The difference of the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first equation be P = x / ( x² - 2x - 15 )
Let the second equation be Q = 4 / x² + 2x - 35 )
Now , A = P - Q
On simplifying , we get
A = x / ( x² - 2x - 15 ) - 4 / x² + 2x - 35 )
Taking the LCM , we get
A = x ( x + 7 ) - 4 ( x + 3 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = x² + 7x - 4x + 12 / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Therefore , the value of A is ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Hence , the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
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Angle 6= (11x+8) and angle 7=(12x-4) what is the measure of angle 4
Answer:
Answer is m∠4=40
Step-by-step explanation:
take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.
m∠6 = m∠7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
x = 12
so
m∠6 = 11x + 8
m∠6 = 11(12) + 8
m∠6 = 132 + 8
m∠6 = 140
m∠4 = 180 - m<6
m∠4 = 180 - 140
m∠4 = 40
Answer:
A
Step-by-step explanation: Took test
Can someone please help me with this I’m stuck and I need to finish but I don’t understand
Answer:
28
Step-by-step explanation:
Because the lines are parallel:
[tex]\dfrac{m}{21}=\dfrac{8}{6} \\\\m=\dfrac{8}{6}\cdot 21=28[/tex]
Hope this helps!
Savings accounts are a reliable way to store money for the future
Answer:
true
Step-by-step explanation:
just took test
figure ABCD is a parallelogram what is the perimeter of ABCD
Mr.Rice students ran a 40 yard dash in the following times 6.8,7.3,7.1 ,7.0,7.2,7.3,7.0 how many race times are recorded
The number of race times recorded as portrayed by the number of data points is seven(7).
What is the number of race times recorded for the dash?From the task content;
It follows that the distance ran be Mr. Rice students was 40 yards.Additionally, it follows from the task content that the times recorded were; 6.8,7.3,7.1 ,7.0,7.2,7.3 and 7.0.
On this note, the number of race times recorded as portrayed by the number of data points is seven(7).
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What is the value of X ?
Answer:
D
Step-by-step explanation:
2² + 6² = x²
4 + 36 = x²
40 = x²
x = 2√10
Which of the lists of letters all have line symmetry? A, B, C, D W, X, Y, Z L, M, N, O S, T, U, V
Answer:
A, W, X, Y, M, O, T, U, V, C, D
Step-by-step explanation:
If you put a line through the middle, then the left and the right side will look the same
tank contains 20002000 liters (L) of a solution consisting of 112112 kg of salt dissolved in water. Pure water is pumped into the tank at the rate of 1212 L/s, and the mixturelong dash—kept uniform by stirringlong dash—is pumped out at the same rate. How long will it be until only 88 kg of salt remains in the tank?
The time taken in draining salt so that only 88 kg of salt remains in tank will be 35.71 sec.
It is given that a tank contains 2000 liters of a solution consisting 112 kg of salt is dissolved in water. Pure water is then pumped at rate of 12 L/sec.
We have to find out that how long it will take to drain out salt such that only 88kg of salt remains in tank.
What will be the amount of water flow ; if a water flows for 4 hours at constant speed of 120 liter /hour ?
The amount of water flow will be 120 liter / hour × 4 hour or 120 × 4 liter or 480 liters.
As per the question ;
In 2000 liters solution there is 112 kg salt.
The pumping speed of water into tank = 12 L/s
The salt pumping per second will be ;
= ( 12L/s × 112kg salt ) / 2000 L
= 0.672 Kg salt/sec
This means that 0.672 kg per second salt comes out .
It should be found that the amount of salt that must be drained so that only 88 kg of salt remain.
So , the amount of salt drained out will be ; (x kg)
⇒ 112kg salt - x kg salt = 88 kg salt
⇒ x kg salt = 112 - 88
⇒ x kg salt = 24 kg
The time taken until only 88 kg of salt remains in the tank will be ;
= 24 / 0.672
= 35.71 sec
Thus , the time taken in draining salt so that only 88 kg of salt remains in tank will be 35.71 sec.
