write the quotient as a power. a^21/a

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]

let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.

Answer:

23

Step-by-step explanation:

3+4x

3+4(5)

3+20

23

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The area of the figure is 21. 25 m². Option D

It is important to note that the figure is a kite.

The formula for calculating the area of a kite is expressed as;

A= pq/2

Where;

Using tangent identity

tan 45 = x/ 2. 5

1(2. 5) = x

x = 2. 5

p = 2. 5 + 2. 5 = 5

q = 2. 5 + 6 = 8. 5

Now, substitute the values into the formula

Area = 5(8. 5)/ 2

Area = 42. 5/ 2

divide the values

Area = 21. 25 m²

Hence, the value is 21. 25m²

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The given inequality solved for y is y > 4

From the question, we are to solve the given linear inequality.

To solve an inequality, we will solve for the variable in the inequality.

The given inequality is

-16 > -4y

The variable in the inequality is y.

Now, we will solve for y

-16 > -4y

Divide both sides by -4

-16/-4 > -4y/-4

4 < y

Thus,
y > 4

Hence, the solution is y > 4

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A plumber has a 36-inch pipe that he needs to cut into two pieces, one 8 inches longer than the other. Each piece's length is x = 14, while the other piece's length is 22.

Therefore,

let x = the first piece and x+14 is the second.

2x + 8 = 36

2x = 28

x = 14, the other piece is 22

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Answer:

b=11

Step-by-step explanation:

lets set up the equation. we know that both sides equal each other so the equation is

2b+7=3b-4 let's move the 2b to the other side so we get

7=b-4 now add the 4 to the other side

11=b

Answer:

B is 11

Step-by-step explanation:

The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5

The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines

By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4

In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us  x and y values close to what we guessed from the graph

By Solving 4x + y = 6 and −2x + y = −5:

4x + y = 6          (1)

−2x + y = −5      (2)

Using elimination, subtract (2) from (1), this gives:

6x = 11            

x = 11/6 = 1.83

Put x = 11/6 into (1):

4(11/6) + y = 6

y = 6 - 4(11/6)

y = 6 -44/6 = -4/3 = -1.33

Since these calculated values are very close to the guessed values

Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best

represented by the graph. So option A is the answer

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Answer:

-8

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

The equation of a line that is perpendicular to y = 7 / 6 x - 8 is y = -6 / 7 x + 8.

The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form.

The lines that are perpendicular to each other will have the products of their slopes as negative 1.

Therefore, let express the equation in slope intercept form.

y = mx + b

where

Therefore,

y = 7 / 6 x - 8

The slope of the equation is 7 / 6.

Therefore, let's find the equation of the line that is perpendicular to y = 7 / 6 x - 8.

m₁m₂ = -1

7 / 6 m₂ = -1

cross multiply

7m₂ = -6

m₂ = - 6 / 7

Hence, the equation of the line perpendicular to y = 7/6x - 8 should have the slope as - 6 / 7.

Hence, the equation can be y = -6 / 7 x + 8.

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In linear equation, 27/2 pancakes are in the box .

What in mathematics is a linear equation?

Number of b pancake mix  to be need  =  1½ cups

Number of box has pancake mix   = 9 cups

Therefore, in order to get the total number of  batches of pancakes  needed for the batches will be calculated thus

             =  1½  * 9

             = 3/2 * 9

             = 27/2

therefore 27/2 pancakes are in the box .

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Answer:

Exponent: B

Base: A

Scientific Notation: C

Step-by-step explanation:

vocabulary

Answer:

Exponent and A

Base and B

Scientific Notation and C

Step-by-step explanation:

Because the Exponent is the number that is going to raise the Base and that Base is the number that you are going to multiply by.

The short word problem that illustrates the given equation is seen below. The value of the variable is 9.

Linear algebra equations are equations that can be expressed in word problems and these equations can be used to solve real-life scenarios. These algebraic equations are designed by the application of the desired set of variables with its arithmetic operations.

A.

In a food factory, Eighteen fried chickens are added to the six times the number of food plates is seventy-two. How much-fried chicken goes into each food plate?

B.

6x + 18 = 72

Subtract 18 from both sides;

6x + 18 - 18 = 72 - 18

6x = 54

Divide both sides by 6.

6x/6 = 54/6

x = 9

C.

The value of the variable is 9, and according to the example we used, it represents the number of chickens that goes into each plate of food.

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The value of the three consecutive integers will be 10, 11, and 12.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Three consecutive integers are such that three times the smallest is 18 more than the largest.

Let the three consecutive number be x, x + 1, and x + 2. Then the equation will be:

3x = (x + 2) + 18

Simplify the equation, then the value of the variable x will be:

3x = x + 2 + 182x = 20x = 20 / 2x = 10

Then the value of the integers will be:

x + 1 = 10 + 1 = 11x + 2 = 10 + 2 = 12

The value of the three consecutive integers will be 10, 11, and 12

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There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal ≤

Greater than and equal ≥

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

-2/5 = -0.4

-11/3 = -3.67

-2.5

Now,

We see that,

-0.4 is greater than -2.5 and -2.5 is greater than -3.67.

This can be represented as an inequality:

-3.67 < -2.5 < -0.4

Thus,

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

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We will need 100 more samples to make the margin error of 0.3 .

acc to our question-

Hence, We will need 100 more samples to make the margin error of 0.3 .

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Answer:

0

Step-by-step explanation:

[tex]m=\frac{-21-(-21)}{-14-36}[/tex]

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

Answer:

$24,067.32

Step-by-step explanation:

If you look up a compound interest calculator and put in the data correctly you should get $24,067.32

Answer: n=1/27=0.037

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0

Simplify 1/9

3n -  1/9  = 0

Rewrite the whole as a fraction using  9  as the denominator :

          3n     3n • 9

    3n =  ——  =  ——————

          1        9  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3n • 9 - (1)     27n - 1

————————————  =  ———————

     9              9  

End of step 2  

27n - 1

 ———————  = 0

    9  

Start of step 3

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 27n-1

 ————— • 9 = 0 • 9

   9  

Now, on the left hand side, the  9  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  27n-1  = 0

Solving a Single Variable Equation:

3.2      Solve:    27n-1 = 0

Add  1  to both sides of the equation :

                     27n = 1

Divide both sides of the equation by 27:

                    n = 1/27 = 0.037

Answer: 82 is the answer

Step-by-step explanation: I just did this question and worked it out and it said it was right

The set of positive integers less than 1000 that are:

a)Divisible by 7 are 142

b)Divisible by 7 but not by 11 are 130

c)Divisible by both 7 and 11 are 12

d)Divisible by either 7 or 11 are 220

e)Divisible by exactly one of 7 and 11 are 220

f)Divisible by neither 7 nor 11 are 780

g)Having distinct digits are 576

f)Having distinct digits and even are 337

A whole number that is greater than zero is known as positive integer

a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.

Total terms: 994, divided by 7, plus (n-1)

There are 142 total terms below 1000 that are divisible by 7.

b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.

The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.

c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.

There are 12 total integers below 1000 that can be divided by 77.

d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.

The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.

Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.

e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.

f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.

Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),

=> Unique digits from 1 to 100 equal 90.

=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),

=> Unique digits from 101 to 200 are: 100 to 28, 72.

=> Unique numbers between 201 and 1000 = 72 x 8 = 576.

h)Different digits and even values equal to 337

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Answer:

The larger share is $450.

Step-by-step explanation:

[tex]\frac{3}{5} =\frac{3x}{5x} \\\\3x-the smaller share\\5x-the larger share\\3x+5x=8x\\8x-money to split\\8x=720 /:8\\x=90\\5x=5*90=450[/tex]

The number of liters of fuel required for the vehicle to travel 1, 428 kilometers is 5. 67

Inverse variation can be defined as the relationship between two variables, so that if the value of one of the variable increases the value of the other variable decreases.

Example: If a varies inversely as b

This can be represented as;

a ∝ 1/b

Then,

ab = k

Where k is the proportionality constant

From the information given, we have that;

x ∝ 1/ y

Then,

xy = k

Substitute the values

476 (17) = k

k = 8092

If x = 1428 and k = 8092

Let's determine the value of y

y = k/x

y = 8092/1428

y = 5. 67 liters

Hence, the value is 5. 67 liters

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The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

As per the given,5280ft

It is known that 1 ft = 12 inches.

5280ft = 5280 x 12 inches

It is known that 1 inch = 2.54 cm

5280 x 12 inches = 5280 x 12 x 2.54 cm

It is known that 1 cm = 0.01 meter

5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter

⇒  1609.344 meters

Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".

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Answer: D

Step-by-step explanation:

-7(-4-(4)(-6))

-7(-4-(4)(-6))

=140