mid-point=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2})\\ Putting\ the\ values\\Mid-point=(\frac{3-6}{2},\frac{5-6}{2})\\=(\frac{-3}{2},\frac{-1}{2})[/tex] ..

Answer:

The answer above is correct, but in decimal form it's

(-1.5,-0.5)

Step-by-step explanation:

The triangles are both similar and congruent triangles

The side lengths of the triangles are given as:

Triangle A = x units, y units and 2 units.

Triangle B = 2 units, x units and y units.

In the above parameters, we can see that the triangles have equal side lengths.

This means that they are congruent by the SSS theorem.

Congruent triangles are always similar.

Hence, the triangles are both similar and congruent triangles

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Answer:

Since there are three pairs of congruent sides, we know the triangles are congruent by the SSS congruence theorem. The corresponding sides of the triangle are also in proportion, so they are also similar by the SSS similarity theorem.

Step-by-step explanation:

Edge 23 sample response

Answer:

  (-10, 0)

Step-by-step explanation:

The parabola opens to the left, and its vertex is at (0, 0). The focus must have an x-coordinate that is negative. The only viable choice is ...

  (-10, 0)

__

The equation is in the form ...

  4px = y^2

where p is the distance from the vertex to the focus.

In the given equation, 4p = -40, so p=-10, and the focus is 10 units to the left of the vertex. In this equation, the vertex corresponds to the values of the variables where the squared term is zero: (x, y) = (0, 0).

Answer:

-the elements in the domain of f(x) for which g(f(x)) is defined

Step-by-step explanation:

In order for g(f(x)) to exist we first must have that f(x) exist, then g(f(x)).

So the domain of g(f(x)) will be the elements in the domain of f(x) for which g(f(x)) is defined.

The description which best explains the domain of (gof)(x) is the elements in the domain of f(x) for which g(f(x)) is defined.

Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).

h(x) is called the composite function.

For two functions f(x) and g(x), the composite function (g o f)(x) is defined as,

(g o f)(x) = g (f(x))

So the domain of g(x) where x contains f(x).

Here when we defined g (f(x)), the domain of the composite function will be the elements in the domain of f(X).

Also these elements must be defined for g(x).

Hence the correct option is A.

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Answer:

Step-by-step explanation:

a) We have been given the points (9,-2) and (9,7)

Use the slope formula to solve this.

m= y2-y1/x2-x1

where (x1,y1)=(9,-2)

and (x2,y2)=(9,7)

m=7-(-2)/9-9

m=7+2/0

m=9/0

Having a zero in the denominator means the slope is undefined. Whenever you have a vertical line your slope is undefined....

b) We have been given (-4,-6) and (5,-6)  

Use the slope formula to solve this.

m= y2-y1/x2-x1

where (x1,y1)=(-4,-6)

and (x2,y2)=(5,-6)

m=-6-(-6)/5-(-6)

m=-6+6/5+6

m=0/11

If the numerator of the fraction is 0, the slope is 0. This will happen if the y value of both points is the same. The graph would be a horizontal line and would indicate that the y value stays constant for every value of x....

Answer: A and C

Step-by-step explanation: Took the test |

                                                                    \/

The true statement is (c) Initially there were 100 wild flowers growing in the meadow.

The function for the number of wild flowers is given as:

[tex]f(x)=\frac{1000}{1+9e^{-0.4x}}[/tex]

Set x to 0

[tex]f(0)=\frac{1000}{1+9e^{-0.4 * 0}}[/tex]

Evaluate the product

[tex]f(0)=\frac{1000}{1+9e^{0}}[/tex]

Evaluate the exponent

[tex]f(0)=\frac{1000}{1+9}[/tex]

Evaluate the sum

[tex]f(0)=\frac{1000}{10}[/tex]

Evaluate the quotient

[tex]f(0)=100[/tex]

The above represents the initial number of wild flowers

Hence, the true statement is (c) Initially there were 100 wild flowers growing in the meadow.

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Answer:

The measure of angle B is [tex]67\°[/tex]

Step-by-step explanation:

we know that

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]

we have

[tex]a=20\ units[/tex]

[tex]b=32\ units[/tex]

[tex]A=35\°[/tex]

substitute the given values and solve for B

[tex]\frac{20}{sin(35\°)}=\frac{32}{sin(B)}[/tex]

[tex]sin(B)=(32)sin(35\°)/20[/tex]

[tex]B=arcsin((32)sin(35\°)/20)[/tex]

[tex]B=67\°[/tex]

Final answer:

The question involves the application of normal distribution and sample means in statistics to analyze per capita red meat consumption. The context provided includes dietary trend changes over time, reflecting shifts in consumer preferences and demand curves.

Explanation:

The student's question pertains to the normal distribution of red meat per capita consumption, a statistical concept used in mathematics to describe how values are spread around a mean. Based on a given mean of 107.107 pounds and a standard deviation of 39.339.3 pounds, we would analyze sample means for groups of 18 individuals. To do this, we use the Central Limit Theorem which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, typically n > 30, but even smaller samples from a normal population will be approximately normal.

As per the historical data from the USDA, we observe changes in per-capita consumption trends for chicken and beef, indicating shifts in consumer preferences affecting the demand curve over time. This information provides context to the type of data involved but does not directly affect the statistical analysis of sample means asked in the question.

Moreover, these statistical concepts could be used to estimate population parameters and analyze shifts in dietary patterns as suggested by the change in the consumption of chicken and beef over the years.

Answer:

D (assuming f(x)=-3x^2+4x+6)

Step-by-step explanation:

Let's find f(2) and f(3).

I'm going to make the assumption you meant f(x)=-3x^2+4x+6 (please correct if this is not the function you had).

f(2) means replace x with 2.

f(2)=-3(2)^2+4(2)+6

Use pemdas to simplify:  -3(4)+4(2)+6=-12+8+6=-4+6=2.

So f(2)=2

f(3) means replace x with 3.

f(3)=-3(3)^2+4(3)+6

Use pemdas to simplify:  -3(9)+4(3)+6=-27+12+6=-15+6=-9

So f(3)=-9

-9 is smaller than 2 is the same as saying f(3) is smaller than f(2) or that f(2) is bigger than f(3).

Answer:

The answer is statement D.

Step-by-step explanation:

In order to determine the true statement, we have to solve every statement.

In any function, we replace any allowed "x" value and the function gives us a value. This process is called "evaluating function". If we want to compare different values of the function for different "x" values, we just have to evaluate them first and then compare.

So, for x=2 and x=3

f(2)=-3*(2)^2+4*2+6=-12+8+6=2

f(3)=-3*(3)^2+4*3+6=-27+12+6=-9

f(2)>f(3)

According to the possible options, the true statement is D.