Two angles are complementary. One angle is
fifteen more than twice the other angle.
What is the measure of each angle?

Using the graph given:

1. 1. Initial height of plane A: 4 miles.

2. Plane B was 1 mile.

3. The time both planes fly at exactly the same height is: 20 seconds.

A graph illustrates the relationship between two variables, one plotted on the x-axis upon which the one plotted on the y-axis depends on.

Like in the graph shown above, the time in seconds is plotted on the x-axis as against the height in miles on the y-axis.

Each point on the graph, (x, y) shows the height (y) of the plane after some seconds (x).

Therefore:

1. The initial height of plane A is at 4 miles.

2. After 40 secs, the height of plane B was 1 mile.

3. The point where the two lines intersect shows when the time and height of both planes are the same. Therefore, at 20 seconds, both planes were flying at the same height of 3 miles.

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(a) Total fixed cost = $ 12500.

(b) Total variable cost for x CDs = $ 5.50 x

(c) The cost function for x CDs is, C(x) = 12500 + 5.50 x

(d) The revenue function for x CDs is, R(x) = 7.20 x

(e) Approximately 7353 CDs must the company sell to break even.

Rasputin sells CDs for a particular artist.

They have advertising costs of $ 3500 and recording costs of $ 9000.

They are the fixed costs.

(a) So total fixed cost = $ 3500 + $ 9000 = $ 12500

Their cost for manufacturing, royalties, and distribution are $ 5.50 per CD.

(b) So the variable cost for x CDs = $ 5.50 x

(c) Hence the cost function for x CDs is,

C(x) = Total Fixed Cost + Variable Cost

C(x) = 12500 + 5.50 x

(d) They sell the CDs to Wow-Mart for $ 7.20.

So the revenue function for x CDs is,

R(x) = 7.20 x

(e) At break even point,

C(x) = R(x)

12500 + 5.50 x = 7.20 x

1.70 x = 12500

x = 12500/1.70

x = 7353 (approximately)

Hence 7353 CDs must the company sell to break even.

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Answer:

Step-by-step explanation:

Step one:

given

we are told that the total number of students is =16

so 25% of these students preferred pizza

Firstly, we want to know what 25% of 16 will be

so

=25/100*16

=0.25*16

=4

This means that only 4 students preferred pizza

Answer:

it's option c 192 square units as area of parallelogram equals products of base and heights

Answer:

3.2 miles

Step-by-step explanation:

\(\frac{5684.106yds}{1}\) · \(\frac{3ft}{1yd}\) · \(\frac{1mile}{5280ft}\) You can cross cancel words just like numbers.  Cross cancel the words: yards and feet.  That will leave you with just miles

\(\frac{5684.106}{1 }\) ·\(\frac{3}{1}\) · \(\frac{1mile}{5280}\)

\(\frac{17052.318}{5280}\)

3.22960568182

This rounded to the nearest tenth would be: 3.2

Helping in the name of Jesus.

By Pythagorean formula and proportion formula, the length of side VW is equal to 6 units. (Right choice: C)

Herein we find a geometric system formed by two right triangles, in which two side lengths are known (WX, XY) and we need to determine the length of side VW.

Both triangles XVW and XYW are similar, where they share the same internal angles and proportional corresponding pair of sides. Then, the system is represented by following proportion formula:

XV / WX = XY / XV

XV² = XY · WX

XV = √(XY · WX)

If we know that XY = 9 and WX = 3, then the value of XV is:

XV = √27

XV = 3√3

Then, the side VW is found by Pythagorean theorem:

VW = √(WX² + XV²)

VW = √(3² + 27)

VW = 6

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Answer:

y=12x

Step-by-step explanation:

According to the table

48=12(4) which is true

60=12(5) which is true

96=12(8) which is true

Answer:

12, 60/5 is 12, 48/4 is 12, 96/8 is 12

Answer:

Salma can run 1 to 8 more miles to run less than 28 miles in total

Step-by-step explanation:

28-19= 9 but she is running LESS than 28 miles so subtract 1 from that 9

Answer:

Quadrant 3

Step-by-step explanation:

Answer:

quadrant 3

Step-by-step explanation:

III (-;-)

Answer:

C

Step-by-step explanation:

Hope that helps!

Answer:

C.

Step-by-step explanation:

Uneven steps,

good luck, i hope this helps :)

Answer:

this is not a rational number

Step-by-step explanation:

cause you cant put it as a fraction

Answer:

Yes.

Step-by-step explanation:

Because it can be written as a fraction:

5 .97 = 5 97/100  or   597/100.

Answer:

it's grade 2

Step-by-step explanation:

this is because 29-40 is grade 2

Answer:

a grade 2

Step-by-step explanation:

because 29-40 marks is a grade 2 lol.

Answer:

1/2 x 1/8 = 1/16 in fraction form.

Answer:

3. 12

4. 10.63

Step-by-step explanation:

3. a^2 + b^2 = c^2

a^2 + 5^2 = 13^2

a^2 = 169 - 25

a^2 = 144

a = √144 = 12

4. a^2 + b^2 = c^2

c^2 = 7^2 + 8^2

c^2 = 49 + 64

c^2 = 113

c = √113 = 10.63

Given:

Four students took a math test on decimals before being tutored. After attending tutoring sessions for a week, they took another test to see if they could improve their scores.

Required:

Here we have to find who's score was lower after tutoring.

Explanation:

Now by considering the red and blue bar in the given figure, we can say that

Kim score was lower after tutoring.

Final Answer:

Kim score was lower after tutoring.

