The image provided contains a set of parallel lines, AB and CD, and a transversal line, EF. If angle ∠ a is equal to 135˚, then which of the other angles is equal to 135˚? SELECT ALL THAT APPLY! *
∠ b
∠ h
∠ c
∠ g
∠ e

Answer:

x=15.714

y=5.715

Step-by-step explanation:

Answer:

x=10, y=20

Step-by-step explanation:

okay so to find x, or the way I did it, we just have to look at the top, we know one line is 180 degrees, and we see three angles, 7x,90, and 20

so 90+20+7x=180

and:110+7x=180

therefore: 7x=70

and finally: x=10

To find y also isn't had if we just look at the blue and green lines we see they are intersecting and opposite angles in intersecting lines are congruent meaning they are the same. So we now know that:

5x+2y=90

and we know x=10

so 5x=50

meaning that: 50+2y=90

therefore: 2y=40

and in conclusion y=20

Answer:

The answer is 7 pens

GIven:

To Determine: The equivalent of the given expression

Distributing the sign outside as shown below:

Hence, the equivalent expression by distributing the sign outside the given expression is:

8.4n+1

The time it takes for the baseball to reach the ground can be found by solving the quadratic equation 16t^2 + 40t - 555 = 0, using the positive value of t. The speed at which the baseball strikes the ground can be calculated using the equation v = 40 + (-32)t with the positive value of t.

To determine how long it takes for the baseball to reach the ground and the speed at which it strikes the ground, we can analyze the motion using the principles of kinematics. The baseball is thrown straight downward with an initial speed of 40 ft/s from a height of 555 ft.

We can use the equation for vertical displacement to calculate the time it takes for the baseball to reach the ground. The equation is given as:

s = ut + (1/2)at^2

In this case, the initial displacement (s) is 555 ft, the initial velocity (u) is 40 ft/s, the acceleration (a) is the acceleration due to gravity (-32 ft/s^2), and we need to solve for time (t).

By substituting the given values into the equation and solving for t, we get:

555 = 40t + (1/2)(-32)t^2

Simplifying and rearranging the equation, we have:

16t^2 + 40t - 555 = 0

Solving this quadratic equation gives us two possible values for t, but we discard the negative value since time cannot be negative in this context. Therefore, the positive value for t represents the time it takes for the baseball to reach the ground.

To determine the speed at which the baseball strikes the ground, we can use the equation for velocity:

v = u + at

Here, the initial velocity (u) is 40 ft/s, the acceleration (a) is -32 ft/s^2, and we substitute the positive value of t we found earlier.

Calculating the value of v, we have:

v = 40 + (-32)t

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Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

Answer:

01234

Step-by-step explanation:

Sequence is smallest to largest therefore the sequence is 01234

Answer:01234

Step-by-step explanation:

Hope this helps.

Answer:

y = 14

Angle O is 41 degrees

Step-by-step explanation:

From the question, since we have an isosceles triangle, then the base angles are equal

This means that the angle at M is (4y-15) too

Mathematically, the sum of the angles in a triangle is 180 degrees

Thus;

7y + 4y-15 + 4y-15 = 180

15y-30 = 180

15y = 180+ 30

15y = 210

y = 210/15

y = 14

Angle O is 4y-15

= 4(14) -15 = 56-15 = 41 degrees

In the figure, it is proved that ∠1 = 180 - ( θ₂ + θ₁ ) and ∠2 =  180 - (θ₂ + θ₁), so both angles are equal.

To prove that the value of angle 1 is equal to the value of angle 2, we will follow the steps below;

Length AD = Length DC, this implies that the corresponding base angles will be equal.

so ∠DAB = ∠DCB = θ₁

Also, since BD is the bisector of ∠ADC;

∠CDB = ∠ADB = θ₂

The value of the ∠ABD is calculated as;

∠ABD = ∠1

∠1 = 180 - (∠ADB + ∠DAB) -----(sum of angles in a triangle)

∠1 = 180 - ( θ₂ + θ₁ ) -------- (1)

The value of ∠DBC is calculated as;

∠DBC = ∠2

∠2 = 180 - (∠CDB + ∠DCB) -----(sum of angles in a triangle)

∠2 =  180 - (θ₂ + θ₁) -------- (2)

So, if we compare equation (1) and equation (2), we can see that ∠1 = ∠2. Hence, it is proved that ∠1 = ∠2

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Answer:

Step-by-step explanation:

2x4=8

4+4=8

Or

2+2+2+2=8

If you cut off one of the corners of a rectangular prism, you would get a triangle.

The rectangular prism is a solid that possesses six rectangular surfaces constituting its three-dimensional shape. If you excise any of the corners of this structure, it will create an opening intersecting through a plane that runs across three neighboring edges converging at the apex.

Owing to the orientation and configuration of the three planes colliding beneath the inaccessible edge, which form right angles with one another as per the shape's design, a resultant triangle displays an exact angle when fused to the original prism with proportions depending on the respective dimensions of the rectangular prism.

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The rate of return for Nichole's investment is approximately 22%.

To calculate the rate of return, we need to determine the percentage increase in value from the initial investment to the final sale.

Nichole bought 500 shares at $8.24 per share, which amounts to a total investment of 500 * $8.24 = $4,120.

After one year, she sold all her shares for $10.10 per share, resulting in a total sale value of 500 * $10.10 = $5,050.

Her profit from the investment is $5,050 - $4,120 = $930.

To find the rate of return, we divide the profit by the initial investment and multiply by 100: ($930 / $4,120) * 100 ≈ 22.6%.

Therefore, her rate of return is approximately 22.6%, which corresponds to option A.

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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The number of batteries expected to last between three years and one month and three years and seven months, is 12,500 batteries.

Given that the mean shelf life of the flashlight batteries is three years and four months and the standard deviation is three months.

To find the number of batteries that can be expected to last between three years and one month (3.08 years) and three years and seven months (3.58 years), we need to calculate the probability within this range.

First, we convert the given time intervals to years:

Three years and one month = 3.08 years

Three years and seven months = 3.58 years

Next, we calculate the z-scores for these values using the formula:

z = (x - μ) / σ

For 3.08 years:

z1 = (3.08 - 3.33) / 0.25 = -1

For 3.58 years:

z2 = (3.58 - 3.33) / 0.25 = 1

Now, we can use the standard normal distribution table or a calculator to find the probabilities corresponding to these z-scores.

The probability of a value falling between -1 and 1 is the difference between the two probabilities.

Let's assume that the distribution is symmetric, so half of the batteries would fall within this range.

Therefore, the number of batteries that can be expected to last between three years and one month and three years and seven months is approximately:

Number of batteries = 0.5 × Total number of batteries = 0.5 × 25,000 = 12,500 batteries.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

(6, -3) aka x = 6 and y = -3

Step-by-step explanation:

since you are given y = -2x + 9, you should start by substituting the expression -2x + 9 for y in the equation 2x + 3y = 3.

here's your equation after plugging in the expression that's equal to y:

2x + 3(-2x + 9) = 3

distribute 3 to -2x

2x + 3(-2x + 9) = 3 ⇒ 3 · -2x = -6x

...and to 9.

2x + 3(-2x + 9) = 3 ⇒ 3 · 9 = 27

now you're left with 2x - 6x + 27 = 3.

combine like terms.

2x - 6x + 27 = 3 ⇒ -4x + 27 = 3

subtract 27 from both sides of the equation. since +27 and -27 cancel each other out, you're left with subtracting 27 from 3, which gives you -24.

now your equation is -4x = -24.

divide both sides of the equation by -4.

-24/-4 = 6

...therefore x = 6.

since you have your x value now, you can plug that into the equation for y in order to solve for y.

y = -2x + 9 ⇒ y = -2(6) + 9

multiply -2 and 6.

y = -2(6) + 9 ⇒ y = -12 + 9

add -12 and 9.

y = -12 + 9 ⇒ y = -3

...and now you've solved for y, which is -3.

therefore, your solution is (6, -3), aka x = 6 and y = -3.

hope this helps! have a nice day <3

The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.

What is synthetic division?

Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."

We are given the expression as (n^3+3n^2-15n+19)

The expression is to be divided by (n-2)

So, by using the synthetic division, we get

2 |  1     3     -15      19    

     -     2      10     -10        

     1     5      -5       9    

Quotient =  n^2+5n-5

Remainder = 9

Hence, the quotient is n^2+5n-5 and the remainder is 9.

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a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62

b. The number of student that are math major but not biology major = 7

c. The number of student that are neither math major nor biology major = 47

d. The number of student that are both math and biology major = 4

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

To calculate the amount you will repay and the annual interest rate charged by the loan company, we can follow these steps:

Step 1: Calculate the number of $500 increments for the loan amount:

Number of $500 increments = loan amount / $500

= $1,693 / $500

≈ 3.386

Since we can't have a fraction of an increment, we round up to 4.

Step 2: Calculate the daily payment:

Daily payment = 25 © * Number of $500 increments

= 25 © * 4

= $100

Step 3: Calculate the total repayment amount:

Total repayment amount = Daily payment * number of days

= $100 * 120

= $12,000

Step 4: Calculate the annual interest rate:

Annual interest rate = (Total repayment amount - Loan amount) / Loan amount * (360 / Number of days)

= ($12,000 - $1,693) / $1,693 * (360 / 120)

Now, let's perform the calculations:

Amount you repay ≈ $12,000

Annual interest rate ≈ (($12,000 - $1,693) / $1,693) * (360 / 120)

Calculating the annual interest rate:

Annual interest rate ≈ (($10,307) / $1,693) * 3

Rounding to four decimal places:

Annual interest rate ≈ (6.0905) * 3

≈ 18.2715

Therefore,

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

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Answer:280

Step-by-step explanation:14 x 20 = 280

Answer:

235 cm

Step-by-step explanation:

First, find the area of the whole rectangle (bxh)

14x20=280

Next, find area of the missing piece

5x9=45 ( to find this, 14-9, times 20-11)

Finally, subtract the missing piece from the total rectangle

280-45=235

The area of triangles is a. 30 inches²,   b.18 inches², and c. 130 yards² for the given triangles.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Area of a triangle = (1/2) × height × base

a) Given

h = 6 inches; b = 10 inches

Area = 6 × 10/2 = 30 inches².

b) Given

h = 9 centimeters; b = 4 centimeters

Area = 9 × 4/2 = 18 inches².

c) Given

h = 13 yards; b = 20 yards

Area = 13 × 20/2 = 130 yards².

Hence the area of triangles is a. 30 inches²,   b.18 inches², and c. 130 yards² .

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Answer:

power of 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

8^4 is 8*8*8*8

8^2 is 8*8

therefore

(8^4) *(8^2) = (8*8*8*8)*(8*8) = 8^(4+2) = 8^6

Answer:

Step-by-step explanation:

Hello

p(A∪B) = p(A) + p(B) - p(A∩B) = 0.5 + 0.4 - 0.15 = 0.9 - 0.15 = 0.75

hope this helps

It's difficult to say whether the conditions for constructing a t-confidence interval are met based on the information provided. To construct a t-confidence interval, three conditions must be met:

The sampling method must be random. It's not specified in the problem whether the method of selecting the vehicles was random or not, so it's impossible to say whether this condition is met.

The sample size must be large enough. A sample size of 100 vehicles is considered to be large enough for the normal/large sample condition to be met.

The population must be approximately normally distributed or the sample size must be large. Since the problem does not specify anything about the distribution of the population, it is not clear if this condition is met.

Given that the information provided does not give enough details to state whether the conditions for constructing a t-confidence interval are met or not.

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Answer:

i dont know what surface means but i could help you

if you mean the Face how is shown below its will be like this 6×3+3×2+6×2

and if you want the figure areas its will be like this 2×(6×3+6×2+3×2) hopefully its helpful

and can you tell me what ` sign means iam not good at engilish sorry about that

Answer:

d Because I just took the test and got it right

Therefore, the general indefinite integral of the given function is: ∫\((7x^3 + 2/3x^2) dx = (7/4)x^4 + (2/9)x^3 + c\), where c is the constant of integration.

To find the general indefinite integral of the given function, we integrate each term separately:

∫\((7x^3 + 2/3x^2) dx\)

Using the power rule of integration, we add 1 to the exponent and divide by the new exponent:

= \((7/4)x^4 + (2/9)x^3 + c\)

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