Which angle measures are correct? Select three options. mAngle2 = 125° mAngle3 = 55° mAngle8= 55° mAngle12 = 100° mAngle14 = 100°

Answer:

(3x+2) (x-4)

Step-by-step explanation:

Answer:

(x - 4)(3x + 2)

Step-by-step explanation:

1.) Use the sum-product pattern

3x^2-10x-8​

3x^2+2x-12x-8

2.) Common factor from the two pairs

3x^2+2x-12x-8

x(3x+2)-4(3x+2)

3.) Rewrite in factor form

x(3x+2)-4(3x+2)

(x - 4)(3x + 2)

Solution

(x - 4)(3x + 2)

No, doubling the length of the sides of a triangle does not result in doubling the area. When the length of the sides of a triangle is doubled, the area of the triangle increases by a factor of four, not two.

The area of a triangle is determined by its base and height. When the sides of the triangle are doubled, both the base and height are doubled as well.

The formula for the area of a triangle is given by A = (1/2) * base * height. If we double both the base and the height, the new area becomes A' = (1/2) * (2 * base) * (2 * height), which simplifies to A' = 2 * 2 * (1/2) * base * height = 4 * A. Therefore, doubling the sides of a triangle results in quadrupling its area, not doubling it.

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Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

Answer:

80°

Step-by-step explanation:

Because the triangle are congruent, the 3rd angle of both triangle needs to bring the sum of the triangle to 180°, so the last angle must be 80

Answer:

The election of 1860  established the Democratic and Republican parties as the majority parties in the United States. It also confirmed deep tensions  surrounding slavery and states’ rights between the North and South. Before Lincoln’s inauguration, eleven Southern states seceded from the Union and just after his swearing-in, the Confederate Army fired on Fort Sumter, starting the Civil War.

Answer: 3/2

Step-by-step explanation: Rate of change is the same thing as the slope.

Juan spent around 81.25 minutes cross-country skiing and approximately 18.75 minutes playing squash.

Let's assume Juan spent x minutes cross-country skiing and (100 - x) minutes playing squash.

The energy expended during cross-country skiing can be calculated by multiplying the energy per minute (50 kJ) by the time spent skiing (x minutes).

Energy expended during cross-country skiing = 50 kJ/min * x min = 50x kJ

Similarly, the energy expended during playing squash can be calculated by multiplying the energy per minute (42 kJ) by the time spent playing squash ((100 - x) minutes).

Energy expended during playing squash = 42 kJ/min * (100 - x) min = 4200 - 42x kJ

The total energy expended by Juan during both activities is given as 4850 kJ.

Total energy expended = Energy during skiing + Energy during squash

4850 = 50x + (4200 - 42x)

Simplifying the equation:

4850 = 50x + 4200 - 42x

4850 - 4200 = 8x

650 = 8x

x = 81.25

Juan spent approximately 81.25 minutes cross-country skiing and (100 - 81.25) ≈ 18.75 minutes playing squash.

Therefore, Juan spent around 81.25 minutes cross-country skiing and approximately 18.75 minutes playing squash.

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Answer:

3x^2 + 6x

Step-by-step explanation:

Just distribute

3x(x + 2)

3x(x) = 3x^2

3x(2) = 6x

3x^2 + 6x

Answer:

(x-4)(x-1)

Step-by-step explanation:

x²-5x+4

x²-4x-x+4

x (x-4)-1(x-4)

(x-4)(x-1)

Hey there!

x² - 5x + 4

x² - 4x - 1x + 4

(x² - 4x) + (-1x + 4)

x(x - 4) - 1(x - 4)

(x - 4)(x - 1) [option C]

Hope it helps ya!

Answer:

They have large leaves with holes in them that the Toucan can use to reach the fruit inside. The Toucan's beak is also used to break open hard-shelled fruits, such as coconuts. The Toucan's beak is also used for defence against predators, as it can be used to peck and jab at them. The adaptations of the rainforest plants are examples of convergent evolution. Both the Toucan and Monstera Plants have adapted to their environment in order to survive. The Toucan has a large beak that helps it to reach fruit in the canopy, while the Monstera Plant has long, grooved leaves with drip tips that allow water to run off and prevent mould. Both adaptations are beneficial for the survival of the species in the rainforest.

Step-by-step explanation:

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

give the guy under me a brainlist lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32

Answer:

36 cm

Step-by-step explanation:

rectangle perimeter = sum of all the side

10+8+10+8=36 cm

Answer:

Step-by-step explanation:

Perimeter =2(10+8)=36 cm.

We know that it can travel 25 centimetres in 12 seconds. First, we break down the minute into seconds.

60/12= 5

______________________________

Now, multiply 25 by 5.

25x5=125

__________________________________

With this knowledge, we just have to convert the centimetres, to meters.

_______________________________

Your answer is 1.25 meters :)

Answer: 1

Step-by-step explanation:

Answer:

39.69%

Step-by-step explanation:

Hope this helps!!

Answer:

The answer is x=0. Believe me that's right.

Answer:

21

Step-by-step explanation:

One number is 3 times another

x and 3x

difference between the numbers is 14,

3x - x = 14

simplify

2x = 14

Divide both sides by 2

x = 7

3x = 21

Answer:

The larger number is 21.

Step-by-step explanation:

let, the smaller number be x.

the larger number be 3*x =3x.

Now,

3x-x=14

or, 2x=14

or, x=14/2

x=7

here,

3x=3*x=3*7=21

Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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Answer:

In standard notation, the number is \(2.6 * 10^4\) light years

Step-by-step explanation:

We have to write the number 26,000 in standard notation,

in standard notation, there is 1 number before the decimal and all others come after the decimal and some power of 10 is multiplied depending upon the number,

in our case,

26000 = 2.6 * 10^4

(since the number is 26 thousand 2.6 ten thousand and ten thousand = 10^4)

Answer:

y=1/4x-17

Step-by-step explanation:

To find the inverse, switch x and y.

y=4(x+17)

x=4(y+17)

Solve for y.

x=4y+68

x-68=4y

y=1/4x- 17

Answer:

67 - 5 = 62

67+5 = 72

Step-by-step explanation:

the real life scenario has been described under this paragraph. take note that I used a number which when added to another number gives 72, and when I subtract this number from the other number, I also get 62

let's assume that a teacher carries out a study in his class and found out that 67percent of his students support indoor sporting activities, if there is an error of 5%, find the minimum and also the maximum percentage of students who are in favor of indoors sporting activities.

|x - 67| = 5

such that

x = 67 +-5

x = 67+5 = 72

x = 67-5 = 62

x= 62, x = 72

Answer:

Step-by-step explanation:

H = V/ pie r^2

H = \(\frac{2200pie}{Pie 5^2}\)

R= 5 because the radius is half the diameter

Pies cancel out leaving you with:

H = 2200/5^2

H = 2200/25

H = 88

Hope this helps :)

The correct option that represents the antiderivative of the given integral ∫ \((x^{11}/(30(-x^{10}/3 - 5))^4) dx\) is option c)\((-x^{10}/3 - 5)^5/(5(-x^{10}/3 - 5)^5) + C.\)

To find the antiderivative of the given integral ∫ \((x^{11}/(30(-x^{10}/3 - 5))^4)\)dx, we can simplify the expression inside the integral first.

Let's rewrite the integral as ∫ \((x^{11}/(30(-x^{10}/3 - 5))^4)\) dx.

Now, let \(u = -x^{10}/3 - 5.\) Taking the derivative of u with respect to x, we get:

\(du/dx = -10/3 * x^{(10/3 - 1)}\)

\(= -10/3 * x^{(7/3)}\)

Next, we can rewrite the integral in terms of u:

∫ \((x^{11}/(30(-x^{10}/3 - 5))^4) dx\) = ∫ \((x^{11}/(30u)^4) dx.\)

Substituting u and du into the integral, we get:

∫ \((x^{11}/(30u)^4) dx\) = ∫ \((x^{11}/(30(-x^{10}/3 - 5))^4) dx\)

= -∫\((1/(30u)^4) du.\)

Now, we can simplify further:

-∫\((1/(30u)^4) du\)= -∫ \((1/(30(-x^{10}/3 - 5))^4) du\)

= -∫\((1/(30(-x^{10}/3 - 5))^4) (-10/3 * x^(7/3)) dx\)

= 10/3 ∫ (\(x^{(7/3)}/(30(-x^{10}/3 - 5))^4) dx.\)

Finally, we can simplify the expression inside the integral:

10/3 ∫\((x^{(7/3)}/(30(-x^{10}/3 - 5))^4) dx\) = \((10/3) * (-(x^{10}/3 + 5))^5/5 + C\)

\(= (-1/3) * (-(x^{10}/3 + 5))^5 + C.\)

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Complete question:

Solve the following integrals:

∫ x 11 30(− x 10 3 −5) 4 dx 5 1 (− x 10 3 −5) 5 +C

b)∫ 5 1 (− x 10 3 −5) 5 x+C (− x 10 3 −5) 4 x+C

d)∫ 4 1 (− x 10 3 −5) 4 +C

The calculated value of the tenth term, b₁₀ of the sequence is 78732

From the question, we have the following parameters that can be used in our computation:

b₁ = -4

bₙ = 3bₙ₋₁

The above means that

We multiply the current term by 4 to get the next term

So, we have

b₂ = 3 * 4 = 12

b₃ = 3 * 12 = 36

b₄ = 3 * 36 = 108

b₅ = 3 * 108 = 324

b₆ = 3 * 324 = 972

b₇ = 3 * 972 = 2916

b₈ = 3 * 2916 = 8748

b₉ = 3 * 8748 = 26244

b₁₀ = 3 * 26244 = 78732

Hence, the tenth term, b₁₀ of the sequence is 78732

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Answer:

a. $13

b. $3

Step-by-step explanation:

Juan wants to start a lemonade stand to earn money. He needs money to purchase the materials before he can sell the lemonade and earn money. His mother agrees to loan him $10. He makes a list of the items he wants to buy.

Cups $2

Lemons $8

Sugar $3

a. How much money do the supplies cost?

b. How much money does he have to spend?

a. Cost of each supply;

Cups $2

Lemons $8

Sugar $3

Total cost of the supplies = $2 + $8 + $3

= $13

b. How much money does he have to spend?

His mother agreed to loan him $10

Total cost of supplies = $13

Amount of money he has to spend = Total cost of supplies - Loan from his mother

= $13 - $10

= $3

Answer:

How much money do the supplies? Answer: $13

How much money does he have to spend? Answer: $10

Step-by-step explanation:

I did it on edge 2021 & got it correct!

Hopefully this helps :)

bye <3