Question 7 (10 points)
Technology required. Clare is flying a kite. She gets tired, so she stakes the kite into the
ground. The kite is on a string that is 30 ft long and makes a 27 degree angle with the
ground. How high is the kite?
a.
30 ft
b.
13.6 ft
C.
26.7 ft
d.
15.3 ft

Answer:

top graph

Step-by-step explanation:

The graph of a proportional relationship is a straight line passing through the origin.

The only straight line graph passing through the origin is the top one

The graph on option A displays a proportional relationship.

Option A is the correct answer.

The equation of a line is given by:

y = mx + c

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

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line on the graph is given as:

y = mx + c ____(1)

The graph on option A.

If the equation of a line is y = mx and the slope is a unit rate the graph shows proportional relationships.

We will select two points on the graph.

i.e

(2, 2) = (a, b) and (3.3) = (c, d)

Slope:

m = (d - b) / (c - a) = 3 - 2 / 3 - 2 = 1 / 1 = 1

Let (2, 2) = (x, y) and putting in (1) we get,

2 = 1 x 2 + c

2 = 2 + c

c = 2 - 2 = 0

c = 0

The slope of the line is 1

The equation of the line is y = x

Thus,

The graph displays a proportional relationship.

Option A is the correct answer.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ2

Answer:

Step-by-step explanation:

The transformations of interest are ...

  f(-x) . . . . reflects across the y-axis

  f(x -h) +k . . . . translates by (h, k)

__

The translation left 4 and up 7 is translation by (-4, 7), so the translated function is ...

  f(x +4) +7

Reflection over the y-axis replaces x with -x (and also reflects the left-translation). The reflected translated function is ...

  g(x) = f(-x +4) +7 = (-x +4)^2 +7 = x^2 -8x +16 +7

  g(x) = x^2 -8x +23

__

Translation right 4 and down 5 is translation by (4, -5), so the translated function is ...

  f(x -4) -5

Reflection over the y-axis replaces x with -x. The new equation is ...

  g(x) = f(-x -4) -5

  g(x) = √(-x -4) -5

The equation that can be used to prove 1 + tan2(x) = sec2(x) is StartFraction cosine squared (x) Over tangent squared (x) EndFraction + StartFraction sine squared (x) Over tangent squared (x) EndFraction = StartFraction 1 Over tangent squared (x) EndFraction. the correct option is d.

In order to prove this, we can use the following identities:

tan(x) = sin(x) / cos(x)

sec(x) = 1 / cos(x)

tan2(x) = sin2(x) / cos2(x)

sec2(x) = 1 / cos2(x)

Substituting these identities into the given equation, we get:

StartFraction cosine squared (x) Over tangent squared (x) EndFraction + StartFraction sine squared (x) Over tangent squared (x) EndFraction = StartFraction 1 Over tangent squared (x) EndFraction

Therefore, 1 + tan2(x) = sec2(x).

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Answer:

yes

Step-by-step explanation:

because it will be easier if the they are like terms

Classroom objects can be categorized as vertical or horizontal. Examples of vertical objects include doors, bookshelves, and clocks, while horizontal objects include desks, tables, and chairs.

In a classroom, there are many objects that are vertical and horizontal. Here are ten examples of each:

Vertical objects in a classroom:

1. Door                     6. Clock

2. Cabinet               7. Electrical outlets

3. Bookshelf            8. Light switches

4. Whiteboard         9. Window blinds

5. Flagpole             10. Bulletin board

Horizontal objects in a classroom:

1. Desks                  6. Keyboard trays

2. Chairs                 7. Carpet tiles

3. Tables                 8. Ceiling tiles

4. Countertops       9. Whiteboard markers

5. Shelves              10. Paper trays

These are just a few examples of vertical and horizontal objects that can be found in a classroom.

It is important to recognize the different shapes and orientations of objects in our environment, as they can affect the way we perceive and interact with them.

For more questions on Bulletin board

https://brainly.com/question/30369348

#SPJ8

Answer:

$44.00 + $85.00 = $129.00

Step-by-step explanation:

The least amount that she needs is $129.00 because we're summing the amount for food and House Rent.

Movies and Shopping are less important.

Answer: 4x2

Step-by-step explanation:

Answer:

\(4x^2\)

Step-by-step explanation:

\((2x)(2x)=(2*2)(x*x)=4x^2\)

If the linear system 6x-8y-10z=-48k, -5x+7y+9z=0, and -3x+4y+hz=0 has infinitely many solutions, x = 6(4) + z = 24 + z , y = -7/5 - z , z is free ,h=2 then k=4 and h=2.

