4.
Nat had some stamps. He divided them into sets
of six to put in his album. He made 17 sets. How
many stamps did Nat have?

f^-1(x) = sq.rt 5(x - 10)/5, sq.rt 5(x - 10)/5 is the inverse of y = 5x^2 +10

Step-by-step explanation:

interchanging the variables

x = 5y^2 + 10

5y^2 +10 = x

5y^2 = x - 10

dividing by 5

5y^2/5 = x/5 + -10/5

y^2 = x/5 + - 10/5

y^2 = x/5 - 2

y = 5 (x-10) 0/5 (sq.rt)

g(5x^2 + 10) = 5x/5

g(5x^2 + 10) = x

f^-1(x) = sq.rt 5(x - 10)/5, sq.rt 5(x - 10)/5 is the inverse of y = 5x^2 +10

Answer:

its A i took the test on Eg2020

Answer: 8 gumballs

Step-by-step explanation:

We can solve this problem with the Rule of three, since we are given as data three factors and one is unknown.

If 2 gumballs cost 8 cents, how many gumballs can we buy with 32 cents?:

[tex]2 gumballs[/tex]-----[tex]8 cents[/tex]

[tex]x[/tex]-----[tex]32 cents[/tex]

Then:

[tex]x=\frac{(2 gumballs)(32 cents)}{8 cents}[/tex]

[tex]x=8 gumballs[/tex] We can buy 8 gumballs with 32 cents

Answer:

[tex]\displaystyle A = \frac{12}{5}[/tex]

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Calculus

Integration

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Splitting Integral]:                                                               [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify bounded region. See attached graph.

y = 3x - 6

y = -2x + 8

Bounded by x-axis and between those 2 lines (already pre-determined; taking an integral always takes it to the x-axis).

Step 2: Analyze Graph

See attached graph.

Looking at our systems of equations on the graph, we see that our limits of integration is from x = 2 to x = 4.

We don't have a continuous top function through the interval [2, 4] (it switches from y = 3x - 6 to y = -2x + 8), so we need to split it into 2 integrals to find the total area.

We can either use the graph and identify the intersection point, which is x = 2.8, or we can solve it algebraically (systems of equations - substitution method):

Our 2 intervals would be [2, 14/5] and [14/5, 4] for their respective integrals.

Step 3: Find Area

Our top functions are the linear lines y = 3x - 6 and y = -2x + 8 and our continuous bottom function is the x-axis (x = 0).

We can redefine the linear lines as f₁(x) = 3x - 6, f₂(x) = -2x + 8, and g(x) = 0.

Integration

We have found the area bounded by the x-axis and linear lines y = 3x - 6 and y = -2x + 8.

Topic: Calculus BC

Unit: Area between 2 Curves, Volume, Arc Length, Surface Area

Chapter 7 (College Textbook - Calculus 10e)

Hope this helped!

Answer:

A = 12/5 units

Step-by-step explanation:

USING ALGEBRA:

We can find the intersection point between these two lines;

Set these two equations equal to each other.

Add 2x to both sides of the equation.

Add 6 to both sides of the equation.

Divide both sides of the equation by 5.

Find the y-value where these points intersect by plugging this x-value back into either equation.

Multiply and simplify.

Multiply 6 by (5/5) to get common denominators.

Subtract and simplify.

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

Add 6 both sides of the equation.

Divide both sides of the equation by 3.

Set the second equation equal to 0.

Add 2x to both sides of the equation.

Divide both sides of the equation by 2.

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

Substitute 2 for b and 14/5 for h.

Multiply and simplify.

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

Final answer:

The approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth is about 14.7 meters.

