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In linear equation , 240 liters of 90% solutions will be used.

What are a definition and an example of a linear equation?

Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,

Since, the total quantity of the mixture = 360,

⇒ x + y = 360 ----- (1),

Also, the resultant solution is of  85% antifreeze solution,

⇒ 75 % of x + 90% of y = 85% of 360

0.75x + 0.90y = 0.85 × 360

0.75x + 0.90y = 306

75x + 90y = 30600 -----(2),

Equation (2) - 75 × equation (1),

We get,

15y = 3600

⇒ y = 240

Hence, 240 liters of 90% solutions will be used.

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Answer:

it 21

Step-by-step explanation:

rr

Function g(x) = 4x -13 after the graph is translated 1 unit right of the graph of f(x) = 4x - 9.

As given in the question,

Function f(x) = 4x -9

Graph g(x) get translated 1 unit right of the graph of function f(x)

It means change in the value of x  equals to x-1

g(x) = 4(x-1) -9

⇒ g(x) = 4x -4 -9

⇒ g(x) = 4x-13

Therefore, function g(x) = 4x -13 after the graph is translated 1 unit right of the graph of f(x) = 4x - 9.

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Solution:

Inequality Form: [tex]4\leq x\leq 7[/tex]

Interval Notation: [tex][4,7][/tex]

_________________________________________________________

As for plotting on your line graph, one point should be a closed circle on 4, then the next should be a closed circle on 7.

__________________________________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Equation has no solution  is |4x-2|=-6

checking option A

|4x-2|=-6  . . . .1

if 4x-2≥0

  4x≥2

  x≥1/2

then |4x-2| = 4x-2

So , .. . . 1 becomes

4x-2=-6

4x=-4

x=-1

But x≥1/2

So x=-1 is not a solution.

if   4x-2≤0

  4x≤2

  x≤1/2

then |4x-2| = -(4x-2)

So , .. . . 1 becomes

-4x+2=-6

4x=8

x=2

but x≤1/2

So x=2 is not a solution.

checking option B

|-2-x| = 9  . . . 2

if -2-x ≥ 0

   x≤-2

then

|-2-x| = -2-x

So,  . . .. . 2 becomes

-2-x=9

x=-11

so it has a solution .

checking option C

|3x+61| = 6 . . . . . 3

if 3x+61≥0

x≥-61/3

then

|3x+61| = 3x+61

So, . . .3 becomes

3x+61=6

x=-55/3

So it has a solution.

checking option D

|-2x+8|=0 . . . . .4

if -2x+8≥0

x≤4

then  |-2x+8| = -2x+8

So , .. . . . .4 becomes

-2x+8=0

x=4

So it has a solution.

Hence option A |4x-2|=-6

has not a solution.

Sometimes equations have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction.

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Answer:

6.6 is the answer

Step-by-step explanation:

Hope it helps you

Here are the inequalities:

x ≥ 8

x < 3

x ≤ 3

x ≤ 8

x < 8

x ≥ 3

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

for example :

2 < 3 means 2 is less than 3

3 >2 means 3 is greater than 2

Steps to interpret an inequality graph :

If the circle above the number is colored, the inequality sign to use is either ≥ or ≤.

If the circle above the number is not colored, the inequality sign to use is either < or >.

If the arrow is pointing to the left, the inequality sign would either be ≤. or <.

If the arrow is pointing to the right, the inequality sign would either be ≥ or >.

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Answer:

x=21

Step-by-step explanation:

21*2+25*2=92

Answer:

x < 23

Explanation:

perimeter of a rectangle = 2(length + width)

Here given:

Setting equation:

[tex]\sf \rightarrow 2(x + 4 + x) < 100[/tex]

[tex]\sf \rightarrow 2(2x + 4) < 100[/tex]

[tex]\sf \rightarrow 4x + 8 < 100[/tex]

[tex]\rightarrow \sf 4x < 100 - 8[/tex]

[tex]\sf \rightarrow4x < 92[/tex]

[tex]\sf \rightarrow x < 23[/tex]

Answer:

2^2 × 3 × 5

Step-by-step explanation:

hope this works :)

The total number of gumballs in the jar calculated using probability is about 181.

Probability is the study of chance. The likelihood of an event to occur given as a fraction is probability.

For a sure event the probability is 1 and for an impossible event the probability is 0.

Carlos draws a sample of 55 gumballs. Out of which the number of green gumballs is 44.

Probability of a green gumball= number of green gumballs ÷ total number of gumballs

P(green) = 44 ÷ 55 = 4/5

Now in the sample the number of green gumballs is 4/5 , and in the jar the number of green gumballs is 145 .

Let us consider there are x gumballs in total in the jar.

P(green)=145 ÷ x

We know that P(green)= 4/5

∴4/5 = 145 ÷ x

or, x = 145 × 5 ÷ 4

or, x = 181.25 gumballs.

or, x ≈ 181 gumballs(As the number of gumballs cannot be a fraction)

Therefore there are about 181 gumballs in total .

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Let's say you wanted to find the cube root of 8

You write it on your paper like this: [tex]\sqrt[3]{8}[/tex]

In your calculator, you'd type this in:  8^(1/3)

The exponent of 1/3 corresponds to a cube root.

In general, the exponent of 1/n is for the nth root

The connection is [tex]\sqrt[n]{\text{x}} = \text{x}^{1/n}[/tex]

Answer:

I believe the Answer is C.

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Answer: y2-y1 and x2-x1

Step-by-step explanation:

5-9=-4

2--6=8

-4,8

Answer: 54.9

Step-by-step explanation:

121 lb converted to kk is 54.885

54.885 rounded to the nearest tenth is 54.9

Answer:

x = { 5; 6; 7}

Step-by-step explanation:

25 ≤ 25 < 36 < 49 < 50

=> x² = {25; 36; 49}

Because x€N => x = {5; 6; 7}

The monthly cost of 57 minutes calls is $12.55.

The monthly cost is $12.03 for 53 minutes and $ 13.59 for 65 minutes call

Therefore we have two points (53, 12.03) and ( 65, 13.59)

slope = (13.59 - 12.03)/ ( 65 - 53)

          = 1.56/ 12

          = 0.13

The intercept is

y = mx + c

12.03 = 0.13×53 + c

12.03 = 6.89 + c

c = 5.14

Equation:

cost = 0.13(minutes) + 5.14

       = 0.13×57 + 5.14

       = 7.41 + 5.14

       = 12.55

Therefore the monthly cost for 57 minutes is $12.55.

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(a) The answer of (g.f)(2) is [tex]\sqrt{23}[/tex] .

(b)The answer of (g + f) (2) is [tex]\sqrt{3}[/tex] -  3 .

(c)The answer of  (g - f) (-1) is [tex]\sqrt{15}[/tex] .

(d)The answer of [tex]\frac{f}{g}(-1)[/tex] is 0 .

We have given two functions f(x) = [tex]1-x^2[/tex] and g(x) = [tex]\sqrt{11-4x}[/tex]

(a) Put x = 2 in f(x) we get  f(2) = 1 - 4 = -3

  (g.f)(2) =  g(f(2))

             = g(-3)

              [tex]=\sqrt{11-4(-3)}\\=\sqrt{11+12} \\=\sqrt{23}[/tex]

which is option (c) .

(b)  Put x = 2 in f(x) we get f(2) = 1 - 4 = -3 and g(2) = [tex]\sqrt{11-8} =\sqrt{3}[/tex]

(g + f) (2) = g(2) + f(2)

              = [tex]\sqrt{3}[/tex] + (-3)

               = [tex]\sqrt{3}[/tex] - 3

which is option (a)

(c) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]

(g - f) (-1) = g(-1) - f(-1)

              = [tex]\sqrt{15}[/tex] + 0

               = [tex]\sqrt{15}[/tex]

which is option (b)

(d) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]

[tex]\frac{f}{g}(-1)[/tex] = f(-1) / g(-1)

          = 0 / [tex]\sqrt{15}[/tex]

           = 0

which is option (d)

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Answer:

f(-3)= 9(-3)^2+3-2= 9(9)+3-2= 81+1 = 82

Answer: 21 degrees

Step-by-step explanation:

Since (2x + 9) + 129 = 180, we can get that 2x = 42 and x = 21. Hope this helped!

Answer:

8

Step-by-step explanation:

sqrt 58 =7.62   closer to 8 than 7

The percentage increase is 103.7%.

Answer:

103.7%

Step-by-step explanation:

Given the following question:

Original price = $1.35
New price = $2.75

Find the percent change. To find the percent change we will use the formula to calculate the percent change of course rounding if needed.

[tex]\frac{np\times op}{op} \times100[/tex]
[tex]\frac{2.75\times1.35}{1.35} \times100[/tex]
[tex]2.75 - 1.35\div1.35\times 100% =[/tex]
[tex]=103.7037037037[/tex]

Round to the nearest tenth:
[tex]103.7037037037[/tex]
[tex]0 < 5[/tex]
[tex]103.7[/tex]

1.35 to 2.75 is a "103.7%" increase.

Hope this helps.

Answer:

(-16, 0)

Step-by-step explanation:

The midpoint can be found using the formula below, where [tex](x_1,y_1)[/tex] is the first endpoint and [tex](x_2, y_2)[/tex] is the other endpoint.

[tex]\boxed{\text{Midpoint}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )}[/tex]

Let the other endpoint be (x, y).

Substitute the given midpoint and one endpoint into the formula above:

(-6, 4)= [tex](\frac{x+4}{2},\frac{y+8}{2} )[/tex]

Comparing the x-coordinate:

[tex]-6=\frac{x+4}{2}[/tex]

Multiply both sides by 2:

x +4= -12

Subtract 4 from both sides:

x= -12 -4

x= -16

Comparing the y-coordinate:

[tex]4=\frac{y+8}{2}[/tex]

Multiply both sides by 2:

y +8= 8

Subtract 8 from both sides:

y= 8 -8

y= 0

Thus, the other endpoint is (-16, 0).

Supplementary:

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The $785 balance on Dan's credit card is currently due. The APR on his credit card is 24.42%. He has to pay the full balance that is $785.2442.

Given that,

The $785 balance on Dan's credit card is currently due.

The APR on his credit card is 24.42%.

We have to find what finance fee would he pay if he didn't pay the balance in full.

To find the balance full he has to pay.

We have to add the balance of current due and APR .

We get,

=$785+24.42%

=$785+0.2442

=$785.2442

Therefore, he has to pay the full balance that is $785.2442.

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Answer: 0

Step-by-step explanation: the slope intercept form is y= mx +b. The equation here is y = -19. It means that the slope, m, is 0. You can also think about it this way. y= -19 graph will show you that for every x value, the y is at -19 since there is no rise over run. it is just a straight line at y= -19

The length of the line segment EF is 106.

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She should buy  five sweaters.

A rational consumer would purchase a good as long as marginal benefit is equal or greater than marginal cost.

Marginal cost is the additional cost generated by producing an additional unit of output. Marginal benefit is the benefit derived from consuming one extra unit of a good.

The marginal benefit of the first five sweaters is greater than the marginal cost. Thus, she should buy  five sweaters.

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