Unit 6, Lesson 18. 6.18 Cool-Down.

Why aren't all solutions to an inequality possible in reality?

(TL;DR at the bottom, but the full explanation is better)

Let's answer this using an example.

The equation 2x + 5 > 10 can represent a lemonade stand's sales. What do each of the numbers represent in a real-life situation?

A solution for this equation would be x = -3:

2x + 5 > 10

2(-3) + 5 > 10

6 + 5 > 10

11 > 10 - True

Another solution is x = 11/3:

2x + 5 > 10

2(11/3) + 5 > 10

(22/3) + 5 > 10

(37/3) > 10

(36/3)+(1/3) > 10

12 and (1/3) > 10

These are solutions to our inequality from a mathematical standpoint but are both implausible in real life.

Assuming that reasonable would mean a full glass, -3 and (11/3) are possible answers, but can't be reasonably sold. -3 glasses of lemonade can't be sold, and neither can (11/3) of a glass of lemonade.

Therefore, these values create a situation where "not all solutions represented by inequation are always possible solutions in reality."

TL;DR:

    Not all solutions are possible because the value that makes the inequation true is not reasonable or feasible under realistic circumstances, such as a fraction value for people or a negative value for possession.

Answer:1200

1 box=240

so if you take 240 x5 you get 1200

Step-by-step explanation:

Answer:

0.75s

Step-by-step explanation:

The expression would be 0.75s where 0.75 represents the cost of the item after the 25% sale, and s representing the regular cost of the item.

Hope this helps :)

Answer:

Step-by-step explanation:

Rule: (x, y) → (-y, -x)

This means that the x, will now become y, and the y will now become x.

U (-7, -4) → (4, 7)

V (1, -4) → (4, -1)

W (-5, -9) → (9, 5)

U' (4, 7)

V' (4, -1)

W' (9, 5)

*View the attached graph*

Hope this helps!

Answer:

19) 280 cm³

20) 120 cm³

Step-by-step explanation:

v= l×w×h

19) 7×5×8 = 280

20) 6×5×4 = 120

Answer:

-3.5

Step-by-step explanation:

6x + 16 = 2x + 2

4x = -14

x = -3.5

Step-by-step explanation:

3 and 7 are equal because they are corresponding angles

6x+16=2x+2

6x-2x=2-16

4x= -14

x= -3.5

Answer:

The 3rd one if I'm not mistaken. Correct me if I'm wrong, I'm so so sorry if it's incorrect

Answer:

Each leg of the right triangle is equal to the radius of the sphere.

Step-by-step explanation:

I took the quiz and it was right

Answer:

Angle ABD is 16 degrees and Angle DBC is 74 degrees

Step-by-step explanation:

Question 6. x+9+11x-3=90. 12x+6=90 -6 on both sides and 12x=84 divide each side by 12 and x= 7 angle ABD is x+9 so 7 +9= 16. Angle measure of ABD is 16 degrees. Measure of angle DBC is 11x -3 so 11 times 7=77. 77-3= 74. So the measure of angle DBC is 74 degrees and this answer is right because they both add up to be 90 degrees. Hope this helped! :)

Answer:

CORRECT OPTION IS 150 CENTIMETERS OR YOU CAN SAY 1.5M :)

Step-by-step explanation:

GIVEN:

Walt grew 10 cm in one year

He is now 1.6m

SOLUTION:

We know that 1 m = 100cm

So 1.6 m = 160cm

So one year ago he was:

160 - 10 = 150cm

So he was 150 cm or 1.5 m one year ago.

Step-by-step explanation:

They have already done the math for you, you just need to draw a line with the length of 3 units, so it would look like this:

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

5/7 is 0.714....

7 is greater that 5 so u round up to 7

Answer:

The percent of increase is 5%

Step-by-step explanation:

The number of times that it is likely to land in the shaded area will be 40 times out of 100 times.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

A dart is thrown at the board 100 times at random.

The number of times that dart hit the board is 40 times. Then the probability is calculated as,

P = 40 / 100

P = 2/5

P = 0.40 or 40%

More about the probability link is given below.

https://brainly.com/question/795909

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formula used : [tex]\sf A = P(1 + \dfrac{r}{n})^{nt}[/tex]

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

✔A) A 2-year loan with a 4.75% interest rate compounded annually.

[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{4.75\%}{1})^{(1)(2)}[/tex]

[tex]\hookrightarrow \sf A = \$10,972.56[/tex]

B) A 3-year loan with a 4.00% interest rate compounded annually.

[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{4.00\%}{1})^{(1)(3)}[/tex]

[tex]\hookrightarrow \sf A = \$11248.64[/tex]

C) A 4-year loan with a 3.75% interest rate compounded annually.

[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{3.75\%}{1})^{(1)(4)}[/tex]

[tex]\hookrightarrow \sf A = \$11586.50415[/tex]

D) A 5-year loan with a 3.00% interest rate compounded annually.

[tex]\hookrightarrow \sf A = 10,000 (1 + \dfrac{3.00\%}{1})^{(1)(5)}[/tex]

[tex]\hookrightarrow \sf A = \$ 11592.74074[/tex]

Thus loan of 2-year loan with a 4.75% interest which is compounded annually will allow him to pay the least interest of only $972.56.

The least interest is 972.56 dollars. Then he has to select a 2-year loan with a 4.75% interest rate compounded annually.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the formula for the amount will be

[tex]A = P (1 + r) ^t[/tex]

A = Amount

P = Loan amount

r = rate of interest

t = time

The interest is given as

Interest = A - P

Charles needs a $10,000 loan in order to buy a car.

A) A 2-year loan with a 4.75% interest rate compounded annually. Then the amount will be

[tex]\rm A = 10000(1.0475)^2\\\\A = 10972.56[/tex]

Then the interest will be

Interest = 10972.56 - 10000

Interest = 972.56

The amount of interest is $972.56.

B) A 3-year loan with a 4.00% interest rate compounded annually.  Then the amount will be

[tex]\rm A = 10000(1.04)^3\\\\A = 11248.64[/tex]

Then the interest will be

Interest = 11248.64 - 10000

Interest = 1248.64

The amount of interest is $1248.64.

C) A 4-year loan with a 3.75% interest rate compounded annually.  Then the amount will be

[tex]\rm A = 10000(1.0375)^4\\\\A = 11586.50[/tex]

Then the interest will be

Interest = 11586.50 - 10000

Interest = 1586.50

The amount of interest is $1586.50.

D) A 5-year loan with a 3.00% interest rate compounded annually. Then the amount will be

[tex]\rm A = 10000(1.03)^5\\\\A = 11592.74[/tex]

Then the interest will be

Interest = 11592.74 - 10000

Interest = 1592.74

The amount of interest is $1592.74.

More about the compound interest link is given below.

https://brainly.com/question/25857212

Answer:

-40m + 24

Step-by-step explanation:

to answer this question you should distribute the -8 to all the digits

-8m + 24 -32m

then you can add like terms

-8m and -32m become -40m

-40m + 24 is the answer

Answer:

1.) 3

2.) 2

3.) 4

Answer:

This line has a slope of 0, with the equation being y = -4

Step-by-step explanation:

  Slope can be found with change in y over change in x

[tex]\frac{-4--4}{-2--3} =\frac{-4+4}{-2+3}=\frac{0}{1} =0[/tex]

       Note: We can tell by just looking at the line it will have a slope of 0. A line straight up and down vertically is one with an undefined slope, but a horizontal line has a slope of 0 since there is no incline/decline.

Answer:

30

24 : 28 would equal 6 : 7

[tex]6/13[/tex] x 65 = 30

Use the proportion of the bracelets

The no. of bracelets are expected to sold are 30 pieces.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given that, A jewelry store recently sold 24 bracelets and 28 other pieces of jewelry, which is 6 : 7 so, for every 6 pieces of bracelets 7 pieces of other types of jewelry are sold.

∴ No. of pieces of bracelets expected to sold are,

= 6/(6 + 7)×65.

= (6/13)×65.

= 6×5.

