what is the slope of (y−2)=3(x−1)

Answer:

The equation that matches the function shown is option;

C. \(y = sin\left (\dfrac{1}{2} \cdot x\right)\)

Step-by-step explanation:

The given graph of the function is a sinusoidal graph

The values of 'x' and 'y' coordinates at the maximum, x-intercept and minimum points are given as follows;

x, \({}\)      y

0    \({}\)   0

π \({}\)       1

2·π   \({}\) 0

3·π \({}\)    -1

4·π \({}\)    0

We note that sin(π/2) = 1, sin(π) = 0 sin(3·π/2) = -1, and sin(4·π/2) = sin(2·π) = 0

Therefore;

y = the sine of half the x-value

Which is presented as follows;

\(y = sin\left (\dfrac{1}{2} \cdot x\right)\).

Answer:

Step-by-step explanation:

To prove that 3^n < n! for every integer n > 6 using mathematical induction, follow these steps:

1. Base case: Verify the statement for n = 7. We have \(3^{7}= 2187 < 7!=5040\) , so the statement is true for n = 7.

2. Inductive hypothesis: Assume that for some integer k > 6,  \(3^{k} < k!\)holds true.

3. Inductive step: Prove the statement for n = k + 1. We want to show that 3^(k+1) < (k+1)!.

4. Multiply both sides of the

by 3. This gives \(3^{k+1} < (k+1)!\)5. We know that \(3^k < k!\).  Since k > 6, we have k + 1 > 3. Multiply both sides of the inequality \(3^k < k!\) by (k + 1) to get (k+1) * 3^k < (k+1) * k!.

6. Using the result from step 4, substitute 3^(k+1) in the inequality: 3^(k+1) < (k+1) * k!.

7. Recognize that (k+1) * k! = (k+1)!. 8. Combine steps 6 and 7 to conclude that 3^(k+1) < (k+1)!. Since the statement holds true for n = 7 and assuming it is true for k implies that it is true for k + 1, we have proven that 3^n < n! for every integer n > 6 using mathematical induction.

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Answer:

One basic property of a parallelogram is that opposite angles have the same value. Hence angle B = angle D. (2n+15°) = (3n-5°). Then have one side for the unknown. The equation will be 3n=2n+15°+5°. To get the n, simplify the equation: 3n-2n = 20° or n = 20°. Afterwards substitute the value of n to the angles. Angle B = (2(20)+15), Angle D = (3(20)-5). Lastly, simplify the equations. Angle B = (40+15°) = 55° and Angle D = (60-5°)=55°. Therefore the value of angles B & D are both 55°.

Step-by-step explanation:

The main limitation of a cross-sectional study design is that researchers cannot infer the temporal sequence between exposure and disease when the exposure is a changeable characteristic.

Cross-sectional studies are observational studies that measure the prevalence of a disease or health outcome at a specific point in time and assess the association between the outcome and exposure to certain risk factors. However, because the data is collected at a single time point, it is impossible to determine the order of events between exposure and outcome. This is particularly problematic when the exposure is a changeable characteristic such as diet or lifestyle habits. In such cases, it is difficult to determine whether the exposure caused the outcome or whether the outcome led to changes in exposure. Despite this limitation, cross-sectional studies can still provide valuable information about the prevalence and distribution of diseases and risk factors in a population.

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The total distance that was covered by the sprinter in Kilometers is:

To obtain the total distance covered by the sprinter, we need to first realize that 1 Km is equal to 1000 meters. That said, the question above requires us to change 2400 meters to kilometers.

Thus we will have:

2400 Meters * 1 km / 1000 meters

= 2.4 km

So, the total distance covered by the sprinter in kilometers is 2.4

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Answer:

Step-by-step explanation:

It depends on how many points the new test was worth but for now, I'll assume it's worth 10% of your grade.  

97*9=873 75*1=75

873+75=948

948/10=94.8 which rounds up to 95

This means your grade will be 95% which is an A.

Good job!

Please give me brainliest

Answer:

3.96 months

Step-by-step explanation:

12 months in a year

12 * 33%= 3.96 months

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =80 \end{cases}\implies A=\cfrac{(80)\pi (6)^2}{360} \\\\\\ A=8\pi \implies A\approx 25.13~mi^2\)

Answer:

Step-by-step explanation:

Answer: 43

Step-by-step explanation: you add all of them up and then do 180- what you get which would be 180-137. It gives you 43.

Answer:

43 degrees

Step-by-step explanation:

straight lines equal 180 so u add all the angles together to reach 180 hope this helps

Answer:

a. 32

b. 32

Step-by-step explanation:

a. 12 + 4y

They gave us the value of "y" which is "5", and substitute that into the expression.

12 + 4y

12 + 4(5)

12 + 20

32

b. 4 (y + 3)

They gave us the value of "y" which is "5", and substitute that into the expression.

