A chopstick model of a catapult launches a marshmallow in a classroom. The path of the marshmallow can be modeled by the quadratic y=−0.07x2+x+2.2,

where y represents the height of the marshmallow, in feet,
and x represents the horizontal distance from the point it is launched, in feet.

When the marshmallow hits the ground, what is its horizontal distance from the point where it was launched?

Example:

[tex](f+g)(x)=f(x)+g(x)[/tex]

To add this, we can substitute in the functions and combine like terms.

We're given:

Add k to k:

[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]

Input x as 4:

[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]

[tex](k+k)(4)=28[/tex]

(k+k)(4) is equivalent to 28.

If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.

Addition of two functions : If f(x) & g(x) be two functions, then

(f+g)(x) = f(x)+g(x)

Given, k(x) = 5x-6

Now, Adding function k with k we get,

(k+k)(x) = k(x)+k(x)

           = (5x-6)+(5x-6)

           = 5x-6+5x-6

           = 10x-12

We have to find, (k+k)(4)

∴  (k+k)(4) = (10×4)-12

                = 40-12

                = 28

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Answer:

-0.875

Step-by-step explanation:

So you have the points -4.25 and 2.50. To find the midpoint you simply add the two and then divide by 2. This results in (-4.25 + 2.50) / 2 = -0.875

The exponential function decays at three-fourths the rate of the quadratic function.

The given inequality is -2≤x≤0.

We need to determine how do the decay rates of the functions compare over the interval.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

We calculate the average slope of each graph in the indicated interval, the slope can be calculated as [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Now, for the exponential function:

[tex]m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}[/tex]

For the quadratic function:

[tex]m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2[/tex]

Now, the ratio of both average slopes is[tex]\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}[/tex].

Therefore, the exponential function decays at three-fourths the rate of the quadratic function.

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Answer:One of the factors of the given expression is (2h + 1).

Step-by-step explanation:

ed

Answer:

C on edge 23

Step-by-step explanation:

because i said so

Answer:

Question?

Step-by-step explanation:

The simplified form of the provided expression is 12x¹⁸ option second is correct.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

[tex]\rm = \sqrt{144x^{36}}[/tex]

[tex]\rm = \sqrt{(12^2)(x^{36})}[/tex]

[tex]\rm = \sqrt{(12^2)}\sqrt{(x^{36})}[/tex]

12x¹⁸

Thus, the simplified form of the provided expression is 12x¹⁸ option second is correct.

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Answer:

12x18

Step-by-step explanation:

Edge 2023

Step-by-step explanation:

please attach a picture for us to see the choices

Answer:

There were 42 fewer students who chose Football than Hockey.

Step-by-step explanation:

Fraction of students who chose Hockey

= 1 - [tex]\frac{1}{6}[/tex] - [tex]\frac{1}{3}[/tex]

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

[tex]\frac{1}{2}[/tex] units = 21

 1 unit = 42

No. of students who chose Football

= 2 units ([tex]\frac{2}{6}[/tex])

= 84 students

No. of students who chose Hockey

= 3 units ([tex]\frac{3}{6}[/tex])

= 126 students

Difference between no. of students who chose Football and Hockey

= 126 - 84

= 42 students

∴There were 42 fewer students who chose Football than Hockey.

Answer:

m=2 and b=8

Step-by-step explanation:

this is a linear equation, which takes on the formula of y=mx+b
therefore in the equation y=2x+8, 2 is the m, and 8 is the b

Answer: The graph crosses the x-axis at x = 2.

Step-by-step explanation:

The root has a multiplicity of 3, meaning that it crosses the x axis at x=2.

The probability notation for the probability of choosing a green marble is P(G)

This is simply defined as the extent to which something is likely to occur.

The probability that an event will occur is given as the ratio of the number of favorable outcomes to the total number of outcomes.

Probability notation is a symbol used in indicating the probability of an occurring event. Since our focus is on the probability of obtaining a green marble, then the probability notation will be P(G). This is illustrated below:

P(G) = nG / nT

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The coordinates of point C that forms the triangle is; (2, -1)

We are told that point D divides line segment AB in the ratio of 5:3.

The line segment division formula is;

(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)

For this question;

x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3

Thus, (x, y) gives us;

(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)

D(x, y) = (7, -1)

Now, we need to find the coordinates of C

We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line

And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).

