Graph a line that contains the following point (-5, 3) and a slope of -6.

So, we want to find the slope of the line that goes through the points (-11 , -13) and (-8,3).

For this, remember that:

Given two points that lie on a line:

The slope of the line that goes through these points can be found if we apply the following formula:

In our question, we are given that:

So,

The only thing we have to do now, is to replace. So,

Therefore, the slope of the line is 16/3

The volume of a solid formed by revolving the region bounded above by the line is (932π/15)

To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.

The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:

\(r = y^2 - 1\)

The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:

h = 3 - 1 = 2

The volume of each disk is then:

\(dV = \pi r^2h dy\)

Substituting r and h, we have:

\(dV = \pi (y^2 - 1)^2 (2) dy\)

To find the total volume, we integrate over the range of y from 1 to 3:

\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)

This integral can be simplified by expanding the squared term:

\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)

V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)

V = 2π [(1/5)(242) - (2/3)(26) + 2]

V = 2π [(242/5) - (52/3) + 2]

V = 2π [(726/15) - (260/15) + 30/15]

V = 2π [(466/15)]

V = (932π/15)

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Note: The full question is

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.

Answer:

To divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

For more examples and explanatTo divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

Step-by-step explanation:

brainliest pls

Answer:

Step-by-step explanation:

For dividing fractions:

Remember:

Keep Change Flip

Keep the first the same

Change the sign to multiplication

Flip the second fraction.

EX.

\(\frac{4}{5}\) ÷ \(\frac{1}{2}\)                           >Keep, Change Flip

=\(\frac{4}{5}\) * \(\frac{2}{1}\)                          >Now it's multiplication, reduce first if you can

                                    (nothing reduces in this problem), so mulitply

                                    across

= \(\frac{8}{5}\)

Answer:

6x ≥ 500

Step-by-step explanation:

I took the test but also it means that in six months, you have to save that amount of money to get exactly or more than 500, so this would be the correct answer!

Answer:

Step-by-step explanation:

1) c

x² = 1

x² - 1 = 0

Degree of quadratic equation should be 2.

2) 'a'- coefficient of x² cannot be 0

option a

3) option c

Standard form: ax² + bx +c = 0

4) c = 5

3x² + 8x = -5

3x² + 8x + 5 = 0

option c

5) b= 0

option a

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

A tessellation is a pattern made by repeating geometric shapes without any gaps or overlaps. These shapes, called tiles or polygons, fit together perfectly to cover a plane or a surface. Tessellations can be found in various forms of art, architecture, and design. They are used to create visually appealing patterns and decorations, as well as to explore mathematical concepts.

Tessellations are utilized in various practical applications, such as tiling floors, walls, and pavements, designing mosaics and quilts, and creating computer graphics and textile patterns. They are also studied in mathematics to understand concepts like symmetry, geometry, and transformations.

For polygons to tessellate, certain conditions must be met at their vertices. At each vertex, the angles formed by the polygons must add up to a whole number of degrees, typically 360 degrees. In other words, the sum of the interior angles of each polygon meeting at a vertex must be a multiple of 360 degrees.

This ensures that the polygons can fit together seamlessly without leaving any gaps or overlaps. Examples of polygons that tessellate include equilateral triangles, squares, and hexagons, as their angles add up to 360 degrees at each vertex.

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Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

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Answer:

Step-by-step explanation:

value after five years = $18,000×(1-0.12)⁵ = 18,000×0.88⁵ = $9,499.17

:::::

The value drops below $2,000 in the 17th year.

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

- 2.7 < - 2.2

Step-by-step explanation:

Answer:

Remember that the area of a circle of radius R is given by:

A = pi*R^2

pi = 3.14

We know that:

Personal Pizza: radius = 10cm

                         price = $5

The area of pizza that you are getting is:

A = 3.14*(10cm)^2 = 314 cm^2

In the other case, we have a pizza with radius of 30 cm, cutted into 8 slices, such that each slice costs $5.

