2(a-7)=a+4
15 6
PLS HELPPPPPPPPPPP​

The equation of the straight line will be -

y = -x + 3

        y = mx + c

        for c = 0

       y = mx

        [m] = Δy/Δx, represents the rate of change or slope of the line.

Given is a line that passes through the point (-12, 15) with slope -1.

Assume the equation to be -

y = mx + c

y = -x + c

15 = - (-12) + c

15 - 12 = c

c = 3

So, the equation will be -

y = -x + 3

Therefore, the equation of the straight line will be -

y = -x + 3

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The value of the N must be in order of the 31 so that the value of the Sn will get exceeded by 4.

Only when the kind of sequence is known can the sum of n words in a sequence be calculated. Normally, while computing the sum of an n-number of terms, we take into account arithmetic progression.

The common distinction between each following phrase and each preceding term remains unchanged throughout this process. Natural numbers are an illustration of AP, where the common difference is 1. Hence, in order to determine the sum of all natural numbers, we must be aware of the formula.

\(S_N = \sum^N_{k=1} \frac{1}{k}\)

= 1 + 1/2 + 1/3 + 1/4 + ..... 1/N

It is a harmonic series,

Therefore, by trial and error method we get N = 31 to exceed Sn = 4

There are some elimination methods,

ln N + 1/N < Sn < ln N+1

we want Sn > 4

ln N+1/N < 4

maximum value of N is ln N+1/N =4

4<ln N+1 → ln N > 3, N > e³

5<ln N+1 → ln 4, N > e⁴

For Sn to exceed it value maybe in between

e³ < N < e⁴.

20.08 < N < 54.5

As I said it is an approximation it won't give exact value.

By taking a value in that range and check for desired value.

for N = 31 Sn willl exceed '4'.

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Complete question:

How large must N be in order for

\(S_N = \sum^N_{k=1} \frac{1}{k}\)

to exceed 100 to exceed 4? Note: Computer calculations show that for SN to exceed 20, N = 272, 400, 600 and for Sn to exceed 100, N = 1.5x10⁴³.

N = ?

Answer:

25 feet per second

Step-by-step explanation:

40 yards = 120 feet

120/4.8 = 25

Answer:

25

Step-by-step explanation:

40 yards = 120 feet

120 ÷ 4.8 = 25

Answer:

x > 19

Step-by-step explanation:

Answer:

m ≤ -19

Step-by-step explanation:

81 ≥ 100 - m

-100  -100

-19 ≥ m

or

m≤-19

hope this helps!!!

The domain of the function is a (-∞, 0) and the range of the function will be f(x) < 0. Then the correct option is C.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

f(x) = 2x – 41

Then the domain of the function is a (-∞, 0) and the range of the function will be f(x) < 0.

Then the correct option is C.

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Answer:

x = 11

The value "11" makes the equation true.

2 ( x - 5 ) = 12

2 ( 11 - 5 ) = 12

2 ( 6 ) = 12

12 = 12

Step-by-step explanation:

Answer:

Please show me the anwers

Step-by-step explanation:

Answer: domain: (-∞,∞), {x |x∈  R}

range: (0,∞), { y | y > 0 }

asymptote: y=0

y-intercept: (0,1)

The points are P = (-5, -1), (-5, 3), (4, -4), and (4, 3).

We can begin by finding the equation of the tangent line to the curve at a general point (x(t), y(t)). Using the chain rule, we have:

dx/dt = 3t² - 6

dy/dt = -2t

The slope of the tangent line is dy/dx, which is equal to (dy/dt)/(dx/dt). So we have:

dy/dx = (-2t)/(3t² - 6)

Now we want to find the points P where this slope is equal to the slope of the given line, which is 2/3. That is:

(-2t)/(3t² - 6) = 2/3

Simplifying this equation, we get:

t² + 1 = 0

This equation has no real solutions, so there are no points P at which the tangent line is parallel to the given line. Therefore, none of the answer choices given are correct.

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Answer:

top

Step-by-step explanation:

In the bottom, y=5x for all of the columns. In the top, y=2x for all except third column, so it is not proportional.

