Convert the following expressions to simplify fraction or integer. If it is not a real number, enter none

Solve for interest

Solve for new balance.

To get side QR we can use the the tangent function:

Now, to find PR we can use the sine function:

Finally to find the remaining angle we have to remember that the interior angles of any triangle have to add to 180, then angle P is 53°.

Given

Starting amount of Ivanna = $180

put per month = $70

Starting amount of Brian = 0

put per month = $100

Find

Amount of money in Ivanna's account

the amount of money in Brian's account

equation to show when the two accounts have the same amount of money

Explanation

Let x be the number of months after today.

so, according to the question ,

Amount of money in Ivanna's account = starting amount + amount per month.

so , 180 + 70x

amount of money in Brian's account = 0 + 100x = 100x

equation to show when the two accounts have same amount of money =

so ,

so , in 4.5 months both have same money

Final Answer

Hence ,

Amount of money in Ivanna's account = 180 + 70x

Amount of money in Brian's account = 110x

Equation to show when the two accounts have same amount of money =

To convert percent to fraction divide it by 100

Then to change 11% to a fraction divide 11 by 100

Since 11 and 100 can not divide by the same number, then

11% = 11/100 in the simplest form

$7 per hour

if I work 1 hour i will earn $7

The absolute change is defined as:

where V1 and V2 are the initial and final values, respectively.

Plugging the values given we have that:

Therefore the absolute change is -102. (The minues sign indicate a decrease)

The percentage change is given by:

plugging the values given we have:

Therefore the percentage change is -85% (Once again the minus sign indicate a decrease)

The given expression is:

Exapanding the above expression,

(The number of 10s are the same as the power of 10).

Now, cancel out the common terms in the numerator and the denominator of the above expression.

The denominator of the above expression can now be expressed as the power of 10 as,

According to the law of exponents,

Hence, we can write

Therefore, 10^4 divided by 10^6 can be expressed as a term with a single power as,

The given functions are

g(x) = x - 8

h(x) = (x + 4)(x + 5)

To find (g/h)x, we would divide g(x) by h(x)

Thus,

g(x)/h(x) = (x - 8)/(x + 4)(x + 5)

To find (g/h)(-3), we would substitute x = - 3 into (x - 8)/(x + 4)(x + 5). Thus, we have

(g/h)(-3) = (- 3 - 8)/(- 3 + 4)(- 3 + 5) = - 11 * 1/2

(g/h)(-3) = - 11/2

All values that are not in the domain are all values of x that does not satisfy the expression. If we put x = - 4 or x = - 5 in the denominator, the denominator would be zero and this makes the expression undefined. these values do not satisfy the g/h

Thus, the values are x = - 4 and x = - 5is

The equation of line in slope intercept form is given by:

Where m is the slope and c is the y-intercept

It is given that the slope of the line is 0 and the y-intercept is -3 so it follows:

Hence the equation is given by:

Hence y=-3 is the equation of the line ith

Given:

There are given that the 209 ounces to convert into the decigram.

Explanation:

According to the concept:

To convert the ounces into the decigram, we need to multiply the mass values by 283.

That means,

The value of 1 ounce is 283 decigram

So,

Final answer:

Hence, the value of the 209 ounces is 59147 decigrams.

By assuming that the rate is constant and the speed is given by

we have that

because 4 minutes is equal to 240 seconds. Then, the distance is given as

Therefore, the depth of the swimmer will be 60 meters plus 0.5 meters. Then, the answer is -60.5 meters (option A)

We can break apart the figure into 4 separate figures and find the area of each of these individual figures. Then sum to get area of total figure.

We break apart the figure as shown below:

First,

Area of Triangle = 0.5 * base * height

Area of Rectangle = base * height

Now, let's find each of the Areas A through D:

Area of A:

To find the base of this triangle, we have to use pythagorean theorem. By which we can write:

Where b is the base. let's solve for b:

Area is

Area of B:

This is a rectangle with base = 10 and height 4, so the area is:

Area = 4 * 10 = 40

Area of C:

Area of C is exactly same as area of B, base is 10 and height is 4. So,

Area = 4 * 10 = 40

Area of D:

Like area of A, we have to find the base of the triangle first, using pythagorean theorem. We can write:

Solving for b:

Now, area of triangle is:

Area of whole figure:

Since mulch costs $3 per square feet, we have to multiply the area by "3", so we have:

It will cost around:

$279.20

The expression that is equivalent to 8(4r) is 32r.

The given expression is 8(4r)

The given expression is an algebraic expression with constant and variables, here, r is the variable, and 4 and 8 are constant terms.

We need to simplify the expression as much as possible.

In order to simplify it, we need to solve the brackets, when we open the brackets, the terms get multiplied by each other,

So, here we go,

8(4r) = 8* 4r = 32r

This is the simplest form that we can have,

So, 8(4r) = 32r

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From the given figure we can see that there is a rectangle with 3 x 4 squares

A semi-circle at the top with about 6 squares

A semi-circle at right with about 4 squares

Then the total number of squares = 12 + 6 + 4 = 22 squares

Since the area of each square is 1 x 1 = 1 cm^2

Then the area of the figure = 22 x 1 = 22 cm^2

The area of the figure is about 22 cm^2

We have the following:

• The first thing is to ,rotate, in the opposite direction of the hands of the clock, in such a way that it is the same.

• Then make a ,translation, from left to right until it overlaps one on the other

Determine relation between side of triangle by using trigonometry.

So y is sin theta times as large as r.

So x is cos theta times as large as r.

So y is tan theta times as lasrge as x.

Solution

For this case we have the following equation:

And on this case we have an hyperbola given by:

Then the correct choice is:

Origin

We know that the year has 52 weeks

From 5 weeks, you work 4. So, we can use the rule of three

Number of weeks Weeks of work

5 4

52 x

The car with the smallest speed (or slowest rate) exists the car with 800 miles in 12 hours.

The ratio of the distance traveled and the time it took to travel that distance yields the rate at which cars move (also known as the speed).

To determine each unit rate (number of miles traveled in 1 hour). To determine the unit rate, we will divide the distance by the time.

rate = distance/time

Substitute the values in the above equation, we get

Then, for each car we will the speeds:

a) S = 750 mi/10 h = 75 mi/h

b) S = 800 mi/12 h = 66.66 mi/h

c) S = 450 mi/6 h = 75 mi/h

d) S = 1000 mi/14 h = 71.428 mi/h

Then we can see that the car with the smallest speed (or slowest rate) is the car with 800 miles in 12 hours.

Therefore, the correct answer is option b) 800 miles in 12 hours.

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In this problem, we have a Binomial Probability Distribution

so

n=700

x=700*(8.9/100)=62.3=62

P(x=62)=0.0313

We will investigate some application of line bisectors.

We have a line segment denoted as ( CR ). A point ( A ) is said to be bisecting the line segment.

Line bisection involves the process of equally dividing the entire line segment in two equal halves! We can also represent this scenario graphically for clearification:

We can also represent line bisection mathematically in terms of two smaller divisions ( CA and AR ) as follows:

Where, the quantities are expressed as magnitudes/lengths of each segment indicated.

We are given expressions for bifurcated line segments |CA| and |AR| in terms of variable ( x) as follows:

Now we will use the expression given for each smaller division of line |CR| and plug it in the general " Bisection " expression developed above:

We have constructed an equation with a single variable ( x ). We can solve this equation for the variable ( x ) using basic mathematical operations as follows:

Once we have solved for the variable ( x ). We will again use the defined expression for each smaller segments and determine the magnitudes as follows:

∠35 and ∠w are vertical angles, therefore:

Since ∠w and ∠x are supplementary, we can conclude:

Therefore:

Diego has written the correct equation.

By definition:

- Rational numbers are those numbers that can be written as simple fractions. A fraction has this form:

Where "a" is the numerator and "b" is the denominator. Both are Integers, and:

- Irrational numbers cannot be written as simple fractions.

Then, knowing those definitions, you can identify that:

1. The number:

Since -5 is an Integer, it can be written as:

Therefore, it is a Rational Number.

2. You can identify that the second number is a Repeating Decimal because the line over the decimal digits indicates that its digits are periodic.

By definition, Repeating Decimals are Rational Numbers.

3. Notice that the next number is:

Since it cannot be written as a simple fraction, it is not a Rational Number.

4. For the number:

You can identify that it is a fraction whose numerator and denominator and Integers. Then, it is a Rational Number.

5. Notice that the last number is:

By definition, π is an Irrational Number.

Therefore, the answer is:

Given:prfit p(n)=61n-5500

Find: profit when he sells 850 tickets.

Explanation: n=850

put in the given equation of profit , we get

Final answer: the profit is 46350.

The total number of experiment, N=20.

From the given data, 9 is obtained 5 times.

The number of times of getting 9, n=5.

Hence, the probability of getting a sum of 9 is,

Hence, option b is correct.

The temperature is 92 degrees celsius. Rounding 92 degrees celsius to the nearest ten will be 90 degrees celsius. The closest ten to 92 is definitely 90.

Therefore,

Given:

The shown represents the difference between the squares

So, the product of the polynomials will be as follows:

So, the answer will be:

This simplifies to:

The degree of our simplified answer is 4

J = (-2, 4) K = (3, 4) L = (2, 1)

Translated 4 units down

J = (-2, 4 - 4) K = (3, 4 - 4) L = (2, 1 - 4)

J = (-2 , 0) K = (3, 0) L = (2, -3)

Translated 1 unit to the left

J = (-2 -1, 0) K = (3 - 1, 0) L = (2 - 1, -3)

J = (-3. 0) K = (2, 0) L = (1, -3)

The first proportion:

can be written like this:

then, we have the following:

For the next proportions, we have the following:

and finally:

Given:

Using the distributive property for the multiplication then combine the like terms

so, the given expression will be:

Note: i² = -1

So, the answer will be: