(a) How high is the ball when it was thrown?(b) What is the maximum height of the ball?

The annuity formula is the following:

Where: PN is the balance in the account after N years

GIVEN:

We are told that two angles F and G are supplementary angles.

The angle measures are as follows;

Required;

To find the measure of the two angles.

Step by step solution;

When two angles are identified as supplementary angles, it means they add up to 180 degrees. Therefore, for the angles F and G, we can set up the following equation;

The two angles therefore are as follows;

ANSWER

Angle F = 105 degrees

Angle G = 75 degrees

If you are looking at the limit of piecewise function at the point where the function changes its formula, then you will have to take one-sided limits separately since different formulas will apply that depending on which side you are approaching from.

For example:

The following piecewise-defined function:

Then,

Lets find the following limits:

Then,

Since, the limits above are different, limit that not exists.

The limit is:

Step 1:

To solve the system of equations graphically, you will find the value of x when y = 0 and y when x = 0 for both equations.

Step 2:

Write the two equations

2x + y = 4

y = x + 1

Step 3

Second equation

Step 4:

Graph the system of equations

The solution to the system of the equations is the coordinates of the point where the two lines meet.

From the graph

The solution to the system of equations is (1, 2)

Final answer

( 1 , 2 )

We have the following lengths for the triangle, which we will label as a, b and c:

To check if they form a right triangle, we have to use the Pythagorean Theorem:

If we substitute the values and get the same result on both sides, the Pythagorean theorem condition will be met and the three sides will form a right triangle.

Substituting a, b, and c into the Pythagorean Theorem:

Solving the squared terms on the left and right sides of the equation:

Adding 64+36 on the left side, we get:

As we can see, we get 100 on the left side and 81 on the right side, since 100 is not equal to 81, The three lengths don't form a right triangle.

Answer: The lengths 8cm, 6cm, and 9cm don't make up a right triangle.

Range of checks will it a checking account as long as the bank up generate more earnings and income at one fellows through a bank is Quarterly APR is 1.38 value more than Monthly APR, when the rate of Yearly  APR is 5.5%.

Earning at Long's Bank are expressed by the equation, I = -0.06 x + 8.3

Earnings at Fellow's Bank are modeled by I = -0.02 x+6.6

Where,x is the number of checks written.

now, we have to find that , at what range of checks will a checking account at Long's Bank generate more earnings income than one at Fellow's Bank.

-0.06 x +8.3 > -0.02 x +6.6

-0.02 x+0.06 x < 8.3 - 6.6

0.04 x < 1.7

Dividing both sides by , 0.04, we get

x< 42.5

So, x ∈[0,42], which is number of checks written.

2.  APR on personal Loans =5.5%

Value of APR when compounded monthly

5.5/12 = 0.4583 ≈ 0.46

Value of APR when compounded Quarterly

5.5/3 = 1.833

= 1.84 (approx)

Difference between Rate , when the APR rate is compounded monthly as compared to when it's compounded quarterly

=1.84 - 0.46

=1.38 (approx)

Quarterly APR is 1.38 value more than Monthly APR, when the rate of Yearly  APR is 5.5%.

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The expression that shows the combined volume of the three boxes is 3.5x.

The volume of the medium box = x

The small box is half the volume of the medium box.

so,

The volume of the small box = x/2

The large box has twice the volume of the medium box.

so,

The volume of the large box = 2x

The expression that shows the combined volume of the three boxes is:

small box volume + medium box volume + large box volume

= x/2 +x +2x

= 7x/2

= 3.5x

The expression that shows the combined volume of the three boxes is 3.5x.

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Answer: D

Step-by-step explanation:

Since linear equations have to be written as the slope intercept form, y=mx+b, and there is no y in the equation, it can't be that, and Quadratic equations have square roots and powers of 2 in them, and cubic equations have powers of 3 in them and have cube roots, and none of these apply to the equation so it has to be D

based on the conservation energy we can easily solve the question-

a. 2749.4kg

b. 0

c. K.E.=5498800J

what is the conservation of energy?