Explanation:

To find the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth, we can use the formula for the period of a pendulum:

T = 2π √(L/g)

Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Given that the period is 2.4 pi seconds, we can substitute this value into the formula:

2.4 pi = 2π √(L/g)

Simplifying the equation, we can divide both sides by 2π:

1.2 = √(L/g)

Squaring both sides of the equation, we get:

1.44 = L/g

Since we don't have the value of g, we cannot solve for L exactly. However, if we assume that g is approximately 9.8 m/s², which is the average acceleration due to gravity on Earth, we can estimate the value of L:

1.44 = L/9.8

Multiplying both sides by 9.8, we find:

L ≈ 14.7 m

Answer:

aaaaaa

Step-by-step explanation:

bc its the only reasonable one

Answer:

1125/8 minutes

Step-by-step explanation:

45/80=x/250

cross product

80*x=45*250

80x=11250

x=11250/80

x=1125/8

Final answer:

To calculate the time it will take for the diver to reach a depth of 250 feet based on the given information.

Explanation:

The depth of a diver is directly proportional to the time since the diver entered the water.

To find the time it will take to reach a depth of 250 feet, we can set up a proportion using the given information: 80 ft / 45 min = 250 ft / x min. Cross-multiply and solve for x to find the time.

Therefore, the time it will take to reach a depth of 250 feet is approximately 140.6 minutes.

Step-by-step explanation:

[tex] - 3(4x - 2) - 2x \\ \\ = - 12x + 6 - 2x \\ \\ = - 14x + 6[/tex]

Answer:

Since this dude got a Bird Brain I got ya'll

Step-by-step explanation:

Whats in Bold is what you put in the drop down menu. :)

So, f(3) = 26. This means that after 3 months, the number of products sold were 26,000.

If f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Finding profit, populations, and distance traveled are some applications of functions. By entering a number into the formula, locating the independent variable on a table or graph, and then computing the resulting dependent variable, functions are employed.

It is given that,

f(t)=5t+11

So for the given condition after three months,

Substitute the value of t as 3,

f(3)=5(3)+11

f(3)=15+11

f(3)=26

Thus, if f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.

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Answer:

Neither positive nor negative—the sum is zero.

Step-by-step explanation:

Final answer:

The mathematics problem involves cancelled positive and negative numbers. Adding a number to its negative results in zero. Therefore, the expression simplifies to zero.

Explanation:

The question provided appears to be a mathematics problem that involves adding a number and its negative equivalent. Specifically, it looks like the sum of 123 and 1/23 plus the negative of 123 and 1/23 is being asked.

When you sum a number and its negative, they cancel each other out, resulting in zero. This is because the definition of a negative number is that it's the additive inverse of its positive counterpart, meaning when the two are added together, their sum is zero. The calculation is straightforward:

123 and 1/23 + (-123 and 1/23) = 0.

Answer:

From 10 to 20 meters.

Step-by-step explanation:

1) If the sparrow has a parabolic trajectory then it must be actually:

[tex]y=-5\left ( x+6 \right )^{2}+10[/tex]

2) If the eagle is at 20 meters high, then we write:

[tex]y=20[/tex]

Since the exact x coordinate was not given.

But since it wants to get the sparrow

3) If we expand the equation we have:

[tex]-5x^{2}-60x-170=0\\\\X_{v}=\frac{-b}{2a}=\frac{60}{-10} = -6\\Y_{v}=\frac{-\Delta}{4a} =\frac{-200}{-20} =10[/tex]

Since the maximum point is equal to 10. The distance where the sparrow is flying ranges from 10 to 20 meters to the eagles spot.

[tex]10\leq d \leq20 \:or \:[10,20][/tex]

4) Since the x coordinate was not given then we can neither precisely calculate the distance where A is nor where B is located.

Answer:

3 meters

Step-by-step explanation:

Answer:

Step-by-step explanation:

x+2y=7

Final answer:

To write an equation with (1,3) as a solution, choose an arbitrary slope and use the given point to solve for the y-intercept, forming a complete linear equation.

Explanation:

To write an equation in two variables that has (1,3) as a solution, you start by understanding linear equations in the form y = mx + b, where m is the slope, and b is the y-intercept. Given the point (1,3), we can choose an arbitrary slope (for example, 2) and plug the point into the equation to solve for b.

Note: y = 2x + b, and with the point (1,3), substituting x with 1 and y with 3 gives 3 = 2(1) + b, which simplifies to b = 1. Therefore, an example equation that fits the criteria is y = 2x + 1.

Answer:

Step-by-step explanation:

y = 5/3x + 5...in y = mx + b form, the slope is in the m position and the y int is in the b position.

so we have a slope of 5/3 and a y int of 5.....(0,5)

the x int can be found by subbing in 0 for y and solving for x

0 = 5/3x + 5

-5/3x = 5

x = 5 * -3/5

x = -15/5

x = -3......so ur x int is (-3,0)

go ahead and plot ur intercepts....(0,5) and (-3,0).....now start at (-3,0)....and since ur slope is 5/3....go up 5 spaces and to the right 3 spaces...plot that point.....then go up 5 and to the right 3...plot that point....keep doing this pattern....u should cross the y axis at (0,5). Then just connect ur dots and u have ur line.

Answer:

This is what I came up with

5. (6,32)

6. That means that when six kites are order it would be the same cost from each company

Step-by-step explanation:

The solution y = 3x + 12 represents a linear relationship between two variables in the given scenario, with an initial cost of $12 and an additional cost of $3 for each unit increase in the independent variable "x." The interpretation of this relationship depends on the specific context of the problem.

The given system of equations can be written in slope-intercept form, which is in the form y = mx + b, where "m" represents the slope of the line, and "b" represents the y-intercept. In this context, the system is as follows:

4 = 3m + b

12 = b

We can solve this system to find the values of "m" and "b."

First, we already know that b = 12 from the second equation.

Now, substitute this value into the first equation:

4 = 3m + 12

Next, isolate "3m" by subtracting 12 from both sides of the equation:

3m = 4 - 12

3m = -8

Finally, divide both sides by 3 to solve for "m":

m = -8/3

So, we have found that m = -8/3 and b = 12.

Now, let's interpret the solution in the context of the scenario:

The equation y = 3x + 12 represents the relationship between "x" (which could represent a quantity like time or another variable) and "y" (which could represent a cost, height, or another quantity). In this specific case, it seems like the equation describes a linear relationship between two variables.

In terms of the scenario, it could mean that there is an initial cost of $12 (the y-intercept) and an additional cost of $3 for each unit increase in "x." This interpretation depends on the context of the problem. For example, if "x" represents the number of items purchased, then $12 could be an initial fee, and $3 could be the cost per item.

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The question probable may be:

 find the system to the solution you have to put in into slope intersecpt form so y=mx+b

so 4=m(3)+b

12=b

y=3x+12 Explain what your solution means in terms of the scenario. *

Answer: 5/8

Step-by-step explanation:

5*3=15

6*4=24

Get 15/24 simplify and get 5/8

How to simplify it?

Divide 15 and 3

Divide 24 and 3

Get 5/8

Answer:

Step-by-step explanation:

Using this formula to find the length of the arc

Arc length = [tex]2\pi r (\frac{\theta}{360} )[/tex]

Here [tex]\theta = \frac{360}{60}\times 45[/tex]   [for 45 minutes]

            [tex]=270^\circ[/tex]

Radius(r) = length of the minute hand = 12 cm

The length of the arc is = [tex]2\pi \times 12\times \frac{270}{360}[/tex]

                                     = 56.57 cm

Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.

Answer:

49

Step-by-step explanation:

7:6:8 so 7+6+8=21

147 divided by 21 is 7

so 1 ratio equals 7

red = 7 so its gonna be 7x7=49

Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.

To find out how many of each bill Dalton has, we can set up a system of equations.

Let's assume Dalton has x number of ten-dollar bills and y number of twenty-dollar bills. The total number of bills he has is given as 7, so we have the equation: x + y = 7.

Additionally, the total value of the bills is given as $100. Since each ten-dollar bill is worth 10 dollars and each twenty-dollar bill is worth 20 dollars, we have the equation: 10x+20y = 100.

Now we can solve the system of equations to find the values of x and y.

Multiplying the first equation by 10 to eliminate x, we have: 10x + 10y = 70.

