========================================================
Explanation:
A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation
5 = 6 + (x/9)
Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1
Then plug in w = x/9 and solve for x.
w = -1
x/9 = -1
x = 9*(-1)
x = -9
We get exactly one solution and it is x = -9
--------------
Check:
5 + x/3 = x/3 + 6 + x/9
5 + (-9)/3 = (-9)/3 + 6 + (-9)/9
5 - 3 = -3 + 6 - 1
2 = 3 - 1
2 = 2
We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.
how many distinct 5-letter strings can be created using the letters a, b, c, d, e if repetition is allowed, but the letters a appears at most twice?
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
Given that
form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice
let's consider that letter a is not there in the string
each letter is repetitive then it is [tex]4^{5}[/tex]
now letter a is considered once
5c1 ×[tex]4^{4}[/tex]
now letter a is repetitive twice
5c2 × [tex]4^{3}[/tex]
[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]
1024+ 1280 + 640 = 2944
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
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0.96 in fracton form
Answer:
As a fraction in simplest form it SHOULD be 24 over 25.
Step-by-step explanation:
"0.96 as a fraction (simplified form)" MagnetsAndMotors (Dr. B's Other Channel)
Answer:
24/25
Step-by-step explanation:
0.96
By counting the numbers after the decimal point which is two.
so we will write: 96/100, since hundred has to two zero.
Then we will divide 96/100 to it simplest form which is 24/25
SUPER EASY ASAP !!!!!!
The function f (x) has steeper slope.
So, The Paige is correct.
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The input output pairs of f (x) are (- 6, 5/2) and (- 1, 17/2)
And, The input output pairs of g (x) are (2, 13/3) and (6, - 1)
Now,
Find the slope for f (x) as;
m₁ = (17/2 - 5/2) / (- 1 - (-6))
m₁ = (15/2) / 5
m₁ = 15/10
m₁ = 3/2
And, Slope for g (x) is;
m₂ = (- 1 - 13/3) / (6 - 2)
m₂ = (- 16/3) / 4
m₂ = - 16 / 12
m₂ = - 4 / 3
Thus, The function f (x) has steeper slope.
So, The Paige is correct.
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The graph below shows distance over time.
A student is walking to class. The student increases their speed for 20 seconds for 3 meters. The student then walks a constant speed for 5 seconds and then increases their speed the last 3 meters to class.
Which of these situations could be represented by this graph?
A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).
In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.
By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).
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Complete Question:
The graph below shows distance over time. Which of these situations could be represented by this graph?
answer choices
A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.
Write the equation of a line that is perpendicular
to -y = -x and contains point (−1,−1)
Answer:
y = - x
Step-by-step explanation:
-y = -x is the same as y=x and to get an equation that is perpendicular to another one you just have to find the reciprocal (opposite) number of the SLOPE. The reciprocal of 1 is -1, therefore the perpendicular equation to -y=-x is y=-1
HELP ASAP GIVING BRAINLIEST
Answer: C
Step-by-step explanation:
Triangle DOG i an iocele with bae angle D and G. Line egment DO i one more than the quare of a number, and line egment OG i two le than four time a number. Line egment DG i three le than twice the number. Find the number, the length of the leg, and the length of the bae
Answer:
the number is 3DO = OG = 10DG = 3Step-by-step explanation:
Given isosceles triangle DOG with DO≅GO, DO = (n²+1), GO = (4n-2) and DG = (2n -3), you want the value of n and the lengths of the sides.
SetupThe expressions for the congruent sides will have the same value, so ...
DG -GO = 0
(n² +1) -(4n -2) = 0
Solutionn² -4n +3 = 0 . . . . . . . . simplify
(n -3)(n -1) = 0 . . . . . . factor
n = 1 or 3 . . . . . . . . values of n that make the factors zero
The length of leg DG is ...
2n -3 = 2{1, 3} -3 = {2, 6} -3 = {-1, 3}
Side DG cannot be negative, so the "solution" n = 1 is extraneous.
GO = 4n -2 = 4(3) -2 = 10
The number is 3, the leg lengths are DO = OG = 10, and the base length is DG = 3.
Rewrite in simplest terms: (-10x+2)+(-9x+8)
The simplest form of the given expression is -19x + 10.
The process or product of making something less complicated and thus easier to do or understand is called simplification. Replace 'of' with 'Multiplication' and '/' with 'Division.' Always perform operations in the order specified by 'BODMAS.' Division and multiplication are both given equal weight (Starting from left) Subtraction and addition have the same.
Given that
(-10x+2) + (-9x+8)
We have to simplify the given expression
= -10x + 2 - 9x + 8
= (-10x - 9x) + (2 + 8)
= -19x + 10
Therefore the simplest form of the given expression is -19x + 10
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PLEASE HELP!
