Martin and Isabelle go bowling. Each game costs $10, and they split that cost. Martin has his own bowling shoes, but Isabelle pays $3 to rent shoes.Which graph shows a proportional relationship? Explain why.

Answer:

Explanation:

Given the functions:

We want to find:

First of all, we need to find:

This is done by inserting the value of h(x) into f(x)

So, we have:

Substituting 7 for x in f[h(x)], we have f[h(7)]

Which is what we are looking for.

Create a quadratic function in one of the forms and show how to convert it to the other two forms.

Step-by-step explanation:

1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.

2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.

3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.

The vertex of the parabola is written as (h, k) where b is the x - coordinate and c - is the y - coordinate

We are presented with a group of graphs in which the x-axis represents time and the y-axis represents speed.

We are told that Joy started by accelerating when she took off, which means the graph should start with a line with positive slope.

She then maintained her speed, which means the slope of the line is 0, orin other words, the line is parallel to the time axis.

Finally, we are told that she saw a sign saying the speed limit had been increased, so she probably accelerated again, meaning the line should have a positive slope again.

Thus, the graph representing the situation is the third option.

7.18° the angle which the road makes with the horizontal.

Define Trigonometric functions

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given,

Height of hill = 250 feet

Length of the slope = 2000 feet

find the angle,

we know, sin(x) = perpendicular / hypotenuse

sin(x) = 250 / 2000

x = sin^-1 (0.125)

x = 7.18°

Hence, 7.18° the angle which the road makes with the horizontal.

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ANSWER

Function f(t) represents a growth by 4%

EXPLANATION

If the function represents a decay it is written as:

and if it represents a growth it's:

We can see if it's a growth or decay by looking at the number we have between parenthesis: if it's greater than 1, then it's a growth and if it's less than 1 then it's a decay.

For function f(t) we have

Therefore, r = 0.04 which, expressed as a percent is 4%

TheseGiven the set: {-18, -16, -14, -12, -10, -8, -6}

This is 7 numbers

Multiplies of -6 are:

This is 3 numbers

Therefore, the probability is given by:

So:

Answer: 3/7

We can write the equation of a parabola in two different ways:

The standard form:

And the vertex form:

If the parabola has a minimum or a maximum depends on the leading coefficient (the coefficient of x²) or in both cases the coefficient a.

Let's see the cases:

If a is positive, the parabola opens upwards, so the parabola has a minimum.

If a is negative, the parabola opens downwards, so the parabola has a maximum

To match the expression with the sum, what you have to do is solve each sum.

Remember that to sum/subtract two fractions, both of them should be expressed using the same denominator,

1)

The denominators of these fractions are "3" and "6", the least common denominator between both values is 6. To express the first fraction as its equivalent with denominator 6, you have to multiply it by 2:

Now you can proceed to add both fractions:

The result for this sum is 1/6

2)

First, simplify both symbols, when a plus symbol and a minus symbol and next to each other, the plus sign gets canceled:

To subtract both fractions the first step is to express them using the same denominator. The least common denominator between 12 and 4 is 12, to express -3/4 as its equivalent with denominator 12, you have to multiply the fraction by 3:

Next, subtract both fractions:

The result is no in its simplest form, 2 and 12 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator by 2:

The result for this expression is -1/6

3)

Same as before, the first step is to express both fractions with the same denominator. the least common denominator for both fractions is 8. To express -1/4 as its equivalent with denominator 8, you have to multiply the fraction by 2

Next, add both fractions:

The result for this sum is 1/8

So the corresponding matches are:

The volume of the cone is 45.28 cubic inches.

The amount of sand inside the cone is measured by its volume.

Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.

The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.

The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]

The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]

The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]

So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]

[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]

The volume of the cone is 45.28 cubic. inches

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From the given problem, there are 3 computer labs and each lab has "s" computer stations.

So the total number of computers is :

Mr. Baxter is ordering a new keyboard and a mouse for each computer, since the cost of a keyboard is $13.50 and the cost of a mouse is $6.50.

Each computer has 1 keyboard and 1 mouse, so the total cost needed for 1 computer is :

Since you now have the cost for 1 computer, multiply this to the total number of computers which is 3s to get the total cost needed by Mr. Brax :

Using distributive property :

Distribute s inside the parenthesis :

One answer is 1st Option 3(13.50s + 6.50s)

Simplifying the expression further :

Another answer is 4th Option 3(20.00s)

Solution

For this case we can find the angle:

m < ECB = 30º

And we can find the angle CEB and we got:

m < CEB = 180 -30 - 45 = 105

And then the angle DAE would be:

m < DAE = 30º

The sequence is not arithmetic

What is a sequence?

A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which might be infinite). Unlike a set, the same components can occur numerous times in a sequence at various points, and the order does important. Formally, a sequence may be defined as a function from natural numbers (the sequence's places) to the items at each point. The concept of a sequence may be extended to include an indexed family, which is defined as a function from an arbitrary index set.

The given sequence 78, 785, 7855, 78555, ... is not arithmetic.

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the first x value, when the y-value of the equation is greater than the y value of equation one, is x=15

Because the y-value of equation 2 with x=15 is 32771, while the y-value of equation 1 is 16875

The equation is modelled by the function,

c(x) = 2.1x^2 - 12.7x + 167.4

The general form of a quadratic equation is expressed as

ax^2 + bx + c

The given function is quadratic and the graph would be a parabola which opens upwards because the value of a is positive

Since x represents the speed, the speed at which the he

According to the given data we have the following:

Cleo can paint a room in 8 hours, so this is=1/8x

Phil can paint the same room in 6 hours=1/6x

In order to calculate how long it take them to paint the room we would solve the following equation:

(1/6)(x)+(1/8)(x)=1

To solve this equation we would first multiply both sides by 24

Hence:

24*(1/6)(x)+24*(1/8)(x)=24

4x+3x=24

7x=24

x=24/7

x= 3 3/7 hours

Therefore It will take them 3 and 3/7 hours to pain the room.

In minutes it will take to them 205 minutes.

the given expression is

f(x) = x^2 + 2x - 15

we will find x intercept by putting f(x) = 0

x^2 + 2x - 15 = 0

x^2 + 5x - 3x - 15 = 0

x(x +5) -3(x + 5) = 0

(x +5) (x -3) = 0

x = -5 & x = 3

so the ordered pairs are

(-5, 0) and (3, 0)

Given:

The diagram is shown alongside.

The height of the monument is 30 ft high.

The angle of elevation is 63 degrees

The objective is to find the distance between the monument and where the girl is standing.

Since it forms a right angled triangle so we can apply trigonometric ratios:

Now,

Perpendicular = 30 ft

Base = ?

Substituting the values,

Therefore, the girl is at a distance of 15 ft from the monument.

Answer:

0.116

Step-by-step explanation:

[tex]\frac{0.232}{2}[/tex] = 0.116

The frequency of middle C = 262 Hz

The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:

This can be re-written as:

Middle C is 9 semitones below the concert pitch

That is, n = -9

To find the frequency of middle C, substitute n = -9 into the equation for F

The frequency of middle C = 262 Hz

The rate of the plane in still air is 1150km/hr and the rate of the plane in the wind is 170km/hr.

The formula for calculating distance is expressed as:

Let the rate of the plane in still air be "x"

Let the rate of the plane in the wind be "y"

if flying against the wind, an airplane travels 7840 kilometers in 8 hours, then;

8 (x - y) = 7840

x - y = 980 ........................ 1

If flying with the wind, the same plane travels 5280 kilometers in 4 hours

4 (x + y) = 5280

x + y = 1,320 ......................2

Add both equations:

x + x = 980 + 1320

2x = 2,300

x = 2300/2

x = 1150 km/hr

Substract x = 1150km/hr into equation 1.

x - y = 1320

1150 + y = 1320

y = 1320 - 1150

y = 170km/hr

Hence the rate of the plane in still air is 1150km/hr and the rate of the plane in the wind is 170km/hr

As given by the question

There are given that the measuring circle.

Now,

From the given circle, the length of the MN is 28 units, because the half of the length of the MN is 14. So just multiply by 2 into half of the given value.

Hence, the length of MN is 28 units.

Now,

For the measure of MN:

The measurement of the angle MN is 74 degrees.

Hence, a measure of arc MN is 74 degrees. and the length of segment MN is 28 units.

Answer

11) a > 3

12) b > (2/3)

Explanation

11) a - 15 > -4 (-6 + 3a)

a - 15 > 24 - 12a

a + 12a > 24 + 15

13a > 39

Divide both sides by 13

(13a/13) > (39/13)

a > 3

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.

Then, the direction of the graph depends on the direction of the inequality sign, for example, the answer here says a is greater than 3. So, the graph will start with an unshaded circle and cover the numbers greater than 3.

12) 3 (6b - 2) > (8 - 3b)

18b - 6 > 8 - 3b

18b + 3b > 8 + 6

21b > 14

Divide both sides by 21

(21b/21) > (14/21)

b > (2/3)

This answer is similar to that of number 11. For the graph, it will start with an unshaded circle and move towards the numbers greater than (2/3)

Hope this Helps!!!

For this problem, we are given a certain expression and we need to write it in the "y=mx+b" form.

We need to isolate the "y" variable on the left side to solve this problem. We have:

The expression is y = (2/3)x+2.

To start we will do what you said, multiply the 6, so:

6*(n-4)=3n

6n-6*4=3n

6n-24=3n

6n=3n+24

6n-3n=24

3n=24

n=24/3

n=8

So the answer is: 8

We have the following:

now,

The answer is:

There are several ways of taking apart the number 14:

1 and 13

2 and 12

3 and 11

4 and 10

5 and 9

6 and 8

7 and 7

Nevertheless, as we can see by the note below that exercise,

"Have your child take apart 16 to make a ten to find 87 - 16",

we can conclude that the exercise is asking how to take apart 14 to make a ten. By doing so, the subtraction operation (28 - 14) gets simpler since you could subtract 4, and then subtract the ten:

14 = 10 + 4 (1 ten and 4 units)

So, when we do 28 - 14, we can do that in two steps:

• 28 - 4 = ,24

• 24, - 10 = 14

Therefore, based on the note below exercise 6, the expected answer is

10 and 4

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

point 1 (2 , 60) x1 = 2 y1 = 60

point 2 (4 , 120) x2 = 4 y2 = 120

Step 02:

slope formula

The answer is:

30

From the given graph, let's determine the tactics which the media outlet used to create the graph.

From the graph, we can see that the scaling of the y-axis was manipulated.

The numbers in the y-axis starts from 8%, while a normal graph is suposed to start from 0%.

Although the graph is correct, but the scaling of the y-axis is misleading. This is because when you look at the graph, you will think there is a major difference between unnemployment before and unemployment after.

Therefore, the tactics the media outlet used to create this graph can be said to be Axis and Scaling manipulation.

Axis and scaling manipulation is a method used in producing misleading graphs to make the data look worse or better than it actually is. This method leads to incorrect conclusions,

ANSWER:

D. Axis and Scaling manipulation.

can you see my messages?

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

A(2, 3), B(8, 7), C(6 1)

Step 02:

Line AB

Slope formula

m = (y2 - y1) / (x2 - x1)

A (2 , 3) x1 = 2 y1 = 3

B (8 , 7) x2 = 8 y2 = 7

Step 03:

Slope of the perpendicular line, m’

m' = -1 / m

Step 04:

Line CD

m' = (y2 - y1) / (x2 - x1)

C (6 , 1) x1 = 6 y1 = 1

D ( x2, y2) x2 = x2 y2 = y2

We must test the numerical values to verify equality,

x2 = 9

y2 = 3

x2 = 4

y2 = 4