What is an equivalent expression to 4x - 16

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:

9120

Step-by-step explanation:

Answer:

24.071

Step-by-step explanation:

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]

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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The system has one solution

Step-by-step explanation:

Let us revise the type of the solutions of a system of equations

The system of equations is:

y = 2x - 12 ⇒ (1)

y = 3x + 12 ⇒ (2)

∵ The equations are in its simplest form

∵ The coefficients of x in the two equations are different

- That is the 1st case above

∴ The system has one solution

Let us prove that by solving the system

To solve the system of equations equate (1) and (2) to find x

∵ 3x + 12 = 2x - 12

- Subtract 2x from both sides

∴ x + 12 = -12

- Subtract -12 from both sides

∴ x = -24

- Substitute the value of x in equation (1) or (2) to find y

∵ y = 3(-24) + 12

∴ y = -72 + 12

∴ y = -60

∴ The solution of the system is (-24 , -60)

The system has one solution

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To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction.

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of 7/6 is 6/7. Therefore, 49/50 ÷ 7/6 = 49/50 x 6/7. When we multiply the numerators (49 x 6) and the denominators (50 x 7), we get 294/350. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 14. Therefore, 294/350 simplifies to 21/25.

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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.

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.

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

Answer:

aaaaaa

Step-by-step explanation:

bc its the only reasonable one

Answer:3/2

Step-by-step explanation:

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.

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:

42.06 ft²

Step-by-step explanation:

          2 sides = 2(2.7 ft × 3.2 ft) = 2 × 8.64 ft² =   17.28 ft²

 Front + back =  2(2.1 ft × 3.2 ft) = 2 × 6.72 ft² =   13.44 ft²

Top + bottom =   2(2.1 ft × 2.7 ft) = 2 × 5.67 ft² =   11.34 ft²

                                                         Total area = 42.06 ft²

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:

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:

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:

Step-by-step explanation:

[tex]\frac{6}{\frac{2}{6} } =6*\frac{6}{2} =6*3=18[/tex]

Answer:

18

Step-by-step explanation:

6/(2/3)

Turn 6 into a fraction first.

(6/1) / (2/6)

(6/1) x (6/2)

36/2

18

Answer:

check the photo.

Step-by-step explanation:

The inverse of the function

f(x) = ax + b is g(x) = (x/a) - (b/a)

(learn it by heart)

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]

the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].

To find the average rate of change of the function over the interval (10 < x < 15), we use the formula:

[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]

We can calculate the change in [tex]\(f(x)\)[/tex] by subtracting the function values at the end and start of the interval, and the change in x by subtracting the end and start values of x.

Given the function values:

- [tex]\(f(10) = 30\)[/tex]

- [tex]\(f(15) = 24\)[/tex]

And the interval [tex]\(10 < x < 15\)[/tex], the change in [tex]\(f(x)\) is \(f(15) - f(10) = 24 - 30 = -6\)[/tex].

The change in x is [tex]\(15 - 10 = 5\)[/tex].

Now, we plug these values into the formula for the average rate of change:

[tex]\[ \text{Average Rate of Change} = \frac{-6}{5} \][/tex]

So, the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].

The complete Question is given below:

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 < x < 15

x       |   f(0)

0       |   42

5       |   36

10      |   30

15      |   24

20     |   18

25     |   12

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:

No the ratio 3:4 is not equal to 4:5

Step-by-step explanation:

3:4 = 3/4 and 4:5 = 4/5

3/4 is equal to 0.75 and 4/5 is equal to 0.8

0.75 [tex]\neq[/tex] 0.8

therefore, 3:4 [tex]\neq[/tex] 4:5

Hope this helps!

Step-by-step explanation:

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

Answer:64

Step-by-step explanation:

Add 79 with 37 an you will get 116 you need to know the total angle for a triangle is 180 so 180 minus 116 is 64

The measure of the angle y for the triangle is 64°.

The triangle is a shape having three sides and the sum of the angles of the triangle is always equal to 180°.

Here in the given triangle, the two angles are 79° and 37°. The measure of the unknown angle y° will be calculated as:-

y + 79 + 37 = 180

Now solve for the value of angle y below,

y = ( 180 - 79 - 37 )

y = 64°

Therefore, the measure of the angle y for the triangle is 64°.

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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:

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

Answer:

∠ ABC = ∠ DBE = 65°

∠ ABD = ∠ CBE = 115°

Step-by-step explanation:

See the diagram attached to this question.

Now, ∠ ABC and ∠ DBE are two vertically opposite angles.

So, 3x + 38 = 5x + 20

⇒ 2x = 18

⇒ x = 9

So, ∠ ABC = ∠ DBE = 3(9) + 38 = 65° (Answer)

Again, ∠ ABC and ∠ ABD are supplementary angles.

Then, ∠ ABC + ∠ ABD = 180°

⇒ ∠ ABD = 180° - 65° = 115°

And ∠ ABD = ∠ CBE {Vertically opposite angles}

So, ∠ ABD = ∠ CBE = 115° (Answer)