Simplify the expression to a + bi form:
√25 + √-81 + √25 - √-16
Answer:
10 + 5i
Step-by-step explanation:
[tex] \rm \implies \sqrt{25} + \sqrt{ - 81} + \sqrt{25} - \sqrt{ - 16} \\ \\ \rm \implies 5 + 9i + 5 - 4i \\ \\ \rm \implies 10 + 5i[/tex]
Which method and additional information would prove δonp and δmnl similar by the aa similarity postulate? segments om and lp intersect at point n; triangles are formed by points lnm and onp; line k intersects with both triangles at point n. use a rigid transformation to prove that ∠opn ≅ ∠mln. use rigid and nonrigid transformations to prove segment pn over segment mn = segment ln over segment on. use a rigid transformation to prove that ∠npo ≅ ∠lnm. use rigid and nonrigid transformations to prove segment ln over segment on = segment pn over segment mn.
The correct option for the method and additional information that would prove triangle ONP and triangle MNL similar by AA similarity postulate is
option B.
B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
Angle Angle AA similarity postulate states that two triangles are similar if : two angles in one of the triangles are congruent (equal) to two angles in the other triangle.
The reason for arriving at the above selection is as follows:
The known parameter in triangle ΔONP and ΔMNL are;Lines MO and LP intersect at vertex point N.The angles on opposite side of the point N (either side of the X shape formed by the two lines) which are ∠ONP and ∠LNM are vertically opposite angles or opposite angles.According to vertically opposite angles theorem ∠ONP and ∠LNM, which are vertically opposite angles are congruent, and we can write.
∠ONP ≅ ∠LNM
The required parameters are:
To find the additional information that would prove ΔONP and ΔMNL by
AA (Angle-Angle) similarity postulate.
Given from the drawing,
One (vertex) angle in one triangle is congruent to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is required to prove that one other angle in triangle ΔONP is congruent to a corresponding angle in triangle ΔMNL.
Prove that:
either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or ∠NML respectively in ΔMNL by performing rigid transformations (transformations that does not change shape) on either ΔONP or ΔMNL including:
Rotating triangle ΔONP by 180° with origin at point N, to form the image ΔO'N'P'.
Translating the vertex point P' in the image ΔO'N'P', to the location of the point L in ΔMNL, and verify that the segments LN and LM in ΔMNL coincide with the segments P'N' and P'O' respectively of triangle ΔO'N'P'.
Therefore, the correct option is option B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
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Answer:
b
Step-by-step explanation:
3.6 x 10^7 + 2.1 x 10.7=
a) 14
b) 5.7
c) 3.6
d) none of these
The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:
= 3.6 x 10^7 + 2.1 x 10.^7
= 5.7 × 10^7
Therefore, the correct option is D.
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I need help please!!!
The tens digit of a two-digit number is twice the ones digit. Its reversed number is 36 less than the original number.
From the calculation, the original number is obtained as 84.
What is the original number?We know that we are told in the question that in the question, we are required to obtain the number and that is what we are going to do below.
Let the tens digit be T and let the units digit be U
We can then write
10U+T = 10T+U-36
Since the reversed number is 36 less than the original number.
Then;
9U = 9T -36
Dividing both sides of the equation by 9
U = T -4
U=2U-4
U=4
T = 8
It then follows that the original number is 84.
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1. Find the y-intercept of the line paing through the point A (3, -2) and B (-1, 3). (5 pt)
find the perimeter and area
Answer:
perimeter = 22 km and area = 18 km^2
Step-by-step explanation:
First I found and labeled the missing lengths. For the one at the top of the shape, I added 1 + 2 + 3 to get the length, since those are what make up the length.
Afterwards I just added up all the side lengths to get the perimeter. 2+6+2+3+2+3+1=22, so the perimeter is 22 km.
To find the area, I split the shape into two, labeled 1 and 2. (Check the image attached) To find the area you multiply length by width, so i did that for shapes 1 and 2. For shape 1, I did 2 x 6 and got 12, and for shape 2 I did 3 x 2 to get 6. To get the total area of the entire shape, add these two areas. 12 + 6 = 18, so the total area is 18 km^2. (km squared)
let me know if anything is confusing :-))
2/3+____=5/6 what Is the answer
Answer: 2/3+ 1/6
Step-by-step explanation: 2/3= 4/6 4/6 + 1/6 = 5/6
Expression that equal to p/6+(q+8)
Answer: (p/6 + q) + 8
Step-by-step explanation:
What is 125 in simplest form?
Answer:
125 in simplest form is 1/8.
Step-by-step explanation:
1.209, 1.9, 3.76, 1.29 order these numbers from least to greatest
Answer:
1.209 < 1.29 < 1.9 < 3.76
Step-by-step explanation:
There are 163 students going on a field trip to pan for gold.
If they are going in vans that hold 9 students each, how many vans are needed? How many students will ride in the van that isn't full?
