translation and reflection​

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

Given;

Percentage of 3 quarts of antifreeze solution = 40%

We have to find,

Quarts to obtain the antifreeze solution of 60%

Now,

The 3 quarts of 40% antifreeze solution contains 0.4 x 3 = 1.2 quarts of pure antifreeze solute

Let,

x is the number of quarts of pure antifreeze needed to make a 60% solution

The equation to solve becomes, where x is the amount of pure antifreeze to be added is

(1.2 + x )/(3 + x) =0.6

(1.2 + x ) = 0.6 * (3 + x)

(1.2 + x ) = 1.8 + 0.6x

x-0.6x = 1.8 - 1.2

0.4x = 0.6

x = 1.5

Therefore,

1.5 quarts of pure antifreeze to the current solution to make a 60% solution

To know more about "Quarts"

Refer this link:

https://brainly.com/question/16606462

#SPJ4

Answer: -12x

Step-by-step explanation: 4x +4 −2 −2x

Calculate x to the power of 1 and get x.

4x+4×( −2 −2x )

Calculate 2 to the power of −2 and get  41.

4x+4×( − 41x)

Divide x by − 41

​by multiplying x by the reciprocal of − 41 .

4x+4×( −1x×4)

Anything divided by -1 gives its opposite.

4x+4(−x×4)

Multiply 4 and −1 to get −4.

4x−4x×4

Multiply −4 and 4 to get −16.

4x−16x

Combine 4x and −16x to get −12x.

−12x

The conditionals and truth values based on the biconditional, 'Two lines are parallel if and only if they do not intersect', are;

A. If two lines are parallel, then they do not intersect; True

B. If two lines are not parallel, then they intersect; True

C. If two lines do not intersect, then they are parallel; True

D. If two lines intersect, then they are parallel; False

E. If two lines intersect, then they are not parallel; True

The given biconditional is presented as follows;

Two lines are parallel if and only if they do not intersect

Therefore;

Which gives;

A. If two lines are parallel then they do not intersect;

The above statement is a true statement, the correct option is therefore;

True

B. If two lines are not parallel, then they intersect.

The above statement is true and the correct option is; True

C. If two lines do not intersect, then they are parallel.

The above statement is; True

D. If two lines intersect then they are parallel.

The above statement is; False

E. If two lines intersect, then they are not parallel.

The above statement is; True

Learn more about conditionals and truth values here?

https://brainly.com/question/17313919

#SPJ1

Answer:

8.19 - 5.2 = 2.99

Step-by-step explanation:

Hope this is correct and it helps you! =D

Answer: step-by-step

Step-by-step explanation:

answer: 10

to solve you have to follow PEMDAS

Answer:

4 24/1000 simplified/reduced to 4 3/125

Step-by-step explanation:

The number 4 in .024 ends in the thousandths place so the mixed number will be ...

4 24/1000

4 24/1000 is simplified to 4 3/125 because we divide the numerator and denominator by 8 to get 4 3/125.

24 ÷ 8 3

4 ----- = 4 -----

1000 ÷ 8 125

Hope this helps :)

Answer: x^3/3

Step-by-step explanation:

Since you have an exponent outside of your 'x' in parenthesis, you're multiplying the exponents together, that being 1 * 3.

Since the exponent of 3 is being multiplied to only the top area, your 3 stays the same, leaving you with x^3/3

If the exponent is being multiplied to the top and bottom, your answer would be x^3/3*3*3 or x^3/27.

Hope this helps!

Answer:

Negative six times the sum of a number and 16.4is22.8

Step-by-step explanation:

D. -6(r+16.4)=22.8

The sentence is that a negative is six times the sum of a number and 16.4 is 22, then in equation form, it will be -6(r + 16.4) =22.8. Hence, option D is correct.

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way.

There are many different kinds of equations, some of which include:

According to the question, the given statement for the equation is,

16.4 is equal to 22.8 when multiplied by a negative six.

Negative six times means -6 times to any number + 16.4.

Assume that number is r.

-6(r+16.4) = 22.8

Hence, from here it is concluded that option D is correct.

To get more information about Equation :

https://brainly.com/question/10413253

#SPJ5

Answer:

m=-13

Step-by-step explanation:

The shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.

Here we know that we have a right triangle, and we know that:The hypotenuse measures √130 units.

The perimeter measures 14 + √130 units.

If we define:

x = shorter leg.

y = larger leg.

Then, using the Pythagorean theorem, we can write:x^2 + y^2 = √130^2 = 130

And for the perimeter equation we know that:

perimeter = x + y + √130 = 14 + √130

We can simplify this equation to:x + y = 14Then we have the system of equations:

x^2 + y^2 = 130

x + y = 14

Isolating one variable in the second equation we get.

x = 14 - y

Replacing that in the other equation we get:

(14 - y)^2 + y^2 = 130

Now we can solve this for y.

196 - 28y + y^2 + y^2 = 130

2y^2 - 28y + 196 - 130 = 0

2y^2 - 28y + 66 = 0

y^2 - 14y + 33 = 0

Using Bhaskara's formula we can get:

y = (14 ± √( 14^2 - 4*1*33))/2*1y = (14 ± 8)/2

Now, remember that y is the larger leg of the triangle, then:y = (14 + 8)/2 = 11For the value of x we use:

x = 14 - y = 14 - 11 = 3x = 3the shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The length and width of the rectangle is found as 19 inches and 5 inches respectively.

Now, as per the given question;

Let width of a rectangle = w inches

Then, length of a rectangle = 3w + 4

Perimeter of a rectangle = 2(length + width)

Substitute the values in the formula of perimeter.

48 = 2(3w + 4 + w)

48/2 = 4w + 4

24 = 4w + 4

20 = 4w

w = 5

Thus, the width of the rectangle is 5 inches.

Put w = 5 inches in its length.

l = 3w + 4

l = 3×5 + 4

l = 15 + 4

l = 19 inches.

Therefore, the length of rectangle is found as 19 inches.

To know more about the perimeter of rectangle, here

https://brainly.com/question/1698995

#SPJ9

The average speed of Lee is 70 km/hr.

To clear up this trouble we want to understand the concept of average speed.

average speed is given while we divide the overall distance blanketed with the aid of the total time taken.

right here, it's miles given that Lee and Johnson each drove a hundred and forty Km. additionally, it's miles given that lee drove for two hours.

So, average speed of Lee = [tex]\frac{140}{2}[/tex]

                                         = 70 km/hr

Here, the average speed at which Lee drove the car and went to business meeting is 70 km/hr.

To learn more about average speed visit the link:

https://brainly.com/question/12322912

#SPJ4

On Earth, a child weighing 30.5 kilograms would weigh 5 kilograms on the moon.

Given:

So, we have to take out 16.5% of 30.5 kilograms.

After rounding off, the weight becomes 5 kilograms.

Therefore, a child who weighs 30.5 kilograms on Earth would weigh 5 kilograms on the moon.

Know more about weights here:

https://brainly.com/question/25973294

#SPJ9

Answer:

1, R 5

Step-by-step explanation:

Long division

[tex]6 \times 1 = 6\\11 - 6\\= 5\\=1\:R5[/tex]

Answer:

63.59

Step-by-step explanation:

Side of square = √81 = 9

Diameter of circle is 9 so radius is 4.5

Area = πr^2 = 3.14(4.5)^2 = 63.59

Answer:13

Step-by-step explanation:

Answer:

There are no values of f to make this equation true.

Hope this helps.

Step-by-step explanation:

In the second part of the equation, 6( 1/16f  - 3 ), 6 * 1/16f is 3/8f. If both sides subtract a 3/8f and both sides add 18, you get 18.5 = 0 meaning there are no values of f to make this equation true.

Answer: a. (x-8)(x-4)

b. (x-8)(x-6)

c. (x-2)(x-1)

Step-by-step explanation:

a. x^2-12x+32=

x^2-4x-8x+32=

x(x-4)-8(x-4)=(x-8)(x-4)

b. x^2-14x+48=

x^2-6x-8x+48=

x(x-6)-8(x-6)=(x-8)(x-6)

c. x^2-3x+2=

x^2-x-2x+2=

x(x-1)-2(x-1)=(x-2)(x-1)

Answer:

Domain: 1 ≤ x ≤ 6

Range 10 ≤ M(x) ≤ 60

Step-by-step explanation:

M(x) = 10x where x represents the number of tickets bought

Assume nobody goes with Victoria. In that case she will go alone, only 1 ticket is bought and total cost = $10

Maximum 5 friends means total of 6 tickets purchased so total cost is $60

Domain refers to the possible input values ie possible x values. Here the domain is 1 ≤ x ≤ 6 also written as [1, 6]

The range is the total possible set of output values. Here output of the function is cost and cost ranges between 10 and 60 inclusive

So Range = 10 ≤ M(x) ≤60 also written as [10, 60]

Total 5040 passwords can be generated when no digits are repeated

• Permutation in mathematics is an arrangement of objects in an definite order. The elements or sets or things are arranged in sequential order or linear order.

• Permutation is classified into four types :

1) where repetition is not allowed

2) where repetition is allowed

3) objects that are non distinct  

4) circular permutation

• The formula for calculating permutation is n!/(n-r)!

As we are given that the password uses four digits from 0-9 and repetition is not allowed.

So, n = 10 and r = 4

Using the formula for permutation we get

= 10! / (10-4)!

= 10!/6!

= 10 * 9 * 8 * 7 * 6! / 6!

= 10 * 9 * 8 * 7

= 5040

Therefore, 5040 four digit passwords are possible when no digit is repeated.

Learn more about permutaion here

https://brainly.com/question/12468032

#SPJ4

Answer:

The value of the expression is 60.

Answer:

120 songs

Step-by-step explanation:

         Eva=4u

       Hank=1u

Eva+Hank=5u

            5u=600

             1u=600/5

                 =120

Let f(x) be the integrand.

[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \implies \int^{4}_{-2} x^3 \text{ dx}=\approx \frac{1}{2}(2)[-8+64+2(0+8)] \\ \\ =\boxed{72}[/tex]

Answer:

pretty sure its 2.9

Step-by-step explanation:

Answer:2.92 or just 3

Step-by-step explanation:

btw read your lesson and pay attentiom

The range of the data collected by Jonathon is [0.25,0.98]

Given that Jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 and asked to find the range of the data collected by Jonathon.

The minimum value of the data collected by Jonathon is 0.25 and the maximum value of the data collected by Jonathon is 0.98

The range of the given data:(minimum value,maximum value)

Here, The minimum value of the data collected by Jonathon is 0.25

The maximum value of the data collected by Jonathon is 0.98

Therefore,The range of the data collected by Jonathon is [0.25,0.98]

Learn more about range here:

https://brainly.com/question/28135761

#SPJ9

The transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)

Let the coordinate be represented as

(x, y)

For a transformation to preserve distance between points when applied to a figure in the (x, y)-coordinate plane, the transformation must be any of the following:

From the list of options, we have

B . (x,y) → (-x+ 2, y + 7)

This transformation is a translation

Hence, the transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)

Read more about transformation at

https://brainly.com/question/4289712

#SPJ1

The value of x when rounded of to nearest tenth is 7 units.

What happens when a line is bisected?
A line, beam, or other component that divides another line segment into two identical pieces is said to bisect. A "Bisector" in geometry is a line that splits a line into two distinct or equal sections. It is applied to angles and line segments. The term "line segment bisector" refers to a line that cuts through the middle of a line segment, whereas the term "angle bisector" refers to a line that cuts through the apex of an angle.

Given, BD bisects AC thus dividing AC into two equal parts.
Thus value of x will be equal to 7 units.

To learn more about this, tap on: https://brainly.com/question/15212227

#SPJ1

Answer: -1 x 2 x 2 x n

Step-by-step explanation:

-4n

factor

which leads to -1 x 2 x 2 x n

Answer:

314 in²

Step-by-step explanation:

A=3.14r^2

π·10^2≈314

The area of the quarter-circle is 314 in²