Jermey subtracted the following rational expressions. his teacher told him that his answer was incorrect. explain jeremys error in the simplification process and provide the correct results.
2x^2-10\x-5 - x^2+15\x-5 = x^2+5\x-5
This is likely what Jeremy did
[tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2+15}{\text{x}-5}\\\\\frac{\text{x}^2+5}{\text{x}-5}\\\\[/tex]
The error happens in line 2
This is what his steps should be
[tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-(\text{x}^2+15)}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2-15}{\text{x}-5}\\\\\frac{\text{x}^2-25}{\text{x}-5}\\\\\frac{(\text{x}-5)(\text{x}+5)}{\text{x}-5}\\\\\text{x}+5[/tex]
On the 2nd step, we subtract all of (x^2+15) and not just the x^2 part. The negative distributes to each term in step 3. Then we combine like terms, factor and cancel out the (x-5) terms.
Therefore, [tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}=\text{x}+5[/tex] is an identity as long as [tex]\text{x} \ne 5[/tex] to avoid a division by zero error.
what is the equation of the line that passes through the point (-4,-3) and has a slope of -3/4
Answer:
Step-by-step explanation:
4. Jay measured the exterior angles in
this polygon. Explain how you know
his measurements are wrong.
80
80
60
75
70
Answer:
535 is not equal to 360
Step-by-step explanation:
the total interior angle = 360 degree
180-80=100
180-80=100
180-75=105
180-70=110
180-60=120
100+100+105+110+120= 535 which is not equal to 360. Since the total interior angle is not 360, Jay's measurements are wrong .
A T-shirt vendor sells yellow shirts and blue shirts at a ratio of 1: 4. What percent of the
shirts are yellow?
Answer:
25%
Step-by-step explanation:
1:4= 1/4
4×25= 100
1×25=25
25/100= 25%
(also 1/4 will always mean 25%)
x + 2y = 13
3x - 5y = 6
Step-by-step explanation:
Using Simultaneous Equation
Substitution method
Recall
x+2y=13. equ.1
3x-5y=6. equ.2
equ.1=
x-2y=13
x=13-2y. equ.3
Substitute 'x' into equ.2
3(13-2y)-5y=6
39-6y-5y=6
39-11y=6
collect like terms
39-6=11y
33/11=11y/11
therefore y=3
Substitute 'y' into equ.1, equ.2 or equ.3
Recall equ.3
x=13-2y
x=13-2(3)
x=13-6
therefore x=7
x=7, y=3
How do you verbally say:
m AB but the AB has a line over it?
Answer:
measure of line segment AB
please need help on this #3
Answer:
a. 5
b. 10
c. 15
d. 4
e. 6
f. 9
Step-by-step explanation:
It asks for the indicated distance, which would translate as the absolute value of the distance between the two points. Using that, it is simple subtraction to find your answer.
-4x(x-a) simplify and remove parenthesis
The simplification of the given expression 4x(x-a) is 4(-x²+a).
What are expressions?A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)So, -4x(x-a):
-4x(x-a)-4x² + 4xa4(-x² + a)Therefore, the simplification of the given expression is 4(-x²+a).
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write equations for the following statements
1)Three fourth of t is 15
2)If you add 3 to one third of 2,you get 30
3)One fourth of a number x minus 4 gives 4
Answer:
i'm not sure the second is right
The order states to give 0.75g of a medication. The label reads 50,000mcg /1ml. How many ml would you give to the client??
Answer: what the states says to
Step-by-step explanation:
Benicio locks his safe by setting
each of the three dials to 8. To unlock the safe, he turns
the left dial 90° counterclockwise, the middle dial
270° clockwise, and the right dial 180° counterclockwise.
Which three numbers, in order, unlock the safe?
The three numbers, in order that will unlock the safe are 2, 2, 4.
We know that there are 8 numbers on each dial. Suppose, The dial is in a shape of a circle. Now, we can divide it into 8 equal pieces with same angles.
For each piece, the angle formed is 360/8 = 45° ( As in a circle, total angle formed without any divisions is 360° )
Now, When we turn the left dial 90° counterclockwise ( anticlockwise)
that is 45° + 45° ( two times 45°). Therefore, the dial moves by two places and we get the first number = 6 ( from 8 to 7 and then from 7 to 6).
Now, We turn the middle dial 270° clockwise. And get 45° + 45° + 45° + 45° + 45° + 45° (six times 45°). Therefore, the dial moves by six places. Hence, we get the second number = 2.
Now, We turn the right dial 180° counterclockwise that is anticlockwise or in backward direction. 180° = 45° + 45° + 45° + 45° ( four times 45°). Therefore, the dial moves by six places and thus we get our third number = 4.
Therefore, The three numbers, in order that will unlock Benicio's safe are 2, 2, 4.
