Simplify (3x^6y^4)(-4x^2y^3)
1: -x^8y^7
2: -12x^12y^12
3: -12x^8y^7
4: -12x^8y^12

Answer:

The area of the rectangle is increasing at a rate of 54 cm2/s.

Step-by-step explanation:

Answer:

See image

Step-by-step explanation:

It cant be wrong

Step-by-step explanation:

Total gum balls = 22 + 18 + 10 + 23 = 73

Probability of red gum = 22/73

The function which represents a graph which has been vertically shifted by 3 units is; y= log (x) + 3.

It follows from the task content that the graph which has been shifted vertically is to be identified.

For a vertical shift, it means that the y value of such graphs must have increased or decreased. This is However, evident in the equation y= log (x) + 3 and hence, is the solution.

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By answering the presented question, we may conclude that Therefore, cylinder the volume generated by rotating the region bounded by \(y = 8x - x^2, y = 12\) about x = 2 is 128π/3 cubic units.

The cylinder, which is frequently a three-dimensional solid, is one of the most fundamental curved geometric shapes. In elementary geometry, it is referred to as a prism with a circle as its basis. A cylinder is also defined as an infinitely curved surface in several modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure with two identical circles as bases linked by a curving surface at the cylinder's height, which is defined by the distance between the bases from the centre. Cold beverage cans and toilet paper wicks are examples of cylinders.

We can see that the region is bounded by the parabola \(y = 8x - x^2\) and the horizontal line y = 12. It is rotated about the vertical line x = 2.

\(h(x) = 12 - (8x - x^2)\)

The radius of the cylindrical shell is the distance from the axis of rotation (x = 2) to the x-value of the slice, which is r(x) = x - 2.

The circumference of the cylindrical shell is 2πr(x), and the thickness is dx. Therefore, the volume of the cylindrical shell at x is:

dV = 2πr(x)h(x)dx

= 2π\((x - 2)(12 - (8x - x^2))dx\)

To find the total volume, we integrate dV from x = 0 to x = 4 (the limits of the region):

V = ∫₀⁴ 2π\((x - 2)(12 - (8x - x^2))dx\)

= ∫₀⁴ 2π\((-x^3 + 12x^2 - 40x + 48)dx\)

= 2π[-¼\(x^4 + 4x^3 - 20x^2 + 48x\)] from 0 to 4

= 2π(64/3)

= 128π/3

Therefore, the volume generated by rotating the region bounded by \(y = 8x - x^2, y = 12\) about x = 2 is 128π/3 cubic units.

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Explanation

Step 1

Two Angles are Supplementary when they add up to 180 degrees

hence,as ZX and ZY are supplementary

also,angle ZY is 57

Step 2

solve the equations.

a) replace ZY from equation (2) into equation (1)

therefore, the answer is

I hope this helps you

Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

Answer:

Points F, J, and H are collinear

Step-by-step explanation:

just took exam

The statement F, J, and H are collinear is not used to prove that ΔFGH is similar to ΔFIJ.

We have to find out which statement is wrong regarding ΔFGH is similar to ΔFIJ.

Here the statement points F, J, H are collinear are not used to prove the similarity of both triangle because if these three points are collinear than there is no triangle possible and when there is no triangle than how we prove similar to them.

So when F,J and H are collinear than we can't prove similar to both the triangles.

But in all the other points we can prove the similarity of both the triangles.

Hence the statement F, J, and H are collinear is not used to prove that ΔFGH is similar to ΔFIJ.

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Answer:

0.028 square kilometers

Step-by-step explanation:

The formula for area in a rectangle is base times height (also known as length times width). Therefore, the area of the rectangular plot of land is 0.4 * 0.07 which is 0.028.

Hope this helps :)

Answer:

0.028

Step-by-step explanation:

yeahhh idek allat more in depth one below me

Answer:

No, the two sides are not congruent.

I flipped my whole laptop around to check loll

In-state corresponds to students who are residents of the same state as the university, out-of-state corresponds to students from different states, and foreign corresponds to students from countries other than the university's country.

To match the vocabulary word with its corresponding example in the context of the state university survey, we need to understand the terms and their meanings.

Here are the vocabulary words and their corresponding examples:

Vocabulary Word: In-state

Example: A student who is a resident of the same state where the university is located.

They pay lower tuition fees compared to out-of-state or foreign students.

Vocabulary Word: Out-of-state

Example: A student who is not a resident of the state where the university is located.

They typically pay higher tuition fees compared to in-state students.

Vocabulary Word: Foreign

Example: A student who is from a country other than the country where the university is located.

They are international students who may have different visa requirements and tuition fees.

To match these vocabulary words with their corresponding examples:

In-state: A student from the same state as the university, paying lower tuition fees.

Out-of-state: A student from a different state than the university, paying higher tuition fees.

Foreign: A student from a country other than the country where the university is located, with potential differences in visa requirements and tuition fees.

By associating each vocabulary word with its respective example, we can accurately describe the three categories of students based on their residency and origin in the context of the state university's survey.

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Answer:

Step-by-step explanation:

There are 10 girls in an athletics club.

e ratio of girls to boys is 5:3.

w many boys are there?

we can solve with an equation

10 : x = 5 : 3

x = 10 * 3 : 5

x = 30 : 5

x = 6

---------------

Answer:

use the app photomath

Step-by-step explanation:

Answer:

A=(-2,-2) B=(-2,-6) D=-5,-2 C=(-5,-6)

Step-by-step explanation:

Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be represented by 6, 8, 10, 15, 20, and 25, among countless other numbers.

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

Input the Pythagorean Theorem with the given numbers:

c^2 = a^2 + b^2

25^2 = 15^2 + 20^2

625 = 225 + 400

625 = 625

Yes, the numbers 15, 20 and 25 form a right triangle and the Pythagorean triple.

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Answer:

40 girls

Step-by-step explanation:

To get the number of girl students, we first do 48 divided by 6 to get 8. Then we do 8 x 5 to get 40.  

Answer:

x-intercept (-3;0) and (1;0)

y-intercept (0;1)

Answer:

The function is neither even nor odd.

Step-by-step explanation:

A function is odd if:

f(x) = - (f-x)

A function is even if:

f(x) = f(-x)

A function is neither odd nor even if neither of the above two equalities are true, that is to say:

f(x) != f(-x) and f(x) != -f(-x)

Which is our case. (because substituting (-x) in place of (x) will not give us either of the equations. So the function is neither odd, nor even.

The value of p is 15

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Davey reads 58 pages on Saturday and on rest of the days p pages per day

Therefore everyday he reads 58+p pages per day

If he reads for 10 days and he reads a total 1408 pages then we have

In a week there is one Saturday

thus

9p+58=1408

9p=1350

p=15

Thus on the other days p is equal to 15 pages per day.

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The complete question is Davey reads 58 pages on Saturday and p pages on other days and on a span of 10 days he reads 1408 pages. Find the value of p.

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

8 + 2x

Step-by-step explanation:

To simplify this expression, combine like terms.

16 - 8 = 8

5x - 3x = 2x

8 + 2x

hope this helps :)

Answer:

Because of the x between the 5 and 3 u have to put them in a bracket form or group like terms. After that u subtract the 16 from 8 and the 5x from the 3x so the answer will be equal to 8 +2x because 16-8=8 and 5x-3x=2x so it will be 8+2x

The price of the couch after the markup gotten during a sale, a store offered a 30% discount on a couch that originally sold for $870 is $791.70.

The concept that will be used here is the discounted price . The discount is represented in the advertisement as a percentage off the list price. As a result, a sale price of $70 will be achieved with a 30% discount on a $100 list price. Another way to understand the phrase is to say that it simply refers to the selling price of an item.

The  price of the couch after the markup can be determine as :

$870 * (1 + 30% ) *  (1 - 30% )

Then this can be simplifIed as :

= $870  *1.3 * 0.7

=$ 791.7

Then Rounding up to the nearest cent will give $ 791.70

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Answer:

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Answer:

Line A does not intersect line B.

Step-by-step explanation:

line A comes close, but does not touch, intersect, or overlap line A. hope this helps, please correct me if i am wrong.

Answer:

B. 18

Step-by-step explanation:

Quadrilateral ABCD is a rectangle.

Diagonals AC and BD intersect at point E.

Diagonals of a rectangle are equal in length.

\(\implies BD = AC\)

Diagonals of a rectangle bisect each other.

\(\implies\frac{1}{2} BD = \frac{1}{2} AC\\\\\implies DE = \frac{1}{2} \times 36\\ \\ \implies DE = 18\)

To make the expression If a = b + c and c ___ 0, then a > b  right, c will be c > 0.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /, and ^) that represents a quantity or a relationship between quantities. It can be  number, variable, or combination of both.

Expressions are used to represent mathematical operations, formulas, and relationships. They can be simple or complex, and they can be evaluated or simplified using mathematical rules and operations.

Now,

The correct relationship symbol that makes the statement true is ">" (greater than).

If a = b + c and c > 0, then a will always be greater than b. This is because adding a positive value (c) to b will increase the result (a) above the value of b.

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The inequality is graphed and attached

There are some points that help in interpreting inequality graphs.

the x values are also called the domain lets assume -4 0 4. this is substituted into the equation 3x - 2y > 2 to get the values in the y direction.

3x - 2 > y

y < 3x - 2

for x = -4

y < 3 * -4 - 2 = -14

for x = 0

y < 3 * 0 - 2 = -2

for x = 4

y < 3 * 4 - 2 = 10

table of values

x      y

-4   -14

0     -2

4     10

y < 3x - 2 is the equation

Then use of dashed lines of dashed lines or solid lines

dashed lines means there is no equality sign in the inequality > OR < hence used for the problem

solid line means there is equality in the inequality  ≤ OR ≥

Another part is the shaded portion

shading above the line defines greater than shading below the line defines less than. The equation has less than and the shading is below the line

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