You have learned some new ways in this module to prove that triangles are similar Please describe some of these new postulates and include a diagram on the whiteboard to help explain how they are applied.

Answer:

V(t) = 25000 * (0.815)^t

The depreciation from year 3 to year 4 was $2503.71

Step-by-step explanation:

We can model V(t) as an exponencial function:

V(t) = Vo * (1+r)^t

Where Vo is the inicial value of the car, r is the depreciation rate and t is the amount of years.

We have that Vo = 25000, r = -18.5% = -0.185, so:

V(t) = 25000 * (1-0.185)^t

V(t) = 25000 * (0.815)^t

In year 3, we have:

V(3) = 25000 * (0.815)^3 = 13533.58

In year 4, we have:

V(4) = 25000 * (0.815)^4 = 11029.87

The depreciation from year 3 to year 4 was:

V(3) - V(4) = 13533.58 - 11029.87 = $2503.71

The depreciation from year 3 to year 4 was $2503.71

The standard exponential function is expressed as:

[tex]y=a(1\pm r)^t[/tex]

r is the rate

t is the time

Given the following parameters

a = 25000,

r = -18.5% = -0.185,

Substitute into the formula

y = 25000 * (1-0.185)^t

y = 25000 * (0.815)^t

In year 3, we have:

y(3) = 25000 * (0.815)^3 = 13533.58

In year 4, we have:

y(4) = 25000 * (0.815)^4 = 11029.87

The depreciation from year 3 to year 4 was:

y(3) - y(4) = 13533.58 - 11029.87 = $2503.71

The depreciation from year 3 to year 4 was $2503.71

Learn more on depreciation here: https://brainly.com/question/25785586

Answer:

(2, -6)

Step-by-step explanation:

Answer:

The Right Answer Is (2,-6)

Step-by-step explanation:

I hope this help you!

Answer:The answer is the 2nd graph cuh

Step-by-step explanation:

Answer:the second graph

Step-by-step explanation:

Answer:

The ordered pair is [tex](-2,3)[/tex]

Step-by-step explanation:

[tex] y=x+5\\

y=-2x-1\\

\implies x+5=-2x-1\\

\implies 3x=-6\\

\boxed{x=-2}\\

\implies y=-2+5=\boxed {3}\\[/tex]

Answer:

(-2,3)

Step-by-step explanation:

Set the two equations equal to each other since they both equal y

x + 5 = -2x - 1

+2x      +2x          Add 2x to both sides

3x + 5 = -1

     - 5   - 5          Subtract 5 from both sides

3x = -6                 Divide both sides by 3

x = -2

Plug this into one of the original equations

y = x + 5

y = -2 + 5              Add

y = 3

Ethan's share is £10, and Chloe's share is £40, resulting in a total of £50.

To determine the amounts Ethan and Chloe received when sharing £50 in the ratio 1:4, follow these steps:

1. Calculate the Total Parts in the Ratio:

  Add the parts of the ratio: 1 + 4 = 5.

2. Determine the Share for Each Part:

  Divide the total amount by the total parts: £50/5 = £10.

3. Multiply the Share per Part by Respective Parts:

  - Ethan's share: £10 * 1 = £10

  - Chloe's share: £10 * 4 = £40

Therefore, Ethan received £10, and Chloe received £40.

In summary, when the ratio is 1:4, the total ratio parts are 5, and each part represents £10. Ethan's share is £10, and Chloe's share is £40, resulting in a total of £50.

Complete question:

Ethan and Chloe shared £50 in the ratio 1:4. What is the amount received by each of them.

Ethan received £10 and Chloe received £40.

Ethan and Chloe shared £50 in the ratio 1:4. To determine the amount received by each of them, we can follow these steps:

1. Calculate the total parts in the ratio:

o The ratio is 1:4, which means there are a total of 1 + 4 = 5 parts.

2. Divide the total amount (£50) into these parts:

o Each part is worth £50 ÷ 5 = £10.

3. Allocate the shares based on the ratio:

o Ethan receives 1 part, which is £10.

o Chloe receives 4 parts, which is 4 × £10 = £40.

Therefore, Ethan received £10 and Chloe received £40.

Complete question:

Ethan and Chloe shared £50 in the ratio 1:4. What is the amount received by each of them?

Final answer:

To solve this problem, we can set up an equation and solve it to find the number. The number is -6.

Explanation:

To solve this problem, let's set up an equation. Let's assume the number is represented by x. The problem states that one third of the number increased by 7 is five, so we can write the equation as:

(1/3)x + 7 = 5

To solve for x, we can subtract 7 from both sides of the equation:

(1/3)x = 5 - 7

Next, we simplify the right side of the equation:

(1/3)x = -2

Finally, to isolate x, we multiply both sides of the equation by 3:

x = -2 * 3

Therefore, the number is -6.

