Please help.. 10 points

The only true statement is A/B + A/C = 2A/B+C. The correct answer is option 1.

Let's evaluate each statement one by one.

1. A/B + A/C = 2A/B+C. This statement is true. We can solve this by taking the least common multiple of the two denominators (B and C).

Multiplying both sides by BC, we get AC/B + AB/C = 2A. And if we simplify, it becomes A(C+B)/BC = 2A. Since A is not equal to 0, we can divide both sides by A and get: (C+B)/BC = 2/B+C

2. a^2b-c/a^2 = b-c. This statement is false. Let's try to solve this: If we simplify the left side, we get \((a^2b - c)/a^2\). And if we simplify the right side, we get: (b-c). The two expressions are not equal unless c = 0, which is not stated in the original statement. Therefore, this statement is false.

3. \(x^2y - xz/x^2 = xy-z/x\). This statement is also false. Let's try to simplify the left side: \(x^2y - xz/x^2 = x(y - z/x)\). And let's try to simplify the right side: \(xy - z/x = x(y^2 - z)/xy\). The two expressions are not equal unless y = z/x, which is not stated in the original statement. Therefore, this statement is false.

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Answer:

A, 1/10

Step-by-step explanation:

multiply 2/5 by 1/4 to get 2/20 which simplifies to 1/10

Answer:

1219.5 more centimeters of fabric

Step-by-step explanation:

First, we need to convert 12.5 meters to centimeters, since the given amount of fabric is in centimeters.

12.5 meters = 12.5 x 100 centimeters/meter = 1250 centimeters

Now we can find the difference between what Ray needs and what he has:

1250 centimeters - 30.5 centimeters = 1219.5 centimeters

Therefore, Ray needs 1219.5 more centimeters of fabric.

Answer:

It would be B

Step-by-step explanation:

24 and 36 greatest common factor is 12 and  its least is 72

Answer:

comparing fossils with other engerys:

Most alternatives energy sources doesn't have as much pollution produce like fossil fuel does,

Fossil comes from underground or persevered by nature, when others can be made by renewable resources, such as Wind(windmills) , sun (solar), and water (those rolly things)

Answer:

56 degrees

Step-by-step explanation:

Assuming this is trigonometry, you use the tangent method. Which means in order to find the angle you put the adjacent side of what your finding and the opposite on top of it.

The equation is tan(angle)= 9/6

You multiply both sides by the arch of tangent and get

angle =tan^-1 (9/6)

I inserted it into my geometry calculator and got 56.30993247, I rounded to the nearest degree and got 56 degrees

Answer:

56°

Step-by-step explanation:

The dimensions of the poster with the smallest area is 24 x 36.

Let's let "W" be the overall width of poster and "H" be the overall height of the poster.

A = H•W

The area of the printed material is 384.

The width of the printed material is W - 4(2) or W - 8.

The height of the printed material is H - 6(2) = H - 12.

So the area of the printed material is (W - 8)(H - 12) and that equals 384

(W - 8)(H - 12) = 384

WH - 12W - 8H + 96 = 384

W(H - 12) - 8H = 288

W = (288 + 8H)/(H - 12)

the area equation (A = H•W), we get:

A(H) = H(288 + 8H)/(H - 12)

A(H) = (288H + 8H2)/(H - 12)

To find the minimum, take the derivative and set it equal to zero.

To take the derivative, we must use the quotient rule

If f(x) = u/v then f '(x) = (u'v - uv')/v2

In this case u = 288H + 8H2 so u' = 288 + 16H

and v = H - 12 so v' = 1 and v2 = (H - 12)² so

A'(H) = [(288 + 16H)(H - 12) - (288H + 8H2)(1)]/(H - 12)²

A'(H) = (288H - 3456 + 16H2 - 192H - 288H - 8H2)/(H - 12)²

A'(H) = (8H² - 192H - 3456)/(H - 12)²

A'(H) = 8(H² - 24H - 432)/(H - 12)²

Setting it equal to zero:

8(H² - 24H - 432)/(H - 12)² = 0

(H² - 24H - 432)/(H - 12)² = 0 This can only be zero if the numerator is zero so:

H² - 24H - 432 = 0

(H - 36)(H + 12) = 0

H = 36 or H = -12

We can neglect the negative answer since the poster can't be a negative height so H = 36. Since H = 36, and we know that W = (288 + 8H)/(H - 12), we can solve for W:

W = (288 + 8(36))/(36 - 12)

W = 24

H = 36

Therefore, the dimensions of the poster with the smallest area is 24 x 36.

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The power generated by the student after 4 seconds is one-fourth of the power generated by the student after 2 seconds.

Power generated by a student when standing up from a chair depends on the height, mass, and acceleration of the student.

If we assume that all other factors remain constant, the power generated by a student can be calculated using the equation:

Power = Work done / time Taken

The energy required to lift a student of mass m to a height h is given by the equation:

mgh, where g is the acceleration due to gravity.

Therefore, the work done in lifting the student from a chair is given by the equation:

mgh.

The acceleration of the student is given by the equation:

a = (final velocity - initial velocity) / time Taken.

For the student standing up from a chair, the initial velocity is zero.

Therefore, the acceleration is given by the equation:

a = (2h / timeTaken²)

The power generated by the student after 2 seconds is:

P1 = (mgh / 2) × (2h / 2²)

P1 = (mgh² / 4)

The power generated by the student after 4 seconds is:

P2 = (mgh / 2) × (2h / 4²)

P2 = (mgh² / 16)

Comparing P1 and P2, we can see that the power generated by the student after 4 seconds is:

P2 = P1 / 4

Therefore, the power generated by the student after 4 seconds is one-fourth of the power generated by the student after 2 seconds.

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Answer:

see below

Step-by-step explanation:

2: letter at the vertex,  placing a letter or number inside .... , or by using 3 letters

3:

WXY

WXZ

YXZ

4: X

Answer:

y < 2

Step-by-step explanation:

The shaded part is all under y = 2

Answer is

y = 2

We're going up since the dashed lines are on the second line of y on the graph. If we were to tell the x axis, then the probability would 4 (right side) and -5 (on the left side).

lmk if im wrong :)

r=13/2

After I solved it it was kinda easy

Answer:

r=13/2

Step-by-step explanation:

Step-by-step explanation:

Magnesium chloride (MgCl2).

Answer:a

A

Step-by-step explanation:

Edge 2021

Answer:

to be quick divide 3/4 ×100=75 percent

1/10=10

.25×100=25

0.8=80

1/2=50 so now u know which one is the smallest from largest so it is 1/10 , 0.25 ,1/2, 3/4, 0.8

Step-by-step explanation:

diagonals of the rhombus bisect each other at right angles .

5a = 90

a = 90/5 = 18

in ∆ OCD:

5a + 2a + b = 180

7a+ b = 180

b = 180 - 7 ( 18)

b = 180 - 126

b = 54 °

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.☺️

Answer:

a = 18°

\( b= 108\degree \)

Step-by-step explanation:

ABCD is a rhombus.

AC and BD are its diagonals

Diagonals of a rhombus bisects at right angles.

Therefore,

5a = 90°

a = 90°/5

a = 18°

2a = 2*18° = 36°

Diagonals of a rhombus bisects the opposite angles.

Therefore,

\( m\angle ADC = 2(2a)\)

\( m\angle ADC = 2\times 36\degree \)

\( m\angle ADC = 72\degree \)

\( m\angle ADC+m\angle DCB= 180\degree \)

(Adjacent angles of a rhombus are supplementary)

\( 72\degree+b= 180\degree \)

\( b= 180\degree-72\degree \)

\( b= 108\degree \)

The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.

An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.

The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Let the length is given as, l = √24 and,

The width is given as, w = √10

Use the formula of area of rectangle,

A = lw

A = √24 × √10

A = 4.89 × 3.16

A = 15.45 ≈ 15 square units.

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Answer:

Domain and range: All possible real numbers.

Step-by-step explanation:

Since both end contains arrows, that means that it keeps going on and on.

Answer:

EVERYONE REPORT ME PLEASE

Answer:

c

Step-by-step explanation:

To disprove the null hypothesis a researcher must develop a number that demonstrates the existence of a difference between two variables. this is called the alternative hypothesis.

Null hypothesis and Alternative hypothesis are two basic types of hypothesis that express the criteria of a research problem as a relationship between two or more variables.

Null hypothesis refers to the hypothesis which clarifies that there is no relationship between two variables.

An alternative hypothesis is the inverse of the null hypothesis which tells that there is a relationship between two variables.

Hence, demonstrating that there exist a difference between two variables is an alternative hypothesis.

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Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

The relative frequency in the class interval with 15 observations is 0.20 or 20%.

The correct answers are: Measurements from a sample are called: statistics. The relative frequency in the class interval with 15 observations is: 0.20.

Statistics are measurements or data collected from a sample of a larger population. They are used to make inferences about the population.

To find the relative frequency of a class interval, you divide the frequency of that interval by the total number of observations. In this case, the relative frequency is:

relative frequency = frequency of interval / total number of observations

relative frequency = 15 / 75

relative frequency = 0.20

Therefore, the relative frequency in the class interval with 15 observations is 0.20 or 20%.

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Answer:

the answer is 40

Step-by-step explanation:

A = 10 x 8 over 2 which is 40

Answer:

Step-by-step explanation:

Given :-

And we need to prove that ,

So let us assume that ,

\(\implies\dfrac{a+b}{3} =\dfrac{b+c}{6} =\dfrac{c+a}{5}=k\)

Where k is a constant . Now equate each of the three terms separately to k . Therefore we have ,

\(\dfrac{a+b}{3}=k\)

\(\implies a + b = 3k \quad \dots (i) \)

Similarly we can say that ,

\(\implies c + b = 6k \quad \dots (ii)\)

\(\implies a + c = 5k\quad \dots (iii) \)

Subtracting (i) and (ii) :-

\(\implies a - c = -3k \quad \dots (iv) \)

Adding (iv) and (iii) :-

\(\implies 2c = 4k \)

\(\implies \boxed{c = 4k }\)

Put this is (ii) :-

\(\implies b +4k = 6k \)

\(\implies \boxed{b= 2k }\)

Similarly we will get ,

\(\implies \boxed{a = k }\)

Proving the given equation :-

\(\implies \dfrac{a+b+c}{a} \\\\\implies \dfrac{k+2k+4k}{k} \\\\\implies \dfrac{7k}{k}=\boxed{\red{ 7}}\)

Hence proved !

There were 21 children who were older than 7 years.

A histogram is a graph that depicts the frequency distribution of a few data points from a single variable. Histograms frequently divide data into "bins" or "range groups" and count the number of data points that belong to each of those bins.

The bar graph graphically represents category data. A histogram is a graph that represents quantitative data. Each pair of consecutive bars is separated by an equal amount of space.

The data from the Histogram can written as

Age group   Number of Children

 1 - 3                         5

 3 - 5                         3

 5 - 7                         6

 7 - 9                        8

 9 -11                        9

 11 - 13                      4

So, the number of children who were older than 7 years

= 8 + 9 + 4

= 21 children

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Answer:

A. h = h₀ + u·t - 1/2·g·t²

B. 30.9 m

C. 4.73 seconds

2. A. h = h₀ + u·t - 1/2·a·t²

B. 67.8 m

C. Approximately 25.73 seconds

3. A. h = h₀ + u·t - 1/2·g·t²

B. 31.38 m

C. Approximately 5.142 seconds

D. Approximately 32.9 m

Step-by-step explanation:

The given parameters are;

The initial height of the ball, h₀ = 15 m

The upward velocity with which the ball is thrown, u = 20 m/sec.

The acceleration due to gravity, g = 9.8 m/s²

A. The relation between the height, h, and the time, t, after the ball is released is given as follows;

h = h₀ + u·t - 1/2·g·t²

B. The height of the ball after 3 seconds is given by substitution as follows;

At t = 3 seconds, h = 15 + 20 × 3 - 1/2 × 9.8 × 3² = 30.9

The height of the ball, h, after 3 seconds is h = 30.9 m

C. The time the ball takes to hit the ground = 2 × The time it takes to maximum height + The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height

The time it takes to maximum height, \(t_{max}\), is given as follows;

v = u - g·\(t_{max}\)

Where;

v = The final velocity = 0 at maximum height

Therefore, we have;

0 = 20 - 9.8 × \(t_{max}\)

∴ \(t_{max}\) = 20/9.8 ≈ 2.0408

The time it takes to maximum height, \(t_{max}\) ≈ 2.0408 seconds

The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height, \(t_{15}\) is  given as follows;

v₂² = u₂² + 2·g·h₀

v₂² = 20² + 2×9.8×15 = 694

v₂ = √694 ≈ 26.344 m/s

v₂ ≈ 26.344 m/s

From, v₂ = u₂ + g·\(t_{15}\), we have;

26.344 = 20 + 9.8×t

9.8·\(t_{15}\) = 26.344 - 20 = 6.344

∴ \(t_{15}\) = 6.344/9.8 ≈ 0.647

The ball will hit the ground after 2 × \(t_{max}\)  + \(t_{15}\) ≈ 2 × 2.0408 + 0.647 ≈ 4.7286

The ball will hit the ground after approximately 4.7286 ≈ 4.73 seconds

2. When the ball is thrown upward from the Moon, we have;

The acceleration due to gravity on the moon, a = 1.6 m/s², therefore, we have;

A. The relation between the height, h, and the time, t, after the ball is released is given as follows;

h = h₀ + u·t - 1/2·a·t²

B. The height of the ball after 3 seconds is given by substitution as follows;

At t = 3 seconds, h = 15 + 20 × 3 - 1/2 × 1.6 × 3² = 67.8

The height of the ball, h,  thrown on the Moon, after 3 seconds is h = 67.8 m

C. The time the ball takes to hit the ground = 2 × The time it takes to maximum height + The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height

The time it takes to maximum height, \(t_{max}\), is given as follows;

v = u - a·\(t_{max}\)

Where;

v = The final velocity = 0 at maximum height

Therefore, we have;

0 = 20 - 1.6 × \(t_{max}\)

∴ \(t_{max}\) = 20/1.6 = 12.5

The time it takes to maximum height, \(t_{max}\) = 12.5 seconds

The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height, \(t_{15}\) is  given as follows;

v₂² = u₂² + 2·a·h₀

v₂² = 20² + 2×1.6×15 = 448

v₂ = √448 ≈ 21.166 m/s

v₂ ≈ 21.166 m/s

From, v₂ = u₂ + a·\(t_{15}\), we have;

21.166 = 20 + 9.8×t

1.6·\(t_{15}\) = 21.166 - 20 = 1.166

∴ \(t_{15}\) = 1.166/1.6 ≈ 0.72785

The ball will hit the ground after 2 × \(t_{max}\)  + \(t_{15}\) ≈ 2 × 12.5 + 0.72875 = 25.72875 ≈ 27.73

The ball will hit the ground after approximately 25.73 seconds

3. The height from which the ball is kicked, h₀ = 1 m

The initial velocity of the ball, u = 25 m/sec

The acceleration due to gravity, g = 9.8 m/s²

The relationship between the height, h and the time, t after the ball is released, is given as follows;

h = h₀ + u·t - 1/2·g·t²

B. The height of the ball after 2 seconds is given as follows;

At t = 2, h = 1 + 25 × 2 - 1/2 × 9.81 × 2² = 31.38

The height of the ball, after 2 seconds, h = 31.38 m

C. The time it takes the ball to hit the ground is given by the following kinematic equation, as follows;

h = h₀ + u·t - 1/2·g·t²

At the ground level, h = 0, therefore, we have;

0 = 1 + 25·t - 4.9·t²

Therefore, by the quadratic formula, we have;

t =  (-25  ± √(25² - 4×(-4.9)×1))/(2 × -4.9)

Therefore, t ≈ 5.142, or t ≈ -0.03969

Given that the time is a natural number, we have, t ≈ 5.142 seconds

D. The maximum height, \(h_{max}\) the ball reaches is given as follows;

From the kinematic equation, v² = u² - 2·g·h,

Where;

v = 0 at maximum height

h = The height the ball reaches above the initial height, we have;

0² = u² - 2·g·h

u² = 2·g·h

h = u²/(2·g) = 25²/(2 × 9.8) ≈ 31.888

\(h_{max}\) = h₀ + h = 1 + 31.888 ≈ 32.9

The maximum height the ball reaches, \(h_{max}\) ≈ 32.9 m

Answer:

(a) 5x + 9 = 2x + 7 + 3x - 15

combine like terms

5x + 9 = 5x - 8

subtract 5x and 9 from both sides

0 = -17

This statement is false, so there are no solutions. This is a contradiction equation.

(b) 7x + 5x - 7 = 21 + 10x

combine like terms

12x - 7 = 21 + 10x

subtract 10x from both sides and add 7 to both sides

2x = 28

divide by 2

x = 14

neither - it's a conditional equation

(c) 24 - 3x = 8 - 2x + 16 - x

combine like terms

24 - 3x = 24 - 3x

This equation is true and will always be true no matter what x value is plugged in. There are an infinite number of solutions. This is an identity equation.

The 8 times table is a mathematical table that lists the products of 8 and the integers from 1 to 10. The table is typically used to help students learn and memorize the multiplication facts for the number 8.

Here is the 8 times table:

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

8 x 7 = 56

8 x 8 = 64

8 x 9 = 72

8 x 10 = 80

As you can see, the 8 times table is a list of the products of 8 and the integers from 1 to 10. By memorizing this table, students will be able to quickly and easily solve multiplication problems involving the number 8. It is important to practice and memorize the 8 times table, as well as other multiplication tables, as they form the foundation for more advanced mathematical concepts.

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The correct form of the partial fraction decomposition for the expression \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\) is:

\(\frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}\) (Option 1).

The given expression can be written in the form \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\). To decompose this into partial fractions, we need to find the values of constants A, B, C, D, E, and F such that the expression can be written in the form of the options given.

Using partial fraction decomposition method, we can write the expression as:

\($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2} = \frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}$\)

Then we multiply both sides by the denominator of the expression on the left and simplify to get:

\($4x^3+3x^2 = A(x+1)(x^2+7)^2 + B(x^2+7)^2 + (Cx+D)(x+1)^2(x^2+7) + (Ex+F)(x+1)^2$\)

Next, we can solve for the unknown constants by equating the coefficients of the same powers of x on both sides of the equation. We will end up with a system of linear equations, which can be solved using various methods.

After solving, we get the coefficients as:

\(A = -\frac{1}{2}$, $B = \frac{5}{4}$, $C = 0$, $D = -\frac{1}{4}$, $E = 0$, and $F = \frac{3}{28}$.\)

Therefore, the correct form of the partial fraction decomposition for the given expression is:

\($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2} = -\frac{1}{2(x+1)} + \frac{5}{4(x+1)^2} - \frac{1}{4(x^2+7)} + \frac{3}{28(x^2+7)^2}$\)

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Complete Question:

Which is the correct form of the partial fraction decomposition for the expression \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\)?