riley makes a mistake in step 2 while doing her homework. What was her mistake? StartFraction x Over x squared minus 5 x + 6 EndFraction + StartFraction x Over x + 3 EndFraction Step 1: StartFraction x Over (x minus 2)(x minus 3) EndFraction + StartFraction 3 Over x + 3 EndFraction Step 2: StartFraction x Over (x minus 2) (x + 3) EndFraction + 3 (x minus 2) Over (x minus 2) (x + 3) EndFraction Step 3: StartFraction x + 3 x minus 6 Over (x minus 2) (x + 3) EndFraction Step 4: StartFraction 4 x minus 6 Over (x minus 2) (x + 3) EndFraction She added the two fractions incorrectly. She used the wrong common denominator. She did not distribute the negative correctly. She did not multiply the first fraction by a factor. Mark this and return
The mathematical mistake that Riley made is that: "She used the wrong common denominator." (Option A)
What is a Common Denominator?A common denominator is a factor that is similar to all the fractions in the sequence of equations.
Hence the correct answer is:
(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))
See the correct sequence of steps below:
Step One - the Expression is given as:
(x/(x-3)(x-2)) + (3/(x+3))
Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.
Hence we have: (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)
Step 3 Apply the Law of Multiplicative Distribution:
Hence we have (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)
Step 4 - Collect Like Items
This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)
Step 5 Sort for like coefficients
This gives us: ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)
Step 6 - check for the sum or difference
This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)
We simplify and factor the expression to get
(2(2x²-6x+6)/(x-3)(x-2)(x+3).
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simplify. ((x/4)+(x/3))/(x/2)
Answer:
x/6
You're welcome! :)
Answer : 7/6
explanation is long
101.19 / 4 using long division
Given AB=10cm, CD=11cm, and AD=39cm, find the length of BC
Answer:
BC = 18 cm
Step-by-step explanation:
As we can see from the diagram:
AB + BC + CD = AD
⇒ 10 cm + BC + 11 cm = 39 cm
⇒ BC + 21 cm = 39 cm
⇒ BC = 39 cm - 21 cm
⇒ BC = 18 cm
What is the measure of arc RT
The measure of arc RT is 156 degree.
Measure of arc RTGiven:
arc TRM=102°
Hence:
arc RST=2×1O2°
arc RST=204°
Measure of arc RT
arc RT= 2(180° - 102°)
arc RT = 2(78°)
arc RT = 156 degrees
Therefore the correct option is B.
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How many liters each of a 35% acid solution and a 80% acid solution must be used to produce 60 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Solving a system of equations we will see that we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.
How many liters of each solution do we need to use?
First, we need to define the variables:
x = liters of the 35% acid used.y = liters of the 80% acid used.We know that we want to produce 60 liters of 65% acid, then we have the system of equations:
x + y = 60
x*0.35 + y*0.80 = 60*0.65
(in the second equation we wrote the percentages in decimal form).
To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:
x = 60 - y
Replacing that in the other equation:
(60 - y)*0.35 + y*0.80 = 60*0.65
y*(0.80 - 0.35) = 60*(0.65 - 0.35)
y*0.45 = 60*0.30
y = 60*0.30/0.45 = 40
So we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.
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The line segment AB has the endpoints (-21, -7) and (-6,3) Point C are partitions the line at a ratio of 4;1 What are the coordinates of point C?
The coordinates of point C are (-9, 1)
How to determine the coordinates of point C?The points are given as:
A = (-21, -7)
B = (-6, 3)
m : n = 4 : 1
The coordinates of point C is calculated as:
[tex]C = \frac{1}{m+n} *(mx_2 + nx_1, my_2+ ny_1)[/tex]
So, we have:
[tex]C = \frac{1}{4+1} *(4 * -6 + 1 * -21, 4 * 3+ 1 * -7)[/tex]
This gives
[tex]C = \frac{1}{5} *(-45, 5)[/tex]
This gives
C = (-9, 1)
Hence, the coordinates of point C are (-9, 1)
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You are offered two different sales jobs. The first company offers a straight commission of 5% of the sales.
The second company offers a salary of $ 210 per week plus 2% of the sales. How much would you have to
sell in a week in order for the straight commission offer to be at least as good?
Answer:
The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.
Step-by-step explanation:
.05x = .02x + 210 Subtract .02x from both sides.
.03x = 210 Divide both sides by .03
x = $7,000.
Find the surface area of the figure. For calculations involving π give both the exact value and an approximation to the nearest hundredth of a unit. Let r = 5 and h = 5
Answer:
100 pi = about 314.16
Step-by-step explanation:
the surface area of a cylinder: SA = 2πrh+2πr^2
we plug in the values of r and h, and get
SA = 50pi + 50pi = 100 pi, which is approximately 314.16
factor 18x^(2)+39x-15
Answer:
[tex]3(2x + 5)(3x - 1)[/tex]
Step-by-step explanation:
Hello!
We can first factor out the greatest common factor between the coefficients: 3.
[tex]f(x) = 18x^2 + 39x - 15[/tex][tex]f(x) = 3(6x^2 + 13x - 5)[/tex]Now, let's work with what we have inside the brackets.
Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]
Given our equation: [tex]6x^2 + 13x - 5[/tex]
a = 6b = 13c = -5We need to find two numbers that add up to b (13) and multiply to ac (-30).
The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.
Factor by Grouping[tex]6x^2 + 13x - 5[/tex][tex]6x^2 -2x + 15x - 5[/tex][tex]2x(3x- 1) +5(3x - 1)[/tex][tex](2x +5)(3x - 1)[/tex]
Now, we simply add the other factor, 3, to the final factored form.
Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]
A
C
Which choice correctly shows the line y
= -X?
NHH
1
-4-3-2-1 1 2 3 4
W23
-2
-3
31
2
1
#
B
D
31
21
2
1
-4-3-2-11 2 3 4
123
-2
The graph is shown in the attached image.
Which of the following sets of numbers could not represent the three sides of a triangle?
Answer:
Step-by-step explanation:
E and F are two events and that P(E)=0.2 and P(F/E)=0.6 what is P(E and F)
The probability of E and F expressed as P(E and F) equals;0.12
How to solve Conditional Probability?We are given;
P(E) = 0.2
P(F|E) = 0.6
Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)
Thus;
P(E and F) = 0.2 * 0.6
P(E and F) = 0.12
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_+_+_= 30
Use only
1,3,5,7,9,11,13,15
You can repeat it
Answer
1 possible solution:
(5x7) in the first blank
(-3!) in the second blank
(-1) in the third blank
Step-by-step explanation:
(5x7) + -(3!) + -(1) 3! equals 3x2x1 or 6
35 + (-6) + (-1)
Which expression is equivalent to √2+4?
OA. (2+4)²
OB. (2+4)²
OC. 6
D. 62
Write the equation of a parabola whose directrix is
y
=
−
1.5
y
=
-
1.5
and has a focus at
(
−
4
,
−
2.5
)
(
-
4
,
-
2.5
)
.
Answer:
y=0.5x²-4x-10.
Step-by-step explanation:
1) according to the definition of parabola:
d1=d2, then
[tex]2) \ |y+1.5|=\sqrt{(x+4)^2+(y+2.5)^2} ;[/tex]
3) after evolution:
-(2y+4)=(x+4)²; ⇔
[tex]y=-\frac{1}{2}x^2-4x-10.[/tex]
Find the equation of an ellipse satisfying the given conditions.
Foci: (-4, 0) and (4, 0); length of major axis: 14?
The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
How to determine the ellipse equation?The given parameters are:
Foci: (-4, 0) and (4, 0)Length of major axis = 14The above means that:
c = 4 and
The semi-major axis, a = 7 i.e 14/2
Calculate b using
[tex]b = \sqrt{c^2 + a^2[/tex]
So, we have:
[tex]b = \sqrt{4^2 + 7^2[/tex]
[tex]b = \sqrt{65[/tex]
Square both sides
[tex]b^2 = 65[/tex]
The standard form of the ellipse is represented as:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
This gives
[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]
Evaluate
[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
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Find all primes p, q such that p^2-p=37q^2-q
The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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PLEASE ANSWER PLEASE ANSWER
2. The spread of the Ebola virus in Africa in 2014 could be modeled by where C(1) represents the number of cases, and t represents the number of days since May 1, 2014). (source: http://www.geert.io/exponential-growth-of
ebola.html) a. [3 pts] Approximately how many cases were there on May 1, 2014 (round to two decimal places)?
b. [3 pts] How many cases were projected by November 24, 2014 (round to 2 decimal places)?
c. [4 pts] Find C(92) and explain what it means in the context of the problem.
(a) The number of cases on May 1, 2014, was approximately 188.59.
(b) The number of cases on November 24, 2014, was approximately 27107.76.
(c) C(92) = 1715.70.
This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.
Computed using the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
We are given that the spread of the Ebola virus in Africa in 2014 could be modeled by the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex], where C represents the number of cases and t represents the number of days since May 1, 2014.
(a) In the question, we are asked for the approximate number of cases on May 1, 2014.
Since, the date is May 1, 2014, t = 0.
Thus, the number of cases, C, can be calculated by putting t = 0, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(0) = 188.59e^{0.024*0}\\\Rightarrow C(0) = 188.59e^0\\\Rightarrow C(0) = 188.59[/tex]
Thus, the number of cases on May 1, 2014, was approximately 188.59.
(b) In the question, we are asked for the approximate number of cases on November 24, 2014.
Since, the date is November 24, 2014, t = 207.
Thus, the number of cases, C, can be calculated by putting t = 207, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(207) = 188.59e^{0.024*207}\\\Rightarrow C(207) = 188.59e^{4.968}\\\Rightarrow C(207) = 188.59*143.739121458\\\Rightarrow C(207) = 27107.76[/tex]
Thus, the number of cases on November 24, 2014, was approximately 27107.76.
(c) We are asked to find C(92).
This can be found by putting t = 92, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(92) = 188.59e^{0.024*92}\\\Rightarrow C(92) = 188.59e^{2.208}\\\Rightarrow C(92) = 188.59*9.09750317953\\\Rightarrow C(92) = 1715.70[/tex]
Thus, C(92) = 1715.70.
This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.
The complete question is:
"The spread of the Ebola virus in Africa in 2014 could be modeled by [tex]C(t) = 188.59e^{0.024t}[/tex] where C represents the number of cases and t represents the number of days since May 1, 2014. (source: http://www.geert.io/exponential-growth-of-ebola.html)
a. [3 pts] Approximately how many cases were there on May 1, 2014?
b. [3 pts] How many cases were projected by November 24, 2014?
c. [4 pts] Find C(92) and explain what it means in the context of the problem.
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20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5)
20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115
Answer:
The simplified form of the above expressions solution is -115.
Step-by-step explanation:
Hello!20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5).. given expression [tex] - 100 + 10( - 3) + ( - 5)( - 6) - 15 \\ - 100 - 30 + ( - 5)( - 6) - 15 \\ - 100 - 30 + 30 - 15 \\ - 130 + 30 - 15 \\ - 100 - 15 \\ - 115[/tex]Evaluate the following expression when y=2.
9y−8y+2
Answer:4
Step-by-step explanation: 9y-8y+2, when y=2
9(2)-8(2)+2=
18-16+2
=4
Please help ASAP! Clear explanations are greatly appreciated!
Using a system of equations, it is found that her normal week is of €285.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Her normal hours.Variable y: Her time and a half hours.The first equation, considering the first sentence, is given by:
x + 8y = 375.
The second equation, considering the second sentence, is given by:
x + 4y = 330.
Then the system is:
x + 8y = 375.x + 4y = 330.Multiplying the second equation by -2, the system is:
x + 8y = 375.-2x - 8y = -660.Adding the equations, we have that her normal week is given by:
x = 660 - 375 = €285.
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The function y=f(x)is graphed below. What is the average rate of change of the function f(x) on the interval 7≤x≤8?
Answer:
40
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 7, 8 ] , then
f(b) = f(8) = 20 ← point (8, 20 ) on graph
f(a) = f(7) = - 20 ← point (7, - 20 ) on graph
average rate of change = [tex]\frac{20-(-20)}{8-7}[/tex] = [tex]\frac{20+20}{1}[/tex] = 40
A jar of tickets for a drawing contains 22 winning tickets and 63 non-winning tickets. What are the odds against winning in the drawing? please help
Answer: 22/85
Step-by-step explanation:
Answer:
22/85
Step-by-step explanation:
1. Based on the circular
angle below. What is the
best measurement
the angle?
for
a. less than 90°
b. more than 90°
C. more than 180°
d. less than 60°
Answer:
B. More than 90
Step-by-step explanation:
Hope this helps!
Determine what type of model best fits the given situation:
Answer:
B. quadratic function graph
A school play sold 575 tickets total They were either adult or student tickets there were 75 fewer student tickets sold than adult tickets how many adult tickets were sold
Answer:
325 adult tickets
Step-by-step explanation:
Let adult tickets be x, student tickets are 75 less than adult tickets, so let student tickets be x-75
The total is 575
x+x-75 = 575
2x = 650
x = 325 adult tickets
WHICH LINE IS PERPENDICULAR TO THE LINE WITH EQUATION Y = -1/2X?
Answer:
y=-1/4x+3 is the answer.
Mark as brainlist pls pls pls pls pls pls pls pls!!!!!!!!!!
Evaluate 2-(-4)+(-y)2−(−4)+(−y)2, minus, left parenthesis, minus, 4, right parenthesis, plus, left parenthesis, minus, y, right parenthesis where y = 7y=7y, equals, 7.
(on khan academy)
The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108
Evaluation of ExpressionThe given expression is:
[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]
Simplifying the expression, we have:
[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]
Substitute y = 7 into the simplified expression
[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]
Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108
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Answer: -1
Step-by-step explanation: khan academy
Find the z-scores for the two normally distributed random variables, measured using different units of length.
a) x = 22 in, where X comes from N (15, 2.5)
b) y = 55.88 cm, where Y comes from N (38.1, 6.35)
Using the normal distribution, the z-scores are given as follows:
a) Z = 2.8.
b) Z = 2.8.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The parameters are:
[tex]\mu = 15, \sigma = 2.5[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 15}{2.5}[/tex]
Z = 2.8.
Item b:
The parameters are:
[tex]\mu = 38.1, \sigma = 6.35[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]
Z = 2.8.
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