Look at the image below.


Find the area of the parallelogram.

The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Answer:

7j+2 or 2+7j

Step-by-step explanation:

(4+8j)+(−2−j)

Subtract 2 from 4 to get 2.

2+8j−j

Combine 8j and −j to get 7j.

2+7j

Step-by-step explanation:

x and y are directly proportional means that

y = kx

y grows with the same factor k applied to x.

the area of a circle (the cross section of a cylindrical pipe) is

pi × r²

r being the radius (which is half of the diameter).

so, the area in terms of the diameter is

pi × (d/2)² = pi × d²/4

so, we know

36 correlates to pi × (d small)²/4

60 correlates to pi × (d large)²/4

therefore (directly proportional),

d small² = 36×4/pi

d small = 12/sqrt(pi)

d large² = 60×4/pi

d large = sqrt(4×15×4/pi) = 4×sqrt(15/pi)

the difference between large and small diameter (increase from small to large) is then

4×sqrt(15/pi) - 12/sqrt(pi)

d small = 100%

1% = 100%/100 = 12/sqrt(pi) / 100 = 12/(100sqrt(pi))

the % of the diameter increase is then

increase/1% =

(4×sqrt(15/pi) - 12/sqrt(pi)) / 12/(100sqrt(pi)) =

= (400sqrt(pi)×sqrt(15/pi) - 1200sqrt(pi)/sqrt(pi)) / 12 =

= (400×sqrt(15) - 1200) / 12 = 100×sqrt(15)/3 - 100 =

= 100×(sqrt(15)/3 - 1) = 29.09944487...% ≈ 29.1%

the diameter has to increase by about 29.1%, so that the pipe can carry 60 liters per second.

please consider : only the area of the cross section and the carrying capacity are directly proportional.

the diameter of the cross section and the area of the cross section are NOT directly proportional.

they have the pi×(d/2)² relationship.

and so, while the capacity and the cycle area both increase by the same factor, the impact on the diameter (or radius) is different.

so, for capacity and area we have

60 = k×36

k = 60/36 = 5/3 = 1.66666666...

and therefore both increase by 66.66666...%.

but because of the square relation between diameter and cross section area, the diameter only increases by 29.1%.

Answer:

252 6-inch tiles can cover the floor completely.

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = L*W

In this case we know that the floor is 9ft long and 7 ft wide, then:

L = 9ft

W = 7ft

Because the tiles are in inches instead of ft, I will rewrite those measures on inches.

Here we need to use:

1ft = 12 in

Then:

L = 9ft = 9*( 12in) = 108 in

W = 7ft = 7ft*(12in) = 84 in

Then the area of the floor is:

A  = 108in*84in = 9,072 in^2

In this case, Ms. Yamagata wants to only use 6-inch tiles to cover all the floor.

The area of a 6-inch tile is:

a = (6 in)*(6 in) = 36 in^2

The total number of 6-inch tiles that she needs to use, is the quotient between the area of the whole floor, and the area of one tile, this is:

N = A/a = (9,072 in^2)/(36 in^2)  = 252

She needs to use exactly 252 tiles to cover the floor.

This means that 5% of the 10-1/2-month-old baby boys in the reference population weigh 16.7 pounds or less, and 95% of these baby boys weigh 16.7 pounds or more.

The determination is based on the definition of a percentile. A percentile is a value below which a certain percentage of the data falls. So, in this case, if a weight of 16.7 pounds is at the 5th percentile for 10-1/2-month-old baby boys, then 5% of the baby boys in the reference population have a weight of 16.7 pounds or less. This also means that the remaining 95% of the baby boys in the reference population have a weight of more than 16.7 pounds.

The calculation of percentiles is based on the ranking of the data set. The data is first sorted in ascending order and then divided into 100 equal parts, with each part representing a percentile. The value at each percentile is the value below which a certain percentage of the data falls.

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The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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Answer:

Let's call the speed of Bug F v_F and the speed of Bug S v_S. Since both bugs started at 0, we can express their positions at any time t as:

Position of Bug F = 12 + v_F * t

Position of Bug S = 8 + v_S * t

To find out when F and S will be 100 units apart, we need to find the time t at which their positions differ by 100 units. In other words, we need to solve the following equation:

|12 + v_F * t - (8 + v_S * t)| = 100

We can simplify this equation by expanding the absolute value and rearranging the terms:

|4 + (v_F - v_S) * t| = 100

Now we can split this equation into two cases:

Case 1: 4 + (v_F - v_S) * t = 100

In this case, we have:

v_F - v_S > 0 (since Bug F is faster)

t = (100 - 4) / (v_F - v_S)

Case 2: 4 + (v_F - v_S) * t = -100

In this case, we have:

v_F - v_S < 0 (since Bug S is faster)

t = (-100 - 4) / (v_F - v_S)

Since we're only interested in positive values of t, we can discard the second case. Therefore, the time at which F and S will be 100 units apart is:

t = (100 - 4) / (v_F - v_S)

t = 96 / (v_F - v_S)

We don't know the values of v_F and v_S, but we can use the fact that Bug F is at 12 and Bug S is at 8, four seconds after they started. This gives us two equations:

12 = 4v_F + 0v_S

8 = 4v_S + 0v_F

Solving these equations for v_F and v_S, we get:

v_F = 3

v_S = 2

Substituting these values into the equation for t, we get:

t = 96 / (3 - 2)

t = 96

Therefore, F and S will be 100 units apart 96 seconds after they start.

Since S is finite, it follows that there must exist distinct elements x and y in S  Without loss of generality, we can assume that x is not equal to y. Therefore, every element in S has an inverse, and S is a group.

what is distinct elements ?

Distinct elements refer to the unique or different items in a set, collection, or sequence. In other words, no element in the set appears more than once.

what is collection ?

A collection is a group of items or objects that are considered together. These items can be anything from physical objects to data elements, and they are typically grouped together for a specific purpose. Collections can be finite or infinite in size, and they can be ordered or unordered.

In the given question,

To prove that S is a group, we need to show that every element in S has an inverse.

Let a be an element in S. Consider the set Sa = {ax | x is an element in S}. Since S is finite, Sa is also finite. Moreover, since S satisfies the cancellation laws, the elements in Sa are all distinct. To see why, suppose there exist distinct elements x and y in S such that ax = ay. Then, by cancellation, we have x = y, which contradicts our assumption that x and y are distinct. Hence, the elements in Sa are all distinct.

Since S is finite, it follows that there must exist distinct elements x and y in S such that ax = ay. Without loss of generality, we can assume that x is not equal to y. Then, by cancellation, we have a = yx^-1. Therefore, every element in S has an inverse, and S is a group.

Consider the semigroup (N, +), where N is the set of non-negative integers and + denotes addition. This semigroup satisfies the cancellation laws since, for any non-negative integers a, b, and c, if a + b = a + c, then b = c. However, not every element in N has an inverse under addition, since there is no non-negative integer x such that 2 + x = 0. Therefore, (N, +) is not a group.

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Answer:

3/14

Step-by-step explanation:

Answer:

im not really sure what that means im so sorry

Step-by-step explanation:

Answer:

$30507.14

Step-by-step explanation:

(8000)(1+.055)^25= 30507.138789 rounded to the nearest penny = $30507.14

If you are dealt 4 cards from a shuffled deck of 52 cards, the probability of getting two queens and two kings is:  0.000133.

Number of ways to get two of the four queens = 4C2 = 6 ways

Number of ways to get  two of the four kings =  4C2 = 6 ways

Number of ways to get none of the deck = 48C0 = 1 way

Hence,

Number of  ways to get four cards  = 6 x 6 x 1

Number of  ways to get four cards  =  36 ways

Number of ways 4 cards can be chosen from 52 cards = 52C4 = 270725 ways

So,

Probability = 36 ways / 270725 ways

Probability = 0.0001329

Probability = 0.000133 (Approximately)

Therefore the probability is 0.000133.

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Answer:

slope = 4

points on graph = (0,0), (1,4)

Step-by-step explanation:

line going through quadrants 1 and 3. Straight line.

Answer:

Step-by-step explanation:

Answer:

$45.80

Step-by-step explanation:

First, let's multiply $2.29 · 2. This gives us $4.58.

Second, multiply $4.58 · 10. This gives you $45.80.

Tonya will need $45.80 to buy the desired amount of juice.

Answer:

she will need $22.90

Step-by-step explanation:

Answer:

\(92.05^{\circ}\)

Step-by-step explanation:

By the exterior angle theorem, the answer is \(m\angle Y+m\angle Z=92.05^{\circ}\).

Answer:

A

Step-by-step explanation:

exterior angle = sum of the other two angles

63.25 + 28.8

92.05°

Answer:

The answer is answer choice E.

Step-by-step explanation:

Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees

y = -1/5x +1/2 linear function has the same slope .

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

First solve for the slope

m =\(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

m=\(\frac{0-\frac{3}{5} }{\frac{1}{2} -\frac{1}{5} }\)

m = \(\frac{-1}{5}\)

Look for the linear equation with the same value of m after determining the slope (parallel equation).

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The value of c such that the function f is a probability density function is 2

The density function is given as:

f(x) = cxe^(−x^2) if x ≥ 0

f(x) = 0 if x < 0.

We start by integrating the function f(x)

∫f(x) = 1

This gives

∫ cxe^(−x^2) = 1

Next, we integrate the function using a graphing calculator.

From the graphing calculator, we have:

c/2 * (0 + 1) = 1

Evaluate the sum

c/2 * 1 = 1

Evaluate the product

c/2 = 1

Multiply both sides of the equation by 2

c = 2

Hence, the value of c such that the function f is a probability density function is 2

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Answer:

D

Step-by-step explanation:

3 | 1   5   - 8   6

   ↓   3    24   48

   ----------------------

    1   8   16    54 ← Remainder

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Answer:

$153

Step-by-step explanation:

The given cubic equation has no roots.

Traditionally, a cubic problem can be solved by converting it into a quadratic equation, which can then be solved by factoring or the quadratic formula. A cubic equation has three roots, just like a quadratic equation has two. Three real roots or one real root and two imaginary roots are both possible for a cubic equation. Cubic equations must also always be arranged in their standard form first.

The following strategies can be used to resolve a cubic equation:

Using Graphical Method to Find Integer Solutions with Factor Lists

Given that the cubic equation is: 8x²-5x³+7-12x

Regrouping the equation in standard form:

- 5x³ + 8x² - 12x + 7

Here, the constant is 7. Take the factors of the constant.

7 = 1, 7

Substitute the value of the factors as follows:

G(1) = - 5(1)³ + 8(1)² - 12(1) + 7 = -5 + 8 - 12 + 7 ≠ 0

G(7) = -5(7)³ + 8(7)² -12(7) + 7 = -1715 + 392 - 84 + 7 ≠ 0

Hence, the given cubic equation has no roots.

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Answer: y=1.125x

Step-by-step explanation:

Answer:13 miles

Step-by-step explanation:10.20-1.75=8.45÷0.65=13

Solution

First, we need to convert the dimensions in feet to inches

Hence, the volume is;

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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