which of the following is the quotient of the rational expressions shown below?
x-4/2x^2÷2x+3/x+4

The width of the rectangle is 4 cm, found by dividing the area of the square (36 cm^2) by the length of the rectangle (9 cm).

To solve the problem we need to first understand two main concepts; the area of a square and the area of a rectangle. The area of a square can be found by squaring the length of one of its sides, which can be described with the formula A = a^2 where a is the side length of the square. Since the perimeter of the square is 24 cm, each side is 24 cm / 4 = 6 cm. Therefore, the area of the square is 6 cm * 6 cm = 36 cm^2.

The area of a rectangle is calculated by the formula A = length * width. We are given that the length is 9 cm and that the area of the rectangle is equal to that of the square, which we found to be 36 cm^2. To find the width, we divide the area by the length: 36 cm^2 / 9 cm = 4 cm. Thus, the width of the rectangle is 4 cm.

344676 I hope that helps

Answer:

Franchise has 11 quarters and 16 dimes.

Step-by-step explanation:

Let d represent number of dimes and q represent number of quarters.

We have been given that the number of dimes is five more than the number of quarters. We can represent this information in an equation as:

[tex]d=q+5...(1)[/tex]

We are also told that Francine has $4.35 in dimes and quarters. We can represent this information in an equation as:

[tex]0.10d+0.25q=4.35...(2)[/tex]

Now, we will substitution method to solve linear equations. Upon substituting equation (1) in equation (2), we will get:

[tex]0.10(q+5)+0.25q=4.35[/tex]

[tex]0.10q+0.50+0.25q=4.35[/tex]

[tex]0.35q+0.50=4.35[/tex]

[tex]0.35q+0.50-0.50=4.35-0.50[/tex]

[tex]0.35q=3.85[/tex]

[tex]\frac{0.35q}{0.35}=\frac{3.85}{0.35}[/tex]

[tex]q=11[/tex]

Therefore, Franchise has 11 quarters.

Upon substituting [tex]q=11[/tex] in equation (1), we will get:

[tex]d=11+5[/tex]

[tex]d=16[/tex]

Therefore, Franchise has 16 dimes.

Alternate interior angles I believe

a) 240 cows

b)80 cows

c) 8 days

Answer:

1) 240 cows.

2) 80 cows.

3) 8 days.

Step-by-step explanation:

1) To find the number of cows that could be fed for 4 days, you need to substitute [tex]x=4[/tex] into the equation, then:

[tex]y=\frac{960}{x}\\\\y=\frac{960}{4}\\\\y=240[/tex]

2) To find the number of cows that could be fed for 12 days, you need to substitute [tex]x=12[/tex] into the equation, then:

[tex]y=\frac{960}{x}\\\\y=\frac{960}{12}\\\\y=80[/tex]

3) Farmer Bill has two feed his 85 cows and 35 cows of his neighbors, then the total number of cows he needs to feed is:

 [tex]y=85+35\\y=120[/tex]

Substitute this value into the equation and solve for "x" to find the number of days he could feed them:

[tex]120=\frac{960}{x}\\\\120x=960\\\\x=\frac{960}{120}\\\\x=8[/tex]

The answer is:

To graph a piecewise function, we need to graph each of the function that compounds the principal function (piecewise function) for the given values of the domain.

So,

For the first function, we have:

[tex]f(x)=y=3x-5\\\\y=3x-5[/tex]

We have that it's a positive slope line with y-intercept at -5, so, calculating the x-intercept we have by making y equal to 0, we have:

[tex]y=3x-5[/tex]

[tex]0=3x-5[/tex]

[tex]x=\frac{5}{3}=1.67[/tex]

Also, we have the domain for the function:

[tex]y=3x-5\leq -1[/tex]

Which domain is coming from the negative infinite to -1:

Domain: (-∞, -1]

Hence, we have that the function has a positive slope, intercepts the y-axis at (0,-5) and the x-axis at (1.67,0), also, it exists from -∞ to -1.

- For the second function, we have:

[tex]f(x)=y=-2x+3\\\\y=-2x+3[/tex]

We have that it's a negative slope line with y-intercept at 3, so, calculating the x-intercept we have by making y equal to 0, we have:

[tex]y=-2x+3[/tex]

[tex]0=-2x+3[/tex]

[tex]x=\frac{3}{2}[/tex]

Also, we have the domain for the function:

[tex]-2x+3, -1<x<4[/tex]

Which domain is coming from the negative infinite to -1:

Domain: (-1,4)

Hence, we have that the function has a negative slope, intercepts the y-axis at (0,3) and the x-axis at (1.5,0), also, it exists from (-1 to 4)

- For the third function, we have:

[tex]y=2[/tex]

We have that it's a horizontal line, existing from 4.

The domain for the function will be:

[tex]2,x\geq 4[/tex]

or:

Domain: [4,∞)

- Graphing:

First function: Green line

Second function:  Black line

Third function: Red line

Note: I have attached two pictures for better understanding, in the first picture we can see the functions that compound the piecewise function without the domain conditions, in the second picture we can see the functions with the domain conditions given by the piecewise function.

Have a nice day!

3.142×40^2×150=753,982.237

if1sec =0.2litres

what about 753.982=

753.982×1/0.2

=22.80

To determine if filling a tank takes longer than an hour, calculate the tank's volume, convert it to liters, and then divide by the fill rate. With a 240π liter capacity and a 0.2 L/s fill rate, it takes approximately 1.05 hours, thus longer than 1 hour.

To determine if it takes longer than 1 hour to fill a water tank with a radius of 40 cm and depth of 150 cm at a rate of 0.2 liters per second, we first calculate the volume of the tank and then the total time required to fill it at the given rate.

Step 1: Calculate the Volume of the Tank

Volume of a cylinder = πr²h, where r is the radius and h is the height.
Here, r = 40 cm and h = 150 cm.

Volume = π(40²)(150) = π(1600)(150) = 240000π cm³.

Step 2: Convert the Volume to Liters

Since 1 liter = 1000 cm³, the volume in liters = 240000π / 1000 = 240π liters.

Step 3: Calculate the Filling Time

Time = volume / rate = 240π / 0.2 = 1200π seconds.
To convert to hours, divide by 3600 (the number of seconds in an hour).

Total time in hours = 1200π / 3600 = π/3 hours, which is approximately 1.05 hours.

Since it takes approximately 1.05 hours to fill the tank, it does take longer than 1 hour to fill the tank.

Answer

914 m^2 to the nearest whole number.

Step-by-step explanation:

The area of the hexagonal base is made up of 6 congruent triangles so its area = 6* 1/2 base* height

= 6 * 1/2 * 12 * 6√3

= 216-√3 m^2.

The area of each slanting triangle = 6 * 15 m^2 so the lateral area of the pyramid

= 6*6*15= 540 m^2

Total surface area = 540 + 216√3

= 914.12 m^2.

hope this helps

and to make it simpler its C or 914.12

nearest cent so so 32.86 but since its money and 32.86 times 7 is 230.02 it should be rounded down so the answer will be 32.85

[tex]\bf h=\cfrac{1}{5}w+\cfrac{8}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(h)=5\left( \cfrac{1}{5}w+\cfrac{8}{5} \right)}\implies 5h=w+8\implies 5h-8=w[/tex]

The equation that can be used to find the number of weeks since planting is (b) w = 5h - 8

The equation is given as:

h = (1/5)w + (8/5)

Multiply through by 5

5h = w + 8

Subtract 8 from both sides

5h - 8 = w

Make w the subject

w = 5h - 8

Hence, the equation that can be used to find the number of weeks since planting is (b) w = 5h - 8

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Answer:

24

Step-by-step explanation:

132 pupils are represented by 11 parts of the ratio

Dividing 132 by 11 gives the value of one part of the ratio

132 ÷ 11 = 12 ← value of 1 part of the ratio, hence

2 parts = 2 × 12 = 24 ← number of teachers on trip

Answer:

24

Step-by-step:

132/11 (132 divide by 11)

=12

12*2 (12multiply by 2)

=24

Answer:

Supplementary Angles are two angles the sum of whose measures is 180º. Supplementary angles can be placed so they form a linear pair (straight line), or they may be two separate angles.

Answer:

b) ∠4 and ∠3

c) ∠4 and ∠5

e) ∠3 and ∠6

:) Hope this helps you to your question

Answer:

12 feet

Step-by-step explanation:

The length of the ladder is 13 ft

The base of the ladder is 5 ft away from the wall

The height(h) the ladder reaches from the bottom of the wall is:

Applying the Pythagorean theorem;

h = [tex]\sqrt{13^2 - 5^2}[/tex] = 12 ft

Answer: 6

Remember: 0.3 repeated = [tex]\frac{1}{3}[/tex]

[tex]3 \frac{2}{3} + 2 \frac{1}{3} = 5\frac{3}{3}\\\\5\frac{3}{3} = 6[/tex]

Answer:

6

Step-by-step explanation:

2.333... = 7/3

3 and 2/3 = 11/3

7/3 + 11/3 = 18/3 = 6

Answer: Apple Juice

Step-by-step explanation: Right of the bat we know 40 out of 80 is 50%. This is already less then the 68% we are given, so therefore it can't be mango jelly. 0.475 would be made into a percent of 47.5%. We know that the fraction would be 475 over 1000, so we need to move the decimal point once to the left for each number, giving us the percent above. 68% is greater than 47.5, making Apple juice the winned

Apple juice good luck

The equation would be h = 25 + m

^^^The reason this is the equation is because the amount of time it takes to do the homework is the 25 min of reading AND the m of completing math problems

Insert 20 in for m and solve for h

h = 20 + 25

h = 45

Insert 25 in for m and solve for h

h = 25 + 25

h = 50

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The answer is $0.69. This is because there are 32 ounces in the bottle, and $22.08/32=0.69, or $0.69.

Step-by-step explanation:

Answer:

x=-4 and x=2

Step-by-step explanation:

You are given the function

[tex]f(x)=\dfrac{x^2+2x-8}{x^2-2x-8}[/tex]

The zeros of the function are those value of x, for which [tex]f(x)=0[/tex]

First, find x for which function is undefined

[tex]x^2-2x-8\neq0\\ \\x^2-4x+2x-8\neq 0\\ \\x(x-4)+2(x-4)\neq 0\\ \\(x-4)(x+2)\neq 0\\ \\x\neq 4\text{ and }x\neq -2[/tex]

Now find points at which f(x)=0:

[tex]f(x)=0\Rightarrow x^2+2x-8=0\\ \\x^2+4x-2x-8=0\\ \\x(x+4)-2(x+4)=0\\ \\(x-2)(x+4)=0\\ \\x=2\text{ or }x=-4[/tex]

For both these values (x=-4 and x=2) function f(x) is defined, then x=-4 and x=2 are zeros of the function.

Final answer:

To find the zeros of the given function, set the numerator equal to zero and solve for x. The zeros are x = -4 and x = 2.

Explanation:

We can notice that both the numerator and denominator share the same factors (x² - 2x - 8). This means that f(x) is undefined where the denominator is zero.

Therefore, the zeros of the function f(x) = x² + 2x - 8 / x² - 2x - 8 can be found by setting the numerator equal to zero and solving for x.

By factoring the numerator and denominator, it becomes easier to identify the zeros.

x² - 2x - 8 = 0

Factoring the expression:

(x - 4)(x + 2) = 0

Therefore, the zeros of the function f(x) are x = 4 and x = -2.

4/10 or 2/5

Hope this helps!

Great Question!

First, 0.4 Is The Same Thing As 0.4/1

Next, Do 0.4/1 Multiplied By 10 And That Equals 4/10.

Finally, Simplify 2/5

In Conclusion, 0.4 Converted To A Fraction Is 2/5

[tex]340 \times \frac{14}{100} = 47.6[/tex]

To find the amount budgeted for tithe on a weekly salary of $340 with a 14% allowance for tithe, multiply the salary by the percentage. The amount budgeted for tithe is $47.60.

To find the amount budgeted for tithe on a weekly salary of $340 with a 14% allowance for tithe, multiply the salary by the percentage. First, convert 14% to decimal form by dividing it by 100: 14% / 100 = 0.14. Then, calculate the amount by multiplying $340 by 0.14: $340 * 0.14 = $47.60.

Answer:

8:16 p.m.

Step-by-step explanation:

You have to find LCM(a,b), where a=48 seconds and b=95 seconds (2 minutes 15 seconds).

1.

[tex]48=2\cdot 24=2\cdot 2\cdot 12=2\cdot 2\cdot 2\cdot 6=2\cdot 2\cdot 2\cdot 2\cdot 3=2^4\cdot 3.[/tex]

2.

[tex]95=5\cdot 19.[/tex]

3.

[tex]LCM(48,95)=2^4\cdot 3\cdot 5\cdot 19=4560\text{ seconds }=76\text{ minutes }=1\text{ hour }16 \text{ minutes. }[/tex]

If they rang together at 7 p.m, then the next time that the timers will ring together will be after 1 hour 16 minutes that is 8:16 p.m.

Answer:

8:16 p.m.

Step-by-step explanation:

You have to find LCM(a,b), where a=48 seconds and b=95 seconds (2 minutes 15 seconds).

1.

2.

3.

If they rang together at 7 p.m, then the next time that the timers will ring together will be after 1 hour 16 minutes that is 8:16 p.m.

Answer:

Emily has a 1 in 9 chance of rolling an odd number for all 3 rolls

Step-by-step explanation:

If there are three odd numbers, you’d simply multiply one sixth three times. One sixth because the dice has six sides and three times because there are three possibilities of getting an odd number

Answer:

-13

Step-by-step explanation:

a^2 + 3ab - b^2?

Plug in a=3 and b= -2

a^2 + 3ab - b^2

=  (3)^2 + 3(3)(-2) - (-2)^2

= 9 - 18 - 4

= -13

Value of expression [tex]a^{2} +3ab-b^{2}[/tex] is -13.

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

Given

[tex]a =3 \ and \ b= -2[/tex]

Value of expression [tex]a^{2} +3ab-b^{2}[/tex]

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

= [tex]9-18-4[/tex]

= [tex]-13[/tex]

Value of expression [tex]a^{2} +3ab-b^{2}[/tex] is -13.

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Answer:

A and C

Step-by-step explanation:

This question is on probability.

In the first option A, when a coin is tossed, two outcomes are obtained, a head or a tail. Angel to mop can be represented by heads and Isaiah to mow can be represented by tail.In this case, a 50% chance is observed.

In the third option, putting each person's name on a separate piece of paper in a bag has two outcomes to be obtained. The probability of picking a person name is 50%. You can pick a paper with Angel's name or Isaiah's name.The picked name will mow the lawn.

In the second option B, when a coin is flipped twice, we obtain 4 outcomes; HH,HT,TH,TT. If either toss is tail, TT, then Angel mows the lawn.However, there are 3 other outcomes that could occur which will make Isaiah to mow the lawn.In this case it will be unfair because the probability for Angle to mow, P(A)=1/4 where as that for Isaiah to mow P(I)=3/4

In the last option D, the probability of rolling a cube with a number 1 or 6 is 1/6. This is the same for geting a 2,3,4,or 5.Angel will mow if the number is 1 or 6 where as  Isaiah will mow if the number is 2,3,4 or 5. This is unfair to Isaiah because geting any number holds a probability of 1/6, while Angels waits for 2 numbers, he waits for 4 numbers.

Answer: Option 1 and 3

Step-by-step explanation:

A fair decision is when both of them have the same probability of winning and losing, in this case, because we have two possible results, we need to find an experiment with a 50/50 chance.

The coin in option 1 is a good option, 50% of the time it will end in tails and 50% of the time it will come up with heads, so this will be a fair decision.

option 3 also works, because we have two pieces of paper, if you draw one, the probability of drawing a specific one is 1/2 (the specific result divide by the total number of possible results) and this is equivalent to 0.5 or 50%.

The other two options have probabilities that are not equal, for example in the fourth option, Angel mows the lawn when the number is 1 or 6, we have 2 out of 6 results where he mows the lawn, this is p = 2/6 = 1/3

then the probability of Isaiah of mowing the lawn is p = 4/6 = 2/3, wich is bigger.

Answer:

We have the following equations:

5 + 3x - 2 and x + 2(x+1) + 1

Before checking the statements. Let's solve the syste of equations:

5 + 3x - 2 = x + 2(x+1) + 1

5 + 3x - 2 = x + 2x+2 + 1

3x + 3 = 3x + 3

Both equations are equivalent. Now, let's judge the statements:

1. The expressions are only equivalent when evaluated with odd values.

Given that the both expression are the same, the expressions are equivalent for ALL values.

Therefore, the statement IS FALSE ❌

2. The expressions are only equivalent for x=3 and x=7.

Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.

Therefore, the statement IS FALSE ❌

3. The expressions should have been evaluated with one odd value and one even value.

If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.

Therefore, the statement IS FALSE ❌

4. The expressions have equivalent values when x=6.

Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).

Therefore, the statement IS TRUE ✅

5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.

Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.

Therefore, the statement IS FALSE ❌

6. The expressions have equivalent values for any value of x.

Given that the both expression are the same, the expressions are equivalent for ALL values of x.

Therefore, the statement IS TRUE ✅

7. When x=10, both expressions have a value of 33

Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.

Therefore, the statement IS TRUE ✅

Answer:

D,F,G

Step-by-step explanation:

It Makes Sense.

Answer:

Cross Multiply.

Step-by-step explanation:

Multiply the denominator (3) of one side and the numerator (n).

Then, multiply the numerator (2) of on side and the denominator (4) of the other.

3n = 8

You divide both sides by 3 to have n be by itself, equaling ~2.6 or 8/3.

It’s your pay after taxes and other expenses.

Answer:Net pay is the amount of pay remaining for issuance to an employee after deductions have been taken from the individual's gross pay. This is the amount paid to each employee on payday.

Step-by-step explanation:

hope it helps!

Mode could work but I believe the best answer would be median.

Answer:

median

Step-by-step explanation:

Median is correct. One extreme outlier can "drag" the mean up or down, while it would have little or no effect on the median.

Answer:

height is 5 units

Step-by-step explanation:

We are required to determine the height of a triangle that has an area of 30 square units and a base measuring 12 units.

The formula for the area of a triangle is given as;

[tex]Area=\frac{1}{2}*base*height[/tex]

We plug in the given values and solve for the height;

[tex]30=\frac{1}{2}*12*height\\\\30=6*height\\height=5[/tex]

Answer:

5 units^2

Step-by-step explanation:

Part a: decaying;

Part b: decays 11% each year( 100-89=11);

Part c:the initial value of the scooter ( money spent to buy the scooter)

The value of Mikayla's scooter, modeled by the exponential decay function f(x)=13500x0.89^x, is decaying at a rate of 11% per year. The initial cost of the scooter was $13,500.

The function f(x)=13500×0.89^x is an example of an exponential decay function because the base (0.89) is less than 1. So, the value of Mikayla's scooter is decaying.

Part a: The value of the scooter is decaying because the base of the exponential function is less than 1.

Part b: The rate of decay is 11% per year. This comes from the fact that 1 - 0.89 = 0.11 or 11%, signifying the percentage decrease each year.

Part c: 13500 represents the initial value of the scooter. This is how much the scooter was worth when it was first purchased by Mikayla.

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