Susie and Amelia solved the same equation using two separate methods. Their work is shown in the table below:
Answers
Answer:
(C)
Step-by-step explanation:
Explanation of Susie's method:
The given equation is:
[tex]2x-3=4x-2[/tex]
[tex]2x-2x-3=4x-2x-2[/tex]
[tex]-3=2x-2[/tex]
[tex]-3+2=2x[/tex] ( she made a mistake when she subtracted 2)
[tex]-1=2x[/tex]
[tex]x=-\frac{1}{2}[/tex]
Susie made a mistake in step 4 when she subtracted 2,
Thus, option C is correct.
Related Questions
How many liters of wine can be held in a wine barrel whose capacity is 28.0 gal? 1 gal = 4 qt = 3.7854 l?
Answers
given that:
1 gal=4 qt=3.7854 l
then:
28 gal will be equivalent to the following number of liters;
28/1*3.7854
=105.9912 l
thus the number of liters of wine that can be held in a wine barrel is 105.99 l
Answer:
105.9912 liters of wine can be held in a wine barrel whose capacity is 28.0 gal.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
Let x be the liters of wine can be held in a wine barrel whose capacity is 28.0 gal.
Given that:
1 gal = 3.7854 l
then
by definition of proportions;
[tex]\frac{1}{3.7854} =\frac{28}{x}[/tex]
By cross multiply we get;
[tex]x = 28 \times 3.7854 = 105.9912[/tex] liters
Therefore, 105.9912 liters of wine can be held in a wine barrel whose capacity is 28.0 gal.
the volume of a square pyramid with height 2.4cm is 3.2cm. what is the width of the base of the pyramid?
Answers
Rewrite each of the following linear equation in equivalent y=mx+b
what's the slope and the y-intercept
HELP ME PLZZ
Answers
2y-3x=10 add 3x to both sides
2y=3x+10 divide both sides by 2
y=1.5x+5, since y=mx+b, m=slope and b=y-intercept
slope=1.5 and the y-intercept is, technically the point, (0, 5)
In a programming team of 20 persons, 1/4 are women and 3/4 are men. to obtain a team with 40% women, how many women should be hired?
Answers
To obtain a team with 40% women in a programming team of 20 people, we need to find out how many women should be hired. Currently, there are 5 women in the team (1/4 of 20). By setting up an equation and solving for x, we find that 5 women should be hired.
Explanation:To obtain a team with 40% women in a programming team of 20 people, we need to find out how many women should be hired. We know that currently 1/4 of the team are women, which means there are 5 women in the team (20 * 1/4 = 5). To find out how many women should be hired, we subtract the number of women in the team from the target number of women in the team:
Number of women to be hired = Target number of women - Current number of women
Number of women to be hired = 0.4 * (20 + x) - 5
Where x is the number of women to be hired. Now we can solve for x:
0.4 * (20 + x) - 5 = x
Distribute and simplify:
8 + 0.4x - 5 = x
Combine like terms:
0.4x - x = 5 - 8
0.6x = 3
Divide both sides by 0.6:
x = 3 / 0.6
x = 5
So, 5 women should be hired to obtain a team with 40% women.
Which graph represents the function f(x) = (x – 5)2 + 3?
Answers
if H(x)=4x-8 and j(x) = -x solve h{j(3)}
Answers
-------------------------------------
j(x) = -x
j(3) = -3 ... replace every x with 3
h(x) = 4x - 8
h(j(3)) = 4*( j(3) ) - 8 ... replace every x with j(3)
h(j(3)) = 4*(-3) - 8 ... replace the j(3) on the right side with -3
h(j(3)) = -12 - 8
h(j(3)) = -20
Write the interval (3,20] as an inequality and using set notation
Answers
A job is shared by 4 workers, w, x, y, and z. worker w does 1/4 of the total hours. worker x does 1/3 of the total hours. worker y does 1/6 of the total hours. what fraction represents the remaining hours allocated to person z?
Answers
answer is : 1/4 hrs was allocated to worker z
A cone-shaped hat is shown:
A cone is shown with slant height 18 cm and radius 5.7 cm. The unknown height is labeled with a question mark, and the line joining the tip of the cone to the base is perpendicular to the base.
What is the approximate height of the hat?
3.51 centimeters, because height = Square root of the difference of 18 and 5.7
17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7
18.88 centimeters, because height = Square root of the sum of the squares of 18 and 5.7
4.87 centimeters, because height = Square root of the sum of 18 and 5.7
Answers
h^2=x^2+y^2
18^2=5.7^2+y^2
y^2=18^2-5.7^2
y^2=291.51
y=√291.51
y≈17.07
It's the second explanation down...
Answer:
B. 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.
Step-by-step explanation:
The formula of height (h) of a cone is: [tex]h=\sqrt{l^2-r^2}[/tex], where,
[tex]l[/tex] = Slant height of cone,
[tex]r[/tex] = Radius of cone.
Upon substituting slant height = 18 cm and radius = 5.7 cm, we will get,
[tex]h=\sqrt{(18)^2-(5.7)^2}[/tex]
[tex]h=\sqrt{324-32.49}[/tex]
[tex]h=\sqrt{291.51}[/tex]
[tex]h=17.0736639301586348\approx 17.07[/tex]
Therefore, the height of cone is 17.07 cm and option B is the correct choice.
Mary creates a table of values for a function and plots the points. She finds that the difference in the y values is the same. What kind of function did she graph? linear quadratic square root exponential
Answers
Answer:
A
Step-by-step explanation:
Which of the following equations has only one solution?
x2 + 4x + 4 = 0
x2 + x = 0
x2 - 1 = 0
Answers
(x+2)^2 = 0
x+2 = 0
x = -2
answer
this one has only one solution
1) x = {-2}
2) x = {0, -1}
3) x = {1, -1}
The first one only has one solution
five friends go out to lunch and they decide to split the bill evenly the bill comes out to 57.25 how much does each person owe?
Answers
True or false X=4 for both 1. 3x+10-(5+3)=14 2. 3x+10(3x-2)=60
Answers
For the first equation,
3x+10-(5+3)=14
Every time we see an X, we need to place a 4 in its place.
3(4)+10-(5+3)=14
Using the order of operations, PEMDAS, we start to solve the equation.
3(4)+10-(5+3)=14
12 + 10 - (5+3) = 14
12 + 10 - (8) = 14
12 + 10 - 8 = 14
22 - 8 = 14
14 = 14
TRUE.
For the first equation, x does indeed equal 4.
However, we still need to see if x equals 4 for BOTH of the equations.
3x+10(3x-2)=60
3(4) + 10(3(4)-2) = 60
12 + 100 = 60
112 = 60
This isn't true.
To conclude, the answer is false. X doesn't equal 4 for both of the equations provided.
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Which value of k would cause the system of linear equations 35x+14y=119 and 5x+2y=k to have an infinite number of solutions?
Answers
The value of k in the equation is k = 17 and the equation 5x + 2y = 17 and
5x + 14y = 119 has infinite number of solutions
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 first equation be represented as A
Now , the value of A is
35x + 114y = 119 be equation (1)
Let the second equation be represented as B
Now , the value of B is
5x + 2y = k
For the system of equations to have infinite number of solutions ,
equation (1) = equation (2)
So , 5x + 2y = 35x + 114y
And , 7 ( 5x + 2y ) = 35x + 114y
So , the value of k = 119/7
On simplifying the equation , we get
k = 17
Therefore , the value of k is 17
Hence , the value of k from the equation is k = 17
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If the diagonals of a quadrilateral do not bisect each other then the quadrilateral could be a
Answers
The diagonals of a quadrilateral do not bisect each other then the quadrilateral could be a scalene trapezoid
What is a trapezoid?
The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
For a scalene trapezoid ,
The four sides are of unequal length
The angles of the scalene trapezoid are not equal
The shortest distance between two parallel sides is known as the altitude
The sides of the scalene trapezoid does not bisect each other
Hence , the diagonal is a scalene trapezoid
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1. In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
If PX = 20, find PQ
Answers
Since C is the centroid, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40
Write each whole number using words.
a) 325
b) 9,542,006
Answers
b) nine million five hundred forty-two thousand and six
We can show that triangle abc is congruent to triangle a prime b prime c prime by translation of
Answers
Final answer:
To show congruence by translation, we need to show that corresponding sides and angles of the triangles are equal.
Explanation:
To show that triangle ABC is congruent to triangle A' B' C' by translation, we need to show that they have the same shape and size.
Translation is a transformation that moves every point of a figure the same distance in the same direction. Therefore, to show congruence by translation, we need to show that the corresponding sides and angles of the two triangles are equal.
For example, if we have AB || A'B' and AB = A'B', BC || B'C' and BC = B'C', and AC || A'C' and AC = A'C', then we can conclude that triangle ABC is congruent to triangle A' B' C' by translation.
Line GJ is tangent to point A at point G.
What is m∠AGJ?
Answers
hope it helps
АG is a radius
A tangent line to a circle is perpendicular to the radius drawn to the tangent point ⇒ m∠АGJ = 90°
Darren drank 2 liters of water.How much millilliters of water did he drank
Answers
2 X 1,000 = 2,000 ML
2,000 milliliter is your answer
Assume that y varies inversely with x. If y=12 when x=5, find y when x=3
Answers
Since when y = 12 x = 5, then c = 12*5 = 60
So xy = 60
Now when x = 3, y = 60/3 = 20
When y varies inversely with x, they follow the rule y = k/x. If y=12 when x=5, the constant 'k' is found to be 60. Using this constant, when x=3, y is found to be 20.
Explanation:In mathematics, when we say that y varies inversely with x, it means that as x increases, y decreases proportionally, and vice-versa. Y and x follow the rule y = k/x, where k is a constant number.
Given that y = 12 when x = 5, we can find the constant by multiplying x and y together, so: k = x * y = 12 * 5 = 60.
Now that we have our constant, we can find y when x = 3 by rearranging the formula to y = k / x which gives us: y = 60 / 3 = 20. So, when x is 3, y is 20.
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What is the equation of the blue graph?
Answers
since the blue graph is 2 lines to the left of the red graph, that would mean it moved -2
so the equation needs to include -2
the correct answer is C
a rectangular school gym has a length of x+24 and a width of x-10. Which measure does (x+24)(x-10) represent?
Answers
l x w = area
(x+24)(x-10) means (x+24) *(x-10) which is to calculate the area
Answer: The measure (x+24)(x-10) represents the AREA of the rectangular school gym.
Step-by-step explanation: Given that a rectangular school gym has a length of (x+24) and a width of (x-10).
We are to find the measure that (x+24)(x-10) represent.
The expression (x+24)(x-10) is the product of the length and breadth of the given rectangular school gym.
Also, we know that
the product of the length and breadth of any rectangle is equal to the area of that rectangle.
Therefore, the measure (x+24)(x-10) represents the AREA of the rectangular school gym.
Order of operations? How to do?
Thanks
Answers
parenthesis first (8+5) = 13
35/5 = 7
13x7 +6
13x 7 = 91 +6 = 97
The following table shows the data collected from 4 random samples of 50 students from a small middle school regarding the type of television shows they prefer to watch:
Television Show Preferences
Sample News Music Movies Cartoons Total
1 2 12 6 30 50
2 3 10 5 32 50
3 5 13 7 25 50
4 6 19 8 17 50
Based on the results in the table, which type of television show is preferred by the majority of students in the samples?
News
Music
Movies
Cartoons
Answers
If we add up the numbers
Number who prefer cartoons = 30+32+25+17 = 104 out of 200
Television show preferred by the majority of students in the samples is Cartoon
What is majority ?Majority is More than half or just the larger part.
What is addition?The addition of two whole numbers results in the total amount or sum of those values combined
Total number of students= 50+50+50+50 =200 students
Total number of student who prefer news =2+3+5+6=16 students
Total number of student who prefer music = 12+10+13+19 = 54 students
Total number of student who prefer movies = 6+5+7+8 = 26 students
Total number of student who prefer cartoon = 30+32+25+17 = 104 students
Hence, television show preferred by the majority of student in the samples is Cartoon
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Given 2 events a and b, and that p(a)=0.30, p(b)=0.45, p(a u b)=0.60. find the probability p(a∩b).
Answers
<=>
p(a ∩ b) = p(a) + p(b) - p(a U b)
I let you do the maths :)
Solve log 6 60 - log 6 30
A.) 2
B.) log 6 2
C.) 5
D.) log 6 30
Answers
Using that formula we get:
[tex]log_6(60) - log_6(30) = log_6(2)[/tex]
so B is your answer :)
If it rained on 3 days out of 20 days,on what percent of the days did it rain
Answers
3/20 = 0.15
Move the decimal two points to the right to get the percent.
It rained 15% of the days.
A garden has 8 white roses and 11 red roses. One rose is plucked from the garden and then one more rose is plucked without replacement let the event w=plucking a white rose for the first time and event r=plucking a red rose for the second time in two or more complete sentences explain the meaning of probabilities p(r/w) and p(w/r) do they have the same value
Answers
P(w/r) is the probability of picking a white rose at first picking and a red rose at second picking.
P(r/w) = [tex] \frac{11}{19} [/tex]×[tex] \frac{8}{18} [/tex] = [tex] \frac{88}{342} [/tex]
P(w/r) = [tex] \frac{8}{19} [/tex]×[tex] \frac{11}{18} [/tex]=[tex] \frac{88}{342} [/tex]
Notice that the second fraction is out of 18 because the second picking of rose will be out of 18 since the first rose is not replaced.
P(r/w) equals to P(w/r)
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The volume of a sphere is found using the formula V=4/3nr^3. The area of a circle is found using the formula A=nr^2. What is the ratio of the volume to the area?
A.
4/3r
B.
4/3r^5
C.
3/4r
D.
4/3nr
Answers
- Your welcome