Answer:

The simplified expression that represents the cost of her purchase is "5x + 27"

Step-by-step explanation:

Since Mikayla bought five shirts each costing $x we need to multiply the number of shirts by the cost, so 5*x, but since three of these shirts came with and additional top that costs $9 we need to take those into account. So the expression that represents the cost of her purchase is:

cost of purchase = 5*x + 3*9

cost of purchase = 5x + 27

Answer:

5x + 27

Step-by-step explanation:

Since Mikayla bought five shirts each costing $x it would be 5x

->if  three of the five came with a matching top for an additional $9 each, it would be 3 x 9.

therefore, the expression that represents the cost of her purchase is:

Total cost of purchase = 5x + (3 x 9)

Total cost of purchase = 5x + 27

Answer:

B

Step-by-step explanation:

The second one gets smaller as it gets taller.

Answer:

Step-by-step explanation:

Answer:

39 bags (at max)

Step-by-step explanation:

160 + 60x《2500

60x《2340

x《39

Answer: the answer would be 39 bags of cement

Step-by-step explanation: 2500- 160= 2340

2340/60 (each bag of cement) it equals 39

Answer:

Step-by-step explanation:

Answer:

The answer is 18 feet squared

Step-by-step explanation:

Answer:

The answer is 18 ft squared

Step-by-step explanation:

i just got 100% i know all the right answers

Answer:

The distance from hot air balloon to the ground  [tex]AC=50.1457 ft[/tex].

Step-by-step explanation:

Labelled diagram of given scenario is shown below.

Given that,

An angle of elevation of Hot air balloon by Angie is [tex]40[/tex]°.

When she  stepped back [tex]200 ft[/tex] then angle of elevation was [tex]10[/tex]°.

Height of Angie is  [tex]5.5 ft[/tex].

To find: How far off the ground is a hot air balloon.

So, from figure

Height of Angie [tex](BC) = 5.5ft[/tex]

  In triangle Δ[tex]ABD[/tex],

         ⇒                    [tex]tan {40\si {\degree}} = \frac{AB}{BD}[/tex]

         ⇒                      [tex]AB = tan (40) \times BD[/tex]          ....................(1)

Now, In triangle Δ[tex]ABE[/tex]

         ⇒                  [tex]tan (10)= \frac{AB}{200+BD}[/tex]

         ⇒                 [tex]AB = tan(10)\times (200+BD)[/tex]

Here, substituting the value [tex]AB[/tex] from Equation (1) we get,

                        [tex]tan(10)\times (200+BD)= tan(40)\times BD[/tex]

                      [tex]tan(10)\times 200+tan(10)\times BD= tan(40)\times BD[/tex]

        ⇒         [tex]BD\times (tan(40)-tan(10))=tan(10)\times 20[/tex]        

        ⇒                   [tex]BD\times 0.6628 = 35.2654[/tex]

        ⇒                       [tex]BD = \frac{35.2654}{0.6628} =53.2067 ft[/tex]        

Now, finding the value of [tex]AB[/tex] from equation (1)

                                 [tex]AB= tan(40)\times 53.2067=0.8391\times 53.2067[/tex]

                                 [tex]AB=44.6457 ft[/tex]              

Therefore Length of [tex]AC= AB+BC[/tex] = [tex](44.6457 + 5.5) ft[/tex]

                                  [tex]AC=50.1457 ft[/tex].

Hence,

The distance from hot air balloon to the ground  [tex]AC=50.1457 ft[/tex].                

Answer:

The diameter of the circle is 19 m

Step-by-step explanation:

The formula of the area of a circle is A = π r², where r is its radius

To find the diameter from the area of the circle equate the formula of the area by the value of the area to find r, then multiply r by 2 because the diameter of a circle is equal twice its radius

∵ The area of the circle is 90.25 π m²

∵ A = π r²

- Equate A by 90.25 π

∴ π r² = 90.25 π

- Divide both sides by π

∴ r² = 90.25

- Take √ for both sides

∴ r = 9.5

∵ The diameter of a circle is twice its radius

∴ d = 2 r

- Substitute r by 9.5

∴ d = 2(9.5)

∴ d = 19

The diameter of the circle is 19 m

Answer:

The diameter would be 19 m

Step-by-step explanation:

hope i helped

Given:

The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.

We need to determine the height of the tree.

Height of the tree:

Let the height of the tree be h.

The height of the tree can be determined using the trigonometric ratio.

Thus, we have;

[tex]tan \ \theta=\frac{opp}{adj}[/tex]

Substituting the values, we get;

[tex]tan \ 34^{\circ}=\frac{h}{25}[/tex]

Multiplying both sides by 25, we have;

[tex]tan \ 34^{\circ} \times 25=h[/tex]

 [tex]0.6745 \times 25=h[/tex]

       [tex]16.8625=h[/tex]

Rounding off to the nearest tenth of a foot, we get;

[tex]16.9=h[/tex]

Thus, the height of the tree is 16.9 feet.