4 ( y + 3 )

4 ( 5 + 3)

Distributive property (multiply what is in the parenthesis by what is out of it (4))

4 * 5 + 4 * 3

20 + 12

32

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

Area is 585

Step-by-step explanation:

Using the area formula A = \(h_{b}\) b / 2 you can substitute the given values into it to find the area of the triangle.

Given Values:

- Base: 45

- Height: 26

So,

26 x 45 / 2

=> 1170 / 2

=> 585

Area: 585

hope this helps and is right. p.s. i really need brainliest :)

Answer:

23 and 33.

Step-by-step explanation:

56 - 23 = 33 and 33 - 23 = 10.

By using what we know about linear functions, we will see that the function that represents the hourly charges is y = $35*x + $20

We assume that the function that we must find is a linear function of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

x would be the time worked and y the corresponding price.

Then we have 3 points on the line:

We know that for a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is given by:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

If here we use the two first points (or any two that you want) we will find the slope:

\(a = \frac{\$ 90 - \$ 55}{2 - 1} = \$35\)

Then the line is something like:

y = $35*x + b

To find the value of b we can use any one of the given points, for example the first one (1, $55) means that when x = 1, we must have y = $55.

Replacing that we get:

$55 = $35*1 + b

$55 - $35 = b = $20

Then the function is just:

y = $35*x + $20

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Answer:

3x+8+5x+12

8x+20=180

A. 80+20=100 No

B. 120+20=140 No

C. 160+20=180 Yes

D. 200+20=220 No

The Answer is C

Hope This Helps!!!

Answer:

x = 20

Step-by-step explanation:

The triangle has 2 congruent sides and is therefore isosceles with 2 congruent base angles, both 3x + 8

5x + 12 and 3x + 8 lie on a straight line and sum to 180° , that is

5x + 12 + 3x + 8 = 180

8x + 20 = 180 ( subtract 20 from both sides )

8x = 160 ( divide both sides by 8 )

x = 20

Answer:

a) 1/3=2/6=3/9=6/18

b) 2/5=4/10=8/20=16/40

Answer:

Step-by-step explanation:

Side "h" ( wall height ) is 35

The height of the wall "h".

\({\boxed{\mathcal{\red{The\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}}}}\)

\(\sf\purple{Using\:Pythagoras \:theorem, \:we\:have}\)

\(( {Perpendicular})^{2} + ( {Base})^{2} = ( {Hypotenuse})^{2} \\ ➡ \: {h}^{2} + ({35 \: ft})^{2} = ({50 \: ft})^{2} \\ ➡ \: {h}^{2} + 1225 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ➡ \: {h}^{2} = 2500 {ft}^{2} - 1225 \: {ft}^{2} \\ ➡ \: {h}^{2} = 1275 \: {ft}^{2} \\ ➡ \: h \: = \sqrt{1275 \: {ft}^{2} } \\ ➡ \: h = 35.707\: ft \: \\ ➡ \: h = 35.71\: ft\)

\(\sf\red{Therefore\:the\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}\)

\(( {35.71 \: ft})^{2} + ( {35 \: ft})^{2} = ({50 \: ft})^{2} \\ ✒ \: 1275 \: {ft}^{2} + 1225 \: {ft}^{2} \: = 2500 \: {ft}^{2} \\ ✒ \: 2500 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ✒ \: L.H.S.=R. H. S\)

Hence verified.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

The distance of the swing of a pendulum decreases by a constant amount each swing. To find the distance of the swing at the tenth swing, you can use the formula:

distance at nth swing = distance at first swing * (1 - decay factor)^(n-1)

Where decay factor is the fractional decrease in distance per swing. In this case, the decay factor is (80 - 76) / 80 = 0.05. Plugging this into the formula above, we get:

distance at 10th swing = 80 * (1 - 0.05)^9 = 53.78 cm

So the distance of the swing at the tenth swing is approximately 53.78 cm.

Number of homeowners planted exactly two of the three vegetables is 434

|P| = 240, |S| = 165, |G| = 142.

|P ∩ S ∩ G| = 36, |P ∩ S| = 0, |P ∩ G| = 0, |S ∩ G| = 0.

Where, P is the set of homeowners who planted peppers, S is the set of homeowners who planted spinach, and G is the set of homeowners who planted garlic

According to inclusion-exclusion

|P∪∪ G| = |P|+|S|+ |G|-|P ∩ S|-|P ∩ G|-|S ∩ G|+ |P∩S∩G|

= 240 + 165 + 142 - 0 - 0 - 0 + 36

= 583

|X| = |P ∩ S' ∩ G'| + |P' ∩ S ∩ G'| + |P' ∩ S' ∩ G|

Substitute the values

= 82 + 45 + 22

= 149

|Y| = 583 - 149

= 434

Therefore, there are 434 homeowners planted exactly two of the three vegetables

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One investigator takes a sample of 100 men age 18-24 in a certain town. Another takes a sample of 1,000 such men.a) The investigator who takes a sample of 1,000 men age 18-24 is more likely to get a bigger average for the heights of the men in his sample. b)The investigator who takes a sample of 100 men age 18-24 is more likely to get a bigger SD for the heights of the men in his sample.

a) The investigator who takes a sample of 1,000 men age 18-24 is more likely to get a bigger average for the heights of the men in his sample.

This is because a larger sample size tends to provide a better estimate of the population mean, and thus, the sample mean tends to be closer to the true population mean.

b) The investigator who takes a sample of 100 men age 18-24 is more likely to get a bigger SD for the heights of the men in his sample.

This is because a smaller sample size tends to provide a less accurate estimate of the population SD, and thus, the sample SD tends to be further from the true population SD.

However, if the population SD is known, then the sample size does not affect the SD of the sample mean.

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The perimeter of the regular hexagon is 42 inches.

Since a regular hexagon can be divided into six equilateral triangles, each triangle shares a side with the hexagon. Let's denote the perimeter of the hexagon as P.

Since the perimeter of one equilateral triangle is 21 inches, each side of the triangle has a length of 21/3 = 7 inches.

Since the hexagon consists of six equilateral triangles, it will have six sides, each of length 7 inches. Therefore, the perimeter of the hexagon is given by:

P = 6 * 7 = 42 inches.

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Answer:

r = -10

Step-by-step explanation:

1. Distribute

1-(r+2)=9

1-r-2=9

2. Subtract the numbers

1-r-2=9

-1-r=9

3. Rearrange the terms

-1-r=9

-r-1=9

Solution: r = -10

The polynomial with the given zeros can be written as:

p(x) = x^3 + 4x^2 + x - 6

If a polynomial has a leading coefficient a and the N zeros {x₁, x₂, ...} then we can write the polynomial as:

p(x) = a*(x - x₁)*(x - x₂)*...

Here we know that the leading coefficient is 1, and the zeros are:

{-3, -2, 1}

Then the polynomial is:

p(x) = (x + 3)*(x + 2)*(x - 1)

p(x) = (x^2 + 5x + 6)*(x - 1)

p(x) = x^3 - x^2 + 5x^2 - 5x + 6x - 6

p(x) = x^3 + 4x^2 + x - 6

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Step-by-step explanation:

2+2=4

4+3+5+4=16

That's the answer hope you understand

Answer:

3+4+5

Step-by-step explanation:

its write answer

Answer:

I-11I

Step-by-step explanation:

To find the distance between two numbers, find the absolute value of each number and add them together.

I-11I = 11

I0I = 0

11 + 0 = 11

Answer:

Hope this helps!

Step-by-step explanation:

The answer is 11. To find the distance between two numbers, find the absolute value of each number and add them together.

Answer:

10

Step-by-step explanation:

took the test on edge

Answer:

the size of C1=54°[converse of a tan chord theorem]

Step-by-step explanation:

since the tan chord theorem state that the angle between a tangent and a chord is equal to the angle sub tended by that chord and in this situation your given the sub tend angle we intend to say is a converse of the tan chord

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Calculation with Lagrange multipliers of its optimum restricted places,

\(f_x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ g_x = 2x\\\\f_y = 1 \ \ \ \ \ \ \ \ \ \ \ \ \ g_y = 2y\\\\\)

Set the multiplier formulas for Lagrange:

\(f_x = \lambda g_x \to 2 = \lambda 2x ............ (i)\\\\f-y = \lambda g_y \to 1 = \lambda 2y................ (ii)\\\\constraint: \\\\\to x^2 + y^2 = 5 .................... (iii)\\\\Taking \ (i)\ divides\ (ii), \ (assuming\ \lambda \neq 0)\\\\\frac{2}{1}=\frac{\lambda 2x}{\lambda 2y}=\frac{x}{y}\\\\\therefore \\\\2y = x\\\\Sub\ into\ (iii)\ to\ find\\\\4y^2 + y^2 = 5 \to y = \pm 1\\\\\)

We get solutions (x,y)=(2,1) and (−2,−1) if combined with 2y = x. These are all the identical points we obtained in (c) and we know the f(2,1) is the max, whereas f(−2, −1) is a minimum.

Answer: 7.6

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be triangle C has the largest area 4.5 square unit.

Because a triangular has two or more extra parts, it is a polygon. It's shape is a simple rectangular. The only three edges that distinguish a triangle from just a triangle are A, B, and C. A singular area rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here,

The largest triangle ,

area wise is:

Triangle C area is:

=> 1/2 *  b * h

=> 1/2 * 3*3

=> 9/2

=> 4.5 square unit

which is the largest area as all the other triangles have 4 square unit area.

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