For his birthday party eugene mixed together 10 gal. of brand a fruit punch and 8 gal. of apple juice. if brand a contains 28% fruit juice, then what percent of the final mixture is fruit juice?

The domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.

We are given the two functions as:

f (x) = x - 4

g (x) = x² - 16

Now, first, we need to subtract f (x) from g (x).

So, we get that:

g (x) - f (x) = x² - 16 - (x - 4)

g (x) - f (x) = x² - 16 - x + 4

g (x) - f (x) = x² - x - 12

Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.

Therefore, we get that the domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.

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Answer:

The fourth option

Step-by-step explanation:

Formula to find the area of a circle is [tex]\pi r^{2}[/tex]

[tex]\pi 7^2[/tex]

[tex]49\pi[/tex]

Using the rules of exponents, the expression (5 x^−5 y^3)^−2 is equivalent to x^10 / (25 y^6) or "x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity".

Given: (5 x^−5 y^3)^−2

1. Distribute the power of two using the Power of a Power Rule. "When a power is raised to another power, multiply the exponents."

5^−2 x^(−5)(−2) y^(3)(−2) =  5^−2 x^10 y^-6

2. Use Negative Rule of Exponent. "A number with a negative exponent should be put to the denominator, and vice versa."

5^−2 x^10 y^-6 = (x^10) / (5^2 y^6)

3. Simplify the constant term.

(x^10) / (5^2 y^6) = x^10 / 25 y^6

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Answer:

Mitchell owes his mom =$18. sum of money his mom reduced =$12.

Step-by-step explanation:

SO IT 6 DOLLARS

Answer: $6

Explanation: $18-$12=$6

Hope this helps!!! have a nice day!

In linear equation, 1875  does Hoppy weight .

What are instances of linear equations?

A = 42b = 56c

a : b : c  = 42 : 100 : 75

total Mr Flopsy weights = 2500

then  Hoppy weight =  75 = 2400/100 * 75

                                  = 1875

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The inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g: TRUE

So,

Given inverse function: f₁(x)=b^(x-h)

First, find out the inverse of this function.

Switch the variables x & y as follows;

Solve for y as shown below and take logarithm both sides:

So,

From the first equation we get the inverse of as f₁ follows:

Therefore, the statement "the inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g" is TRUE.

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The Domain of set is {0, 2, 4, 6}

The Range of the set is {3, 2, 1, 0}

What is Range of set?

The range is the set of possible output values, which are shown on the y-axis.

The function is given as;

y = -1/2 x + 3

Now, The values of x are given as;

x = 0, 2, 4, 6

Hence, The value of y are find as;

When x = 0

y = -1/2 * 0 + 3 = 3

When x = 2

y = -1/2 * 2 + 3

y = 2

When x = 4

y = -1/2 * 4 + 3

y = 1

When x = 6

y = -1/2 * 6 + 3

y = 0

Hence, All values of y are {3, 2, 1, 0}

So, The Domain of set is {0, 2, 4, 6}

The Range of the set is {3, 2, 1, 0}

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The statement that best represents the range of the function in this context is 0 <= L(c) <= 500

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

L(c) = 10c

From the question, we understand that:

Maximum number of children = 50

This means that

c =50

So, we have

L(50) = 10 * 50

Evaluate

L(50) = 500

Hence, the statement that best represents the range of the function in this context is 0 <= L(c) <= 500

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The electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.

The correct option is D.

A negative point charge has an electric field focused at it. Thus, the electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.

The electric field is defined as that of the electric force per unit of charge. The direction of the field is assumed to represent the direction of the force it would impose on a positive test charge. The electric field radiates outward from the a positive charge and inward from a negative point charge.

The field lines never cross. The field lines lie parallel to the charge's surface. The quantity of charge and indeed the number of field lines are proportionate.

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I understand that the question you are looking for is:

What is the direction of the electric field directly to the east of an isolated negative point charge?

A. north

B. south

C. east

D. West

He will use 18 teaspoons of baking powder for the oatmeal recipe

A recipe requires 2 cups of flour and 2.5 cups of oats

For each cup he must add 1.5 teaspoons of baking powder

He uses 15 cups of oats

Each recipe uses 2 cups of flour, the teaspoons of baking powder used in one recipe is

1.5 × 2 = 3

2.5 cups of oats is used for one recipe, he uses 15 cups of oats, this means that the number of recipes is 6 (15/2.5)

Since the number of recipes is 6 and 3 teaspoon of baking powder is used for one recipe, then the number of teaspoons used is

= 6 × 3

= 18

Hence he used 18 teaspoons of baking powder

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If PQRS is a square & TR= 17, then

PR= 34

QS= 34

QT= 17

PQ= [tex]17\sqrt{2}[/tex]

A square in geometry is a two-dimensional plane figure having four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are somewhat comparable, however only the opposite sides of a rectangle are equal. So, only if all four of a rectangle's sides are the same length can it be said to be a square.

