How many quarts of water should be added to 6
quarts of 80% antifreeze solution to dilute it down
to 30%?

[tex]\\ \rm\Rrightarrow 26+6b\geqslant 2(3b+4)[/tex]

[tex]\\ \rm\Rrightarrow 26+6b\geqslant 6b+8[/tex]

[tex]\\ \rm\Rrightarrow 6b-6b\geqslant 8-26[/tex]

[tex]\\ \rm\Rrightarrow 0\geqslant -14[/tex]

Hence

It has no solutions

Answer:

A. All Real Numbers

Step-by-step explanation:

26 + 6b ≥ 2(3b + 4)

~Simplify

26 + 6b ≥ 6b + 8

~Subtract 26 to both sides

6b ≥ 6b - 18

~Subtract 6b to both sides

0 ≥ -18

Best of Luck!

Answer:

It is Tn = 9n - 11

Step-by-step explanation:

It is an arithmetic progression:

[tex]T_{n} = a + (n - 1)d[/tex]

a is the first term, a = -2

n is number of terms

d is common difference, d = 7-(-2) = 9

[tex]T_{n} = - 2 + \{ (n - 1) \times 9 \} \\ T_{n} = - 2 + 9n - 9 \\ T_{n} = - 11 + 9n \\ T_{n} = 9n - 11[/tex]

Answer:

[tex]T_{n}[/tex] = 9n - 11

Step-by-step explanation:

There is a common difference between consecutive terms, that is

7 - (- 2) = 16 - 7 = 9

This indicates the sequence is arithmetic with nth term

[tex]T_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 2 and d = 9 , then

[tex]T_{n}[/tex] = - 2 + 9(n - 1) = - 2 + 9n - 9 = 9n - 11

Answer:

In transformations a reflection across the x axis produces a mirror image.

Answer: 11%

Step-by-step explanation:

729-648.81=80.10

What percent is 80.10 of 729

%/100 = is/of (this may help you)

X/100 = 80.10/729 (cross multiplication)

(80.19*100)/729 =

11%

Step-by-step explanation:

Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.

Then we have to writer a linear equation, for which I got: y-27/4x+25. We also had to find the cost per t-shirt, for which I got: $31.75. The last part I don't understand, however: fidn the shipping and handling charge.

The second word problem is:

It costs Consolidated Cereals Corporation $1050 to produce 100 boxes of corn flakes and $1250 to produce 500 boxes. I found the cost function: c(x)=1/2x+1000 but don't know how to determine the fixed cost and the variable cost per box (mainly because I have no idea what those are.)

Cost= m x+b

x is the cost per shirt, b is the handling charge

295=40m+b

565=80m+b

subtract the first equation from the second:

370=40x solve for m, the cost of each shirt. Then solve for b, put all that into y= mx+b

One the second question,

Cost= variable cost * n + Fixedcosts or

cost= n*v+F

1250=500v+f

1050=100v+f

subtract the second equation from the first

200=400v solve for v, and it is 1/2 dollar. Solve for f, the fixed cost, and it looks as if it is 1000 dollars.

Answer:

7

Step-by-step explanation:

The equation of direction variation is

y = kx where k is the constant of variation

y = 7x  so 7 is the constant of variation

Answer:

7

Step-by-step explanation:

The equation of direction variation:-  

y = kx where k is the constant of variation -> Eq 1  

y = 7x  -> Eq 2

Comparing Eq 1 and Eq 2,

k=7

Answer:

x=1,296

Step-by-step explanation:

6x=7,776

  x=7,776/6

   x=1,296

Answer:

am I supposed to change this to a statement like a sentence then one is to fifty thousand

Answer:

44

Step-by-step explanation:

Take the miles you already traveled and subtract it from the total.

73-29=44

4200

Step-by-step explanation:

10 × 150 = 1500

18 × 150 = 2700

So

1500 + 2700 = 4200

Answer:

5

Step-by-step explanation:

Given:

77 + 20 = 97

450 + 20 = 470

Keep multiplying 97 with random numbers until it passes 470.