= 30 pieces.

learn more about ratios here ;

https://brainly.com/question/13419413

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here is your picture for the question

Answer:

2. 212264

Step-by-step explanation:

Area of circle: 3.14(r^2)

we need to divide the 520 in half first

520/2 = 260

Now we do the equation!

3.14(260^2)

We get 212264 as our final answer :)

Havea great day!!

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Answer: 60

Step-by-step explanation:

the answer is fx=60

Answer:

114.9 meter

Step-by-step explanation:

v=(2/3)πr^3

diameter=2r

r=7.6/2

r=3.8

(2/3)π* (3.8)^3

~36.58π meter

if the teacher wants you to use 3.14 as π (like instead of writing the symbol of π), then 36.58*3.14=114.9 meter

Answer:

In 254 revolutions, the bicycle will travel [tex]997.85m[/tex].

Circumference :
The circumference of bicycle is given as,
[tex]C = \pi d[/tex]
Where [tex]d[/tex] is diameter of bicycle.
Given that, [tex]d = \frac{5}{4}, \pi = 22/7[/tex]
Substitute values in above equation.
[tex]C = \frac{22}{7} * \frac{5}{4}[/tex]
[tex]C = \frac{110}{28} = 3.93[/tex]
In 254 revolutions of the bicycle wheel is, [tex]C = 254 * 3.93 = 997.85m[/tex]
In 254 revolutions , the bicycle will travel [tex]997.85m[/tex]
Learn more about the Circumference of circle here:
brainly.com/question/14283575

Your question was incomplete. Complete question is here:
"A counter recorded 254 revolutions of the bicycle wheel shown below how far did the bicycle travel. Use 22/7 as pi and the diameter of the wheel is 5/4."

Answer:

88mm^2

Sorry for not answering it early I know this answer is probably useless for you now

Step-by-step explanation:

Ok, suppose we were to divide this figure into two parts figure 1 & 2

like this... the picture is goven above

So, we can clearly see that figure 1 is a square as it has equal dimensions

and figure 2 is a rectangle because it should given in ur question but this is the only way to find out the area

So in figure 1 the dimensions are already give that the square is 8mm and on the other hand in figure 2 it is a rectangle, here only length is given - 6mm but width is not given. To find out the width it's simple, since the base of figure 1and2 is 12mm and the base of figure 1 is 8cm we can subtract it to get there rest of the base that is the base of figure 2.

So we get,

Base of figure 2 = Total base - Base of figure 1 = 12mm - 8mm = 4mm

Now since we have the dimensions, we only have to find the area of those two figures and add both areas to get the total are of the whole figure.

Area of figure 1

Area of square = side*side = 8*8 = 64mm^2

Area of figure 2

Area of rectangle = length*breadth = 4*6 = 24mm^2

Total area of the figures

Area of figure 1 + Area of figure 2 = 64mm^2+ 24mm^2 = 88mm^2

Answer:

y≤3

Step-by-step explanation:

5y+4≤22−y

Step 1: Simplify both sides of the inequality.

5y+4≤−y+22

Step 2: Add y to both sides.

5y+4+y≤−y+22+y

6y+4≤22

Step 3: Subtract 4 from both sides.

6y+4−4≤22−4

6y≤18

Step 4: Divide both sides by 6.

6y/6≤18/6

y≤3

Hey there!

Let's solve your inequality step-by-step.

[tex]\fbox{5y+4≤22−y}[/tex]

Step 1: Simplify both sides of the inequality.

[tex]\fbox{5y+4≤−y+22}[/tex]

Step 2: Add y to both sides.

[tex]\fbox{5y+4+y≤−y+22+y}[/tex]

[tex]\fbox{6y+4≤22}[/tex]

Step 3: Subtract 4 from both sides.

[tex]\fbox{6y+4−4≤22−4}[/tex]

[tex]\fbox{6y≤18}[/tex]

Step 4: Divide both sides by 6.

[tex]\fbox{6y/6 ≤ 18/6}[/tex]

[tex]\fbox{y≤3}[/tex]

Answer:

[tex]\fbox{y≤3}[/tex]

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Answer:

a

Step-by-step explanation:

b