Simplify. (In the problems where you combine fractions with unlike denominators leave the denominators in factored form.)

Answers

Answer 1

Answer:

[tex] \dfrac{a}{a - 4} [/tex]

Step-by-step explanation:

You are subtracting fractions, so as usual with fraction subtraction, you need a common denominator. To get a common denominator, you need to factor each denominator.

[tex] \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{a^2 - 16} = [/tex]

Factor the right denominator. It is a difference of two squares.

[tex] = \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

The left denominator is (a + 4). The right denominator is (a - 4)(a + 4). The LCD is (a - 4)(a + 4), so multiply the left fraction by (a - 4)/(a - 4).

[tex] = \dfrac{3a}{a + 4} \times \dfrac{a - 4}{a - 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{3a^2 - 12a}{(a - 4)(a + 4)} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

Be careful when you do the subtraction of the numerators, 3a² - 12a minus 2a² - 16a. 3a² - 12a - (2a² - 16a). The minus of the subtraction changes each sign inside the parentheses, so you end up with 3a² - 12a - 2a² + 16a. Be especially careful with the +16a.

[tex] = \dfrac{3a^2 - 12a - (2a^2 - 16a)}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{3a^2 - 12a - 2a^2 + 16a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a^2 + 4a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a(a + 4)}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a}{a - 4} [/tex]

Related Questions

y=-1/4x+3

Convert to standard form

I need help understanding how to do this...

Answers

Answer:

y=y

Step-by-step explanation:

y=y because y has the same value as y

Which is the coldest temperature? Explain how you determined this using the number

Answers

The coldest temperature is -273.15°C

2 Demi teaches drum classes. The equation B = 50t gives the dollar amount she earns as a function of the time in hours she teaches. Demi also takes spin classes. The graph shows how much she has left on a gift card as a function of the time in hours Demi is in class. Does Demi earn more teaching 1 hour of drum class or spend more taking 1 hour of spin class? Show your work.

Answers

Using the slope intercept form (y = mx + b) to find the function of the graph, results in
B = -100/5t + 500 or B = -20t + 500.
After 1 hr or t = 1 Demi earns B = 50(1) or $50 teaching
After 1 hr or t = 1 Demi spends B = -20(1)
-$20 on spin class (and her gift card amount would equal $480, although I think the GC amount is irrelevant to the question of earn more or spend more).
If it’s asking just the rate of increase or decrease the slope of 50t is greater than the slope of -20t.
The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.

The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.

What is the Slope intercept form?

The equation of a straight line whose slope and y-intercept are given. Suppose a non-vertical line has a gradient or slope of m and y-intercept equal to c. Let (x, y) be any point on the line and a line intersect the y-axis at the point (0, c).

y = mx + c

Using the slope-intercept form (y = mx + b) to find the function of the graph,

B = -100/5t + 500

Or B = -20t + 500.

After 1 hr or t = 1 Demi earns B = 50(1) or $50 teaching

After 1 hr or t = 1 Demi spends B = -20(1)

-$20 on spin class.

If it’s asking just the rate of increase or decrease, the slope of 50t is greater than the slope of -20t.

Thus, The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.

Learn more about slope;

https://brainly.com/question/3605446

If the average rate of travel is 100 miles per day, about how long would it take to
travel down each river in days?

Answers

Answer:

Distance, rate and time problems are a standard application of linear equations. When solving these problems, use the relationship rate (speed or velocity) times time equals distance.

Explanation:

For example, suppose a person were to travel 30 km/h for 4 h. To find the total distance, multiply rate times time or (30km/h)(4h) = 120 km.

The problems to be solved here will have a few more steps than described above. So to keep the information in the problem organized, use a table. An example of the basic structure of the table is below:

The center of the circle is located at (-4,-3). What is the area? Use 3.14 as an approximation for pi.

Answers

Answer:

78.5 units²

Step-by-step explanation:

First, we need to plot the center point of the circle. (Shown in image). Once we plotted the center point, we need to count how many units is the radius away from the boundary.

Note: I have marked each unit by a "red point". Simply, count the number of "red points" to determine the radius.

⇒ Radius according to graph: 5 units

We can substitute the radius in the "area of circle" formula to determine the area. Keep in mind that pie is represented as 3.14.

⇒ Area of circle = πr²⇒ Area of circle = π(5)²

Now, let's evaluate the area by simplifying the expression. Keep in mind that pie is represented as 3.14.

⇒ Area of circle = π × (5)²⇒ Area of circle = π × 5 × 5⇒ Area of circle = π × 25⇒ Area of circle ≈ 3.14 × 25 [π = 3.14]⇒ Area of circle ≈ 78.5 units²

Question
Find the circumference of the circle. Round your answer to the nearest hundredth.

The circumference is about
inches.

Answers

Answer:

Circumference of a cicle in terms of radius:

Circumference = 2·π·r = 2·3.14·3 = 18.85(*)

In terms of diameter:

Circumference = π·d = 3.14·6 = 18.84(*)

In terms of area:

Circumference C = √4·π·A = √4·π·28.27 =18.85

Step-by-step explanation:

given:

radius= 3in.

to find:

the circumference of the circle.

solution:

formula C=2πr

=2·π·3

≈18.84956in

nearest hundredth= 18.85in

Find the length of the third side. If necessary, write in simplest radical form.

IMAGE DOWN BELOW!

SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER

Answers

Answer:

Step-by-step explanation:

As it is a RIGHT triangle, the formula is a^2+b^2=c^2.

We are given one leg and the hypotenuse. That means 4^2x2+b^2=81.

To find 4 root 2 square, you square them individually then multiply.

4^2=16 times 2 (root 2 squared is 2).

Simplified, that gives 16x2=32,

81-32=49.

The last leg is seven.

TEST IV. Suppose mZ1 = 651 = 650 and m29 = 132º. Find the measure of the following:

Answers

Answer:

1.65°

2.115°

3.132°

4.48°

5.67

MARK A BRAINLESS THIS ANSWER

The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges $2 for the first time they service your lawn, and the price will multiply by a factor of 0. 85 every week thereafter. Green Thumbs charges $350 for the first time they service your lawn, and then charges an additional $30 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?

Answers

The cost-savings if the Yert Family chooses the cheaper company is: $450.50

How do you determine the cheaper company?

First, we determine the cost of the service of each company. Comparing that will give us an idea of the company whose service is cheaper.

Second, we subtract the lower sum from the higher. This gives us the cost savings by the Yert Family.

Step 1

Expressing the payment plan for Green Lawns, we have:

First week= $2
Second week = (2 + (2*0.85) ) = 3.7

Third week= (3.7 + (2*0.85) ) = 5.4

Using the above cumulative method, we arrive at the series of payments due per week

The series of payment are given as follows:
2 + 3.7 + 5.4+7.1+8.8+10.5+12.2+13.9+15.6+17.3+19+20.7+22.4+24.1+25.8+27.5+29.2+30.9+32.6+34.3+36.0+37.7+39.4+41.1+42.8+44.5+46.2+47.9+49.6

= $799.50

Step 2

Expressing the payment plan for Green Thumbs, we have:

350 + (30*30) = $1,250

Step 3

Hence (assuming they go for Green Lawns) the cost savings will be:

$1,250.00 - $799.50 = $450.50

Learn more about Cost-Saving exercises at:
https://brainly.com/question/910760

Can y’all help with this? (It’s exponential and decaying factors). Thanks!!

Answers

Answer:

2.37×10^-11 milliliters

Step-by-step explanation:

The exponential model for decay is ...

y = a·b^x

where 'a' is the initial value, 'b' is the decay factor, and x is the number of intervals over which the decay is taking place.

Here, you're given an initial value of a=500 mL.

