Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a
brief evaluation of your work.
Activity
In the first Lesson Activity, you derived an equation to model a car wash. The equation is y = 5x - 75. In this activity, you will graph this equation.
Question 1
Is it possible to graph the line that represents this equation by using two points found in the previous Lesson Activity, (15, 0) and (0, -75)? Explain
your answer.

The value of the sets are A ∩ ∅  = ∅ and A' ∪ U  = {f, g, h, p, q, r}.

Given: U = {f, g, h, p, q, r} and A = {g, p, r}

We are to find: (a)A ∩ ∅  and (b) A' ∪ U

(a) A ∩ ∅  

The symbol ∩ means intersection. This tells us what sets have in common. Also, the symbol ∅ means an empty set or null. That is a set that does not have any element

The intersection of a set with the empty set is the null set. Thus:

A ∩ ∅  = ∅

(b) A' ∪ U

The set U is called the universal set

A' means elements not in set A but in set U

The symbol ∪ means union, A' ∪ U will give a list of elements in A' and U combined without repetition. Thus:

A' ∪ U = {f, h, q} ∪  {f, g, h, p, q, r}  = {f, g, h, p, q, r}

Therefore, A ∩ ∅  = ∅ and A' ∪ U  = {f, g, h, p, q, r}. They should be entered into the boxes accordingly

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Answer: over budget by $64



Step-by-step explanation:

$99 coat

$75 Shoes

$240 tv

Total=414

total-budget=

Budget =$350

414-350

= 64

[tex] = ( \sin(180 + 45) )^{2} - ( \cos(180 + 90) )^{2} + ( \frac{ \sqrt{3} }{1} )^{2} \\ = ( - \sin(45) )^{2} - ( - \cos(90) )^{2} + 3 \\ = ( - \frac{1}{ \sqrt{2} } ) ^{2} - ( \frac{0}{1})^{2} + 3 \\ = \frac{1}{2} - 0 + 3 \\ = \frac{1}{2} + 3 \\ = \frac{7}{2} [/tex]

ATTACHED IS THE SOLUTION

Answer: 78 ÷ 3 = 26

Step-by-step explanation:

     We are given that there are 3 groups shown. This means we will be dividing by 3.

     We are given that each group has 2 ten rods (20) and 6 ones cubes (6). This means the answer is 26.

     Lastly, 26 * 3 = 78, meaning we are dividing 78 by 3.

This gives us:

     78 ÷ 3 = 26

By division, the following results are obtained

[tex]2 \div 7756\\[/tex] = 0.0025

[tex]77.56 \div 0.2 = 387.8[/tex]

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

The quotients of the two divisions are shown below-

[tex]2 \div 7756\\[/tex] = 0.0025

[tex]77.56 \div 0.2\\7756 \div 20 \\387.8[/tex]

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According to the SSS Postulate, two triangles are congruent if three of one triangle's sides are congruent with three of another triangle's sides.

A postulate is an assertion that is not backed by any evidence. Axiom is another name for a postulate. For instance, you would believe Pam if she said that all of her siblings were at least five feet one tall since you are aware of her height and that of all of her siblings, who are all taller than her.

When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

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Answer:

B) 7,720,360 sq. km

Step-by-step explanation:

8,508,238 - 787,878 = 7,720,360 sq. km

Hope this helped :)

Using the simplification, the value of u is 13/15.

In the given question we have to find the value of u.

The given expression is -1/2u+3/5=1/6

Simplifying the given expression to find the value of u.

-1/2u+3/5=1/6

Subtract 3/5 on both side, we get

-1/2u=1/6-3/5

Now equal the denominator to simplify

-1/2u=1/6 *30-3/5 *30

-1/2 *30u=5-3*6

-15u=5-18

-15u= -13

Divide by -15 on both side, we get

u = 13/15

Hence, the value of u is 13/15.

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The highlighted point is (9, -7) . A shape or item is said to be rotated when it is spun around a central point (center) without being moved in any other direction. Size and shape are unaffected by rotation. Basic Transformations in Geometry.

A shape or item is said to be rotated when it is spun around a central point (center) without being moved in any other direction. Size and shape are unaffected by rotation. Basic Transformations in Geometry.

If the picture is the point (-7, -9)

Detailed explanation:

When the point (x, y) rotates 90 degrees counterclockwise with respect to the origin, its image is (-y, x)

When the point (x, y) rotates 180 degrees counterclockwise around the origin, its image is (-x, -y)

The picture of the point (x, y) if it were rotated 270 degrees counterclockwise with respect to the origin is (y, -x)

The highlighted point is (9, -7)

∴ x = 9 and y = -7

The provided point is turned 270 degrees counterclockwise with respect to the origin.

Utilizing the third rule listed above

The illustration of the point is (y, -x)

That is to say, alter the x-sign coordinate's before switching them.

∵ x = 9 and y = -7

The illustration if the point is (-7,-9).

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Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

Answer:

3.3 miles with a bar notation on decimal 3

Step-by-step explanation:

convert 2/3 to decimal (2 divided by 3)

multiply 5 by decimal of 2/3

add bar notation on repeating decimal

The required value of the land after 20 years is $53,163.95.

Given that,
A piece of land was purchased for $65,000. The value of the land has slowly been decreasing by 1% annually, the land worth in 20 years is to be determined.

Here,
As the function decreases by 1% annually,
The expression for the decrease,
y = 65000(1-0.01)ˣ
y = 65000(0.99)ˣ
Put x = 20
y = 65000(0.99)²⁰
y = $53,163

Thus, the required value of the land after 20 years is $53,163.95.

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As per the system of linear equations concept, the solution of x is -1.282

Linear equations:

Linear equation is referred as the algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given,

Here we have the equations -4x - 1 = 5ˣ + 4

Now, we need to find the value of x by using the graph.

In order to plot the graph for the given linear equation,

First, we have to split the equation into two,

Like the following:

y = -4x - 1

y = 5ˣ + 4

Now, we plot the graph of both equations

Then we get the graph like the following.

Where the red line represents the equation y = -4x - 1 and the green line represents the equation y = 5ˣ + 4.

While we looking into the graph, we have identified the solution is,

x = -1.282

Therefore, the solution of x is -1.282

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Answer:

-11

Step-by-step explanation:

6(x-6)+2=8x-12

6x-36+2=8x-12 First take care of the parenthesis

6x-34=8x-12 then combine numbers

-2x-34=-12 Subtract 8 from both sides

-2x=22 Add 34 to both sides

x= -11 Divide by -2 on both sides

Answer:

Step-by-step explanation:

Solution

Steps

6(x−6) +2 = 8x−12

Expand by applying the distributive law:     a(b−c)=ab−ac

6(x−6)=6x-36

6x−36+2 = 8x−12

6x−34 = 8x−12

Add 34 to both sides

6x−34+34=8x−12+34

Simplify

6x=8x+22

Subtract 8x from both sides

6x−8x=8x+22−8x

Simplify

−2x=22

Divide both sides by −2

x=−11

Answer:

B (5,9)

Step-by-step explanation:

when working with fractions as slopes we use rise over run (broken down)

3 (numerator)--rise-how unit to go up or down

--

4 (denominator)--run--how many units to the left or right

since our slope is positive we will be going up 3 and 4 to the right.

if the slope is negative we go down and to the left.

hope this explanation helps for future questions

The completed table of the two column method to prove DE = FD is presented as follows;

Statement [tex]{}[/tex]                             Reason

1. CE = CD + DE[tex]{}[/tex]                    Segment addition postulate

2. FG = FD + DG              [tex]{}[/tex]     Segment addition postulate

3. CE = FG              [tex]{}[/tex]               Given

4. CD + DE = FD + DG      [tex]{}[/tex]    Substitution property of equality

5. CD = DG              [tex]{}[/tex]              Given

6. DG + DE = FD + DG    [tex]{}[/tex]      Substitution property of equality

7. DE = FD               [tex]{}[/tex]              Subtraction property of equality

A two column method consists a number of statements alongside the reasons that are known to make the statements true.

The segment addition postulate state that a point B is located on a segment AC if and only if AB + BC = AC, therefore;

The substitution property of equality states that if a = b, and a + c = d, then b + c = d

Which gives;

Similarly; CD = DG, then DG + DE = FD + DG

The subtraction (and addition) property of equality states that a quantity of known value can be subtracted (or added) to both sides of an equation and both sides of the equation remains equal.

Mathematically, if x = y, then x - z = y - z, therefore;

Then;

∴ DE = FD

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It is a function because the mapping .

(A) Due to the fact that there are no two values in Set B that have only one value in Set A mapped to them, the mapping diagram above represents a function.

(B) A function's very special property is that it associates one output with each input.

(C) Set A represents the domain, whereas Set B represents the range. Therefore, there would be exactly one value in the range that was unique for each value in the domain and would be present for each value in the domain.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The subsets X and Y are referenced to as the function's domain and codomain, correspondingly. A function is described as a relationship between a group of inputs with one output each. A function is, to describe it simply, a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a codomain, or range. A function is a type of rule that produces one output from one input. Y=X2 is a good illustration of this. Any input for x yields a single output for y.

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Latrina will serve 640 hors d’oeuvres to the 240 people at her wedding .

In the question ,

it is given that

At Latrina's wedding

number of  hors d’oeuvres offering that 3 people will get = 8 offering

So, the number of offering of hors d’oeuvres that 1 person will get = 8/3  .

we need to find that

how many hors d’oeuvres will she serve for 240 people .

So ,

the number of  hors d’oeuvres offering that 240 people will get =(8/3)×240

= 8 × 80

= 640

Therefore , Latrina will serve 640 hors d’oeuvres to the 240 people at her wedding  .

The given question is incomplete , the complete question is

Latrina is planning to serve hors d’oeuvres at her wedding. She plans on offering 8 hors d’oeuvres for every 3 people. If she has invited 240 people to the wedding, how many hors d’oeuvres will she serve?

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Answer: y= (2/3)x - 2

Step-by-step explanation:

The biggest way to remember equations like these is to know rise over run which means however many times it goes up until it intersects with both x and Y will be on the top of the fraction and however many times it goes to the right until it intersects with both x and y will be on the bottom of the fraction. So since it hits (0, -2) then intersects at (3,0) it will be 2/3x and the Y is where X equals zero so it would be -2. Hope that helps!

Answer:

y  =  [tex]\frac{2}{3}x - 2[/tex]

Step-by-step explanation:

Step 1:

Choose two points on the graph, (x1, y1) and (x2, y2), to find the slope.

Find the ratio between change in y-values and change in x-values.

m = (y2 - y1) / (x2 - x1)

Points I picked:

(x1, y1) = (0, -2)

(x2, y2) = (3, 0)

Then,

m = (0 - (-2)) / (3 - 0)

m = 2/3

Step 2 :

Find the y-intercept from the graph. That is the point at which the line intersects the y-axis.  

The y-intercept is -2.

b  =  -2

Step 3 :

Use the slope (m) and y-intercept (b) to write the equation in slope-intercept form:

y = mx + b

Substitute m = 2/3 and b = -2

y  =  2/3 x - 2

After solving the given equation for r, the value of r is √T/4π.

So, the formula equation is:

Now, solve for r as follows:

Therefore, after solving the given equation for r, the value of r is √T/4π.

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Use the distributive property to multiply 2 times 4−2w.

Subtract 8 from 8 to get 0.

Divide both sides by −4.

Divide −4 by −4 to get 1.

Answer:

w = 1

Step-by-step explanation:

2(4 - 2w) - 8 = -4

(2*4 + 2*-2w) - 8 = -4

(8 - 4w) - 8 = -4

-4w + 8 - 8 = -4

-4w = -4

w = -4/-4

w = 1

Check:

2(4 - 2*1) - 8 = -4

2(4-2) -8 = -4

2(2) - 8 = -4

4 - 8 = -4

Answer:

the number greater than 5 is only 6 in the case of a coin.

Step-by-step explanation:

in a coin numbers greater than 5 is only 6

probability= No of required outcome/ No of possible outcome.

P.B= 1/6

in a coin there is head or tail

P.B of getting tail

P.B= Tail/Head + Tail

P.B= 1/2

The coin of course, has two sides, heads and tails. Assume we are talking about a six-sided die. Let's look at the individual probabilities.

There are only two sides to the coin, tails being one of them, so:
p(tails) = 1/2

The die goes from 1 to 6. We need to see the numbers that fit the inequality:

p(5 < x ≤ 6)
There is only one integer that is greater than five and less than or equal to six, and that is six. If there is only one number out of six, then:
p(>5) = 1/6

When dealing with probabilities, to determine the probability of two things happening, multiply both probabilities.

1/2 x 1/6 = 1/12

Answer:

See below.

Step-by-step explanation:

Each of the graphs shows a line segment, but because of the arrowheads, each situation is different.

Left graph.

The line segment has a point at each end. The graph is of just the line segment shown.

The lowest x-coordinate is -4.

The greatest x-coordinate is 3.

The lowest y-coordinate is 2.

The greatest y-coordinate is 5.

Domain: -4 ≤ x ≤ 3

Range: 2 ≤ x ≤ 5

In interval notation:

Domain: [-4, 3]

Range: [2, 5]

Middle graph.

The line segment has a point at the right endpoint but an arrowhead at the left. The graph is a ray that starts at point (2, 2), goes through point (-4, 5) and keeps going forever past point (-4, 5) in the direction of the segment.

The lowest x-coordinate is -∞.

The greatest x-coordinate is 2.

The lowest y-coordinate is 2.

The greatest y-coordinate is ∞.

Domain: x ≤ 2

Range: x ≥ 2

In interval notation:

Domain: (-∞, 2]

Range: [2, ∞)

Right graph.

The line segment has an arrowhead at each end. The graph is a line that includes the line segment shown. A line has no beginning and no end; therefore, it goes on in both directions forever.

The lowest x-coordinate is -∞.

The greatest x-coordinate is ∞.

The lowest y-coordinate is -∞.

The greatest y-coordinate is ∞.

Domain: all real numbers

Range: all real numbers

In interval notation:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Answer:

1.  Domain: [-4, 3]    Range: [2, 5]

2.  Domain: (∞, 2]    Range: [2, ∞)

3.  Domain: (-∞, ∞)    Range: (-∞, ∞)

Step-by-step explanation:

Domain: The set of all possible input values (x-values).

Range: The set of all possible output values (y-values).

An open circle indicates the value is not included in the interval.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

Note:  Assume that each square on the given graphs is 1 unit.

Question 1

There are closed circles at both endpoints of the line: (-4, 2) and (3, 5).

Therefore, the values are the endpoints of the intervals.

Question 2

There is a closed circle at (2, 2).

There is an arrow at one endpoint, so as x → -∞, y → ∞.

Question 3

There are arrows at the endpoints of the line.

Therefore, the domain and range are unrestricted.

1. The completion of the inventory table is as follows:

                                   Units  Unit Cost    Total Cost

Jan. 1  Beg. Inventory     8       $6.00                 $48

Apr. 11 Purchases         24       $11.00              $264

May 17 Purchases        30      $14.00              $420

Dec. 5 Purchases         19      $16.00              $304

2. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:

                                      LIFO           FIFO         Weighted-Average

Ending inventory          $704          $845                $767.40

Cost of goods sold       $332          $191                $268.60

FIFO (First-in, First-out) is based on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

LIFO:

Ending inventory = $704 ($48 + $264 + 28 x $14)

Cost of goods sold = $332 ($1,036 - $704)

FIFO:

Ending inventory = $845 (11 x $11 + 30 x $14 + 19 x $16)

Cost of goods sold = $191 ($1,036 - $845)

Weighted Average:

Ending inventory = $767.40 (60 x $12.79)

Cost of goods sold = $268.60 (21 x $12.79)

                                   Units  Unit Cost    Total Cost

Beg. Inventory Jan. 1     8       $6.00                 $48

Apr. 11 Purchases         24      $11.00              $264

May 17 Purchases        30     $14.00              $420

Dec. 5 Purchases         19     $16.00              $304

Total                              81                           $1,036

Units sold                      21

Ending inventory         60

Average cost per unit = $12.79 ($1,036/81)

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Answer:

what are the given ratio?

Step-by-step explanation:

The no. of truffles than can be included in the box is 135.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches.

∴ The volume of the box is,

= (15×12×1.5) inches³.

= 270 inches³.

Given each truffle has a volume of 2 iches³.

∴ No. of truffles than can be included in the box is,

= (270/2).

= 135.

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Answer A ; 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.

Answer B ;  T-intercept is -4934/37, or approximately -133. This indicates that Minnesota had a population of 2000–133 in 1867.

Answer A : P=37t+4934 can be used to represent Minnesota's population in thousands over the t years after 2000.

P-intercept is the P value at time t=0.

P=37*0+4934\sP=0+4934\sP=4934

So, 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.

Answer (B) : The term "t-intercept" refers to the value of the function t when P=0 0=37t+4934 -4934=37t divide by 37 -4934/37=t -133.351351351 = t

Hence T-intercept is -4934/37, or approximately -133. This indicates that Minnesota had a population of 2000–133 in 1867.

P=37t+4934 P-intercept means the value of P at t=0 P=37*0+4934 P=0+4934 P=4934

Given that Minnesota's population in thousands, t years since 2000, it can be expressed by the equation:

So, 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.

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Answer: Marks bakery

Step-by-step explanation:

divide 450 by 3 = 150 loaves of bread Ann baked per day

divide 560 by 4= 140 loaves of bread Mark bakes per day

Thus Marks bakery bakes bread at a faster rate.