60 POINTS
Three points determine △ABC. The distance between A and B is 16.2 feet. The distance between B and C is 12.9 feet. What is the range for the distance between A and C? The range of the distance from A to C is greater than___feet and less than___feet.

Solution

For this case we have the following equation given:

4r + 1.1 = 6.6r -3.84

We can subtract 4r in both sides and we got:

1.1 = 2.6r -3.84

Then we can add 3.84 in both sides and we got:

2.6 r = 4.94

And then the value of r we got:

To round a number to a specific place, look at the number to the right of that place. If the number is less than 5, round down. If it is greater than or equal to 5, round up.

Question 1: 613 rounded to the nearest ten is 610.

The tens digit in 613 is 1. To the right of 1 is 3. Therefore, the approximation of 613 is:

THIS STATEMENT IS TRUE.

Question 2: 1,970 rounded to the nearest hundred is 1,900.

The hundreds digit in 1,970 is 9. To the right of 9 is 7. This means that we will round up by adding 1 to 9. Therefore, the approximation will be:

THIS STATEMENT IS FALSE.

Question 3: 54,318 rounded to the nearest thousand is 54,000.

The thousands digit is 4. To the right of 4 is 3. Therefore, the approximation is:

THIS STATEMENT IS TRUE.

Question 4: 476,022 rounded to the nearest ten thousand is 470,000.

The ten thousands digit is 7. To the right of 7 is 6. This means that we will round up. Therefore, the approximation is:

THIS STATEMENT IS FALSE.

The capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.

The capacitance of a body is defined as the charge holding ability of a body. Mathematically, capacitance is the ratio of charge and potential as follows -

C = dQ/dV

Given is the total capacitance measures .04 microfarad. If the circuit is supplied by an AC power source operating at 2 kHz.

From this we can write -

Capacitance [C] = 0.04 microfarad = 4 x 10⁻⁸ farad.

Frequency of AC supply [f] = 2 KHz = 2 x 10³ Hz

The capacitive reactance is given by -

X[C] = 1/2πfC

X[C] = (1/2 x 3.14 x 2 x 10³ x 4 x 10⁻⁸)

X[C] = 1/(50.24 x 10⁻⁵)

X[C] =  0.0199 x 10⁻⁵

X[C] = 1.99 x 10⁻⁷ ohms

Therefore, the capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.

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y = (1/2)x² + 2x + 2 is the equation of the parabola in the graph.

From the graph, the parabola has a vertex at point (-2,0) and passes through point (0,2).

The general equation for a parabola with vertex is (h,k) is;

y = a( x - h)² + k

First we determine 'a' by substituting the given coordinates into the equation.

y = a( x - h)² + k

2 = a( 0 - (-2))² + 0

Solve for a

2 = a(2)²

2 = a( 4 )

a = 2/4

a = 1/2

Now, plug the vertex (-2,0) and a (1/2) into the general equation.

y = a( x - h)² + k

y = (1/2)( x - (-2))² + 0

Simplify

y = (1/2)( x +2) )² + 0

y = (1/2)( x + 2 )²

Expand using FOIL method

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

y = (1/2)( x² + 2x + 2x + 4 )

y = (1/2)( x² + 4x+ 4 )

Apply distributive property

y = (1/2)(x²) + (1/2)4x + (1/2)(4 )

y = (1/2)x² + 2x + 2

Therefore, the equation of the graph is y = (1/2)x² + 2x + 2.

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Info given

For this problem we know that Jaylen drive for 2 hours at 60 mph

The velocity is v= 60 mi/hr and the time t= 2 hr

Solution

We can use the definition of distance given by:

And replacing we got:

And then the answer would be 120 mi

The segment AB is perbenticular to XY.

Here 90 degrees is an interior angle for Arc XB and Arc AY

Similarly, 90 degrees is an interior angle for Arc XA and Arc BY

Sort the list in increasing order:

The median is 13, therefore the upper quartile Q3 is given by:

Answer:

25

Answer:

(y+10)(y-4)

Step-by-step explanation:

-40y^2

/ \

10y -4y

Answer:

y>2x+1

Step-by-step explanation:

1. there is 'y=2x+1' graph is represented.

