Module 2: Lesson 1
Spark Your Learning: Which is the Better Deal/
1. Which best describes the difference between a rebate and a discount, and how is the tax
rate used to find the total cost? (Fill in the oval)

O For a rebate the tax, the tax is calculated on the full price, and the customer receives the
rebate later. For a discount, the tax is calculated on the reduced price after the discount is
applied.

O For a rebate the tax, the tax is calculated on the reduced price after the discount is
applied. For a discount, the tax is calculated on the full price, and the customer receives the
rebate later.

Based on the explanation below, the solution for c from the equation in the question is 2 - d.

Before answering the question, the correct complete question is provided as follows:

Solve for c from the equation 7(c+d)=14.

We can now solve for c from the equation in the question as follows:

7(c+d)=14

c + d = 14 / 7

c + d = 2

c = 2 - d

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The average rate of change of the function f(x)  = 8x² - 6 is given as  8h + 16x

It quantifies how much the function changed per unit on average throughout that time span. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

f(x) = 8x^2 - 6

Avge rate : [ f(x+h) - f(x)]/(x +h - x)

f(x+h) = 8(x+h)^2 - 6

f(x) = 8x^2 - 6

f(x+h) - f(x) = 8x^2 + 8h^2 + 16xh + 6 - 8x^2 -6 = 8h^2 + 16xh

Avg rate = ( 8h^2 + 16xh)/h

= 8h + 16x

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The average rate of change of the function over the interval is 8(b + 1)

The given parameters are

Function: f(x) = 8x^2 - 6

Interval: [1, b]

Calculate f(1) and f(b) using the function definition

So, we have

f(1) = 8(1)^2 - 6 = 2

f(b) = 8(b)^2 - 6 = 8b^2 - 6

The average rate of change of the function over the interval is then calculated as

Rate = [f(b) - f(1)]/[b - 1]

This gives

Rate = [8b^2 - 6 - 2]/[b - 1]

Evaluate

Rate = [8b^2 - 8]/[b - 1]

Factorize the numerator

Rate = [8(b + 1)(b - 1)]/[b - 1]

Divide through by b - 1

Rate = 8(b + 1)

Hence, the average rate of change of the function over the interval is 8(b + 1)

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Triangle OCE is congruent to Triangle OVE.

triangle LAP is congruent to triangle YAP.

9.

Triangle OCE is congruent to Triangle OVE

side CE=CV

angle COE= angle VOE

angle C = angle V

By AAS congruency Triangle OCE is congruent to Triangle OVE.

10.

angle LAP =angle YAP

AP common side

LA=PY

By SAS congruency so triangle LAP is congruent to triangle YAP.

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Answer:

Question 7: 20° and 160°, Question 8: 10° and 80°

Step-by-step explanation:

Complementary angles add to 90° and supplementary angles add to 180°.

Answer:

Step-by-step explanation:

If you're asking to determine if the slope is positive or negative by plotting these points and drawing a line to connect them and deriving the slope from that,

No, the slope is positive.

Actors that can be manipulated by humans or artificial intelligence (AI) all descend from the Pawn class. A player or AI entity's physical representation in the world is called a "Pawn." This means that the player's or AI entity's physical interactions with the outside environment, such as collisions and other physical interactions, are likewise controlled by the Pawn. This can be perplexing in some situations because some game types might not have an obvious player mesh or avatar. Regardless, the Pawn continues to reflect a player or other entity's actual position, rotation, etc. within the game. A unique class of Pawn that can move around is called a Character.

The default relationship between Controllers and Pawns is one to one, which means that each Controller can only have one Pawn under their control at any given moment. Additionally, a Controller does not necessarily hold a Pawn that spawns while a game is being played.

When someone is manipulating you, they are likely mentally forcing you to do something you don't truly want to do, the expert claims. You may feel compelled to do it, afraid to do it, or guilty if you don't.

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Answer:

4 7/8

Step-by-step explanation:

First lets make 6 1/2 an improper fraction
Multiply the denominator by the whole number and add the result to the numerator to get the improper fraction

6 1/2

13/2

Multiply the numerators by eachother, same with the denominators

3* 13
---------
4*2

39/8

Finally, simplify by dividing 39 by 8

4 7/8

Number of groups of 3/4 are in 6 1/2 is, 26/3

We have to given that,

To find number of groups of 3/4 are in 6 1/2.

Let us assume that,

Number of groups of 3/4 are in 6 1/2 = x

Hence, We get;

x = (6 1/2) ÷ (3/4)

x = (13/2) × (4/3)

x = (13 × 4) / (2 × 3)

x = (13 × 2) / 3

x = 26/3

Therefore, There are 26/3 groups of 3/4 are in 6 1/2.

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Answer:

Step-by-step explanation:

32 meals;

to solve, divide 24 by 0.75 (3/4) or you can do 24/1 times 4/3

Answer: 3 = b (maybe, usually unsure)

Step-by-step explanation: bing

y = mx + b, this is the formula.

b = y-intercept
m = slope

1. We know that (-1,6) is our pair.

2. The formula when written with the info is y = -3x + b

3. We know that -1 is the x and the y is 6, so subbing the x and y in the formula, it is 6 = -3(-1) + b.

4. When multiplied, it becomes 6 = 3 + b

5. Then we combine like terms, by subtracting 3 into 6, making 3 = b

6. So, it is 3 = b

Answer:

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

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry

[tex]\large\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

[tex]\textsf{Vertex}=(h, k)[/tex]

[tex]\textsf{Focus}=(h,k+p)[/tex]

[tex]\textsf{Directrix}:y=(k-p)[/tex]

[tex]\textsf{Axis of symmetry}:x=h[/tex]

If p > 0, the parabola opens upwards.

If p < 0, the parabola opens downwards.

From inspection of the given graph:

Therefore:

Substitute the found values of h, k and p into the formula:

[tex]\implies (x-(-3))^2=4(-1)(y-3)[/tex]

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

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Answer:

18

Step-by-step explanation:

24 x 20 = 480 (amount of seats on main floor)

786 - 480 = 306 (amount of seats needed on balcony)

306 ÷ 17 = 18 (amount of seats on each row of balcony)

Step-by-step explanation:

The main floor has 24*20 = 480 seats.

So you need 786- 480 = 306 more seats

There are 17 rows in the balcony and let's say there are x seats in each row. Since you need 323 seats, this means

19x = 323

x = 306/17

x = 18

So there must be 18 seats in each row up in the balcony.

Answer: x=1/2, x=-4/3 ==> A and F

Step-by-step explanation:

6x² +5x-4 = 0

6x²-3x+8x-4 = 0

3x(2x-1)+4(2x-1) = 0

(3x+4)(2x-1)=0

3x+4=0

3x=-4

x=-4/3

2x-1=0

2x=1

x=1/2

x=1/2, x=-4/3 ==> A and F

Tom drives 243 miles in 3 hours.

What is speed?

So, to find how many miles Tom can drive in 3 hours:

Tom drives 81/2 miles every 1/30 hour.

81/2 miles = 40.5 miles

1/30 hours = 30 minutes

So, in 30 minutes Tom drives 40.5 miles.

Then, in 1 hour Tom will drive 40.5 + 40.5 = 81 miles.

Miles Tom will drive in 3 hours = 81 × 3 = 243 miles.

Therefore, Tom drives 243 miles in 3 hours.

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Answer:

-21 If that is a option

Step-by-step explanation:

Answer: I hope this helps.

Step-by-step explanation:

Answer: 5,2 2,3 2,2

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

41+78+119

Easy just remember this formula

Step-by-step explanation:

We know that,

[tex] ➟\sf \: fv \: of \: annuity \: = p( \frac{(1 + r) {}^{n} - 1}{r} )[/tex]

where,

FV of annuity = $35,450

P = monthly payment,

r = rate of interest = 5.5% annually = [tex] \frac{5.5}{12}%[/tex]

n = number period = 20 years = 240 months

Putting all the values,

[tex] \sf35450 = p( \frac{(1 + \frac{0.055}{12} ) {}^{240} - 1}{ \frac{0.055}{12} } )[/tex]

[tex] \sf \: p = \frac{35450}{( \frac{(1 + \frac{0.055}{12} ) {}^{240} - 1}{ \frac{0.055}{12} } )}[/tex]

[tex] \sf \: p \: = \: \$81.36[/tex]

Therefore, they should deposit $81.38 monthly.

Answer:

54º, 108º and 18º respectively

Step-by-step explanation:

The concentration of a contaminant that enters a lake is a function of time and initially rises rather quickly. However, it is due to the lake's inherent mixing and self-cleansing activity.

Concentration in chemistry is calculated by dividing a constituent's abundance by the total volume of a mixture. The terms "concentration" can refer to any type of chemical mixture, but are most frequently used to describe the solutes and solvents in solutions. There are four different types of concentrations that can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. There are different types of molar (quantity) concentrations, including normal concentration and osmotic concentration.

Concentration is frequently expressed qualitatively in everyday, non-technical language using words like "dilute" for solutions with a low concentration and "concentrated" for solutions with a high concentration.

If y increases quickly with x, the slope of the graph will be greater (i.e. will be steeper). The slope of the graph will be lower if y increases slowly with x. (i.e. will be less steeper). Straight lines result from constant slope in graphs. 1. Less investment results in a significant boost in production at first. Consequently, graph

1) Begins with a steeper slope. The rate of expansion slows down at the end, therefore the graph

2) will be more gradual. So, D is the proper graph. 2. The slope of the graph increases while train speed stays constant. As a result, graph will be

3) Straight line So, C is the proper graph.  The focus rises quickly at first. Small time therefore yields large

4) an improvement in concentration Therefore, graph will be steeper in beginning. At end, the concentration becomes constant, so graph will be almost horizontal at end.

5)Thus correct graph is B. In beginning, the population increases slowly. Thus large time gives less increase in population. Therefore, graph will be less steep in beginning. At end, the population increases rapidly, so graph will be more and more steeper at end. Thus correct graph is A.

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The linear equation that shows how many packages of breadsticks Dirk bought as (1/4)b.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Dirk who brought [b] breadsticks to a potluck. The breadsticks are packaged in bags of 4.

Assume that he bought [x] bags of breadsticks. Then, we can write the linear equation that shows how many packages of breadsticks Dirk bought as -

x = (1/4)b

Therefore, the linear equation that shows how many packages of breadsticks Dirk bought as (1/4)b.

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Her door should be 3 cm on scale .

It is given that dimension of the kitchen table is 60m by 2 m .

Let the width of the door be " x".

We given Mal's Kitchen door is 1.2 m wide .

The ratio is given by

   [tex]x:1.2[/tex]     ......(1)

She decides on a scale of 1 to 40 which means 1 : 40    .....(2)

Equating equation (1) and (2) , we get

     [tex]x:1.2=1:40[/tex]

Representing in fraction , we get

        [tex]\frac{x}{1.2} =\frac{1}{40} \\\\x=\frac{1.2}{40} \\\\x=0.03m\\x=3cm[/tex]

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The complete question is mention below :

Mai wants to make a scale drawing of her kitchen. her kitchen is a rectangle with length 6m and width 2m. She decides on a scale of 1 to 40. Mal's Kitchen door is 1.2 m wide. How wide should the door be on the scale drawing?How wide should the door be on the scale drawing?

Answer:

-3 is in between - 2 and - 4, - 9 is in between - 8 and - 10

follow and likes and plot the point (-3,-9)

Answer:

your dot will be next to -10

Step-by-step explanation:

The inequality that represents the heights of every other person who ever lived is, 9 ≥ x

We have to find the inequality that represents the heights of every other person who ever lived, where the tallest person who ever lived was approximately 9 feet tall, according to the question.

Here x denotes the height of every person who ever lived,

So, the inequality is, 9 ≥ x

Every person ever lived, must be equal to or lesser than 9 feet.

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A parallelogram has an area of 20 units².

Solution:

Explanation:

Using the distance formula, calculate the length of the base b:

[tex]\begin{aligned}&\mathrm{d}=\sqrt{\left(\mathrm{y}_2-\mathrm{y}_1\right)^2+\left(\mathrm{x}_2-\mathrm{x}_1\right)^2} \\&\mathrm{~b}=\sqrt{(3-0)^2+(5-0)^2}=\sqrt{9+25}=\sqrt{34}\end{aligned}[/tex]

Using the perpendicular distance from a line to a point formula, calculate the height h:

Determine the baseline:

In Ax + By + C = 0 form, the bottom line is:

[tex]\begin{aligned}&\frac{3}{5} \mathrm{x}-\mathrm{y}=0 ; 5\left(\frac{3}{5} \mathrm{x}-\mathrm{y}=0\right)=3 \mathrm{x}-5 \mathrm{y}=0\\&\mathrm{A}=3 ; \mathrm{B}=-5 ; \mathrm{C}=\mathrm{O}\\&h=\frac{|3 \cdot 0+(-5) \cdot 4+0|}{\sqrt{3^2+(-5)}}=\frac{|-20|}{\sqrt{9+25}}\\&\mathrm{h}=\frac{20}{\sqrt{34}}\\&\mathrm{A}=\mathrm{bh}=\sqrt{34} \cdot \frac{20}{\sqrt{34}}=20 \text { units }^2\end{aligned}[/tex]

Therefore, a parallelogram has an area of 20 units².

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The complete question is given below:

In this problem, you will explain using simple plane geometry how to compute the area of a parallelogram in terms of cartesian coordinates.

The length of a bacterial cell is about 5.36 x104 m, and the length of an amoeba cell is about 6.2 x 104 m.

Thus length of a bacterial cell is 0.864 times of length of an amoeba cell.

Given that the length of a bacterial cell is about 5.36 x 10⁻⁴ m, and the length of an amoeba cell is about 6.2 x 10⁻⁴ m.

Ratio of the size of the cell is

B/A = 5.36 x 10⁻⁴/6.2 x 10⁻⁴

B/A = 5.36/6.2

      =  0.864

Thus length of a bacterial cell is 0.864 times of length of an amoeba cell.

micro organism are prokaryotes, lacking nicely-defined nuclei and membrane-sure organelles, and with chromosomes composed of a unmarried closed DNA circle. they come in many sizes and styles, from minute spheres, cylinders and spiral threads, to flagellated rods, and filamentous chains.

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Answer: $455

Step-by-step explanation:

I would think you would divide 260 by 4 and that would get you 65 and then multiply 65*7 and that would be $455

Based on the depth of the local river in January and the depth of the river in July, the difference between depths in January and July is 22 feet.

The difference in the depth between July and January can be found as:

= Absolute value of depth in July - Absolute value of depth in January

Solving for the difference in depth gives:

= 27 - 5

= 22 feet

In conclusion, the difference in depths between January and July is 22 feet.

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Answer: False

Step-by-step explanation:

4 x 10^6 = 4000,000

400,000 is 4 x 10^5

Answer:

False

Step-by-step explanation:

10^6=1,000,000   ==> 10^6 has 6 zeros after the '1', making 10^6=1 million.

4*10^6=4,000,000, not 400,000

Answer:

6

Step-by-step explanation:

1-3=-2

-2+8=6