What Are The Dimensions Of The Rectangle With Maximum Area? (2024)

In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.

How to solve Exponential functions?

We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;

420t + 5750

where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;

t = 2006 - 1995

t = 11 years

Thus;

f(11) = 420(11) + 5750

f(11) = 10370 dollars

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IN OTHER WORDS WE ARE LOOKING FOR WHOLE NUMBERS BETWEEN -6 AND 2

[tex] - 5 \\ - 4 \\ - 3 \\ - 2 \\ - 1 \\ 0 \\ 1[/tex]

ATTACHED IS THE SOLUTION

Answer:

1,0,-1,-2,-3,-4,-5

Step-by-step explanation:

Answer:

The distance between two points (x₁,y₁) and (x₂,y₂) on the coordinate plane is d=√((x₂-x₁)²+(y₂-y₁)²)

√(8 - 3)² + (7 - 5)² = √29 ≈5.3851648071345

Answer:

q=1

Step-by-step explanation:

2(q+4)=10

q+4=5

q=1

:]

Answer:

3

Step-by-step explanation:

2 x 3 6 4 10

a) Point = could be any point A to D = for example A

b) Line : AD

Could be any line named by the endpoints.

c) Segment: Fragment of a line

AB

d) Ray: part of a line that has a fixed star but no end:

BE

e) Angle : Could be any angle, the middle letter is where the angle rests.

f) 3 collinear points: A,B,C

3 points that are in the same line

g)Opposite rays: same end point but opposite directions

BE and BC

h) Plane: infinite set of points forming a connected flat surface.

ABDC

i) 3 non collinear points: AEC

Three points that aren't on the same line

j) another name for m

As per given by the question,

There are given two figure on coordinate grid, figures 1 and 2.

Now,

From concept of similar figure:

Similar figure means, that have the same shape and exactly the same in every way, on the other hand;

The similar figure means they are same shape but not the same size, then these figure is also called similar figure.

Now,

From concept of the congruent figure:

The congruent means, that two figure exactly the same that means, we can say that they are congruent, when both figure have same shape and same size.

So,

According to both concept, similar and congruent;

The given figure 1 and 2 is simililar, because of same shape. But due to different size, both figure have not congruent.

So, the given figures 1 and 2 is similar, but not congruent.

Hence, the option first is correct.

Answer: f(3) = 0.84375

Step-by-step explanation:

f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)

So we just plug in 3 for x and simplify (use PEMDAS)

f(3) = 2(0.75)^3

f(3) = 2(0.421875)

f(3) = 0.84375

Answer:

[tex]\frac{27}{32}[/tex]

Step-by-step explanation:

It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]

We can represent 0.75 as: [tex]\frac{3}{4}[/tex]

And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]

calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]

using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]

Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]

When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]

From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]

Which is our answer!

Using vertical angles, it is found that:

A. The solution for y is of y = 4.

B. The angle measures are given as follows:

<A = 66º.<C = 114º.<D = 114º.

Vertical Angles

If two angles are opposite by the same vertex in crossing segments, these angles are called vertical angles, and they are congruent, that is, they have the same measure.

In the context of this problem, the angles of 6y + 42 and of 66 are vertical, hence the value of y is calculated as follows:

6y + 42 = 66

6y = 24

y = 24/6

y = 4.

Angles A and C are supplementary, meaning that the sum of their measures is of 180º, hence:

<C + 66º = 180º

<C = 180º - 66º

<C = 114º.

Angles C and D are vertical, hence the measure of angle D is calculated as follows:

<D = 114º.

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The most appropriate choice for HCF of two numbers will be given by -

Maximum number of performers in each row so that all the rows are equal in length = 8

What is HCF?

HCF means Highest Common Factor. HCF of two numbers a and b is the largest number that is divides both a and b.

Number of instruments = 24

Number of flag bearers = 16

Maximum number of performers in each row so that all the rows are equal in length = HCF of 24 , 16

[tex]24 = 2^3 \times 3\\16 = 2^4[/tex]

HCF = [tex]2^3[/tex] = 8

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Looking at the diagram of the triangular prism and its net, we can see that

a = width of the base = 5 cm

b = the slant height = 13 cm

c = length of the base = 15 cm

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

Given :

The statistician reported that the mean serve speed was 100 miles per hour

the standard deviation of the serve speeds was 15 mph

Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric

To find :

What percentage of the player's serves were between 115 mph and 145 mph?

Solution :

μ =100

σ = 15

P ( 115 < x <145)

= P ( [tex]\frac{115-100}{15}[/tex] < x-μ /6 <[tex]\frac{145-100}{15}[/tex] )

= P ( [tex]\frac{15}{15}[/tex] < z < [tex]\frac{15}{15}[/tex] )

= p ( 1<z<3)

= p( z<3)-p(z-1)

=0.9987-0.8413

=0.1574

p ( 115<xx<145)= 15.74 %

p( 115<x<145)= approximately 16%

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

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Using trigonometric ratio. SOHCAHTOA

[tex]\begin{gathered} \cos 63^{\circ}=\frac{adjacent}{\text{hypotenus}} \\ \cos 63^{\circ}=\frac{x}{16} \\ x=16\cos 63^{\circ} \\ x=16\times0.45399049974 \\ x=7.26384799583 \\ x\approx7.3 \end{gathered}[/tex]

Inequality: [tex]x-7\ge 15[/tex]

Solution: [tex]x\ge 22[/tex]

Inequality is a mathematical statement which depicts the relation between two or more mathematical variable or quantities which involves in relation which is not equal or inequal.

Given the statement is "A number decreased by 7 is at least 15"

Let the number be the variable x.

Now decreased by 7 = x-7

Suitable inequality sign for at least statement is [tex]\ge[/tex]

So the required inequality is given by,

[tex]x-7\ge15[/tex]

Solving the same we get,

[tex]x-7+7\ge 15+7[/tex]

[tex]x\ge 22[/tex]

Thus the number is [tex]x\ge 22[/tex]

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Given:

The graph of the function f is given and the function g is as:

[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]

Required:

To graph the function g.

Explanation:

The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.

The graph of the function

[tex]\frac{1}{2}f(x+2)[/tex]

here

[tex]a=\frac{1}{2}[/tex]

So the graph of g has undergone a vertical shrinking by a factor of

[tex]\frac{1}{2}[/tex]

The graph of the function

[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]

reflect the graph of

[tex]\frac{1}{2}f(x+2)[/tex]

across the x-axis by multiplying the y coordinate of the points on the graph of

[tex]\frac{1}{2}f(x+2)[/tex]

by -1.

Thus the graph of the function

[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]

is as:

Final Answer:

The graph of the function g is attached in the explanation part.

An acute triangle is a triangle with three acute angles, whereas an obtuse triangle is a triangle with one obtuse angle and two acute angles.

An obtuse angle is a angle which is more than 90°.

In our problem, the triangle has a 110° angle, and 110°>90°; therefore, the answer is obtuse triangle

The slope of the line to represent the volume of water in a pool over time would described as -10

From the given table we have to choose points to find the slope of the line

The domain is defined as the set of possible inputs of the function.

The range is defined as the set of all possible outputs of the function.

The slope of the line is the change in y coordinate with respect to the change in y coordinates

Slope of the line m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Where m is the slope of the line

[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are the coordinates of the two points

We have to choose two points

The two points (2,44) and (4,26)

m = [tex]\frac{26-46}{4-2}[/tex]

m = -20/2

m = -10

Hence, the slope of the line to represent the volume of water in a pool over time would described as -10

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The equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.

How simplification method work?

In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.

According to the question, the given equation can be simplified by using simplification method and it is written below:

The given equation is: 3x - 6 = 18

3x = 18 + 6 = 24 ⇒ 3x = 24

Similarly, 3x - 6 = 18

3(x - 2) = 18

Hence, the equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.

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Anlges A and D are right angles becuase they measure 90

Angle C is Acute because it is smaller than 90

Angle B is Obtuse because it is grather than 90

no, theyre not! false.

it would be SAS.

Answer:

See below

Step-by-step explanation:

Slope of given line is 1 y = (1) x + 2

parallel line has same slope

so it will start to look like this y = (1) x + b

sub in the point 5,7 to find b = 2

final answer y=x+2

Answer:

12 is the number that comes after 11 and before 13. 12 represents the number between 11 and 13. 12 is a composite number.

Step-by-step explanation:

12 is the number that comes after 11 and before 13.

12 represents the number between 11 and 13. 12 is a composite number.

Let's draw the figure to better understand the problem.

Answer:

This is a 30 60 90 triangle. They are saying the hypotenuse is 3x + 6 and the shortest side is 8x - 4. In a 30 60 90 triangle, the hypotenuse is 2 times the short side meaning that/

3x + 6 = 16x - 4

Now we can solve...

10 = 13x

x= [tex]\frac{10}{13}[/tex]

Given the expression below

[tex]8+6(6-2(5-4))[/tex]

Step 1: Using PEMDAS rule

P=> Parenthesis

E=>Exponent

M=>Multiplication

D=>Division

A=>Addition

S=> Subtraction

From the rule above, we will start our simplification with the parenthesis

Step 1: simplify (5-4)

[tex]\begin{gathered} 8+6(6-2(5-4) \\ 8+6(6-2(1)) \end{gathered}[/tex]

Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))

[tex]8+6(6-2(1))\Rightarrow8+6(6-2)\Rightarrow\cdot=8+6(4)[/tex]

Step 3: Expand 6(4)=>6 x 4

[tex]8+6(4)\Rightarrow8+6\times4\Rightarrow8+24[/tex]

Step 4: Add 8 and 24

[tex]8+24=32[/tex]

Hence, the final answer is 32

Answer: your answer would be 32

Step-by-step explanation:

using PEMDAS we would first go by parentheses and use the order by each step.

Answer:

good jb

Step-by-step explanation:

From the graph, we can see that the set of ordered pairs which belongs to the line are

D). (2, 100), (3, 150), (5, 250)

Because x-axis is the first coordinate and y-axis is the second coordinate. In options B and C, they are

arranged in the wrong place. In option A, point (3,125) doesn´t belong to the line.

Answer:

1187.49

Step-by-step explanation:

[tex]P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49[/tex]

Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.​

__________________________________

30 miles / 2 hours = 15 miles/hour

_________________________________________

Answer

15 miles/hour

The given expression is

y = (x²-7x)^5 (3x^5-5x)

To differentiate, we would apply the product rule which is expressed as

(fg)' = f'g + fg'

Let f = (x²-7x)^5 and g = (3x^5-5x)

f' = 5(2x - 7)(x²-7x)^4

g' = 15x^4 - 5

By applying the product rule, it becomes

y' = 5(2x - 7)(3x^5-5x)(x²-7x)^4 + (15x^4 - 5)(x²-7x)^5

Let f(x) = 9x - 8. Find (f o f)(1).​

we know that

(f o f)(1).=f(f(1))

step 1

find f(1)

f(1)=9(1)-8

f(1)=1

substitute

f(f(1))=f(1)=1

therefore

the answer is 1