We can rewrite the system of equations as an augmented matrix [A|B], where A is the coefficient matrix and B is the column vector on the right-hand side:

[ 6  -8 -10 | -48k ]

[-5   7   9 |   0  ]

[-3   4   h |   0  ]

We can perform row operations on the matrix to put it in reduced row echelon form, which will allow us to determine the solutions of the system. After performing row operations, we obtain:

[ 1   0  -1 |  6k ]

[ 0   1   1 | -7/5]

[ 0   0  h-2 |  0  ]

From the last row of the matrix, we see that h-2=0, which implies that h=2. From the first two rows of the matrix, we can see that x- z=6k and  y+ z=-7/5. Since the system has infinitely many solutions, we can express x and y in terms of z, giving:

x = 6k + z

y = -7/5 - z

Substituting these expressions into the second row of the matrix, we obtain:

-5(6k+z) + 7(-7/5 - z) + 9z = 0

Simplifying this equation gives:

-30k - 10z - 7 + 9z = 0

Solving for k gives k=4.

Therefore, the solutions of the system are:

x= 6(4) + z = 24 + z

y = -7/5 - z

z is free

h=2

Learn more about linear system here:

https://brainly.com/question/26544018

#SPJ11

Answer:

A

Step-by-step explanation:

To evaluate 3K^2 - 6K for K = 5, we substitute K = 5 into the expression:

3K^2 - 6K = 3(5)^2 - 6(5)

Simplifying, we get:

3(25) - 30 = 75 - 30 = 45

Therefore, 3K^2 - 6K, with K = 5, is equal to 45.

option:-

\( \: \)

Given:-

Now , Put the given value of k in eqⁿ

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

hope it helps!:)

Answer:

No

Step-by-step explanation: he is 3 and 1/3 feet tall. 3 feet is 36inch and 1/3 feet is 4 inches, so 36+4 is 40 inches

Info given

We have a total of people given (82). We also know that we have 54 children of under 12 years and under some children were under 3 years

We define x as the number of children under 3 years.

We want to find C for the total cost. We don't have the unitary prices but we can assume it as C1 (over 3 and lower than 12) and C2(adults) for children and adults.

Solution:

With C the total amount collected and C1 and C2 described above.

The height of the rocket at the end of the 25 seconds is 275 ft.

We have given that,

a rocket rises at 5 ft/s between 0 and 10 seconds,

therefore

V₁ = 5 ft/s

T₁ = 10 seconds

Height in first 10 seconds = ?

we know the formula to find the height,

i.e Height = velocity × time

⇒ H₁ = V₁ × T₁

        = 5 × 10

   H₁ = 50 ft

Therefore height of the rocket in the first 10 seconds is 50 ft.

Now it given that, rocket rises at 25 ft/s for another 15 seconds.

i.e V₂ = 15 ft/s

    T₂ = 15 seconds

    H₂ = ?

H₂ = V₂ × T₂

    = 15 × 15

H₂ = 225 ft

Therefore height of the rocket in next 15 seconds is 225 ft.

Now we will find the height of the rocket at the end of the 25 seconds.

i.e H = H₁ + H₂

       = 50 + 225

    H = 275 ft

Hence the height of the rocket at the end of 25 seconds is 275 ft.

To know more about height here

https://brainly.com/question/29576808

#SPJ4

A circle graph with each of the four budget categories is shown in the image attached below.

In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

In order to use a protractor to create a circle graph (pie chart), you would have to first of all draw a circle with a chosen radius, and then draw a line for each angle as follows;

Newsletter = 15% = 0.15(360) = 54°

Supplies = 20% = 0.20(360) = 72°

Special activities = 55% = 0.55(360) = 198°

Other expenses = 10% = 0.10(360) = 36°

Read more on pie chart here: brainly.com/question/23608372

#SPJ1

9514 1404 393

Answer:

  yes, yes, no, no

Step-by-step explanation:

An equation is linear if no term has a variable with an exponent other than 0 or 1. There can be no products of variables.

The equations with terms x³ or x² will not be linear.

(a, b) linear (yes)

(c, d) not linear (no)

The given problem states that "A varies directly as the square root of m and inversely as the square of n."  When m=16 and n=8, the value of a is approximately 0.5.

The given problem states that "A varies directly as the square root of m and inversely as the square of n." Mathematically, this can be represented as:

A = k * (sqrt(m)) / (n^2)

where k is the constant of variation.

To find the value of k, we can use the given information: when m=81 and n=3, a=2. Plugging these values into the equation, we get:

2 = k * (sqrt(81)) / (3^2)

2 = 9k / 9

2 = k

So, the equation becomes:

A = 2 * (sqrt(m)) / (n^2)

Now we can find the value of a when m=16 and n=8:

a = 2 * (sqrt(16)) / (8^2)

a = 2 * 4 / 64

a = 8 / 64

a ≈ 0.125

Therefore, when m=16 and n=8, the value of a is approximately 0.5.

Learn more about square root here:

https://brainly.com/question/29286039

#SPJ11

A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ \(= \frac{360}{n}\)

θ  \(=\frac{360}{5} = 72\)

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

Read more about the pentagon:

https://brainly.com/question/11759904

#SPJ4

The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

Answer:

C2H5OH + 3O2 --> 2CO2 + 3H2O

Step-by-step explanation:

Balanced, there is:

- 2 Carbons coming from the ethanol going into the Carbon Dioxide.

- 6 Hydrogens coming from the ethanol going into the water

- 1 Oxygen coming from the ethanol and 6 Oxygens coming from 3O2 going (so 7 in reactants) going to 4 in the Carbon Dioxide and 3 to the Water

The balanced form of the chemical equation is:

C2H5OH(l) + 3O2(g) → 2H2O(g) + 2CO2(g)

A balanced chemical equation is a representation of a chemical reaction using the chemical formulas of the reactants and products, with stoichiometric coefficients indicating the relative numbers of molecules or moles of each substance involved.

We have,

In this balanced equation, the stoichiometric coefficients have been adjusted to ensure that the same number of atoms of each element appears on both sides of the equation.

The balanced equation shows that one molecule of ethanol (C2H5OH) reacts with three molecules of oxygen (O2) to produce two molecules of water (H2O) and two molecules of carbon dioxide (CO2).

Note that the state of matter is also included in the balanced equation

(l = liquid, g = gas).

Thus,

The balanced form of the chemical equation is:

C2H5OH(l) + 3O2(g) → 2H2O(g) + 2CO2(g)

Learn more about balanced of chemical equation here:

https://brainly.com/question/13860773?referrer=searchResults

#SPJ7

Answer:

A the first one

Step-by-step explanation:

hope this helps

Answer:

D.

Step-by-step explanation:

7h is the amount of money Jim makes per hour. You can find the amount of money Susan makes by dividing the amount she made to the hours:

15/2 = 7.50

Susan charges $7.50, which is higher than Jim's hourly rate. which is the correct answer would be a statement (D)

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

To find the hourly rate for Jim, you can plug in different values for h (the number of hours) in the equation t = 7h + 10 and solve for t (the total). For example, if h = 1, then t = 7(1) + 10 = 17. This means that if Jim babysits for 1 hour, he charges $17.

If you divide the total amount that Jim charges by the number of hours he works, you get his hourly rate. In this case, the hourly rate is t/h = 17/1 = $17/hour.

To find Susan's hourly rate, you can divide the total amount that she charges by the number of hours she works. For example, if Susan babysits for 2 hours, she charges $15, so her hourly rate is $15/2 = $7.50/hour. If Susan babysits for 4 hours, she charges $30, so her hourly rate is $30/4 = $7.50/hour.

Since Susan charges $7.50/hour, which is higher than Jim's hourly rate of $17/hour, the correct statement is D.) Susan charges $7.50, which is higher than Jim's hourly rate.

Learn more about the equations here:

brainly.com/question/10413253

#SPJ2

The first step to isolate the variable term on one side of the equation is to move all constant terms to the other side by adding or subtracting the appropriate terms.

To isolate the variable term on one side of the equation, the first step is to gather all terms containing the variable on one side and move all constant terms to the other side.

In the given equation:

2/3x = -1/2x + 5

We have variable terms on both sides: 2/3x and -1/2x. To isolate the variable term, we can start by moving the -1/2x term to the left side by adding 1/2x to both sides of the equation.

Adding 1/2x to both sides:

(2/3x) + (1/2x) = (-1/2x) + (1/2x) + 5

Simplifying the left side:

(2/3x + 1/2x) = 5

To combine the fractions, we need a common denominator. The common denominator of 3 and 2 is 6, so we can rewrite the left side:

(4/6x + 3/6x) = 5

Combining like terms on the left side:

(7/6x) = 5

Now, the variable term 7/6x is isolated on one side of the equation. To completely isolate the variable, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which in this case is 6/7.

Multiplying both sides by 6/7:

(6/7) * (7/6x) = (5) * (6/7)

Simplifying:

1x = 30/7

The variable x is now isolated on the left side, and the equation simplifies to:

x = 30/7

Moving all constant terms to the opposite side of the equation by appropriately adding or deleting terms is the first step towards isolating the variable term on one side of the equation.

for such more question on variable

https://brainly.com/question/18042457

#SPJ8

The measure of the intercepted arc is equal to 134 degrees

The measure of arc BD is calculated using the inscribed angle theorem, this theorem have that  the measure of the inscribed angle is equal to half the measure of the intercepted arc.

This is represented mathematically as

inscribed angle = 1/2 x intercepted arc

Where

inscribed angle = 67

intercepted arc = ?

then we have that

inscribed angle = 1/2 x intercepted arc

67 = 1/2 x intercepted arc

intercepted arc = 2 x 67

intercepted arc = 134 degrees

Learn more about inscribed angle theorem at

https://brainly.com/question/3538263

#SPJ1

Answer:

6.7

Step-by-step explanation:

20.5-8=12.5 so

14.7-8=6.7

Answer:

5/16

Step-by-step explanation:

There are a total of 16 different outcomes because 2*2*2*2 = 16.

There are 5 different ways for him to get 3 or more heads:

HHHT

HHTH

HTHH

THHH

HHHH

Therefore the probability is 5/16

Answer:

34, and if 55 was replaced with 33, the new median would be 33.

Step-by-step explanation:

The median is the number that is in the middle of a data set, once the numbers are organized from least to greatest. If we put the numbers in order (18, 22, 24, 32, 34, 39, 55, 57, 59), the number in the middle is 34. If we do the same, but replace 55 with 33, (18, 22, 24, 32, 33, 34, 39, 57, 59), we get 33 as the median.

The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

Learn more about Erosion: https://brainly.com/question/17905503

#SPJ4

In the case of Alicia, The single net increase is 5.821% of the original price.

Alicia is buying shoes at a department store that offers a 15% discount on all shoes. Additionally, she has a store card that gives her another 5% discount. However, at checkout, the cashier tells her that there will be two increases, one of 2% for commissions and another of 18% for general sales tax. To determine if there is a net discount or increase, we need to calculate the total discount and total increase separately and compare them.

First, let's calculate the total discount:

Next, let's calculate the total increase:

If the total discount is greater than the total increase, then there is a net discount. If the total increase is greater than the total discount, then there is a net increase.

Therefore, we need to compare:

Simplifying both expressions, we get:

Since 1.0506 x Original Price is greater than 0.20 x Original Price, we can conclude that there is a net increase.

To calculate the amount of the single net increase, we can subtract the discounted price from the increased price:

Simplifying the expression, we get:

Therefore, the single net increase is 5.821% of the original price.

Learn More about discount

https://brainly.com/question/23865811

#SPJ4

Complete Question:

Alicia will buy shoes in a department store that advertises a 15% discount on all shoes, plus she has the store card and therefore they will give her another 5% discount. When paying: the cashier tells you that they will make 2 increases, one of 2% for commissions and the other of 18% for general sales tax. Determine if it is the case, how much is the discount or single increase?

The alternative hypothesis would be: The proportion of people who own cats is smaller than 90%.

The null hypothesis for this test would be: The proportion of people who own cats is equal to or greater than 90%.

To conduct the hypothesis test, we would need to collect a random sample of 1400 individuals and determine how many of them own cats. Based on this information, we could calculate the sample proportion of cat owners and use this to test the claim that the population proportion is smaller than 90%.

We would use a one-tailed hypothesis test with a significance level of 0.005. If the p-value for our test is less than 0.005, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90%.
Hi! I'd be happy to help you with this question. You want to test the claim that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

To do this, we will set up our null and alternative hypotheses as follows:

Null Hypothesis (H0): The proportion of people who own cats is equal to 90% (p = 0.90)
Alternative Hypothesis (H1): The proportion of people who own cats is smaller than 90% (p < 0.90)

Here's a step-by-step explanation of how to test this claim:

1. Determine the sample size (n) and the number of cat owners in the sample (x): In this case, n = 1400, and x = 615.

2. Calculate the sample proportion (p-hat): p-hat = x/n = 615/1400 ≈ 0.439.

3. Determine the significance level (alpha): In this case, alpha = 0.005.

4. Calculate the standard error (SE) of the sample proportion: SE = sqrt[p*(1-p)/n] = sqrt[0.9*(1-0.9)/1400] ≈ 0.008.

5. Calculate the z-score: z = (p-hat - p)/SE = (0.439 - 0.9)/0.008 ≈ -57.63.

6. Find the critical z-value for a one-tailed test at the 0.005 significance level: z-critical = -2.576 (from a standard normal distribution table).

7. Compare the calculated z-score with the critical z-value: Since the calculated z-score (-57.63) is less than the critical z-value (-2.576), we reject the null hypothesis.

In conclusion, based on this analysis, we have enough evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

Learn more about alternative hypothesis at: brainly.com/question/27335001

#SPJ11

Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

Learn more about median of numbers in https://brainly.com/question/26177250

#SPJ11