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Algebraic fraction equations
Solving question
Step-by-step explanation:
Please mark brainliest :)
Let A= { 10,11,12,13}
n(A)
The number of non-empty subsets of A
The given set A = {10, 11, 12, 13}, has the cardinal number n(A) = 4, and it has 15 non-empty subsets.
In the question, we are given a set A = {10, 11, 12, 13}.
We are asked for the cardinal number of the set n(A).
Also, we are asked for the number of non-empty subsets of A.
The cardinal number of any set A is given as n(A), which represents the number of elements in set A.
For the given set A = {10, 11, 12, 13}, the number of elements are 4.
Thus, the cardinal number of the set A is, n(A) = 4.
The number of non-empty subsets of any set A, with cardinal number n, is given by the formula, 2ⁿ - 1.
The given set A = {10, 11, 12, 13}, has the cardinal number n(A) = 4.
Thus, the number of non-empty subsets of set A = 2⁴ - 1 = 16 - 1 = 15.
Thus, the given set A = {10, 11, 12, 13}, has the cardinal number n(A) = 4, and it has 15 non-empty subsets.
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You invest $15,000 in two funds (stock A and stock B) paying 6.3% and 7.1%
simple interest respectively. The total annual interest is $1050. How much did
you invest in each fund?
a = amount invested at 6.3%
how much is 6.3% of "a"? (6.3/100) * "a", namely 0.063a.
b = amount invested at 7.1%
how much is 7.1% of "b"? (7.1/100) * "b", namely 0.071b.
we know the total amount invested is $15,000, so whatever "a" and "b" might be, we know that a + b = 15000.
we also know that the yielded amount in interest is $1050, so if we simply add their interest, that'd be 0.063a + 0.071b.
[tex]\begin{cases} a + b = 15000\\ b = 15000 - a\\[-0.5em] \hrulefill\\ 0.063a+0.071b=1050 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.063a+0.071(\underset{b}{15000-a})=1050}\implies 0.063a+1065-0.071a=1050 \\\\\\ 0.063a-0.071a=-15\implies -0.008a=-15\implies a=\cfrac{-15}{-0.008} \\\\\\ \boxed{a = 1875}\hspace{15em}\boxed{\stackrel{15000~~ - ~~1875}{b = 13125}}[/tex]
What is the purpose of a compass? Select all that apply.
*
It draws circles.
It is a handy hole punch.
It measures a set distance once locked in place.
It measures the degrees of an angle.
Find n(A) for the set A
Reason:
Your teacher wants you to find out how many elements are in set A.
Focus on the numerators only.
That sequence is 1,2,3,..., 37,38 which consists of 38 numbers.
If you wanted to focus on the denominators, then we go from 3 to 40 which is a gap of 40-3 = 37, but then add on 1 to account for the first item. So we get to 37+1 = 38.
Solve for x using the image below:
Answer:
x=-14
Step-by-step explanation:
7x+156=9x+184
2x=-28
x=-14
Find the volume of a rectangular prism if the length is 4x, the width is 5x, and the height is x2 + x + 2. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
Group of answer choices
20x3 + 20x2 + 40x
20x4 + 20x3 + 40x2
20x4 + x + 29
20x4 + 9x3 + 18x2
Answer:
2D
Step-by-step explanation:
i times two is 5
Can someone help me with this question? It's due tomorrow :(
Answer: Angle B = 32deg, Angle D = 43deg, and Angle F = 105deg
Step-by-step explanation:
Angle B = Angle C, Angle D is on a line = to 180 deg, the line is intercepted into a 137deg portion, and a 43deg portion, all angles in a triangle add up to 180, so 32+43=75, 180-75=105 (Angle F)
Please let me know if this helped!
HELP PLEASE!!!!!!!
Find the measurement of the angle indicated for each trapezoid.
The required measure of the angle of the trapezoid is 50° and 101°.
The angle can be defined as the one line inclined over another line.
Where angle measures in degree and radian.
Here,
For trapezoid one 1.
The Sum of the adjacent angle is 180°.
So, 130 + ∠C = 180
∠C = 180 - 130
∠C = 50
For trapezoid 2.
Sum of all the angle should be equal to 360°
but ∠Q = ∠S
110 + 48 + 2∠Q = 360
∠Q = 101°
Thus, the required measure of the angle of the trapezoid is 50° and 101°.
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The greatest amount of rainfull is time as great as the least amount of rainfull
Answer:
16 times
Step-by-step explanation:
The question is asking :
what number multiplied by the least amount would give me the greatest amount?? Let that number be x, so we can say:
least amount * x = greatest amount
From the plot, we can see that the least amount is 1/8 inches
The greatest amount is 2 inches now we can put it into the formula and find x:
1/8 * x = 2
x = 2/(1/8)
x = 16
Evaluate -4a² + 2a - 1 when a = - 3.
Answer:
-43
Step-by-step explanation:
-4(-3)² + 2(-3) - 1
=-4×9+2(-3)-1
=-36+2(-3)-1
=-36-6-1
=-43
Solve using long division (6x^3-8x+5) ÷ (2x-4)
The solution to the long division 6x³ - 8x + 5 divided by (2x-4) is 3x² - 6x + 8 and the remainder is -27
The long divisionWhen 6x³ - 8x + 5 is divided by (2x-4) the answer in this format
q(x) + r(x) / b(x) is express as 3x² - 6x + 8
The long division application is uploaded as a picture below.
The answer should be express in this format:
q(x) + r(x) / b(x)
where,
q(x) = quotientr(x) = remainderb(x) = divisorThe quotient is the result obtained by dividing one value by another. The quotient is 3x² - 6x + 8 .
The remainder is the number left over after performing the division. The remainder is -27
The divisor is the value that divides another completely or with a remainder. The divisor is 2x - 4
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How many baseball cards did he start with?
Answer:
108
Step-by-step explanation:
22+86=108
Answer:
108 baseball cards
Step-by-step explanation:
x = baseball cards he started with
x - 22 = 86
add 22 to both sides
x = 108
108 baseball cards
Question Find the distance between the points A(13, 2) and B(7, 10)?
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{13}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{10})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~7 - 13~~)^2 + (~~10 - 2~~)^2} \implies AB=\sqrt{( -6 )^2 + ( 8 )^2} \\\\\\ AB=\sqrt{ 36 + 64 } \implies AB=\sqrt{ 100 }\implies AB=10[/tex]
Question 10a
Fred and Nancy had dinner at a French restaurant. The cost of all their food, without
tax, was $62. The meal tax imposed by the state is 0.06 times the bill. How much was
the total bill, including tax?
Answer:65.72
Step-by-step explanation: first you multiply 62 x 0.06 which is 3.72 and you add 3.72 to 62 which is 65.72
Tickets of a program at college cost $5 for general admission or $4 with a student ID. If 180 people paid to see a performance and $795 was collected, how many of each type of ticket were sold?
The number of tickets for general admission is 75 and with student id's is 105.
Given that,
Tickets of a program at college cost $5 for general admission or $4 with a student ID.
180 people paid to see a performance and $795 was collected, how many of each type of ticket were sold is to be determined.
Here,
Number of admission with general admission = x
Number of admission with college id = y
According to the given conditions,
x + y = 180
x = 180 - y - - - - - - (1)
5x + 4y = 795 - - - - - (2)
Now put the value of the equation in equation 2
5 (180 - y) + 4y = 795
900 - 5y + 4y = 795
-y = 795 - 900
-y = -105
y = 105
Now put y in equation 1
x = 180 - 105
x = 75
Thus, the number for tickets with general admission is 75 and with student id is 105.
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A dairy needs 378 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 4% butterfat must be used to obtain the desired 378 gallons?
We need 251.33 gallons of the milk with 7% butterfat and 126.67 gallons of the milk with 4% butterfat to make the desire 378 gallons.
Given,
The amount of milk needed in the dairy = 378 gallons
The quantity of butterfat needed in the milk = 6%
We have to find the amount of milk containing 7% and 4% butterfat used to obtain 378 gallons:
Now,
The amount of milk containing 7% butterfat = x gallons.
The amount of milk containing 4% butterfat = y gallons.
Now, we can have the equation as:
x + y = 378
Percentage of butterfat needed = 6%
0.07x + 0.04y = 0.06 x 378
0.07x + 0.04y = 22.68
Solve for x and y :
x + y = 378 ---------------------- (1)
0.07x + 0.04y = 22.68 -------------- (2)
From Equation (1) :
x + y = 378
x = 378 - y ------------------ Substitute into (2)
0.07(378 - y) + 0.04y = 22.68
26.48 - 0.7y + 0.04y = 22.68
26.48 - 0.03y = 22.68
26.48 - 22.68 = 0.03y
3.8 = 0.03y
y = 3.8 / 0.03
y = 126.67 ---- sub into (1)
x + y = 378
x + 126.67 = 378
x = 378 - 126.67
x = 251.33
Therefore,
Amount of milk containing 7% butterfat = x = 251.33 gallons
Amount of milk containing 4% butterfat = y = 126.67 gallons.
That is,
We need 251.33 gallons of the milk with 7% butterfat and 126.67 gallons of the milk with 4% butterfat to make the desire 378 gallons.
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Which of the following values are in the domain of the function graphed
below? Check all that apply.
Answer:
B
Step-by-step explanation:
The domain of a graph is its turning point
PLS HELP will give Brainlist
Answer:
J: (-4,5)
K: (-4,4)
L: (-5,4)
K: (-6,6)
Step-by-step explanation:
