Is (2, 7) a solution to this system of equations? y = 3x + 1 y = 2x + 5 yes or no​

Step-by-step explanation:

The limit of (sin(x)) / x as x approaches 0 is a well-known limit in calculus, known as the limit definition of the derivative of the sine function.

lim (x -> 0) (sin(x)) / x = 1

This limit can be proven using L'Hopital's rule or by considering the Taylor series expansion of the sine function about x = 0:

sin(x) = x - (x^3) / 6 + (x^5) / 120 + ...

As x approaches 0, the higher order terms in the Taylor series become arbitrarily small, and the expression (sin(x)) / x approaches 1. This shows that the limit of (sin(x)) / x as x approaches 0 is equal to 1.

The inverse statement is false.

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Answer:

4(3 + 20)

Step-by-step explanation:

Since the 4 is shared among the two terms, we factor it out and write what is left over inside the parenthesis: 4(3 + 20).

12=4*3

80=4*20

4(3 + 20)

So 12 +80 = 4(3 + 20) = 92

Answer:

1. 38 oz / 2 lbs 6 oz

2. 254 in / 7 yd 2 in

3. 21 pt / 3 gal 2 qt 1 pt

4. 18,480 ft / 3 mi 2,640 ft

5. 180 oz / 6 lbs 12 oz

6. 525 s / 8 min 45 s

7. 318 in / 8 yd 2 ft 10 in (9.99996 inches not simplified)

8. 9 pt / 4 qt 1 pt

9. 15,885 s / 4 hr 24 min 45 s

The first answers are the ones I got originally and the second answers are the simplified ones.

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer: The surface area of the rectangular prism is approximately 4 square yards.

Step-by-step explanation: Given that the volume of the rectangular prism is 160 cubic yards, we can find the dimensions of the prism using the formula:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

So, we have:

160 = lwh

Now, we need to find two other measurements in order to calculate the surface area of the rectangular prism. However, we do not have enough information to find all three dimensions. Therefore, we will assume one dimension and find the other two.

Let's assume that the height of the rectangular prism is 10 yards. Then, we can rearrange the formula for the volume to solve for the product of the length and width:

lw = V/h = 160/10 = 16

Now, we have two equations:

lw = 16

wh = 160/10 = 16

Solving for w in the first equation, we get:

w = 16/l

Substituting this expression for w in the second equation, we get:

l(16/l)h = 16

Simplifying, we get:

h = 1

Therefore, the dimensions of the rectangular prism are:

length = l

width = 16/l

height = 10

Now, we can calculate the surface area of the rectangular prism using the formula:

SA = 2lw + 2lh + 2wh

Substituting the values we found, we get:

SA = 2(l(16/l)) + 2(l(10)) + 2((16/l)(10))

SA = 32/l + 20l + 160/l

To find the minimum value of this expression, we can take its derivative with respect to l and set it equal to zero:

dSA/dl = -32/l^2 + 20 + (-160/l^2)

0 = -32/l^2 + 20 - 160/l^2

52/l^2 = 20

l^2 = 52/20

l ≈ 1.44

Substituting this value of l back into the expression for SA, we get:

SA ≈ 4 square yards

Therefore, the surface area of the rectangular prism is approximately 4 square yards.

The expression for the sequence of operations is  3s - u - t .

In the question ,

it is given that ,

the sequence of operation is given as " triple s, subtract u from the result, then subtract t from what you have" .

we have to write an expression for the above operation ,

So ,

first step is : triple s ,

that means the expression is  3s .

next subtract u from the result , that means ⇒ 3s - u .

next we have to subtract t from what we have ,

that means ⇒ 3s - u - t .

Therefore , the final expression is 3s - u - t .

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Answer:

Step-by-step explanation:

4ox-16=4[10x-4]this is because 4 is the common factor in both 40and 16

16x-24x-4±12=4[4x-6x-1±3]

-8x-8=8[-1-1]

The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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Answer:

  B.  g(x)

Step-by-step explanation:

g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.

f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.

g(x) has the smallest minimum value

Answer:

\(38-8\left(n-1\right),\:n=123:\quad -938\)

\(\mathrm{For}\:38-8\left(n-1\right)\:\mathrm{substitute}\:n\space\mathrm{\:with\:}\space123\)

\(38-8(123-1)= -938\)

\(-938\)

Step-by-step explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Check the picture below.

Answer:

So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 2^4 × 3.

Step-by-step explanation:

I just googled it. So B. I think.

Answer:

a = (u-2b)/6

Step-by-step explanation:

First get a by itself by subtracting 2b from both sides:

u-2b = 6a

Then isolate the variable by dividing both sides by six:

(u-2b)/6 =a

Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

The line of best fit for this set of points is y = -1.00x + 9.00.

Coefficient is a value that is used to indicate the degree or amount of a certain property or characteristic. It is usually used in mathematics and physics, and is a numerical measure of how two variables are related. For example, the coefficient of friction is a number that indicates how much resistance there is between two surfaces when one is sliding over the other. In economics, the coefficient of elasticity is used to measure how much of a change in one variable affects a change in another.

Linear regression is a technique used to find the line of best fit for a given set of points. To use linear regression, we must first calculate the mean of all the x and y coordinates. The mean of the x coordinates is 4, and the mean of the y coordinates is 4.5.

We then calculate the sum of the squared differences between the x and y coordinates and their respective means. This sum is 36.5.

Next, we calculate the sum of the products of the differences between the x and y coordinates and their respective means. This sum is -25.

Using the formula for linear regression, we can calculate the slope of the line of best fit. The slope is -1.00.

To calculate the y-intercept of the line of best fit, we use the slope and the mean of the x and y coordinates. The y-intercept is 9.00.

The line of best fit for this set of points is y = -1.00x + 9.00.

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Answer:

The range is [7, -infinity)

Step-by-step explanation:

Since the leading coefficient is negative and it is a degree 2 polynomial, it is a parabola opened for downwards.

Given:

15)

Answer: option b) 34

16)

Answer: option c) 0

17)

Answer: option d)

Answer:

Step-by-step explanation:

An easy way is to substitute values into both equations and compare:

A. x = 0.8

B. x = 0.9

C. x = 1.9

D. x = 1.1

As we see the most accurate one is A

Let's graph both function(Attached)

Let's round 0.775

\(\\ \sf\longmapsto 0.775\)

\(\\ \sf\longmapsto 0.77\)

\(\\ \sf\longmapsto 0.8\)

Option A is correct

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

V = 4/3 units

Step-by-step explanation:

See attachment for calculation.

Then we substitute for y and z in the rewritten equation

x = 6 - 2y - 3z, where

y = 1

z = 2/3

x = 6 - 2(1) - 3(2/3)

x = 6 - 2 - 2

x = 2

Recall I stated that the volume of a rectangular box is

V = xyz, now we substitute for all the unknown variables.

V = 2 * 1 * 2/3

V = 4/3 units.

Answer:

56.25min or 56min and 15 sec

Step-by-step explanation:

First find how long it will take to run 1 mile, 6.25 mins, then multiply 6.25 by 9

The linear function parallel to the line represented by y = 3x/4 - 1/2 is given as follows:

y = 3x/4 + 1/2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

When two lines are parallel, they have the same slope.

The slope of the line y = 3x/4 - 1/2 is given as follows:

m = 3/4.

Hence the equation of the parallel line is given as follows:

y = 3x/4 + 1/2.

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Answer:c

Step-by-step explanation:

c

Answer:b

Step-by-step explanation:

However, I can still give you some general steps to solve a math problem in 200 words.

Step 1: Read the problem thoroughly and understand what it's asking you to find. This may involve identifying the given information and what you need to find. Also, identify any constraints on the problem, like time or cost.

Step 2: Plan how to solve the problem. Think about what mathematical operations or formulas you can use to find the answer. Make a list of the steps you need to take to solve the problem. Also, determine the units for your answer.

Step 3: Solve the problem. Use the mathematical operations or formulas you've identified in step 2 to find the answer. Show all of your work, including any calculations, so that you can easily check your work later.

Step 4: Check your answer. Make sure that your answer makes sense and that it satisfies any constraints given in the problem. Also, check that your units are correct. If your answer doesn't make sense, go back and review your work to see if you made an error.

Step 5: Reflect on what you've learned. Think about what you did well and what you could improve upon in future problem-solving situations. This will help you become a more effective problem solver in the future.

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