A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is another name for a rectangle with two sides that are opposite and the same length.

The following is a list of a square's most significant characteristics:

We know that,

Diagnose of a square are equal in magnitude and bisect each other.

So, In the given figure,

diagonals PR and QS are bisected at T.

RT = PT = 17

Hence,

PR=2RT=2*17=34

PR= 34

QS=34

[tex]QT=\frac{1}{2}QS = \frac{1}{2}*34 = 17[/tex]

QT=17

PQ = side of square

Let PQ= QR= a

In ΔPQR

[tex]PQ^{2} + QR^{2} = PR^{2}[/tex]

[tex]PQ^{2}+ PQ^{2} = 34^{2}[/tex]

[tex]2PQ^{2} = 34*34[/tex]

[tex]PQ = \sqrt{17*34} = 17\sqrt{2}[/tex]

PQ = [tex]17\sqrt{2}[/tex]

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Answer:

==============================

We have the following linear equation to represent given situation:

Solve it for x to get the average number of miles:

In linear equation, He ride 3 miles each day.

Variable: x = Constant distance distance traveled each day.

Equation : 10+4x= 22

What is a formula for linear equations?

Total distance needs to travel = 22 miles

Distance already traveled = 10 miles

He will ride bicycle for 4  more days.

Let x = Constant distance distance traveled each day.

Total distance = 10+4x

10+4x = 22

4x = 22 - 10

4x = 12

  x = 3

Hence, he rode 3 miles each day.

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The simplified form is [tex]4 ^{\frac{2+t}{3} }[/tex].

Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.

The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.

Converting mixed numbers to an improper fraction,

[tex]16^{1/3} . 4^{t/3} \\4^{2/3} .4^{t/3} \\4^{\frac{2+t}{3} }[/tex]

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True response is that the function represented by the graph is Increasing on (-∞, 0) and decreasing on (0, ∞)

A function is said to be increasing in its domains if the value of its range is increasing in that domain.

Similarly, if the function is decreasing in its domain then it's range must be decreasing with the domain.

When the value of x(domain) is increasing on the left side. The value of y(range) is increasing constantly. But when the value of x increases further after 0, then the value of y is decreasing constantly.

So we can say, the following function represented on the graph is increasing in the interval of ( -∞,0) and decreasing in (0,∞).

As per the situation described in the graph the option third which say increasing on (×,0) and decreasing on (0,×).

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The function y = 4 (3) x which can also be written as 12 x - y = 0 is a linear function.

We are given the function:

y = 4 (3) x

Multiply 4 and 3, we get that:

y = 12 x

Now, subtract y from both the sides, we get that:

12 x - y = 0

We can see that the degree of each variable is 1 .

So, it will be a linear function.

Therefore, we get that, the function y = 4 (3) x which can also be written as 12 x - y = 0 is a linear function.

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The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

The expression is given as

R = x^2/y

Where

y = 3.8 x 10^5

x = 5.9 x 10^4

Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y

So, we have

R = (5.9 x 10^4)^2/3.8 x 10^5

Evaluate the exponent

So, we have

R = 34.81 x 10^8/3.8 x 10^5

Evaluate the quotient

So, we have

R = 9.16052631579 x 10^3

Approximate the above expression

So, we have

R = 9.2 x 10^3

Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

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 [tex]\frac{ln(e^2)}{2}[/tex] = 1, by properties of logarithm.

Given: [tex]\frac{ln(e^2)}{2}[/tex]

Now,

=> [tex]\frac{ln(e^2)}{2}[/tex] = [tex]\frac{2 (ln(e))}{2}[/tex]

=>  [tex]\frac{ln(e^2)}{2}[/tex] = ln (e)

=>  [tex]\frac{ln(e^2)}{2}[/tex] = 1

Hence,  [tex]\frac{ln(e^2)}{2}[/tex] = 1, by properties of logarithm.

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Step-by-step explanation:

Technically none of these are the right answer. The decrease in his account would be -27.

But out of the given choices, I'll go with option C because he has $8 left in his savings

The domain of the function is (0,∞) , {x|x>0}

and the range of the function is (−∞,∞),  {y|y ∈ R}

given the function is y = 3 log x

Set the argument in  log x greater than 0 to find where the expression is defined.

x > 0

The domain is all values of x that make the expression defined.

Interval Notation:

(0,∞)

Set-Builder Notation:

{x|x>0}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{y|y∈R}

Determine the domain and range.

Domain: (0,∞) , {x|x>0}

Range :  (−∞,∞),  {y|y ∈ R}

Hence we get the required domain and range of the given function.

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Finding LCM for the problem, you should cut the cornbread into 6 parts, Sue will get 3 parts and Dena will get 2 parts.

LCM is referred to as the least common multiple for a set of numbers that can be divided by the same whole number as a result.

At first, we have to find LCM of 2 and 3, which is the denominator of 1/2 and 1/3, and its 6 and we will cut it into 6 pieces.

So, Sue will get 3 pieces from the cornbread ( 3/6 = 1/2 ) and Dena will get 2 pieces from the cornbread ( 2/6 = 1/3 ).

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Answer:

196 degrees, reflex.

Step-by-step explanation:

The angles fit around a point, therefore, they add up to 360 degrees.
Let [tex]x[/tex] be the size of the third angle.

[tex]x + 113 + 51 = 360 \\x + 164 = 360 \text{ / Subtract 164 on both sides} \\x + 164 - 164 = 360 - 164} \\x = 196[/tex]

The angle is larger than 180 degrees and smaller than 360 degrees, therefore, its a reflex angle.

Answer:

196 degrees, reflex.

Step-by-step explanation:

Answer:

[tex]\left[\begin{array}{ccc}-48&-60\\44&30\end{array}\right][/tex]

Step-by-step explanation:

0.5 X + 3A = B implies

X = 2(B-3A)

3A simply means multiplying each cell by 3

[tex]3A = \left[\begin{array}{ccc}12&24\\-33&-3\end{array}\right][/tex]

B-3A is a corresponding cell by cell subtraction

[tex]B-3A = \left[\begin{array}{ccc}-24&-30\\22&15\end{array}\right][/tex]

Finally multiply that by 2, result is at the top.

The values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2) are ( 0, B, 2B)

In the above question, a horizontal line is given whose equation is Ax + By = C which passes through a point (-4, 2)

We can make two observations from the given information of horizontal line passes through point (-4,2) which are as follows:

1. The slope of a horizontal line will be parallel to the x-axis whose slope will be, m=0.

2. The given point and the line meet at (-4,2).

Now as the point (-4,2) lie on the line it will satisfy the equation of the horizontal line

We get,

A(-4) + B(2) = C

-4A + 2B = C ..... eqn 1

Also, we can write the given equation in the slope-intercept form which is

y = mx + c

By = -Ax + C

y = [tex]\frac{-A}{C}[/tex]x + [tex]\frac{C}{B}[/tex]

So, we can imply that m =  [tex]\frac{-A}{C}[/tex] = 0

A = 0

Putting this in eqn 1 we get,

-4A + 2B = C

0 + 2B = C

C = 2B

Hence, we conclude that values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2) are ( 0, B, 2B)

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A sequence of events or things is a number of events or things that come one after another in a particular order. The nth term of

for 6,21,46,81 is 5n²+1.

A sequence of events or things is a number of events or things that come one after another in a particular order.

Write down the nth term of this quadratic number sequence.

6,21,46,81...

number sequence has nth term = an² + bn + c.

Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence =6,21,46,81

1st difference = 15,25,35

2nd difference = 10,10

If you divide the second difference by 2, you will get the value of a.

10/2=5

So the first term of the nth term is 5n².

ext, substitute the number 1 to 4 into 5n².

n=1,2,3,4

5n²=5,20,45,80

Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

5n²+1=6,21,46,81.

Therefore nth term for 6,21,46,81 is 5n²+1.

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Answer:

y = 105

x = 31

Step-by-step explanation:

We have y and 75 as consecutive interior angles.
(Consecutive interior angles are are found between the two parallel lines and on the same side of the transversal)

Sum of two consecutive interior angles = 180°

so we have y + 75 = 180
y = 180-75 = 105

So y = 105

y and (3x+12) are opposite angles and are equal
So 3x+12 = y
3x + 12 = 105
3x = 105-12 = 93
x = 93/3 = 31

So x = 31

Answer: 1955 and 2005 .

Year

1955

1960

1965

1970

1975

1980

1985

1990

1995

see if i help u now ?

Step-by-step explanation:

Answer:

365 * 88 (^7) =  B=10

Answer:

y = - x + 8

Step-by-step explanation:

y = - x + 8