Which best proves why the expressions 4(x+3)+2x and 6(x+2 must be equivalent expressions

Answer:

x = 32

Step-by-step explanation:

24 x 4 = 3x

24 x 4 = 96

96 / 3 = 32

x = 32

Answer:

x = 32

Step-by-step explanation:

You want to find x.

First, simplify and combine like terms. Using PEMDAS, do the parenthesis first.

(3 x 8) x 4 = 3x

24 x 4 = 3x

96 = 3x

Now, divide each side by 3 to isolate x.

x = 32

Answer:

you gave no context....so ill just guess 3.

DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.

1.) 2+3 = y + 12

Make y the formula's subject after adding the LHS.

5 = y + 12

Y = 5 - 12

Y = - 7

The answer to the equation is -7

2.) 2 + 13 = 1 +8

The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).

3.) y - 7 = 2 - 11

RHS is added, and y is become the formula's subject.

Y - 7 = -9

Y = -9 + 7

Y = -2

The equation's answer is -2.

The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12

2 + 13 = 1 +8

y - 7 = 2 - 11

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The length of each arc intercepted by each slice is 2.09 inches.

The area of each slice 18.85 square inches .

To find the length of each arc intercepted by each slice and the area of each slice of a pizza that is 12 inches in diameter, follow the steps below. Length of each arc intercepted by each slice

The formula to find the length of each arc is given by:

L = θ/360 * 2πr

WhereL = length of arc

θ = angle of arc in degrees

r = radius of circle (diameter/2)

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

L = 60/360 * 2π* 6L = 1/6 * 12πL = 2π/3 ≈ 2.09 inches

The formula to find the area of each slice is given by:

A = θ/360 * πr²

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

A = 60/360 * π* 6²A = 1/6 * 36π

A = 6π ≈ 18.85 square inches

Thus, the length of each arc intercepted by each slice is approximately 2.09 inches and the area of each slice is approximately 18.85 square inches.

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Answer:

2/3a^5

Step-by-step explanation:

we know that 2/7x2/7x2/7 = 8/27

a^15  cube will be a^5

because we know (2^3)^2 = 2^6

so (a^5)^3 = a^15

2/3a^5

Answer:83 1/3

Step-by-step explanation: Converting all of these to improper fractions gives us 173/9 + 221/8 + 259/7. Let's first worry about adding 173/9 and 221/8. To get a common denominator lets simply use 72 (8x9). The adjusted fractions are 1384/72 + 1989/72. Now we just do simple addition, we get 3373/72. Now the pesky 259/7. We will repeat the same process, let's use 504 as a denominator now (7x72). We now have 23611/504 + 18389/504 making our final answer 42000/504 or 250/3 or 83 1/3 simplified.

According to the information, Jerome should use cube modeling to start making his animal in 3D because this alternative has a cube as its starting point.

Cube modeling is a term that refers to a type of modeling of three-dimensional elements in technological devices whose main characteristic is that it uses cube models as a starting point to model a figure.

In general, the designer must take the cube as a reference and modify it to obtain a different figure. In this case Jerome must modify the cube that he already has and create a more complex shape from it.

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The population the instructor is interested in is Lake Tahoe Community College math students, specifically looking at their average number of days absent from class in a quarter.

The population that the Lake Tahoe Community College instructor is interested in is the students who are enrolled in the math classes at the college during a quarter. This would include any student who is enrolled in a math course and has attended any classes during the quarter. It does not include students who are enrolled in other courses or students who have not attended any classes during the quarter. The population is limited to math students at Lake Tahoe Community College only and does not include students from other colleges or universities. The instructor is interested in the average number of days a student is absent from class during a quarter and this requires information from every student in the population. Therefore, the population of interest is Lake Tahoe Community College math students.

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Answer:

(motorboat speed is 40 km/h)

(current speed) = 10 km/h

Step-by-step explanation:

Ok, let the speed of the water current be x and the speed of the motorboat be y. Then, the speed of the motorboat upstream

against the current is (x - y)

Putting it into the equation, we get,

5h (x - y) = 150 km or

(x - y) = 30 km/h -  1

Now, downstream speed is (x + y).

Again, forming it into equation, we get,

3(x + y) = 150

x + y = 50 km/h  -   2

Adding both equations, we get,

2x = 80 km/h

x (motorboat speed is 40 km/h)

40 - y = 30 km/h

y(current speed) = 10 km/h

Answer:

still water (s): 40 mph

current rate (c): 10 mph

Step-by-step explanation:

We are given two things:

1) 5 hours to travel 150 mi upstream

2) return trip 3 hours downstream

Note that when the boat goes upstream, it must push against the current, versus when it goes downstream, the current helps the boat to move. Also keep in mind the trip is always 150 mi both ways.

With that said, lets set up the problem. First, let s be the rate of the boat in still water, and let c be the rate of the current. We must keep in mind that when the boat goes upstream, it impedes its overall speed. So our equation for that looks like:

5(s-c)=150 (use for upstream)

And downstream would look like:

3(s+c)=150 (use for downstream)

Now that we have both equations, the next step is to expand them. You should get the two following equations:

5s-5c=150 AND 3s+3c=150.

Essentially, we are going to need to solve a system of equations here. You must add them to solve. First, multiply the first equation above by 3 and get 15s-15c=450 and multiply the second one by 5 and get 15s+15c=750.

When we add them we will get the following equation as a result: 30s=1200. Now divide both sides by 30 revelaing s to be 40. Now substiute in:

3(40)+3c=150

120+3c=150

-120      -120

3c=30

c=10

The system of equations is now solved revelaing the speed of the boat in still water to be 40 and the current speed to be 10.

Answer:

296

Step-by-step explanation:

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

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Answer:

D

Step-by-step explanation:

Answer:

D. the distance between A and C

Step-by-step explanation:

|-2| = 2

its the distance between -2 and 0

The number of years it will take for the account to be worth $15,000 according to the task content is; 29.164 years.

It follows from the task content that the interest is compounded annually and hence, we have;

15000 = 10000(1.014)^x

1.5 = (1.014)^x

log (1.5) = x log(1.014)

x = log (1.5)/log(1.014)

x = 29.164 years.

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Solving for M, we get M = 5. Therefore, Michael is currently 5 years old.

Let's represent Ana's age as "A" and Michael's age as "M". We know that A = 2M since Ana is twice as old as Michael. Three years ago, Ana's age was (A-3) and Michael's age was (M-3). We also know that (A-3) = (M-3)+2 since Ana was two years older than Michael is now.
Now we can simplify and solve for M:
A-3 = M-1
2M-3 = M-1
M = 2
Therefore, Michael is 2 years old.
To solve this problem, let's represent Michael's age with the variable M, and Ana's age with the variable A. We know that A = 2M and that A - 3 = M + 2.
Now, substitute A with 2M: 2M - 3 = M + 2. Solving for M, we get M = 5. Therefore, Michael is currently 5 years old.

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Answer: y−intercept=1/ 17 =17.00000

Step-by-step explanation: y-3x-17  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis

Answer: 1,004.8 cubic meters (choice D)

Work Shown:

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*8^2*15

V = 1,004.8

the solution of  given close figure is In the given figure there are 13 triangle

A triangle is a closed, two-dimensional geometric shape that has three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angles.

There are 13 triangles in the given figure

Part 1)ΔACE,

Part 2)ΔABF

Part 3)ΔAFE

Part 4)ΔACD

Part 5)ΔACD

Part 6)ΔACD

Part 7)ΔECB

Part 8)ΔEDF

Part 9)ΔEBA

Part 10)ΔADE

Part 11)ΔCBD

Part 12)ΔBDF

Part 13)ΔBDE

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c) It would be larger, because higher confidence requires a larger margin of error.

When increasing the confidence level from 95% to 99%, the margin of error of the confidence interval tends to increase. This is because a higher confidence level means we want to be more certain or have a higher level of confidence in capturing the true population parameter.

To achieve a higher confidence level, we need to widen the interval to account for more potential variability in the population. As a result, the margin of error increases, reflecting the increased uncertainty and the need for a larger range of values to capture the true population parameter with higher confidence.

Therefore, the margin of error of a 99% confidence interval, based on the same sample, would be larger compared to the 95% interval.

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Answer:

Faster runner speed: 11 mph

Slower runner speed: 9 mph

Distance from starting point: 9.9 miles

Step-by-step explanation:

Let the slower runner speed be: x

Faster runner speed: x+2

1 hour 6 minutes = 1.1 hours

Slower: 1.1(x) = 1.1x miles

Faster: 1.1(x+2) = 1.1x+2.2 miles

This means that the faster runner had gone 2.2 miles more than the slower runner.

1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)

1.1x > 11 - 2.2 miles

1.1x > 8.8 miles

x > 8.8 / 2.2 miles

x > 8 mph

1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)

x < 11 / 1.1 miles

x < 10 miles

8 < x < 10

Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.

Slower runner distance to the end:

1.1(9) = 9.9 miles

11 - 9.9 = 1.1 miles

Faster runners distance from the end (when coming back)

1.1(9+2) = 1.1(11) = 12.1 miles

12.1 - 11 = 1.1 miles

The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point

The runners meet at a distance of 8.8 miles from the starting point.

According to statement, each runner must run back and forth on a 11-mile course. After supposing that each runner moves at constant speed, expressions for each runner are presented below:

Fast runner reaches the end

\((v+2)\cdot 1.1 = 11\) (1)

Fast runner comes back from the end

\(x = \left(v+2\right)\cdot (1.1-t)-(v+2)\cdot t\) (2)

Slow runner meets fast runner

\(x = v\cdot 1.1\) (3)

Where:

By (1), we obtain the speed of the slow runner:

\(v = \frac{11}{1.1}-2\)

\(v = 8\,\frac{mi}{h}\)

The position from the starting point is calculated by (3):

\(x = (8\,mi)\cdot \left(1.1\,h\right)\)

\(x = 8.8\,mi\)

The runners meet at a distance of 8.8 miles from the starting point. \(\blacksquare\)

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The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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In this case, the company sold its bonds for $64,800 cash, which is the amount to be reported on the statement of cash flows.
The correct answer is:
d. $(64,800)

When a company sells its bonds, the cash received from the transaction is reported on the statement of cash flows under the financing activities section.

The sale of the bonds resulted in a cash inflow of $64,800, which is reported as a financing activity on the statement of cash flows. However, since the company sold the bonds at a loss of $3,800, this loss also needs to be reported as a separate line item under cash flows from financing activities. It is important to note that while the sale of the bonds improved the company's cash flow, it also resulted in a loss for the company. This loss represents a decrease in the company's equity and is reported on the balance sheet as a reduction in retained earnings.
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Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

Answer:

The 6 pack

Step-by-step explanation:

i searched it up

The required option that has a lesser price per mini football is a package of 8.

Given that,
at a toy store, Colton can buy a package of 6 mini footballs for $7.50. or a package of 8 mini footballs for $9.60. wich option has the lesser price per mini football is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
For 6 package footballs the cost of a mini football = 7.50 / 6 = $1.25.
For 8 package footballs the cost of a mini football = 9.60 / 8 = $1.20.

Thus, the required option that has a lesser price per mini football is a package of 8.

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Answer:

El número de facturas

5 lempiras = 10 billetes

20 lempiras = 15 billetes

Step-by-step explanation:

Vamos a representar

El número de facturas de

5 lempiras = x

20 lempiras = y

Nuestro sistema de ecuaciones se da como:

x + y = 25 ..... Ecuación 1

x = 25 - y

5 × x + 20 × y = 350

5x + 20y = 350 .... Ecuación 2

Sustituiríamos x por 25 - y en la ecuación 2

5 (25 - años) + 20y = 350

125 - 5 años + 20 años = 350

125 + 15 años = 350

15 años = 350 - 125

15 años = 225

y = 225/15

y = 15

Resolviendo para x

x = 25 - y

x = 25 - 15

x = 10

Por lo tanto, el número de facturas

5 lempiras = 10 billetes

20 lempiras = 15 billetes

The maximum height the rocket will reach is approximately 327.5 meters.

First, let's find the velocity of the rocket when the fuel runs out.

Using the formula:

v = u + at

where v is final velocity, u is initial velocity (0 m/s), a is acceleration (8 m/s²), and t is time (10 seconds of fuel), we get:

v = 0 + (8 m/s²) x (10 s) = 80 m/s

So, when the fuel runs out, the rocket will be traveling upwards at a velocity of 80 m/s.

Next, we need to find the time it takes for the rocket to reach its maximum height after the fuel runs out.

Using the formula:

v = u + at

where v is final velocity (0 m/s), u is initial velocity (80 m/s), a is acceleration (9.8 m/s²), and t is time, we get:

0 = 80 m/s + (-9.8 m/s²)t

Solving for t, we get:

t = 8.16 seconds

So, it will take the rocket 8.16 seconds after the fuel runs out to reach its maximum height.

Now, we can calculate the maximum height using the formula:

s = ut + (1/2)at²

where s is the displacement (maximum height), u is initial velocity (80 m/s), a is acceleration (9.8 m/s²), and t is time (18.16 seconds).

Plugging in the values, we get:

s = (80 m/s)(8.16 s) + (1/2)(-9.8 m/s²)(8.16 s)²

s = 327.5 meters

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Answer:

\(h>11\)

Step-by-step explanation:

We have the inequality:

\(-2(h-5)<-12\)

Solve. Divide both sides by -2. Since we are dividing by a negative, we must flip the inequality sign. Thus:

\(h-5>6\)

Add 5 to both sides:

\(h>11\)

Therefore, our solution is all numbers greater than 11 .

This means that if we substitute any number greater than 11 into our original inequality, the inequality will be true.

To find parametric equations for the line passing through the points (0, 1/2, 1) and (9, 1, -3), we can use the following approach:

Let's denote the parametric equations as:

x = x₀ + at

y = y₀ + bt

z = z₀ + ct

where (x₀, y₀, z₀) is a point on the line and (a, b, c) are the direction ratios.

We can determine the direction ratios by subtracting the coordinates of the two points:

(a, b, c) = (9 - 0, 1 - 1/2, -3 - 1) = (9, 1/2, -4)

Now, we can choose one of the given points as the point (x₀, y₀, z₀). Let's choose (0, 1/2, 1):

x = 0 + 9t = 9t

y = 1/2 + (1/2)t = (1/2)(1 + t)

z = 1 + (-4)t = 1 - 4t

Therefore, the parametric equations for the line passing through the points (0, 1/2, 1) and (9, 1, -3) are:

x = 9t

y = (1/2)(1 + t)

z = 1 - 4t

These equations describe the position of any point (x, y, z) on the line as a function of the parameter t.

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Answer:

$21.00 and the pound is 6

Step-by-step explanation: