Answer:
A. [tex]\frac{82}{3}[/tex]
Step-by-step explanation:
Step 1: We know .3333... is [tex]\frac{1}{3}[/tex], we rewrite the equation as [tex]\frac{1}{3}[/tex]
[tex]27\frac{1}{3}\\ \frac{1+(27)(3)}{3}\\\frac{1+81}{3}\\\frac{82}{3}\\[/tex]
Therefore the answer would be A. [tex]\frac{82}{3}[/tex]
Answer:
A. 82/3
Step-by-step explanation:
[tex]3\overline{|\smallspace82}\space\space\space\space\\\mathrm{Divide}\:8\:\mathrm{by}\:3\:\mathrm{to\:get}\:2\\\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Multiply\:the\:quotient\:digit}\:\left(2\right)\:\mathrm{by\:the\:divisor}\:3\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Subtract}\:6\:\mathrm{from}\:8\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\[/tex]
[tex]\mathrm{Bring\:down\:the\:next\:number\:of\:the\:dividend}\\[/tex]
[tex]\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Divide 22 by 3 to get 7
[tex]\begin{matrix}\space\space\space\space\emptyspace2\emptyspace7\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Multiply the quotient digit 7 by the divisor
and sbtract 21 from 22=1
= 27 remainder 1
The sprocket on the crankshaft of an engine power the camshaft by a chain assembly. If the engine crankshaft is turning 3250 revolutions per minute and the sprocket has a radius of 1.5 inches, to the nearest inch how many inches of chain travel past the sprocket in one minute? To the nearest foot how many feet of chain travel past the sprocket in one minute?
Answer:
30,631 inches2553 feetStep-by-step explanation:
The length of one revolution of the sprocket is ...
C = 2πr = 2π(1.5 in) = 3π in
Then the length of 3250 revolutions is ...
3250(3π in) = 30,630.53 in
About 30,631 inches of chain travel past the sprocket in one minute.
__
There are 12 inches in a foot, so the number of feet is ...
30,630.53 in/(12 in/ft) = 2552.54 ft
About 2553 feet of chain travel past in one minute.
One airplane is located 200 km north and 50 km east of an airport. A second plane at the same altitude is located 30 km north and 100 km north and 100 km west.
The distance between the planes is closest to:
A. 150 km
B. 200 km
C. 300 km
D. 350 km
E. 400 km
Answer: B
Step-by-step explanation:
We can define the North as our positive y-axis, and the East as the positive x-axis.
The position of the airport is the (0, 0)
Then the position of the first plane is: (200 km north and 50 km east)
(50km, 200km)
The position of the other plane is: (30 km north and 100 km west)
(-100km, 30km)
Now, if we have two points (a, b) and (c, d)
The distance between those points is:
D = √( (a - c)^2 + (b - d)^2)
Then the distance between the planes is:
D = √( (50km - (-100km))^2 + (200km - 30km)^2)
D = √( (150km)^2 + (170km)^2)
D = 226.7km
Then the distance is closest to 200km, the correct option is B.
On a coordinate plane, we have:
North represents the positive y-axisSouth represents the negative y-axisEast represents the positive x-axisWest represents the negative x-axisThe closest distance between the planes is 200km
The positions of the two planes is given as:
[tex]A = (50,200)[/tex] --- 50km east and 200km north
[tex]B = (-100,30)[/tex] --- 100km west and 30km north
The distance between the planes is calculated using the following distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(50--100)^2 + (200-30)^2}[/tex]
[tex]d = \sqrt{150^2 + 170^2}[/tex]
[tex]d = \sqrt{51400}[/tex]
[tex]d = 226.72km[/tex]
From the list of given options, 200km is the closest to 226.72km
Hence, the closest distance between the planes is 200km
See attachment for the positions of both planes
Read more about distance at:
https://brainly.com/question/16310813
Find the slope of (3,-3) and (0,3)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 2}}}}}[/tex]Step-by-step explanation:
Let the points be A and B
A ( 3 , -3 ) ⇒( x₁ , y₁ )
B ( 0 , 3 )⇒ ( x₂ , y₂ )
Finding the slope
Slope ( m ) = [tex] \sf{ \frac{y2 - y1}{x2 - x1} }[/tex]
plug the values
⇒[tex] \sf{ \frac{3 - ( - 3)}{0 - 3} }[/tex]
We know that , [tex] \sf{( - ) \times ( - ) = ( + )}[/tex]
⇒[tex] \sf{ \frac{3 + 3}{0 - 3} }[/tex]
Calculate
⇒[tex] \sf{ \frac{6}{ - 3} }[/tex]
⇒[tex] \sf{ - 2}[/tex]
Hope I helped!
Best regards!!
Answer:
-6/3=. -2
Step-by-step explanation:
Determine whether the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if [tex]\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}[/tex]
here;
[tex]d_1 = (-1, \ 2, \ -3)[/tex]
Thus;
[tex]r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t[/tex]
[tex]d_2 =(2, \ -4, \ +6)[/tex]
[tex]s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t[/tex]
∴
[tex]\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}[/tex]
Hence, we can conclude that r(t) and s(t) are parallel.
Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so that the coefficient of x2 is 1.
Answer:
The equation is [tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]
Step-by-step explanation:
From the question we are told that
The diameter endpoints is (-8, -3, -10) and (-6, 1, -4)
Generally the equation of a sphere with center coordinates (a, b , c ) and radius r is mathematically represented as
[tex](x - a )^2 + (y -b )^2 + (z -c)^2 = r^2[/tex]
Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows
[tex](a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ][/tex]
[tex](a, b , c) = [ -7 , -1.5 , -7 ][/tex]
Now the length of the diameter is evaluated as
[tex]|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }[/tex]
[tex]|d| = \sqrt{56 }[/tex]
[tex]|d| = \sqrt{4 * 14 }[/tex]
[tex]|d| = 2 \sqrt{ 14 }[/tex]
Now the radius is mathematically represented as
[tex]r = \frac{|d|}{2}[/tex]
[tex]r = \frac{ 2 \sqrt{14} }{2}[/tex]
[tex]r = \sqrt{14}[/tex]
So
[tex](x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2[/tex]
[tex](x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14[/tex]
[tex]x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14[/tex]
[tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]
Write down the next three terms in each sequence -8,-11,-14,-17
what is the length of the hypotenuse triangle if both sides are 36
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{36 \sqrt{2} \: \: units}}}}}[/tex]Step-by-step explanation:
Given,
Perpendicular ( P ) = 36
Base ( b ) = 36
Hypotenuse ( h ) = ?
Finding the hypotenuse :
Using the Pythagoras theorem :
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
plug the values
⇒[tex] \sf{ {h}^{2} = {36}^{2} + {36}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{ {h}^{2} = 1296 + 1296}[/tex]
Add the numbers
⇒[tex] \sf{ {h}^{2} = 2592}[/tex]
Squaring on both sides
⇒[tex] \sf{h = 36 \sqrt{2} }[/tex] units
Hope I helped!
Best regards!!
Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 + 47 + 18). The expressions that four students created are shown in the table below. Expressions Generated by Students Student Expression Jeremy (20 + 13 + 15) + (20 + 47 + 18) Layla (20 + 47 + 18) + (13 + 15 + 20) Keith (13 + 20) + (20 + 47 + 18) + 15 Melinda (13 + 15 + 20 + 20) + (47 + 18) How many of the students correctly applied only the associative property to rewrite the expression? one two three four
Answer:
The correct option is four.
Step-by-step explanation:
The associative property implies that the values are added however we want, i.e. the numbers can be grouped in any way and the answer would still be the same.
The associative property of addition is:
[tex](a+b)+c=a+(b+c)[/tex]
The expression provided is:
(13 + 15 + 20) + (20 + 47 + 18)
The answer provided by four students are:
Jeremy : (20 + 13 + 15) + (20 + 47 + 18)
Layla : (20 + 47 + 18) + (13 + 15 + 20)
Keith : (13 + 20) + (20 + 47 + 18) + 15
Melinda : (13 + 15 + 20 + 20) + (47 + 18)
So, all the four students correctly applied only the associative property to rewrite the expression.
The correct option is four.
Answer: The answer is A or one lol
Step-by-step explanation:
Find the anhle measure x in the figure
Answer:
x=25°
Step-by-step explanation:
Sum of angles of a triangle equals 180°
x + 10° + 2x + 15° + 3x + 5° = 180°6x + 30° = 180°6x = 180° - 30°6x = 150°x = 150°/6x = 25°Use the Venn diagram to list the set of elements of A ∩ B in roster form.
Answer:
A. {e, h}
Step-by-step explanation:
In a Venn diagram, the set of elements in any intersection can simply be visualised. The elements contained in the region where the circles representing different sets overlap, are the set of elements of intersection.
In the Venn diagram given, the set of elements contained in the region where the circles representing A and B overlap are {e, h}.
{e, h} is common to both set A and set B.
If (x - 3) 2 = 5, then
Answer:
Step-by-step explanation:
2(x-3) = 5
Distribute.
2x - 6 = 5
Eliminate the 6.
2x = 11
Divide by 2.
x = 11/2
Answer:
[tex]\frac{11}{2}[/tex]
Step-by-step explanation:
We can use distributive property to simplify the equation, [tex]2x-6=5[/tex]. Now, we can move -6 to the right hand side. [tex]2x=11[/tex]. Finally, we can divide 2, [tex]x=\frac{11}{2}[/tex] or [tex]x = 5\frac{1}{2}[/tex]
Whats 1+2+3+4+5 add them together pls
Answer:
15
*ignore this answers have to be a minimum of 20 characters.
Answer:
15
Step-by-step explanation:
1+2=3
3+3=6
6+4=10
10+5=15.
What is the value of the expression
Hi there! Hopefully this helps!
------------------------------------------------------------------------------------------------------------
The answer: [tex]\frac{7}{9}[/tex].~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]\sqrt[]{2}[/tex] × [tex]\frac{8\sqrt{2} }{3}[/tex] ÷ 3 - 1
First, we express [tex]\sqrt{2}[/tex] × [tex](\frac{8\sqrt{2}}{3})[/tex] ≈ 5.333333333 as a single fraction.
[tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} } - 1[/tex] ≈ 0.777777778
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now we express [tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} }[/tex] ≈ 1.777777778 as a single fraction.
[tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{3 \times 3} - 1[/tex] ≈ 0.777777778
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply [tex]\sqrt{2}[/tex] ≈ 1.414213562 and [tex]\sqrt{2}[/tex] ≈ 1.414213562 to get 2.
[tex]\frac{2 \times 8}{3 \times 3} - 1[/tex] ≈ 0.777777778
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply 2 and 8 to get 16.
[tex]\frac{16}{3 \times 3} - 1[/tex] ≈ 0.777777778
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply 3 and 3 to get 9.
[tex]\frac{16}{9} - 1[/tex] ≈ 0.777777778
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Convert 1 to fraction [tex]\frac{9}{9} = 1.[/tex]
[tex]\frac{16}{9} - \frac{9}{9}[/tex] ≈ 0.777777778
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since [tex]\frac{16}{9}[/tex] ≈ 1.777777778 and [tex]\frac{9}{9} = 1[/tex] have the same denominator, subtract them by subtracting their numerators.
[tex]\frac{16 - 9}{9}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Then you get................
[tex]\frac{7}{9}[/tex]
A test of a hybrid car resulted in 4,840 miles driven using
88 gallons of gas. At this rate, how many gallons of gas will this vehicle
need to travel 1,155 miles?
Answer:
Hey there!
We can write the proportion:
[tex]88/4840 = x/1155[/tex]
101640=4840x
x=21
The car would need 21 gallons of gas to travel 1155 miles.
Let me know if this helps :)
Answer:
21 gallons
Step-by-step explanation:
4,840 miles = 88 gallons
=> 1155 miles = x gallons
=> Cross-multiply
=> 4840 * x = 1155 * 88
=> 4840x = 101640
=> 4840x/4840 = 101640/4840
=> x = 21
The car can travel 1,155 miles using 21 gallons.
At a concert, floor tickets are $20 each, and
balcony seats are $10 each. 324 floor tickets were
sold & the box office collected $10,000. How many
balcony tickets were sold?
Answer: 352 tickets
Step-by-step explanation:
because multiplying $20 floor tickets by 324 (how many were sold) gives you 6480
subtract from 10000
gives you 3520 (amount made from balcony)
divide by $10
Step-by-step explanation:
Let No. of balcony ticket sold be x
Rate of floor ticket = $20
Rate of balcony ticket = $10
Total Box Office collection :
324 * 20 + 10 * x = $ 10,000
X = 352 tickets
can someone please help me
Answer:
Mark answer C and D as correct
Step-by-step explanation:
Recall that a bisector cuts the side in two equal segments, then KH has to be half of 136 that is KH = 68
Also KHZ and HLZ are right angle triangles that share the same hypotenuse, so they are congruent triangles, which means that HL must equal KH and therefore the full side HJ must be 68 times 2 = 136
the brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use pi = 3.14.
0.9 hours
1.6 hours
2.6 hours
5.1 hours
Answer:
The colony of bats will take 1.612 hours to cover an area of 80,000 square miles.
Step-by-step explanation:
As the colony of bats emerges from a cave and spreads out in a circular pattern, the area covered ([tex]A[/tex]) by the colony, measured in square miles, is represented by the following geometrical formula:
[tex]A = \pi\cdot r^{2}[/tex]
Where:
[tex]r[/tex] - Distance of the bat regarding the cave, measured in miles.
In addition, each bat moves at constant speed and distance is represented by this kinematic formula:
[tex]r = r_{o}+\dot r \cdot \Delta t[/tex]
Where:
[tex]r_{o}[/tex] - Initial distance of the bat regarding the cave, measured in miles.
[tex]\dot r[/tex] - Speed of the bat, measured in miles per hour.
[tex]\Delta t[/tex] - Time, measured in hours.
The distance of the bat regarding the cave is now substituted and time is therefore cleared:
[tex]A = \pi \cdot (r_{o}+\dot r \cdot \Delta t)^{2}[/tex]
[tex]\sqrt{\frac{A}{\pi} }-r_{o} = \dot r \cdot \Delta t[/tex]
[tex]\Delta t = \frac{1}{\dot r} \cdot \left(\sqrt{\frac{A}{\pi} }-r_{o} \right)[/tex]
Given that [tex]\dot r = 99\,\frac{mi}{h}[/tex], [tex]A = 80,000\,mi^{2}[/tex], [tex]\pi = 3.14[/tex] and [tex]r_{o} = 0\,mi[/tex], the time spent by the colony of bats is:
[tex]\Delta t = \left(\frac{1}{99\,\frac{mi}{h} } \right)\cdot \left(\sqrt{\frac{80,000\,mi^{2}}{3.14} }-0\,mi \right)[/tex]
[tex]\Delta t \approx 1.612\,hours[/tex]
The colony of bats will take 1.612 hours to cover an area of 80,000 square miles.
Answer:
B: 1.6 hours
Step-by-step explanation:
if [tex]\frac{10}{x} +\frac{2}{x} =12[/tex], what is x?
Hi
I guess that the most obvious answer is
x = 1
Answer:
x = 1
Step-by-step explanation:
10/x + 2/x = 12
x(10/x + 2/x) = 12*x
10x/x + 2x/x = 12x
10 + 2 = 12x
12 = 12x
x = 12/12
x = 1
Verify:
10/1 + 2/1 = 12
10 + 2 = 12
A weather forecasting website indicated that there was a 60% chance of rain in a certain region. Based on that report, which of the following is the most reasonable interpretation? Choose the correct answer below.
A. 60% of the region will get rain today.
B. In the region, it will rain for 60% of the day.
C. There is a 0.60 probability that it will rain somewhere in the region at some point during the day.
D. None of the above interpretations are reasonable.
Answer:
C. There is a 0.60 probability that it will rain somewhere in the region at some point during the day.
Step-by-step explanation:
The probability that it will rain is given by =p= 60% = 0.6
60% chance of rain in a certain region means that the probability of rain in the given region is 0.6 at any time of the day in any part of the region.
So Choice C is the best option.
Choice A is wrong because 60% of the region does not mean 60% of the rain.
Choice B is also wrong because 60% of the day does not mean 60% of the rain.
The weather report tells about the rain , not the region or part of the day. So choice C is the best option
A man drove 16 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Use the Pythagorean theorem.
Distance = sqrt(16^2 + 5^2)
Distance = sqrt(256 + 25)
Distance = sqrt(281)
Distance = 16.763
Rounded to the nearest tenth = 16.8 miles
(3,4) (-3,8) ( 6,8) is a function?
The relation {(3, 4), (-3, 8), (6, 8)}, is a function, because
all the x–coordinates are different.
It's important to understand that even though two of the y-coordinates
are the same, this relation is still a function.
The y-coordinates do not have any affect
on whether the relation is a function.
