Name the remainder for the quotient and describe or show how you found the remainder.

Need to Find :- The area of the trapezium.

We are here provided with height and two parallel bases of trapezium and we are interested in finding out the area of the trapezium.

As we know that,

\(\implies\sf \red{Area_{trapezium}= \dfrac{1}{2}\times (sum\ of \ parallel\ sides )\times height}\)

On substituting the respective values,

\(\sf: \implies Area =\dfrac{1}{2}\times (7cm +13cm)\times 10cm \\ \)

\(\sf : \implies Area = 20cm \times 5cm \\\)

\(\sf : \implies \underline{\boxed{\pink{\frak{ Area = 100cm^2}}}}\\\)

\(\underline{\underline{\textsf{ $\therefore$Hence the area of the trapezium is \textbf{100 cm$\bf ^2$ }.}}}\)

Given :

To find :

Solution :

We know,

\({\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}= \dfrac{1}{2 } \times (b_{1} + b_{2}) \times h} }}\)

Now, Substituting the values :

\({\qquad \dashrightarrow{ \sf{Area_{(Trapezoid)}= \dfrac{1}{2 } \times (7 + 13) \times 10} }}\)

\({\qquad \dashrightarrow{ \sf{Area_{(Trapezoid)}= \dfrac{1}{2 } \times 20 \times 10} }}\)

\({\qquad \dashrightarrow{ \sf{Area_{(Trapezoid)}= \dfrac{1}{2 } \times 200} }}\)

\({\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}=100} }}\)

Therefore,

The statement is not always true.

The statement is only sometimes true.

We have,

Part A:

The statement "the product of two negative rational numbers is greater than either factor" is never true.

Let a = -1/2 and b = -1/3.

Then ab = (-1/2)(-1/3) = 1/6, which is less than both a and b.

Let c = -1/4 and d = -2/3.

Then cd = (-1/4)(-2/3) = 1/6, which is also less than both c and d.

Both of these examples demonstrate that the product of two negative rational numbers can be less than either factor and therefore the statement is not always true.

Part B:

The statement "the product of two positive rational numbers is greater than either factor" is sometimes true, but not always. To see why, consider the following examples:

Let e = 1/2 and f = 1/3.

Then ef = (1/2)(1/3) = 1/6, which is less than both e and f.

Let g = 2/3 and h = 3/4.

Then gh = (2/3)(3/4) = 1/2, which is greater than both g and h.

These examples demonstrate that the product of two positive rational numbers can be less than either factor (in the first example) or greater than both factors (in the second example).

Therefore, the statement is only sometimes true.

Thus,

The statement is not always true.

The statement is only sometimes true.

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Answer:

C

Step-by-step explanation:

Answer:

I pretty sure its D but if im wrong sorry.

Step-by-step explanation:

7m + 12 = -4m + 78

7m + 4m = 78 - 12

11m = 66

m = 6

I hope you understand...

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Let

x -----> number of orange balls

y -----> number of green balls

we have that

x+y=123 -----> x=123-y ------> equation A

y=5x+9 -----> equation B

Solve the system of equations

substitute equation A in equation B

y=5(123-y)+9

solve for y

y=615-5y+9

y+5y=615+9

6y=624

y=104

Find out the value of x

x=123-104

x=19

therefore

Answer: 5

the scale length of 15cm and 3cm is 15/3 = 5

Step-by-step explanation:

Answer:

Red: 47.5%, Yellow: 30%, Blue: 22.5%

Step-by-step explanation:

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:her for ppoints

Step-by-step explanation:

Answer

domain (-inf,inf) range (-inf, 7)

Step-by-step explanation:

I think

When selecting numerous groups of nine 12- to 14-year-olds at random from the population, we can expect that a certain percentage of these groups will have a group mean cholesterol value falling within the range of 145 to 165 mg/dl. This can be answered by the concept of Standard deviation.

To determine the percentage of groups where the group mean cholesterol value falls between 145 and 165 mg/dl, we need to consider the distribution of cholesterol values in the population and calculate the probability of obtaining a group mean within the specified range.

Obtain the population data: Gather information about the cholesterol values of the entire population of 12- to 14-year-olds. This data will provide us with the necessary information to make statistical inferences.

Calculate the mean and standard deviation: Compute the mean (μ) and standard deviation (σ) of the cholesterol values in the population. These measures will help us understand the overall distribution of cholesterol levels.

Use the Central Limit Theorem: Given that we are selecting groups of nine individuals at random, we can assume that the distribution of sample means will approximate a normal distribution, even if the original population distribution is not normal. This is due to the Central Limit Theorem.

Determine the probability: With the assumption of a normal distribution for the sample means, we can use the calculated population mean (μ) and standard deviation (σ) to find the probability of obtaining a group mean between 145 and 165 mg/dl. This probability can be calculated using standard normal tables or statistical software.

Calculate the percentage: Once we have the probability, we can multiply it by 100 to obtain the percentage of groups where the group mean cholesterol value falls within the specified range.

Therefore, by following these steps and using the population data and statistical methods, we can determine the percentage of groups in which the group mean cholesterol value would be between 145 and 165 mg/dl.

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Answer:

x =2

Step-by-step explanation:

Answer: D

Step-by-step explanation:

You could plug it in your calculator, just make sure your mode is in radians because there is a pi in your questions

Answer:

none

Step-by-step explanation:

I can't find any question there

The value of x is 13.85.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

(7x + 1)° and (6x - 1)° makes a straight angle.

This means,

(7x + 1) + (6x - 1) = 180

7x + 1 + 6x - 1 = 180

13x = 180

x = 180/13

x = 13.85

Thus,

x is 13.85°

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Answer:

  B)  108°

Step-by-step explanation:

You want the interior angle measure for a regular pentagon.

The interior angles of a regular n-gon will have measure ...

  180° -360°/n

When n = 5, the interior angles have measure ...

  180° -360*/5 = 180° -72° = 108°

The interior angles of a regular pentagon are 108°.

__

Additional comment

The 360°/n comes from the fact that the sum of exterior angles for any convex polygon is 360°. For a regular n-gon, those exterior angles are congruent, so each is 360°/n. The interior angle is its supplement.

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Answer:

x = 80°

Step-by-step explanation:

From the picture attached,

Two lines are parallel and third line (transversal) is intersecting these lines at two different points.

m(∠x) = 80° [Exterior alternate angles are equal in measure]

Therefore, x° = 80° is the answer.

Answer:

Perimeter: 26 units

Area: 24 units²

Step-by-step explanation:

12 + 9 + 5 = 26

A = 1/2BH

A = 1/2 12(4)

A = 1/2 48

A = 24

Answer:

Step-by-step explanation:

Z. 1/25 it’s just a guess theough

You can open those brackets and distribute one brackets content with multiplication to other bracket contents.

The products which result in a sum or difference of cubes is given by:

Option D: \((x+4)(x^2 -4x + 16)\)

If there are two terms which are with power 3 (ie cubed), and they both are in addition or subtraction, then that is called sum or difference of cubes for two terms.

Example: \(a^3 - b^3\) is difference of cubes.

There is a formula too which you can use in case if you need it which goes like this:

\(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\\ \\ a^3 - b^3 = (a-b)(a^2 + ab + b^2)\)

Option A: \((x-4)(x^2 + 4x - 16)\)

\((x-4)(x^2 + 4x - 16) = x^3 + 64 -4x^2 + 4x^2 -16x - 16x = x^3 +4^3 -32x\)

Thus, not a sum or difference of cubes

Option B: \((x-1)(x^2 - x+ 1)\)

\((x-1)(x^2 - x+ 1) = x^3 - 1 + x + x -x^2 - x^2 = x^3 - 1 + 2x - 2x^2\)

Thus, not a sum or difference of cubes

Option C: \((x + 1) (x - 1)\)

\((x + 1) (x - 1) = x^2 - 1 + x - x = x^2 - 1\)

It is difference of squares but not of cubes.

Option D: \((x+4)(x^2 -4x + 16)\)

\((x+4)(x^2 -4x + 16) = x^3 + 64 -4x^2 + 16x + 4x^2 - 16x = x^3 + 64 = x^3 + 4^3\\ (x+4)(x^2 -4x + 16) = x^3 + 4^3\)

Thus, it is sum of cubes.

Thus, only Option D: \((x+4)(x^2 -4x + 16)\) is expressible as sum or product of cubes (here it is expressible as sum of cubes \(x^3\) and \(4^3\).

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Answer:

c and e

Step-by-step explanation:

Answer:

$0.45 or 45 cents

Step-by-step explanation:

If i'm not mistaken.

in one pound, there are 16 ounces. Therefor, just divide 7.20 by 16 and you get 0.45. or 45 cents.

Hope this helps, brainliest is appreciated! :)
Have a great day! cx

~Mitsuna

Answer:

4 lbs

Step-by-step explanation:

The weight is in the y-axis and the amount of water is in the x-axis, so if you want to find what the weight is when the tank is empty, you just look at where the line is on the y-axis when x = 0.

4 pounds is the weight of an empty tank

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

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

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

(0, 4) and (1, 12)

Slope = 12-4/1

=8

Now let us find the y intercept which is weight of empty tank

4=8(0)+b

b=4

Hence, 4 pounds is the weight of an empty tank

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Option (A) :  least: 10 hours; greatest: 14 hours

The function f(x) = sin x has all real numbers in its domain, but its range is

−1 ≤ sin x ≤ 1.

How to solve such range questions?

Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question

Given: d(t) = 2sin(xt) + 12

=  −1 ≤ sin (xt) ≤ 1.

=  −2≤ 2 sin (xt) ≤ 2.

=  10 ≤ 2sin (xt) + 12 ≤ 14

=   10 ≤d(t) ≤ 14

Thus  least: 10 hours; greatest: 14 hours

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The maximum mass of carbon dioxide that could be produced by the chemical reaction between 1.2 g of butane and 2.75 g of oxygen is 4.40 g.

To calculate the maximum mass of carbon dioxide produced, we first need to determine the limiting reactant. We compare the number of moles of butane and oxygen by dividing their respective masses by their molar masses. The molar mass of butane (C4H10) is 58.12 g/mol, and the molar mass of oxygen (O2) is 32.00 g/mol.

Using these values, we find that the number of moles of butane is 1.2 g / 58.12 g/mol = 0.0206 mol, and the number of moles of oxygen is 2.75 g / 32.00 g/mol = 0.0859 mol. Since butane has fewer moles than oxygen, it is the limiting reactant.

Next, we need to determine the molar ratio of carbon dioxide to butane using the balanced chemical equation. The balanced equation is:

2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O

From this equation, we can see that for every 2 moles of butane, 8 moles of carbon dioxide are produced. Therefore, for the 0.0206 mol of butane, we can calculate the corresponding mass of carbon dioxide as follows:

0.0206 mol butane * (8 mol CO2 / 2 mol butane) * (44.01 g/mol CO2) = 0.361 g CO2

Thus, the maximum mass of carbon dioxide that could be produced is 0.361 g. However, it is important to note that this assumes ideal conditions and complete conversion, so in reality, the actual yield may be lower due to factors like incomplete reactions or side reactions.

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Answer:

26 per week

Step-by-step explanation:

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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Answer:

1 1/4

Step-by-step explanation:

2 1/4 ÷ 1 4/5

9/4 ÷ 9/5

9/4 x 5/9

5/4

1 1/4

The derivative of \(r\) with respect to \(\theta\) can be found using the chain rule. Let's proceed with the differentiation:

\frac{dr}{d\theta} = \frac{d}{d\theta}\left(\cos\left(\frac{\theta}{3}\right)\right)

To differentiate \(\cos\left(\frac{\theta}{3}\right)\), we treat \(\frac{\theta}{3}\) as the inner function and differentiate it using the chain rule. The derivative of \(\cos(u)\) with respect to \(u\) is \(-\sin(u)\), and the derivative of \(\frac{\theta}{3}\) with respect to \(\theta\) is \(\frac{1}{3}\). Applying the chain rule, we have:

\frac{dr}{d\theta} = -\sin\left(\frac{\theta}{3}\right) \cdot \frac{1}{3}

Now, let's evaluate this derivative at \(\theta = \pi\):

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\sin\left(\frac{\pi}{3}\right) \cdot \frac{1}{3}

The value of \(\sin\left(\frac{\pi}{3}\right)\) is \(\frac{\sqrt{3}}{2}\), so substituting this value, we have:

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\frac{\sqrt{3}}{2} \cdot \frac{1}{3} = -\frac{\sqrt{3}}{6}

Therefore, the slope of the tangent line to the polar curve \(r = \cos(\theta / 3)\) at the point specified by \(\theta = \pi\) is \(-\frac{\sqrt{3}}{6}.

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Answer:

g(x)=(x+5)^2

Step-by-step explanation:

the account looks like this, because you invert the sign 5 is negative to the left, so for the result to be negative in the account it has to be positive

g(x)=(x+5)^2

(x+5)^2=0

x+5=0

x=0-5

x=-5

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