97 × 4 = 388

97 × 5 = 485

So, the skier will have to pay daily passes 5 times to be more expensive than the season pass.

Hope this helped.

Answer:

Step-by-step explanation:

Let say a and b the 2 natural integers with 0 < a< b.

Since a*b=GCF(a,b)*LCM(a,b)

a*b < 3*20=60

[tex]\begin{array}{c|c|c|c|c|c}a&b&a*b&GCF&LCM&GCF*LCM\\---&---&---&---&---&---\\3&6&18&3&6&18\\3&9&27&3&9&27\\3&12&36&3&12&36\\3&15&45&3&15&45\\3&18&54&3&18&54\\6&9&54&3&18&54\\---&---&---&---&---&---\\\end {array}[/tex]

Answer:

The forest will cover an area of approximately 2994 square kilometers after 10 years.

Step-by-step explanation:

A forest covers an area of 5000 square kilometers. Each year, the area of the forest decreases by 5%. We want to determine its area after 10 years.

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x is the time that has passed (in this case in years).

Since the original area is 5000 square kilometers, let a = 5000.

Each year, the area decreases by 5%. In other words, for each subsequent year, the forest's area will be 100% - 5% = 95% = 0.95 of its previous year. Hence, r = 0.95.

Thus, our function is:

[tex]\displaystyle f(x) = 5000(0.95)^x[/tex]

Then after 10 years (x = 10), the area will be:

[tex]\displaystyle f(10) = 5000(0.95)^{(10)}= 2993.6846...\approx 2994\text{ km}^2[/tex]

In conclusion, the forest will cover an area of approximately 2994 square kilometers after 10 years.

Answer:

180 degrees

Step-by-step explanation:

Answer:

qss-qvcj-kwr join guys iam bored

Answer:

just solve equation and you will get to know that

15 is d becoz both 8 gets cancelled

and

16 is b becoz then equation is simplified to x = smthng

Answer:

for additive inverse you change the sign of the given number so i think its 7

Step-by-step explanation:

Step-by-step explanation:

3+21+7+3+21+7

Answer:

117 is the answer of your questions

Step-by-step explanation:

supplement=180

given angle=63

180-63=117

Answer:

0

Step-by-step explanation:

(10-1=9)(10-2=8)(10-3=7)(10-10=0)

9*8*7*0=0

Answer:20 minutes per pound

we know that

To find the unit rate divide the total time by the total weight

Convert mixed number to an improper fraction

Convert hours to minutes

so

Find the unit rate

therefore

20 minutes per pound

Answer:

16 is a natural, whole and integer

Step-by-step explanation:

16 is a natural, whole and integer

it is not rational or irrational because

rational numbers are written in p/q as well as irrational

natural numbers start from 1 till infinite

whole numbers start from 0 to infinite

integers include all the positive and negative numbers

Step-by-step explanation:

steps are in the picture.

Note:If you need to ask question about it ,i can make you understand.thanks

Answer:

D. 10

Step-by-step explanation:

[tex]{ \sf{(12x + 12) \degree = 79\degree + (5x + 3)\degree}} \\ { \sf{ \{outer \: angle \: is \: equal \: to \: sum \: of \: inner \: angles \}}} \\ { \sf{12x - 5x = 79 + 3 - 12}} \\ { \sf{7x = 70}} \\ { \sf{x = 10}}[/tex]

Answer:

180-87 = 93

Step-by-step explanation:

supplementary angles add up to 180°

so (the other angle + 87)=180°

other angle =180-87=93°

Answer:

93 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees. Therefore, the equation for finding the supplementary angle to 87 would be:

[tex]87 + x = 180\\x=180-87\\x=93[/tex]

Have a nice day. Feel free to ask questions. Spread the love.

Answer:

c. {1/15,16,1/17,18}

Step-by-step explanation:

please follow me

Answer:

[tex]{ \sf{set \:A \: and \: B }}[/tex]