Find the midpoint of AC.B (0, a)C (a, a)D (a,0)a(4)2A (0,0)Enter the value thatbelongs in the green box.Midpoint Formula: M = (*¹*²₁¹²)RE

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.

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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Answer:

-147

Step-by-step explanation:

We can solve this by plugging in p = 5 and q=−2 and then evaluating using PEMDAS which tells us the order we do the math in by operation

Remember,

PEMDAS means

Parenthesis

Exponents

Multiplication and Division ( perform going left to right )

Addition and Subtraction ( perform going left to right )

-3(p-q)²

==> plug in p = 5 and q = -2

-3(5-(-2))²

==> remove parenthesis on -2

-3(5 + 2)²

==> do the operations inside of the parenthesis

-3(7)²

==> do the exponents

-3(49)

==> multiply -3 and 49

=-147

C) y= 2x

1) Examining that table, we can notice that the value of y is precisely twice the value of x

x | y

5 10

7 14

9 18

2) Hence, we can state since y is twice x that the function can be written as:

y=2x

3) So the answer is C) y= 2x

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:

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.

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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Solution:

Given:

Two cylinders on each other;

Using the formula of the volume of a cylinder;

For the cylinder at the bottom, the following were given;

Using the formula of the volume of a cylinder;

Hence, the volume of the object is the total volume of both cylinders.

Therefore, the volume of the object is 366 cubic inches.

Yes are congruent , SSS because the graph shows us two equal sides, if they are equal, then the upper and lower sides of the quadrilateral will be equal, for this reason we already have two equal sides, and since the triangles share the diagonal we can say that their three sides are equal

red and green sides are equal one by one,the red ones are the same because the drawing says so, and the green ones are the same because in a parallelogram the opposite sides have the same measure.

we already have that two of the three sides of each triangle are equal,and we can conclude that the third side is also the same, since the triangles share it

then the triangles are equivalent since their three sides are equal SSS

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

The given equation is:

The differential is given as:

Make dy/dx the subject of the formula:

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.

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 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):

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.

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

(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

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

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

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.

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.

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

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

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.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

cheese:

purchased amount = 3 3/8 lb

used amount = 2 3/4

Step 02:

equation:

remaining amount = purchased amount - used amount

The answer is:

5/8 lb = 0.625 lb

we have the equation

Remember that

when the stone hit the ground, the value of h is zero

so

For h=0

solve the quadratic equation

the solution is the positive value

t=3 sec

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

Average rate can be calculated like the slope

where (x2,y2) is a right point yo (x1,y1)

But we need the values of x=8 and x=9

we realize the change between values of y is the last value by 3 then if

we have the corresponding values for x=8 and x=9

now replace on the formula of the slope using the points (8 , 6561) and (9 , 19683)

where (9 , 19683) is (x2,y2) and (8 , 6561) is (x1,y1)

the avreage rate of change for the interval 8 to 9 is 13122

We realize the values of the average are multiplied by 3 too, then we can fi

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

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.