1. Which of these pairs of quantities are proportional to each other? For the quantities that are
proportional, what is the constant of proportionality?
a. Radius and diameter of a circle
b. Radius and circumference of a circle
c. Radius and area of a circle
d. Diameter and circumference of a circle
e. Diameter and area of a circle

Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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Answer:

2/3 + 1/6 + 2/8

=(2×8+1×4+2×3)/24

=(16+4+6)/24

=26/24

=13/12

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To the nearest percent, the percent by which the population grew from 2010 to 2020 is; 2%

Percentage increase is defined as the difference between the final value and the initial value, expressed in the form of a percentage.

Now, we are told that;

Initial Population in 2010 = 59000

From 2010 to 2015, the population grew by 7.3%. Thus;

Population in 2015 = 1.073 * 59000 = 63307

Now, we are told that from 2015 to 2020, it fell by 5.3%. Thus;

Population in 2020 = 63307 * (100% - 5.3%)

= 59952

Thus, percentage increase from 2010 to 2020 = (59952 - 59000)/59000) * 100% = 1.61% ≈ 2%

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y = -3

Slope intercept form is y = mx + c.

"m" is the slope and "c" is the y-interecept.

The slope is calculated by dividing the change in y values by change in x values. However, you can see from these two points that as the value of x changes, the value of y stays the same (-3). This means the slope is zero, as it doesn't move up in the y-direction at all.

This means y = 0x + c

You can substitute 14 for y and -3 for x from the first point to get:

-3 = 0(14) + c

-3 = c

y = 0x + -3

Which is the equation of the line in slope-intercept form.

This is the same as saying y = -3, as for every x value, y will always be -3.

Answer:

If x-3 is directly proportional to the square of y, then we can say that:

(x-3) = ky^2

Where k is a constant of proportionality.

If x=5 when y=2, we can substitute these values into the equation to find the value of k:

(5-3) = k(2)^2

2 = 4k

k = 0.5

Now that we have the value of k, we can use it to find the value of x when y=6:

(x-3) = (0.5)(6)^2

x-3 = 18

x = 21

So, if x is directly proportional to the square of y and x=5 when y=2, then x=21 when y=6.

Answer:

The (1/4) slope is the prive per ticket.  The y intercept is the money in the cash box before any tickets were sold.

Step-by-step explanation:

Let y be the money and x the numbers of tickets sold, as requested.  We are told that the equation for this situation is:

   y = (1/4)x + 8

Let's assume the money is in units of dollars.  The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents.  The y-intercept is the value of y when x=0, which means zero tickets have been sold.  That means that the cash box had $8 before any sales were made.  [perhaps to use for making change].

The description of a solution to the problem modeled by the function y = 2x + 8 is given as follows:

The time needed to complete 40 parts  is of 16 minutes.

The function for this problem is defined as follows:

y = 2x + 8.

In which the variables are defined as follows:

Hence, solving the function for x, we are going to obtain the time needed to produce y parts, giving the description of a solution for this problem.

When y = 40, the solution for x is given as follows:

40 = 2x + 8

2x = 32

x = 32/2

x = 16 minutes.

The interpretation of this solution is that a time of 16 minutes is needed to obtain a production of 40 parts.

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Answer:

541

Step-by-step explanation:

if you have a 1 in the ones place and a 4 in the tens place and a 5 in the hundreds place this will be your number

Answer:

Step-by-step explanation:

The equation for a parabola is of the form y = ax^2 + bx + c, where a, b, and c are constants. The graph of a parabola is a U-shaped curve that is symmetrical about a line called the axis of symmetry.

In the equation (x-1)^2 = y+2, we can rewrite it as y = (x-1)^2 - 2. This is the standard form of a parabola with a = 1, b = 0, and c = -2.

The vertex of the parabola is the point on the graph where the parabola reaches its highest or lowest point. For a parabola in standard form, the vertex is always of the form (h,k), where h and k are the values of x and y, respectively, at the vertex. The vertex of this parabola is (1,-2).

The axis of symmetry of the parabola is a line that divides the parabola into two mirror images. For a parabola in standard form, the axis of symmetry is always the line x = h, where h is the value of x at the vertex. The axis of symmetry of this parabola is the line x = 1.

The directrix of a parabola is a line that is used to define the parabola. For a parabola in standard form, the directrix is always the line y = k + p, where k and p are constants and p is the distance from the vertex to the directrix. The directrix of this parabola is the line y = -2 + p, where p is the distance from the vertex to the directrix.

