Find the constant of proportionality when x = 2 and y = 1.5.Record your answer and fill in the bubbles on your answer document. Be sure to usethe correct place value.

Point: (x,y) = (-4,8)

We have to graph the point and set a vertical line.

Line equation:

x= -4

For any value of x, it always will be -4.

To rationalize the denominator we have to multiply it by the conjugate, as follows:

The latter considering the property (a-b)(a+b)=a^2-b^2.

Finally we have:

The the answer is D. 3

Since Sam can paint 5 rooms in 10 hours, since:

then Sam would have to paint at least 3 rooms to make $150.

The range of hours would be from 6 to 10 hours, since 3 rooms takes 6 hours to paint.

Ok, so

Ivanna is driving on the freeway at a constant speed. She then speeds up to pass a truck. After passing the truck, she exits the freeway and slows

down.

Notice that if the speed is constant, that means that the speed won't increase or decrease its value.

Then, the proper graph could be:

And the correct answer for (a) is c.

Now, the sight-seeing ship is stopped in the water for an hour. This means that it didn't change its distance. Then, the captain heads the ship back to the shore at a constant rate, which means that the distance to the shore is 0. The ship stays there for a while and then returns to the open sea.

Now, the correct graph will be:

The correct option is a.

You have 7 ones

3 fives

2 tens

6 twenties

This is a total of 7+3+2+6 = 18 bills

First we want to know the probabilitity that you will draw a five

P(five dollar bill) = number of fives/ total = 3 / 18 = 1/6

Now we have 7 ones

2 fives

2 tens

6 twenties

This is a total of 7+2+2+6 = 17 bills left ( assuming you get to keep the bill)

Now we want to know the probability of getting a twenty dollar bill

P( twenty dollar bill) = number of twenties / total = 6/ 17

Multiply the probabilities together

1/6 * 6/17 = 1/17

The probability of getting a five and then a twenty is 1/17

We have to use the formula for standard deviation of a probability distribution:

x P(x) x*P(x) (xi - μ)^2*P(x)

0 0.11 0 0.180

1 0.64 0.64 0.050

2 0.13 0.26 0.067

3 0.1 0.3 0.296

4 0.02 0.08 0.148

The expected value μ would be the sum of the values of the third column of the table.

Therefore μ = 1.28

The sum of the values of the fourth column would be: 0.7416

Taking the square root of the last value, we have: 0.861

The answer is option D

Given

Height of man = 6ft

Shadow of man = 9ft

Shadsw of building = 322.5ft

Find

Height of building

Explanation

At a particular time in the day the proportion of the shadow of man will be equal to that of the building

So triangle ABC will be similar to PQR

Hence the ratio of their corresponding sides will be equal

Therefore,

PQ = 215ft

which is the required length

Final Answer

The height of the building is 215ft

The expression 5c+2ad+10-3d*6k has 4 terms , second term has 3 factors and constant term is 10.

Given expression:

5c+2ad+10-3d*6k

5c+2ad+10-18dk

Here terms = 5c, 2ad, 10, 18dk = 4 terms.

factors in second term = 2,a,d = 3 factors.

constant term is 10.

Therefore he expression 5c+2ad+10-3d*6k has 4 terms , second term has 3 factors and constant term is 10.

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Given data:

Total: 11210

7761 good risk

2499 medium risk

950 poor risk

a) Probability of choose a customer with good risk (gr):

b) Probability that a customer is not a poor risk (pr):

The fact that y varies directly with x means that they have a relation like:

Where k can be any number. We know that y=6 when x=-2 which means that k is given by:

Then if y=9 we get:

So x=-3 when y=9.

Answer:

2x + 9 + 3x + x = 7x + 5

Explanation:

The expression on the left side is equal to

2x + 9 + 3x + x

Adding the like terms, we get

(2x + 3x + x) + 9

6x + 9

Then, the given equation is

2x + 9 + 3x + x = __x + __

To make this equation have one solution, the coefficient of x on the right side has to be different from 6, which is the coefficient of 6x + 9.

Therefore, we can fill the empty spaces as

2x + 9 + 3x + x = 7x + 5

Solving this equation, we get:

(2x + 3x + x) + 9 = 7x + 5

6x + 9 = 7x + 5

6x + 9 - 5 = 7x + 5 - 5

6x + 4 = 7x

6x + 4 - 6x = 7x - 6x

4 = x

Therefore, the only solution is x = 4.

f(-2) = -10 and g(-2) = -11



Find (f +g)(-2).

we have that

(f +g)(-2)=f(-2)+g(-2)

substitute the given values

(f +g)(-2)=-10+(-11)=-21

The equations are the linear velocity and angular moment respectively.

Since we have that the rotation of the Earth takes 24 hours, we transform it into seconds, that is:

So, it has a period of 86400 seconds.

We now, transform the radius to the IS (from miles to meters), that is:

And, since the latitude is 68.4711° we solve in the function given at the start, that is:

Then we divide this value by the time it takes to do a revolution of the Earth, the previously calculated 86400 seconds, that is:

So, the linear velocity at that latitude is approximately 0.464 Km/s.

Answer:

Given that,

GH and JH are congruent.

IG and IJ are congruent.

The third side of the triangle GHI is HI and also for the triangle JHI is HI

HI is common for both the triangle GHI and triangle JHI.

we get,

By using SSS congrurnce criteria: SSS (Side – Side – Side) Congruence. If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

we conclude that,

Hence proved.

We need to use the cosine of the angle, in this case:

Cos(37°) = 30 yd / X

Thus, X = 30 / Cos(37) = 30 / 0.7986 = 37.56

The maximum height attained by the projectile is 403.79 meters = 1324.77 feet.

The height formula has the following formula:

h = h₀ + v₀t - gt²/2

In which h₀ is the initial height, v₀ is the initial speed and g = 9.8 m/s² is the gravity.

Given, We are working with the gravity in meters, so we must convert the feet measures to meters.

Each feet has 0.3048 meters.

So 288 feet per second = 87.78 meters per second.

35 foot = 10.66 meters.

This means that:

h₀ = 10.66, v = 87.78

so,

h(t) = 10.66 + 87.78 - 4.9t²

The maximum height is attained at the moment of time in which the velocity is 0. The velocity is the derivative of the height. So:

v(t) = h'(t) = -9.8t+87.78

v(t) = 0

9.8t = 87.78

t = 8.96

The maximum height is attained at 8.96s. This height is

h(t) = 10.66 + 87.78t - 4.9t²

h(8.96) = 10.66 + (87.78×8.96) - (4.9×(8.96)²)

= 10.66 + 786.50 - 393.37

= 403.79 m

The maximum height attained by the projectile is 403.79 meters = 1324.77 feet.

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To get the probability of an event, we need two things:

1. The total number of possibilities

2. The total number of possibilities considered favorable

For the first event A which is landing on a number less than 3, we only have one favorable possible which is landing on 2.

For the second event B which is landing on a 5, we also only have one favorable possible which is landing a 5 itself.

Now, for both events, the total number of possibilities is 4.

So, the probability of landing on a number less than 3 is 1/4 while the probability of landing on a 5 is also 1/4.

So, the probability of landing on a number lesser than 3 AND landing on a 5 is:

Answer:

The probability of landing on a number lesser than 3 AND landing on a 5 on the next spin is 1/16.

A line (option B)

Explanation:

A line contains an infinite number of points. It has no width. It is one dimentional.

A plane has is two dimentional. Hence it has awidth and length.

The correct answer is a line

GIven:

Required:

To find the value of

Explanation:

To find the value of f(x+h) we have to substitute (x+h) in the function f(x) instead of 'x'

The simplify with the given question.

Simplifying for the value,

Final Answer:

ANSWER

EXPLANATION

Given;

To make r the subject of formula, flip the equation

Divide both sides by L;

If each year the computer loses $200 of it's value, in 3 years it'll have lost 3 times that amount i.e. $600.

So, after 3 years the computer will have $600 less the value than when Tim bought it:

After 3 years, the value of the computer will be $600

The loss of the computer's value can be model as:

Where 1200 is the initial value, 200 is how much it's devalued per year. 'x' represents the years since Tim bought the computer and 'y' represents it's value after 'x' years.

The given equation is:

The differential is given as:

Make dy/dx the subject of the formula:

If we multiply 20 by squareroot 6, the answer would be 20(squareroot6). So it is a rational numbersquare root.

But in a, if we multiply 0.25 that is 1/4, by 15 it will be 15/4, so. itis a rational number

In b:

It is rational.

However, let's do the operation.

Therefore, it is a natural number and not a rational. The answer is c

(a)

P (Z > -1.62 ) = 0.94738

(b)

P (Z ≤ 1.72) = 0.95728

(c)

P (-058 < Z < 1.91 ) = 0.69097

Z<1.91 = 0.97193

Z<-0.58 = 0.28096

0.97193 - 0.28096 = 0.69097

The point at the base of the mountain is described as point zero, that is they are still at sea level. If Melissa now moves to a position 27 metres above sea level, that is positive 5, assuming we are now measuring along a vertical number line. Brian however moves to a location which is 21 metres below sea level, or negative 21 along the vertical number line. Since we are measuring distances, the distance from point zero to both hikers' new position will be measured in absolute values only, that is both distances will be measured as positive.

Hence the distance between Melissa and Brian is;

Distance = 27 + 21

Distance = 48

The difference in altitude between both hikers is 48 metres

x=5

1) Since y varies directly with x, then we can write a table

x | y

2 14

35

2) Since y is 7 times the value of x, then we can state that

x | y

2 14

5 35

3) So this variation can be expressed as y=7x and x=5

In order to graph the function, we need first to find the coordinates of the points. To do so, we need to apply the values of x given in the domain and calculate the corresponding values of y. So we have that:

So the points are (-5, 0), (0, -1), (5, -2) and (10, -3).

Graphing these points, we have that:

STEP - BY - STEP - EXPLANATION

What to find?

The time taken for each person to mow the lawn alone.

Given:

Time take for the two to mow the lawn together = 60 minutes.

Brian could mow himself 22 minutes more than it would take andy.

Let x be the time taken for Andy to mow the lawn.

Let x + 22 be the time taken for Brian to mow the lawn.

Step 1

Form the equation.

Step 2

Divide both-side of the equation by 60.

Step 3

Cross-multiply.

Step 4

Open the parenthesis.

Step 5

Solve the above using factorization method.

Either (x-110) = 0 or x+12 =0

x =110 or x =-12

Since there is no negative timing, we will consider only the positive value.

Hence, x=110

Therefore,

The time taken Andy to mow = 110 minutes.

The time taken for Brian to mow = x+ 22 = 110+22 = 132

ANSWER

It takes Brian 132 minutes to mow the lawn himself.

It takes Andy 110 minutes to mow the lawn himself.

Answer:

Explanation:

The sum of the angles in a triangle is 180 degrees. The angles in the given triangle are 2x, 6x + 4 and 2x + 6

Thus,

2x + 6x + 4 + 2x + 6 = 180

By collecting like terms, we have

2x + 6x + 2x + 4 + 6 = 180

10x + 10 = 180

10x = 180 - 10 = 170

x = 170/10

x = 17

The smallest angle in the triangle is 2x. Thus,

Smallest angle = 2 * 17

Smallest angle = 34 degrees

From the statement, we know that:

• John takes a loan for A₀ = $12,000,

• at a simple interest rate of r = 7.9% = 0.079per year,

• to be paid back in 36 monthly instalments.

1) The total amount to be paid is given by:

2) The monthly payments are given by:

The monthly payments are $412.33.