The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
x/2 = y/3 ..... equation (A)y/3 = z/4 .... equation (B)x/2 = z/4 .... equation (C)We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
---------------------
The key takeaway from the last section is that
z = 2xy = 1.5xLet's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
inverse of
f(x)=6x+5
Asap?
Robert wrote two patterns. Pattern 1 started at 2 and followed the rule "add 4." Pattern 2 started at 1 and followed the rule "add 3." Pattern 1 is represented by x-coordinates, and Pattern 2 is represented by y-coordinates. Which table shows the ordered pairs for these two patterns?
X Y
1 2
4 6
8 10
12 14
X Y
2 1
6 4
10 7
14 10
X Y
1 2
2 6
3 10
4 14
X Y
2 1
4 4
6 7
8 10
Answer:
the 2nd one lol
Step-by-step explanation:
Answer:
number 2ᕙ(＠°▽°＠)ᕗStep-by-step explanation:
PLEASE HELP ME!!!
Maggie's brother is 7 years younger than four times her age. The sum of their ages is 68.
How old is Maggie?
=============================================
Explanation:
m = Maggie's age (some positive whole number)
4m = four times her age
4m-7 = seven years younger than 4m = brother's age
Add up her age (m) and her brother's age (4m-7) to get a sum of 68.
m+(4m-7) = 68
5m-7 = 68
5m = 68+7
5m = 75
m = 75/5
m = 15
Maggie is currently 15 years old.
Her brother is currently 4m-7 = 4*15-7 = 60-7 = 53 years old.
Their current year ages add to: 15+53 = 68 which confirms the answer.
Which expression is equivalent to 3 2 times 3-5 ?
Answer:
A)
Step-by-step explanation:
A tram moved downward 9 meters per second for 54 seconds. What was the total change in the tram's elevation?
Answer:
6
Step-by-step explanation:
Answer:
-486
Step-by-step explanation:
determine whatever ABCD is a parallelogram by using the midpoint formula.
A(3,3) B (1.2) C(-3.1) D (-1.4)
Answer:
Not a parallelogram.
Step-by-step explanation:
By the midpoint formula, the midpoint of a segment between [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] is:
[tex]\begin{aligned} \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)\end{aligned}[/tex].
A quadrilateral is a parallelogram if and only if the midpoints of the two diagonals are the same.
The two diagonals of quadrilateral [tex]{\sf ABCD}[/tex] are segment [tex]\sf{AC}[/tex] and segment [tex]{\sf BD}[/tex], respectively.
Using the midpoint formula, the midpoint of segment [tex]{\sf AC}[/tex] (between [tex]{\sf A}\; (3,\, 3)[/tex] and [tex]{\sf C}\; (-3,\, 1)[/tex]) would be:
[tex]\begin{aligned} & \left(\frac{3 + (-3)}{2},\, \frac{3 + 1}{2}\right) \\ =\; & (0,\, 2)\end{aligned}[/tex].
Likewise, the midpoint of segment [tex]{\sf BD}[/tex] (between [tex]{\sf B}\; (1,\, 2)[/tex] and [tex]{\sf D}\; (-1,\, 4)[/tex] would be [tex](0,\, 3)[/tex].
Thus, quadrilateral [tex]{\sf ABCD}[/tex] would not be a parallelogram since the midpoints of its two diagonals are not the same.
a student answered 86% of the questions on a test correctly. he received a grade of 98%. how many questions were on the test?
Let the number of questions on the test equal X which would be 100%
They answered 86 which equaled 98
Set up a ratio:
X/86 = 100/98
Cross multiply:
98X = 8600
Divide both sides by 98:
X = 87.75
Round to 87 questions
Need all answers a lot of points
help help help help help help help help
Answer:
necklace
Step-by-step explanation:
It is the only one with a negative elevation
3 In AABC, 2C = 90°, then which of the following is true? a) ABP = BCP + AC b) AC2 = AB? + BC2 c) BC2 = AB? + ACP d) AC = AB + BC
Answer:
a bit hard q
Step-by-step explanation:
becoz i am not good at algebra
You went 160 miles in 20 hours. What is the constant of proportionality that relates the y, the distance in miles to x, the time in hours?
