Parallel Lines M and N are cut by Transversal T as shown.
Which statement is true?

The total amount in the compound interest account. 8000 is compounded semiannually at a rate of 11% for 22 years is $92371.97

The given parameters are:

Principal, P = 8000

Rate, r =11%

Time, t = 22 years

Semiannually means that n = 2.

The total amount in the compound interest account. 8000 is compounded semiannually at a rate of 11% for 22 years is then calculated as:

Amount = P + P *(1 + r/n)^nt

So, we have:

Amount = 8000 + 8000 * (1 + 11%/2)^(22 * 2)

Evaluate the expression

Amount = 92371.97

Hence, the total amount in the compound interest account. 8000 is compounded semiannually at a rate of 11% for 22 years is $92371.97

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Answer:the slope is 3

Source: trust me bro

Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

A linear (y = mx + b), quadratic (y = ax²), or exponential (y = a(b)*) function that models the data is 1000(810/1000)^x.

The slope-intercept version of the equation for a straight line is written as Y = mx + b.

The parabola-like form of the y=ax^2 graph. The graph would be situated depending on the sign of a.

 x              y

-10          1000

-9             810

-8             640

-7             490

-6             360

Now, y=mx+b

Forming the equation, and subtracting

1000=m(-10)+b   ______(1)

810=m(-9)+b   _______(2)

-___________________

190=-m

m=-190

now, substituting the value of m in equation 1

Thus, b=-900

y=-190x-900

If y=ax^2

at x=-10

y=1000

1000=a(-10)(-10)

1000=100a

10=a

Thus y=10x^2

=>y=ab^x

substituting x=-10, y=1000

1000=ab^(-10)

(1000)b^-10=a

and

810=ab^-9

(810)(b^-9)=a

Thus b = 810/1000 and a=1000

So, y=1000(b)^x=1000(810/1000)^x

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Answer:

Step-by-step e

-35

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The word problem quadratic equation is solved to get t = 1.616 seconds

information given in the question

A ball is thrown from an initial height of 3 feet

an initial upward velocity of 24 ft/s

The ball's height / (in feet) after t seconds is given by the following.

h = 3 + 24t - 16rt²

The quadratic equation given is of the form h = 3 + 24t - 16rt²

applying the quadratic formula which is given by

= ( -b ± sqrt ( b² - 4ac ) ) / 2a

where

a = -16

b = 24

c = 3

= ( - (24) ± sqrt ( (24)² - 4 * -16 * 3 ) ) / 2 * -16

= ( - 24 ± sqrt ( 576 - -192 ) ) / -32

= ( - 24 ± sqrt ( 768 ) ) / -32

= ( - 3 ± 2sqrt ( 3 ) ) / -4

= 1.616  OR   -0.116

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Step-by-step explanation:

and his did u use adding if it's adding or

anything I can help!

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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Answer:

31.4

Step-by-step explanation:

You subtract 80.00 from 48.60, and you get your answer 31.4

Answer:

128.6

Step-by-step explanation:

You have to do the inverse operation.

So you add 48.60 to each side of the equation. This cancels out the -48.60 which isolates the variable. And on the other side of the equation it leaves you with 128.6. Therefore d = 128.6

Answer:

Factors are often given as pairs of numbers, which multiply together to give the original number. These are called factor pairs. A square number will have one factor pair consisting of one factor multiplied by itself. This factor is called the square root of the given number.

Answer:

rational

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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Answer:

Either location costs the same when they play 4 games

Step-by-step explanation:

The total cost for playing putt-putt consists of fixed rentals and a variable amount per game.

On one location Ben and his friends can pay $2 rentals plus $7.50 per game.

If x is the number of games played, then the total cost at this location is:

C1(x) = 7.50x + 2

At another location, it would cost $8 for rentals plus $6 per game. The second function is:

C2(x) = 6x + 8

It's required to find the number of games x in order for either location to cost the same amount.

It can be done by equating both cost functions:

7.50x + 2= 6x + 8

Subtracting 2 and 6x:

7.50 - 6x = 8 -2

Operating:

1.5x = 6

Dividing by 1.5:

x = 6 / 1.5

x = 4 games

Either location costs the same when they play 4 games

Answer:

23

Step-by-step explanation:

First of all we find the total number of students:

4+6+2+2+3+4+6+3=30

Then we find the amount of freshmen’s

4+3=7

Now we find the Fraction which represents the freshmen to all ratio:

\(\frac{7}{30}\)

which is equal to:

0.2333...

Which can be converted into a percentage by multiplying it by 100

0.2333...×100=23.333...

Which is rounded down as the third digit, the 3, gets rounded down

so the answer is 23

The base area of the prism is 2x² + 5x - 18

From the question, the given parameters are

Volume = 2 x cubed + 9 x squared minus 8 x minus 36

Height =  x + 2

Rewrite properly as

Volume = 2x³ + 9x² - 8x - 36

Height =  x + 2

The base area is calculated as

Base area = Volume/Height

Using the synthetic division, we have

Set the divisor to 0

x + 2 = 0

This gives

x = -2

So, we have the representation to be

-2 | 2   9  - 8  - 36

Write out 2

So, we have

-2 | 2   9  - 8  - 36

     2

Multiply 2 and -2

This gives

-2 | 2   9  - 8  - 36

          -4

     2

So, we have

-2 | 2   9  - 8  - 36

          -4

     2    5

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10

     2    5   -18

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10   36

     2    5   -18    0

This means that

Base area = 2x² + 5x - 18

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Answer:

7.2×10^-3

Step-by-step explanation:

8 × 10^4×9 × 10^–8

=8×9×10^(4-8)

=72×10^-4

=7.2×10^-3

Answer:

on the y-axis

Step-by-step explanation:

Answer:

It is located on the y-axis

Answer:

I think it is C

Step-by-step explanation:

Forgive me if I am wrong the reason I think so is  I did one like this last week. Sorry if it is wrong trying to remember.

The y-intercept of the function is (0, c)

The coefficients b determine the horizontal shift of the parabola compared to the parent function

If a is negative, the parabola opens downward

The y-intercept of the function is (0, c).

This means that when x = 0, the y-value is equal to c.

The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.

The coefficient b determines the horizontal shift of the parabola compared to the parent function.

The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.

A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.

If a is negative, the parabola opens downward.

The coefficient a determines the shape of the parabola.

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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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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Answer:

1/15 or 0.0667

Step-by-step explanation:

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bardai

chatgpt

red marble on the first draw is 2/6, or 1/3

red marble on the second draw, given that the first marble was red, is 1/5

(1/3) * (1/5) = 1/15

Answer: Since 1 and 2 have the same measure, angle CED is also equal to 1 and 2. Therefore, triangle CED and triangle CAB are similar by the Angle-Angle (AA) criterion.

Using the properties of similar triangles, we can set up the following proportion:

$\frac{CE}{CA}=\frac{CD}{CB}$

Substituting the given values:

$\frac{CE}{x+4}=\frac{x}{14}$

Cross-multiplying:

$14CE = x(x+4)$

$14CE=x^2+4x$

We also know that triangle ADE and triangle ABC are similar by the AA criterion. Therefore, we can set up the following proportion:

$\frac{DE}{AB}=\frac{AE}{AC}$

Substituting the given values:

$\frac{DE}{18}=\frac{AE}{x+4}$

Cross-multiplying:

$AE = 18\frac{DE}{x+4}$

Now, we can substitute the value of $AE$ in terms of $DE$ into the first equation:

$14CE=x^2+4x$

$14\frac{DE}{x+4}=x^2+4x$

$14DE=x^2+4x(x+4)$

$14DE=x^2+4x^2+16x$

$18x^2+16x-14DE=0$

We can now use the quadratic formula to solve for $x$:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-16\pm\sqrt{(16)^2-4(18)(-14DE)}}{2(18)}$

$x=\frac{-16\pm\sqrt{256+1008DE}}{36}$

Since $DC=x$, we can now use this equation to find the value of $DC$ for a given value of $DE$. For example, if $DE=5$, we have:

$DC=\frac{-16\pm\sqrt{256+1008(5)}}{36}$

$DC\approx 2.3$ or $DC\approx -3.1$

Since distance cannot be negative, we choose the positive solution:

$DC\approx 2.3$ units.

To find $DE$, we can substitute the value of $DC$ back into one of the earlier equations:

$\frac{CE}{x+4}=\frac{x}{14}$

$\frac{CE}{2.3+4}=\frac{2.3}{14}$

$CE\approx 1.34$ units

Now we can use the second similarity proportion to find $DE$:

$\frac{DE}{18}=\frac{AE}{x+4}$

$\frac{DE}{18}=\frac{18-1.34}{2.3+4}$

$DE\approx 3.64$ units

Therefore, $DC\approx 2.3$ units and $DE\approx 3.64$ units.

Step-by-step explanation:

Answer:

Divide it by two

Step-by-step explanation:

Divide it by two

Answer:

you have to divide the numbers by 2