Hence, Option B is the correct answer.

Correct option is B. The height of the tree can be found using the tangent of the angle of elevation, which is the ratio of the tree's height to the distance from the base. Applying the formula, the height is approximately 16.9 feet, matching option B.

To calculate the height of the tree given the angle of elevation and the distance from the point on the ground to the base of the tree, we can use trigonometric functions, specifically the tangent function in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the point on the ground to the tree).

Using the formula:

tangent(angle) = opposite / adjacent

Substitute the given values:

tangent(34°) = height of the tree / 25 ft

Now solve for the height:

height = 25 ft * tangent(34°)

Use a calculator to find:

height = 25 ft * 0.6745

height = 16.9 ft

Therefore, the height of the tree is approximately 16.9 feet (to the nearest tenth of a foot), making option B the correct answer.

Step-by-step explanation:

Putting value of y

-8x = 6x - 14

-8x - 6x = - 14

-14x = - 14

x = - 14/-14

x = 1

Final answer:

An earthquake with a magnitude of 8 is 100 times stronger than an earthquake with a magnitude of 6, as each whole number increase on the Richter scale represents a 10-fold increase in energy released.

Explanation:

The formula m=log(I/S) determines the magnitude of an earthquake, where I is the intensity of the earthquake and S is the intensity of a standard earthquake. To calculate how many times stronger an earthquake with a magnitude of 8 is than an earthquake with a magnitude of 6, we use the fact that each whole number increase on the Richter scale represents a 10-fold increase in the amount of energy released.

So, for an increase of one unit in magnitude:
10^1 = 10 times stronger
For an increase of two units in magnitude (from magnitude 6 to magnitude 8):
10^2 = 100 times stronger

Therefore, an earthquake with a magnitude of 8 is 100 times stronger than an earthquake with a magnitude of 6 when considering the energy released.

An earthquake with a magnitude of 8 is 1.33 times stronger than an earthquake with a magnitude of 6.

1. Understand the formula:

The formula m = log(I/S) relates the magnitude (m) of an earthquake to its intensity (I) and the intensity of a standard earthquake (S). The logarithm used is typically base-10.

2. Substitute the values:

We are given that the magnitude of the two earthquakes are 8 and 6. Let's substitute these values into the formula:

Earthquake 1: m1 = log(I1/S) (magnitude 8)

Earthquake 2: m2 = log(I2/S) (magnitude 6)

3. Simplify the equation:

We want to find the ratio of the intensities (I1/I2). To do this, we can manipulate the equations and solve for I1/I2:

Divide both equations by m2 (magnitude of earthquake 2):

m1 / m2 = log(I1/S) / log(I2/S)

Since both sides of the equation have the same base (10), we can equate the exponents:

m1 / m2 = I1/I2

4. Calculate the ratio:

Now, plug in the magnitudes (m1 = 8, m2 = 6):

8 / 6 = I1/I2

5. Solve for the ratio:

Simplify the fraction:

I1/I2 = 4/3

Therefore, an earthquake with a magnitude of 8 is 1.33 times stronger than an earthquake with a magnitude of 6.

Answer:

The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.

Step-by-step explanation:

The Mom's plot is longer in ranges, therefore, she would have more variability than the dad.

Answer:

B

Step-by-step explanation:

Answer: $125

Step-by-step explanation:

1500/12=125

C is correct,

A is wrong as it halves both the angles and lengths by two which is the same as what she did in the first place so it cannot be correct.

B is also wrong for a similar reason, a triangle cannot have less than 180 degrees, which is impossible as the angles just change naturally which is why all triangles must have 180 degrees, which is the reason she is wrong in the first place.

And D is just incorrect, if she wanted to have shorter sides she should have only decreased all the lengths as it the the ratio of angles that determine the shape of a triangle while the sum of all angles is 180 degrees.

Answer: C

Step-by-step explanation:

Answer:

Yes, the sales tax in their city is an example of regressive tax

Step-by-step explanation:

Firstly, we need to understand what is meant by the term regressive tax.

What is meant by a regressive tax system is a system of taxation in which there is a decrease in tax rate as there is an increase in amount subjected to tax.

Now, the key to knowing if what we have in the question is a regressive taxation is by calculating the percentage of the tax that was paid.

For the Roosevelt’s , the percentage of tax paid would be 16,000/91,000 * 100% = 17.6%

For the Jasper’s, the percentage of tax paid would be 16,000/37,000 * 100% = 43.24%

We can see that at a lower amount subjected to tax, the Jasper’s paid more and thus we can conclude irrevocably that sales tax in their city is an example of a regressive tax

Answer:

The population is 168,900,000 to the nearest hundred thousand

Step-by-step explanation:

In this question, we are tasked with calculating the population of Brazil given its population in 1995 and her growth rate per decade.

