Find an equation for the perpendicular bisector of the line segment whose endpoints
are (-2, 4) and (-8,-6).

The given list of numbers 3,9,15,21..form an Arithmetic Progression(AP).

A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A fixed number is added to the term preceding it in the sequence to obtain each term, with the exception of the initial term.

Given list of numbers is 3,9,15,21 ...

To determine whether the series is an Arithmetic Progression, find the difference of the terms which should be constant in an AP.

9 - 3 = 6

15 - 9 = 6

21 - 15 = 6

Therefore, as each term of the given series differs from its preceding term by 6 it is an AP.

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we get that the volume of each object is

so the reamining space is:

The table shows that each output(y) is obtained by multiplying each input(x) value by 2.

Thus, an equation for the given multiplicative relationship is:

The cost of 3 pounds =$2.40

For the cost of 1 pound, divide the cost of three pounds noodles with 3.

The student is not correct ,

The cost of unit pound is $0.8

The missing factor in the given expression x³ = x²(?) is; x

The laws of exponents are;

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we are given the expression;

x³ = x²(?)

The question mark indicates a missing term. Thus, we will use division property of equality to divide both sides by x² to get;

x³/x² = x

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Simple interest typically favors consumers who pay their bills or loans on time or early each month because it is frequently calculated on a daily basis. The loan's simple interest rate is 4.5%.

Simple interest typically favors consumers who pay their bills or loans on time or early each month because it is frequently calculated on a daily basis.

In the aforementioned student loan example, if you paid a $300 payment on May 1st, $238.36 would be applied to the principle. On April 20, if you made the same payment, $258.91 would be applied to the principal. Your main balance will decrease more quickly and the loan will be paid off faster than anticipated if you can make an early payment every month.

On the other hand, if you pay the loan back late, you pay more in interest than if you pay it on time. If your payment is due on May 1 and you make it on May 16 (using the same car loan example), you will be charged interest for 45 days at a cost of $92.46. Consequently, only $207.54 of your $300 payment is applied to the principal. If you frequently make late payments over the course of a loan, your final payment will be more than anticipated because the principal did not decrease at the anticipated rate.

Principal amount,

P=$5000

Future value,

A=$5900

Time,

t=4years

Let us determine the loan's simple interest rate:

A=P(1+rt)

5900=5000(1+r*4)

5900=5000(1+4r)

5900=5000*1+5000*4r

5900=5000+20000r

5900−5000=20000r

900=20000r

20000r=900

r=900/20000

r=9/200

r=0.045

r=0.045/100%

r=4.5%

Therefore, the loan's simple interest rate is 4.5%.

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Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of observing no positive reading if all the subjects are telling the truth is 9/10.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Positive reading when telling the truth = 10%

No positive reading when telling the truth = 90%

The probability of observing no positive reading if all the subjects are telling the truth

= 90%

= 90/100

= 9/10

Thus,

The probability of observing no positive reading if all the subject are telling the truth is 9/10.

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Answer:

8

Step-by-step explanation:

Given: # of girls = 5+2x boys

GIRLS = 21

(21-5)/2

= 16/2

=8

The value of the function is -9

Functions are simply defined as mathematical expressions, rules, laws o theorem that compares or explains the relationship between two variables.

These variables are known as;

Based on the information given, we have that;

To determine the value of the function,  (f +g)(-3), we have to add the functions for both f(x) and g(x)

We have;

(f +g)(x) = 2x - 1 + (-4x -2)

expand the bracket

(f +g)(x) = 2x - 1 - 4x - 2

Now, substitute the value of x as -3, we have;

(f +g)(-3) = 2(-3) - 1 - 4(-3) - 2

expand the bracket

(f +g)(-3) = -6 -1 + 12 - 2

Add or subtract the values

(f +g)(-3) = -9

Hence, the value is -9

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The required fraction is 1/14.

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

For illustration: There are five kids in all.

Five in three are female. So, three-fifths of the population are girls.

Of the 5, two are boys. So, two-fifths of the population are boys.

As in this question 1 out of the 2 boxes are shaded.

Thus the required fraction is 1/2

Thus the required number is [tex]\frac{1}{7}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{14}[/tex].

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The number of bags of mulch that is needed to cover the playground is 3,605 bags.