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Using the Factor Theorem, the polynomials are given as follows:

1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]

2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Item a:

The parameters are:

[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]

Item b:

The roots are:

[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

Item 3:

The roots are:

[tex]x_1 = x_2 = 3, x_3 = -2[/tex]

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

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Answer:

B

Step-by-step explanation:

x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function

Step-by-step explanation:

3x8=24

24x30=720

720÷18=40 cents

Answer:

1. F

2. F

3. T

4. F

5. F

6. T

7. T

8. F

9. F

10. T

Step-by-step explanation:

1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.

2. They do not lie on the same line.

3. Points A, B, C, D all lie in the same plane therefore making them coplanar.

4. Points X, Y do not lie in the same plane as A, B.

5. Point X does not lie in the same plane as C, D, B

6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.

7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.

8. Plane AXY cannot be defined as point X and Y are not in a plane.

9. Lines AB and CD cannot both be in a different plane.

10. Both rays sum up to equal Line XY.

Answer:

X1 2/7

Step-by-step explanation:

Step-by-step explanation:

We can write it in radical form, and the denominator of the exponent became the power of the radical. That is

And

We can also write it as

And that's the simplified form of the given exponential form .

A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,

x - y =1300

x = 1300 + y

Also,  at the end of the year the total interest from the two investments was $1270. Therefore, we can write,

0.13x + 0.07y = 1270

Substitute the value of x from the above,

0.13(1300 + y) + 0.07y = 1270

169 + 0.13y + 0.07y = 1270

0.20y = 1101

y = 5505

substitute the value of y in the first equation,

x - y = 1300

x = 6805

Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.

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Answer:

f(2) =  18

Step-by-step explanation:

Put '2' into the equation where 'x' is to get :

f(2)  =  2 (2^2) + 5 (sqrt(2+2)

        =  8        + 5 (2)   =  18

Answer:

17.5 mph

Step-by-step explanation:

Let the speed of the boat in still water be B mph
Let the rate of the current be R mph

When going upstream the effective speed is B-R mph. In terms of values given effective upstream speed = 42/3 = 14 mph

So,

B-R = 14  ... (1)

Similarly downstream speed is  B + R (faster downstream)

B + R = 42/2 = 21 ....  (2)

(1) + (2) ==> 2B = 35

B = 35/2 = 17.5 mph

Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

Answer:

6.871 decimeters

Step-by-step explanation:

687.1 square centimeters = 6.871 square decimeters

1 dm² = 100 cm²

Answer:

6.871

Step-by-step explanation:

calculator

Answer:

First figure out the angle measure of CBA and DBE to find out what Angle measure of ABE is.

Angle CBA and DBE are vertical angles, meaning they are congruent.

so set the equation as:

(2x+21)=(5x)

21=5x-2x

21=3x

x=7

It doesn't matter in which angle you plug 7 you get the same angle measure, so : 5x=5(7)=35 degrees

So to find angle measure of ABE:

We know that ABE and DBE form linear pair, so

180-35=145 degrees

145 degrees is the answer.

Hope it helps!

Answer:

∠ABE = 145°

Step-by-step explanation:

because angle CBA and ABE form a straight line, we know that they must add together to 180 degrees

and because DBE and ABE also form a straight line/angle, they must add together to 180 degrees

we can set this up as a system of equations (I will be writing ABE as "y")

2x + 21 + y = 180

5x + y = 180

We can combine this to beL

2x + 21 + y = 5x + y

 - 2x              -2x

21 + y = 3x + y

   - y       - y

21 = 3x

x = 7

If we plug this back into our original equations (which is set to 180 degrees), we can find y

2(7) + 21 + y = 180

14 + 21 + y = 180

35 + y = 180

- 35       - 35                  

y = 145

(remember, "y" is angle ABE)

we can check this value (ABE = 145) by substituting our second equation

5(x) + ABE = 180

35 + 145 = 180

       180 = 180

(TRUE)

so, the measure of ∠ ABE is 145°

hope this helps!!

Answer:

Step-by-step explanation:

The domain includes all x values, and here, it is [-2, 4].

The conclusion is a=c statement

A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:

If P, then Q.

P occurs.

Consequently, Q occurs.

The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.

Hence, By modus Ponens

a=b∧b=c ⇒ a=c

So, given a=b∧b=c Then

⇒a=c.

Hence the conclusion is a=c statement .

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The length QT is 36 units

The attached image represents the missing information in the question

From the image, we have:

RQ =QT

Substitute known values

5x + 1 = 3x + 15

Evaluate the like terms

2x = 14

Divide by 2

x = 7

Substitute x = 7 in QT = 3x + 15

QT = 3 * 7 + 15

Evaluate

QT = 36

Hence, the length QT is 36 units

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