Simplify x^2-4x-32/x^2+7x+12
Answers
(x - 8)(x + 4) / (x+3)(x+4)
If x ≠ -4
Then it equals to:
(x-8) / (x+3)
Answer see form:
Related Questions
Jonathan bought a new computer for $1,728 using the electronics store's finance plan. He will pay $96 a month for 18 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Answers
Answer:
[tex]y=1728-96x[/tex]
Step-by-step explanation:
Given : Cost of computer = $1728
He will pay $96 a month for 18 months.
To Find: Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Solution:
He pays per month = $96
Let the number of months be x
So, He pays in x months = 96x
Since the total Cost of computer is $1728
So, amount left to be paid = [tex]1728-96x[/tex]
Let y be the unpaid amount after x months
So, equation becomes : [tex]y=1728-96x[/tex]
Hence An equation can Jonathan use to find out how much money he still owes after each month of the plan is [tex]y=1728-96x[/tex]
If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?
Answers
g(x) = f(-x); -x has been substituted in for x.
In the diagram AB and AC are tangent to the circle. Find the length of the radius D.C.
Answers
Otherwise, you need to give more information.
Answer:
D. 6 on e2020
Step-by-step explanation:
just took test
How often is the number of house representatives assigned to states reallocated? every 2 years every 6 years every 10 years never?
Answers
The members of the executive branch are the president, vice president and the cabinet. The president holds all the power for this branch of the government and the other members report to the president. The legislative branch writes up and votes on laws. This is called legislation. The legislative branch also known as congress has two parts: the House of Representatives and the senate. Other powers of the congress include declaring war, confirming presidential appointments for groups like the Supreme Court and the cabinet and investigating power. According to Article 1, Section 2, Clause 1, the House of Representatives shall constitute members every 2 years by the people of the state.
martha and mary had 375 jelly beans in all. after mary ate 24 jelly beans and martha ate 1/7 of her jelly beans, they each had the same number of jelly beans left. how many jelly beans did each girl have at first?
Answers
Let x = number of beans with Martha
Let y = number of beans with Mary
Since total beans is 375,
x + y = 375
Mary ate 24 beans, after this she must be having x - 24 beans
Similarly after eating 1/7y beans, mary must be having y - y/7 beans
Setting them equal to each other
x - 24 = y - y/7
Solving both equations gives x = 186, y = 189
The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8
Answers
xy = c, where c is a constant
when y = 40 and x = 5 -> c = 40*5 = 200
So xy = 200
Then, when x = 8, y = 200/8 = 25
Answer: 64
Step-by-step explanation:
i put it into math-way
You invest $9000 with a 6% interest rate compounded semiannually. After 9 yrs, how much money is in your account?
Answers
Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056
Answers
a vendor has learned that, by pricing pretzels at $1.50 sales will reach 91 pretzels per day. raising the price to $2.25 will cause the sales to fall to 58 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each
Answers
We are given with two points so we can derive the equation using the two-point form.
That is,
y – y1 = ((y2 – y1)/(x2 – x1))(x – x1)
We may choose which among our derived coordinates will be 1 and 2. Substituting to the equation,
y – 91 = ((58 – 91)/(2.25 – 1.5))(x – 1.5)
y – 91 = -44(x – 1.5)
Simplifying further,
y – 91 = -44x + 66
y = -44x + 157
Thus, the equation above gives the number of pretzels that can be sold given the price.
To model the number of pretzels sold per day as a function of the price in dollars using a linear equation, calculate the slope of the line using two known points, and then use the slope and one point to find the y-intercept. The resulting linear equation is y = -44x + 157, where y represents the number of pretzels sold and x represents the price in dollars.
To write a linear equation that models the number of pretzels sold per day when the price is x dollars each, we can start with two given points that represent the sales and price data: (1.50, 91) and (2.25, 58).
Using these points, we can first find the slope of the demand line.
The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Plugging in our values, we get:
m = (58 - 91) / (2.25 - 1.50) = (-33) / (0.75) = -44
The slope of the demand function is -44. This means that for each dollar increase in price, 44 fewer pretzels are sold.
Next, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can use one of the given points. Let's use (1.50, 91).
91 = (-44)(1.50) + b
b = 91 + 66
b = 157
The y-intercept, b, is 157. Knowing both m and b, we can now write the equation of the line:
y = -44x + 157
This equation models the number of pretzels sold, y, at a price of x dollars each.
The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?
Answers
Final answer: 2.77 oz
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.