Answer:

\(d=\sqrt(x2-x1)^{2} + (y2-y1)^{2}\)

Step-by-step explanation:

1- Identify the x and  the y

x1= 3

x2=7

y1= 2

y2= 9

2- solve the equation:

d=\(\sqrt\\)(7-3))\(^{2}\)  + (9-2)\(^{2}\)

d= \(\sqrt\)(4)\(^{2}\)        + (7)\(^{2}\)

= \(\sqrt\)16        + 49

= \(\sqrt\)65

d=8.06 answer rounded to the nearest hundredth

Answer:

Third Option: It is not a good fit for the data. Most of the data points are above the line.

Step-by-step explanation:

First of all, if we graph the line y = 100x, we get the following data points:

0, 0

1, 100

2, 200

3, 300

4, 400

5, 500

6, 600

7, 700

8, 800

9, 900

10, 1000

11, 1100

12, 1200

Once we graph the following data points and draw a line connecting them in the scatter plot, we can check if the line is the best fit.

Then we get the answer.

No, the line y = 100x is not the line of best fit for the given scatter plot. The line of best fit is a straight line that is the best approximation of the given set of data. It is used to study the nature of the relation between two variables. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible).

Look at the picture I attached.

Answer:

c

Step-by-step explanation:

\(a) (1/6)^{-8}=6^8>1 \\ \\ b) (5^{-4})^{-9}=5^{36}>0 \\ \\ c) 2^{-3}=1/8<1 \\ \\ (d) \frac{6^{-4}}{6^{-5}}=6>1\)

Since each triangle is a right triangle we can apply trigonometric functions:

Sin a = opposite side / hypotenuse

Where;

a = angle = 60° ( we are looking at the bottom left one)

Opposite side = 30 cm

Hypotenuse = AB

Replace:

Sin60 = 30 / AB

Solve for AB

AB = 30 / sin 60

AB = 34.64 cm

Theorem 6.11, also known as the parallelogram law, states that the sum of the squares of the lengths of the two diagonals of a parallelogram is equal to the sum of the squares of the lengths of all four sides. Mathematically, we can express this as:

\(AC^2 + BD^2 = AB^2 + BC^2 + CD^2 + DA^2\)

where AB, BC, CD, and DA are the four sides of the parallelogram, and AC and BD are the two diagonals.

To construct a parallelogram using Theorem 6.11, we can start by drawing two perpendicular lines intersecting at a point, which will be the point where the diagonals of the parallelogram intersect. We can then measure the lengths of these two perpendicular lines and use them as the lengths of the two diagonals of the parallelogram. We can then draw the two diagonals of the parallelogram and measure their lengths, and use Theorem 6.11 to calculate the lengths of the four sides of the parallelogram. Finally, we can draw the four sides of the parallelogram using these lengths.

Here is an example of how to construct a parallelogram using Theorem 6.11:

Draw two perpendicular lines that intersect at a point, and label the point of intersection as O.

Measure the lengths of the two perpendicular lines, and label them as AC and BD, which will be the lengths of the two diagonals of the parallelogram.

Draw the two diagonals of the parallelogram, AO and CO, and measure their lengths.

Use Theorem 6.11 to calculate the lengths of the four sides of the parallelogram:

\(AB^2 = AO^2 + BO^2 - 2(AO)(BO)\)cos(∠AOB)

\(BC^2 = BO^2 + CO^2 - 2(BO)(CO)\)cos(∠BOC)

\(CD^2 = CO^2 + DO^2 - 2(CO)(DO)\)cos(∠COD)

\(DA^2 = DO^2 + AO^2 - 2(DO)(AO)\)cos(∠DOA)

where ∠AOB, ∠BOC, ∠COD, and ∠DOA are the angles between the two diagonals and the sides of the parallelogram.

Draw the four sides of the parallelogram using the calculated lengths.

Note that there are many ways to construct a parallelogram, and Theorem 6.11 is just one of them.

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Given Information :-

⠀

A rectangular prism, with dimensions,

⠀

To Find :-

⠀

⠀

Formula Used :-

⠀

\( \qquad \star \: \underline{ \boxed{ \green{ \sf Volume = l \times b \times h }}} \: \star\)

⠀

Here, we have already been provided with the base area that is the value of the product of length and breadth. Now, we just have to multiply the base area by height.