The decay factor is 1 more than the decay rate, so is ...

b = 1 -12% = 0.88

We are asked for the remaining amount after 240 intervals (breaths), so that will be ...

y = 500·0.88^x

y = 500·0.88^240 ≈ 2.37×10^-11 . . . . milliliters

Additional comment

That's about 640 million molecules of air--not very much. After 400 breaths, there is about 1 molecule of the original air remaining.

13
3. It's About Time, in Langley, British
Columbia, is Canada's largest custom clock
manufacturer. They have a grandfather
clock that, on the hours, chimes the
number of times that corresponds to the
time of day. For example, at 4:00 p.m., it
chimes 4 times. How many times does the
clock chime in a 24-h period?
9. A training program requires a pilot to fly

Answers

Using an arithmetic sequence, it is found that the clock chimes 132 times in a 24-h period.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of the first n terms is given by:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

In this problem, as the day is divided in two 12-hours period, the total will be twice the sum of the 12 elements of the following sequence:

{0, 1, 2, 3, ..., 11}

In which [tex]a_1 = 0, a_11 = 11, n = 12[/tex].

Then:

[tex]T = 2\frac{12(0 + 11)}{2} = 12 \times 11 = 132[/tex]

The clock chimes 132 times in a 24-h period.

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

A rectangular piece of metal is 10 inches wide and 14 inches long.
a. What is the perimeter?
b. What is the area?

!need to finish test by 2:20!

Answers

(10+14) x2 =48
[ rectangle perimeter = (wide +long)x2 ]
Answer: 48 inches

Hello There!!

Given,

Length= 14inches and breadth= 10inches

1) To Find Perimeter of rectangle

We know, Perimeter of rectangle= 2(Length+Breadth)

[tex]2(14 + 10) \\ = 2 \times 24 \\ = 48 \: \text{inches}[/tex]

2)To Find Area of rectangle

We know, Area of rectangle= Length × Breadth

[tex]14 \times 10 \\ = 140 \: \text{in} ^{2}[/tex]

Hope This Helps

You send an email with a file size of 4 kilobytes. one kilobyte is 2-0 bytes. what is the file size of your email in bytes? write your answer as a power.

Answers

The file size sent in kilobytes was converted to bytes, the 4 kilobytes is equivalent to 80 bytes

Unit Conversion

Given Data

File Size = 4 kilobytes

We are told that 1 kilobytes = is equivalent to 20 bytes

hence 4 kilobytes will be equivalent to x bytes

cross multiplying we have

4*20 = x

x = 80 bytes

Therefore, the file size is 80 bytes

Learn more about unit conversion here:

https://brainly.com/question/13016491

If f(x) = x3 + 12x2 +41x + 30 and f(-6) = 0, then find all of the zeros of
f(x) algebraically.

Answers

Answer:

-6, -5, -1

Step-by-step explanation:

Based on the question, (x+6) is a factor of f(x).

With this, you can do the long division method of dividing f(x) with (x+6) {Refer to the image}.

You'll get x²+6x+5 as a result.

Factorise it and you'll get

x²+6x+5 = (x+1)(x+5)

Then let (x+1)(x+5) = 0, x = -1, -5

Zero's of f(x) are -6, -5 -1

[tex]\text{Given that,}\\\\f(x) = x^3 +12x^2 +41x +30~~ \text{and} ~~ f(-6)=0\\\\\text{Since f(x)=0 when x = -6,}~ ~x-6 ~\text{is a factor of f(x).}\\\\x^3+12x^2+41x+30 = 0\\\\\implies x^3+6x^2+6x^2+36x+5x+30=0\\\\\implies x^2(x+6) +6x (x+6) +5(x+6)=0\\\\\implies (x+6)(x^2+6x+5)=0\\\\\implies (x+6)(x^2+5x+x+5)=0\\\\\implies (x+6)\textbf{[}x(x+5)+(x+5)\textbf{]}=0\\\\\implies (x+6)(x+1)(x+5)=0\\\\\text{Hence the roots are,}~ x = -6,~ x=-1~ \text{and}~ x = -5[/tex]

Which of the following best describes the expression 9(x + 7)? (5 points)

a
The sum of 9 plus some number plus 7

b
The product of 9 plus some number plus 7

c
The product of 9 and some number plus 7

d
The sum of 9 multiplied by some number plus 7

plsss help asap

Answers

Answer:

I guess D. the sum of 9 multiplied by some number plus 7

Find the value of m, expressed as a common fraction so that this relation is not a function.
{(-2m+1,-4),(-6m+8,0)}

Answers

Answer:

m = 7/4

Step-by-step explanation:

If the two points have same input with different outputs, then this relationship is not a function, according to definition of the function.

Make the x-values same and solve for m

- 2m + 1 = - 6m + 86m - 2m = 8 - 14m = 7m = 7/4

Let's see

x must be equal on both sides as it's not a function

-2m+1=-6m+84m=8-14m=7m=7/4

please help its easy

Answers

Answer:

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

Step-by-step explanation:

[tex] \frac{12 - 3}{12} [/tex]

[tex] \frac{9}{3} [/tex]

cross out the common factor.

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

Answer:

9/12 (or 3/4)

Step-by-step explanation:

If you subtract the number of brownies that Brittany's brother will eat, you will have 9 remaining brownies. So, that means 9 out of the original 12 brownies will be left, or 9/12. Also, you can simplify the fraction. Both 9 and 12 can be divided by 3.

9/12 divided by 3/3 equals 3/4. 3/4 is the fraction in it's simplest form.

So, 9/12 (or 3/4) of the brownies are left.

I hope this helps! Have a lovely day!! :)

Claire invests £200,000 in a savings account for 4 years. The account pays compound interest rate at 1.6% per annum. Calculate the total amount of interest Claire will get at the end of 4 years

Answers

Answer:

£13,110.49

Step-by-step explanation:

solution:

(A) = P( 1 + r/n) ^nt

P(Principal) = £200 000

r(interest rate) = 1.6% = 0.016

The total amount been saved after 4 years is calculated as:

A = P( 1 + r/n) ^ nt

A = £200,000( 1 + 0.016/1)¹× ⁴

A = £200,000(1.016)⁴

A = £213,110.48991

A = £ 213,110.49

Claire will get approximately £ 213,110.49 within 4 years.

A model robot uses the scale 1 inch : 2 feet. If the model robot was 5 inches tall, the real robot would be __ feet tall

Answers

Answer: 10 feet

The ratios:

1 inch : 2 feet

5 inch : x feet

Finding x:

1 * 5 = 5

2 * 5 = 10

The real robot would be 10 feet tall.

Answer:

10 inches

Step-by-step explanation:

because 1 in= 2 ft
we can multiply 5 by 2 which is 10

your answer is 10 ft tall.

Help please + I need explanation

Answers

Answer:

61 degrees

Step-by-step explanation:

The THREE angles in the diagram sum to 180 degrees ( straight line = flat wall)

3x+1 + 58 + 4x-19 = 180

solve for x = 20 then A = 3x+1 = 61 degrees

A fruit seller sells 41 watermelons on Thursday and 59 watermelons on Friday. The cost
of each watermelon is ₹99. Find the total amount earned by the fruit seller.

Answers

Answer:

₹9900

Explanation:

On thursday sold : 41 watermelonsOn friday sold : 59 watermelons

Total sold : (41 + 59) = 100 watermelons

Amount earned : 100 * 99 = ₹9900

#Thursday

Melons sold=41

Money earned=41(99)

4059$

#Friday

Melons sold=59

Money earned

59(99)5841

Total:-

5841+4059=$9900

What is the slope of the line that passes through the points(1,6) and (13,2)?

Answers

Answer:

[tex]\boxed{\sf{-\dfrac{2}{3} }}[/tex]

Step-by-step explanation:

Use a slope formula.

Slope formula:

[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }[/tex]

y2=2

y1=6

x2=13

x1=1

Rewrite the problem.

[tex]\sf{\dfrac{2-6}{13-1}=\dfrac{-8}{12}=\dfrac{-8\div4}{12\div4}=\dfrac{-2}{3}=\boxed{\sf{-\dfrac{2}{3}}}[/tex]

Therefore, the slope is -2/3, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

help please thankkkkk youuuuuuuu :))))))))))

Answers

Answer:

426

Step-by-step explanation:

To determine how to round up or down, we look at the place after the one we want to round to. In this case, we look at the tenths place.

If the tenths place is [tex]\geq 5[/tex] then you round up, and if it is [tex]\leq 4[/tex] you round down.

We see that the number is five and we round up to 426

The movie started at 7:35 PM and lasted 1 hour and 40 minutes. What time did
the movie end?

Answers

Answer:

9:15 PM

Step-by-step explanation:

1 hour and 40 minutes after 7:35 is 9:15

It ended 9:15 pm
Explanation: from 7:35 1+40 = 09:15 pm

Jack had m math problems to complete during his vacation. He solved the same
number of problems every day and finished them all in 5 days.
Suppose Jack was solving 15 problems per day. Use this information and the answer
to part (a) to build an equation.

Answers

Answer:

M/5 =15

Step-by-step explanation:

The answer to part a was m/5. m/5 is the amount of questions Jack does per day. If 15 is supposedly the number of question he does per day, then m/5 and 15 are equal. Making m/5=15. Good luck fellow RSM student.

Find the value of X
Find the measures of the following angles

Answers

Answer:

angle X = 80; angle Y = 100; angle W = 100; x = 10

Step-by-step explanation:

opposite angles are always equal, which means that angle Z and angle X are equal.

angle X = 80º

now, angle Z plus angle Y makes a straight line, which means 180º (if you put the two angles next to each other)

that means 80 + (11x - 10) = 180

11x = 110

x= 10

by using this, we can find angles Y and W since opposites are equal

11x - 10 would be 100 and angles Y and W would be 100

pls help and do quick!

find x

Answers

Answer:

x = 90

Step-by-step explanation:

If the line is straight.

Angles on a straight line add up to 180

2x = 180

x = 90

Students voted to have a guinea pig or a hamster qs a class pet. Of thise students, 18 voted to have a guinea pig. This number represents 72% of the students who voted. What is the toatal number of students who voted

Answers

Answer:

The total number of students that voted is 25.

Step-by-step explanation:

18 students = 72% of the students who voted

Divide the percentage of students by 100.

72% ÷ 100 = 0.72%

Then, divide 18 by 0.72%.

18 ÷ 0.72% = 25

So, the total number of students that voted is 25 students.

Hope this helped !

At a carnival game, you may win an inflatable crayon, you may win a small stuffed animal, or you may win nothing at all. If the probability of winning nothing is 0.72 and the probability of winning a small stuffed animal is 0.19, what is the probability of winning an inflatable crayon? Express your answer as a decimal.

A:0.91
B:0.28
C:0.09
D:0.81

Answers

Answer:

C:0.09

Step-by-step explanation:

probability of winning nothing = 0.72 = [tex]\frac{72}{100}[/tex]

probability of winning a small stuffed animal = 0.19 = [tex]\frac{19}{100}[/tex]

probability of winning nothing + probability of winning a stuffed animal

= [tex]\frac{72}{100}[/tex] + [tex]\frac{19}{100}[/tex] = [tex]\frac{91}{100}[/tex]

probability of winning an inflatable crayon = 1 - [tex]\frac{91}{100}[/tex]

= [tex]\frac{100}{100}[/tex] - [tex]\frac{91}{100}[/tex]

= [tex]\frac{9}{100}[/tex]

= 0.09

How long to have 1 bitcoin when you put in 1 a day with a growing rate of 3.3% per 3 months. Current price of bitcoin 39,110. Each mont is 30 days.

Answers

Answer:

5 years

Step-by-step explanation:

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