Please answer and thank you
Answer:
Step-by-step explanation:
18 Vans. That will hold 162 Students if 9 student per Van
19 Vans since we need 163.
Answer: 19 Vans, and All but one will be full the one that isn't full holds one Student.
find the annual salary of a person who is paid $835.50 per week
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5 × 52 = 43446
A square and rectangle are shown below. The width of the rectangle is the same as
the length
of a side of the square, both represented by .x. The length of the rectangle is one
foot more
than twice its width. The perimeter of the rectangle is 26 feet more
than that of the square.
(a) Write an expression for the length of the rectangle in
terms of.x. Label on the drawing.
x
Answer:
Step-by-step explanation:
x=26
643251 to the nearest then thousands
Answer:
64000
Step-by-step explanation:
When you are rounder you must look at the last number to determine if you are rounding up or down.
What is the sum of (3x + 4) + (9x – 10)?
Answer:
[tex]12x -6[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
During one month andre used 785 gallons of water at his home. There are approximately 3. 8 liters in 1 gallon. Which measurement is closest to the number of liters andre used during this month?.
Andre used 2983 gallons of liquid all through this month.
Given;
Andre used 785 gallons of water at his house in a single month. In a gallon, there are roughly 3.8 liters.
To get the measurement that is closest to the number of liters Andre used during this month;
The total gallons of water used in a month = 785 gallons
The quantity of water in a single gallon = 3.8 liters
Therefore, the number of liters Andre used during this month;
U = total gallons of water used in a month * quantity of water in a single gallon
U = 785 * 3.8
U = 2983
Hence, the number of liters Andre used during this month is 2983 gallons.
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In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?
For the given triangle, its greatest possible perimeter is 45 cm.
What is the perimeter?The term perimeter has to do with the distance round on object. In this case we do have a triangle and the triangle has three sides. The perimeter of the triangle would be the distance round the triangle.
From the statements we have;
Third side = 15
second side = x
first side = 3x
Then;
x + 15 > 3x
15 > 3x - x
15> 2x
x < 7.5
Thus;
For the first side; 3 * 7.5 = 22.5
For the second side = 7.5
Third side = 15
Greatest possible perimeter of the triangle = 22.5 + 7.5 + 15
= 45 cm
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what is they intercept of this quadratic function? f(x) = -x2 + 10x - 22
Answer:
(0,-22)
Step-by-step explanation:
Plug in 0 for x and solve for y
Help me with this question
Point A, C and F lies on the given line y = [tex](\frac{1}{4} )^{x}[/tex] .
Given in question,
y = [tex](\frac{1}{4} )^{x}[/tex]
y = [tex]4^{-x}[/tex]
Points A(-2,16), B(2,8), C(-1,4), D(0,4), E(1,4), F(0,1) and G(-2,0)
We will points in the equation.
For point A(-2,16)
[tex]16 = 4^{-(-2)}[/tex]
[tex]= 4^{2}[/tex]
[tex]16=16[/tex] True
For point B(2,8)
[tex]8= 4^{-2}[/tex]
[tex]=\frac{1}{4^{2} }[/tex]
[tex]=\frac{1}{16}[/tex]
[tex]8=\frac{1}{16}[/tex] False
For point C(-1,4)
[tex]4=4^{-(-1)}[/tex]
[tex]=4^{1}[/tex]
[tex]4=4[/tex] True
For point D(0,4)
[tex]4=4^{-0}[/tex]
[tex]4= 1[/tex] False
For point E(1,4)
[tex]4=4^{-1}[/tex]
[tex]4=\frac{1}{4}[/tex] False
For point F(0,1)
[tex]1=4^{-0}[/tex]
[tex]1=1[/tex] True
For point G(-2,0)
[tex]0=4^{-(-2)}[/tex]
[tex]= 4^{2}[/tex]
[tex]0=16[/tex] False
Hence, only point A,C and F satisfies the equation.
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How many minutes are in 1 hour and 3/4? How do you solve it as well?
Answer:
Step-by-step explanation:
105 min
60 min in a hour and then 3/4 of a hour is 45 min.
Total: 105 minutes
Find the equation of the line passing through the given point and parallel to the given line.
( 1, 9 ), y = 4x + 2
( 5 , 2 ), y = -2x + 7
The line equation passing through the given points and parallel to the given lines are:
Line 1: y=-4x+13...(i)
Line 2: y=2x-12...(ii)
Line 1
The first line is passing through point (1,9) and parallel to the y=4x+2 line.
Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=4x+2 has:
ay = bx + c, m= -b/a
y=4x+2, m=-4
We could use the line equation formula, where:
y-y1 = m (x-x1)
we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:
y-9 = -4(x-1)
y-9=-4x+4
y=-4x+13...(i)
Line 2
The first line is passing through point (5,2) and parallel to the y=-2x+7 line.
Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=-2x+7 has:
ay = bx + c, m= -b/a
y=-2x+7, m=-2
We could use the line equation formula, where:
y-y2 = m (x-x2)
we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:
y-2 = 2(x-5)
y-2 = 2x-10
y=2x-12...(ii)
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