What adds to be the bottom number but also multiplies to be the top? The top is 36 and the bottom is 12.

The result of simplifying the expression  x³/₅ / x³/₁₀  using the exponent rules is [tex]\sqrt[10]{}[/tex](x³)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

[(x)³/₅ ] /  [(x)³/₁₀]

Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:

x⁽³/⁵ ⁻³/¹⁰⁾

(x)⁽⁶⁻³⁾/¹⁰

(x)³/¹⁰

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt[10]{}[/tex](x³)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

7 14/15

Step-by-step explanation:

The total cost of the laptop, including the sales tax, is $974.57.

The total cost of the laptop is the addition of the listed price and the sales tax (dollars).

The listed price refers to the retailer's (seller's) price before the addition of the sales tax.

After adding the sales tax to the listed price, the total cost is obtained.

Therefore, sales tax, which is a proportional tax, increases the cost of goods and services to consumers.

Listed price before tax = $887.99

Sales tax rate = 9.75%

Total cost after tax = $974.57 ($887.99 x 1.0975)

Thus, the total cost of the laptop after factoring in the sales tax is $974.57.

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Answer:

r = -10

Step-by-step explanation:

1. Distribute

1-(r+2)=9

1-r-2=9

2. Subtract the numbers

1-r-2=9

-1-r=9

3. Rearrange the terms

-1-r=9

-r-1=9

Solution: r = -10

The value of BC the nearest hundredth is 15.01 .

From the image , we are able to see that CA = seven and angle A = 65°

Using ,Trigonometric Ratios , we get

Tan A = Perpendicular / Base

Tan 65° = BC / CA

2.144 =BC / 7

2.144 ×7 = BC

15.011 = BC

On rounding off to the closest hundredth , we have a tendency to get BC = 15.01

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The multiplication of the expression ( 3 + √2)( 4 +√2 ) is 14 + 7√2.

Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.

Consider the expression,

y = ( 3 + √2)( 4 +√2 )

Using the distributive property,

a( b + c ) = ab + ac

y = ( 3 + √2)( 4 +√2 )

y = 3( 4 + √2 ) + √2( 4 + √2 )

y = 3 × 4 + 3 × √2 + √2 × 4 + ( √2 )²

y = 12 + 3√2 + 4√2 + 2

y = 14 + √2( 3 + 4 )

y = 14 + 7√2

The value of the expression ( 3 + √2)( 4 +√2 ) when simplified is 14 + 7√2.

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A composite function exists as a function that depends on another function. The value for (f(1+h)-f(1)) / h = 2

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the function be f(x) = 2x - 3

f(1+h) = 2 (1+h) -3 = 2h - 1

f(1) = 2(1) - 3 = -1

(f(1+h)-f(1)) = (2h - 1 ) + ( -1) = 2h

simplifying the equation, we get

(f(1+h)-f(1)) / h = 2h/ h

(f(1+h)-f(1))/h = 2

Therefore, the value of (f(1+h)-f(1))/h = 2.

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The average rate of change of 2|x| on the interval [-3, 5] is 0.5

The function is given as

2|x|

Rewrite as

f(x) = 2|x|

The interval is given as

[-3, 5]

So, we have

f(-3) = 2|-3| = 6

f(5) = 2|5| = 10

The average rate of change of 2|x| on the interval [-3, 5] is then calculated as

Rate = (f(5) - f(-3))/(5 --3)

This gives

Rate = (10 - 6)/(5 --3)

Evaluate

Rate = 0.5

Hence, the average rate of change of 2|x| on the interval [-3, 5] is 0.5

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[Mathematical Situation]

Solve for  [tex]b_1[/tex];  [tex]A=\frac{1}{2} (b_{1} + b_2)h[/tex]

Solution:

[tex]b_1=\frac{2a}{h}-b_2[/tex]

Hope this helps!

Answer:

tan A +tanb

Step-by-step explanation:

1-tan a tan b

i think so

Answer: 20 quarts for two "standard" sized pots.

Step-by-step explanation:

Answer:

5-1, known colloquially as four, 4, or 1+3.

Step-by-step explanation:

The students chose pizza as their favorite school lunch based upon the data will be 130 students.

Let the assumed fraction for those who choose pizza be 3/10.

From the information, 400 students were surveyed about their favorite school lunch.

Therefore, the students chose pizza as their favorite school lunch based upon the data will be:

= Fraction for pizza × Total students

= 3/10 × 400

= 120 students

Note that an overview was given as the graph wasn't found.

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We get that the relation  { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.

We are given a relation as:

{ ( 2 , 1 ) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) }

We need to find that whether it is a function or not.

A relation is a set that shows a relationship between two values. A function  is from a set X to a set Y assigns to each element of X exactly one element of Y.

Here, we can see that it is a function as one value of x only has one image in the set y.

Therefore, we get that the relation  { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.

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The distance is  mathematically given as

D=1066.66667

The TIME function is included as part of Excel's Date and Time features. With the assistance of TIME, we are able to create a time by employing various components for the hours, minutes, and seconds.

While conducting financial analysis, it's possible that we'll need to date a report. Under these conditions, the TIME function may be used to convert a text string into a format that presents the time as a decimal representation of the seconds, minutes, and hours. Additionally, the function's capabilities include the ability to merge several values into a single time value.

formula= TIME (hour, minute, second)

distance = rate X time

D = RT

T = D/R

20 feet per second = 1200 feet per minute

16 feet per second = 960 feet per minute

(D/R) + 19 + (D/R) = 21

(D/R) + 19 + (D/R) = 21

(D/1200) + 19 + (D/960) = 21,

This is the equation we can use to find the distance from the flowerbed to the​ hive.

