Five less than a number (n) 28 is . Which equation shows this relationship?

Alternate interior angles are supplementary when transversal on parallel lines is perpendicular.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles.

Given,

To prove alternate interior angles are supplementary.

In the figure

EF is a transversal intersecting the two line AB and CD at 90°.

AB||CD

∠3 and ∠6, ∠4 and ∠5 are alternate interior angles.

∵ EF⊥ AB and EF⊥CD

∴ ∠3 = ∠6 = ∠4 = ∠5 = 90°

Thus sum of alternate interior angles,

∠3 + ∠6 = 90° + 90° = 180°

∠4 + ∠5 = 90° + 90° = 180°

For supplementary angles sum of angles should be 180° .

Hence, when transversal is perpendicular to the parallel lines, the alternate interior angles are supplementary.

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Therefore , the solution of the given problem of trigonometry comes out to be cot(θ) = 9/5.

The link between the squares spline and trigonometric The field is thought to have been created with in late 1700s, however it probably got its start in the third century BC through the union of the astronomical & mathematical sciences. Precise mathematical approaches can be used to solve a wide variety of geometric equations or to calculate things that they might be used in. The six fundamental trigonometric operations are what trigonometry is all about.

Here,

Given : tan(θ) = y/x

Given that the termination side in this instance traverses (-9, -5), the tangent is as follows:

tan(θ) = -5/-9 = 5/9

The cotangent is hence the tangent's inverse:

=> cot(θ) = 1/tan(θ) = 9/5.

Therefore , the solution of the given problem of trigonometry comes out to be cot(θ) = 9/5.

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Answer: The overall average of the weights is 24 pounds.

Step-by-step explanation:

To find the overall average of the weights, we need to calculate the weighted mean. A weighted mean is a type of average that takes into account the number of items or observations in each group.

In this case, we know that the average of the first 3 weights is 20 pounds and the average of the next 12 weights is 25 pounds.

To find the overall average, we will use the following formula:

( (number of items in first group * average of first group) + (number of items in second group * average of second group) ) / (number of items in first group + number of items in second group)

The formula can be applied as:

( (3 * 20) + (12 * 25) ) / (3 + 12) = (60 + 300) / 15 = 360 / 15 = 24

- C

The angular speed of the wheel, in radians per second is equal to 52.37 rad/sec.

In Mathematics, an angular speed can be defined as the rate of change of angular displacement of a physical object with respect to time. This ultimately implies that, angular speed is a measure of how fast and quickly a physical object revolves or rotates relative to another point or how its angular position changes with respect to time.

Mathematically, the angular speed of a physical object can be calculated by using this formula:

ω = 2πF or ω = Δθ/Δt

Where:

Substituting the given parameters into the angular speed formula, we have;

Angular speed of the wheel, ω = 2 × 3.142 × 500

Angular speed of the wheel, ω = 3142 rad/min

In rad/sec, we would divide by 60;

Angular speed of the wheel, ω = 3142/60

Angular speed of the wheel, ω = 52.37 rad/sec.

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0.000004% is the probability that four aces appear together when a pack.

What in mathematics is probability?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.  

                                    Statistics describes the examination of events subject to probability.

The first ace is a  4 aces and 52 cards =  4/52 chance

there are three aces left and 51 cards in total.

The second ace is 3/51,

since,

The third ace = 2/50 (1/25)

the fourth is 1/49.

          = 4/52 * 3/51 * 1/25 * 1/49  

          =  1/270725

          =  0.000004%.

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The solution will remain the system since the same two inequalities still make up the system.

Answer:

Step-by-step explanation:

The answer is [−3,3]. The average rate of change of f(x)=x^2+10 over an interval [a,b] is given by (f(b)-f(a))/(b-a). Since f(x)=x^2+10 is a polynomial of degree two, it is always increasing, and so its average rate of change is always positive. Thus, the average rate of change of f(x) over any interval [a,b] where a<b is positive, so the answer is [−3,3].

There are two types of relative extremas for a function, described as follows:

On the graph, these relative extremas of a function are the turning points of the function.

The function for this problem is defined as follows:

f(x) = 2x³ - 39x² + 180x + 4.

For the function defined in this problem, the graph is given by the image presented at the end of the answer, with the points representing the relative extremas marked.

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Answer:

x-intercept is (-16,0) and y-intercept is (0,2)

Step-by-step explanation:

To find the x-intercept of the equation 1/2x = -4y - 8, we need to set y to 0 and solve for x.

1/2x = -4(0) - 8

1/2x = -8

x = -8*2

x = -16

So the x-intercept of the equation is (-16,0)

To find the y-intercept of the equation 1/2x = -4y - 8, we need to set x to 0 and solve for y.

1/2(0) = -4y - 8

-8 = -4y

y = 8/4

y = 2

So the y-intercept of the equation is (0,2)

Answer:

the x-intercept of the equation is (-16, 0).
the y-intercept of the equation is (0, 2).

Step-by-step explanation:

To find the x-intercept and y-intercept of the equation 1/2x = -4y - 8, we can set one of the variables to zero and solve for the other variable.

For the x-intercept, we set y = 0 and solve for x:

1/2x = -4(0) - 8

1/2x = -8

x = -8 * 2

x = -16

So the x-intercept of the equation is (-16, 0).

For the y-intercept, we set x = 0 and solve for y:

1/2(0) = -4y - 8

-4y = -8

y = 2

So the y-intercept of the equation is (0, 2).

Answer:

0.3, 0.323, 0.333

Step-by-step explanation:

Answer:

0.3,0.323,0.333

Hope it helps!

By increasing the mass of an object , the Elastic Potential Energy (EPE) is increased

Elastic potential energy ( EPE) is energy stored as a result of applying a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process. The deformation could involve compressing, stretching or twisting the object.

The effect of doubling mass on potential energy is similar to doubling the height. By doubling the mass, the potential energy is also doubled, which becomes the reason to begin the work.

This means that adding more mass to an object will increase the elastic potential energy.

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Answer:To write a proportion as a percentage, you first convert it to a decimal and then multiply it by 100.

The proportion of Year 12 pupils in the music club is 32/85.

To convert to a decimal, divide 32 by 85:

32/85 = 0.376

To convert this decimal to a percentage, multiply by 100:

0.376 * 100 = 37.6

So, the proportion of Year 12 pupils in the music club as a percentage is 37.6%.

To convert a proportion to a percentage, you can multiply it by 100.

The proportion of Year 12 pupils in the music club can be represented as 32/85.

Multiplying by 100, we get:

(32/85) * 100 = 37.65

So, 37.65% of the pupils in the school are Year 12 pupils in the music club.

Rounded to 1 decimal place, the answer is 37.7%.

On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Answer:

The y-intercept is 450, and it represents how much money he has in his account when he starts out with 0 essays proofread

Step-by-step explanation:

Looking at the standard slope-intercept equation, we see:

y = mx + b

Where b is the y-intercept. In our equation, our b is replaced by 450:

y = 15x + 450

So, the y-intercept is 450, and it represents how much money he has in his account when he starts out with 0 essays proofread.

Hope this helped!

The total number of children Mr. and Mrs. Jones are having is 13 children.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

In set theory, the set containing every element in a collection is the union of all its sets. It is one of the fundamental operations that allows sets to be joined together and connected to one another. A union of zero sets is referred to as a nullary union, because it is by definition equivalent to the empty set.

The symbol "∩" can be used to represent the intersection of sets. According to the definition given above, the intersection of two sets A and B is the collection of all the items that are shared by both sets.

8 refused to go to the family cottage = set A

7 refused a resort spot on the ocean. = Set B

9 refused a camping trip. = Set C

3 will go neither to the family cottage nor the resort = A∩B

4 will go neither to the resort nor on a camping trip = B∩C

6 will go neither to the family cottage nor on a camping trip = A∩C

2 will not go to the family cottage, the resort spot on the ocean or the camping trip = A∩B∩C

The total number of children = A + C - (A∩B + B∩C + A∩C) + A∩B∩C

= 8+7+9 -(3+4+6) + 2 = 13

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A chord is a combination of three or more tones (notes) played together.

To determine the notes in a chord, we need to calculate the intervals between the notes. An interval is the distance between two notes. Intervals are measured in half steps (or semitones). A half step corresponds to the interval between two adjacent keys of a piano.

In a major chord, the formula for determining the intervals is 1-3-5. This means the root note (1st note) is a major third (4 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is C, the 3rd note is E and the 5th note is G. The intervals in this chord are C to E (4 half steps) and C to G (7 half steps). Therefore, the chord is a C major chord.

In a minor chord, the formula for determining the intervals is 1-b3-5. This means the root note is a minor third (3 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is F, the 3rd note is Ab and the 5th note is C. The intervals in this chord are F to Ab (3 half steps) and F to C (7 half steps). Therefore, the chord is a F minor chord.

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Answer: in a triangle if all its angle measure less than 90 degree is called an acute triangle.

Step-by-step explanation: In equilateral triangle all of its 3 angle measure equally and are less than 90 degree thus making it an acute triangle.

Step-by-step explanation:

that depends on the type of triangle and what other pieces of information you have about the triangle.

I think you might aim for the geometric mean theorem.

it is the relation between the height on the hypotenuse in a right triangle and the two line segments (p, q) it creates on the hypotenuse (= p + q).

height = sqrt(p×q)

The savings plan balance after 18 months will be 15,028.63 dollars.

So the answer is a) $15,028.63

What is the annuity problem?

An annuity is a series of equal payments made at regular intervals.

APR (Annual Percentage Rate) = 6%

Monthly payments = $800

Number of months = 18

We can use the formula for the future value of an annuity (FV) to find the savings plan balance after 18 months. The formula for the future value of an ordinary annuity is:

FV = PMT x (((1 + r)^n - 1) / r)

Where:

FV = future value of the annuity

PMT = the regular payment made

r = the interest rate per period (in this case, the monthly interest rate)

n = the number of payments or periods

The interest rate is given as an annual percentage rate (APR), so we need to divide it by the number of periods per year to find the interest rate per period. In this case, 6% / 12 months/year = 0.5% per month.

FV = 800 x (((1 + 0.005)^18 - 1) / 0.005)

FV = $15,028.63

Hence, the savings plan balance after 18 months will be 15,028.63 dollars.

So the answer is a) $15,028.63

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Answer:

A

Step-by-step explanation:

Answer:

x = 2, -6

Step-by-step explanation:

3x + 6 = ±12
=> If 3x + 6 = 12
3x = 6
x = 2
=> If 3x + 6 = -12
3x = - 18
x = -6

Answer: 2

Step-by-step explanation: To find the value of x, we need to use the order of inverse operations. Inverse operation(s) means to do the opposite of the operations used. So, instead of adding, we subtract, instead of multiplying, we'll divide. So, the opposite of 6 + 12 is 12 - 6. So, that's 6. Now, instead of multiplying 6 by 3, we need to divide 6 by 3. That's 2. Therefore x = 2. Now, to check our answer, we plug 2 in for 6. So, | 3(2) + 6 | is the positive value of 3(2) + 6, which is 6 + 6.

12 = 12

So, therefore the absolute value of |3x+6|=12 is 2. I hope this helped!

The percent error of Alex's measurement is 5.714%.

Percent error is a measure of how accurate a measurement is compared to the true value. It is calculated by taking the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplying by 100%.

In this case, the measured value is 3.7 cm and the true value is 3.5 cm.

To calculate the percent error, we can use the following formula:

Percent error = |(measured value - true value) / true value| x 100%

Plugging in the given values, we get:

Percent error = |(3.7 - 3.5) / 3.5| x 100%

= |0.2 / 3.5| x 100%

= 0.05714 x 100%

= 5.714%

This means that Alex's measurement is off by 5.714% from the true value, indicating that the measurement has a low accuracy.

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Answer:

n=3

Step-by-step explanation:

324/2^ n. = 30

324/30 = 2^n

Log 324/30 = Log 2^n = n x Log2

n = Log 324/30 ÷ Log 2

n = 3.43...

as n musg be an integer, thus

take n=3. or 4 will makd the midel height cliase to 30m

Daryl's weekly allowance, given the amount he ended with and the amount spent on clothes, is  $ 30

To find the weekly allowance, first find the amount that Daryl had after he had spend half his allowance on clothes. This amount can be found by the formula:

= Amount Daryl ended with - Amount gotten from cleaning oven

= 25 - 10

= $ 15

The amount of $ 15 is the amount out of Daryl's weekly allowance that he had after he had spent on clothes. The $15 is therefore half of the weekly allowance which means that the weekly allowance is:

= 15 x 2

= $ 30

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Answer:

Step-by-step explanation:

add the 2 equations:

3x+18+4x+15

simplify:

7x+33

we know that all angles on a straight line is 180 degrees.

7x+33=180

solve that equation:

7x=147

x=21

from here substitute x=21 into both equations.

3x+18

3x=63

63+18=81

left angle is 81 degrees

4x+15

4x=84

84+15=99

right angle is 99 degrees

we can check this by adding them both: 99+81=180

its right as all angles on a straight line add to 180, which these do.

hope this helped

The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.

The absolute value (or modulus) |x| of a real number x is the non-negative value of x without regard to its sign.

It is represented as |a|, which defines the magnitude of any integer ‘a’.

it defines removing any negative sign in front of a number and thinking of all numbers as positive.

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.

When x itself is negative (x<0), then its absolute value is necessarily positive

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So on solving the provided question we cans say that probability that we got red balls is - P(R)  = 1/3

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

given,

red balls = 4

blue balls = 5

green balls = 3

Probability that we got red balls is -

P(R) = 4/12 = 1/3

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A line would be drawn on the graph for x 324 and tinted also on left side of the line until x = 0.

Social justice theories are based on the concept of unequal, namely the notion that individuals are not similar, particularly in terms of position, rights, and showed that the type. It is susceptible to misinterpretation in public conversation, nevertheless, as it typically has distinct meanings to different people. However, some characteristics apply to everyone.

54 total pages

Football card pages = 18

Pages remaining = 54 - 18 Equals 36

As a result, the remaining 36 pages may each hold 9 cards.

Therefore, the remaining spaces are 36 * 9 = 324.

Inequality: 324 spots available

A line would be drawn on the graph for x 324 and tinted also on left side of the line until x = 0.

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Answer:

1200

Step-by-step explanation:

step 1: Locate and underline the hundreds place (2) then look at the digit to the right (1): 1212

Step 2: The digit to the right (1) is 4 or below. So, we replace it with a 0 (zero) to get 1200 as the answer.

In short: 1212 rounded to the nearest hundred is 1200.

Answer:

Step-by-step explanation:

a) The probability of obtaining 2 heads when a coin is thrown twice is (2/5) * (2/5) = 4/25.

b) To find the probability of obtaining at least one head, we can find the probability of obtaining no heads (0 heads) and subtract that from 1. The probability of obtaining 0 heads is (3/5) * (3/5) = 9/25. The probability of obtaining at least one head is 1 - (9/25) = 16/25.

Answer:

259 miles

Step-by-step explanation:

To find this, we need to multiply his 8 gallons by [tex]\frac{7}{8}[/tex] since he only uses 7 gallons of gas. In turn, we also need to multiply 296 by [tex]\frac{7}{8}[/tex]. We get:

[tex]296 * \frac{7}{8} = 37 * 7 = 259[/tex]

So, Ian drove 259 miles last weekend.

Hope this helped!