⠀

Solution :-

⠀

\( \sf : \implies Volume =14 \: {in}^{2} \times 7 \: {in}^{} \\ \\ \\ \sf : \implies Volume = \underline{ \boxed{ \frak{ \orange{ {98 \: in}^{3} }}}} \: \star \: \: \: \: \: \: \: \: \\ \\ \)

Thus, the volume of the rectangular prism is 98 m³.

⠀

\( \underline { \rule{227pt}{2pt}} \\ \\ \)

Answer:

98

Step-by-step explanation:

14 x 7=98

Juan's claim is incorrect. We have to disprove Juan's claim. He says that the solution to the given system of equations is unique only to the equations y = 5x-2 and y = 1/2x +7.

What we can do is that, we can introduce a third equation. This third equation should have the same solution as the first two.

Example of such an equation is,

y = -3x + 1

We can solve the system of three equations,

y = 5x - 2

y = 1/2x + 7

y = -3x + 1

We can use the first two equations first and find values of x and y,

5x - 2 = 1/2x + 7

Multiplying both sides by 2,

10x - 4 = x + 14

Subtracting x from both sides,

9x - 4 = 14

Adding 4 to both sides,

9x = 18

Dividing both sides by 9,

x = 2

Now we know x = 2.

We can use either of the first two equations to find y,

y = 5x - 2 = 5(2) - 2 = 8

This satisfies all three equations.

So finally we can say Juan's claim is not correct. There are other equations there having the same solution as the first two.

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To find the sum of interior angles of this polygon you have to use the equation

S=180(n-2)

where n is the number of sides

S=180(6-2)

S=180(4)

S=720 degrees

The sum of all angles is 720 degrees

\(110 + x + 25 + x - 30 + x + x + 115 = 720\)

\(4x = 720 - 110 - 25 - 115 + 30\)

\(4x = 720 - 220\)

\(4x = 500\)

\(x = \frac{500}{4} = 125\)

We do know that he needs to average at least 82 on all of his test quizzes combined in order to achieve an average of at least 75 overall. The correct answer is B) x > 82.

To find out what scores Ben needs to achieve an average of at least 75 on all of his quizzes and tests, we can use the following formula:

(total score on all quizzes and tests) / (number of quizzes and tests) >= 75

We know that Ben has taken four quizzes so far, with scores of 62, 77, 73, and 81. That means his total score on those quizzes is:

62 + 77 + 73 + 81 = 293

To get an average of at least 75, Ben will need a total score of:

75 * 5 = 375

This includes his previous total score of 293, so he needs to score a total of:

375 - 293 = 82

on his test quizzes. Since we don't know how many test quizzes there are or how much each one is worth, we can't determine exactly what score Ben needs on each quiz. However, we do know that he needs to average at least 82 on all of his test quizzes combined in order to achieve an average of at least 75 overall. Therefore, the correct answer is B) x > 82.

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The equation of the line that passes through the point (8, 4) and is parallel to the line y = 4x + 2 is y = 4x − 28.

Two lines are parallel if they have the same slope. The given line y = 4x + 2 has a slope of 4. Therefore, any line that is parallel to this line must also have a slope of 4. We can use the point-slope form of the equation of a line to find the equation of the line that passes through the point (8, 4) with a slope of 4:

y - y1 = m(x - x1)

where m is the slope, x1, and y1 are the coordinates of the given point. Substituting the values into the equation, we get:

y - 4 = 4(x - 8)

Simplifying the equation gives:

y = 4x - 28

Therefore, the equation of the line that passes through the point (8, 4) and is parallel to the line y = 4x + 2 is y = 4x − 28.

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The net of a triangular prism consists of two triangles and three rectangles.

In the net of a triangular prism, we can observe two types of polygons: triangles and rectangles.

First, let's discuss the triangles.

A triangular prism has two triangular faces, which are congruent to each other.

These triangles are equilateral triangles, meaning they have three equal sides and three equal angles.

Each of these triangles contributes two polygons to the net, one for each face.

Next, we have the rectangles.

A triangular prism has three rectangular faces that connect the corresponding sides of the triangular bases.

These rectangles have opposite sides that are parallel and equal in length.

Each rectangle contributes one polygon to the net, resulting in a total of three rectangles.

To summarize, the net of a triangular prism consists of two equilateral triangles and three rectangles.

The triangles represent the bases of the prism, while the rectangles form the lateral faces connecting the bases.

Altogether, there are five polygons in the net of a triangular prism.

It's important to note that the dimensions of the polygons may vary depending on the specific size and proportions of the triangular prism, but the basic shape and number of polygons remain the same.

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Three segments a, b, and c using net sales as the basis for allocation is = $475,000.

Based on the given conditions,

Three segments are a , b , c

The segment a of trump enterprises have net sales = $300,000

The segment b of trump enterprises have net sales = $150,000

The segment c of trump enterprises have net sales = $50,000

a net sales + b net sales + c net sales = $300,000 + $150,000 + $50,000

= $500,000

If the unit is eliminated, then the a net sales and b net sales will be gone, but the c net sales will be allocated to other business units.

So instead of losing $500,000,

A decision is made to allocate the pool = $25,000

The company's net sales as the basis for allocation by $500,000 - $25,000 = $475,000

Therefore,

Three segments a, b, and c using net sales as the basis for allocation is =

$475,000.

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Answer: An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. Every pair of endpoints on a circle either defines one minor arc and one major arc, or two semicircles. Only when the endpoints are endpoints of a diameter is the circle divided into semicircles.

A semicircle is a two-dimensional geometric shape that consists of a curved arc and a straight line segment that connects the two endpoints of the arc. Here are the steps to identify a semicircle:

Look for a curved arc that forms a half-circle shape.

Locate the center point of the arc, which is also the midpoint of the line segment connecting the two endpoints.

Check that the line segment connecting the endpoints is a diameter of the circle.

Confirm that the arc and line segment together form a continuous, closed shape that divides the circle into two equal halves.

Finally, compare the shape to a circle to make sure that it is only half of a complete circle.

If all of these conditions are met, then the shape is a semicircle.

5.) The measure of angle D of the given triangle would be = 59.5°

To calculate the missing angles, sine rule is used which is ;

Sine rule = a/sin A = b/sin B

Where a = 23

A = 56°

b = 24

B = X

That is;

23/sin56° = 24/sinx

Make sin X the subject formula;

Sin X = sin56×24/23

= 0.829037572×24/23

= 19.89690174/23

= 0.865082684

X = Sin-1 (0.865082684)

= 59.89214806

= 59.9° (approximately)

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Answer:

cost of admission for each child was $4.00, and each adult was $25.33

Step-by-step explanation:

When solving questions like these , I like to break down the problem so I understand it better.

Let x ---> cost of the admission for each child

Y ---------> cost of the admission for each adult

9x+3y = 112 ---> equation A

8x + 3y = 108 ---> equation B

Subtract B from A

9x+3y=112

-8x+3y = 108

x = 112-108

x = 4

Find value of y by substituting value of x into equation

9(4)+3y=112

Solve for y

36+3y = 112

3y = 112=36

3y = 76

y = 25.33

Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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Answer:

3

Step-by-step explanation:

Answer:

Answer 2

Step-by-step explanation:

The probability that exactly one fourth of the questions will be answered correctly is approximately 0.00166.

Given,

Number of multiple choice questions = 40

Each question has four possible answers, and only one of them is correct.

Thus, Probability of getting a question correct = 1/4.

Probability of getting a question incorrect = 1 - 1/4 = 3/4

Let X be the number of questions answered correctly by the student.

Since there are 40 questions in total,

X can take any value between 0 and 40, inclusive.

To find the probability that exactly one fourth of the questions will be answered correctly, we need to calculate the probability that X = 10.

Using the binomial distribution formula,

The probability of answering exactly k questions correctly out of n total questions is given by :

P(X = k) = nCk x pk x (1-p)n-k

where, nCk is the number of ways to choose k questions from n total questions,

p is the probability of answering a question correctly, and

1-p is the probability of answering a question incorrectly.

So, the probability of answering exactly 10 questions correctly is :

P(X = 10) = 40C10 x (1/4)10 x (3/4)30P(X = 10) ≈ 0.00166.

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Answer:5

Step-by-step explanation: