how many quarts of pure antifreeze must be added to 3 quarts of a ​40% antifreeze solution to obtain a 60​% antifreeze​ solution?

Answer:

[tex]5\left(y+5z\right)\left(y-5z\right)[/tex]

Step-by-step explanation:

[tex]\mathrm{The \;given \;equation \;is \; 5y^2-125z^2}[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}5:\quad 5\left(y^2-25z^2\right)\\\\= 5\left(y^2-25z^2\right)[/tex]

[tex]\left y^2-25z^2\right[/tex]
[tex]25z^2 = \left(5z\right)^2[/tex]
==> [tex]\left y^2-25z^2\right = y^2-\left(5z\right)^2[/tex]

[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]y^2-\left(5z\right)^2=\left(y+5z\right)\left(y-5z\right)[/tex]

So the factored expression is
[tex]5\left(y+5z\right)\left(y-5z\right)[/tex]

By solving a system of equations, we can see that the chemist needs to use 375 mL of the 2% acid, and the other 225% of the 10% acid.

Let's define the variables that we will need to write our system of equations:

We know that the chemist wants to make 600mL of a 5% acid solution, so we can write the system of equations:

x + y = 600

x*0.02 + y*0.10 = 600*0.05

If we isolate y on the first equation, then we get:

y = 600 - x

Now we can replace that on the other equation so we get:

x*0.02 + (600 - x)*0.10 = 30

With this, we can get the value of x.

x*0.02 + 60 - x*0.10 = 30

-x*0.08 = 30 - 60 = -30

x = 30/0.08 = 375

So the chemist needs to use 375 mL of the 2% acid, and the other 225% of the 10% acid.

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Answer:

The answer to your question is 42

the answer is 42 because the parentheses around the -6 and the -7 mean to multiply them and that two negatives make a positive so -6 * -7 equals 42

Hope this helps!

Answer:

see explanation

Step-by-step explanation:

the function is positive for values of y above the x- axis

the line goes on forever on the left side and terminates at x = 15 on the right side.

the interval where the function is positive is (- ∞, 15 ]

the x- intercept is where the line crosses the x- axis ( y = 0 )

x- intercept = 15

the y- intercept is where the line crosses the y- axis (x = 0 )

y- intercept = 3

Answer:

5 √(5)^2 = 25

Step-by-step explanation:

The square root of 5^2 is 5. Then we will have to multiply by 5 to get our answer. So we'd do 5 x 5 and it'd equal 25. Therefore our final answer is 25.

I hope this helps, have a blessed day! :D

Answer:

bro this is so easy it's letter d

Answer:

520

Step-by-step explanation:

10 missed in 100 free throw ( because of 100%)
=> 1 missed in (100/10) free throw
=> 52 missed in (52*100/10) free throw
                             = 520 free throw


Hope it helps!
Brainliest?

The value of the variable x is 5 and the lengths of PL and LQ are 9 and 48, respectively.

In this problem we find a line segment generated by points P and Q and in which a point L divides the line segment PQ in two sections: PL and LQ. In accordance with the statement, we have the following equations describing the geometric system:

PQ = PL + LQ              

PQ = PL + LQ

57 = (2 · x - 1) + (9 · x + 3)

Now we proceed to clear the variable x with the resulting equation:

57 = 11 · x + 2

55 = 11 · x

x = 5

And finally we find the length of each line segment:

PL = 2 · 5 - 1

PL = 9

LQ = 9 · 5 + 3

LQ = 48

The value of the variable x is 5 and the lengths of PL and LQ are 9 and 48, respectively.

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Answer X=43 ,4X=172, (8X-3)=101

Step-by-step explanation:

Perimeter = addition of all sides ie;

556=X+4X+8X-3

556=13X-3

556+3=13X

559/13=13X/13

X=43

replace x with 43 to get their

Step-by-step explanation:

I guess this means from 2018 to 2019 (and not to 2010).

so, compared to 2018 the numbers of 2019 were 104% (100% of 2018 plus 4% increase).

104% = 68,280,000

100% = 104%/1.04 = 68,280,000/1.04 =

= 65,653,846.15 ≈ 65,653,846

the number of passengers in 2018 were about

65,653,846

Her total commission was $560.

As 10% of the first $1,000, 15% of the next $2,000, and 20% of sales beyond $3,000 are commissions that she receives. She sold $3,400 worth of tires last week.

What does "total commission" mean?

The commission serves as a benefit or an inducement for the worker to close agreements so that the business can increase revenue and profits. The total commission is calculated by multiplying the total sales by the commission percentage.

After dividing the outcome by 100, multiply the sale price by the commission percentage. Perform the subsequent calculation: Each blue gadget costs $70. The salesman receives a 14% commission on each sale, or $9.80.

The percentage or fixed payment connected to a specific number of sales is referred to as a "commission rate." A commission, for instance, can be $30 or 6% of sales.

It is therefore $560.

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Answer:

Ann = 67 stickers

Josh = 60 stickers

Claire = 30 sickers

Answer:

d = 510 km

Step-by-step explanation:

She travelled the final 4 hours at a constant speed of 60 km/h.

distance = speed × time

distance = 60 km/h × 4 hours

distance = 240 km for the last 4 hours

She already had travelled 270 km in the first 3 hours.

d = total distance = 270 km + 240 km = 510 km

Answer: d = 510 km

Answer:

Solve for x: [tex]x = \frac{3y+1}{4y-2}[/tex]

Evaluate x for y = 1: [tex]x = 2[/tex]

Step-by-step explanation:

[tex]Original:y=\frac{2x+1}{4x-3}\\Multiply\ out\ the\ denominator:(4x-3)*y = 2x+1\\Distribute: 4xy - 3y = 2x+1\\Group\ Like\ Terms:4xy-2x = 3y+1\\Factor\ Out\ x: x(4y-2) = 3y+1\\Divide\ to\ get\ x\ alone:x = \frac{3y+1}{4y-2}\\\\Plug\ in\ the\ value\ for\ y:x = \frac{3(1)+1}{4(1)-2}\\Multiply:x = \frac{3+1}{4-2}\\Add:x = \frac{4}{2}\\Simplify/Divide:x=2[/tex]

The distance from Tacoma to Seattle is estimated as 25 miles.

Distance is defined as an object's total movement without regard for direction. Distance can be defined as the amount of ground an object had also covered regardless of its beginning or ending point.

Now, as per the given question;

The following are the distances between cities:

120 miles from Portland to Tacoma

145 miles from Portland to Seattle

120+x = 145

x = 145 - 120

x = 25 miles

Therefore, the distance from Tacoma to Seattle is estimated as 25 miles (according to the given graph).

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The complete question is -

Item 17 The cities Portland, Oregon; Tacoma, Washington; and Seattle, Washington, in respective order, lie approximately in a straight line. The distance from Portland to Tacoma is 120 miles. The distance from Portland to Seattle is 145 miles. Find the distance from Tacoma to Seattle.

(see attached figure)

The number of boxes of candy that Mariana sells is 3/10.

A fraction is a non integer that is made up of a numerator and a denominator. An example of a fraction is 3/10. 3 is the numerator and 10 is the denominator.

In order to determine the boxes of candy that Mariana sold, multiply the fraction of boxes that Mariana sold by the number of boxes of candy that Juan sold.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is x.

Boxes that Mariana sells = fraction of boxes that Mariana sells x number of boxes that Juan sold

1/10 x 3 = 3/10

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Answer:

Below

Step-by-step explanation:

b = 180 - 81° (because of the Z angle law)

b = 99°

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Given the function [tex]h(t)=\frac{1}{t+1}[/tex], we can find [tex]h(\frac{1}{2} )[/tex] by substituting [tex]\bf{t=\frac{1}{2}}[/tex].

When t= [tex]\frac{1}{2}[/tex],

[tex]h(\frac{1}{2})[/tex]

[tex]=\frac{1}{\frac{1}{2}+1 }[/tex]

[tex]=\frac{1}{(\frac{3}{2} )}[/tex]

[tex]=\bf{\frac{2}{3}}[/tex]

Additional:

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Answer:

0.2083

Step-by-step explanation:

Answer: 54

Step-by-step explanation:

2[(4+5)⋅3]

⇒2[9⋅3]

⇒2[27]

⇒54

Using proportions, it is found that the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.

The Ruiz family is exchanging Euros for USD dollars, considering the following currency rate:

1 euro = 1.35261 USD.

Considering that the amounts in USD are rounded to the nearest hundredth, the use the following rule

1 euro - 1.35 USD.

It asks if the Ruiz family will be getting the most accurate answer.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, we suppose a 1000 euros amount, them:

Hence the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.

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The number of students in each bus are 54 students .

Given that, 331 students went on a field trip. Six buses were filled and 7 students traveled in cars.

Now you may get that only 7 students out of 331 are travelled in cars whereas others travelled by bus.

number of total students travelled by bus are 331-7 = 324 students

Therefore 324 students travelled in 6 buses.

Number of students travelled in each bus = 324/6 = 54 students.

Therefore number of students travelled in each bus is 54 students .

verification:

number of buses = 6

number of students in each bus = 54

Therefore total number of students in 6 buses = 6*54 = 324 students.

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Step-by-step explanation:

1. [tex] \frac{48}{8} +\frac{44}{8}= 11 \frac{1}{2} [/tex]

[tex]2.\frac{10}{10} + \frac{30}{10} = 4[/tex]

[tex]3.\frac{6}{4} + \frac{2}{3} = 2 \frac{1}{6}[/tex]

[tex]4.\frac{1}{8} + \frac{2}{16} = \frac{1}{4}[/tex]

[tex]5.\frac{4}{4} + \frac{14}{16} = 1 \frac{7}{8}[/tex]

[tex]6.\frac{4}{3} + \frac{2}{9} = 1 \frac{5}{9}[/tex]

[tex]7.\frac{2}{4} + \frac{4}{8} = 1[/tex]

[tex]8.\frac{20}{5} + \frac{15}{5} = 7[/tex]

[tex]9.\frac{2}{4} + \frac{4}{6} = 1 \frac{1}{6}[/tex]

[tex]10.\frac{4}{7} + \frac{6}{21} = \frac{6}{7}[/tex]

[tex]11.\frac{4}{2} + \frac{16}{18} = 2 \frac{8}{9}[/tex]

The decay rate of a certain new cell phone is 0.333

For given question,

The average lifetime of a certain new cell phone is three years.

The manufacturer will replace any cell phone failing within two years of the date of purchase.

Also, the lifetime of these cell phones is known to follow an exponential distribution.

We need to find the decay rate.

We know that an exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.

since the average lifetime of a certain new cell phone is three years, the decay rate would be 1/3 = 0.333

Therefore, the decay rate of a certain new cell phone is 0.333

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Our initial equation:

17h - 7 = 10h - 2 + 7h

I want to get variables ("h") on one side, and numbers on the other, hence I will add 2 to both sides to shift numbers to the left side.

17h - 5 = 10h + 7h

Now I want to simplify the "h" on the right side.

17h - 5 = 17h

Now I will move the variable from the left to the right.

-5 = 0

17h - 17h is zero, think of h being equal to 1 if you don't get it.

-5 = 0 is a false inequality, there are no solutions.

THERE ARE NO SOLUTIONS.

Answer: They are parallel

Step-by-step explanation:

Turn them both into slope-intercept form:

 y = -x + 8

y = -x - 1

Since the slope on both of them are the same (-1), they are parallel