using a lever a person applies 60 n of force and moves the lever 1 m this moves a 200 newton rock at the other end by 0.2 m

The factors of the polynomial 8x^2 + 12x are (4x) and (2x + 3x).

A factor of a polynomial is a polynomial that when multiplied by another polynomial results in the original polynomial. The factor of 8x^2 + 12x is a polynomial that when multiplied by another polynomial results in 8x^2 + 12x.

To find the factors of 8x^2 + 12x, we can use different methods such as the factoring by grouping or by finding the common factor.

One possible factorization of 8x^2 + 12x is (4x)(2x) + (3x)(4x).

Taking out the common factor 4x :

8x^2 + 12x = (2x + 3x)(4x)

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If Connie deposits $30 into an account. The average rate of change in the value of the account for the first 3 years is: B. $1. 58/year.

Given data:

Equation V(t) = 30 (1. 05)^t

Where,

t = time, in years, since opening the account = 3 years

Average rate of change = [30 (1. 05)^t]  - 30/3

Average rate of change = [30 (1. 05)^5]  - 30/3

Average rate of change = ($34.73 - $30)/3

Average rate of change = (#4.73)/3

Average rate of change = $1.58

Therefore the correct option is B.

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The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.

Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.

In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.

If jack buys 21 tickets, find the probability that he will win!

In any the order, the different triples of tickets that a player can have can be found by a combination.

The total number of events would be

[tex]= \: _{100}C_{3}[/tex]

[tex]= \frac{100!}{3! \:97!} }[/tex]

[tex]= \frac{98 \times 99 \times 100}{2 \times 3}[/tex]

= 161700 different triples

Jack has 21 tickets. So, the probability that Jack will win is

P = 21/161700

P = 0.00013

Hence, Jack will win with the probability of 0.00013.

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Answer:

a = 4

b = 4

c = -1

d = 4

e = -1

f = 4

g = -1

Step-by-step explanation:

that should be right

The length of the hypotenuse is 10 cm.

Pythagoras' Theorem is the way in which you can find the missing length of a right-angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), the Opposite (which doesn't touch the hypotenuse), and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

However, it can also be written in the form of c²=a²+b²

In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.

As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.

3²=9 and 4²=16.

As you're looking for C, you've got to add these together

9+16=25

As a²+b²=c², this means that the answer for C is the square root of 25.

√25= 5

Let the length of the hypotenuse be represented by l, the base be represented by b and the height be represented by h.

We are given that b = 6 cm and h = 8 cm.

Using Pythagoras' theorem,

l² = b² + h²

Substitute the values,

⇒ l² = 6² + 8²

⇒ l² = 36 + 64

⇒ l² = 100

∴ l = 10

Thus, the length of the hypotenuse is 10 cm.

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Expressions is equivalent to -m²-7m+21.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.

When reduced to their most basic form, two or more ratios are said to be similar if their values are the same. Equivalent ratios include 1:2, 2:4, and 4:8. In their simplest form, all three ratios have the same value of 1:2.

Since both expressions' values are constant for all values of x, the equivalent expressions 3(x + 2) and 3x + 6 are also identical expressions. 3x + 6 = 3 × 4 + 6 = 18.          

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The numbers that will be used in the numerator and denominator to calculate the probability that 2 selected students out of 10 are all boys

(6/10) and (5/9) respectively.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, In a class of 10, there are 4 girls and 6 boys.

The sample space N(S) = 10.

Number of boys N(B) = 6 and similarly N(G) = 4.

The probability that 2 selected students out of 10 are all boys will be,

P(B, B) = (6/10)×(5/9).

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The greatest common factor of 27 − 18r = 9(3-2r).

What is the greatest common factor?

In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero.

Here, we have

Given: 27 − 18r

We have to determine the greatest common factor by applying the distributive property.

Distributive property = multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. i.e a × (b + c) = (a × b) + (a × c)

27 − 18r = 9(3-2r)

Hence, the greatest common factor of 27 − 18r = 9(3-2r).

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Hyperbola is a smooth graph lying in a plane, having two branches, which are mirror images of each other and connected to one end and continues infinitely.

Hyperbola is a conic section, two right angled cones are intersected at a certain angle.

The main components of hyperbola is. Foci (It has two foci), Centre of hyperbola ( The midpoint of two foci of the hyperbola), Major axis, Minor axis, Vertices, Latus rectum of hyperbola, eccentricity

The equation of hyperbola is  [tex]\frac{x^{2}}{a{2} }-\frac{y^{2} }{b^{2} } = 1[/tex]

All hyperbola has two graphs, which is two curves with separate vertex and focus.

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The shape of the base of a right circular cylinder is circle.

What is right circular cylinder?

