LESSON 8 SESSION 2
Name
Practice Showing That the
Slope of a Line Is Constant
> Study the Example showing that the slope of a
line is constant. Then solve problems 1-5.
Example
Cece draws a graph representing her
family's car trip to the beach. She wants
to show her father that their gas
mileage in miles per gallon was the
same for the entire trip. Cece chose
three points on the line and drew
vertical line segments from the points to
the x-axis. How can she use these
segments to prove that the gas mileage
was constant for the trip?
Distance (mi)
250
150
100
30
0
(S. 155)
(1,31)
8 10
What was the gas mileage for the trip in the Example?
6
Gasoline Used (gal)
The vertical line segments create three
similar right triangles. Because the
triangles are similar, the quotient of the length of the vertical side to the length
of the horizontal side is the same for each triangle. These quotients are slopes
between (0, 0) and the points Cece chose. Because Cece could have chosen any
points on the line to make the similar triangles, the slope is constant for the
whole line. So, the gas mileage is constant for the whole trip
For the graph in the Example, find the slope between the origin and each of the
points Cece chose.
Vocabul
slope
for any two
a line, the
shange
change
of

Answer:

The two numbers are 17 and 44.

Step-by-step explanation:

x --> smaller number

y --> larger number

x + y = 61

y = 3x - 7

x + 3x - 7 = 61

4x - 7 = 61

4x = 68

x = 17

y = 3(17) - 7

y = 51 - 7

y = 44

Answer: y= (7a+9b)/8

Step-by-step explanation:

I can only provide the answer now, If you want more explanations reply this

Step-by-step explanation:

(2y - a)/3 = (a + 3b)/4

first we get rid of the fractions by multiplying everything first by 3 and then also by 4 ;

(2y - a) = 3(a + 3b)/4

4(2y - a) = 3(a + 3b)/4

8y - 4a = 3a + 9b

8y = 7a + 9b

y = (7a + 9b)/8

The set of ordered pairs that represent 90 degrees counter clockwise rotation about he origin is

3) A' (-6, 1) B' (-6, 6) C' (-2, 1)

Rotation is a from of transformation that involves circular movement about an axis.

There two types of rotation

The transformation rule for 90 degrees clockwise rotation is as follows

(x, y) for a scale factor of r → (-y, x)

From the graph the coordinates are read and following the given transformation rule we have

preimage   image

A (1, 6)   →   A' (-6, 1)

B (6, 6)  →  B' (-6, 6)  

C (1, 2)  →   C' (-2, 1)

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Answer:

$2940

Step-by-step explanation:

30 percent *4200 =

(30:100)*4200 =

(30*4200):100 =

126000:100 = $1260

4200-1260=$2940

Answer:

Step-by-step explanation:

Correct Answer: C.

First we can see that the slope is negative, meaning the graph is decreasing.

Then we go to the point (-1,0) and go down 2 and 3 right. if that point is on the line, then we know it's correct.

Answer: 13g

Step-by-step explanation: because each gram is 1000 milligrams

Using the theories of quantitative​ variables, we got that Graphical display is the first thing that should be​ done when we are analyzing two quantitative​ variables.

Comparing the Two Quantitative Variables As we did when considering only one variable, we begin with the graphical display. A scatterplot is the most useful display technique for comparing the two quantitative variables. We plot on the y-axis the variable we consider for the response variable and on the x-axis we place the explanatory or the predictor variable.

Hence, When analyzing two quantitative​ variables,  the first thing that should be​ done is Graphical display.

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The rule for given translation is (x,y)→(x + 3, y - 4).

In mathematics, the phrases translation, rotation, and reflection are all used to describe the change of forms. This refers to a form moving beyond a mirror line or a fixed point. While being translated, rotated, or reflected, the shape doesn't change. The constant rotation of a shape around a fixed point or across the mirror line is known as translation. Rotation defines the way a form moves about a central axis. Shapes can be rotated by a specific number of degrees either clockwise or counterclockwise.

The rule for translation of given figure will be,

We need to move x for 3 units to left and y for 4 units downwards to get the translation, so the rule is:

(x,y)→(x + 3, y - 4).

Therefore, the rule for given translation is (x,y)→(x + 3, y - 4).

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Answer:

slope = - [tex]\frac{7}{13}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, - 10 ) and (x₂, y₂ ) = (- 4, - 3 )

m = [tex]\frac{-3-(- 10)}{-4-9}[/tex] = [tex]\frac{-3+10}{-13}[/tex] = [tex]\frac{7}{-13}[/tex] = - [tex]\frac{7}{13}[/tex]

The shopper bought a watermelon costing $4.45.

Let x represent the cost of watermelon

y = cost of napkin + cost of paper plates

The tax rate on non-food items is 5%, hence:

5% of y = 0.19

0.05y = 0.19

y = $3.8

The total for the three items he bought was $8.25 before tax,

x + y = 8.25

x + 3.80 = 8.25

x = 4.45

The shopper bought a watermelon costing $4.45.

A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.

Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.

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The sequence is geometric and the common ratio is 1/7

An arithmetic sequence is a sequence of numbers in which each differs from the preceding one by a constant value e.g 2, 4, 6, etc. That is: 6-4 = 4-2 = 2

A geometric sequence is a sequence of numbers with a constant ratio between each number and the one before e.g.  9, 27, 81, etc. That is: 81/27 = 27/9 = 3

Given: 147, 21, 3

This sequence does not have a common difference. Thus, it is not arithmetic

This sequence has a common ratio. Thus, it is geometric

common ratio = 21/147 = 1/7 or 3/21 = 1/7

Therefore, the sequence is geometric and has a common  ratio of 1/7

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If the dealer gives Bernie the listed trade- in price for his car,  he will pay $391.97  monthly.

Given that,

Bernie has decided to purchase a new car of $ 18,575.

The sales tax is 7.40%

Now,

18,575 x 7.40% = 1,374.55

Now, summing up the result of sales tax and purchase price, we get,

18,575 + 1,374.55 = 19,949.55

Bernie will give registration fees of $795

and, a documentation fees: $110

Now , we will sum up all the above information, i.e.,  

= 19,949.55 + 795 + 110

= 20,854.55

Now, divide the result of documentation fees and registration fees by 5

                         20,854.55 ÷ 5 = 4,170.91

Dividing the above result by 12,                      

                          4,170.91 ÷ 12 = 347.58

Now, the finance the rest of the cost for five years at an interest rate 12.77%.

                       347.58  x 12.77% = 44.39

And,

                       347.58 + 44.39 = 391.97

Therefore, If the dealer gives Bernie the listed trade - in price for his car,  he will pay $391.97  monthly.

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Answer:

There are 54 Republicans, and 58 Democrats

Step-by-step explanation:

See the attached image

Answer:

- 3/4

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95km/h is the average speed for the whole journey

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement

Given,

Simon drives 75 km at an average speed of 120 km/h

9 km at 70 km/h without stopping.

We need to find the average speed.

Average speed = Total distance/Total time

The total distance is 75km+9km

84 km

The average speed is sum of speeds by two

120+70=190/2=95km/h

Hence, 95km/h is the average speed for the whole journey

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[tex]y = \cfrac{2}{5}x + 0\implies y=\cfrac{2}{5}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Using the Work time problem solving technic, Betty and Bullwinkle to mow the entire lawn in 30 minutes if they are working together.

As we know that if A is complete the work of z in x days and B is complete the same work (z) in y days then both of can do complete work together then Equation of both A and B are completing work (z) together in

( 1/x + 1/y = 1/z ) days

Since Betty can mow a lawn is 120 minutes, then

Betty's mowing rate is 1/120th of a lanw per minute.

Since Bullwinkle can mow a lawn is 40 minutes, then Bullwinkle mowing rate is 1/40th of a lawn per minute.

Suppose working together they can a lawn in x minutes.

both together they can mow a lawn is x minutes, then their combined mowing rate is 1/x th of a lawn per minute.

To get the equation,

the sum of their mowing rates must equal their combined mowing rate,

1/40 + 1/120 = 1/x

Solve that by multiplying through by LCD of 40 and 120 is 120 then 4x = 120 => x = 30

Hence, when both are working together they complete the work together in 30 minutes .

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Answer:

Step-by-step explanation:

Area of circle equation:

Circumference of circle equation:

Use circumference equation to find the radius:

Find the area:

Answer:

Solution

=5(X+10)+X

=5×x+5×10+x

=5x+50+X

=6x+50

Step-by-step explanation:

Your answer is 6x+50.

The values of m<4 and m<6 are 160° and 20° respectively

To solve this problem, we need some angle geometry knowledge:

Given that: m<6 = 1/8 m<4

Since m<6 = 1/8 m<4. Thus, m<4 = 8.m<6

m<6+ m<4 =  m<6 + 8.m<6 = 9.m<6    (Algebra)

m<6+ 8.m<__ = 180° will be:

m<6+ 8.m<6 = 180°      

Note: m<6 + m<5 = 180° (angles on a straight line) and m<5 = m<6 (alternate angles)

m<6+ 8.m<6 = 180°

9.m<6 = 180°

m<6 = 180/9 = 20°

m<4 = 8 x m<6

m<4 = 8 x 20° = 160°

Therefore, the values of m<4 = 160° and m<6 = 20°

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Answer:

27 miles, 40.5 miles, and 47.25 miles

Step-by-step explanation:

9 miles in 2/3 hours. To get to a whole number, we can multiply by the reciprocal of 2/3, which is 3/2. 2/3*3/2=1. Now lets multiply 9 by 3/2. 9*3/2=13.5

We now have a unit rate which is 13.5 miles each hour.

Now lets solve for 2 hours.

13.5*2= 27 miles

Now lets solve for 3 hours.

13.5*3=40.5 miles

Now lets solve for 3.5

13.5*3.5= 47.25 miles

Yes, the graphs of a power function and its inverse are symmetric about the line y=x.

What is an inverse function?

A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

What is a power function?

Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.

Here,

The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.

Hence, the graphs of a power function and its inverse are symmetric about the line y=x.

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The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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Answer:

$193.60

Step-by-step explanation:

160x1.21=$193.60

160+21%=$193.60

The smallest possible perimeter of the triangle is, 72.4 inches.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

As given the longest side of an acute triangle measure 30 inches.

The two remaining sides' combined length must be longer than the opposite side.

The sum of the two remaining sides should be greater than 30 inches if the side is 30.

Assume the other two sides add up to 31 inches.

So, The perimeter of a triangle is equal to the sum of its three sides, which comes to 30 + 31 = 64 inches.

Consequently, the circumference must be greater than 64 inches.

Hence, based on the possibilities, the triangle's smallest conceivable perimeter is 72.4 inches.

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If  the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature

A linear graph can be either increasing, decreasing or constant.

Here the price of the car is being discounted $200 every week, so as the number of weeks increase, the price of the car decreases

So, the graph for this situation will be linearly decreasing.

The slope of this kind of graph is negative/

Therefore, If  the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature

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Answer:

$712.50

Step-by-step explanation:

.95(750) = 712.5  If they give 5% to the seller, they get to keep 95%

Answer:

Step-by-step explanation:

Answer: I Can't Read it

Step-by-step explanation: Its to far

Answer: I don't know  

Step-by-step explanation: