Determine an equation for each
parallel line described.


What is the equation of a line
parallel to y = -5x + 3 that
passes through (3, 1)?

Answers:

The house's value decreased by   $31,760  

The current value is    $365,240  

===========================================================

Work Shown:

8% of 397,000 = 0.08*397000 = 31,760 is the amount of lost value in the home. In other words, the value has dropped by this much.

The current value is 397,000-31,760 = 365,240

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

If you didn't care about how much value was lost, and only cared about the current value, then you can take this slight shortcut

100% - 8% = 92%

92% of 397,000 = 0.92*397000 = 365,240

If the house lost 8% of its value, then it keeps the remaining 92% to be currently valued at $365,240

This shortcut is useful if you wanted to chain together many percentage increases or decreases together.

The comparison statement which is true among the other given answer choices is; Choice A; -3/4<-2/3.

It follows from the task content that the comparison statement which is true among the answer choices given be determined.

On this note, one must recall that the arrangement of numbers on the number line is such that numbers are arranged in increasing order of value from left to right. For instance; -3 < -2 while; 2 < 3.

Hence, the answer choice which is correct is; Choice A; -3/4 < -2/3 as evident from the fact that; -0.75 < -0.667.

The concept above follows from the conversion of the numbers to decimals while using the number line arrangement of numbers.

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Answer:

all of them are prime.

Step-by-step explanation:

Answer:

9. 4(x -4)

10, 6 (3k + 7)

11. Prime

12. 4(5m -2n)

Step-by-step explanation:

The answer is C.....................

Answer:

0.1764    

0.2025  

Step-by-step explanation:

Let x be a perfect square such that √x lies between 0.4 and 0.5

Then y = √x

Then we have the inequality
0.4 < √x < 0.5

==> 0.4 < y < 0.5

So the number x must lie between 0.4² = 0.16 and 0.5² = 0.25

So the square of any number between 0.4 an 0.5 will be a perfect square fitting the requirement

Let's take y = 0.42. Then y² = 0.42² = 0.1764

y = 0.45 gives y² = 0.2025

So two perfect squares whose square root values lie between 0.4 and 0.5 are 0.1764 and 0.2025

In fact squaring any value between 0.4 and 0.5 will provide such a number

The value of Log0.5 16 is -4.

Let log0.5 16 = x ⇒ 0.5x = 16 ⇒ ( 5 10 ) x = 2 × 2 × 2 × 2. ⇒ ( 1 2 ) x = 2 4. ⇒ 1 2 x = 2 4. ⇒ 2- x = 24 ⇒ - x = 4 ⇒ x = - 4.

Thus, log0.516 = - 4.

Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity). Let's examine the Richter scale, which uses a logarithmic function to determine the size of earthquakes.

Scottish mathematician John Napier (1550–1617) created logarithms in the 17th century as a tool for computation. He derived the term from the Greek words for ratio (logos) and number (arithmos).

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Answer:

Step-by-step explanation:

its e223r252t23t22t.2t23t'23.t'2.t'2.t'2.t2't.23't.2't.32'.t2'.trfff i think

Answer:

6

Step-by-step explanation:

5+3−2

=8−2

=6

---------

The expressions matched with their corresponding simplified expressions are

(5⁻⁹)⁴         →   1/5³⁶

5⁹/5⁴         →   5⁵

5⁴ × 5⁹      →   5¹³

(5⁴)⁹          →   5³⁶

5⁻⁹/5⁴       →   5⁻¹³

From the question, we are to match each of the given expressions on the left with the terms of the right

First, we will simplify each of the expressions

Multiplying the exponents

5⁻⁹ˣ⁴

= 5⁻³⁶

= 1/5³⁶

Applying the division law of indices

5⁹/5⁴ = 5⁹⁻⁴

= 5⁵

Applying the multiplication law of exponents

5⁴ × 5⁹ = 5⁴⁺⁹

= 5¹³

Multiplying the exponents

5⁴ˣ⁹

= 5³⁶

Applying the division law of indices,

5⁻⁹⁻⁴

= 5⁻¹³

Hence, the expressions matched with their corresponding simplified expressions is

(5⁻⁹)⁴         →   1/5³⁶

5⁹/5⁴         →   5⁵

5⁴ × 5⁹      →   5¹³

(5⁴)⁹          →   5³⁶

5⁻⁹/5⁴       →   5⁻¹³

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Based on the calculations, the length of the arc of this circle is equal to: C. 61.3 ft.

In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle is given by:

Arc length = 2πr × θ/360

Substituting the given parameters into the formula, we have;

Arc length = 2 × 3.142 × 13 × 270/360

Arc length = 61.269 ≈ 61.3 feet.

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There are 5/9 groups in 1

6 divided by 9/5 is 3 1/3.

An improper fraction is a non integer where the numerator is greater than the denominator. An example is 9/5.

In order to determine the the number of groups of 9/5 that are in 1, divide 1 by 9/5

1 ÷ 9/5

1 × 5/9

9/9 × 5/9 = 5/9

6 ÷ 9/5

6 × 5/9 = 10 / 3 = 3 1/3

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if 60 men do a piece of work in 27 days, then 18 men can do the same work in 90 days.

The unitary approach is a strategy for problem-solving that involves the first determining the value of a single unit, then multiplying that value to determine the required value.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. In the aforementioned issue, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are solved using the concepts of ratio and proportion.

From the unitary method:

Number of days required to complete a work by 60 men = 27 days

Number of days required to complete a work by 1 man =  27*60

Number of days required to complete a work by 18 men = [tex]\frac{27*60}{18}[/tex]= 90days

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The value of

x = 1/9

y = 1/63

We have given two equations :

   1/x - 1/3y = -12   ... eq. (1)

- 4/5x + 7y = -1/5    ... eq. (2)

First we will multiply the 1st equation by 4/5,

We get, 4/5x - 4/15y = -48/5   ... eq. (3)

Now, we will add the equation 3 and equation 2

     4/5x - 4/15y = -48/5

   - 4/5x + 7y     = -1/5

____________________

          7y - 4/15y = -49/5

     (105y - 4)/15y = -49/5

              105y - 4 = (-49/5) × 15y

              105y - 4 = -49 × 3y = -147y

        105y + 147y = 4

                         y = 4/252

                        y = 1/63

We get the value of  y which is 1/63,

Now, we will solve the eq. 1 by putting  is equal to 1/63.

                      1/x - 1/3y = -12

        1/x - (1 × 63/3 × 1) = -12

                          1/x -21 = -12

                                1/x = 21 - 12 = 9

                                 x = 1/9

Hence, we get the value of x and y as 1/9 and 1/63 respectively.

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42 cans each 1.5 litres in capacity can be filled from a tank containing 63 litres of water.

Given, the capacity of each can is 1.5 litres and the tank holding 63 litres of water. We have to find the number of cans that can be filled from the tank containing 63 litres of water.

Let x number of cans can be filled from the tank containing 63 litres of water having each 1.5 litres in capacity, we have

x = 63/1.5

x = 630/15

x = 42

∴ The required answer is 42.

Hence, 42 cans each 1.5 litres in capacity can be filled from a tank containing 63 litres of water.

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Answer: 160 L

Step-by-step explanation:

There is 24 weeks in 6 months. 6x4= 24

24 weeks divided by 3 (the amount of weeks Danny’s family consumes 20L of milk). You end up with 8 weeks.

Then multiple 8 weeks time the 20 L.

The length of the base and height of the triangle as described in the task content are; 6cm and 3cm respectively.

It follows from the task content that the Area of the triangle is; 9 cm².

Since, Area = (1/2)b × h. where h = (b-3).

Therefore we have;

9 = (1/2)b × (b-3)

18 = b² -3b

b² -3b -18 = 0.

On this note, by solving quadratically; we have; b = 6 or b = -3.

The base of the triangle is therefore 6 as it cannot be a negative measure.

Consequently, the height, h = (b-3) = 6-3 = 3.

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-3/8 - 7/12 =

First we need to get the denominators same.

(-3 x 3/8 x3) - (7 x 2/12 x 2) =

-9/24 - 14/24 =

-9 - 14/24 =

-23/24

Answer = -23/24

Answer:

5/24

Step-by-step explanation:

y-x y is 7/12 so its positive x is -3/8 so its negative the answer is 5/24

The correct statement for y = x - 13 is C. It is the graph of y = x translated 13 units to the right to the parent function y = x.

A function can be thought of as output for the given or specified set of inputs.

Given a parent function y = x and it is a linear function and also reflexive.

The function y = x - 13 implies

x - 13 = 0 or x = 13.

∴ The graph of the function y = x - 13 will shift to the right along the x-axis by 13 units to the right. This is also known as translation.

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Answer:The correct statement for y = x - 13 is C. It is the graph of y = x translated 13 units to the right to the parent function y = x.

Step-by-step explanation:

What is a function?

A function can be thought of as output for the given or specified set of inputs.

Given a parent function y = x and it is a linear function and also reflexive.

The function y = x - 13 implies

x - 13 = 0 or x = 13.

∴ The graph of the function y = x - 13 will shift to the right along the x-axis by 13 units to the right. This is also known as translation.

Answer:

d

Step-by-step explanation:

Answer:

2 is the answer of this question

Answer:

1/27

Step-by-step explanation:

pb.chips.juice

pb.chips.milk

pb.chips.water

pb.cookies.juice

pb.cookies.milk

pb.cookies.water

pb.fruit.juice.

pb.fruit.milk

pb.fruit.watet

time that by three (as every section has three )

or

1/3 of cheese

1/3 of cookies times 1/3 x 1/3 x 1/3 = 1/27

1/3 of water

After modelling the mathematical statement and solving its equivalent mathematical relation, we get x = -36.

Equation modelling is the process of writing a given mathematical statement in the form of a numeric mathematical expression taking into considerations the operations, constants and other variables.

Given in the question is a number such that twice the difference of a number and 9 is equal to three times the sum of the number and 6.

Assume that the number is x. Now, we will model the equation and solve for x. According to the question, the following mathematical relation represents the statement-

2(x - 9) = 3(x + 6)

2x - 18 = 3x + 18

x = - 36

Therefore, the number is -36.

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8.75

-1 2/3 × (-5 1/4)

=35/4

= 8 3/4

= 8.75

Answer:

12

Step-by-step explanation:

If the perimeter is 56, then 2(W+L) = 56.

If the length is 4 more than the width, then we can write the length as

Width+4 = L or W+4=L

Now, we can plug this back into the equation of 2(W+L)= 56

2(W+(W+4)) = 56

2(2w+4) = 56

4w+8=56

Minus 8 on both sides of the equation

4w = 48

divide both sides by 4

w = 12

A wave is a disturbance that moves along a medium from one end to the other. If one watches an ocean wave moving along the medium (the ocean water), one can observe that the crest of the wave is moving from one location to another over a given interval of time. The crest is observed to cover distance. The speed of an object refers to how fast an object is moving and is usually expressed as the distance travelled per time of travel. In the case of a wave, the speed is the distance travelled by a given point on the wave (such as a crest) in a given interval of time. In equation form,

If the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2.0 m/s. On the other hand, if the crest of an ocean wave moves a distance of 25 meters in 10 seconds (the same amount of time), then the speed of this ocean wave is 2.5 m/s. The faster wave travels a greater distance in the same amount of time.

Reflection phenomena are commonly observed with sound waves. When you let out a holler within a canyon, you often hear the echo of the holler. The sound wave travels through the medium (air in this case), reflects off the canyon wall and returns to its origin (you). The result is that you hear the echo (the reflected sound wave) of your holler.

Noah stands 170 meters away from a steep canyon wall. He shouts and hears the echo of his voice one second later. What is the speed of the wave?

In this instance, the sound wave travels 340 meters in 1 second, so the speed of the wave is 340 m/s. Remember, when there is a reflection, the wave doubles its distance. In other words, the distance travelled by the sound wave in 1 second is equivalent to the 170 meters down to the canyon wall plus the 170 meters back from the canyon wall.

Speed of a Wave Lab - Sample Data

Trial    Tension(N)   Frequency(Hz)   Wavelength(m)    Speed(m/s)

1               2.0               4.0                     54.00                16.2

2               2.0               8.03                    2.00                16.1

3               2.0              12.30                   1.33                16.4

4               2.0              16.2                     1.00                 16.2

5               2.0               20.2                    0.800               16.2

6               5.0               12.8                    2.00                 25.6

7               5.0               19.3                    1.33                 25.7

8               5.0               25.5                    1.00                 25.5

In the first five trials, the tension of the rope was held constant and the frequency was systematically changed. The data in rows 1-5 of the table above demonstrate that a change in the frequency of a wave does not affect the speed of the wave. The speed remained a near constant value of approximately 16.2 m/s. The small variations in the values for the speed were the result of experimental error, rather than a demonstration of some physical law. The data convincingly show that wave frequency does not affect wave speed. An increase in wave frequency caused a decrease in wavelength while the wave speed remained constant.

The last three trials involved the same procedure with a different rope tension. Observe that the speed of the waves in rows 6-8 is distinctly different than the speed of the wave in rows 1-5. The obvious cause of this difference is the alteration of the tension of the rope. The speed of the waves was significantly higher at higher tensions. Waves travel through tighter ropes at higher speeds. So while the frequency did not affect the speed of the wave, the tension in the medium (the rope) did. In fact, the speed of a wave is not dependent upon (causally affected by) properties of the wave itself. Rather, the speed of the wave is dependent upon the properties of the medium such as the tension of the rope.

Variables Affecting Wave Speed

What variables affect the speed at which a wave travels through a medium? Does the frequency or wavelength of the wave affect its speed? Does the amplitude of the wave affect its speed? Or are other variables such as the mass density of the medium or the elasticity of the medium responsible for affecting the speed of the wave? These questions are often investigated in the form of a lab in a physics classroom.

Suppose a wave generator is used to produce several waves within a rope of a measurable tension. The wavelength, frequency and speed are determined. Then the frequency of vibration of the generator is changed to investigate the effect of frequency upon wave speed. Finally, the tension of the rope is altered to investigate the effect of tension upon wave speed. Sample data for the experiment are shown below.

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Answer:

57 hours

Step-by-step explanation:

19*3 = 57 1/3 pounds

Cook for 1 hour per 1/3 pound

57 hours

Answer:

Step-by-step explanation:

1 hour = 60 min

1/3 of 1 hour = 1/3 x 60 = 20 minutes

19 x 20 = 380 mins

380 minutes = 6 hours and 20 minutes

The value of the equation (6 x 10^-5)(7 x 10^11) in scientific notation is 4.2 x 10^7

The equation is given as

(6 x 10^-5)(7 x 10^11)

Rewrite properly as

(6 x 10^-5)(7 x 10^11) = (6 x 10^-5) x (7 x 10^11)

Remove the bracket

So, we have

(6 x 10^-5)(7 x 10^11) = 6 x 10^-5 x 7 x 10^11

Rewrite the product as

So, we have

(6 x 10^-5)(7 x 10^11) = 6  x 7 x 10^-5 x 10^11

Evaluate the product

So, we have

(6 x 10^-5)(7 x 10^11) = 42 x 10^6

Evaluate the product

So, we have

(6 x 10^-5)(7 x 10^11) = 4.2 x 10^7

Hence, the value of the the equation (6 x 10^-5)(7 x 10^11) in scientific notation is 4.2 x 10^7

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