The definition of a right circular cylinder is a cylinder with a closed circular surface, two parallel bases on either end, and elements that are perpendicular to the base. Right cylinder is another name for it. The distance between each point on the closed circular surface of a right circular cylinder and the cylinder's axis, which is a straight line, is constant. The two circular bases of the right circular cylinder are parallel to one another and have the same radius. It is a certain geometric shape that is widely utilised in everyday life.

The diagram of a right circular cylinder is attached below and it can be observed that the base is circular in shape.

Hence, the shape of the base of a right circular cylinder is circle.

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The cat is 17.5 millimeters away from the pupil.

Given is the image of Cat as shown in the figure.

It is given that both the triangles are similar. So, we can write -

10/7 = 25/x

{x} = 25 x 7/10

{x} = 17.5

Therefore, the cat is 17.5 millimeters away from the pupil.

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Answer:

Step-by-step explanation:

Use the Pythagoras Theorem to find x

Pythagoras theorem = [tex]a^2 + b^2 = c^2[/tex]

In this case a is 10 c is 20 b is x

Remember that the longest side of a triangle is always named as c

[tex]10^2 + b^2 = 20^2\\100 + b^2 = 400\\b^2 = 400-100\\b^2 = \sqrt{300}\\ b = 17.32\\[/tex]

Answer:30 minutes

Step-by-step explanation:

600/3=200

200/2=100

5x100=500

1000/500=2

4x100=400

1000/400=2.5

2.5-2=0.5hours

'S' is the incenter, so Angle Bisectors type of segments are drawn.

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Batters struck out more, and their batting averages got worse. The correct option is B

Strike zone is the area over home plate between the batter's knees and mid-chest where a pitched ball is considered a "strike" if it crosses the plate within this area and the batter does not swing.

The location and size of the strike zone is specified in the official rules of Major League Baseball and other baseball organizations and it is used to determine the outcome of each pitch in a game.

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To calculate an expected value with absolute certainty is b. When your data points have various probabilities of occurring.

Expected cash flow is the sum of the cash flows times the likelihood that they will occur. Future financial inflows and outflows are calculated before accepting a project to help assess whether or not to take it on. The expected value is obtained by multiplying the supplied number by its likelihood. It is applied when estimating future projects.

Reasons why the other response is incorrect:

a. The present value of the data points, such as cash flows, is calculated and compared to cash outflows when they occur over different time periods.

c. It is impossible to accurately predict the value of an unknown future event.

d. When only one data point is available, it can be used for the desired outcome. If there are several possible outcomes or data points, probable outcomes can be estimated.

Note that the full question is:

When would you calculate an expected value?

a. When your data points occur on different dates

b. When your data points have various probabilities of occurring

c. When you need to know the exact outcome of a future, unknown event

d. When you only have one data point

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−1 (also known as negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.

Now, According to the question:

Multiplying a number by −1 is equivalent to changing the sign of the number – that is, for any x we have (−1) ⋅ x = −x. This can be proved using the distributive law and the axiom that 1 is the multiplicative identity:

x + (−1) ⋅ x = 1 ⋅ x + (−1) ⋅ x = (1 + (−1)) ⋅ x = 0 ⋅ x = 0.

Here we have used the fact that any number x times 0 equals 0, which follows by cancellation from the equation

0 ⋅ x = (0 + 0) ⋅ x = 0 ⋅ x + 0 ⋅ x.

0, 1, −1, i, and −i in the complex or cartesian plane

In other words,

x + (−1) ⋅ x = 0,

so (−1) ⋅ x is the additive inverse of x, i.e. (−1) ⋅ x = −x.

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Using Pythagoras Theorem, the lengths are 1)3√8 cm 2)2[tex]\sqrt{65}[/tex] cm 3) 8√2 cm and 4) 12 cm.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

1) Here the diagonal of the square is the hypotenuse.

Base length = 6 cm and Altitude length = 6 cm

(Diagonal length)² = 6² + 6²

                              = 72

Diagonal length = √72 = 3√8 cm

2) Longest side is the hypotenuse.

Length of longest side = [tex]\sqrt{14^2+8^2}[/tex] = [tex]\sqrt{260}[/tex] = 2[tex]\sqrt{65}[/tex] cm

3) When height divides the triangle into two, there are two right angled triangles.

Height is the altitude of the right angled triangle.

Hypotenuse is 12 cm and base is half of 8 cm.

Height² = 12² - 4²

Height² = 128

Height = [tex]\sqrt{128}[/tex] = 8√2 cm

4) Here, the base of the isosceles triangle is twice the base of the right triangle.

Base² = 10² - 8² = 36

Base of the right triangle = √36 = 6 cm

Base of the isosceles triangle = 2 × 6 = 12 cm

Hence using Pythagoras theorem, all the lengths are found.3

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The number of seconds it takes for a rocket launched with a starting velocity of 96 ft/s to reach an altitude of 45 ft is  t = 3/2 or t = 4.

