Simplify the following rational expression. Be sure to state the condition.

Answer:

Step-by-step explanation:

-38 + -12x < -200

Answer:

-38 - 12x > -200

x = 13.5 min

Step-by-step explanation:

let x = minutes of the dive

-38 ft - 12 ft/min(x) > -200 ft

-12 ft/min(x) < -162 ft

x > -162/-12   **flip the inequality when you divide by a (-) number

x > 13.5 min

Starting at -38 ft, he has to dive longer than 13.5 minutes to go deeper than -200 ft at a rate of -12 ft/min

a. The model represents exponential growth.

b. The annual percentage increase is 3%.

c. After 2390 decades the population was about 590000.

The formula for exponential growth is [tex]y = y_₀.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_₀.e^{(-kt)}.[/tex]

Given, The population P(in thousands) of Austin Texas during a recent decade is approximated by [tex]y = 492(1.03)^t[/tex].

The model represents exponential growth as time can not be negative.

The annual percentage increase in the model [tex]y = 492(1.03)^t[/tex] is 3%

as 1.03×100% = 103%.

The time when the population was about 590000 since the beginning of a decade is,

[tex]590000 = 492(1.03)^t[/tex].

[tex](1.03)^t = 590000/492[/tex].

[tex](1.03)^t = 1199.1869[/tex].

[tex]log_{1.03}1.03^t = log_{1.03}1199.1869[/tex].

t = 2389.84 Or 2390 decades.

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Answer:

Step-by-step explanation:

You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.

The total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.

Multiplying the ratio units by £5, we find the distribution to be ...

  Laura : Tom : Alex = £40 : £35 : £20

Answer:

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Step-by-step explanation:

Given ,

To Find : How much money will each of them receive

Let us take the variable as 'x' to find the money received by them

When we convert it to a equation

8x+7x+4x = 95

19x = 95

x = [tex]\frac{95}{19}[/tex]

x = 5

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Hence, the money received by each of them is  £40, £35 and  £20

The percentage of the total marks that Edet gets is 60%

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this situation, the score of Edet will be:

= 48 + 52 + 46 + 46 + 44 + 52

= 288

Total score = 80 × 6

= 480

The percentage will be:

= 288 / 480 × 100

= 60%

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Answer:

The three statements that are always true regarding this diagram are:

m∠3 + m∠4 + m∠5 = 180°

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠3 = m∠6

Here's why:

The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.

The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.

Step-by-step explanation:

The annual cost if she chooses to make monthly payment is $1920 and money saved is $170

The given parameters that will help us to determine the incomes are

a)  Annual cost if she chooses to make one annual monthly installment is $1920

b) Money saved is she makes one annual payment is $(1920-1750)= $170

3) Volume of gas = 60 L

Efficiency rating = 10.2km/L

Average drive = Volume / Efficiency = 60/10.2 = 5.9km/L

b) Cost of gas = 149.9⊄⊄/L

Number of liters =60

= 60*149.9

=$8994

c) Constant gas price = $149.9⊄/L

Number of weeks /year = 52

=52*149.9

= $7795

4) Morgan pay $15/hr

Number of hours per week = 40

Gross monthly income = 40*15*4

=$2400

b)   Monthly income $2400

Amount left after deduction = 85%

=0.85*2400

Net income = $2040

In conclusion Mindley receives $1920 monthly and saves $170

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Answer:

That's easy! four thousand two hundred and seven or 4,000+200+7

Step-by-step explanation:

4x - 2y = 6

2y = 4x - 6

y = (4x - 6)/2

y = 2x - 3

Answer:

10. Yes
11. No
12. Yes
13. Yes
14. No
15. No

Step-by-step explanation:

Use the vertical line test to determine whether or not a relation is a function. The vertical line test is when you draw a line through a relation and if that line intersects the relation more than ONCE, the relation is not a function.

10. Is a function, the vertical line only intersects the relation once.
11. Isn't a function, intersects the relation more than once.
12. Is a function, intersects the relation only once.
13. Is a function, only intersects the relation once.
14. Isn't the function, intersects the relation more than once.
15. Isn't a function, the relation intersects the function more than once.

Hope this helps.

A'(-2, -3) would result if A (2, -3) was reflected over the x axis. Point (2,3)'s representation under the x-axis is (2,-3). from the y-axis P image (-a,b).

Changing the sign of the value on the opposite axis, in this case the y-value, is all that is required to reflect a point such as (-2,3) across the x-axis in a question. As a result, this location has a y-value of 3. A positive number, this. A negative sign produces a result of -3.

While the Y coordinate remains the same when you reflect across the Y-axis, the X coordinate changes sign. Determining the reflection of (2, 3) across the Y-axis is therefore (-2, 3). The Y-coordinate of each point must be negative while reflecting across the X axis, but the X value must remain constant.

Therefore the correct answer is option a ) A'(-2, -3)

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On one tank of gas Charlie will drive 612 km

At a cost of 149.9, Charlie will fill the tank with the sum of 8994

Annual cost of filling the tank 467688

Information from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L

Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride

= 60 * 10.2

= 612 km

Cost of filling the tank

The cost per liter is 149.9 for 60 L we have

= 149.9 * 60

= 8994

Filling the tank once week, the cost for filling in one year is

1 year is 52 weeks

= 8994 * 52

= 467688

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Answer:

SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system. ...

Check the solution in both equations.

Step-by-step explanation:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

a) The function is continuous in it's entire domain.

b) The increasing and decreasing intervals for the function are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.

The lateral limits for the function in this problem are defined as follows:

The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.

The intervals of increase and decrease are given as follows:

The function for this problem is the piece-wise function A(x).

Item a asks if the function is continuous.

Item b asks when the function is increasing and when it is decreasing.

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Answer:

7/

Step-by-step explanation:

3/4 * 7/

3 can be crossed

Leaving 7/

Answer:

Step-by-step explanation:

According to question, we know that

His Sister has "1/5*$25 which is equal to $5, and his father has "40%*$25 which is equal to 0.4 * $25 = $10". So, the money Hafiz, his sister and his father have in total

= $25+$5+$10 = $40

Hafiz = $25

Sister = [tex]\frac{1}{5}[/tex]

Father = 40%

Total money of Hafiz, Sister, and Father altogether.

[tex]\frac{1}{5} X[/tex] $25

= $5

40% (0.4) x $25

= $ 10

$ 25 + $ 5 + $ 10

Answer:

k = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

[tex]\frac{3}{4}[/tex] = k

Answer:

The ratio of the number of quarters to the number of dimes in the box is 9:10

Step-by-step explanation:

If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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Answer: We can set up a system of equations to represent this problem. The first equation represents the total value of the nickels and dimes in terms of the number of nickels and dimes that Nevaeh has:

0.05x + 0.1y = 0.80

The second equation represents the total number of nickels and dimes that Nevaeh has in terms of the number of nickels and dimes that she has:

x + y = 11

To graphically solve this system of equations, we can use the slope-intercept form of the linear equations.

y = -2x + 22

y = -1/2 x + 8

The solution would be the point where the lines intersect , which x = 4, and y = 7 .

So she has 4 nickels, and 7 dimes.

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Let me get to know you:)

The first equation will be multiplied by 3 and that of the second by 4.

An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.

Given that are two equations to be solved by using elimination method,

-4x+4y = 32.....(i)

3x-y = 12......(ii)

To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4

-12x+12y = 96.....(iii)

12x-4y = 48....(iv)

Solving the equations, we get,

8y = 144

y = 18

Put y = 18 in eq (ii)

3x-18 = 12

3x = 30

x = 10

Hence, the first equation will be multiplied by 3 and that of the second by 4.

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Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

The exact value of tan  θ = 15/ 8

Trigonometric Identities are defined as the equalities involving trigonometry functions and also one that holds true for all the values of the variables  in the given equation.

The trigonometric functions are;

From the information given, we have;

tan θ = opposite/ adjacent

To determine the adjacent sent

17² - 15² = x²

x = √64

x = 8

Substitute the value

tan θ = 15/8

Hence, the value is 15/8

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Answer:

The mechanic spent 12 hours on the repair.

Step-by-step explanation:

The mechanic spent 12 hours on the repair.

Answer:

dunno la saya , gak bisa bahasa ingeris

The no. of customers they serve per day is equal to 14.

It is given that the total number of customers served in first year of business was 5110.

We have to find that what will be the average of servings per day ?

What do you mean by average ?

The average is the ratio of sum of all numbers to the total no. of numbers.

As per the question ;

Total number of people served in a year = 5110

We know that ;

1 year = 365 days

So ;

To calculate the average of servings per day we need to divide total number of servings by no. of days in 1 year.

i.e.,

Average of customers per day ;

= 5110 ÷ 365

= 14 customers per day

Thus , the no. of customers they serve per day is equal to 14.

Answer:

Below

Step-by-step explanation:

0 ft -4.2 + 3.4 - 10 = -10.8 ft     or 10.8 ft below the surface

The current value of property is 4000

The capitalization rate (also known as cap rate) is used in the world of commercial real estate to indicate the rate of return that is expected to be generated on a real estate investment property. Formula: Capitalization Rate = Net Operating Income / Current Market Value

Given here cap rate as 10% and income as 40000, Thus Current market value of property is = 40000/10

                                 =4000

Hence, The current value of property is 4000

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