The focus of a parabola is a point on the axis of symmetry that is used to define the parabola. For a parabola in standard form, the focus is always the point F(h,k+p), where h and k are the values of x and y, respectively, at the vertex, and p is the distance from the vertex to the directrix. The focus of this parabola is F(1,-2+p), where p is the distance from the vertex to the directrix.

To sketch the graph of this parabola, we can start by plotting the vertex at (1,-2). Then we can draw the axis of symmetry, which is the line x = 1. Next, we can choose a value for p and draw the directrix y = -2 + p. Finally, we can use the vertex and focus to plot points on either side of the axis of symmetry, and connect these points to form the U-shaped curve of the parabola.

[asy]

unit size(1cm);

real p = 1.5;

pair F, V;

F = (1,-2+p);

V = (1,-2);

draw((-2,0)--(4,0));

draw((0,-4)--(0,4));

draw((-2,V.y)--(4,V.y),dashed);

draw((F.x,p)--(F.x,-4),dashed);

label("$x$", (4,0), E);

label("$y$", (0,4), N);

label("$y = (x - 1)^2 - 2$", (4,-3), E);

a dot("$F$", F, NW);

a dot("$V$", V, S);

label

The mean absolute deviation of the number of goals is 0.8 goals

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

The average distance between data points and a center point is referred to as mean absolute deviation. N is the number of words in the sample, where xi is the sample's individual value and x is the sample's mean or average.

The mean of the goals scored is = (2+3+5+3 +2)/5 = 3

The Mean Absolute Deviation is = [tex]\frac{1}{5}\{|(2-3)| + |(3-3)| + |(5-3)| + |(3-3)| + |(2-3)|}\}\\[/tex] = 4/5 = 0.8

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The solution indicates 40 positive three-digit integers of this kind are available.

The numbers used for counting as well as organizing are known as natural numbers in mathematics. Cardinal numbers and ordinal numbers are two different types of numbers that are used for counting and ordering, respectively.

Left of zero on the number line, a negative number is an integer. It is not zero, though.

Any solution x will mod 23 will also have x+23n as a solution, for some integer n.

Since;

900/23 = 39 3/23,

we know:

There are 39 or 40 three-digit integers of this form.

As it happens,

100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n,

hence 40 solutions to the equation.

The equation reduces, mod 23, to

10x = 11

Its solutions are x = 23n +8.

This shows There are 40 three-digit positive integers of this form.

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Answer:

#1

Step-by-step explanation:

boxes   apples

3            6

6           12

9          18

10         20

ratio of apples to boxes is 2:1.   2 apples each box.  Divide the number of apples by 2 to get the number of boxes.  multiply boxes by 2 to get apples.

#2

boxes    cherries

3             12

5           20

6            24

7            28

if you divide cherrie by 4 you get the number of boxes.

Multiply boxes by 4 to get cherries.

Ratio of cherries to boxes is 4 to 1.

By adding a duplicate of the identity matrix to the augmented matrix, which was formed, it is possible to find the inverse of a square matrix using row reduction.

If the matrix is capable of being reduced to the identity, the identity matrix will simultaneously change into the inverse matrix. A rectangular array of numbers, arranged in rows and columns, is referred to as a matrix. The dimension, or order, of a matrix, indicates how many rows and columns there are in the array. For example, if a matrix has m rows and n columns, its order is expressed as mxn.

Correct Question :

How do you find the inverse of a 4x4 matrix?

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An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By reflecting the given function across the across the y-axis (y = x), we have the following:

f(x) = x/3 - 6

g(x) = f(-x)

g(x) = -x/3 - 6.

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The equation of the function shown in the graph is f(x) = (-2x)^2.

In mathematics a function is a relation between two states that assigned to each element of the first set exactly one element of the second set in order words it is the rule that is describe how unstead of values is related to another set a values function are used to model real voice scenario and to solve mathematical problems example of function include linear equation polynomials and trigonometric function.

This is based on the equation of the parent function, which is f(x) = (-/-)^2. The graph shows that the function has been shifted two units to the left, which is why the coefficient of x is -2 instead of -1.

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The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.

What is Triangle ?

Triangle can be defined as which contains three sides, three angles and the sum of the angles is 180 degrees.

Given ,

ABCD is an isosceles trapezoid with legs AB and CD and base BC.

If the length of AB is (7y - 4),

the length of BC s (4y - 6),

and the length of CD is (8y - 18).

The two legs are of equal length In any isosceles trapezoid that means:

7y - 4 = 8y - 18

Add 18 on both sides in the above equation.

