Use the table to make a function

Answer:

Part A:

The graph of g(x) = |x - 7| is a V-shaped graph that opens upward, with a vertex at x = 7 and y = 0. The graph of the function is symmetrical about the vertical line x = 7. The domain of the function is all real numbers, and the range is all non-negative real numbers, including zero.

Part B:

The transformation from f(x) to h(x) is a vertical shift upward by 2 units. The vertex of the parent function f(x) = |x| is at (0, 0), and the vertex of the transformed function h(x) = |x| + 2 is at (0, 2). The range of the parent function f(x) is all non-negative real numbers, including zero. The range of the transformed function h(x) is all non-negative real numbers greater than or equal to 2. The transformation shifts the entire graph of the parent function upward, increasing the y-values of all points on the graph by 2 units.

It took Bunolo 100 minutes (or 1 hour and 40 minutes) to complete the 10 km race at an average speed of 6 km/h.

To find out how long it took Bunolo to complete a 10 km race with an average speed of 6 km/h, we can use the formula:

time = distance / speed

where "distance" is the distance of the race and "speed" is the average speed at which Bunolo ran. We can convert the speed to km/minute to get the time in minutes.

To do this, we can divide the speed in km/hour by 60 (the number of minutes in an hour) to get the speed in km/minute:

6 km/hour ÷ 60 minutes/hour = 0.1 km/minute

Now, we can substitute the distance and speed values into the formula to get the time in minutes:

time = 10 km / 0.1 km/minute = 100 minutes

Therefore, To complete the 10 km race with the average speed of 6 km/h, it took Bunolo 100 minutes.

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Answer:

C) E = 118°; T = 118°

-----------------------------------

The given figure is a kite since it has two pairs of congruent sides as marked.

Its one pair of opposite angles are congruent. That is:

Sum of all interior angles of a quadrilateral is 360°:

Both the missing angles are 118°.

Based on the given data set, the following statements are true:

The other statements are false because:

Lastly, The interquartile range is not 10. As calculated above, Q1 is 46 and Q3 is 52, so the IQR is 52-46=6.

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See transcribed text below

Use the following data set to answer the question.

(54, 45, 48, 51, 53, 44, 52}

Which statements about the data set are true? Select all that apply.

The standard deviation is approximately 3.7.

The interquartile range is 10.

There are no outliers.

The outlier is 54.

The standard deviation is approximately 49.6.

The interquartile range is 8.

The value of x justify the equation is x = 8.

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equal sign."='

These two expressions on either side of the equals sign are called the "left hand side" and "right hand side" of the equation. Generally, we assume the right hand side of an equation is zero.

Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters.

Given:

48 = 5(2x - 7) + 3

Distribute 5:

48 = 10x - 35 + 3

Combine like terms:

48 = 10x - 32

Add 32 on both sides,

48 + 32 = 10x - 32 + 32

80 = 10x

Divide by 10 on both sides,

80/10 = 10x/10

x = 8

Check this value

Plug in x to verify it's a solution

48 = 5(2(8) - 7) + 3

48 = 5(16 - 7) + 3

48 = 5(9) + 3

48 = 45 + 3

48 = 48

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The correct answer is 45.28°

In order to get that answer, you must set up the arc length formula.

l = m/360 • 2πr

4.9 = m/360 • 12.4π

We are trying to find the angle measure; therefore, we are going to divide.

4.9 = 0.10821m

Flip the equation

0.10821m = 4.9

0.10821m/0.10821 = 4.9/0.10821

m = 45.28°

We can use the formula angle = (arc length / radius) or an online calculator to find the angle of the slice, which is approximately 47 degrees in this case.

To find the measure of the angle of one slice of pizza, we can use the formula:

angle = (arc length / radius)

However, we are not given the radius of the pizza, so we first need to find it. One way to do this is to use the length of one side of the slice and the central angle of the slice. We know that the central angle of the slice is twice the angle at the center of the pizza that the slice occupies, so we can find this angle by:

angle at center = (angle of slice) / 2

We can then use the law of cosines to find the length of the radius:

radius² = (side length / 2)^2 + (side length / 2)² - 2 * (side length / 2) * (side length / 2) * cos(angle at center)

Once we have the radius, we can use the formula above to find the angle of the slice. However, since this calculation can be quite involved, it may be simpler to use an online pizza slice angle calculator. Using this tool with the given values, we find that the angle of one slice of pizza is approximately 47 degrees.

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Answer:

  Two solutions:

Step-by-step explanation:

Given right ΔABC, with tan(A) = 3/2 and b = 5, you want the exact lengths of sides a and c.

To completely solve a triangle, you need to know at least one side, at least one angle, and one other side or angle. Here, we're given one side and one angle, so cannot solve the triangle using the given information.

We know another angle is 90°, but we don't know which one.

Often, side c is the one designated as the hypotenuse, but that is not necessarily the case. So, there are two solutions.

This case corresponds to the red triangle shown in the attachment.

In this triangle, the leg adjacent to angle A is side b, so we have ...

  Tan = Opposite/Adjacent . . . . . trig relation

  3/2 = a/5

  a = 15/2

The Pythagorean theorem can be used to find the length of side c.

  c² = a² +b²

  c² = (15/2)² +5² = 225/4 +25 = 325/4

  c = √(325/4)

  c = (5/2)√13

This case corresponds to the blue triangle shown in the attachment.

The given tangent of angle A tells us the ratio ...

  Tan = Opposite/Adjacent

  3/2 = a/c

  a = 3/2c . . . . . multiply by c

The Pythagorean theorem tells us ...

  b² = a² +c²

  5² = (3/2c)² +c² = 13/4c² . . . . . . substitute for b and a

  c² = (4/13)(5²) = (10/13)²·13 . . . . . . multiply by 13/13

  c = (10√13)/13 . . . . . . . . . . . . square root

  a = 3/2c = (15√13)/13 . . . . . . find 'a'

The area of the figure is 52 square units

The perimeter of the figure is 36 units

The graph is attached

The perimeter of the figure is found by summing the length of the sides

F(-5, 2) - G(-3, 2) = 2 units

G(-3, 2) - H(-3, 4) = 2 units

H(-3, 4) - J(1, 4) = 4 units

J(1, 4) - K(1, 1) = 2 units

K(1, 1) - L(4, 1) = 3 units

L(4, 1) - M(4, -2) = 3 units

M(4, -2) - N(6, -2) = 2 units

N(6, -2) - P(6, -3) = 1 units

P(6, -3) - Q(-5, -3) = 11 units

Q(-5, -3) - F(-5, 2) = 5 units

The perimeter = 2 + 2 + 4 + 2 + 3 + 3 + 2 + 1 + 11 + 5 = 36 units

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Answer:

The function f: A -> B is defined by:

f(x) = { 11, if x = -1 or x = 2,

-1, if x = 0,

-2, if x = 1,

0, if x = 3 or x = 4 }

The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.

To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.

To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.

Therefore, the function f is one-to-one and onto both.

The values in the table are 7, 11, 15, and 19.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We are assuming the table to be:

x             value

2            2x2 + 3 = 7

4           4x2 + 3 = 11

6           6x2 + 3 = 15

8           8x2 + 3 = 19

Thus,

The values in the table are 7, 11, 15, and 19.

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The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

Function 1 is given as,

y = - 2x - 4

The slope is -2 and the y-intercept is -4.

From the graph, the equation of function 2 is given as,

x / 2 + y / 4 = 1

2x + y = 4

y = - 2x + 4

The slope is -2 and the y-intercept is 4.

The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

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The missing graph is attached below.

Step-by-step explanation:

inversely means

y = k/x

therefore

30 = k/4

120 = k

y = 120/10 = 12

FYI :

directly would mean

y = kx

The value of y will be 12 when x is equal to 10.

The relationship between two variables known as "inverse variation" occurs when the value of one variable increases while the value of the other variable decreases.

Given that, y varies inversely with x.

Here, y∝1/x

y=k/x

xy=k

When x is 4, y is equal to 30, we get

k=4×30

k=120

When x=10, we get

10y=120

y=12

Therefore, the value of y will be 12 when x is equal to 10.

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Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.

In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.

In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.

The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

The measure of LQ is equal to the sum of the measures of angles R and T:

LQ = 63 + 150 = 213 degrees

The measure of LS is equal to the sum of the measures of angles Q and U:

LS = 117 + 30 = 147 degrees

So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.

Step-by-step explanation:

Answer:

C. 77.3% decrease

Step-by-step explanation:

To calculate the percent change, we can use the formula:

percent change = (new value - old value) / old value * 100

Plugging in the values, we get:

percent change = (20 - 88) / 88 * 100 = -68 / 88 * 100 = -0.772727 * 100 = -77.3

Since the new value is lower than the old value, this is a decrease, and the answer is -77.3, or 77.3% decrease.

The expression for f(x) - g(x) - h(x) is 6x - 5x² + 6.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 3x + 5

g(x) = 4x² - 2

h(x) = x² - 3x + 1

Now,

f(x) - g(x) - h(x)

= 3x + 5 - (4x² - 2) - (x² - 3x + 1)

= 3x + 5 - 4x² + 2 - x² + 3x - 1

= 6x - 5x² + 6

Thus,

6x - 5x² + 6 is the expression.

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The area of the trapezoid is A = 2285.47 units²

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be represented as A

Now , the value of A is

Let the height of the trapezium be h = 52.6

Let the length of the shorter base a = 39.1

Let the length of the longer base b = 47.8

Now , Area of Trapezoid = ( ( a + b ) h ) / 2

On simplifying , we get

Area of trapezoid A = ( ( 47.8 + 39.1 ) 52.6 ) / 2

Area of trapezoid A = ( 86.9 x 52.6 ) / 2

Area of trapezoid A = 4,570.94 / 2

Area of trapezoid A = 2285.47 units²

Hence , the area of the trapezoid is 2285.47 units²

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It says that raise school is 1. 7 miles from his house the student walks 17 miles in a 5-day school week

If the school is 1.7 miles from the student's house, then the round trip distance between the house and school is 2 times 1.7 miles, or 3.4 miles per day.

A mile is defined as the unit of length, which is exactly equal to 5280 feet, or 1760 yards, and standardized as exactly 1609.344 meters by the International agreement in 1959. It is the largest unit that is commonly used to measure the distance between places that are far from each other.

To find out how many miles the student walks in a 5-day school week, we can multiply the daily distance by the number of school days in a week:

3.4 miles/day x 5 days/week = 17 miles/week

Therefore, the student walks 17 miles in a 5-day school week

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Answer:

C = $24 + 0.45x

Step-by-step explanation:

If we let total amount spent by a guest to the park as $C and number of tickets bought is x then the algebraic expression to represent the total amount spent by a guest is

C = $24 + 0.45x

The sin 20° can be expressed as D. cos 70⁰

We will need to find the value of given angles one after the other . for instance By creating an angle of 70 degrees with the x-axis and then determining the coordinates of the point (0.342, 0.9397) on the unit circle, it is possible to determine the value of sin 70 degrees. The y-coordinate is equal to the value of sin 70°. (0.9397). ∴ sin 70° = 0.9397.

The given angle is

Sin 20° = 0.342

option A;

tan 20⁰ =0.364

Option B:

sin 70⁰ =  0.9397

Option C :

cos 20° = 0.9397.

Option D :

cos 70 degrees = 0.342

Therefore, option D is correct.

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The common region to both the graphs represents the solution set of the given inequalities.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.

Assume that you worked {x} hours Mowing lawns and {y} hours babysitting.

We can write the inequalities as -

x + y ≤ 15

3x + 5y ≥ 60

Refer to the graph attached. The common region to both the graphs represents the solution set.

Therefore, the common region to both the graphs represents the solution set of the given inequalities.

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Answer:

Not Possible

Step-by-step explanation:

No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.

Here are some that are equivalent:

20(2+1)

2(20+10)

40+20

60

Answer:

If you want it simplified, it is 3x + 14!

Hope it helps!

After solving the equation for n and b we find out that Lin bought 1 necklace and 4 bracelets.

We can set up the following system of equations based on the given information: n = number of necklaces, b = number of bracelets

4n + b = 20 (Lin spends $20 on necklaces and bracelets)

where 4n represents the cost of n necklaces and b represents the cost of b bracelets. This system of equations can be used to solve for n and b. we can solve for n and b using the system of equations:

n + 1b = 5

4n + 1b = 20

We can use the first equation to solve for n in terms of b: n = 5 - b

Substitute this expression for n into the second equation: 4(5 - b) + b = 20

Simplifying this equation, we get: 20 - 4b + b = 20

Solving for b, we get: b = 4

Substituting this value of b back into n = 5 - b, we get: n = 1

Therefore, Lin bought 1 necklace and 4 bracelets

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Complete Question

At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys. Find the number of necklaces and bracelets Lin purchased.

Answer:

Step-by-step explanation:

5x - 10 - 4 = 6

5x - 14 = 6

5x = 20

x = 4

Option C is the solution

If we have four variables, then four equations will we have in our system of linear equations.

A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation that can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point where the line intersects the y-axis.

Linear equations can be used to model a wide range of real-world phenomena, from simple physics problems such as calculating the speed of a moving object, to economic models that describe the relationship between price and demand. They are also widely used in fields such as engineering, finance, and statistics.

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Answer:

y = -2x + 8

When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.

Step-by-step explanation:

Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.

For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]

A combination is a way of selecting items from a collection where the order of selection does not matter.

We will have to apply the formula separately for vegetarian and meat items.

Combinations available

A. 1 vegetarian item and 2 meat items              

    [tex]^{5} C_{1} and ^{4} C_{2}[/tex]                                 (In combination "and" means to multiply)                                                                                        

   = [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]

   = [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]

   = 5.3.2

   = 5.6

   = 30

B. 2 vegetarian items and 1 meat item

    [tex]^{5} C_{2} and ^{4} C_{1}[/tex]

   = [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]

   = [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]

   = 5.2.4

   = 10.4

   = 40

C. 3 vegetarian items and no meat item

   = [tex]^{5} C_{3} and ^{4} C_{0}[/tex]

   = [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]

   = 5.2

   = 10

Now, we will add all the different combination

Total combinations = 30+40+10

                                = 80 different type of dinners

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Rounded to the nearest minute, the answer is 12 minutes.

The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.

The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.

To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:

h(t) = 10 sin(2πt/10) + 11

To find out when h(t) is greater than 19, we solve the inequality:

10 sin(2πt/10) + 11 > 19

Subtracting 11 from both sides, we get:

10 sin(2πt/10) > 8

Dividing by 10, we get:

sin(2πt/10) > 0.8

The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:

sin(2πt/10) = 0.8

sin(2πt/10) = -0.8

Using a calculator, we find that these equations have solutions at:

t = 1.167, 8.833, 3.5, 6.5

These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.

Therefore, the total time spent higher than 19 meters is:

(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes

Rounded to the nearest minute, the answer is 12 minutes.

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