Which equation can be used to solve for x, the increase in side length of the square in inches?
x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0
Answers
Then the enlarged side becomes (x+4) and the square = (x+4)²
The final area should be (x+4)² = 81
Let's expand:
x²+ 8x + 16 = 81
x² + 8x + 16 - 81 = 0
x² + 8x - 65 = 0
Answer:
[tex]x^2+8x-65=0[/tex]
Step-by-step explanation:
Side length of square = 4 inches
Let x be the increase in length
So, New length = x+4
Area of square = [tex]Side^2[/tex]
Area of enlarged square = [tex](x+4)^2[/tex]
Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]
Area of enlarged square = [tex]x^2+16+8x[/tex]
We are given that The final area needs to be 81 square inches.
So, [tex]x^2+16+8x=81[/tex]
[tex]x^2+16+8x-81=0[/tex]
[tex]x^2+8x-65=0[/tex]
So, Option C is true
Hence equation can be used to solve for x, the increase in side length of the square in inches is [tex]x^2+8x-65=0[/tex]
3/10, 0.222, 3/5, 0.53 in order from greastest to least
Answers
3/5 = 0.6
order from greatest to least
3/5, 0.53, 3/10 and 0.222
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
Answers
Answer: The required value is
[tex](f-g)(x)=x^2+8.[/tex]
Step-by-step explanation: The given functions are:
[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]
We are given to find the value of [tex](f-g)(x).[/tex]
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
[tex](s-t)(x)=s(x)-t(x).[/tex]
Therefore, we have
[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]
Thus, the required value is
[tex](f-g)(x)=x^2+8.[/tex]
Answer:
3x2 - 6 its the answer
Calculate M6 for f(x)=4⋅ln(x^2) over [1,2].
Answers
According to this formula if we have to calculate [tex] \int\limits^a_b {f(x)} \, dx [/tex]
then we will divide the interval [a,b] into n subinterval of equal width.
Δx = [tex] \frac{b-a}{n} [/tex]
So we will denote each of interval as follows
[tex][x_0 , x_1] , [x_1, x_2], ................[x_{n-1} , x_n][/tex] where [tex]x_0 = a , x_n = b[/tex]
Then for each interval we will calculate midpoint.
So we can calculate definite integral as
[tex] \int\limits^a_b {f(x)} \, dx = \triangle x f(y_1) + \triangle x f(y_2)+ ...............+ \triangle x f(y_n)[/tex]
where [tex]y_1 , y_2 , ....................y_n [/tex] are midpoint of each interval.
So in given question we need to calculate [tex]M_6[/tex] . So we will divide our interval in 6 equal parts.
Given interval is [1,2]
[tex]\triangle x = \frac{2-1}{6} = \frac{1}{6} [/tex]
So we will denote 6 interval as follows
[tex][1 , \frac{7}{6}] , [ \frac{7}{6} , \frac{8}{6} ] , [ \frac{8}{6} , \frac{9}{6} ] , [ \frac{9}{6} , \frac{10}{6} ] , [ \frac{10}{6} , \frac{11}{6} ] , [ \frac{11}{6} , 2 ] [/tex]
Now midpoint of each interval is
[tex]y_1 = \frac{1+ \frac{7}{6} }{2} = \frac{13}{12} = 1.084[/tex]
[tex]y_2 = \frac{ \frac{7}{6} + \frac{8}{6} }{2} = \frac{15}{12} = 1.25[/tex]
[tex]y_3 = \frac{ \frac{8}{6} + \frac{9}{6} }{2} = \frac{17}{12} = 1.417[/tex]
[tex]y_4 = \frac{ \frac{9}{6} + \frac{10}{6} }{2} = \frac{19}{12} = 1.584[/tex]
[tex]y_5 = \frac{ \frac{10}{6} + \frac{11}{6} }{2} = \frac{21}{12} = 1.75[/tex]
[tex]y_6 = \frac{ \frac{11}{6} + \frac{12}{6} }{2} = \frac{23}{12} = 1.917[/tex]
So [tex]M_6[/tex] for the given function is
[tex]M_6 = \triangle x [f(y_1) + f(y_2) + f(y_3) + f(y_4) + f(y_5) + f(y_6) ][/tex]
[tex]= \frac{1}{6}[0.6452+1.7851+2.7883+3.6796+4.4769+5.4243][/tex]
[tex]= \frac{1}{6} * 18.7994 = 3.1333 [/tex]
So [tex]M_6 value for function is 3.1333[/tex]
To calculate M6 for f(x)=4⋅ln(x^2) over [1,2], differentiate the function to find f'(x). Integrate f'(x) over the given interval to find the area under the curve. Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.
Explanation:To calculate M6 for the function f(x) = 4⋅ln(x^2) over the interval [1,2], follow these steps:
Differentiate the function to find f'(x).Integrate f'(x) over the given interval to find the area under the curve.Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.In this case, since f(x) = 4⋅ln(x^2), we have f'(x) = 8/x. Integrate f'(x) from 1 to 2 to get M6.
Learn more about Calculating definite integrals here:https://brainly.com/question/10680842
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A new crew of painters can paint a small apartment in 12 hours. AN EXPERIENCED crew can paint the small apartment in 6 hours. How many hours does it take to paont the apartment when the two crews work together?
Answers
so.. in 1 hour, they have done 1/t of the whole work.
now, the new crew, working by itself can do the whole job in 12 hours, that means, in 1 hour, they have done only 1/12 of all the work.
the experienced crew, can do the job in 6 hours, that means in 1 hour, they have done 1/6 of all the work.
now, let's add their rates for 1 hour worth, to see what we get.
[tex]\bf \begin{array}{clclcllll} \cfrac{1}{12}&+&\cfrac{1}{6}&=&\cfrac{1}{t}\\ \uparrow &&\uparrow &&\uparrow &&\\ new\ crew&&experienced&&total\\ rate/hr&&rate/hr&&work/hr \end{array}\\\\ -------------------------------\\\\ \textit{let's multiply both sides by \underline{12t}, to toss away the denominators} \\\\\\ t+2t=12[/tex]
and pretty sure you know how much that is.
What is the answer to this question?
Answers
Now that you know the formula, plug in and solve.
SA = 2(5)(8) + (5)^2
SA = 80 + 25
SA = 105
Now that you see that the question is asking for the answer in yards, you convert feet into yards.
3 feet = 1 yard.
105 is divided by 3 and you get 35.
The answer is 35 square yards.
Poisson suppose you have 5 cakes made ready to sell. what is the probability that you will sell out?
Answers
Assume further that the mean number of cakes sold per day is lambda.
Let k=5 = number of cakes sold during the day, then the Poisson pmf (probability mass distribution) is given by
P(k)=lambda^k*e^(-lambda)/k!
or
P(5)=lambda^5*e^(-lambda)/5!
=lambda^5*e^(-lambda)/120
If the average number of cakes sold is 4 per day, then
P(5)=4^5*e^(-4)/120
=0.156 is the probability of selling exactly 5 cakes.
The probability of selling 5 cakes or more (i.e. the sixth and subsequent customers will be told to come back the next day) is then
P(k>=5)=1-(P(k=0)+P(k=1)+P(k=2)+P(k=3)+P(k=4)
=1-(0.018316+0.073263+0.146525+0.195367+0.195367)
=0.371163
(for mean number of cakes sold per day = 4 )
At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?
Answers
now, 4 years later in 2010, t = 4, there are 900 skaters, and the rate of decrease is 5%.
[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &900\\ I=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &4\\ \end{cases} \\\\\\ 900=I(1-0.05)^4\implies 900=I(0.95)^4\implies \cfrac{900}{0.95^4}=I \\\\\\ 1105\approx I\qquad thus\qquad \boxed{A=1105(0.95)^t}[/tex]
[tex]\bf \\\\ -------------------------------\\\\ \textit{now in 2006, 4 years earlier, year 0, t = 0} \\\\\\ A=1105(0.95)^0\implies A=1105\cdot 1\implies A=1105[/tex]
The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898
Answers
The probability that the mean leg length is less than 20 cm is practically 0.
Explanation:To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.
We can standardize the sample mean using the formula:
z = (x - μ) / (σ / sqrt(n))
Where:
z: the z-scorex: the value of the sample meanμ: the population meanσ: the population standard deviationn: the sample sizeSubstituting the given values:
z = (20 - 43.7) / (4.2 / sqrt(9))
z = -23.7 / (4.2 / 3)
z = -23.7 / 1.4
z ≈ -16.93
Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.
Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°
Answers
[tex]u = \ \textless \ cos(45),sin(45)\ \textgreater \ [/tex]
In same way you can find component form of u+v
[tex]u+v = \ \textless \ 2cos(90), 2sin(90)\ \textgreater \ [/tex]
By property of vector subtraction:
v = (u+v) - u
[tex]v = \ \textless \ 2cos(90) - cos(45), 2sin(90) - sin(45)\ \textgreater \ [/tex]
[tex]v = \ \textless \ -\frac{\sqrt{2}}{2}, 2-\frac{\sqrt{2}}{2} \ \textgreater \ [/tex]
When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75
Answers
$29.75 divided by 5 books is $5.95, answer A.
36.75 - 5b = 7
-5b = 7 - 36.75
-5b = - 29.75
b = -29.75 / -5
b = 5.95 <=== 5.95 per book
The table shows the outputs y for different inputs x:
Input
(x) 3 7 11 15
Output
(y) 4 6 8 10
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)
(10 points)
Answers
B. For the table, y is 8 when x is 11.
Plug in the value to determine the y value for the equation.
f(x)= 5(11)-21
f(x)= 55-21
f(x)= 34
Since 34>8, the value of the equation f(x) is greater when x=11.
C. 99=5x-21
120=5x
x=24
Final answer: 24
Answer:24
Step-by-step explanation:
a rectangular floor is 18 feet long and 12 feet wide. what is the area of the floor in square yards
Answers
1 yard=3 feet
Divide 18 and 12 by 3
18/3=6
12/3=4
A=bh
A=4*6
A=24 yards ^2
hope this helps:)
please mark thanks and brainliest:)
1 yard = 3 feet
18/3 =6
12/3=4
6*4 = 24 square yards
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
Answers
In this case, we can use the z statistic to find for the proportion of students who failed the exam. The formula for z score is given as:
t = (x – u) / s
where,
x = the sample score = 60
u = sample score mean = 82
s = standard deviation = 11
Substituting all given values into the equation:
t = (60 – 82) / 11
t = - 2
Based from the standard proportion distribution tables for z, this corresponds to:
P = 0.0228
This means that 2.28% of the students failed the exam or equivalent to:
failed students = (0.0228) * 85 = 1.938
approximately 2 students failed the exam
Answer:
2 students failed the exam
Step-by-step explanation:
Please help quick !!
Answers
√3/2
√3=1.73205080757
1.73205080757/2
=0.866025404
1) IS CORRECT
Solve the rest using the same technique.
Hope this helps! A thanks/brainliest answer would be appreciated :)
PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2
Answers
1.
the line of symmetry is x=2, means that the x coordinate of the vertex is x=2.
the point x=2 is the midpoint of the roots [tex]x_1[/tex] and [tex]x_2[/tex].
so
[tex] \frac{x_1+x_2}{2}=2 [/tex]
[tex]x_1+x_2=4[/tex]
Remark: in the x-axis, if c is the midpoint of a and b, then [tex]c= \frac{a+b}{2} [/tex]
2.
since [tex]x_1[/tex] and [tex]x_2[/tex] are roots
[tex]a(x_1)^{2} -8(x_1)-3=0[/tex] and [tex]a(x_2)^{2} -8(x_2)-3=0[/tex]
3.
equalizing:
[tex]a(x_1)^{2} -8(x_1)-3=a(x_2)^{2} -8(x_2)-3[/tex]
[tex]a(x_1)^{2} -8(x_1)=a(x_2)^{2} -8(x_2)[/tex]
[tex]a(x_1)^{2}-a(x_2)^{2} =8(x_1) -8(x_2)[/tex]
in the left side factorize a, in the left side factorize 8:
[tex]a[(x_1)^{2}-(x_2)^{2}] =8(x_1 -x_2)[/tex]
in the right side use the difference of squares formula:
[tex]a(x_1 -x_2)(x_1 +x_2) =8(x_1 -x_2)[/tex]
simplify by [tex](x_1 -x_2)[/tex]
[tex]a(x_1 +x_2) =8[/tex]
substitute [tex](x_1 +x_2)[/tex] with 4:
[tex]a*4 =8[/tex]
a=2
Answer: C)2
A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram?
Answers
Answer:
7
Step-by-step explanation:
If p is a positive integer,then p(p+1)(p-1) is always divisible by?
Answers
I am not quite sure what the choices are, but the answer to that problem is:
If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.
The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.
For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.
And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.
Answer: From the choices, select the even number
Final answer:
If p is a positive integer, p(p+1)(p-1) is always divisible by 3.
Explanation:
If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.
This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.
In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.
What is the next number in the series? 71 62 53 44 35 ?
Answers
To further prove this;
71 --> 62.
-10 and + 1.
62 --> 53.
-10 and +1
and so on.
However, if that's a little too complicated, there's an alternate method.
All you have to do is subtract 9 from the current number.
To further prove this;
71 - 9 = 62
62 - 9 = 53
53 - 9 = 44
and so on.
So, let's subtract 9 from our most current number, 35.
35 - 9 = 26.
The upcoming number in your sequence is 26.
I hope this helps!
How do you solve this
Answers
(5x^7y^2)/2