7y - 4 + 18 = 8y - 18 + 18

7y + 14 = 8y

Now, subtract 7y on both sides in the above equation.

7y + 14 - 7y = 8y - 7y

Simplify the above expression in order to get the value of 'y'.

y = 14

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Answer:

90670998.89999999999999

Answer:

y=4x+12

Step-by-step explanation:

if a line is parallel to another they have the same slope ,,

y=mx+c

where m represents the slope

and c represents the intercepted part of y axis

so the slope equals 4 from y=4x+11

to find the intercepted part c ,, substitute by the given point in the equation y=mx+c

(-2,4),, and slope is 4

4= 4×-2+c

4= -8+c

c= 12

so the equation is

y=4x+12

Answer:

y =4x-18

Step-by-step explanation:

y +2 = 4(x - 4)

y +2 =4x-16

y = 4x-18

Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.

To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.

For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:

h(5) = √(5-3) - 2

= √2 - 2

= 1.4 - 2

= -0.6

Therefore, the value of h(x) for x = 5 is -0.6.

You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.

Step-by-step explanation:

Answer:

g[f(x)]

Step-by-step explanation:

Given functions:

[tex]f(x)=x-3[/tex]

[tex]g(x)=\sqrt{x}-2[/tex]

Composite functions are when the output of one function is used as the input of another.

Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):

[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]

The polynomial is a mathematical expression containing variables and coefficients and can be written as a sum of terms of various degrees. In this case, the polynomial is composed of three terms of varying degrees: 5x²y, 8xy² and 9. The degree of this polynomial is the highest degree of the terms, which is 4.

1. Identify the terms of the polynomial: 5x²y, 8xy² and 9

2. Identify the degree of each term: 5x²y has degree 3, 8xy² has degree 4 and 9 has degree 0

3. Determine the highest degree among the terms: The highest degree is 4

4. The degree of the polynomial is then the highest degree among the terms, which is 4.

A polynomial is a mathematical expression consisting of variables and coefficients and can be written as a sum of terms of varying degrees. In this case, the polynomial consists of three terms: 5x²y, 8xy² and 9. To determine the degree of the polynomial, we must first identify the degree of each term. The term 5x²y has degree 3, the term 8xy² has degree 4 and the term 9 has degree 0. The degree of the polynomial is then the highest degree among the terms, which is 4. This means that the polynomial has a degree of 4, as the highest degree among its terms is 4. The degree of a polynomial is an important factor in solving equations and other mathematical problems, as it can determine the complexity of the equation.

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The number of groups of like terms is 3

An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.

These algebraic expressions are also composed of mathematical operations, such as;

A term can be described a single variable, number or numbers and variables that are multiplied together.

From the information given, we have the terms;

3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰

The similar terms are;

3x¹³,  3x¹⁰,  3¹³

Hence, the number is 3

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The probability of the two cards being D and D, P(D, D), is 4/9. The correct option is: 4/9.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Calculating probability of selecting a card:

From the question, we are to determine the probability of selecting two cards with D and D

From the formula for probability, we have that

P(D) = Number of favorable outcomes to D / Total number of possible outcomes

From the given information,

Number of favorable outcomes to D = 2

Number of possible outcomes = 3

Thus,

P(D) = 2/3

Then,

The probability of selecting two cards that have D and D with replacement is

P(D, D) = P(D) × P(D)

P(D, D) = 2/3 × 2/3

P(D, D) = 4/9

Hence, the probability is 4/9.

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Answer: Five Days

Step-by-step explanation:

Isabella can hike 8 miles per day. So:

[tex]\frac{30miles}{8miles} = 3.75 days[/tex]

It will take:

[tex]\frac{70 miles}{8 miles} = 8.75 days[/tex]

..in total to hike 70 miles.

So, subtracting the two values:

[tex]8.75 - 3.75 = 5[/tex]

She still needs to hike five days in order to finish the trail.

The quadrilateral's image points will be,A(3, 3) → A'(-3, 3) R(5, 7) → R'(-7, 5) M(7, 5) → M'(-5, 7) Y(5, 1) → Y'(-1, 5).

If a point (x, y) is rotated 180 degrees anticlockwise with respect to the origin, the rotational rule is:

(x, y) → (-y, x) (-y, x)

Consequently, the image point's coordinates following rotation will be (-y, x).

Using this guideline,

The quadrilateral's image points will be,

A(3, 3) → A'(-3, 3)

R(5, 7) → R'(-7, 5)

M(7, 5) → M'(-5, 7)

Y(5, 1) → Y'(-1, 5)

By graphing the image points we can get the graph of the image quadrilateral A'R'M'Y'.