Energy can only be transformed form one form to another of energy, i.e, energy can never be destroyed. in partcular problem potential energy transforms to kinetic energy.

a. mass of people at full capacity=5400lb

                                                  =2449.40kg

total mass of coaster= 2449.40+300

                                  =2749.40

b. the velocity of the coaster at its peak position is 0

c. the kinetic energy at the bottom is same as the potential energy at the peak. which is-

P.E.=mgh

     =2749.4×10×200

      =5498800J

so the kinetic energy at bottom is

K.E.=5498800J

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ANSWER

EXPLANATION

Exponential decay is modeled by the equation,

Where a is the initial value, in this case, a = $25,000, and r is the decay - or decrease, rate. In this problem, r = 0.05.

The equation is,

Solve the subtraction to write it in the asked form,

Let's break it down:

first number = 30

Qoutient is the result obtained when you divide a number by another number.

quotient of 30 and the sum of 5 and 7​ means we will divide the first number (30) by the second statement after the 'and' (5 and 7).

quotient of 30 and the sum of 5 and 7​ is:

Let:

x = Jackson age

y = Jackson's mom age

Jackson's mom is 44, which is four times as old as Jackson, so:

Solution

(a) setting f(x) = 0

(b)

when x = 0

y = f(0) = -108

Hence, the height is 108

(c)

Maximum = (1.5, 15.188)

(d)

Minimum (-1.702, -300) and (4.702, -300)

(e) From the graph, the interval of increasing is

(f) From the graph, the interval of decreasing is;

g)

A)

The arithmetic sequence is modeled by the following equation:

Where a_n is the nth term, a_1 is the first term and r is the rate.

We can see in the sequence that the first term is 6, and each number is the previous number plus 5, so the rate of our sequence is 5.

So, in order to find the 100th term, let's use n = 100 in our equation:

So the 100th term is 501.

B) The expression for the nth term is the general expression used for arithmetic sequences:

We can find this expression generalizing the following equations:

C)

In order to check if 1000 is an entry in the sequence, we can use the value of a_n = 1000 and try to find the value of n:

Our value of n is not a whole number, so the entry 1000 is not a valid entry.

We can also see in our sequence that the last digit is always 6 or 1. So checking the entry 1000, the last digit is 0, so we know that this is not a valid entry.

D)

In order to check if 201 is an entry in the sequence, we can use the value of a_n = 201 and try to find the value of n:

Our value of n is a whole number, so the entry 201 is a valid entry.

All numbers in our sequence ends with 1 or 6. So, checking the entry 201, the last digit is 1, therefore we know that this is a valid entry.

-25

1) To evaluate this expression, given the value of n. We need to plug it into the expression

n² -9n -7 Plug into that n=6

(6)² -9(6) -7 Distribute the factors

36 -54-7 Add/ Subtract

36-61

-25

2) Hence, the answer is -25

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given data

STEP 2: Write the equation of a parabola

STEP 3: Get the value of h

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix. Therefore:

STEP 4: Get the standard form of equation

Hence, the standard form becomes:

The solution:

Given:

We are required to find the median of the given data.

Step 1:

Rearrange the data in ascending order of magnitude.

Step 2:

Pick the middle numbers and find their average.

Therefore, the correct answer is 3.

cosine (θ) = 4/5

1) Given that the sin(θ) is in Quadrant I , and θ lies in this quadrant too

Let's remind the signal fo that:

2) Let's use the Pythagorean Identity to find the value of the cosine (θ):

3) As the value of the sine and the cosine in Quadrant I is positive then we can state the cosine (θ) = 4/5

Answer:

(a)14 seats

(b)1,050 seats

Explanation:

The theater has 10 seats in the first row and 30 seats in the 6th row.

We can model this as an arithmetic progression problem where:

• The first term, a = 10

• The last term, l = 30 when n=6

We know that for an arithmetic progression:

Therefore, the number of seats in the 11th row will be:

(b)The theater has a total of 21 rows.

To determine the total number of seats, we use the formula for the sum of an arithmetic progression.

We define the variables:

• Since the theatre has a total of 21 rows, therefore n=21

• The first term, a = 10

• Common difference, d = 4

We substitute into the formula above:

There are a total of 1,050 seats in the theater.

The ratio of history to math is given by

which is equal to

Then, the answer for the history to math is 2:3 or, in fraction form is

On the other hand the ratio history to science is 28:35, which in fraction form is written as

Similarly, the ratio math to science is 42:35, which in fraction form is

Now, if we add 1 science book and 2 math book, we have 36 science books and 37 math books, then the ratio history to math is 28:37, which in fraction form is written as

and the ratio history to science is 28:36. which in fraction form is written as

and the ratio math to science is 37:36, which in fraction form is written as

Andrew is Andre is running an ATM hurdle race. There are eight equally spaced for those on the racetrack first hurdle is 12 meters from the start line in the last turtle is 15.5 meters from the Finish Line

To graph the inequality:

we first write it like an equation:

Now, we know that a linear equation always represent a line; to graph we it we need to points; the easiest points to get are the x and y intercept.

The x-intercept happens when y=0, from the equation we have:

then we have the point (5,0)

The y-intercept happens when x=0, from the equation we have:

then we have the point (0,4)

Now that we have two points we plot them on the plane and join them with a solid straight line, we need to do this since the inequality is not a strict one:

Finally we need to decide which area to shade to do this we notice that the sign on the inequality is a less or equal to, this means that we have to shade the area below the line, therefore the graph of the inequality is:

To graph the second inequality:

we write it like an equation:

Now we know that this is an horizontal lines that intersects the y-axis at -4, therefore we draw a dashed line at this height on the plane, we need to use a dashed line since this is a strict inequality:

Finally we need to determine what region to shade, since the inequality express that y has to be greater than -4 then we shade the upper part, therefore the graph of the inequality is:

Answer

The statement given in mathematical terms is

12 + [4 × (6 - 2x)] < 7 + 2x

On solving, the solution of the inequality is

x > 2.9

Explanation

Let the unknown number be x,

Twelve increased by the product of four and the quantity of six decreased by twice a number is less than seven increased by twice the same number. In mathematical terms,​

12 + [4 × (6 - 2x)] < 7 + 2x

We can then try to solve this

12 + [24 - 8x] < 7 + 2x

12 + 24 - 8x < 7 + 2x

36 - 8x < 7 + 2x

We can then rewrite this as

7 + 2x > 36 - 8x

2x + 8x > 36 - 7

10x > 29

Divide both sides by 10

(10x/10) > (29/10)

x > 2.9

Hope this Helps!!!

ANSWER

x = 0.00004

EXPLANATION

To solve this we have to apply the exponent of the base of the logarithm rule,

The base of log usually is 10, if no other base is indicated, so in this problem, we use both sides as exponents of 10,

Solving in the calculator and rounding to 5 decimal places,

Solution

In the diagram,

∠DCE = ∠ACB = 60 (vertically opposite angle are equal)

∠ABC = ∠CDE = 72 (alternate angle are equal)

∠BAC + ∠ACB + ∠CBA = 180

=> ∠BAC = 180 - ∠ACB - ∠CBA = 180 - 60 - 72 = 48

Also, ∠CED = ∠BAC = 48

SInce ∠A = ∠D, ∠B = ∠E and ∠C = ∠C

Hence △ABC is similar to △DEC

Whenever there is a negative sign in from of some terms in parenthesis, we negate all the terms inside it.

+ becomes -

- becomes +

Thus, we can simplify the expression as:

The parenthesis around 'm - 3' isn't required.

Now, we fully simplify it by adding up the m's [variables] and the numbers.

Thus, we have:

The fully simplified form:

SOLUTION

Guven the information on the question tab;

Let us take a look at a 5 by 5 checkerboard.

The following paths are possible;

(a).

Let us call the unknown number a, then we know that

(b).

Let us call the unknown number b, then we know that