What is Velocity?

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

Let's begin with the equation for projectile motion, which is h = vt - 16t2.

h is the object's height in this formula.

The initial velocity is v, and the time is t.

We are aware that the starting speed is 80 feet per second.

so that we can substitute an 80 in our formula for v.

We also know that the item rises 96 feet above the ground.

ground, allowing us to substitute an integer of 96 for h in our formula.

The result is 96 = 88t - 16t2.

We set this equation's value to 0 in order to solve it by

16t2 - 88t + 96 = 02. 16t2 - 88t + 96 = 02.

We may now divide both sides by 8 to obtain the result 2t2 - 11t + 12 = 0.

To achieve (2t - 3(t - 4) = 0, we may now factor the left side.

This implies that either 2t - 3 = 0 or t - 4 = 0.

Hence, t = 3/2 or t = 4.

Since the item will be, there are two possible answers.

Both when going up and down, it was 96 feet above the ground.

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The constant of proportionality from the proportional relationship is 3/2

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.

To determine the constant of proportionality, we need to use the proportional relationship given.

y = kx

k = constant of proportionality

3/8 = k(1/4)

Solve for k

k = [(3/8) / (1/4)]

k = 3/2

k = 1.5

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The quotient of a division problem is found by dividing the dividend by the divisor.

When two numbers are divided, the outcome is referred to as the quotient in mathematics. The dividend is the quantity that is being divided. The divisor is the quantity by which we divide. We will have a remnant if the divisor is not a dividend factor.

One other perspective on the quotient exists. Keep in mind that division is simply repeated subtraction. Therefore, the quotient indicates how many times the dividend can be reduced by the divisor.

This demonstrates the interconnectedness of the four fundamental arithmetic operations. It will be demonstrated later in the session how multiplication can be used to verify the quotient in a division problem. 

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Answer:

23.4

Step-by-step explanation:

Perimeter is the sum of length of all the sides.

The 2 sides on the left (the shorter ones) are equal.  Let x = short side:

3² + 4² = 25 = x²

x = √25 = 5

The 2 sides on the right (the longer ones) are equal.  Let y = long side:

3² + 6² = 45 = y²

y = √45 = 6.71

P = 2x + 2y = 2(5) + 2(6.71) = 23.4

We can solve the system of equations by using the elimination method, the solution is:

x = 5.25

y = -1.75

Here we want to solve the system of equations:

x + y= 3.5

x - y = 7

To solve it, we can use the elimination method. To do it, we can add/subtract the equations in such a way that one of the variables gets eliminated.

I will directly add the two equations.

(x + y) + (x - y) = 3.5 + 7

x + x + y - y  = 10.5

2x = 10.5

Now we can solve this for x.

x = 10.5/2

x = 5.25

Replacing that in one of the equations, we will get:

x - y = 7

5.25 - y = 7

5.25 - 7 = y

-1.75  =y

The solution for the system of equations is:

x = 5.25

y = -1.75

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The equivalent expression to the complex number (3 + 4i) + (3-5i) is option C: 6 - i.

What is complex number?

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.

The complex number expression is -

(3 + 4i) + (3 - 5i)

= 3 + 4i + 3 - 5i

= 3 + 3 + 4i - 5i

= 6 - i

Therefore, the value for the expression is 6 - i.

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The statement describes the percentage of people in the nation who eat out without making any inferences or assumptions.

The statement made by the person is a descriptive statement. This means that the statement simply describes the percentage of people in the nation who always eat out. It does not make any assumptions or inferences based on the data or evidence given. A descriptive statement is one that simply states facts or information without making any assumptions or interpretations about it. It is important to note that a descriptive statement does not imply any cause and effect relationship between the facts or data given. For example, in this statement, there is no inference being made that the people who eat out are healthier or more likely to be successful than people who don't eat out. It is simply stating the percentage of people in the nation who always eat out.

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Hey there!

So, we are given the following to solve:

Solve for y.

[tex]-\frac{y}{3}+19=33[/tex]

_______________________________

1. Move 19 to the right side.

[tex]-\frac{y}{3}=14[/tex]

2. Multiply both sides by 3.

[tex]3(-\frac{y}{3})=14*3[/tex]

3. Simplify.

[tex]-y=42[/tex]

4. Divide both sides by -1.

[tex]\frac{-y}{-1}=\frac{42}{-1}[/tex]

5. Simplify.

[tex]y=-42[/tex]

__________________________________

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Answer:

see explanation

Step-by-step explanation:

m + 8

can be expressed as

the sum of m and 8

Answer:

cooking method

Step-by-step explanation:

I am not sure if you mean the food or not

Answer:

my

Step-by-step explanation:

namajeff