Answer:
X = Y times 8
Step-by-step explanation:
You need to figure out how many miles you can go in an hour.
160/x and 20/1
20x=160
x=8
You can go 8 miles in 1 hour.
Therefore, if X is 1 and Y is 1
1 = 8
1 hour equals 8 miles
6 O
Which function is graphed on the coordinate plane below?
Ty
x
f(x) = 2x - 6
Of(x) = 2x + 6
f(x) = -2x + 6
Mark this and retum
Save and Exit
Next
Submit
Step-by-step explanation:
we don't see all possible answer options.
but it does not matter.
the line is clearly
y = 2x - 6
why ?
the slope is always the factor of x.
and the slope is defined as ratio of "y coordinate change / x coordinate change".
and we can clearly see, for every change in x by +1, y changes by +2. zu, the slope is 2/1 = 2.
and when x = 0, the graph shows us the y-intercept with y = -6.
hence the above mentioned equation.
The Function is graphed on the coordinate plane is y= 2x- 6.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have points from the graph as (3, 0) and (0, -6).
So, the slope of line is
slope= (-6 -0)/ (0-3)
slope = -6/ (-3)
slope= 2
Now, using the slope intercept form
y= mx + b
y= 2x + b
Now, put x= 3 and y= 0 we get
0= 6 + b
b = -6
So, the required function is
y= 2x - 6.
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help please! a is wrong, that was my initial answer.
Answer:
D -1
Step-by-step explanation:
[tex]-6(3a+4)=3a-3[/tex]
[tex]-18a-24=3a-3[/tex]
[tex]-18a-3a=-3+24[/tex]
[tex]-21a=21[/tex]
a = [tex]\frac{21}{-21} =-1[/tex]
Hope this helps
A rectangular garden has a length of 3x + 13 feet and a width of 3x feet. Which expression represents the
area of the garden in square feet?
Answer:
40
Step-by-step explanation:
so it is 3X3 +13 =40
amanda is 25 years old. in 5 years she will be twice as old as simone how old i simone
Find x- and y-intercepts of 4x + 2y = 10
Answer:
Below is the graph
Hope This Helps!!!
Answer:
( 5/2 , 0 ) x- intercept , ( 0 , 5 ) y- intercept
Step-by-step explanation:
To find x- intercept , set y = 0
4x + 2(0) = 10
x = 5/2
To find y- intercept , set x = 0
4(0) + 2y = 10
y = 5
how to find the perimeter of a triangle with vertices
Answer:
P = A + B + C
Step-by-step explanation:
Essentially, just add the length of each side. The sum is the perimeter.
Hit brainliest if this was helpful :)
add each side
hope ithelps you
Work out the difference between 38.3 and 1.72
Answer:
36.58
Step-by-step explanation:
38.3-1.72=36.58
The value of the expression 38.3 - 1.72 will be 36.58.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The numbers are given below.
38.3 and 1.72
Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have
⇒ 38.3 - 1.72
⇒ 36.58
The value of the expression 38.3 - 1.72 will be 36.58.
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Find the value of x.
Answer:
x = 12
Step-by-step explanation:
Angle Bisector Theorem: PS / PQ = RS / QR
24/14 = x/7
cross-multiply:
14x = 168
x = 12
Calculate the average travel time for each distance, and then use the results to calculate. A 6-column table with 3 rows in the second, third, and fifth columns and 1 row in the other columns. The first column labeled Number of Washers has entry 1 washer mass = 4. 9 grams. The second column labeled Trial has entries trial number 1, trial number 2, trial number 3. The third and fourth columns labeled Time to travel 0. 25 meters t subscript 1 (seconds) have entries in the third column 2. 24, 2. 21, 2. 23 and average in the fourth column. The fifth and sixth columns labeled time to travel 0. 5 meters t subscript 2 (seconds) have entries in the fifth column 3. 16, 3. 08, 03. 15 and in the sixth column average. The average time that it takes for the car to travel the first 0. 25m is s. The average time to travel just between 0. 25 m and 0. 50 m is s. Given the time taken to travel the second 0. 25 m section, the velocity would be m/s.