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The question is incomplete, complete question:

Quadrilateral ARMY is rotated 180 degrees about the origin. Draw the image of this rotation.

There are 7 white cars, 16 blue cars,  14 red cars and 5 silver cars.

Two or more expressions with an Equal sign is called as Equation.

Let w represents white cars

b represent blue carr

r represents red cars

s represents silver cars

There were three times more silver colour cars than red cars

3s=r...(1)

There were 2 more blue cars than red and silver cars together

b+2=r+s..(2)

There were twice more white cars than red.

2w=r..(3)

42 cars altogether in the parking lot.

w+b+r+s=42

After solving the above equation we get

s=5, b=16, w=7 and r=14

Hence, there are 7 white cars, there are 16 blue cars, there are 14 red cars and 5 silver cars.

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The reasons and responses to the graphs in the question are as follows:

Graph 1.

The amplitude of the first graph is (1/2) which is the height from the midline to the peak

The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function

The period of the graph is 2·π, which is the period of the parent cosine function

Therefore, the correct option is

Graph 2: Please find attached the graph of the function g(x) = 2×cos(x)

Graph 3: The frequency of a sinusoidal function is given as follows;

The period of the graph = π

Therefore;

The frequency of the sinusoidal graph is 2

Graph 4.  Required:

To find the equation that represents the function of the graph

Solution;

The period of the function, T = π

The graph of the function has a maximum at x = 0, therefore, the graph is similar to a cosine function, y = cos(B·x)

Where;

B = 2·π/T

Therefore;

B = 2·π/π = 2

Therefore;

The equation that represent the function in the graph is f(x) = cos(2·x)

Question 5. The given function is f(x) = cos(2·x)

The frequency factor in the given function, B = 2

The period, T = 2·π/B

Therefore, T = 2·π/2 = π

The period of the function, f(x) = cos(2·x), is 2

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Leo's balance after 8 months is $1725.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

1500, 1530, and 1560 is a geometric sequence.

First term.

a = 1500

Common ratio.

r = 1.02

The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].

Now,

For n = 8,

8th term.

= 1500 x [tex]1.02^7[/tex]

= 1500 x 1.15

= 1725

Thus,

The balance after 8 months is $1725.

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It is given that a 45-45-90 triangle whose each leg is 12 cm, then the length of the hypotenuse can be found out as 12/√2

since the hypotenuse is one of the legs multiplied by √2.

dividing the hypotenuse by √2 will get the length of one leg. since it is a 45 45 90 triangle, the length of the two legs are the same.

It is given that  a 45-45-90 triangle whose each leg is 12 cm, then the length of the hypotenuse can be found out as:

By using the Pythagoras theorem, we have

a^2+b^2= c^2

Substituting the given values, we have

12/√2

Thus, the length of the hypotenuse will be

12/√2

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Answer:

8 + v

Step-by-step explanation:

assuming Lamar didn't buy any other cupcakes outside of the chocolate and vanilla ones mentioned, the expression that gives you the total amount of cupcakes bought for the party is 8 + v. since you don't know the number of vanilla cupcakes Lamar bought, it is represented as the variable v in this problem. Then just add 8 and the variable v together. hope this helped :]

If there are [tex]2\pi[/tex] radians and [tex]360 \textdegree[/tex] in one full rotation and an angle has a measure of [tex]2.1 radians[/tex] then the angle is 33.4 percent of a full rotation , and the measure of the angle in degrees is [tex]120.2\textdegree[/tex] .

we know that in 1 full rotation , the radians is 2π ;

and in 1 full rotation , the degree is 360 degree ;

We know that the relation between the degree and the radian measure is

⇒ [tex]1 radian = \frac{180\textdegree}{\pi }[/tex] ;

Part(i) ;

we have to express the 2.1 radians as a percent of full rotation ;

we get ; ⇒ [tex]\frac{2.1}{2\pi } \times 100\%[/tex]

on simplifying further ,

we get ; [tex]\approx 33.4\%[/tex] .

Part(ii)  ;

we have to determine the measure of the angle in degrees.

from part(i) , we find the percent is [tex]33.4\%[/tex] ,

So , [tex]33.4\%\times 360\textdegree[/tex]

On simplifying ,

⇒ [tex]\frac{33.4}{100} \times 360\textdegree[/tex]

[tex]\approx 120.2\textdegree[/tex] .

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