14. The population of a town increased from 2,692 in 2008 to 5,712 in 2010. Find the absolute and percent increase. Give the percent increase to at least one decimal place.Absolute increase: peoplePercent increase: %

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Corresponding angle postulate

Corresponding angles:

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position.

Here we need to prove ∠3 ≅ ∠7

From the properties of the two parallel line cut by the transversal line, these angle is corresponding angles.

i.e., ∠3 ≅ ∠7 (by the properties of the corresponding angles)

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Answer:

the 1st, 2nd, and 4th one because those ordered pairs, the y axis is the same . sooo thats what makes it a non function .

Answer: \({2} \frac{3}{4} = \frac{6}{8}\)  here is your two correct answers for your answer

if you want to be friends we can just thank me and i'll give you some points and thank you back. o just add me as a friend please because i riley riley riley riley riley need some friends right know and can you rate e with 5 stars please so peace i'm out

Answer:

The answer is 11

Step-by-step explanation:

55÷5= 11

The important variables are the two types of test questions which can be represented as :

Variables are used to represent unknown values which could be worked out in a mathematical expression or problem.

The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer

Therefore, the correct option is C. m for multiple choice, s for short answer

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Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

----------------------------------------------------------------------------------------------------------

    -y = -7x

+

    y = -4x + 3

----------------------------------------------------------------------------------------------------------

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

To Express one quantity as a percentage of another.

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Answer:

3b

Step-by-step explanation:

Answer:

Option C. 4.0313×10²⁷ molecules.

Step-by-step explanation:

We'll begin by calculating the volume of oxygen in the room. This can be obtained by calculating the volume of the room since the gas will eventually fill the room.

Width (W) = 5 m

Length (L) = 10 m

Height (H) = 3 m

Volume (V) =?

V = L × W × H

V = 10 × 5 × 3

V = 150 m³

Thus, the volume of oxygen is 150 m³

Next, we shall convert 150 m³ to L. This can be obtained as follow:

1 m³ = 1000 L

Therefore,

150 m³ = 150 m³ × 1000 L / 1 m³

150 m³ = 150000 L

Finally, we shall determine the number of molecules of oxygen in the room. This can be obtained as follow:

22.4 L = 6.02×10²³ molecules

Therefore,

150000 L = 150000 × 6.02×10²³ / 22.4

150000 L = 4.0313×10²⁷ molecules

Thus, the number of molecules of oxygen in the room is 4.0313×10²⁷ molecules

Answer:

9000

Step-by-step explanation:

If for every amount of $d , $0.20d is tipped, then for amount of $56, $11.6 will be tipped to the waiter

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

If for every $d , $0.20d is tipped, then this means that the total amount spent is $56 and the amount Anthony's family tip the waiter is calculated as:

0.2 × 56

= $11.6

Therefore the waiter was tipped $11.6

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Answer:

A dinner bill of d dollars calls for a tip of 0.20d dollars. You want to find how much the family tipped the waiter for a bill of d=$56.

Evaluate the expression 0.20d for d=56.

0.20d

=

0.20(56)

=

11.2

The family tipped the waiter $11.20.

The solution of the expression is (a² - 2ab + b²).

Given that,

The expression is,

(a⁴ + 4b⁴) ÷ (a² + 2ab + 2b²)

Now, we can write the first term as,

(a⁴ + 4b⁴) = (a² - 2ab + b²) (a² + 2ab + b²)

Hence the expression is written as,

(a⁴ + 4b⁴) ÷ (a² + 2ab + 2b²)

[(a² - 2ab + b²) (a² + 2ab + b²)] ÷ (a² + 2ab + 2b²)

(a² - 2ab + b²) (a² + 2ab + b²) / (a² + 2ab + 2b²)

(a² - 2ab + b²)

Therefore, The solution is (a² - 2ab + b²).

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Answer:

1. x  =  − 7  +  2 y

2. x  =  1  −  2 y /3

Step-by-step explanation:

Answer:   [1]    x + 2y = 7

  [2]    3x - 2y = -3

Answer:

30

Step-by-step explanation:

discounting by 20% is the same as marking to 80% of the original cost. 80% = .8

set up equation and solve

.8x=24

x=30

1 upon 2

make me as brienliesr

Answer:

Original Salary: \(5,957.14\)

Increase in 3%: \(6,135.85\)

Step-by-step explanation:

So when something increases by x%, the new value is (100+x)% the original value. So 6255, is 105% the original value. This means to find the original value, we have to find the number that has 6255 as 105% of it's value. Whenever you try to find x% of a number, you multiply it by the decimal value of the percentage, which is found by dividing by 100. So to find x%, you do: \(o*\frac{x}{100}\) where o = original value, x=percent. In this case the percent is 105%, which when divided by 100 is 1.05. So this gives us the equation: \(o*1.05=6255 \implies o = \frac{6255}{1.05} = 5,957.14\). This is his original salary. You need to do this process, do not make the mistake of subtracting 5% from 6255. This is because 5% of 6255 does not equal the 5% of the original value. 5% of 6255 should be greater than 5% of the original value, since the new value is an increase of 5%. So since we have his original salary, we can calculate the salary increase had it been 3%. to do this we multiply by 1.03 (103% divided by 100). This gives us the equation: \(5,957.14*1.03=6,135.85\)

Step-by-step explanation:

6 cm, 8 cm, and 10 cm (B) form a triangle.

The Triangle Inequality Theorem states that the sum of the lesser two sides must be greater than the third.

Answer:

The height of the squirrel is 31 feet.

Step-by-step explanation:

You need to know your Right Triangle Trigonometry to do this problem.

Rt Triangle trig is all about ratios. Angles and ratios.

In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.

tan Angle = opposite/adjacent

tan 48° = x/28

multiply both sides by 28

28•tan48° = x



You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"



Enter 28 × tan48° =

It will return 31.0971504152

Your question asks you to round to the nearest whole.

x = 31

The squirrel's height in the tree is 31ft.

Answer:

9.53 AU

Step-by-step explanation:

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Square abοve wοuld have the same area as square F is b)square C.

The regiοn that an οbject's shape defines as its area. The area οf a figure οr any οther twο-dimensiοnal geοmetric shape in a plane is hοw much space it οccupies.

Here the square A is cοntains 4- 1 unit squares.

Then length οf the square = 2 units,

If Square A is dilated by scale factοr 1/2 then,

Length οf square  F = \(2\times \frac{1}{2}\) = 1unit.

Area οf square F = 1*1 = 1 square unit.

Then in the given squares , square C οnly has 1 unit side length.

Hence the cοrrect οptiοn is b) Square C.

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Answer: 1 1/5

Step-by-step explanation:

9 - 7 4/5 = 1 1/5

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Answer:

Step-by-step explanation:

Given that,

To find the standard form of the equation of the parabola with a focus at (0, 9) and a directrix y = -9.

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation

Focus of the prabola = (h , k + F ) =  (0, 9)

Since the directrix, y =  -9

F = -9

k + F = 9

k = 0

Vertex of the parabola = (h,  k  )

                                    =  (0, 0)

Standard equation of the parabola

( y - k ) = 4a (x - h)²

( y - 0 ) = 4a (x - 0)²

y = 4 * 9 x²

y = 36 x²

Thus, the required expression for the parabola with focus at (0, -9) and a directrix y = 9 is y = 36x².