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Please answer this correctly
Answer:
0-19: Make it 4 units tall
20-39: Make it 2 units tall
40-59: Make it 5 units tall
60-79: Make it 3 units tall
80-99: Make it 1 unit tall
Step-by-step explanation:
0-19: 4, 6, 19, 19 (4 numbers)
20-39: 29, 38 (2 numbers)
40-59: 40, 41, 41, 57, 58 (5 numbers)
60-79: 62, 66, 73 (3 numbers)
80-99: 87 (1 number)
Please help me :( with this
Answer:
21
Step-by-step explanation:
Similar triangles. MNL is just ABC but 3/4 the size.
x = 8*3/4 = 6
perimeter woudl be 6+6+9 = 21
There are 390 students at Walker Elementary this year. This is a 30% increase from the previous year. How many students were at Walker Elementary last year?
Answer:
There were 300 students
Step-by-step explanation:
Original * 30 = increase
Add the increase to get the new number
original + increase = 308
original + original*30% = 390
Factor out original number
original ( 1+30%) = 390
Change to decimal form
original ( 1+.30) = 390
original ( 1.30) = 390
Divide by 1.3
original = 390/1.3
=300
3. Which of the following values is not possible in probability?
A. P(x) = 1
B. x P(x) = 3 C. P(x) = 0.5
D. P(x) = -0.5
Answer:
D . P(x)=-0.5
Step-by-step explanation:
i think please mark my answer as a brainliest answer and follow me.
I promise brainliest and a exter 25 poinst to the first to answer What is the solution to the inequality 2x ≥ -4? Click the number line until the correct answer is shown...
:
Answer:
the answer is the arrow going to the right because its not a negative number and a closed circle
Step-by-step explanation:
so that means that 2x is at LEASt more than -4 opposed to this sign> wich just means greater than
because when you work with variables you usually cannot find the exact amount especially when you are rounding so you know that its biigger than no less than or at least -4
the answer is the arrow going to the right because its not a negative number and a closed circle
please please mark as brainliest
A population of protozoa develops with a constant relative growth rate of 0.7781 per member per day. On day zero the population consists of six members. Find the population size after four days. (Round your answer to the nearest whole number.) P(4)
Answer:
[tex] P(t) = A (1+r)^t [/tex]
Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:
[tex] P(t)= 6(1.7781)^t [/tex]
And replacing t=4 we got:
[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]
So then after 4 days we would expect about 60 protzoa
Step-by-step explanation:
For this case we can use the following function to model the population of protzoa:
[tex] P(t) = A (1+r)^t [/tex]
Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:
[tex] P(t)= 6(1.7781)^t [/tex]
And replacing t=4 we got:
[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]
So then after 4 days we would expect about 60 protzoa
I NEED HELP PLEASE HELP ME
Answer:
3
Step-by-step explanation:
Solving the inequality
2x-1>=5
2x>=6
x>=3
The graph should have a shaded circle on 3 and a line pointing to values increasing.
Eliminate the variable t from the set of parametric equations. Graph the equation X=5cost Y=5sint Please explain this, I need to know how to do these kinds of equations for my trig final
Answer:
x^2 + y^2 = 25
Step-by-step explanation:
x = 5 cos t
cos t = x/5
y = 5 sin t
sin t = y/5
cos^2 t + sin^2 t = 1
(x/5)^2 + (y/5)^2 = 1
x^2/25 + y^2/25 = 1
(x^2 + y^2)/25 =1
x^2 + y^2 = 25
If the probability of a machine producing a defective part is 0.05, what is the probability of
finding exactly 5 defective parts from a sample of 100? (Assume that the process follows a
binomial distribution and round answer to four places)
Answer:
0.1800 to 4 places of decimals.
Step-by-step explanation:
Using the Binomial formula
Probability = 10C5* (0.95)^95 * (0.05)^5
= 100! / 95!*5! * (0.95)^95 * (0.05)^5
= 0.1800178.
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Square root is finding what number times what gets your goal.
10 x 10 = 100 so 100 squared is 10.
5 x 5 = 25 so 25 squared is 5.
4 x 4 = 16 so 15 squared is 4.
You get it? :)
Have a nice day!
The sum of two fractions can always be written as a
Answer: decimal
Step-by-step explanation:
because i did this quiz
(02.04 MC) Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3. y = −3x − 13 y = −3x + 11 y = −3x + 13 y = −3x + 1
Answer:
it is b
Step-by-step explanation:
the answer is b because
A sample of 899 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. A. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen. B. There is sufficient evidence to conclude that the mean consumption of popcorn has risen. C. There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. D. There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
Answer:
The correct answer to the following question will be Option A.
Step-by-step explanation:
Marketing Analyst seems to be responsible for information and evaluation that directs its marketing team and directs its marketing approach by defining the target clients as well as the competitiveness of the product.A survey of 899 American citizens requires appropriate evidence to demonstrate that perhaps the marketing strategy is working even though there was not considerable evidence to suggest that even the total demand for popcorn had increased.Other given choices are not related to the given circumstances. So that option A seems to be the appropriate choice.
In the United States, the mean and standard deviation of adult men's heights are 70 inches (5 feet 10 inches) and 4 inches, respectively. Suppose the American adult men's heights have a normal distribution Whe probability that a randomly chosen American man is taller than 6 feet (72 inches) is equal to:___________. (round off to fourth decimal place, use the given table)
a. 0.6853
b. 0.0062
c. 0.3085
d.0.6915
e. None of these
Answer:
[tex]P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)[/tex]
And we can find this probability using the complement rule and the normal standard table:
[tex]P(z>0.5)=1-P(z<0.5)= 1- 0.69146= 0.3085[/tex]
And the best solution would be:
c. 0.3085
Step-by-step explanation:
For this case we can convert all the values to inches in order to standardize the solution:
[tex] 5ft * \frac{12 in}{1ft}= 60 in[/tex]
[tex] 6ft * \frac{12 in}{1ft}= 72 in[/tex]
Let X the random variable that represent the heights of US mens, and for this case we know the distribution for X is given by:
[tex]X \sim N(70,4)[/tex]
Where [tex]\mu=70[/tex] and [tex]\sigma=4[/tex]
We are interested on this probability
[tex]P(X>72)[/tex]
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)[/tex]
And we can find this probability using the complement rule and the normal standard table:
[tex]P(z>0.5)=1-P(z<0.5)= 1- 0.69146= 0.3085[/tex]
And the best solution would be:
c. 0.3085
Using the normal distribution, it is found that the probability that a randomly chosen American man is taller than 6 feet (72 inches) is equal to:
c. 0.3085
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
Mean of 70 inches, thus [tex]\mu = 70[/tex].Standard deviation of 4 inches, thus [tex]\sigma = 4[/tex].The probability of being taller than 72 inches is 1 subtracted by the p-value of Z when X = 72, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 70}{4}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
1 - 0.6915 = 0.3085
Thus, option c.
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WILL MARK BRAINLIEST PLEASE HELP
Answer:
1) h = -1/2t^2 +10t
2) h = -1/2(t -10)^2 +72
3) domain: [0, 20]; range: [0, 50]
Step-by-step explanation:
1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...
h = a(t -10)^2 +50
To find the value of "a", we must use another point on the graph. (0, 0) works nicely:
0 = a(0 -10)^2 +50
-100a = 50 . . . . . . subtract 100a
a = -1/2 . . . . . . . . . divide by -100
Then the standard-form equation is ...
h = (-1/2)(t^2 -20t +100) +50
h = -1/2t^2 +10t
__
2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.
h = -1/2(t -10)^2 +72
__
3.) The horizontal extent of the graph for Firework 1 is ...
domain: 0 ≤ t ≤ 20
The vertical extent of the graph for Firework 1 is ...
range: 0 ≤ h ≤ 50
In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.
a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?
b. Roughly what proportion of vehicle speeds exceeded 57 mph?
Answer:
(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) Roughly 16% of vehicle speeds exceeded 57 mph.
Step-by-step explanation:
We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.
For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.
Let X = vehicle speed at impact
SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])
Here, [tex]\mu[/tex] = population average speed = 42 mph
[tex]\sigma[/tex] = standard deviation = 15 mph
Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;
68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;
[ [tex]\mu-\sigma , \mu+\sigma[/tex] ] = [42 + 15 , 42 - 15]
= [57 , 27]
So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.
It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.
This means that roughly 16% of vehicle speeds exceeded 57 mph.
Please help! Correct answer only, please! Jason has the following averages in his math class: homework avg: 80 quiz avg: 84 test avg: 74 final exam: 60 if the teacher weights homework at 20%, quizzes at 30%, tests at 40%, and the final exam at 10%, what is jason's class average? A. 74 B. 77 C. 79 D. 82
Answer:
77
Step-by-step explanation:
80*0.2 + 84*0.3 + 74*0.4 + 60*0.1 = 76.8 = 77
g Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) Group of answer choices three eigenvalues, all of them real. three eigenvalues, all of them complex. two real eigenvalues and one complex eigenvalue. one real eigenvalue and two complex eigenvalues. only two eigenvalues, both of them real. only two eigenvalues, both of them complex. only one eigenvalue -- a real one. only one eigenvalue -- a complex one.
Answer:
(A)three eigenvalues, all of them real.
(D)one real eigenvalue and two complex eigenvalues.
(G)only one eigenvalue -- a real one.
Step-by-step explanation:
Given an [tex]n \times n[/tex] matrix, the characteristic polynomial of the matrix is the degree n polynomial in one variable λ:
[tex]p(\lambda) = det(\lambda I- A)[/tex]
If such [tex]n \times n[/tex] matrix A has real entries, its complex eigenvalues will always occur in complex conjugate pairs.
Therefore, for a [tex]3 \times 3[/tex] matrix with real entries, the following are possible:
(A)three eigenvalues, all of them real.
(D)one real eigenvalue and two complex eigenvalues.
(G)only one eigenvalue -- a real one.
A [tex]3 \times 3[/tex] matrix with real entries cannot have the following:
(B)three eigenvalues, all of them complex.
(C)two real eigenvalues and one complex eigenvalue.
(E)only two eigenvalues, both of them real.
(F)only two eigenvalues, both of them complex.
(H)only one eigenvalue -- a complex one.
on solving x/2 +5/3=_1/2 we get x=
Step-by-step explanation:
I hope it's correct... Hope this is what you want
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. F(x) = 3(x - 2)² - 2
Step-by-step explanation:
→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.
→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.
→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.
→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.
This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."
Given the following information, find the probability that a randomly selected dog will be a golden retriever or a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles: 20, pugs: 38a) 39.5%b) 60.5%c) 58.0%d) 46.9%
Answer: a) 39.5%
Step-by-step explanation:
For random selections, we assume that all the dogs have the same probability of being selected.
In this case, the probability will be equal to the number of golden retrievers divided the total number of dogs.
We have 58 golden retrievers, and the total number of dogs is:
31 + 58 +20 + 38 = 147
Then the probability is:
P = 58/147 = 0.395
If we multiply it by 100%, we obtain the percentage form:
0.395*100% = 39.5%
So the correct option is a.
Solve the equation then write how many solutions there is in this problem: 8x-3+14=24x+5
Answer:
x = 0.375
Step-by-step explanation:
Step 1: Simplify both sides of the equation
8x − 3 + 14 = 24x + 5
(8x) + (−3 + 14) = 24x + 5
8x + 11 = 24x + 5
- 24
-16x + 11 = 5
-11
-16x = -6
-16x/-16 = -6/-16
x = 3/8
x = 0.375