Subtracting this equation from the second equation, we get: 10x + 20y - (10x + 10y) = 100 - 70.

Simplifying, we have: 10y = 30.

Dividing both sides of the equation by 10, we find that y = 3.

Substituting this value back into the first equation, we can solve for x: x + 3 = 7.

Subtracting 3 from both sides, we find that x = 4.

Therefore, Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.

The system of linear inequalities are:

[tex]a + b \geq 20\\\\2.50a + 7b\leq 80[/tex]

Solution:

Let "a" be the number of small candles bought

Let "b" be the number of large candles bought

Cost of each small candle = $ 2.50

Cost of each large candle = $ 7

He needs to buy at least 20 candles

Therefore, number of small candles and number of large candles bought must be at least 20

Thus, we frame a inequality as:

[tex]a + b\geq 20[/tex]

"at least" means greater than or equal to

Here, we used "greater or equal to" symbol because, he can buy 20 candles or more than 20 candles also

He can spend no more than 80 dollars

Which means, he spend maximum 80 dollars or less than 80 dollars also

So we have to use "less than or equal to" symbol

Thus, we frame a inequality as:

Number of small candles bought x Cost of 1 small candle + number of large candles bought x Cost of 1 large candle [tex]\leq[/tex] 80

[tex]a \times 2.50 + b \times 7 \leq 80\\\\2.50a + 7b\leq 80[/tex]

Thus the system of linear inequalities are:

[tex]a + b \geq 20\\\\2.50a + 7b\leq 80[/tex]

Answer:

24.071

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I also took a quiz with this question and I got the right answer.

To find the slope of g(x), use the slope formula(m):

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]        And plug in two points, I will use:

(0, 2) = (x₁, y₁)

(5, 4) = (x₂, y₂)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{4-2}{5-0}[/tex]

[tex]m=\frac{2}{5}[/tex]

You could do the same to find f(x) by finding two points and using the slope formula, or you could use this to tell visibly:

[tex]m=\frac{rise}{run}[/tex]

Rise is the number of units you go up(+) or down(-) from each distinguished point

Run is the number of units you go to the right from each distinguished point

If you look at the graph, you can see the points (0, -1) and (3, 1). From each point, you go up 2 units and to the right 3 units (you can make sure by using another point). So the slope of f(x) is  [tex]\frac{2}{3}[/tex]

Whichever line looks more vertical(and is positive) has the greater slope. So the slope of f(x) is greater than the slope of g(x). The answer is option A

Answer:

w=4.9

Step-by-step explanation:

If you are solving for w, you want to isolate the variable. If it is easier to write it out, it would look something like this..

-5 x w = -24.5

To get w by itself, use the inverse of multiplication, which is division. Divide the expression to the left of the equal sign by -5. Remember, what you do to one side, you must do to the other. When you divide -24.5 by -5, you end up with

w=4.9

The width of the garden is 9 feet.

The length of the garden is 15 feet.

Step-by-step explanation:

Area of the rectangle = length[tex]\times[/tex]width

⇒ 135 = (x+6)x

⇒ 135 = x² + 6x

⇒ x²+6x-135 = 0

Using factorization method,

x²+6x-135 = 0

⇒ (x+15)(x-9) = 0

∴ x = -15 and x = 9

The width of the garden is 9 feet.

The length of the garden is (x+6) = 15 feet.

By assigning a variable to the width of the garden and using the provided length and area, we can create and solve an equation which tells us that the width of the garden is 9 feet and the length is 15 feet.

Let's assign the width of the vegetable garden as 'x', so the length of the garden would be 'x + 6' feet because we know it is 6 feet longer than the width. The area of a rectangle is computed by multiplying the length and the width. So, the equation we come up with, based on the question, is 'x(x + 6) = 135' square feet.

Let's solve this equation. We first expand the multiplication on the left-hand side which gives us 'x2 + 6x = 135'. By rearranging this equation, we set it to zero: 'x2 + 6x - 135 = 0'. Subsequently, we can factor this equation to ' (x - 9)(x + 15) = 0'. Setting each factor equal to zero gives us the solutions 'x = 9' or 'x = -15'. However, since a negative width doesn't make sense in this context, we discard '-15'. Therefore, the width of the garden is 9 feet, and the length is 9 + 6 = 15 feet.

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Answer:

9120

Step-by-step explanation:

The missing figure is attached down

The volume of the cone is 88.49 cm³ to the nearest hundredth ⇒ A

Step-by-step explanation:

The formula of the volume of a cone is V = [tex]\frac{1}{3}[/tex] πr²h, where

From the attached figure:

∵ The diameter of the base of the cone is 6.5 cm

∵ The radius = [tex]\frac{1}{2}[/tex] diameter

∴ r =  [tex]\frac{1}{2}[/tex] × 6.5 = 3.25 cm

∵ The length of the height of the cone = 8 cm

- Substitute r and h in the formula of the volume above

∵ V =  [tex]\frac{1}{3}[/tex] × π × (3.25)² × 8

∴ V = 88.48819308 cm³

- Round it to the nearest hundredth

∴ V = 88.49 cm³

The volume of the cone is 88.49 cm³ to the nearest hundredth

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Question:

Simplify [tex]\left(s^{2}-2 s-9\right)+\left(2 s^{2}-6 s^{3}+s\right)[/tex]

Answer:

The solution is [tex]-6 s^{3}+3 s^{2}-s-9[/tex]

Explanation:

The expression is [tex]\left(s^{2}-2 s-9\right)+\left(2 s^{2}-6 s^{3}+s\right)[/tex]

Let us simplify the expression by removing the parentheses, [tex](a)=a[/tex]

Thus, the expression becomes,

[tex]s^{2}-2 s-9+2 s^{2}-6 s^{3}+s[/tex]

Let us group the like terms, we get,

[tex]-6 s^{3}+s^{2}+2 s^{2}-2 s+s-9[/tex]

Adding the similar terms, we have,

[tex]-6 s^{3}+3 s^{2}-s-9[/tex]

Thus, the solution of the expression [tex]\left(s^{2}-2 s-9\right)+\left(2 s^{2}-6 s^{3}+s\right)[/tex] is [tex]-6 s^{3}+3 s^{2}-s-9[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

 Area of shades region [tex]=45[/tex] square inches

Step-by-step explanation:

In the given figure accordingly, we have to find the Area of the shaded region

Area of shaded region= Area of big triangle - Area of the small triangle.

          Area of a  triangle=  [tex]\frac{1}{2} *base*altitude[/tex]

Altitude is the perpendicular height of the triangle from its top to base.

Base of big triangle=12 inches,    Altitude of big triangle=6+3= 9 inches

Area of Big triangle  

                                     [tex]=\frac{1}{2}* 12*9\\\\=6*9\\\\=54[/tex]

Base of small triangle= 6 inches,    Altitude of small triangle= 3 inches

Area of the small triangle=

                                            [tex]=\frac{1}{2} *6*3\\\\=3*3\\\\=9[/tex]

        Area of shades region [tex]=54-9\\[/tex]

                                              [tex]=45[/tex] square inches

Answer:

option B.) 5 + 2r = 20 is correct

Step-by-step explanation:

Carrie mows a lawn, she charges a flat fee of $5 plus an hourly rate, r.

The amount Carrie earns for mowing lawns for t number or hours

= 5 + rt

Carrie worked for 2 hours and charged a total of $20.

Therefore we can write

20 = 5 + r [tex]\times[/tex] 2    [tex]\Rightarrow[/tex] 20  =  5 + 2r

Therefore option B.) 5 + 2r = 20 is correct

Answer:

2 examples would be

7 3/20

or

7  9/60.

Step-by-step explanation:

0.15 = 15/100

= 3/20.

So 7.15

= 7 3/20

Answer:

Step-by-step explanation:

7.15 to fraction

= 7.15 × (100/100)

= 715/100

= 143/20

= 7 3/20