What are the values of (-2)^4 and -2^4?
8 and -8
16 and 16
-8 and -8
16 and -16

Solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).

To solve an equation for a given variable is to make the variable the subject of the formula. To do this, isolate the variable to one side of the equation using appropriate properties of equality.

Given the equation,

y = x(ab/a - b)

Multiply both sides by 1/x

y/x = ab/(a - b)

Multiply both sides by (a - b)

y/x × (a - b) = ab/(a - b) × (a - b)

y(a - b)/x = ab

(ay - by)/x = ab

ay - by = abx

ay - by + by = abx + by

ay = abx + by

ay - abx = abx + by - abx

ay - abx = by

a(y - bx) = by

Divide both sides by (y - bx):

a(y - bx)/(y - bx) = by/(y - bx)   [division property of equality]

a = by/(y - bx)

Thus, solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).

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The number of cookies prepared from 1.33 cups of butter are 48.

A ratio in mathematics signifies how many one number appears to contain another. For instance, when there are eight oranges as well as six lemons in a fruit bowl the orange-to-lemon ratio is eight to six, or 8:6, which really is similar to the proportion 4:3.

Now, as per the given question.

In this item, we have been asked to calculate the total number of cookies that may be made by having;

Let 'x' be the cookies made by 1.33 cups of butter.

When, six dozen cookies with 2 cups of the butter = 72 cookies with 2 cups of the butter.

We will use the ratio & proportion formula to solve this problem:

a/b = c/d

Let us now enter the values:

72 cookies/ 2 cups of butter = x / 1.33 cups of butter

Cross multiplying the equations;

72 cookies × 1.33 cups of butter = x × 2 cups of butter

Thus,

x = (72 cookies × 1.33 cups of butter)/2 cups of butter

x = 48

Thus,  48 cookies will be made in proportion to 1.33 cup butter.

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The complete question is-

You are making cookies and are missing a key ingredient eggs. You have most of the other ingredients needed to make the cookies, except you have only 1.33 cups of butter and no eggs. You note that the recipe calls for two cups of butter and three eggs (plus the other ingredients) to make six dozen cookies. You call a friend and have him bring you some eggs. If you use all the butter (and get enough eggs), what number of cookies will you make?

Answer:

I don't know what u wanted me to solve for but here you go

Step-by-step explanation:

Answer:

x = 1 and y = 1

Step-by-step explanation:

The value of x is ±√(42 -  y² - z²).

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.

Given:

x² + y² + z²=k

As, it is given that k = 42.

So, x² + y² + z²=k

x² + y² + z²= 42

x² = 42 -  y² - z²

x=±√(42 -  y² - z²)

Hence, the value of x is ±√(42 -  y² - z²).

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The maximum income the doctor can get in a day is $1280

Time required for routine office visits = 15 minutes

Time required for physical visits = 45 minutes

Maximum physical visits possible in a day = 10

Maximum routine visits possible in a day = 12

Available hours for appointment = 9 hours or 540 minutes

Cost of routine appointment = $60

Cost of physical appointment = $70

In order to maximize income, she should do maximum possible routine visits as it gives more return in less time and the remaining time can be used to do physical visits, therefore:

No. of routine visits the doctor should do = 12

Time consumed in 12 visits = 12*15 = 180 minutes

Time remaining = 360 minutes

No. of physical visits she should do = 8

Time consumed in 8 physical visits = 8*45 = 360 minutes

Total income the doctor will generate in a day  = 12*60 + 8*70

= 720 + 560 = $1280

Hence, the maximum income of the doctor will be $1280

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The average (division) change of the price of one share per one day is $7.896

The given parameters are

Total = $39.48

Number of days =  5 days

The average (division) change of the price of one share per one day is calculated as

Average = Total/Number of days

So, we have

Average = $39.48/5

Evaluate the quotient

Average = $7.896

Hence, the average (division) change of the price of one share per one day is $7.896

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The number of miles in a day at which the rental costs for Company A and Company B are the same is 200 miles per day

Let the truck is driven X miles per day

Charges of company A will be = 90+0.4X

Charges of company B will be =30+0.7X

Let us find out value of X when charges of both companies are same

which means that   90+0.4 X= 30+0.7X

                            90-30      = 0.7X-0.4X

                            60    = 0.3X

                             60/0.3 = X

                             X= 200

The charges of both companies will be same if truck is driven 200 miles per day

Company A will have better deal if truck is driven more than 200 miles per day ( because per mile rate of company A is less than company B)

A mile is defined as 1760 yards, or around 1.6 kilometers, in length. They traversed the desert for 600 km by car. She's only a half-mile away. singular noun. A large distance is indicated by the word "miles," particularly in the phrase "miles distant."

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Answer:

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

The two given angles form a linear pair.

Sum of the two angles is 180°, set equation and solve for e:

Angle between hour and minute hand= 204°

a figure which is formed by two rays or lines that shares a common endpoint is known as Angle.

The hour hand has covered 2 h and 48 min from position 12 o'clock (reference position). And in case of minute hand 22 min from reference. Required angle is angle covered by minute hand minus the angle covered by hour hand (clearly minute hand has covered greater angle in comparison with hour hand).

For calculating angle covered by minute hand:

In 60 min the min hand covers 360°

60 min = 360°

1 min = 6° ; 48 min = 288°

For calculating angle covered by hour hand:

12 h ( of hour hand) = 360°

1 h = 30°

For [2 + (48/60)] h, the angle covered= [2 + (48/60)]*30° = 84°

Angle between hour and minute hand = (288–84)° = 204°

It is the acute angle between hour and minute hand. For finding reflex angle subtract the obtained acute angle from 360°. So the reflex angle will be 299°.

Angle between hour and minute hand= 204°

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Answer:

Step-by-step explanation:

If a - b = b = c = 2, what is the value of: (a − b)² + (b − c)²/(a - c)²​ ihx-ezjm-mww​

(a) The linear equation giving the median salary "y" in terms of the year "x" is y = 0.034x + 1.266.

(b) The median player salary in the year 2048 will be approximately $2.9.

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Answer:

[tex]x=\frac{ln(12)}{3}[/tex]

Step-by-step explanation:

We can solve this equation by taking the natural log of both sides.

This gives us the equation: [tex]ln(e^{3x})=ln(12)[/tex]

And the definition of natural log is basically, "what do I have to raise e to, to get this result"

The result is just e^3x, so I have to raise e to what? Well that's just 3x, you could also use log properties to bring the exponent in front and realize ln(e) = 1

So this gives us: [tex]3x=ln(12)[/tex]

Now divide both sides by 3: [tex]x=\frac{ln(12)}{3}[/tex]

Answer:

to figure out the total for each person what you need to do is divide 483.30 by 5

483.30 / 5= 96.66

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Given:

[tex]2 \frac{2}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]

Convert the mixed number into an improper fraction by multiplying the whole number with the denominator of the fraction, adding it to the numerator of the fraction, and placing it all over the denominator of the fraction:

[tex]\implies 2\frac{2}{7}=\dfrac{2 \times 7+2}{7}=\dfrac{16}{7}[/tex]

Therefore:

[tex]\implies \dfrac{16}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]

[tex]\implies \dfrac{\frac{16}{7}}{0.6x}=\dfrac{\frac{4}{21}}{0.25}[/tex]

Cross multiply:

[tex]\implies \dfrac{16}{7} \times 0.25 = \dfrac{4}{21} \times 0.6x[/tex]

[tex]\implies \dfrac{16\times 0.25}{7} = \dfrac{4\times 0.6x}{21}[/tex]

[tex]\implies \dfrac{4}{7} = \dfrac{2.4x}{21}[/tex]

Cross multiply again:

[tex]\implies 4 \times 21=2.4x \times 7[/tex]

[tex]\implies 84=16.8x[/tex]

Divide both sides by 16.8:

[tex]\implies \dfrac{84}{16.8}=\dfrac{16.8x}{16.8}[/tex]

[tex]\implies 5=x[/tex]

[tex]\implies x=5[/tex]

Answer:

The value of x is 5.

Step-by-step explanation:

Let's solve for the value of x,

→ 2 2/7 : (0.6x) = 4/21 : 0.25

→ 16/7 : (0.6x) = 4/21 : 0.25

→ (16/7) × 0.25 = (4/21) × 0.6x

→ 4/7 = (2.4x)/21

→ 2.4x × 7 = 4 × 21

→ 16.8x = 84

→ x = 84/16.8

→ [ x = 5 ]

Hence, the value of x is 5.

[tex]2A +B = -2 \cdot (2z +8 -2z-4) = -2 \cdot 4 = -8[/tex]

The quotient is 10/3 .

Sharing something equally is one way to view division.

Whatever we all equally share in this problem must be a part, not a whole. What are some examples of things we typically consider to be parts? We do, however, discuss food in casually.

3/4  of a pan of brownies or 2 1/2slices of pizza could be included. Additionally, we weigh some goods in division of a pound, notably bulk foods and sweets.

There are some materials that we purchase in division of a whole, such as lengths of fabric, rope, or ribbon that are sold in units of a yard. Any of those objects could be divided into equal portions as part of your word puzzle. Here are two illustrations:

At the supermarket, Dayana and her 3/4 friends purchased a candy bag weighing 2 1/2  lb. How much candy will each individual receive if they decide to divide it equally?

(2 1/2)/(3/4)= (5/2)/(3/4)= (5[tex]\times[/tex]4)/(3[tex]\times[/tex]2)=20/6=10/3

The quotient is 10/3 .

This means that after Dayana cuts each piece of board, its length will be  10/3 yards.

Therefore, the quotient is 10/3.

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1, 3, and  5 are true

Answer:

y = -0.6x - 1.6.