Then, if yo pay $5, the area of pizza that you get is an eight of the area of a circle of radius 30cm

This is:

A' = (1/8)*(3.14*(30cm)^2) = 353.25 cm^2

We can see that in the second case the area is larger, then the second option is the better deal, as you are getting a larger pizza area for the same price.

Answer:

no

Step-by-step explanation:

Answer:

x = 7deg

Step-by-step explanation:

7x + 10 + 15x + 16 = 180 (angles adjacent to each other in a //polygon are supplementary)

22x = 154

x = 7deg

This is a question on polygons and angles. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

The integral ∫1[∞]​ex²x​dx converges, and its value is approximately 0.07425.

To determine if the integral ∫1[∞]​ex²x​dx converges or diverges, we will use the test for convergence of improper integrals. This test states that if the integral can be written in the form ∫a[b]​f(x)dx, and if either a or b is infinite, then the integral converges if and only if the limit of ∫c[d]​f(x)dx as c approaches a and d approaches b exists and is finite.

Let's apply this test to the integral ∫1[∞]​ex²x​dx. We can rewrite the integral as ∫1[∞]​e(x²) / x dx. We can see that the function inside the integral, e(x²) / x, is continuous and positive for all x greater than or equal to 1.

Next, we will apply the limit test to determine if the integral converges. Let's set d to ∞, and let c be any number greater than or equal to 1. Then we have:

∫c[∞]​e(x²) / x dx = [ 1 / 2 e(x²) ] from c to ∞

Taking the limit as c approaches ∞, we get:

lim(c → ∞) [ 1 / 2 e(x²) ] from c to ∞ = 0

Since the limit exists and is finite, we can conclude that the integral ∫1[∞]​ex²x​dx converges.

To compute the value of the integral, we can use integration by substitution. Let u = x², then du/dx = 2x, which gives dx = du / 2x. Substituting these into our integral, we get:

∫1[∞]​e(x²) / x dx = ∫1[∞]​e(u) / (2u) du

We can integrate this using the substitution v = 2u, then dv/du = 2, which gives du = dv / 2. Substituting these into our integral, we get:

∫2[∞]​e(u) / (2u) du = 1/2 ∫2[∞]​e(v) / v dv

This integral is a well-known integral, called the exponential integral, and its value is approximately 0.1485.

Therefore, the value of the integral ∫1[∞]​ex²x​dx is approximately 0.1485/2, or 0.07425.

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A reflection over a line l  moves every point P  of the plane to the point P ′  on the perpendicular from  P to the line l and on the same distance from l .

If the line is the  x  -axis, a point P  =  ( p 1   p 2 )  moves to the point  P ′  =  ( p 1 , − p 2 ) .

The image of the triangle A B C  is the triangle  A ′ B ′ C ′ with  B ′  =  ( 9 , − 5 )

Answer:

What is the question? I cannot see :(

Answer:

Step-by-step explanation:

2x+3x+4x=180 degrees

9x=180 fdegrees

x=180/9

x=20

2x=40

3x=60

4x=80

Answer:

18

Step-by-step explanation:

The measures of the angles of a triangle are in the ratio 2:3:4 means we have one interior angle measuring 2x, another measuring 3x, and the last one measuring 4x. We know the sum of the measures of the interior angles of a triangle is 180 degrees.

We need to solve the following equation to find first x, and then find the measurement of each interior angle of the triangle.

2x+3x+4x=180

(2+3+4)x=180

(9)x=180

x=180/9

x=20

So one interior angle measures 2x=2(20)=40.

Another measures 3x=3(20)=60.

The last measuring 4x=4(20)=80.

The exterior angles of this triangle therefore measure the following:

180-40=140

180-60=120

180-80=100

So the un-simplified ratio of the measures of the exterior angles is as follows:

140:120:100.

Let's simplify that.

It is easy to see each number is divisible by 10.

Let's reduce it by dividing each by 10:

14:12:10

Let's simplify more (as we want the most simplified ratio).

Each number is divisible by 2 since they are all even.

Let's reduce again but not by dividing by 2:

7:6:5

So the simplified ratio of the measures of the exterior angles of the triangle is a:b:c=7:6:5 and so a+b+c=7+6+5=18.

Answer is 18.

The solution is : 22 meters would be saved if it were possible to walk through the pond.

Here, we have,

There is a pond between two points A and B.

To avoid the pond, one must walk to the south from point A to point C (say) by 34 meters and then to the east from point C to point B by 41 meters.

Now, it is clear that Δ ABC is a right triangle with AB as the hypotenuse that is the minimum distance from A to B through the pond.

The two legs of the right triangle are AC and CB.

Applying Pythagoras Theorem,

AB² = AC² + CB²

      = 34² + 41²

      = 2837

⇒ AB = 53 meters (Rounded to the nearest meter)

Therefore, (34 + 41) - 53 = 22 meters will be saved if it were possible to walk through the pond.

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complete question:

To get from point A to point B you must avoid walking through a pond. To

avoid the pond, you must walk 34 meters south and 41 meters east. To the

nearest meter, how many meters would be saved if it were possible to walk

through the pond?

Part 1: To get the 10 ounce of honey bees travel 34375 miles.

Part 2: To get the 10 ounce of honey bees visited 1.25 millions flowers.

A ratio that connects a part to the entire is a percentage.

Part 1:

Using the unit conversion:

1 pound = 16 ounce

1 pound of honey  ----> 55,000 miles

16 ounce of honey  ----> 55,000 miles

Let 'x' be the number of mile to get the 10 ounces of honey.

x/10 = 55,000/16

x = 55,000*10 / 16

x = 34375 miles.

To get the 10 ounce of honey bees travel 34375 miles.

Part 2:

Flowers visited to get 10 ounces of honey.

16 ounce of honey  ----> 2 million flowers.

Let 'y' be the number of flowers visited to get 10 ounces of honey.

x/10 = 2 million/16

x = 1.25 millions

To get the 10 ounce of honey bees visited 1.25 millions flowers.

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Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

Answer:

The place value of 4 in 265 473 is 40,000

Answer:

Step-by-step explanation:

Order:

3 is in the ones place and has a value of 3

7 is in the tens place and has a value of 70

4 is in the hundreds place and has a value of 400

5 is in the thousands place and has a value of 5000

6 is in the ten thousands place and has a value of 60,000

2 is in the hundred thousands place and has a value of 200,000

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

I want to say that

Step-by-step explanation:

just only click the question. because now I am confused which I have to solve

Answer:

D. 1/2x + 30 = 3/4(x + 30)

Step-by-step explanation:

we'll use james = y and sarah = x

y = 1/2x

y + 30 = 3/4(x + 30)

now sub in y:

1/2x + 30 = 3/4(x + 30)

Answer:

30

Step-by-step explanation:

The soccer ball is above 15 feet between 0.25 seconds and 1 second.

To determine when the soccer ball is above 15 feet, we need to find the values of t that satisfy the inequality h(t) > 15.

Given the quadratic function h(t) = -16t² + 20t + 11, we can rewrite the inequality as follows:

-16t² + 20t + 11 > 15

Subtracting 15 from both sides:

-16t² + 20t - 4 > 0

Simplifying further:

-16t² + 20t - 4 = -4(4t² - 5t + 1) = -4(t - 1)(4t - 1) > 0

Now, we can solve for t by finding the values that make the inequality true. We have two factors: (t - 1) and (4t - 1).

Setting each factor greater than zero and solving for t:

t - 1 > 0 => t > 1

4t - 1 > 0 => 4t > 1 => t > 1/4

So, we have t > 1 and t > 1/4. To satisfy both conditions, t must be greater than the maximum of 1 and 1/4, which is 1.

Therefore, the soccer ball is above 15 feet for t > 1 second.

The correct answer is:

C. The soccer ball is above 15 feet between 0.25 seconds and 1 second.

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