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Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?
a) 45 degrees
b) 60 degrees
c) 120 degrees
d) 135 degrees

Answer:

<8, -8>

Step-by-step explanation:

X= -1 - (-9) or -1 + 9

Y= -6 - (2)

Answer:

⟨8, −8⟩

Step-by-step explanation:

draw this on graph paper and then count how far the one point is from the other.

The horizontal number goes first, then the vertical.

hope this helps!

Answer:

1. y = 2(x + 2)

Step-by-step explanation:

if we substitute the values,

we get 6 = 2*1 + 4

6 = 6

therefore, it is correct.

The system of equations has no solution. hence option d is correct.

Equation is described as the state of being equal, and it is commonly represented as a math expression with equal values on both sides, or it refers to a problem involving numerous variables.

here, we have,

to find solution to the system:

The given equation is

y=2x+8  ..(1)

3(-2x + y) = 12  ...(2)

Substitute the y value in equation 2 from equation (1)

3(-2x + 2x+8) = 12

               3(8)=12

                24≠12

Hence the system of equations has no solution.

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complete question:

What is the solution to the system of equations

below?

y=2x+8

3(-2x + y) = 12

1) no solution

2) infinite solutions

3) (-1,6)

4) (1/2,9)

The equation of the line passing through points (-1, 2) and (1, -1) is y = -1.5x + 0.5

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the slope of the line and b is the y intercept

The line given passes through the point (-1, 2) and (1, -1). The equation is:

y - 2 = [(-1-2)/(1 - (-1)](x - (-1)]

y - 2 = -(3/2)(x + 1)

y = -(3/2)x - (3/2)

y = -1.5x + 0.5

The equation of the line is y = -1.5x + 0.5

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The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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To find the radius of convergence, we can use the ratio test. By applying the ratio test to the series ∑(7n(x-3)n), we can determine the value of r.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a series is L as n approaches infinity, then the series converges if L < 1 and diverges if L > 1. Applying the ratio test to the series ∑(7n(x-3)n), we have:

L = lim(n→∞) |(7(n+1)(x-3)^(n+1))/(7n(x-3)n)|

= lim(n→∞) |7(x-3)/(n+1)|

= |7(x-3)/∞|

= 0.

Since the limit L is 0, which is less than 1, the series converges for all values of x. Therefore, the radius of convergence r is infinity, indicating that the series converges for all values of x.

The interval of convergence i is determined by the range of x values for which the series converges. Since the series converges for all x values, the interval of convergence is (-∞, +∞), or in interval notation, (-∞, +∞).

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For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = \(\sqrt{MK^2 + LK^2}\)

LM = \(\sqrt{8^2 + 3.56^2}\)

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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Answer:

Acute

Step-by-step explanation:

Mean, median and mode are the measures of central tendency that are used to describe a statistical sample. These measures are commonly used in statistical analysis and are important in understanding the general characteristics of a data set.

Here is a brief explanation of each of these measures Mean: The mean is the arithmetic average of a set of data. It is calculated by summing up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to outliers, meaning that if there are any extreme values in the data set, the mean will be affected.Median: The median is the middle value in a set of data. It is the value that divides the data set into two equal parts. If there is an even number of values in a data set, the median is the average of the two middle values.

The median is less sensitive to outliers than the mean, meaning that extreme values will not have as much of an effect on the median. Mode: The mode is the most common value in a set of data. It is the value that appears most frequently in the data set. The mode is not sensitive to outliers, meaning that extreme values will not affect the mode. The mode can be used to describe the typical value of a data set. In summary, the mean tells you about the average value of a data set, the median tells you about the middle value of a data set, and the mode tells you about the most common value in a data set. These measures of central tendency are useful for understanding the general characteristics of a data set.

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The value of the angle m<CED = 74 degrees

To determine the value of the angle, we need to take note of the following;

From the information given, we have that;

m<BEC = 106 degrees

But we have that;

m<BEC + m<CED = 180 degrees

Substitute the values, we have;

m<CED = 180 - 106

subtract the values

m<CED = 74 degrees

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Answer:

Assume that the expression is:

r = √(A)/3

Multiply both sides by 3:

3r = √(A)

Finally, square both sides to get:

A = (3r)²

= 9r²

I hope this helps!

Step-by-step explanation:

The value of a will be 3r².

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The expression is;

r = √a/3

Now,

The expression is;

r = √a/3

Square both sides to get:

r² = a/3

Multiply both sides by 3:

3r² = a

Thus, The value of a will be 3r².

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Answer:

Buffalo

Step-by-step explanation:

jfvjuvf

Answer:

90

Step-by-step explanation:

its a right angle

Answer:

The correct equation in slope-intercept form is:

y= 6x+14

Step-by-step explanation:

Given the equation

y-2=6(x+2)

y-2 = 6x+12

Adding 2 to both sides

y-2+2=6x+12+2

y= 6x+14

Thus, the correct equation in slope-intercept form is:

y= 6x+14

1) WHAT WAS YOUR MISTAKE

In the 2nd step, you had added 4 to the right-hand side of the equation instead of 2. The reason is that both sides should have been added by 2. But, you mistakenly added 4 to the right-hand side of the equation instead of 2.

2) SUGGESTION TO AVOID MISTAKE

You must make sure not to disturb the balance of two sides of the equation, meaning whatever the operation (add/subtract, multiply or divide) you do, you make sure to do the same operation on both sides of the equation.

Answer:

\(\huge\boxed{\$ \ 8.15}\)

Step-by-step explanation:

DVD Player = $49.95

DVD Holder = $19.95

Personal Stereo = $21.95

Total Cost of all the things:

=> $49.95 + $19.95 + $21.95

=> $91.85

Left Money:

=> $100 - $91.85

=> $8.15

Answer:

8 cubes

If we want to cover the base of the prism having dimensions 2 cm × 1 cm with cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base

Step-by-step explanation:

The simplification of the the given expression  2/1 - 5/2 : 15/4 is  1/2 : 15/4

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We have been given the number expression that is; \(\dfrac{2}{1} - \dfrac{5}{2} :\dfrac{15}{4}\)

Taking LCM on Left sides by 2:

\(\dfrac{2}{1} - \dfrac{5}{2} :\dfrac{15}{4}\\\\\dfrac{2\times 2}{2} - \dfrac{5}{2} :\dfrac{15}{4}\\\\\\\dfrac{4}{2} - \dfrac{5}{2} :\dfrac{15}{4}\)

Now solve the LCM part;

\(\dfrac{4 - 5}{2} :\dfrac{15}{4}\\\\\\\dfrac{-1}{2} :\dfrac{15}{4}\)

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The complete question is

Simplify the given expression  \(\dfrac{2}{1} - \dfrac{5}{2} :\dfrac{15}{4}\).

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

from my side it's blurry

Answer:

(3x - 2) (x - 2)

Step-by-step explanation:

im smart

If the bottle can only hold 13 ounces, then the probability the bottle will overflow is approximately 0.0032 or 0.32%.

First, we need to calculate the z-score, which is the number of standard deviations that the mean value of 12.2 ounces is away from the bottle's capacity of 13 ounces. We can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the bottle capacity (13 ounces), μ is the mean value of soda dispensed by the machine (12.2 ounces), and σ is the standard deviation (0.3 ounces).

Substituting the values, we get:

z = (13 - 12.2) / 0.3 = 2.67

The z-score of 2.67 means that the bottle capacity of 13 ounces is 2.67 standard deviations away from the mean value of soda dispensed by the machine.

Substituting the values, we get:

P(Z > 2.67) = 1 - P(Z ≤ 2.67) = 1 - 0.9968 = 0.0032

Therefore, the probability of the soda bottle overflowing is approximately 0.0032 or 0.32%.

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Answer:

r = 6

Step-by-step explanation:

The value of radius of the sphere rounded to the nearest whole number is,

⇒ r = 6 cm

We have to given that,

Volume of a sphere = 905 cm

Since, We know that,

Volume of sphere = 4/3 (πr³)

Where, 'r' is radius of sphere.

Now, Substitute the given value, we get;

⇒ 905 = 4/3 (πr³)

⇒ 905 × 3 = 4 × 3.14 × r³

⇒ 2,715 = 12.56 × r³

⇒ r³ = 216.16

⇒ r = ∛216.16

⇒ r = 6 cm

Thus, The value of radius of the sphere rounded to the nearest whole number is,

⇒ r = 6 cm

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Answer:

100

Step-by-step explanation:

"A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. " For the question "Are the conditions for inference met?" we say No, the 10% condition is not met. This is further explained below.

Generally, the confidence interval is simply defined as a predetermined interval across which some parameter has a certain chance of falling

In conclusion, with a resultant confidence interval of; confidence interval ( -8.373, -3.627) For the hypothesis test question "Are the inference requirements met?" Our company is certain that the 10% threshold has not been reached.

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Answer:

B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

If a radius of a circle and a tangent to a circle intersect at the point of tangency, then the radius and the tangent are perpendicular.

Answer: B.

The difference between group 1 and group 2 is the species of group 1 are vertebrates and species of group 2 are invertebrates.

Vertebrates are those animals that have a spinal cord.

Invertebrates are those who do not have a spinal cord or vertebrae.

The animals, of group 1 are alligator, fish, frog, bird, and zebra, all are vertebrates.

The animals of group 2 are jellyfish, octopus, tarantula, and earthworms.

Thus, the correct option is C, group 1 are vertebrates, and group 2 is invertebrates.

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Step-by-step explanation:

Your monthly payments with taxes and insurance included would be $2,903.71. This is calculated by taking the loan amount of $450,000 and multiplying it by the simple interest rate of 6.00%. The result is $27,000, which is then divided by the length of the loan, 30 years. This gives you

the principal and interest portion of your monthly payment, which is $2,033.33. To that, you add your yearly taxes of $2,000 and insurance of $1,500, divided by 12 months, to get an additional $416.67 and $125, respectively. Adding these two numbers together gives you your total monthly payment of $2,903.71.

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

c = 256

Step-by-step explanation:

Good Luck :)

Answer:

B

Step-by-step explanation:

Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope. Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .

Answer:

B

Step-by-step explanation:

B because the slope/ gradient is -1/2, which is the reciprocal of the equation's gradient that we have, which is 2.

Answer:  median would be less than the mean.