Answer:

27

Step-by-step explanation:

Say the youngest sibling is a. Anna would be a+1, and the oldest would be a+2. If the sum of all of them are 81, then 3a+3 = 81. minus three on both sides, and you get 78. So 3a = 78/3 = 26. if the youngest is 26, then Anna will be a + 1 so 27.

The age of Anna where she is the middle of three siblings is 27 years.

Given data:

Let's represent Anna's age as "x." Since Anna is the middle sibling, the ages of her siblings would be x - 1 and x + 1, since they are consecutive integers.

According to the information given, the sum of their ages is 8181:

x + (x - 1) + (x + 1) = 81

Now, combine like terms:

3x = 81

Divide both sides by 3:

On simplifying the equation:

x = 81/3

x = 27

Hence, Anna's age is 27 years.

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The complete question is attached below:

Anna is the middle of three siblings whose ages are consecutive integers. If the sum of their ages is 81, find Anna's age.

The energy consumes by the residential sector in 2008 was 1200 trillion btu. This is a problem from percentage.

Here, the energy consumption in different sector in New York State (2008) is

Transportation sector 28%

Residential sector 30%

Commercial sector 32%

Industrial sector 10%

So, the total energy consumption is = 28% + 30% + 32% + 10% =100%.

Therefore, the power consume by Residential sector is 4000x30% = 1200 trillion btu.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number; it has no unit of measurement.

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Answer:

y = -4x -4

Step-by-step explanation:

we need to get two points to calculate the gradient

points chosen are (-2,3) and (-3,7)

Gradient = change in y coordinates/ change in X coordinates

G = (7-3)/(-3- -2)

= 4/-1

= -4

to write the equation in slope -intercept form we need one known point (-2,3) and one unknown point (X,y) and the gradient.

G = ∆y/∆x

-4 = (y - 3)/ (X - -2)

-4 = (y-3)/ (X+2)

we now cross multiply

-4(X + 2) = y - 3

-4x -8 = y-3

-4x -8+4 = y

y = -4x -4

Mr. Lopez spread the stones at a pace of 0.059 cubic yards per hour.

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

"Per unit of time" is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).

The word "per" is used to denote the division of the units of the two measurements that make up a rate when discussing its units (for example a heart rate is expressed "beats per minute"). A rate that is defined using two numbers of the same units will provide a dimensionless quantity that can be stated as a percentage (for instance, the global literacy rate in 1998 was 80%), fraction, or multiple. Examples of these rates include tax rates and literacy rates.  

2/34 = 0.0588 equals to 0.059 ( approximately).

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The area of triangle ABC with vertices is 22 square units

The vertices are given as:

A(4, -3) B(9,-3) , and C(10, −11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

This gives

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Evaluate the sum of products

Area = 0.5 * |44|

Remove the absolute bracket

Area = 0.5 * 44

Evaluate

Area = 22

Hence, the area of ABC with vertices is 22 square units

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Answer:

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

From the right triangle we get the sum:

From the exterior angle theorem we get the sum:

Subtract the first equation from the second to get:

Answer:

y = 25

Step-by-step explanation:

Solution 1:

The line X is on, is a supplementary angle.

180-115 is 65

There are two Xs

A triangle adds up to 180

180- 65- 65= 50

50/2= 25

Solution 2:

The line X is on is a supplementary angle.

180-115 is 65

180- 65 - 90 (right angle)= 25

Answer:

No

Step-by-step explanation:

To know if a number is completely divisible by 3, you can add up its digits. If its digits equal a number divisible by 3, then the number itself is divisible by 3.

9817

9 + 8 + 1 + 7

= 25

2 + 5

= 7

Since 25 isn't divisible by 3, 9817 isn't completely divisible by 3 either.

Have a lovely rest of your day! :)

The equation that can be used to find x, which is the width of the walkway will be (16 + 2x)(12 + 2x) = 396.

It should be noted that an expression is used to show the relationship that's exists between the variables.

The equation that can be used to find x, which is the width of the walkway will be:

= (16 + x + x) (12 + x + x) = 396

= (16 + 2x)(12 + 2x) = 396

In conclusion, the correct option is C.

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Answer:

b=5

Step-by-step explanation:

Here,

b + 13 = 18

or, b = 18 - 13

or, b = 5

Hence, b=5

Answer:

B = 5/b, b  0

Step-by-step explanation:

Bb+13=18

Subtract 13 from both sides.

Bb=18−13

Subtract 13 from 18 to get 5.

Bb=5

The equation is in standard form.

bB=5

Divide both sides by b.

b

bB

​

=

b

5

​

Dividing by b undoes the multiplication by b.

B=

b

5

​

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

Work Shown:

[tex]a^2 + b^2 = c^2 \ \ \text{ ... pythagorean theorem}\\\\12^2 + 9^2 = c^2\\\\144 + 81 = c^2\\\\225 = c^2\\\\c^2 = 225\\\\c = \sqrt{225}\\\\c = 15\\\\[/tex]