A force of 100N was a necessary to lift a rock A total of 150 joules of work was done How far was the rock lifted?​

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

That's the answer.

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

step by step explanation

please mark me as brilliant

By placing the given value in equation , we get u + v - 4u = (-20, 13)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

To evaluate u + v - 4u, we first need to find the vector 4u, which is obtained by multiplying the vector u by the scalar 4:

4u = 4(5,-2) = (20,-8)

Now, we can add u and v, and subtract 4u from the result:

u + v - 4u = (5,-2) + (-5,7) - (20,-8)

= (5 - 5 - 20, -2 + 7 + 8)

= (-20, 13)

Therefore, u + v - 4u = (-20, 13).

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The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.

The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.

Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.

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Answer:

Percent of Change

Step-by-step explanation:

The ratio of the change in an amount to the original amount expressed as a percent is known as the change of percent.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

Final amount - initial amount = change

And, change / initial amount = change of percentage

Hence "The ratio of the change in an amount to the original amount expressed as a percent is known as the change of percent.".

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Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

Answer:

f(x) = 13 when x = 10.

Step-by-step explanation:

\(f(x)=\frac{x}{2}+8\)

\(f(10)=\frac{10}{2}+8\)

\(f(10)=5+8\)

\(f(10)=13\)

Therefore, f(x) = 13 when x = 10.

13

Hope it helps.

Do comment if you have any query.

Answer:

Rectangular Cross Section Surface

Answer:

Step-by-step explanation:

The size of the city in 10 years is equal to 29,802.32

Given the following data:

To calculate the size of the city in 10 years:

In this exercise, you're required to determine the size of this city in the next ten (10) years.

Mathematically, the exponential growth of a population is given by this formula;

\(P = a(1+r)^t\)

Where:

Substituting the given parameters into the formula, we have;

\(P = 3200(1+0.25)^{10}\\\\P = 3200(1.25)^{10}\\\\P = 3200 \times 9.3132\)

P = 29,802.32

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Answer:

1080 seconds.

Step-by-step explanation:

There are 60 seconds in a minute. As provided in the question, Lillian spent eighteen minutes, so 18x60=1080.

Answer:

1,080 seconds

Step-by-step explanation:

The number that lies between √5 and √6 on the number line will be 2.3333... then the correct option is A.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

Given numbers √5 and √6. The decimal form of the numbers are given below:-

√5 = 2.23

√6 = 2.45

On the number line by plotting these three numbers the number 2.3333 is located between the numbers √5 and √6.

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Answer:

x2-3x-33=x+4

<=> x2-3x-x-33-4=0

<=> x2-4x-37=0

<=> x=2 + square root(41) or 2- square root(41)

Answer: Its techically rain because water vapor gets collected in the sky to make clouds and when the clouds are full they rain. But considering the answer choices, it should be precipitation because most precipitation falls as rain.

Hope it helps!

Answer: 3/8

Explanation: I believe, sorry if I'm incorrect

Answer:

1/4 = 2/8

1/2 = 4/8

3/8 is greater than 2/8 (1/4) but less than 4/8 (1/2)

Answer:

\(x = - \frac{1}{56} \)

Step-by-step explanation:

-x/56x = 2

-1/56 = 2

x = -1/56

Answer:

71

Step-by-step explanation:

The measure of angle WXY will be thee ame as the measure of the intercepted arc, 109°.

W and Y are both tangent to the circle; this means angle XWZ and angle XYZ are both 90°.

Every quadrilateral has a total measure of 360°; to find the measure of WZY, we subtract:

360-90-90-109 = 71°

The measure of angle WZY (∠WZY) is; 71°

From the attached image, we can say that the measure of ∠WXY will be the same as the measure of the intercepted arc, 109°.

Now, W and Y are both tangent to the circle and this means that ∠XWZ and ∠XYZ are both equal to 90°.

Now, every quadrilateral has a total internal sum of angles as 360°.

Thus,  ∠WZY is gotten from;

∠WZY = 360 - (90 + 90 + 109)

∠WZY = 71°

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Answer:

the answer is 3x minus 2 because when u combine the x terms it's 3x and 2 doesn't have any other like term

Answer:

-0.970199

Step-by-step explanation:

The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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Answer:

The answer is 48.

Step-by-step explanation:

The best way is to follow the question through. Calculate the Greatest Common Factor, in this case being 2. And the Least Common Multiple, being 60. She then subtracts the difference, in this case being 60 - 2, which gives you an answer of 48.

Answer:

308

Step-by-step explanation:

so to find how much a rectangular prisim is by

length * with* height

11* 7 * 12

= 924 cubic feet

and then we just divid by 3

=308

Reflection over y-axis = -P

P(-3, 3)

R(3,3)

Answer:

R(3, 3)

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

Yea, how would you get to Dallas with-out being in texas!? lol

Step-by-step explanation:

Answer:

I mean yeah, Dallas is in Texas if that's what you mean.

Step-by-step explanation:

Answer:

\( \frac{0.75x - 3}{x - 1} \)

Step-by-step explanation:

Equation of a rational function is

\( \frac{p(x}{q(x)} \)

where q(x) isn't zero.

There is a vertical asymptote at

\(x = 1\)

So this mean that our denomiator must have a zero that occur at x=1.

That zero is

\(x - 1\)

So our denomiator is

\( \frac{p(x)}{x - 1} \)

Since our horinzontal asymptote is a non zero value, the numerator must be a linear equation as well.

So our rational function is

\( \frac{ax + b}{x - 1} \)

We know the graph pass through (0,3)

So if we apply that logic,

\( \frac{a(0) + b}{0 - 1} = 3\)

\( \frac{b}{ - 1} = 3\)

\(b = - 3\)

And it passes through (4,0)

\( \frac{a(4) + b}{3} = 0\)

\(4a + b = 0\)

\(4a + ( - 3) = 0\)

\(4a = 3\)

\(a = \frac{3}{4} \)

So our rational equation is

\( \frac{0.75x - 3}{x - 1} \)

Answer:

a 1760.

b 32.1

c 8.5 × 10^8

d 5.09×10^-5