The first step is to determine the volume of the surface of the city playground. The volume is the product of the length, width and height of the playground.

Volume = length x width x height

4 x 40.5 x 66.75 = 10,813.50 inches³

The second step is to determine the number of bags of mulch that is needed to cover the surface of the playground.

Number of bags of mulch = volume of the playground / volume one bag can cover

10,813.50 inches³ / 3 = 3,604.5 bags ≈ 3,605 bags

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Answer:

=24.19×10^14

Step-by-step explanation:

we will just all add to get the distance

=4.1×10²×5.9×10¹²

=4.1×5.9×10²×10¹²

=24.19×10^14

ANSWER:

2034.72 cubic units

STEP-BY-STEP EXPLANATION:

The volume of the cylinder is given by the following equation;

The radius is equal to 6 and the height is equal to 18, let's substitute them and calculate the volume of the shown cylinder, like this:

The volume of cylinder is equal to 2034.72 cubic units

The equation is:

So to know that, we can find the intercept in the y axis by replacing x=0 so:

So if you see the functions the only one that intercept the y axis in -4, then the solution is option (D)

Answer:

Here is the answer: sin(3π/2) = -1

So 3π/2 is the correct choice.

Answer:

8 sec^2 x + 4 tan^2 x − 12 = 0     →     sec^2x = tan^2x + 1

8 [ tan^2x + 1] + 4tan^2x - 12  = 0

8tan^2x + 8 + 4tan^2x - 12  = 0

12tan^2x - 4   = 0     divide through by 4

3tan^2x - 1  = 0

3tan^2x  =  1  

tan^2x  = 1/3      take the square root of both sides

tanx = ±1 / √

We're only given one angle: the angle that measures 35°.

This angle and ∠1 are supplementary angles, meaning they add up to 180°. To find ∠1, subtract 35 from 180:

180 - 35 = 145°

The angle and ∠2 are corresponding angles, meaning they are on the same sides of the diagonal line and the transversal.

Corresponding angles are always equal.

Therefore, ∠2 = 35°.

∠1 = 145°

∠2 = 35°

The slope according to the given points of line is (B) m = 1/2.

So, points are: (-9,6) and (-3,9)

Now, substitute the values in the formula as follows:

Therefore, the slope according to the given points of the line is (B) m = 1/2.

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The correct question is given below:
What is the slope of the line through (-9,6) and (-3,9)? Choose 1 answer:

A. 2

B. 1/2

C. -1/2

D. -2

Answer:

|AC| = 132 cm  (nearest centimetre)

Step-by-step explanation:

Pythagoras Theorem

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The formula is:

[tex]\large\boxed{c^2=a^2+b^2}[/tex]

where:

From inspection of the given right triangle:

Substitute the given values into the formula and solve for AC:

[tex]\begin{aligned}c^2 & = a^2+b^2 &\\\\\implies AC^2&=AB^2+BC^2\\ AC^2&=45^2+124^2\\ AC^2&=2025+15376 \\ AC^2&=17401\\\sqrt{ AC^2}&=\sqrt{ 17401}\\ AC&=131.91285\\AC&=132\; \sf cm \; (nearest\;centimetre)\end{aligned}[/tex]

Therefore, |AC| is 132 cm to the nearest centimetre.

SOLUTION

From the question, it means that

The least possible value of a and will be a ngative number, gotten by multiplying a negative value by a positive value. So this should be

the smallest value of a, that is the -6 multiplied by the biggest value of b = 4

Hence the answer is -24

The equation in standard form is mathematically given as

[tex](x-3)^2 +(y-3)^2 = 4^2[/tex]

This is further explained below.

Generally, A mathematical notion, such as an equation, number, or expression, maybe written down in a form called a standard form, which is a form that adheres to a predetermined set of guidelines.

The standard form is used if a condensed representation of a very big or very tiny number is required.

For instance, the number 4.5 billion years is represented by the numeral 4,500,000,000.

