Three students attempt to define the geometric object called an angle.
Can you match the teacher's comments to the definitions?

If we know the measure of two of the three angles of a triangle, since the sum of the angles in a triangle aways is 180º, we can write the equation for angles a, b and c:

Let's suppose we know x and y, then z is:

Given:

The markdown of a bicycle = $1500

Which is 20% of the original selling price

Let the original selling price = x

so, 20% of x = 1500

so,

so, the answer will be:

a) the original selling price = $7,500

b) the new selling price = 7500 - 1500 = $6,000

5,9460.

1) Let's multiply 1988 by 30:

Notice that we multiplied the units, 0 x 1988 and then 3 x 1988 and then we added both numbers.

2) Hence, 1,988x 30 is equal to 5,9460.

Given the exponential function:

Let's determine if the exponential function represents growth or decay.

Take the exponential function:

Where b is the base.

• If the base of an exponential function is greater than one, the exponential function represents growth

• If the base of an exponential function is between 0 and 1, the function represents a decay function.

Here, the base of the exponential function, b is 1.061 which is greater than 1, the function represents a growth function.

SInce it is represents a growth function, let's determine the percentage rate of increase.

The general formula for exponential growth is:

Where r is the growth rate.

Thus, we have:

The growth rate, r is = 0.061

The percentage rate of increase is:

Therefore, the percentage rate of increase is 6.1%

ANSWER:

The function represents growth

Percentage rate of increase = 6.1%

Let H denote the age of Hullan.

Let T denote the age of Thomas.

Huilan is 8 years younger than Thomas

Mathematically,

The sum of their ages is 76.

Mathematically,

Now let us substitute eq. 1 into eq. 2

Therefore, the age of Thomas is 42 years.

By using the supplementary relations and the fact that angle 2 is congruent to angle 3, we will get that:

∠1  ≈ ∠4

Here we know that:

With the first two, we can write the equations:

∠1 + ∠2 = 180°

∠3 + ∠4 = 180°

Both equations have the same value in the right, then we can write:

∠1 + ∠2 = ∠3 + ∠4

Now, we know that ∠2 ≈ ∠3, then we can rewrite the equation as:

∠1 + ∠2 = ∠3 + ∠4

∠1 + ∠2 - ∠3 = ∠4

And ∠2 - ∠3 ≈ 0, then:

∠1 + ∠2 - ∠3 = ∠4

∠1 + 0 ≈ ∠4

∠1  ≈ ∠4

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Considering the equation for the circumference of a circle, we have that:

1.

2. The circumference of the circle is given as follows:

Circumference = 3.14 x 10 in = 31.4 in.

Considering a circle of diameter d, it's circumference is given by the diameter d multiplied by the number π, as follows:

C = πd.

Hence, for Circle D, as for any circle, the ratio is given as follows:

C/d = π = 3.14 (rounding π).

For Circle E, the circumference is given as follows:

C = 200 x 3.14 = 628

For Circle F, the diameter is given as follows:

3.14d = 942.5

d = 942.5/3.14

d = 300.

For item 2, the diameter is of 10 inches, hence the circumference of the circle is found applying the rule as follows:

Circumference = 3.14 x 10 in = 31.4 in.

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Answer:

3x¹²

Step-by-step explanation:

1. Rule (x) = x

2. (x¹²) = x¹²

3. x¹²*3

4. 3x¹²

Step-by-step explanation:

look for the LCM of 3 and 10 and since it does not have a LCM you will multiply the two variables. After multiplying, you will then divide your answer by the denominator and multiply it with the denominator

CHECK THE ABOVE PHOTO FOR THE REST

We are given the following function that models the temperature T as a function of the latitude L:

T = - 0.68 L + 89.5

We see that the temperature is in fact a linear function of slope -0.68 degrees/latitude.

Since the latitude of the Equator is 0 degrees, then, the equation tells us that the temperature at the Equator is:

T = - 0.68 (0) + 89.5 = 89.5 degrees of annual temperature. But this is NOT related to the slope.

The other two statements (B and C) are not correct,

The last statement D is correct, since for every degree increase in latitude, there is an annual decrease of temperature by 0.68 degrees, and this is what the slope expresses.

Please select answer D.

The horizontal distance between points A and B is:

1/5 of this distance is:

Then, the x-coordinate of point X is:

The vertical distance between points A and B is:

1/5 of this distance is:

Then, the y-coordinate of point X is:

Finally, the coordinates of X are (-3.6, -2.2)

Altogether, you will pay $631.24 if the interest is compounded at the end of every year for 4 years or $620 if it is based on simple interest.

Compound interest accumulates the interest and adds it to the principal for calculating subsequent interest.

On the other hand, simple interest does not accumulate the interest to add to the principal before computing the next year's.

N (# of periods) = 4 years

I/Y (Interest per year) = 6%

PV (Present Value) = $500

PMT (Periodic Payment) = $0

Results:

FV = $631.24

Total Interest = $131.24

Simple interest = $120 ($500 x 6% x 4)

Future value at simple interest = $620 ($500 + $120)

Thus, depending on how interest is calculated, you will repay between $620 and $631.24.

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ANSWER

Option B

EXPLANATION

Given;

Note that the pentagon is a regular polygon (all the angles are equal).

Hence;

The measure of angle STU is;

Hence, substitute the values of the angles;

Therefore, the measure of angle STU is 223 degrees

In this case we are making deposits each year in out account. This will be compounded at a 6% interest.

After 20 years of working and making deposits, the principal accumulated has to be able to give $30,000 per year for 30 years.

We can start with the principal. We assume that during retirement, the account yield 6% interest from the capital still in the account.

Then, we can calculate this principal as the present value of an annuity with payments PMT = $30,000, rate of interest r = 0.06 and n = 30 years.

The calculation is:

Now we know the amount of capital that has to be accumulated with the deposits.

This value is the future value of an annuity of n = 20 years at a rate r = 0.06.

But now, we need to calculate the yearly deposit D.

We can calculate it as:

Answer: the yearly deposit has to be $11,225.73.

The probability of the complement of event E is 0.56,

For any event A, we define the complement of A as:

[tex]A^c[/tex]

Where the complement refers to all the elements in the sample space that are not A, and the relation between the probabilities is:

P([tex]A^c[/tex]) = 1 - P(A).

In this case, we have an event E and we know that:

P(E) = 0.44

Then the probability of the complement will be:

P([tex]E^c[/tex]) = 1 - P(E) = 1 - 0.44 = 0.56

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Answer:

its parallel

Step-by-step explanation:

because it is

Answer:

Step-by-step explanation: 0.50+0.25=0.75

so your answer would be 1/4 of a probability

Solution

We are given the relation

Step-by-step explanation:

try this option, all the details are in the attachment.

Let x represent the rental cost for each movie.

Let y represent the rental cost for each video game.

From the information given,

Lamar rented 3 movies and 8 video games for a total of $58. The equation representing this scenario would be

3x + 8y = 58

Also,

he rented 5 movies and 2 video games for a total of $23. The equation representing this scenario would be

5x + 2y = 23

We would solve both equations by applying the method of elimination. To elimimate x, we ould multiply the first equation by 5 and the second equation by 3. We have

15x + 40y = 290

15x + 6y = 69

Subtracting the second equation from the first, we have

15x - 15x + 40y - 6y = 290 - 69

34y = 221

Dividing both sides by 34,

34y/34 = 221/34

y = 6.5

Substituting y = 6.5 into 5x + 2y = 23, we have

5x + 2(6.5) = 23

5x - 13 = 23

Adding 13 to both sides, we have

5x - 13 + 13 = 23 - 13

5x = 10

x = 10/5

x = 2

Rental cost for each movie = $2

Rental cost for reach video = $6.5

Given that triangle ABD= traingle CDB then;

side AB= DC and

side AD = BC

thus equate side AB and DC as;

7y =3y +20

collect like terms as;

7y-3y = 20

4y = 20

y= 20/4 = 5

The formula to calculate the amount for compound interest is given to be:

where

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

From the question provided, we have the following parameters:

Therefore, we can solve as follows:

The amount after 4 years is $2,431.01.

Answer:

it doesn't have a solution

Step-by-step explanation:

Answer:

do you have picture if the question so I can help I

The total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.

So, the probability that the randomly selected dogs are yellow Labradors:

Probability in 1st selection:

Probability in 2nd selection: Without replacement

Total Probability: 1/2 × 6/13 = 6/26 ⇒ 3/13

Therefore, the total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.

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The statements which are true about this exponential function include the following:

C. It will take approximately 14 minutes for 100 people to hear the rumor.

D. Initially, only one person had heard the rumor.

Mathematically, an exponential function can be modeled by using this equation:

f(x) = abˣ

Where:

At the initial time (t₀), the value of t₀ is zero (0) and the number of people who heard the rumor is given by:

N(t) = 300/(1 + 299e^{-0.36t})

Substituting the initial time (t₀) into this exponential function, we have;

N(t₀) = 300/(1 + 299e^{-0.36t₀})

N(0) = 300/(1 + 299e^{-0.36 × 0})

N(0) = 300/(1 + 299e^{0})

N(0) = 300/(1 + 299)

N(0) = 300/300

N(0) = 1 person.

At t = 14, the number of people who heard the rumor is given by:

N(t₁₄) = 300/(1 + 299e^{-0.36t₁₄})

N(14) = 300/(1 + 299e^{-0.36 × 14})

N(14) = 300/(1 + 299e^{-5.04})

N(14) = 300/(1 + 299(0.00647374831))

N(14) = 100 people.

In conclusion, there are 300 people in the enclosed space rather than 299 people.

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Answer:

4.163 × 10^7

Step-by-step explanation:

The step by step explanation is in the image attached

hope this helps!!

The graph for y = 3x + 1 is given below

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.

Y = 3 x -3+4

y = 3x +1

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Given:

Area of Pacific ocean = 161.8 12 x 10⁶ square kilometers

Area of Atlantic ocean = 85133000 square kilometers

Let's find how many times greater is the area of the pacific ocean than the Atlantic ocean.

To find how many times greater, divide the area of the Pacific ocean by the area of the Atlantic ocean.

Thus, we have:

Therefore, the area of the Pacific ocean is 1.9 times greater than the area of the Atlantic ocean.

ANSWER:

1.9 times

For f(x)= x ^3 - x ^2 , which gives an output of 48?

_____________________

replace values ​​directly in the expression

x ^3 - x ^2

f(2)= 2 ^3 - 2 ^2

______________________________________

f(-8) = -572

f(-4) = -80

f(4) = 48

f(8) = 448

____________________________

Answer f(4) = 48