The graph below shows an exponential function and a quadratic function.

mc012-1. Jpg

How do the functions compare over the interval mc012-2. Jpg?
The exponential grows at approximately half the rate of the quadratic.
The exponential grows at approximately the same rate as the quadratic.
The exponential grows at approximately twice the rate of the quadratic.
The exponential grows at approximately four times the rate of the quadratic.

Step-by-step explanation:

Let's call the time it took Pat and Rich to drive to the beach "x".

The time it took them to drive back was twice as long, so it took 2x hours.

The total time spent traveling was x + 2x = 3x hours.

Since they spent 9 hours traveling, 3x = 9 hours.

So, x = 9 hours / 3 = 3 hours.

This means it took Pat and Rich 3 hours to drive to the beach and 2 * 3 = 6 hours to drive back.

Line AB and CD are two parallel lines

The slope of a line is defined as the change in y- the coordinate with respect to the x-coordinate and the formula is given by    

Note:

Here we have  

AB formed by (-4, 7) and (-2, 6)

Slope of AB = (6 - 7)/(-2 + 4) = -1/2

CD formed by (2, -2) and (-8, 3)

Slope of CD = (3 + 2)/(-8 - 2) = 5/-10 = -1/2

Here Slope of AB = Slope of CD  

As we know the slope of parallel lines is equal

Therefore,

Line AB and CD are two parallel lines

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The following mathematical expression matched with its translation:

1. x + y = 6 (the sum of two numbers is six)

2. x + y (the sum of x and y)

3. xy (the product of two numbers)

4. x ÷ y (x divided by y)

5. y ÷ x (y divided by x)

6. y = x - 6 (six less than a number is y)

7. x - y (x minus y)

8. 6 x = y (six times a number equals y)

9. xy = 6 (the product of two numbers is six)

10. y - x (x subtracted from y)

Mathematical expression can be translated as thus;

the sum of two numbers is six

Let the unknown numbers be x and y respectively

So,

x + y = 6

six less than a number is y

x - 6 = y

also written as

y = x - 6

six times a number equals y

6 × x = y

6x = y

also written as

y = 6x

Therefore, mathematical expressions are algebraic representation of mathematics in words.

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The cost of 1 hot dog is $2.25

Proportion is a mathematical comparison between two numbers.

Given that, the cost of 4 hot dogs are $9, we need to find the cost of 1 hot dog,

Let the cost of 1 hot dog be x, therefore, setting the proportion,

4 / 9 = 1 / x

x = 9/4

x = 2.25

Hence, the cost of 1 hot dog is $2.25

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The angles  on the quadrilaterals she drew are 47 in number.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles

As there are four rectangles, The total number of angles in a rectangle are 4 × 4 = 16 angles.

The number of triangles is 3, the total number of angles is 3 × 3 = 9 angles.

Number of pentagons are 2,  the total number of angles is 2 × 5 = 10 angles.

The number of trapezoids are 3, the total number of angles is 3 × 4 = 12 angles.

Total number of angles on the quadrilaterals she drew is 16 + 9 + 10 + 12 = 47 angles.

Hence, the angles  on the quadrilaterals she drew 47.

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Answer:

Step-by-step explanation:

The reflection of point A will be at (3, -4) - that is 2 units directly below the red X.

The experimental probability that the team made a goal on any given shot is 0.0625

From the question, we have the following parameters that can be used in our computation:

A soccer team made 2 goals out of 32 attempts in a game

The experimental probability that the team made a goal on any given shot is calculated as:

P = 2/32

Evaluate the quotient

P = 0.0625

Hence, the probability is 0.0625

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The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12%  and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)

Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)

Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470

Now

y = 1470 + 350
y = $1820

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The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.

Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per​ hour, with a standard deviation of 4 miles per hour.

[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].

Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.

Therefore, 75% of the vehicles would fall into this category.

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Answer: The perimeter triples.

Step-by-step explanation:

Since there is a direct variation, if the side length triples, so does the perimeter.

Mr. Lopez cover in sand by 50 yd².

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Mr. Lopez is looking to fill a part of a park with sand.

And, The shape below represents the part of the park being covered in sand.

Now, We will find the area of figure as;

The park is mix of two figure rectangle and triangle.

Hence, We get;

Area of rectangle = 5 × 8

                           = 40 yd²

And, Area of triangle = 1/2 × 4 × 5

                                 = 10 yd²

Thus, The area of given figure is,

⇒ Area = 40 yd² + 10 yd²

⇒ Area = 50 yd²

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Answer: c

Step-by-step explanation:

-3v - 2v > 35

combine like terms: -5v > 35

divde by the same term (isolate the variable): -5v/-5 , 35/-5

v < -7

Answer: pls braiinliest :D

To find the equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4, we can use the concept of the slope of a line. The slope of a line perpendicular to another line has a negative reciprocal slope.

The slope of the line y = 4/5x + 4 is 4/5. The negative reciprocal of 4/5 is -5/4.

So, the slope of the line passing through (8, -2) and perpendicular to y = 4/5x + 4 is -5/4.

Next, we can use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values, we get:

y - (-2) = -5/4 (x - 8)

Expanding and solving for y, we get:

y = -5/4x + 26/2

y = -5/4x + 13

The equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4 is y = -5/4x + 13.

Step-by-step explanation:

Explanation:

The two horizontal sides are parallel. The side marked 34 is half as long as side x.

In other words, side x is twice as long as the side marked 34.

x = 2*34 = 68

For more information, search out "midsegment of a triangle".

Answer:

The possible numbers of players are multiples of 6 (6, 12, 18, etc.).

Step-by-step explanation:

For the coach to be able to form teams of 6 players each, the total number of players must be divisible by 6. This means that if there are 6, 12, 18, 24, 30, etc. players, the coach can divide them evenly into teams of 6. Any other number of players would result in either having a team with more or fewer than 6 players, or leaving some players out. Hence, the possible numbers of players are multiples of 6.

The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

The given graph is an exponential function and should take the form;

[tex]f (x) = a (b)^x[/tex]

Hence, using values from the graph;

For ( -1, 0.2 ) = a • b..........(i)

For (0, 0.8); 10.5 = a • b².........(ii)

=> x=0 and y= 0.8

So.

0.8=a(1/2)^0

0.8=a

Thus, the rule for the function is; y=0.8(1/2)^x

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Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

Answer:15

Step-by-step explanation:

i did the math

Answer:

15

Step-by-step explanation:

15 x 2=30

15x3=45

The length of CE in the triangle is 20.

A triangle is a three-sided polygon that consists of three edges and three vertices.

From the given triangle ABC

BC=CD which are congruent sides

x-5=14

x=19

AB=DE

2x+3=6

2x=3

x=3/2

Now DE 2x+3=2(3/2)+3=6

CE=CD+DE

=14+6

=20

Hence, the length of CE in the triangle is 20.

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The number of students who got actually enrolled are, 5400

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, a large university accepts ​60% of the students who apply. Of the students the university​ accepts, ​45% actually enroll, there are 20,000 students​ apply,

Since, the students whose application has been accepted = 20000 × 60%

= 12000

Now, the students who got admission = 12000 × 45%

= 5400

Hence, the number of students who got actually enrolled are, 5400

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The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.

If two variables of two quantities, x and y, are represented on a graph to show their relationship, they are proportional quantities if for every ratio of y to x, the value we get is the same, which means they have a constant of proportionality, k.

Using the points on the graph in the image attached below, the table can be completed as follows:

Part A:

Number of T-shirts (x): 1   2   3   4

Time in minutes (y):     5  10  15 20

Part B: Find the ratio of y to x for each of the points on the graph.

5/1 = 5

10/2 = 5

15/3 = 5

20/4 = 5

The table derived from the graph is:

Number of T-shirts (x): 1   2   3   4

Time in minutes (y):     5  10  15 20

B. The quantities are proportional.

The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.

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"Your question is incomplete, probably the complete question/missing part is:"

The missing information are in the attachment below.

Answer:

"of -1 and 2."

Step-by-step explanation:

The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.

Answer:

It's the third choice.

Step-by-step explanation:

IF y varies inversely as x then y = k/x   where k is a constant,

and k = xy    

For the 3rd choice

-1 * -2/7 = 2/7

4 * 1/14 = 2/7 and

6 * 1/21 = 2/7

so, this is inverse variation.

The domain of the function is given as follows:

[-10,10].

The domain of a function is the set containing all the input values of the function.

Hence, on the graph, the domain of the function is composed by the values of x of the function, and is given as follows:

[-10,10]. (closed due to the closed circle).

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The statement “Every sample space S is a finite set” is false because some sample spaces can be infinite, such as rolling a continuous random variable.

The statement “Every sample space S is a finite set” is false. A sample space is the set of all possible outcomes of a random experiment. While some sample spaces may be finite, not all sample spaces are. There are situations where the sample space can be infinite, such as when rolling a continuous random variable like a dice.

For example, the sample space of rolling a fair six-sided die is finite, consisting of the numbers {1, 2, 3, 4, 5, 6}. However, the sample space of choosing a real number between 0 and 1 is infinite, as there are infinitely many possible outcomes between 0 and 1.

Therefore, it is incorrect to say that every sample space is a finite set.

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The solution of the expression is, 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ h (9) = 2x - 3

Now, Substitute x = 9, we get;

⇒ h (9) = 2 × 9 - 3

⇒ h (9) = 18 - 3

⇒ h (9) = 15

Thus, The solution of the expression is,

⇒ h (9) = 15

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Answer:

1/2 bucket

Step-by-step explanation:

Each of the 8 buckets is 1/4 full.

The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.

Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.

1/4 × 2 buckets = 1/2 bucket

Answer: 1/2 bucket

The set of pairs for which x and y vary inversely is given as follows:

{(-1, -2/7), (4, 1/14), (6, 1/21)}.

(third set).

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse relation, the relation is modeled as follows:

y = k/x.

Meaning that when x increases, y decreases at a constant rate.

The constant is then obtained as follows:

k = yx.

Hence the third relation is then the relation for which x and y vary inversely, as:

k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.

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The rate of change of the hypotenuse is given as follows:

dh/dt = 2 in/sec.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The hypotenuse is then given as follows:

h² = x² + y².

For this problem, the hypotenuse has the value given as follows:

h² = 33² + 44²

h = square root(33² + 44²)

h = 55.

Applying implicit differentiation, the rate of change of the hypotenuse is obtained by the equation as follows:

h dh/dt = x dx/dt + y dy/dt.

Replacing the values, the rate of change is calculated as follows:

55dh/dt = 33 x 10 - 44 x 10

55dh/dt = -110

dh/dt = -110/55

dh/dt = 2 in/sec.

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