The average travel time is simply the mean travel time between the given points
The average time that it takes for the car to travel the first 0.25m is 2.23s. The average time to travel just between 0.25m and 0.50m is 0.9s. Given the time taken to travel the second 0.25 m section, the velocity would be 0.28m/s.(a) The average time to travel the first 0.25m
The time travel in the first 0.25m are: 2.24s, 2.21s and 2.23s.
So, the average time to travel is:
[tex]Time = \frac{2.24s + 2.21s + 2.23s}{3}[/tex]
[tex]Time = \frac{6.68s}{3}[/tex]
[tex]Time = 2.23s[/tex]
(b) The average time to travel just between 0.25m and 0.50m
The time travel in the 0.50m are: 3.16s, 3.08s and 3.15s.
So, the average time to travel this distance is:
[tex]Time = \frac{3.16s + 3.08s + 3.15s}{3}[/tex]
[tex]Time = \frac{9.39s}{3}[/tex]
[tex]Time = 3.13s[/tex]
The average time to travel between both distance is the difference between the average time of each distance.
So, we have:
[tex]Average = 3.13s - 2.23s[/tex]
[tex]Average = 0.9s[/tex]
(c) The velocity in the second 0.25m section
The distance and time are:
[tex]Distance = 0.25m[/tex]
[tex]Time = 0.9s[/tex]
So, the velocity is:
[tex]Velocity = \frac{Distance}{Time}[/tex]
This gives
[tex]Velocity = \frac{0.25m}{0.9s}[/tex]
[tex]Velocity = 0.28m/s[/tex]
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find x and y for this triangle
Answer:
x = 1.25
x = 1.75
Step-by-step explanation:
I marked the points of this triangle in the attached image so it's easier to explain.
ΔABC is similar to ΔADE, and all pairs of corresponding sides are proportional as a result.
[tex]\frac{DE}{BC}=\frac{AD}{AB}=\frac{AE}{AC}[/tex]
The length of the sides BC and DE is given, so I'll start with that and set it equal to the proportion between AB and AD.
[tex]\frac{DE}{BC}=\frac{AD}{AB}\\\\\frac{10}{8}=\frac{x+5}{5}\\\\10\times5=(x+5)\times8\\50=8x+40\\10=8x\\x=1.25[/tex]
Now, you can do the exact same thing for y:
[tex]\frac{DE}{BC}=\frac{AE}{AC}\\\\\frac{10}{8}=\frac{y+7}{7}\\\\10\times7=(y+7)\times8\\70=8y+56\\14=8y\\y=1.75[/tex]
A cyclist travels 4 miles in 20 minutes and then a further 6 miles in 30 minutes without stopping. Calculate the cyclist's average speed in mph.
Answer:
24mph
Step-by-step explanation:
convert 20 mins and 30 mins to hrs by dividing by 60
4/(20/60)=12
6/(30/60)=12
12+12=24
Cyclist's average speed is 12 mph.
What is Speed?Speed is calculated as the ratio of the distance travelled by an object to the time taken to cover the distance.
It can also be defined as the rate of change of position of anything in any direction.
Speed is a scalar quantity as it does not have direction.
Total distance travelled by the cyclist = 4 miles + 6 miles
= 10 miles
Total time taken by the cyclist = 20 minutes + 30 minutes
= 50 minutes
We need the average speed in mph or miles per hour.
We know that,
60 minutes = 1 hour
1 minute = 1/60 hour
50 minutes = [tex]\frac{1}{60}[/tex] × 50 hour
= [tex]\frac{5}{6}[/tex] hour
Average Speed = Total distance travelled / Total time taken
= 10 miles / (5/6) hour
= 10 × [tex]\frac{6}{5}[/tex]
= 12 miles per hour
Hence the average speed of the cyclist is 12 miles per hour.
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The map shows two walking trails in a park. Both paths end at the picnic area, located at C(6, 1). Trail A starts at A(−6, 6), and Trail B starts at B(−10, −11). If each unit on the map represents 0.5 mile, how many miles longer is Trail B than Trail A?
Answer:
12 miles
Step-by-step explanation:
because of slope
3. You miss a free throw 3/10 of the time
A) likely
B) unlikely
C) certain
D) equally likely
You miss a free throw 3/10 of the time is unlikely event. Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, miss a free throw 3/10 of the time.
Here, 3/10 =0.3
The total probability is always equal to unity.
If the event is “certain” to happen, the probability will be 1.
If the event is “likely” to happen, the probability will be between 1/2 and 1.
If the event has an “equal chance” to happen or not, the probability will be 1/2.
If the event is “unlikely” to happen, the probability will be between 0 and 1/2.
You miss a free throw 3/10 of the time is unlikely event.
Therefore, option B is the correct answer.
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Write the equation of the line that passes through the point -3,4 and slope of 6
A store sells hardcover books for $8 and paperback books for $5. You buy 7 books, represented by the equation x + y = 7, where x is the number of hardcover books and y is the number of paperback books. The equation 8x + 5y = 41 represents the total cost. How many of each type of book did you buy?
Answer:
Total number of Hardcover books is TWO while the number of Paperback books is FIVE
Step-by-step explanation:
No. of hardcover book = x
No. of paperback book = y
Cost of one hardcover book = $8
Cost of one paperback book = $5 We are given that:
x+y=7 (Equation 1)
8x+5y=41 (Equation 2)
We can find out value of x and y by solving both equations simultaneously.
Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE
Step-by-step explanation:
P l e a s e NO LINKS!
Which word has reflectional symmetry across a horizontal line?
A. BOOK
B. LOOK
C. NOOK
D. ROOK
Answer:
A BOOK
Step-by-step explanation:
pretty sure its that
The word BOOK shows a reflection symmetry across a horizontal line.
Hence, option (A) is correct.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Solve with the help of options,
(A)
BOOK
To find the reflection across a horizontal line,
When word B reflected over horizontal line, it is symmetrical
Word O is symmetrical.
And K is also symmetrical across a horizontal line.
Therefore, BOOK is a reflection symmetry across a horizontal line.
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The graph of y = f(x) is the solid black graph below. Which function represents the
dotted graph?
Submit Answer
O y = f(x + 3) - 5
O y = f(x - 3) - 5
O y = f(x - 3) + 5
O y = f(x + 3) + 5
Answer:First option, y=f(x+3)+5
Step-by-step explanation:
analyse the transformation first
From the dotted function, when compared to the solid black line, is moved 3 units to the left, and moved upwards by 5 unitsInput transformation
In graphing, when a value is shifted horizontally, its transformation is equal to: -(x2-x1), and in this instance, we end up with a value of +3so, f(x+3) is the first componentWhen a function is shifted horizontally, it is proportiante to the distance it moves, so (y2-y1)in this instance, it is 0 - -5=5so the transformation vertically is +5Final answer, when all values are added is y=f(x+3)+5
(-r-5)-(-2r-4) help me solve pls lol
[tex]r - 1[/tex]
Step by step explanation: Step 1: Distribute[tex]( - r - 5) - ( - 2r - 4) \\ ( - r - 5) + 2r + 4[/tex]
Step 2: Eliminate redundant parenthesis[tex]( - r - 5) + 2r + 4 \\ - r - 5 + 2r + 4[/tex]
Step 3: Add numbers[tex] - 3 \purple{ - 5} + 2r + \purple{4} \\ - r \purple{ - 1} + 2r[/tex]
Step 4:Combine like terms[tex] \purple{ - r } - 1 + \purple{2r} \\ \purple{1r} - 1[/tex]
Step 5:Multiply by 1[tex]1r - 1 \\ r - 1[/tex]
Hopefully it's help
I copy MissJoy2 answer cuz her/his answer is right
h(x) = 2x2 + x + -3
Find h(2)