2. the shaded reqion is y>2x+1.

The correct linear inequality represented by the graph is y > 2x + 1. The correct option is C.

An inequality is a mathematical statement that compares two values or expressions and shows their relationship using the symbols < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

To see why, note that the line shown in the graph has a y-intercept of 1 and a slope of 2 (i.e., it passes through the points (0,1) and (1,3)).

If we plug in any point above this line, we get a y-coordinate that is greater than 2x + 1. For example, if we plug in the point (2,6), we get:

6 > 2(2) + 1

6 > 5

All points above the line satisfy the inequality y > 2x + 1.

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Using mathematical operations of addition, multiplication, division, and subtraction, the final score was:

K = 42 points

W = 51 points.

What are mathematical operations?

The basic mathematical operations for getting mathematical results from numbers, values, and variables include addition, multiplication, division, and subtraction.

In this situation, we apply these four basic mathematical operations.

Fizzy = 2 points

X = 5 points

Total scores = 93 points

The points in 8 Fizzy = 16 points (8 x 2)

The points in 5 X s = 25 points (5 x 5)

The equation showing the total scores of K = total scores + 16 - 25

= (93 + 16 - 25)/2

= 42 points

The equation showing the total scores of W = total scores - 16 + 25

= (93 - 16 + 25)/2

= 51 points

Hence, Final scores are K = 42 and W = 51.

Thus, applying mathematical operations, the final score shows that K scored 42 points while W scored 51 points, totaling 93 points for the two teams.

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Answer:

a= 2

b = 6

c = 2

d = 2

e = 7

f = 2

g = 1

h = 1

R = .3 (repeating)

Step-by-step explanation:

Answer:

I'm just here for points :3

Step-by-step explanation:

I don't know math

Answer:

Domain: [-6, 2]

Range: [-4, 0]

Function: Yes

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A relation is a function if each x value corresponds to only one y-value.

Answer

Walter saved $54

Explanation

Walter earns $144.

He spent 25% of it on books.

25% of $144 = 0.25 × 144 = $36

Amount left after spending 25% = $144 - $36 = $108

He then saves 50% of the remaining money

50% of $108 = 0.5 (108) = $54

Hope this Helps!!!

Answer:

first area is length by width

then our L is 4 and W is 5

=20

and volume is ,area 18 then 18 by 7=126

Answer:

1. How do we transform System A into System B

Answer is First choice with -3 filled in box

-3 x Equation [A1]  ⇒ Equation [B1]    (first choice; fill in -3)

2. How do we transform System B into System A

answer is the Last choice with 5 filled in the box

5 x Equation [B2] + Equation [B1] => Equation [C1]
In the last choice fill in 5 in the box

Step-by-step explanation:

-3 x [A1] => -3 (-9x - 5y = -2)

=> - 3(-9x) -3(-5y) = 3(-2)

=> 27x + 15y = 6   which is B1

5 x [B2]

=> 5(-4x - 3y) = 5(3)

=> -20x -15y = 15

5 x [B2] + B1

=>

-20x  -15y = 15
+
  27x + 15y  = 6

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

     7x + 0  = 21

or 7x = 21 which is C1

Step-by-step explanation:

system A to system B :

-3 × equation A1 -> equation B1

5 × equation B2 + equation B1 = equation C1

Therefore the original price is $299

the selling price is $228

The objective of this excercise is to clear the variable t. We need to pass every term with a t to one side of the inequality and every term without it to the other side:

then we have:

And finally we have that:

(1.57 x 10^5)-(9.5 x 10^4) The answer will be 62000 or Alternative form is 6.2 x 10^4

Given in the question:

(1.57 x 10^5)-(9.5 x 10^4)

To solve the above question:

Now, According to the question:

(1.57 x 10^5)-(9.5 x 10^4)

Factor Greatest Common Factors out :

10^4 (15.7 - 9.5)

Calculate the sum or difference

10^4 x 6.2

Express the number in scientific notation;

6.2 x 10^4

Calculate the power

6.2 x 10000

Calculate the product or quotient

62000

And, Alternative form is 6.2 x 10^4

Hence, (1.57 x 10^5)-(9.5 x 10^4) The answer will be 62000 or Alternative form is 6.2 x 10^4

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The length of AC must be 3 cm letter B

Second question

Both B and C are correct.

Answer:

take square root on both side

Step-by-step explanation:

Answer:

hope this makes sense

Step-by-step explanation:

1.05 x 10x 10x10x10=10000000000

10500000000

10000000000= 1.05 x 1.05 ×10000000000= 10500000000

10500000000 = 1.05 x10 x10

The rule we will use is

x1 = 2 and x2 = 6

y1 = -3 and y2 = 7

z1 = -4 and z2 = -4

Now we will find the answer in decimal using the calculator

The answer is 10.77032961

Round it to 3 decimal places, then

We can observe that f(x) is a parent function and g(x) is transformation of f(x).

Specifically, the applied transformations are:

• A vertical shift 4 units downside.

• A horizontal shift of 2 units left side.

The image below shows the functions

As you can observe, the blue function g(x) was shifted two units left and 4 units down.

Additionally, the functions intercept at (-0.631, 0.5).

If the code for HTML is JVON, it means that:

letter 8th (H) is letter 10th (J). Letter 20th (T) is letter 22th (V) and so on.

It means that the encoding is taking the letter 2 positions forward.

Hence C=E, O=Q, M=O, I=K, T=V.

The answer is EQOOKV.

Answer:

mean ≈ 10.7 pounds

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{12+9+9+12+16+6}{6}[/tex] = [tex]\frac{64}{6}[/tex] ≈ 10.7 pounds ( to the nearest tenth )

In the expression -3a + 5b - 15;

The constants are; -3, 5 and -15

The variables are; a and b.

A constant of an Algebraic Expression is simply a value that cannot be changed by inputting another value. For example in the algebraic expression; y³ = 4x³ - 7

The constants here will be 4 and -7 as they cannot be changed

Now, the variables in algebraic expressions are those that can be changed with different values and the equation will still be valid. For example, in the equation y³ = 4x³ - 7, the variables are y and x.

Thus, in our expression -3a + 5b - 15, the constants will be -3, 5 and -15 while the variables would be a and b.

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$8860

$8860 is the amount that is reduced after 5 years for the principal amount of $20,000 at a rate of interest 15%.

Here ,

Given , P = $20,000

           r = 15% = .15%

           n = 5

since amount is getting decreased ,

formula of compound interest becomes,

   A = [tex]p(1 - r)^{n}[/tex]

here P = principal amount  , r = rate of interest and n = number of years.

      = 20000(1 - .15)⁵

      = 20000 x 0.443

      = 8860

 A = $8860

So , After paying $20,000 the value decreases by 15% after 5 yrs the value will be $8860.

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We get the cost of the system and cost of the games  as $126 and $378 respectively.

Given, the price of the video game and several games are sold for $504.

The cost of the game is 3 times as much as the cost of the system.

we need to determine the cost of the system and the cost of the game = ?

Let x = the cost of the games.

Let y = the cost of the system.

therefore, x+y=504

and y = 3x

substitute the value of y.

⇒ x + y = 504

⇒ x + 3x = 504

combine like terms.

⇒ 4x = 504

Divide both sides by 4.

⇒ x = 504/4

⇒ x = 126

The cost of the system is $126.

Use y = 3x substituting 126 for x.

g = 3(126)

g = 378

The cost of the games is $378.

Hence we get the cost of the system and cost of the games as $126 and $378 respectively.

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We have the following:

The first thing is to transform the mixed numbers to decimal numbers, in the following way:

a.

to calculate the remaining time we must subtract the times where music is heard from 6 hours

Therefore, the answer is 2.5 hours or 5/2 hours battery remaining

b.

To calculate the fraction we must calculate that it represents 2.5 or 5/2 hours in the total, that is, 6 hours

The diagram is: