The triangles are similar, which angle is congruent to

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

28 degrees

Step-by-step explanation:

We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.

By combining like terms, we get 6x + 12 = 180.

Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.

Answer:

Step-by-step explanation:

The simple short answer is because all real numbers are to be squared.

If any negative value is put into x^2, the value will become positive. That's because an even number of negatives are positive.

For example y = x * x

Let x = - 3

y = (-3)(-3)

y = 9 because there are an even number of negatives.

Notice that if break x^2 into x * x, you should see more clearly that each x is equal to - 3

Both the fox and the dog need to make 28 leaps before the fox is caught.

Given that,

The fox has a start of 60 leaps.

The fox can make 3 leaps to the dogs 2.

This means that for every 3 leaps taken by the fox, the dog will take 2.

The dog travels in only 3 leaps as far as the fox goes in 7.

This means that for every 3 leaps the dog takes, the fox takes 7 leaps.

Now, we have to find out how many leaps the fox and the dog need to make before the fox is caught.

Assume that the fox and the dog both sprint for "x" number of jumps before the fox is apprehended.

For the fox,

The total distance travelled would be ⇒  60 + 3x

(since the fox can make 3 leaps for every 2 leaps of the dog, and the fox starts with a 60-leap advantage).

For the dog,

The total distance travelled would be ⇒ 2x

(since the dog can make 2 leaps for every 3 leaps of the fox).

Now we know that the dog travels in only 3 leaps as far as the fox goes in 7,

Therefore,

3 leaps of the dog = 7 leaps of the fox

This can be expressed as:

2x = (60 + 3x)( 7/3 )

Simplifying this equation, we get:

2x = 140 + 7x

5x = 140

x = 28

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Answer:

5 ≤ x ≤ 10             5 ≤ y ≥ -1

Step-by-step explanation:

Answer: 14 ounces

Step-by-step explanation:

         To find the mean, we add up all the values and divide by the number of values.

\(\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces\)

The congruence theorem that proves that ΔWXZ ≅ ΔYZX is: a.AAS

What does a math congruent mean?

Congruent refers to having precisely the same form and size. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

The image given shows that

∠W ≅ ∠Y

∠X ≅ ∠Z

XZ ≅ XZ

Therefore, the congruence theorem that proves that ΔWXZ ≅ ΔYZX is: a.AAS

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The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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Given:

Principal = $14000

Rate of interest = 10% compounded semiannually.

Time = 11 years.

To find:

The accumulated value of the given investment.

Solution:

Formula for amount or accumulated value after compound interest is:

\(A=P\left(1+\dfrac{r}{n}\right)^{nt}\)

Where, P is the principal values, r is the rate of interest in decimal, n is the number of times interest compounded in an year and t is the number of years.

Compounded semiannually means interest compounded 2 times in an years.

Putting \(P=14000,r=0.10,n=2,t=11\) in the above formula, we get

\(A=14000\left(1+\dfrac{0.10}{2}\right)^{2(11)}\)

\(A=14000\left(1+0.05\right)^{22}\)

\(A=14000\left(1.05\right)^{22}\)

\(A\approx 40953.65\)

Therefore, the accumulated value of the given investment is $40953.65.

Answer:

A = $41,867.06

A = P + I where

P (principal) = $14,000.00

I (interest) = $27,867.06

Step-by-step explanation:

Given: Investment = $14,000 Annual Rate: 10% compounded semiannually = 11 year

To find: The accumulated value of an investment

Formula: \(A = P(1 + \frac{r}{n}) ^n^t\)

Solution: First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 14,000.00(1 + 0.1/12)(12)(11)

A = 14,000.00(1 + 0.008333333)(132)

A = $41,867.06

Henceforth:

The total amount accrued, principal plus interest, with compound interest on a principal of $14,000.00 at a rate of 10% per year compounded 12 times per year over 11 years is $41,867.06.

The model should visually represent that Ms. Duda's class hung 100 lanterns before lunch, which is 20% of the total 500 lanterns.

To draw a model showing what percent of 500 lanterns Ms. Duda's class hangs before lunch, we can use a rectangular bar model.

Draw a rectangular bar to represent the total number of lanterns, which is 500. Label it as "Total Lanterns."

Divide the rectangular bar into two parts. One part should represent the number of lanterns hung before lunch, which is 100. Label this section as "Lanterns Before Lunch."

Calculate the percentage of lanterns hung before lunch by dividing the number of lanterns hung before lunch by the total number of lanterns and multiplying by 100. In this case, (100/500) * 100 = 20%.

Draw an arrow pointing to the "Lanterns Before Lunch" section, and write "20%" next to it to represent the percentage.

The model should visually represent that Ms. Duda's class hung 100 lanterns before lunch, which is 20% of the total 500 lanterns.

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The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

yes its correct

Step-by-step explanation:

but for the check where did you get the 12? you might want to redo that part but otherwise its right

Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

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Answer:

I believe the answer should be 90:90:180. I may be wrong.

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Answer:

5y(x^2 - 3)

Step-by-step explanation:

Hope this helps :)

Answer:

D.

Step-by-step explanation:

Mean : 7 + 5 + 6 + 4 + 7 + 8 + 12 = 12 + 10 + 7 + 20 = 30 + 19 = 49. 49/7= 7

Mode : 7.

Median 4 , 4, 6, 7, 7, 8, 12.    7 is the middle number

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

$163.24

Step-by-step explanation:

you have to add the two values together since his paycheck last week was MORE than his paycheck this week.

154.01+9.23= 163.24

Answer:

none of these

Step-by-step explanation:

the side lengths are are 2√5/5, 2, and 4.

sin(x) = opp/hyp

sin(x) = 2/2√5

Answer: 20500

Step-by-step explanation:

Rounding 408 to the nearest ten will give 410. Since it is above 4, we'll add 1 to the 0 in the tens value and this will be 410.

Rounding 52 to nearest ten is 50.

Therefore, we'll multiply 410 by 50. This will be:

= 410 × 50

= 20500

Therefore, the correct option is D.

Answer:

---------------

Let the radius be r.

Use circumference formula and find the value of r:

Find the area using the circle area formula:

The matching choice is (B).

Answer:

Step-by-step explanation:

Answer:

The function g(x) = (x + 2)³ − 6 is obtained by applying three transformations to the parent function f(x) = x³.

First, g(x) is shifted 2 units to the left by subtracting 2 from x inside the parentheses:

g(x) = (x + 2 - 2)³ − 6 = (x)³ − 6

This shows that option C, "g(x) is shifted 2 units to the left and 6 units down," is not correct.

Next, g(x) is shifted 6 units down by subtracting 6 from the entire function:

g(x) = (x + 2)³ − 6 - 6 = (x + 2)³ - 12

This shows that option A, "g(x) is shifted 2 units to the right and 6 units down," is correct.

Finally, g(x) is not shifted left or right by any additional units, but it is shifted 2 units up by adding 2 to the constant term:

g(x) = (x + 2)³ − 6 + 2 = (x + 2)³ - 4

This shows that option B, "g(x) is shifted 6 units to the right and 2 units up," is not correct.

Therefore, the correct answer is option A: g(x) is shifted 2 units to the right and 6 units down.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06\)

Answer:

Step-by-step explanation:

a) 1.8 kg in grams is 1800 g

b) If 6 toys weigh 1800g; then 1 toy weighs 300 g(6:1)

c) If 1 toy weighs 300 g, 4 toys weigh 1200 g and you convert in kg which is 1.2 kg