The total cost, including shipping, for ordering five uniforms is $61. The total cost, including shipping, for ordering nine uniforms is $ 105. find the slope.

Answer:

If x is an exponent in all those functions, then the function that grows the fastest is D, because it has the highest base 5 which is raised to x.

Step-by-step explanation:

The function  [tex]f(x) = 2\times5^x[/tex]  grows fastest. The correct answer is option D.

Given that the following functions:

[tex]f(x) = 5\times2^x[/tex]                      (1)

[tex]f(x) = 4\times3^x[/tex]                        (2)  

[tex]f(x) = 3\times4^x[/tex]                        (3)

[tex]f(x) = 2\times5^x[/tex]                       (4)

To determine which exponential function grows the fastest, compare the bases of the functions. The base of an exponential function determines how quickly it grows.

Let's compare the bases:

(1) The base is 2.

(2) The base is 3.

(3) The base is 4.

(4) The base is 5.

Since the base determines the rate of growth, conclude that  [tex]f(x) = 2\times5^x[/tex]  grows the fastest among the given options because 5 is the largest base.

In other words, as x increases, the function  [tex]f(x) = 2\times5^x[/tex]  will have the steepest increase in value compared to the other options.

Hence, the function  [tex]f(x) = 2\times5^x[/tex]  grows fastest.The correct answer is option D.

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Answer:

h=4=30

c=2=60

Hope that help

Answer:

line (3)

Step-by-step explanation:

note that [tex]\frac{x}{4}[/tex] + 3 - 3 = - 12 - 3

should then be [tex]\frac{x}{4}[/tex] = - 14 Not - 9

first error occurs in line (3)

Answer:

52+38

Step-by-step explanation:

An even number plus another even number results in an even sum. Examples such as 44 + 46 equaling 90 show this arithmetic principle.

The question pertains to the addition of two even numbers that equal 90. An even number is any integer that can be exactly divided by 2, which means its last digit will be 0, 2, 4, 6, or 8. When adding two even numbers, the result is always an even number.

For instance, if we consider the numbers 44 and 46, both are even:

This is just one example of even numbers adding up to 90. There are multiple pairs of even numbers that can sum up to 90, demonstrating the fundamental arithmetic principle that the sum of two even numbers is always even.

Answer:

Formula:

The general formula for the surface area (SA) of a prism is:

SA = 2B + Ph

Step-by-step explanation:

where:

B is the area of one base (since there are two identical bases, we multiply by 2).

P is the perimeter of the base (the total length of all sides of the base polygon).

h is the height of the prism (the distance between the two bases).

Steps to Find the Surface Area:

Identify the base shape and calculate its area:

Depending on the type of prism (triangular, rectangular, etc.), use the appropriate formula to find the area of one base.

Find the perimeter of the base:

Add up the lengths of all the sides of the base polygon.

Calculate the lateral surface area:

Multiply the perimeter of the base (P) by the height of the prism (h). This gives you the total area of all the lateral faces.

Sum the areas:

Add the area of two bases (2B) you calculated in step 1 and the lateral surface area from step 3. This will be the total surface area of the prism.

Tips:

Make sure you identify the correct height of the prism. It's the perpendicular distance between the two bases, not the length of a slanted lateral face.

If the lateral faces are not all the same shape (e.g., a truncated prism), you might need to calculate the area of each lateral face separately and add them all up.

By following these steps and using the formula, you can find the surface area of any prism!

Answer:

The total area of the two triangles is 100 inches²

Step-by-step explanation:

To solve for the area of a triangle we use the formula [tex]\frac{1}{2} bh[/tex]

(or base*height divided by 2)

First I solved for the area of the blue triangle.

The base is 12 inches and the height is 10 inches.

[tex]\frac{1}{2}[/tex] * 12 * 10 equals 60 inches².

For the orange triangle the base is 8 inches and the height is 10 inches.

[tex]\frac{1}{2}[/tex] * 8 * 10 equals 40 inches².

60in² + 40in² = 100in²

Answer:

Its C. 25

Step-by-step explanation:

I just divided 100 by 4

4x = 100      divide both sides by 4

x = 25 → c.

--------------------------

5x = 25     divide both sides by 5

x = 5 → c.

---------------------------

3x + 5 = 17       subtract 5 from both sides

3x = 12      divide both sides by 3

x = 4 → a.

--------------------------

3x + 14 = 11      subtract 14 from both sides

3x = -3     divide both sides by 3

x = -1 → b.

Answer:

Service a charges $30 per mow plus an additional $20 flat fee each month, however, Service b only charges $30 per mow, so Service b would be cheaper.

Step-by-step explanation:

This question is asking you to compare costs using linear equations.  In a linear equation, 'x' represents the independent variable, in this case the number of times the yard is mowed, and 'y' represents the dependent variable, or the monthly cost.  30 is the slope, or rate of change, which in this problem is the cost per time the yard is mowed.  In the equation for Service a, we can see that it is a charge of $30 per time, however, there is also an additional fee of $20 - which is our y-intercept.  However, Service b has two points (0,0) and (5,150).  Using these two points, we can find the slope, or rate, by subtracting the 'y' values over the 'x' values, or (150-0)/(5-0), to get 30.  Since Service b has the starting point of (0,0), or cost is $0 when there are 0 lawns mowed, then they do not have a flat fee.  

Answer:

Option c is correct option

it  will be about 5.6 weeks until 50 percent of the campus is watching the show

Step-by-step explanation:

we are given

w(x)=[tex]x+125^{\frac{1}{3} }[/tex]

w(50)=[tex]50+125^{\frac{1}{3} }[/tex]

w(50)=[tex]175^{\frac{1}{3} }[/tex]

w(50)=[tex]\sqrt[3]{175}[/tex]

w(50)=5.59

we have to convert it  into one decimal form

5.59=5.6

hence option c is correct option.

Computing w(50) using the provided function yields a value of approximately 5.6, which means it will take about 5.6 weeks for 50 percent of the campus to start watching the student-produced reality show. Thus, the correct answer to the student's question is option (C).

To compute w(50) based on the given function [tex]w(x)=(x+125)^{(1/3)}[/tex], we substitute x with 50:

[tex]w(50) = (50+125)^{(1/3)}[/tex]

Calculate the value inside the parenthesis:

[tex]175^{(1/3)}[/tex]

Taking the cube root of 175 gives us approximately:

5.6

Thus, w(50) ≈ 5.6, and we can interpret this in context by stating:

It will be about 5.6 weeks until 50 percent of the campus is watching the show.

This means the correct answer from the provided options is C. It takes approximately 5.6 weeks for the reality television show produced by the students to reach a viewership of 50 percent of the campus.

Answer:

15

Step-by-step explanation:

4g(3)+2[g(2)]²

4((3+4)/√7(3)-5)+2[(2+4)/√7(2)-5]²

=15

Answer:

Answer is option c. (15)

Answer:

4+y = -36

y = -40

The definition of a rational number is the ratio of two integers

Lets rewrite .57 as a fraction

.57 = 57/100

Both 57 and 100 are integers and 57/100 is the ratio of integers so .57 is rational.

Step-by-step explanation:

4+y = -36

Subtract 4 from each side

4+y-4 = -36-4

y = -40

The definition of a rational number is the ratio of two integers

Lets rewrite .57 as a fraction

.57 = 57/100

Both 57 and 100 are integers and 57/100 is the ratio of integers so .57 is rational.

Answer:

8/9 of a song per minute

Step-by-step explanation:

We want to find the rate, which is songs per minutes

songs/ minute

2/3 /  3/4

We can use copy dot flip

2/3 * 4/3

8/9  songs per minute

Answer:

Length of rectangle ≥ 2 yd.

Step-by-step explanation:

Suppose the length of rectangle = X yd.

Given the width of rectangle = 2 yd.

Area ≥ 4 yd²

Length * width ≥ 4 yd²

2X ≥ 4 yd²

X ≥ 2 yd

So, length of rectangle must be at least 2 yd.

****************************************************************************************

Answer:

length = 1 feet and width = 3 feet.

Step-by-step explanation:

Suppose the width of rectangle = X feet.

then length of rectangle = (2X - 5) feet.

Given the perimeter of rectangle = 8 feet.

The formula is Perimeter = 2 * (length + width)

8 = 2 * (2X - 5 + X)

8 = 2 * (3X - 5)

8 = 6X - 10

6X = 8 + 10 = 18

X = 18/6 = 3.

so 2X - 5 = 2(3) - 5 = 6 - 5 = 1.

Hence, length = 1 feet and width = 3 feet.

Answer:

See below.

Step-by-step explanation:

The slope of the line is (5-1) / (3 - -3)

= 4/6  = 2/3

Point slope form:

y - y1 = m(x - x1)

Plugging in m = 2/3 and the point (-3,1):-

y - 1 = 2/3(x + 3) (answer)

Slope-intercept form:-

y - 1 = 2/3(x + 3)

y = 2/3x + 2 + 1

y = 2/3x + 3 (answer)

Standard Form:-

y = 2/3x + 3

Multiply through by 3:-

3y = 2x + 9

-2x + 3y = 9  (answer).

