A piece of land is in the shape of a rectangle. What is the ratio of the length to the width?

Given the system of equations :

Multiply the first equation by -2:

Add the equations (2) and (3) to eliminate x :

Substitute with y in equation (1) to find x :

So, the solution of the system is :

Answer:

Given that,

Total surface are=102 m square.

To find the side length of A,

Let the side length of A be a,

we get,

One side of the A is 3, we get that

A=product of one side and a

we get,

Substitute for A=27 we get,

The required side length of A is 9 m

Answer:

Step-by-step explanation:

See the steps below:

The value of n is 15.

Solution:

The cost to fill the propane tank is modeled by the function;

The practical domain of this function is;

Hence, the range of this function is;

Thus, the practical range is;

Answer:

100 is the number

Step-by-step explanation:

For this equation, it may be helpful to replace words with symbols.
The question is:
if 6% of x is the same as 5% of 120, then what is x?

The comma splits the sentence into two parts

if 6% of x is the same as 5% of 120 is the main focus, and the second part requires you to find x.

In the question "if 6% of x is the same as 5% of 120"
the word "of" can be replaced with " * ", and the words "is the same as" can be replaced with "=". The if can be dropped

The question becomes:

6% * x = 5% * 120

This equation can be easily solved.

6% = 0.06
5% = 0.05

So,

0.06x=0.05*120

0.06 x = 6

x = 6 / 0.06

x = 100

Answer:

Domain: A, [tex](-\infty, \infty)[/tex]

Range: [tex][4, \infty)[/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer : r = 3%

The cations and Anions for the given compounds are;

1) CuS: Cation; Cu²⁺ and Anion: Su²⁻

2) (NH₄)₂O; Cation; NH₄⁺ and Anion: O²⁻

3)Mn₃(PO₄)₂; Cation; Mn²⁺  and Anion: PO₄³⁻

4) VBr₅; Cation; V⁵⁺ and Anion: Br⁻

Cations are defined as Positively charged ions that are formed by loss of electrons by an atom. In a cation, number of electrons are less than number of protons.

Anions are defined as Negatively charged ions that are formed by gaining of electron by an atom. In anions, number of electrons are more than the number of protons.

Thus;

1) CuS

Cation; Cu²⁺

Anion: Su²⁻

2) (NH₄)₂O

Cation; NH₄⁺

Anion: O²⁻

3) Mn₃(PO₄)₂

Cation; Mn²⁺

Anion: PO₄³⁻

4) VBr₅

Cation; V⁵⁺

Anion: Br⁻

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The number of pounds of doughs available is given as:

The fraction of a pound used for one medium is given as:

The expression's decimal is equivalent to (B) 0.24.

So, ( 8 × 3 ) ( 1/10 × 1/10 ):

Solve as follows:

Therefore, the expression's decimal is equivalent to (B) 0.24.

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The correct question is given below;
Which of the following decimals is equivalent to (8 x 3) (1/10 × 1/10)

A. 0.024

B. 0.24

C. 2.4

D. 24.0​

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Simplify the expression

Hence, x = 3

Answer:

The two numbers are 4 and -4

Step-by-step explanation:

Turn the words into equations: let's assign one number to be x and the other to be y

x+8=y

x*y=-16

To solve, substitute the value of y in the first equation into y in the second equation.

This gives x*(x+8)=-16

Simplifying gives x^2+8x=-16

x^2+8x+16=0

(x+4)^2=0

x=-4

plug this value of x back into the first equation, -4+8=y, y is 4

Now to make sure the answer is correct: 4 is 8 more than -4, and 4*-4 does equal 16

f(x)=9-x^2

Average rate of change

x=0 to x=3

x=-1 to x=5

x=-2 to ×=2​

we know that

The average rate of change is equal to

Part 1) we have

a=0

b=3

f(a)=f(0)=9-(0)^2=9

f(b)=f(3)=9-(3^2)=0

substitute the given values in the expression above

the rate of change is -3

Part 2) we have

a=-1

b=5

f(a)=f(-1)=9-(-1)^2=8

f(b)=f(5)=9-(5)^2=-16

substitute the given values in the expression above

the rate of change is 4/3

Part 3) we have

a=-2

b=2

f(a)=f(-2)=9-(-2)^2=5

f(b)=f(2)=9-(2)^2=5

substitute

the rate of change is zero

As it is a proportional relationship then this relationship can be described by a line. To find the equation of the line that passes through the points shown in the table, you can first find the slope and then use the point-slope formula.

The approximate surface area of the right triangular prism is 141.5 cm².

The surface area of a triangular prism can be found as follows;

surface area of a triangular prism = (perimeter × length) + (2 × base area)

Therefore,

perimeter of the triangular base = 5 + 5 + 5

perimeter of the triangular base = 15 cm

length = 8 cm

The base area = 1 / 2 bh

where,

The base area = 1 / 2 × 4.3 × 5

The base area = 1 / 2 × 21.5

The base area = 10.75 cm²

Hence,

surface area of a triangular prism = (15 × 8) + 2(10.75)

surface area of a triangular prism = 21.5 + 120

surface area of a triangular prism = 141.5 cm²

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Answer:

Step-by-step explanation:

Solution:

Given the side lengths of a triangle ABC;

The side lengths form a Pythagorean triple if ithe square of the longest side is equal to the sum of squares of the remaining two sides.

Thus;

Hence, they do not form a Pythagorean triple.

CORRECT OPTION: (B) No, they do not form a Pythagorean triple.

Answer:

Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.

Step-by-step explanation:

Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.

SOLUTION

From the diagram of the box plot

A. The IQR for the male's data is approximately 14 - 5 = 9

B. The median for female is 7

The median for male is estimated 10

Difference 10 - 7 = 3.

C. The mean would be better to compare males with females because from the box plot diagram, more males saw the movie than females.

D. The possible reason for the outlier in the data set could be due to more females attending the movie than normal.

The average rate of change of the function f(x) on the interval−6≤x≤2 is  -0.5

This is further explained below.

Generally, The average rate of reaction is referred to as the change in concentration of any of the reactants or any of the products per unit of time during a specific period of time. This change may occur at any point throughout the reaction.

A single rate is applicable to property that is located in more than one place and that is calculated by weighting the separate rates that are calculated for each location.

In conclusion, The average rate of change on x e(a, b)

[tex]\begin{aligned}m &=\frac{f(b)-f(a)}{b-a} \\\\m &=\frac{f(2)-f(-6)}{2-(-6)} \\\\&=\frac{2-(-(-6))}{8}=\frac{6}{2} \\\\=-0.5\\\\\end{aligned}[/tex]

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Simple interest is the cost of borrowing money without accounting for the effects of compounding.12672 is the size of Kathleen’s total interest when she retires.

Simple interest is the cost of borrowing money without accounting for the effects of compounding.

Given that Kathleen begins working and at age 32 she invests $6000.00 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65.

Let us calculate the age or time

65-32 =33 years

A=P(1+rt)

A= Final Amount

P=Principle amount=6000

r = rate of interest=6.4%

t is time =33 years

Substitute these values in Formula.

Convert 6.4% to decimal number by dividing with 100.

A=6000(1+0.064(33))

A=6000(1+2.112)

A=6000(3.112)

A=18672

The final Amount she got is 18,672.

To find the interest amount we have to substitute initial amount from final amount.

18672-6000

=12672

Hence 12672 is the size of Kathleen’s total interest when she retires.

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Answer: Heather: $10, Kareem: $19, Tom: $57

Step-by-step explanation:

f(x) = 8(x -3) (option C)

Explanation:

let y = inverse of f(x)

Interchange x and y:

The answer is 18

You first multiply both sides by 6 which will make 15, now 90

then divide both sides by 5 so that will make 90, 18 thus x=18 is correct

The quadratic equation with roots a and b is given by:

Here a=1/2 and b=-4.

So the equation is given by:

The quadratic equation is as shown above.

Given data:

The given radius is JK=JM=3.

The given length is LM=2.

The tangent is always perpendicular to the radius, the expression for the Pythagoras theorem is,

Substitute the given values in the above expression.

Thus, the first option is correct.

originally, the cost was to be divided among all members

Where m is the number of members and x was the cost per person originally

When 5 people decided not to go, x was increased $14 and m decreased 5...

Now, we have two equations that we need to solve...

if we subtract the two expressions, we get the above

Now, we simplify...

Now, we solve for m

we obtain that m=25, meaning there are 25 members, so 25-5=20, this is, 20 people went to the expedition

The most appropriate choice for functions will be given by -

f (x) - (-g(x)) =  f(x)  + g(x) holds for  f(x)=3x-7-and g(x) = -2x+5.

f (x) - (-g(x)) =  f(x)  + g(x) holds for every functions

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

For f(x) - (-g(x))

-g(x) = -(-2x  + 5)

       = 2x - 5

f (x) - (-g(x)) = (3x - 7) - (2x - 5)

                      3x - 7 - 2x + 5

                       x - 2

For f(x)  + g(x)

f(x)  + g(x) = (3x - 7) + (-2x + 5)

                = 3x - 7 - 2x + 5

                = x - 2

So f (x) - (-g(x)) =  f(x)  + g(x) holds here

Since addition and subtractions can be done on functions,

f (x) - (-g(x)) =  f(x)  + g(x) holds for every functions.

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The range will be impacted by A. The range will increase by 12.

A range simply means the difference between the highest and the lowest number.

Highest number = 34

Lowest number = 15

Range = 34 - 15 = 19

When the highest number is 46, the range will be:

= Highest number - Lowest number

= 46 - 15

= 31

The difference will be:

= 31 - 19

= 12

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Answer:

The range will be impacted by A. The range will increase by 12.What is a range?A range simply means the difference between the highest and the lowest number.Highest number = 34Lowest number = 15Range = 34 - 15 = 19When the highest number is 46, the range will be:= Highest number - Lowest number= 46 - 15= 31The difference will be:= 31 - 19= 12

Step-by-step explanation:

  A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the points A, B, C, D, and E in the aforementioned figures are vertices.

Fill in the square for 2 x ² + 8 x + 7.

To continue, tap...

2 ( x + 2 ) 2 − 1 Set y to the newly created right side.

y = 2 ( x + 2 ) 2 − 1

Find the values of a, h, and k using the vertex form, y = a (x h ) 2 + k. a = 2 h = 2 k = 1

Find the (h,k) vertex. ( 2, 1 ) .

2 x ² + 8 x - 7

Discover the initial derivative.

4 x + 8

Solve the problem 4 x + 8 = 0 by setting the first derivative to 0.

To continue, tap... x = − 2

Locate the values at which the derivative is ambiguous.

All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number.

At each x value where the derivative is 0 or undefined, evaluate 2 x 2 + 8 x 7.

( − 2 , − 15 ).

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