Mathematically, we use an exponential function to calculate this population.

This can be written as P = I(1 + r)^n

where P is the population in 2015 which we are looking for,

I is the initial population which is 162,300,000

r is the rate of increase per decade given as 2% = 2/100 = 0.02,

n is the number of times between the years we are expecting this growth. The difference between the years 2015 and 1995 is 20 years which signifies 2 decades(1 decade is 10 years). Thus our n is 2

We plug these values into the equation above;

P = 162,300,000(1+0.02)^2

P = 162,300,000(1.02)^2

P = 168,856,920 which is 168,900,000 to the nearest hundred thousand

Answer:

The mountain is 1.89 miles tall

Step-by-step explanation:

Firstly, we need to compute the value in feet of the total distance traveled by the group.

We were told they traveled 2000 feet per day for 5 days, the total distance they have hiked would be 2000 * 5 = 10,000 feet

Now, we need to convert this to miles

Mathematically ;

1 foot = 0.000189 mile

Hence, 10,000 feet = 10,000 * 0.000189 = 1.89 miles

This means the mountain is 1.89 miles tall

Answer:

V(cylinder) = πr²h

h=3 cm

r=2 cm

V(cylinder) = πr²h = π*2²*3 =12π cm³

Answer : 12π cm³.

Answer:

A

Step-by-step explanation:

12π cm³

Explanation: Probability of NOT getting a tail in 3 coin toss is (12)3=18 . Probability of getting at least 1 tail in 3 coin toss is 1−18=78

Answer:

30 ft^2

Step-by-step explanation:

Area of rectangle is length x width

= 15ft x 2ft = 30 ft^2

Final answer:

To find the coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1, we use the formula for internal division of a line segment, resulting in the coordinates (4, 0).

Explanation:

The coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1 can be found using the formula for internal division of a line segment. Since AC:CB is 2:1, we consider the section ratio to be 2/3 and multiply it by the difference in the corresponding x and y coordinates of A and B, then add to the coordinates of point A.

The x-coordinate of point C is calculated as follows:
Cx = Ax + (Bx - Ax) * m/(m+n)
Where Ax is the x-coordinate of point A, Bx is the x-coordinate of point B, and m/n is the ratio (2/1 in this case), so m=2 and n=1.
Cx = (-8) + (10 - (-8)) * 2/(2+1) = -8 + 18 * 2/3 = -8 + 12 = 4

The y-coordinate of point C is calculated similarly:
Cy = Ay + (By - Ay) * m/(m+n)
Cy = 4 + ((-2) - 4) * 2/(2+1) = 4 + (-6) * 2/3 = 4 - 4 = 0

Thus, the coordinates of point C are (4, 0).

Answer:

11

Step-by-step explanation

u need to do the problem using order of operation

first u do division it is 10 divided by 10 which is 1

10 plus the answer of 10 divided by 10 which is 11

Answer:

11

Step-by-step explanation:

using PEMDAS:

first divide 10/10 and then you get 1+1 which equals 11

Answer:

The surface area of the sphere is 86525.84 square yards

Step-by-step explanation:

The widest circle of the sphere has the same radius of the sphere

Use the circumference of the circle to find its radius, then use it to find the surface area of the sphere

The formula of the circumference of the circle is C = 2π r

The formula of the surface area of the sphere is SA = 4π r²

∵ The circumference of the widest circle is 521.24 yards

∴ C = 521.24

- Equate the formula of the circumference by it

∴ 2π r = 521.24

∵ π ≈ 3.14

∴ 2(3.14) r = 521.24

∴ 6.28 r = 521.24

- Divide both sides by 6.28

∴ r = 83 yards

Now use the formula of the surface area of the sphere to find it

∵ The radius of the sphere = the radius of the widest circle

∴ The radius of the sphere is 83 yards

∵ SA = 4π r²

- Substitute r by 83 and π by 3.14

∴ SA = 4(3.14)(83)²

∴ SA = 86525.84

The surface area of the sphere is 86525.84 square yards

Answer:

The approximated length of arc x is 4 inches ⇒ C

Step-by-step explanation:

That means the diameter of the inner circle is less than the diameter of the outer circle by 4 inches (2 in from each side)

The circumference of the inner circles formed from 20 congruent arcs of length x inches

Now let us find x

The formula of the circumference of a circle is C = π d, where d is the diameter of the circle

∵ The diameter of the inner circle is 24 inches

∴ d = 24

∴ C = 24 π

∵ C = 20 x

- Equate 20 x by 24 π

∴ 20 x = 24 π

- Divide both sides by 20

∴ x = 3.769911184

- Round it to the nearest unit

∴ x ≅ 4

The approximated length of arc x is 4 inches