Which set of numbers could represent the side lengths of a right triangle? ​

The population will exceed 7569 at moments beyond 7.4 years hence from 8 years (to the nearest years)​

Exponential function is a function of the form f(x) = a e^(kt)

Considering the given problem,

the initial value = a

the base factor = k

the exponents in time = t

Information given in the problem are

solving for the time wen the population will exceed 7569

7569 = 1600 x e(0.21 * t)

7569 / 1600 = e(0.21 * t)

take ㏑ of both sides

㏑ (7569 / 1600) = ㏑ e(0.21 * t)

㏑ (7569 / 1600) = 0.21t

t = ㏑ (7569 / 1600) / 0.21

t = 7.40

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Answer:

the choice A.

\( {f}^{ - 1} (x) = 3 - 7x\)

I hope I helped you^_^

Answer:

Step-by-step explanation:

Last year Alex was 6-1 = 5 feet tall.

1/5 = 0.20 = 20%

The increase in height is 20%

Answer:

the answer is -2.1

Step-by-step explanation:

you get this by putting that -4 where the x is and solving so it would look something like this

1.7x+4.7    for x= -4

1.7(-4) + 4.7

-6.8 + 4.7

-2.1

Answer:

slope is 25 because the equation is y=25x+50

Step-by-step explanation:

heres the official answer

Answer:

O   x >9

The arrow points left

Step-by-step explanation:

Explanation:-

Given   2 < x-7

adding '7' on both sides, we get

⇒   2 + 7 < x -7 +7

⇒  9 < x

⇒  x>9

Given inequality   2 < x -7

The arrow points left

Final answer:-

solution is  x >9

The arrow points left

Answer:

B,D,F

Step-by-step explanation:

Answer:

system of equations are

y=53x + 10, y=55x

Step-by-step explanation:

y=mx+b where x is the number of tickets purchased and y is the total cost.

We need to frame the equation for each option

Option 1: $53 for each ticket plus a shipping fee of $10

1 ticket cost = 53

So x tickets cost = 53x

shipping fee = $10 so b= 10

So equation becomes y=53x + 10

Option 2: $55 for each ticket and free shipping

1 ticket cost = 55

So x tickets cost = 55x

shipping fee =0 so b= 0

So equation becomes y=55x

Answer:254.469

Step-by-step explanation:Use the formula π = c/d to get 254.469.

The measure of Angle A and Angle B are 54° and 122° respectively.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC,

The measure of angle A = (n + 20)°

The measure of angle B = (3n - 10)°

The measure of angle C = n°

Now,

The sum of all the angles of the triangle = 180°

So, we can formulate;

(n + 20)° + (3n - 10)° + n° = 180°

Solve for n as;

n + 20 + 3n - 10 + n = 180

5n + 10 = 180

5n = 180 - 10

5n = 170

Divide by 5, we get;

n = 170/5

n = 34

Thus, The measure of angle A = (n + 20)°

                                               = 34 + 20

                                               = 54°

And, The measure of angle B = (3n - 10)°

                                             = 3 x 34 + 20

                                             = 102 + 20

                                             = 122°

Therefore,

The measure of Angle A and Angle B are 54° and 122° respectively.

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The general indefinite integral of 6(1 + tan^2(α)) dα is 6(tan(α)) + C, where C represents the constant of integration.

To find the general indefinite integral of 6(1 + tan^2(α)) dα, we can use trigonometric identities to simplify the integrand.

Recall the trigonometric identity:

1 + tan^2(α) = sec^2(α)

Substituting this identity into the integral, we have:

∫ 6(1 + tan^2(α)) dα = ∫ 6(sec^2(α)) dα

Now, integrating sec^2(α) with respect to α gives us the tangent function:

∫ sec^2(α) dα = tan(α) + C

Applying this result to the integral, we have:

∫ 6(sec^2(α)) dα = 6 ∫ sec^2(α) dα = 6(tan(α)) + C

Therefore, the general indefinite integral of 6(1 + tan^2(α)) dα is 6(tan(α)) + C, where C represents the constant of integration.

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Answer:

y=5x+6

Step-by-step explanation:

The equation of line passes through the point (2, 16) will be;

⇒ y = 5x + 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (2, 16).

And, The parallel line is,

⇒ y = 5x + 8

Now,

Since, The equation of line passes through the point (2, 16).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = 5x + 8

m = dy/dx = 5

m = 5

Thus, The equation of line with slope 5 is,

⇒ y - 16 = 5 (x - 2)

⇒ y - 16 = 5x - 10

⇒ y = 5x - 10 + 16

⇒ y = 5x + 6

Therefore, The equation of line passes through the point (2, 16) will be;

⇒ y = 5x + 6

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

False because the variables are x and y. The numbers are not the variables.

Step-by-step explanation:

The 98% confidence interval for the difference in proportions of patients needing pain medication between the old and new procedures is (-0.003, 0.061).

To construct a 98% confidence interval for the difference in the proportions of patients needing pain medication between the old and new procedures, we can use the formula:

p1 - p2 ± z*sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

where p1 is the proportion of patients in the old procedure group who required medication, p2 is the proportion of patients in the new procedure group who required medication, n1 is the sample size of the old procedure group, n2 is the sample size of the new procedure group, and z is the critical value for a 98% confidence interval (which is approximately 2.33).

Plugging in the given values, we get:

12/65 - 14/90 ± 2.33sqrt((12/65)(53/65)/65 + (14/90)*(76/90)/90)

Simplifying this expression, we get:

-0.003 < 0.052 < 0.061

Therefore, the 98% confidence interval for the difference in proportions is (-0.003, 0.061).

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Answer:

Martin Drove about 60,000

Martin Drove exactly 53,558

Step-by-step explanation:

90,000 - (20,000 +10,000) = x

60,000 = x

86,456 - (24,901 - 7,997) = x

53,558 = x

Answer:

Answer:

Martin Drove about 60,000

Martin Drove exactly 53,558

Step-by-step explanation:

90,000 - (20,000 +10,000) = x

60,000 = x

86,456 - (24,901 - 7,997) = x

53,558 = x

Step-by-step explanation:

Answer:

88.5

Step-by-step explanation:

First you multiple 9.5 and 8 and you should get 76.0

last you add 12.5 and 76.0 and you should get 88.5

and make sure you line up the decimals when adding.

hope this helps

Answer:

300

Step-by-step explanation:

Total= 40+96+2*30+104= 300

Answer:

Two negatives, positive answer:

-3 - (-4) = 1

Two negatives, negative answer:

-45 - (-1) = -44

Answer:

h = 15 cm

Step-by-step explanation:

Area of triangle equals the area of rectangle. As the dimensions of the rectangle is given, we can first find the area of the rectangle.

      \(\boxed{\bf Area \ of \ the \ rectangle = length * width}\)

                                               = 10 * 9

                                               = 90 cm²

Area of triangle = area of rectangle

                          = 90 cm²

base of the triangle = b = 12 cm

 \(\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}\)  where h is the altitude and b is the base.

         \(\bf \dfrac{1}{2} b* h = 90 \\\\\dfrac{1}{2}*12* h = 90\)

                      \(\bf h = \dfrac{90*2}{12}\\\\\boxed{\bf h = 15 \ cm}\)

The answer of the given question based on model is , the linear model of the form "pt" for this scenario is pt = 10 + 8t

To find a linear model of the form "pt" for the given scenario, we can use the formula:
pt = p0 + nt
where pt represents the total number of tulips after t years, p0 represents the initial number of tulips, and n represents the number of tulips planted each year.
In this case, Kimberly currently has 10 tulips in her yard, so p0 = 10.

And each year she plants 8 more tulips, so n = 8.
Therefore, the linear model of the form "pt" for this scenario is:
pt = 10 + 8t

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Answer:

if you have a calculator...

Step-by-step explanation:

take 85 to the 5th power and then divide that by 3.

Answer:

20

Step-by-step explanation:

correct on edge

Answer:

Exponential function

Step-by-step explanation:

It is better if the situation on ground is represented by an exponential equation.

This is because, since we have the number of teams reducing by exactly half at every playoff round, this means that we have a base of 2 which can be raised to a negative power since we are talking about a decrease.

We can then place the number of rounds as an adjoining power to what the two is raised and this easily will get us the number of teams which is eventually decreased at every point of the playoffs

The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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The integral of dv divided by 2 ln(1+2x) with respect to x from 0 is equal to a function F(x) plus a constant of integration.

To solve the given integral, we can use the method of integration by substitution. Let's substitute u = 1 + 2x, which implies du = 2 dx. Rearranging the equation, we have dx = du/2. Substituting these values, the integral becomes ∫(dv/2 ln u) du. Now, we can split the integral into two separate integrals: ∫dv/2 and ∫du/ln u.

The integral of dv/2 is simply v/2, and the integral of du/ln u can be evaluated using the natural logarithm function: ∫du/ln u = ln|ln u| + C, where C is the constant of integration. Substituting back u = 1 + 2x, we get ln|ln(1 + 2x)| + C.

Therefore, the solution to the given integral is F(x) = v/2 + ln|ln(1 + 2x)| + C, where F(x) is the antiderivative of dv/2 ln(1 + 2x) with respect to x, and C represents the constant of integration.

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Answer:

33.165

Step-by-step explanation:

Answer:

33.165

Step-by-step explanation:

4.95*6.7= 33.165

hope this helps

Answer:

3... 5,7....x,y....12

Step-by-step explanation:

Numbers of Terms: 3

Coefficients: 5 and 7

Variables: x and y

Constant: 12

Answer:

Number of Terms: 3

Coefficients: 5, 7

Variables: x, y

Constants: 12

Step-by-step explanation:

Expression: 5x + 7y + 12

Number of Terms: 3

Coefficients: 5, 7

Variables: x, y

Constants: 12

Answer:

See the picture down below

Step-by-step explanation:

When you are drawing a line you should first mark the y-intercept, which in this case it's (0,-3) because the the b in the equation is -3. Then we will go 2 units up then 1 unit right. Keep going until you've run out of room. Then draw the line going through all the points.

The graph of  y = 2x - 3 is attached and slope of the given graph is 2.

A line is an infinitely long object with no width, depth, or curvature.

y=mx+b is the standard form of a line, where m is slope and b is the y intercept.

When a line passes through (x₁, y₁) and (x₂, y₂) then slope

m=y₂-y₁/x₂-x₁

The given equation is  y = 2x - 3

When we compare this with standard form

m is 2 which is slope.

To draw graph we have to find few values of x and y.

If x=0,

then y=-3

(0, -3) is one point in the line.

If x=1

then y=-1

(1, -1) is second point in the line.

if x=2

y=1

if x=3

then y=3

if x=4

then y=5

Hence, the graph of  y = 2x - 3 is attached and slope of the given graph is 2.

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The total work done by the force field F along the path C is 201.

To determine the work done by the force field F along the given path C, we need to evaluate the line integral ∮CF⋅dr.

Let's break down the path C into its individual line segments:

1. From the origin (0, 0, 0) to (1, 0, 0)

2. From (1, 0, 0) to (1, 5, 1)

3. From (1, 5, 1) to (0, 5, 1)

4. From (0, 5, 1) back to the origin (0, 0, 0)

Now, we can calculate the line integral along each segment and sum them up to find the total work done.

1. Along the first line segment, the vector dr = dx i, and the force field F = z² i + 4xy j + 4y²k.

  Integrating F⋅dr from 0 to 1 with respect to x gives us ∫[0,1] (z² dx) = ∫[0,1] (0² dx) = 0.

2. Along the second line segment, the vector dr = dy j, and the force field F = z² i + 4xy j + 4y²k.

  Integrating F⋅dr from 0 to 5 with respect to y gives us ∫[0,5] (4xy dy) = ∫[0,5] (4xy dy) = 100.

3. Along the third line segment, the vector dr = -dx i, and the force field F = z²i + 4xy j + 4y²k.

  Integrating F⋅dr from 1 to 0 with respect to x gives us ∫[1,0] (z² dx) = ∫[1,0] (1^2 dx) = 1.

4. Along the fourth line segment, the vector dr = -dy j, and the force field F = z² i + 4xy j + 4y² k.

  Integrating F⋅dr from 5 to 0 with respect to y gives us ∫[5,0] (4xy dy) = ∫[5,0] (4xy dy) = 100.

Adding up the work done along each segment, we have 0 + 100 + 1 + 100 = 201.

Therefore, the total work done by the force field F along the given path C is 201.

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Answer:

Step-by-step explanation:

The triangle is being reflected over the y-axis.

A(x, y) → (x, -y)

A(1, 4) → (1, -4)

A'(1, -4)

B(x, y) → (x, -y)

B(4, 3) → (4, -3)

B'(4, -3)

C(x, y) → (x, -y)

C(2, 1) → (2, -1)

C'(2, -1)

Hope this helps!