Gracie has made 2 gallons o punch that contains 50% juice. After Gracie pours out some of her mixture and replaced with an equal amount of pure 100% juice, she has 2 gallons of punch that contains 65% juice. How many gallons of the original mixture did Gracie pour out? Express your answer as a common fraction.

Answer:

x = 4

y = 28

Step-by-step explanation:

1) y = 7x

2) y = 2x + 20

substitute y = 7x into equation 2:

7x = 2x + 20   now you can solve for x:

7x - 2x = 20

5x = 20

x = 20/5 = 4

Plug x = 4 into either equation 1 or 2 to solve for y:

y = 7x = 7(4) = 28

Answer:

5.83095189485

Step-by-step explanation:

Formula to find the area: A=πr^2

Formula to find circumference: C=2πr

Diameter is twice the length of the radius, so if you're given diameter of 3, the radius is half of that, which that would be 1.5.

A=π(1.5)^2 A= 3.14x1.5^2 = 7.065

Don't forget to round that and that becomes 7.07.

C=2π(1.5) C= 2x3.14x1.5 = 9.42

That stays as it is.

Area= 7.065

Circumference= 9.42

wish I could help but I don’t learn these things

Answer:

answer is in picture

Step-by-step explanation:

Answer:

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question

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Answer:

It would look like that I think

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

I think the answer of this question is 24.

Answer:

n = 15

Step-by-step explanation:

This is a right triangle, and so the Pythagorean Theorem applies:

x^2 + 8^2 = 17^2

Solving for x^2:  17^2 - 8^2 = 289 - 64 = 225, and so x = 15.

n = 15

Answer:

22

Step-by-step explanation:

I timesed 11 by 12 which is 132 and then timesed 10 with 11 which then gave me 110. I then subtracted 132 with 110 which gave me the answer 22. if we remove 11 from the 22 books we then end up with 11. then times it by 12 = 132. then if you subtract 10 of the 22 books then we end up with 12. then times it by 11 which is 132 as well.

Step-by-step explanation:

n = 0 : 2(0) -1 = -1

n = 1 : 2(1) - 1 = 1

n = 2 : 3

n = 3 : 5

n = 4 : 7

n = 5 : 9

sum = -1 + 1 + 3 + 5 +7 + 9 = 25

The equation given as -y = 3x is a direct variation. The constant of variation is - 1/3

It shows the relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.

A straightforward correlation between two variables is referred to as direct variation. In this case, the constant of variation will be k.

This will be Illustrated as:

y = kx

-1 = 3k

Divide

k = -1/3

The constant is - 1/3.

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The graph of the function g(x) is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) equals log2 x

Express the equation properly

So, we have

f(x) = log₂(x)

Also, we have

g(x) = -log₂(x - 3)

The transformation from f(x) to g(x) is that:

This means that

g(x) = -f(x - 3)

So, we apply the above transformations on the graph of f(x) to form g(x)

See attachment for graph of g(x)

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Answer:

2. -1/2

4. 3/2

Step-by-step explanation:

Gradient = (Y1 - Y2)/(X1 - X2)

2.

Point 1: (4, -1)

Point 2: (-2, 2)

Gradient = (-1 - 2)/(4 - (-2)) = -3/6 = -1/2

3.

Point 1: (4, 6)

Point 2: (-4, -6)

Gradient = (6 - (-6))/(4 - (-4)) = 12/8 = 3/2

What is the image of ( 12 , − 4 ) after a dilation by a scale factor of 1/4 centered at the origin is (3, -1)

Transformation is the movement of a point in the coordinate plane. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease of a figure by a scale factor k. If the value of k > 1, then it is an enlargement but if k < 1, it is a reduction.

The point (12, -4) is dilated by a scale factor of 1/4 using the rule (x, y) ⇒ (x/4, y/4). The new point is (4, -1)

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In the recorded test scores 90 is the mode, as it appears most frequently in the set of ff test scores.

Job applicants submitted their ff test results, which were as follows: 65, 68, 70, 75, 88, 90, 90, 91, and 92. Following that, the Mean (Average) is 81, Median (Middle) is 88, and Mode (Most Common) is 90. The mode can be calculated quite easily.

After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.

The mode is the one that is most prevalent. the quantity that happens the most frequently, or the quantity that appears the most frequently overall. The mode of the numbers 4, 2, 4, 3, 2, and 2 is 2, since it appears three times, more than any other number. The most frequent number in a set of numbers is called the mode.

To find the mode, we first need to put the test scores in order from lowest to highest:

65, 68, 70, 75, 88, 90, 90, 91, 92

Then we can count how many times each number appears:

65: 1 time

68: 1 time

70: 1 time

75: 1 time

88: 1 time

90: 2 times

91: 1 time

92: 1 time

As we can see, the number 90 appears the most with 2 times, so the mode of this set of data is 90.

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Answer:

[tex]log_{a}[/tex] 12

Step-by-step explanation:

using the properties of logarithms

• nlog x ⇔ log[tex]x^{n}[/tex]

• log x + log y = log (xy)

[tex]\frac{1}{2}[/tex] [tex]log_{a}[/tex] 16 + [tex]\frac{1}{3}[/tex] [tex]log_{a}[/tex] 27

= [tex]log_{a}[/tex] [tex]16^{\frac{1}{2} }[/tex] + [tex]log_{a}[/tex] [tex]27^{\frac{1}{3} }[/tex]

= [tex]log_{a}[/tex] [tex]\sqrt{16}[/tex] + [tex]log_{a}[/tex] [tex]\sqrt[3]{27}[/tex]

= [tex]log_{a[/tex] 4 + [tex]log_{a}[/tex] 3

= [tex]log_{a}[/tex] (4 × 3)

= [tex]log_{a}[/tex] 12

Answer:

7 is the answer

Step-by-step explanation:

Han is wrong , we do not agree with him. The value of the 7 in 735,208 is not the 10 times the value of the 7 in 137,342.

The value of 7 here refers to the place value of 7 , in 735,208  7 is at lakhs place whereas in 137,342 , 7 is in thousandth place .

Therefore , Han is wrong as because if we will the 7 in 137,342. when multiplied by 10 will go to the ten thousandth place and not the lakh place.

The  place value is a measure which is used to represent the position of each digit in a number . Based on their position in the number, digits are assigned place values such as ones, tens, hundreds, thousands, ten-thousands, and so on. For example, 1 in 512400 has a place value of ten thousands, i.e. 10000.

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Answer:

A directed segment is a segment that has distance (length) and direction. Hope this helps.

The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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XY = 6 units  is the length of XY in AXYZ .

What is a right-angle triangle, exactly?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.

                         Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

using the sine ratio in the right triangle and the exact value

  sin30° = 1/2, then

    sin30° = XY/XZ = XY/12 =  1/2  ( cross - multiply)

     2XY = 12  ( divide both sides by 2 )

        XY = 6

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The complete question is -

Use right triangle XYZ to complete the following parts.

Part A

12

XY =

30°

? Question

What is the length of XY in AXYZ?

Type the correct answer in the box. Use numerals instead of words.

units

Answer:

1. C

2. D

Step-by-step explanation:

Answer:

For the first question it is C(3rd one) and for the second question it is D(last one)

Step-by-step explanation:

So lets think about what we know here.

We know that Lena was walking at a normal speed.

Then she stopped.

Then she moved slowly.

Since x is time, and y is distance from school, we know that x is going to costantly change, while y will depend on what is happening.

First off, we know she is goiong to school. now away from it. This means that any graph with a increasse in the y value will be incorrect. This gets rid of a and b, whihc are the first two answers.

So y should go up nomrallu, since she was just walking at first.

Now, we know that the distance from school must stop, and then begin to decrease at a slower pace. When lookking at the graphs, only C continues to decrease, while D is constantly not moving.

So the answer is C.

Next.

we know that kala drives at a constant speed.

We  know she starts going faster.

Then she slows down.

So we can isntantly remove any graph that completly stops in speed, which means y would be 0, since she is always moving. This gets rid of A and B.

Then we have  C and D

Well, remember that after Kala is going at a normal speed, she sped up.

Only one graph has a large spike in speed after a constant speed. THis is D.

So the answer must be D

Hope this helps!

Answer:

1568

Step-by-step explanation:

14 x 17.5 x 6.4 = 1568

Answer:

Step-by-step explanation:

To solve this problem, you have to find the volume.

Volume:

[tex]\sf{V=l*w*h}[/tex]

Length is 14

Width is 17.5

Height is 6.4

Solve.

Multiply.

[tex]\sf{14*17.5*6.4=1568}[/tex]

[tex]\large\boxed{1568}[/tex]

Therefore, the correct answer is 1568.

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Here,

Given : The parallelogram  has M angle  =100 degree

And to Find :L angle

In a parallelogram sum of the adjacent angle is 180°, So

So ,

Using this parallelogram property ,

we find :

=>100 + L =180

=> L = 80

Thus,

We get the L value using parallelogram properties.

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

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Answer:

8 feet

Step-by-step explanation:

4 parking spots ('4x'), three one-foot dividers = 35

4x + 3 = 35

4x = 32

x = 8

Answer: 8ft.

Step-by-step explanation:

Were doing this in class

Answer:

I'm already past this but the answer is 21

The measure of angle B is, 67°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Interior angles are,

⇒ ∠ C = 83°

⇒ ∠ B = 6x + 7

An exterior angle is,

⇒ ∠ A = 15x

Now, We know that;

The sum of two interior angles in a triangle is equal to the exterior angle in a triangle.

⇒ 83° + 6x + 7 = 15x

⇒ 90 = 15x - 6x

⇒ 90 = 9x

⇒ x = 10

Thus, The measure of B is,

⇒ m ∠B = 6x + 7

             = 6×10 + 7

             = 60 + 7

             = 67

⇒ m ∠B =  67

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