(D/1200) + (D/960) = 2

(D(1200)(960))/1200 + (D(1200)(960))/960 = 2(1200)960

960D + 1200D = 5(1200)960

2,160D = 2304000

D=1066.66667

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ln (1) = 0, by properties of logarithms.

Now,

ln (1) = [tex]log_e(1)[/tex]

By properties of logarithms, we get that: [tex]log_b(1) = 0[/tex], for any value of b.

Hence, ln (1) = 0, by properties of logarithms.

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The vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.

The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.

It is given that:

The coordinates are:

Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).

After applying dilation with a scale factor of 3:

E(−3, 4) → E'(-3x3, 4x3) = E'(-9, 12)

Similarly,

F(−2, 4) → F'(-6, 12)

G(−2, −2) → G'(-6, -6)

H(−3, −2) → H'(-9, -6)

Thus, the vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.

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The given expression can be rewritten as  [tex]6 ^{-9}=\frac{1}{6^9}[/tex].

There are different power rules, as presented below:

For solving this exercise, you should identify the power rules you will apply. For this question, you can apply the following rule:

"Power -  repeat the base and multiply the exponents."

Lilke the base is 6 and the exponents are 3 and -3, then you can rewrite the expression as:

[tex](6^3) ^{-3}=6 ^{-9}=\frac{1}{6^9}[/tex]

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Answer: It is correct.

The first step here is to distribute the numbers

4 times 2x is 8x

4 times -5 is -20

Therefore, you're left with 8x-20

I hope this helps!

The expression which models the maximum number of days in which she can rent the car is 20x + 10 ≤ 80

The maximum amount to spend = 80

Fixed charge per day $20

Charge per mile = $0.10

The inequality which represents the number of days Can be expressed thus :

(Charge per day × number of days) + (charge per mile × number of miles) ≤ 80

20x + 0.10 × 100 ≤ 300

20x + 10 ≤ 300

Hence, the required inequality expression is 20x + 10 ≤ 80.

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The angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle

The angle measures are given as:

35° 91° 65° 28°

As a general rule:

Angles that are less than 90 degrees are acute angles

This means that

The angles 35° 65° and 28° are acute angles

Also, we have

Angles that are between 90 degrees and 180 degrees are obtuse angles

This means that

The angle 91° is an obtuse angle

Hence, the angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle

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Complete question

What angle measure is this? 35° 91° 65° 28°

acute, right, obtuse, straight, or reflex

Based on the number of customers who owned parrots, dogs and parrots, and dogs, the number who owned either a dog or a parrot were 55 customers

The number of people who owned a parrot was 42. 33 people also owned a dog. Some of these people owned both a dog and a parrot and they numbered 20.

To find the number of customers who owned either a dog or a parrot, the formula is:
= Number of customers who owned a dog + Number of customers who owned a parrot - Number of customers who owned both a dog and parrot

= 33 + 42 - 20

= 75 - 20

= 55 customers

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Answer: 20/12

Step-by-step explanation:

15 is the greatest number of people they can be without having any leftovers

Given data

45 hotdogs in 30 individual bags of chips

Given data

45 hotdogs in 30 individual bags of chips

The greatest common factor of 45 and 30 is 15

using ratio

45 : 30

3 : 2

This means that one person will receive 3 hotdogs in 2 bags. Also 15 people will get the equal amount without left overs

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complete question

Amari and Ethan planned an end of season soccer party to purchase 45 hotdogs in 30 individual bags of chips which person will receive the same amount of food what is the greatest number of people they can be without having any leftovers

Sam would need to drive for the two plans to cost the same is 130 miles.

Let, x = Number of miles driven

      y = Total cost

The first plan:

Initial fee = $65

Cost of 1 mile = $0.3

Cost of drive x mile = $0.3x

In total, you will pay

y = 0.3x + 65 for the first plan.

The second plan:

There are no initial costs, but

Cost of 1 mile = $0.80

y = 0.80x

Now we have two equations

y = 0.3x + 65

y = 0.80x

As we know that y is equal to both 0.3x + 65 and 0.80x, this means we can equate the right hand sides and solve for x.

    0.3x + 65 = 0.80x

0.80x - 0.3x = 65

            0.5x = 65

                 x =  65÷0.5

                 x =  130

The cost of two plans will be same when Sam drive 130 miles.

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Answer:

You start with 18.000 gallons and want to know when you reach 6.000 gallons, with a daily use of 450 gallons. This means you need to know how many days it take to use 18.000 - 6.000 = 12.000 gallons. This can simply be calculated with 12.000/450, which gives 26 2/3 day

Step-by-step explanation:

Answer:

6.  Slope = 2

7.  y-intercept = 5

8.  Equation:  y = 2x + 5

Step-by-step explanation:

To find the slope of a line, define two points on the line:

Substitute these values into the slope formula and solve for m:

[tex]\implies \textsf{slope}\:(m)=\dfrac{7-5}{1-0}= \dfrac{2}{1}=2[/tex]

Therefore, the slope of the graph is [tex]\boxed{2}[/tex].

The y-intercept is the y-value of the point at which the line crosses the y-axis.

From inspection of the given graph, the y-intercept is [tex]\boxed{5}[/tex].

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

Where:

Substitute the found slope and found y-intercept into the formula to create an equation for the line:

[tex]\boxed{y=2x+5}[/tex]

The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees

Transformation involves changing the position and size of a shape.

The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees

From the figure, we have:

So, the scale of dilation from shape A to B is:

Scale = 1/2

Hence, the single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees

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