Answer:

630.8 for the nearest tenth, and 631 for a whole number.

Step-by-step explanation:

The values of x and y that satisfy the system of equations are x = (1/3 ± i√(19))/1 and y = (±i√(19) + 2)/2.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

The equations 3x − 1 + 2y = 0 and 3x2 − y2 + 4 = 0

Now,

To find the corresponding values of y, we can plug these values of x into the expression for y that we found earlier:

[tex]y = -1/2(3x - 1). For x = (1/3 + i√(19))/1, we get: y = -1/2(3(1/3 + i√(19))/1 - 1) = -1/2(i√(19) - 2) = (i√(19) + 2)/2. For x = (1/3 - i√(19))/1, we get: y = -1/2(3(1/3 - i√(19))/1 - 1) = -1/2(-i√(19) - 2) = (-i√(19) + 2)/2.[/tex]

These are the values of y that satisfy the system of equations.

Therefore, by quadratic equations the answer will be x = (1/3 ± i√(19))/1 and y = (±i√(19) + 2)/2.

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Answer: 15.065 grams

Step-by-step explanation:

Given: Jose and Alexia needed to weigh three samples of rock to the nearest thousandth.The weight of the first sample = 3.346 grams

The weight of the second sample = 2.479 grams

The weight of the third sample = 9.240 grams

Add all together such that the total weight=[tex]3.346+2.479+9.240[/tex]

⇒The total weight of the samples = 15.065 grams.

Therefore, the samples weigh 15.065 grams altogether.

Answer:

7.25

Step-by-step explanation:

4 times 2 is 8 so then add another half and you will get 10 so multiply 2.5 times 2.5

Kellan should use 6.25 cups of water to make a batch of lemonade with 10 scoops of lemonade powder.

To determine how much water should be used, we can set up a proportion using the lemonade powder to water ratio. Since 4 scoops of lemonade powder are used for every 2.5 cups of water, we can write the proportion as:


4 scoops / 2.5 cups = 10 scoops / x cups

To solve for x, we can cross-multiply and divide:


4x = 10 * 2.5

4x = 25

x = 6.25 cups

Therefore, Kellan should use 6.25 cups of water to make a batch of lemonade with 10 scoops of lemonade powder.

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Final answer:

The missing factors in the expression 3x³+12x²-9x are obtained by factoring out the common term 3x and then factoring the quadratic expression x²+4x-3. The final factorization is 3x(x+6)(x-1).

Explanation:

To find the missing factors in the expression 3x³+12x²-9x, we first factor out the common term, which is 3x.

So, the expression becomes 3x(x²+4x-3). Next, we need to find two numbers that multiply to -3 and add to 4. These numbers are 6 and -1, so we can further factor the quadratic as 3x(x+6)(x-1). In conclusion, the missing factors of the given expression are x+6 and x-1.

D) feet

A tree 1.5 x 10^3 is 1500 centimeters. That's about 300 inches, which would better be measured in feet.

You can use the fact that normally people use those measurements which are whole numbers or not elongated decimal number mostly and not much big numbers.

The most appropriate unit to measure the length of the tree out of the given options is

Option D:  feet

Normally people use those measurements which are whole numbers mostly and if not, then not too much long after decimal and not much big numbers.

A tree is measured suitably if we use feet. It is because the normal tree height is from few feet to few hundred feet.

If you measure tree height in centimetres, then as you can see in the question, the number before cm unit is quite big to handle by normal people.

If you measure in too big unit like kilometres, then the height would be expressed mostly like 0.some digits.

That's why we choose feet.

Since 1 cm = 0.0328 feet

thus, height of specified tree in feet would be

[tex]\rm 0.0328 \times 1.5 \times 10^{3} = 49.2 \: feet[/tex]

See the number before feet. Its not too big nor too small, and easy to remember and converse. That's why feet is appropriate.

Thus,

The most appropriate unit to measure the length of the tree out of the given options is

Option D:  feet

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Answer:

91 boxes

hope it helps

Step-by-step explanation:

you will divide $500.00 by $5.50 to find you how many cookies need to be sold

500 ÷ 5.50 = 90.9

so they need to sell about 91 boxes in order meet their goal

To check your work you can multiply

5.50 x 91 = $500.50

Using the divison operation, the number of cookies that must be sold in other to meet their target is 91

The Number of cookies that must be sold to meet their target can be obtained using the divison operation thus :

Hence,

Number of cookies to be sold = $500 ÷ 5.50 = 90.90 = 91(nearest whole number)

Therefore, the Number of cookies that must be sold to meet their target is 91.

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Answer:

The answer is A

Hoped it helped <3 tell me if I am wrong

Step-by-step explanation:

Answer:

your answer would be C

Step-by-step explanation:

follow the numbers up the graph

Answer:

C. After 6 minutes, Sam is 60 meters from the dock.

Step-by-step explanation:

Answer:

They would be going at 56 miles per hour.

Step-by-step explanation:

You just take the miles they traveled (1,750) and divide it by the hours it took to get ther (31) the equation qould look like this 1,750 / 31 = 56  

miles per hour is measured by how far you go and how long it takes to get there!

Answer: The answer is 56 miles per hour

Step-by-step explanation:

you divide 1,750 by the time it took which  was 31

you would get 56.4516129032 then you round to the nearest whole number which is 56

i hope this helps- brycefoster

[tex]\bf \begin{cases} 4x-2y=5\\ \boxed{y}=2x+10 \end{cases}~\hspace{7em}\stackrel{\textit{substituting \boxed{y} in the 1st equation}}{4x-2\left( \boxed{2x+10} \right)=5} \\\\\\ 4x-4x-20=5\implies -20\ne 5[/tex]

which makes no sense, our variable went poof, but that is a flag that this system has no solution, let's quickly solve both for "y" to put them in slope-intercept form,

[tex]\bf 4x-2y=5\implies 4x-5=2y\implies \cfrac{4x-5}{2}=y\implies ~\hfill \stackrel{\stackrel{m}{\downarrow }}{2}x-\cfrac{5}{2}=y \\\\\\ ~\hfill y=\stackrel{\stackrel{m}{\downarrow }}{2}x+10[/tex]

so, notice, the slopes(m) are exactly the same for both, whilst the y-intercept differs, meaning both lines are parallel and therefore never touch each other, thus, no solution.

the untrue equation of -20 = 5, is another way to say, "no solution".

Answer:

Multiply the output value by 2 for  each input value increases by 1

Step-by-step explanation:

Function f is an exponential function

Since it is an exponential function , we find out common ratio of output first

WE divide second term by first term to get common ratio

[tex]\frac{\frac{1}{16}}{\frac{1}{64}}[/tex]

[tex]\frac{1}{16} * \frac{64}{1}= 4[/tex]

Change in output = 4

Now we find change in input

Input increases by 2 so change in input = 2

Factor that increase the output is  [tex]\frac{4}{2} = 2[/tex]

Answer:

Step-by-step explanation:

The given table represents an exponential function, that means that variables show a sequence which have an increasing factor that we can find by division.

If we divide the second values by the first value, we could find the factor of the exponential function.

[tex]\frac{1}{16}\div \frac{1}{64} =\frac{1}{16} \times \frac{64}{1}=4[/tex]

So, [tex]f(x)[/tex] increases by a factor of 2.

Now, using the table we see that [tex]x[/tex] values increases by a difference of [tex]+2[/tex], not a factor.

At the moment, while the input value increases by 2, the output value increases by 4.

This means that if the input value increases by 1, the output value increases by 2.

Therefore, the answer is 2.

24 = 2 · 2 · 2 · 3

36 = 2 · 2 · 3 · 3

GCF(24, 36) = 2 · 2 · 3 = 12

24 = 12 · 2

36 = 12 · 3

Answer:

24 + 36 = 12 · 2 + 12 · 3 = 12 · (2 + 3)

Step-by-step explanation:

Answer:

b = sqrt(11)

Step-by-step explanation:

Using the Pythagorean theorem

a^2 + b^2 = c^2

and substituting what we know

5^2 + b^2= 6^2

25 + b^2 = 36

Subtract 25 from each side

25-25 + b^2 = 36-25

b^2 = 11

Take the square root of each side.

sqrt(b^2) = sqrt(11)

b = sqrt(11)

We only take the positive because length must be positive.

Use the Pythagorean theorem

[tex]a^2+b^2=c^2[/tex]

a,b - legs

c - hypotenuse

We have c = 6 and a = 5. Substitute:

[tex]5^2+b^2=6^2[/tex]

[tex]25+b^2=36[/tex]     subtract 25 from both sides

[tex]b^2=11\to \boxed{b=\sqrt{11}}[/tex]