In conclusion,

[tex]x^2 + y^ 2- 6x-6y+2=0[/tex]

Therefore

[tex](x^2 - 6x) +(y^2-6y) +2 =0\\\\(x^2 - 2(3)x +3^2) -3^2 + (y^2 - 2(3)y +3^2) -3^2+2 = 0\\\\(x-3)^2 +(y-3)^2 = 4^2[/tex]

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The expression of the confidence interval (78.5, 154.7) in the form of x¯ ± ME is; CI = 116.6 ± 38.1

We are given the confidence interval as;

CI = (78.5, 154.7)

Now, we want to express the given confidence interval in the error bound form which is; x¯ ± ME

where;

x¯  is sample mean

ME is margin of error

Now, the boundaries of the interval as two points is the midpoint between them which would be (78.5 + 154.7)/2 = 116.6.

This is right in the middle of 78.5 and 154.7.

This value of 116.6 is the sample mean represented by x¯, since x¯ is in the middle of the interval. This means that 78.5 and 154.7 are the same distance (the margin of error, ME) away from 116.6. .

116.6 - 78.5 = 38.1 and 154.7 - 116.6 = 38.1

Thus, the expression is;

CI = 116.6 ± 38.1

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After evaluating the limit we have came to find that the limit of      [tex]\lim_{x\rightarrow \Pi }cos(x)[/tex] as x approaches π is –1

As an input or as an index approaches a specific value in mathematics, a limit is the value that the function, sequence, or index approaches. The definitions of continuity, derivatives, and integrals all require limits, which are fundamental to calculus and mathematical analysis.

In addition to having a connection to the category theory concepts of limit and direct limit, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit

⇒ [tex]\lim_{x\rightarrow \Pi }cos(x)[/tex]

Evalúe π as x

= cos (π)

= cos 180°

= cos(180° – 0°)

= – cos 0°

= – (1)

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Answer:

4 1/3

Step-by-step explanation:

I believe it is 4 1/3 because all the other ones like 9=3 and 12=4 are divided by 3 so if you divide 14 by 3 you get 4 1/3 as your answer.

The equation of the line which is perpendicular and goes through the point (8,2) is slope-intercept form of y = x - 6.

What is slope-intercept form?

The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6

The equation of the required line in slope-intercept form is expressed as:

y-y0 = m(x-x0) where:

m is the slope

(x0, y0) is the point on the lin

Given the equation of the line as y = -x

Get the slope of the line

mx = -x

m = -1

Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))

y-y0 = m(x-x0)

y - 2 = 1(x-8)

y - 2 = x - 8

y = x - 8 + 2

y = x - 6

Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.

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There are 3024, 9072 and 27216 baskets are produced in 4th,  5th and 6th days respectively.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A manufacturing unit produced 112, 336 and 1008 Easter baskets on days one, two and three.

Now,

On first day, there are 112 baskets.

And, On second day, there are 336 baskets.

So, Clearly 112 x 3 = 336

That's mean every day the number of produce baskets are three times the previous day.

So, On fourth day;

Number of Easter basket produce = 1008 x 3 = 3,024

On fifth day;

Number of Easter basket produce = 3,024 x 3 = 9,072

On sixth day;

Number of Easter basket produce = 9,072 x 3 = 27,216

Thus, There are 3024, 9072 and 27216 Easter baskets are produced in 4th,  5th and 6th days respectively.

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we have the following:

therefore, the answer is the first option

The linear equation relating the given condition is y + 10x - 62 = 0 .

Each solution in the scenario with two variables can be understood as the Cartesian coordinate system of such a point on the Euclidean plane.

Let the linear relation between the two variables  be given by y=mx + c

Now we put the values to get the constants.

58 = 2m + c

52 = 5m + c

solving we get :

52 - 5m = 58 - 2m

or, -6 = 3m

or, m = -2

Now we put those values in the equations

52 = 5m + c

or, 52 = -10 + c

or, c = 62

The equation relating the sunglasses is y + 10x - 62 = 0 .

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Answer: it's A if ur on that question six flvs question counting that was so hardddddddddddddddddddddddddddd

Step-by-step explanation:

The answer to the expression 120% (_____) 1 is:
120% > 1. See the explanation related to the percentage problem below.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently indicated by the percent symbol, "%."

To overcome the above problem, we must transform the two numbers into the same form.

Because adding zeroes to the ending of a decimal does not modify the value, we know that 1 = 1.00.

To convert a decimal to a percentage, multiply it by 100 and add a percent sign.

1.00 * 100 = 100%

Hence, 1 = 100%

Because 120% is greater than 100%, it is right, therefore, to state that:

120% > 1

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