Answer:

x = \(27.5^{o}\)

Step-by-step explanation:

complementary angles are two or more angles whose sum is equal to \(90^{o}\).

Thus given that;

m<BAM = x + 24

m<CTX = x + 11

So that,

m<BAM + m<CTX = 90

⇒ (x + 24) + (x + 11) = 90

x + 24 + x + 11 = 90

2x + 35 = 90

2x = 90 - 35

2x = 55

x = \(\frac{55}{2}\)

 = 27.5

The value of x is \(27.5^{o}\).

So that,

m<BAM = x + 24

             = 27.5 +24

             = \(51.5^{o}\)

m<CTX = x + 11

            = 27.5 + 11

           = \(38.5^{o}\)

Answer:

x = 25

Step-by-step explanation:

combine like terms ans then solve for x

The equation that best represents this solution is:

40t + 1,280 = 2,680

What is the algebraic equations?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

Each time Sophia shops at the grocery store, she earns 40 points. If she needs a total of 2,680 points to receive a free prize and she has already earned 1,280 points, then she needs to earn an additional 2,680 - 1,280 = 1,400 points. Let t represent the number of times Sophia visits the store.

Since Sophia earns 40 points every time she shops at the grocery store, the total number of points she will earn after t visits is 40t. Therefore, we can set up the following equation:

40t = 1,400

Solving for t, we can divide both sides of the equation by 40:

t = 1,400/40

t = 35

Hence, Sophia will need to shop at the grocery store 35 more times in order to earn the additional points she needs for a free prize.

The equation that best represents this solution is:

40t + 1,280 = 2,680

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Answer:

Step-by-step explanation:

(2). 1 yd ≈ 0.9144 m

1 yd³ ≈ 0.76455 m³

2 yd³ ≈ 1.53 m³ ≈ 2 m³

(3). 1 ft ≈ 0.3048 m

1 ft² ≈ 0.0929 m²

162 ft² ≈ 15.1 m²

(4). 1 mi ≈ 1.60934 km

1 mi² ≈ 2.59 km²

503 mi² ≈ 1302.8 km²

Answer:

7x+11x=90

18x=90

x=5

one angle = 35 degrees

another angle = 55 degrees

Step-by-step explanation:

Answer:

(-10, 19)

Step-by-step explanation:

Hey there!

In order to find the value of x and y, you need to make a system of equations

Now the question says to use elimination

The elimination method is when you make two values the same and then eliminate them with the proper sign: addition, subtraction, etc.

In this case, the step of making equal values is already done for us since there is 2y in both equations

\(-5x-2y=12\\3x+2y=8\\\\-2x=20\\x=-10\\\)

What was done was called elimination

I added both equations together and when you add -2y and 2y, they eliminate each other

Now when you simplify the system, you get that x is equal to -10

Now we can substitute this value into the first or second equation

I am going to do the first equation

\(-5(-10)-2y=12\\50-2y=12\\-2y=-38\\y=19\)

So after substituting the x value in the equation, we got the y value

Which is 19

So the solution to this system of equations is:

(-10, 19)

Answer:

d

Step-by-step explanation:

Answer:

A rectangle is bounded by the x-axis and the semicircle y = √(25 - x²). What length and width should the rectangle have so that its area is a maximum?

Step-by-step explanation:

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(σ)= 1.55

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) =\(z_{\alpha /2}\frac{\sigma}{\sqrt n}\)

So n= \((z_{\alpha /2}\frac{\sigma}{ME})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

The given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n = \((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(σ)= 2×1.55

Standard deviation of resistance(σ)= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n= \((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Check the picture below.

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

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A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16, RT= 32  and UV ≈ 8.2.

A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16.

Finding R T and U V is our goal.

First, let's assume that the figure RSTU is a rhombus since its perimeter and one-half of a diagonal's length are both provided. RT is the result of adding the segments RV and VT.

RT=RV + VT

We are informed that the RV is sixteen. If RV and VT are congruent, then V T equals 16. So:

R T = 16 + 16 = 32

In order to determine the UV length, we must first determine the RU length. Since a rhombus's sides are the same length, we can divide its perimeter by four to determine

RU= Perimeter/ 4

If we simplify and replace Perimeter with 72, we get:

RU = 72 / 4

RU =18

Since UB is a member of the right triangle RUV created by the intersection of the diagonals, we can now use the Pythagorean theorem to determine its length. So:

U V²+ R V² =  RU²

If R V = 16 and R U = 18, we obtain:

U V² + 16 ²= 18²

By way of summary, we have:

U V² + 256 = 324

U V² + 256 − 256 = 324 − 256

√ UV = √ 68

UV = 8.2462

UV ≈ 8.2

Our recommendations are as follows:

RT= 32

UV ≈ 8.2.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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Answer:

108,0000 liters

Step-by-step explanation:

It should be 108,0000 liters because if there are 60 seconds per minute and the pump was on for 39 mins, 60 x 30 = 1800  

Then 1800 seconds times 600 liters per second equals 108,0000 liters

Answer:

Step-by-step explanation:

The candy bar cost, in dollars, is $1.05

Say the price of a piece of bubble gum is x.

This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.

We can then solve from there.

We have given that,

(x+1)+x=1.10

Simplify above expression

2x+1=1.10

2x=0.10 - Subtract From Both Sides

x=0.05 - Divide From Both Sides

So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.

What is the cost?

Cost is the value of money that a company had to spend to produce its goods or services.

Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.

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Answer:

Soda = 2.35

Pack of bubble gum = 1.15

Chocolate bar = 1.64

2.35 + 1.15 + 1.64 = 5.15

Answer: Dottie spent a total of $5.15.