Deandre buys candy that costs $6 per pound. He will spend at least $42 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Deandre will buy.
What type of solution set will this have?
Answer:
A) No solution
Step-by-step explanation:
The absolute value of a quantity is either zero or positive. It cannot be negative.
For the absolute value of a quantity to be less than or equal to -1, it means the absolute value of the quantity is negative. This cannot be, so there is no solution.
Answer: A) No solution
Answer:
no solutions
Step-by-step explanation:
An absolute value is non negative
The smallest value of an absolute value is 0
0 ≤ -1
This is never true so there is no solution
Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
Answer:
The equations needed to solve this problem are:
y = 12 + 6x
y = 12x
The number of posters completed by each Avenger will be 24.
Step-by-step explanation:
The information provided are:
Ms. Ironperson has completed 12 posters and will complete 6 more per day.Mr. Thoro has not started yet but can make 12 per day. The variable x denotes the number of days and y denotes the number of posters.So, after x day the number of poster completed by Ms. Ironperson will be:
y = 12 + 6x
And after x day the number of poster completed by Mr. Thoro will be:
y = 12x
Thus, the equations needed to solve this problem are:
y = 12 + 6x
y = 12x
Compute the value of x as follows:
12x = 12 + 6x
6x = 12
x = 2
The number of posters completed by each Avenger is:
y = 12x = 12 × 2 = 24
Thus, the number of posters completed by each Avenger will be 24.
5 less than a number is equivalent to 1 more than three times the number. what is the number
Answer:
X = -3
Step-by-step explanation:
x - 5 = 3x + 1
-6 = 2x
x = -3
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
;)
The equation formed by the information, 5 less than a number is equivalent to 1 more than three times the number is x - 5 = 3x + 1. And the number is x = -3.
What are linear equations in one variable?The simplest equation used to express and solve for an unknown quantity is a linear equation in one variable. It's simple to depict graphically since it's always a straight line. A linear equation is a simple technique to convey a mathematical proposition. Unknown quantities can be represented by any variable or symbol, however, in most cases, the unknown quantity in a linear equation in one variable is represented by the variable 'x'. A collection of basic strategies are used to solve a linear equation. To determine the final value of the unknown quantity, the variables are isolated on one side of the equation and the constants are isolated on the other side of the equation.
How do we solve the given question?We are given that 5 less than a number is equivalent to 1 more than three times the number. We are asked to determine the number.
To determine the number, we will let the unknown number be x.
We will now try to make the two equal expressions, equate them to get a linear equation in one variable, and then solve the equation to find x.
First expression: 5 less than the number, that is, x - 5
Second expression: 1 more than three times the number, that is, 3x + 1.
Both the expressions are equal, so we equate them to get our equation:
x - 5 = 3x + 1
To solve for x, we do the following steps.
1. Subtract 3x from both sides of the equation:
x - 5 - 3x = 3x + 1 - 3x
or, -2x -5 = 1 (Simplifying)
2. Add 5 to both sides of the equation:
-2x - 5 + 5 = 1 + 5
or, -2x = 6 (Simplifying)
3. Divide both sides of the equation by (-2):
-2x/(-2) = 6/(-2)
or, x = -3 (Simplifying).
∴ The equation formed by the information, 5 less than a number is equivalent to 1 more than three times the number is x - 5 = 3x + 1. And the number is x = -3.
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Solve Square root of -144 =
-12i
-12
12
12i
Answer:
12i
Step-by-step explanation:
Step 1: Write it out
√-144
Step 2: Factor
√144(√-1)
Step 3: Evaluate
12i
1 Out of 30 students surveyed, 17 have a dog. Based on these results
predict how many of the 300 students in the school have a dog
Answer:
170
Step-by-step explanation:
17 dogs per 30 students or 17/30
Same ratio for 300 students:
300*17/30 = 170So 170 students have a dog
A musical instrument company reduced the time it takes for a worker to build a guitar. Before the reduction it took 5 hours. Now in 7 hours they can build 3 guitars. By how much did they reduce the time it takes to build each guitar?
Answer:
2 2/3 hours
Step-by-step explanation:
Before it was 5 hours for 1 guitar, or 5 hours/guitar
Now it is 7 guitars in 3 hours or 7/3 hours/guitar
7/3 = 2 1/3
5 hours - 2 1/3 hours = 15/3 hours - 7/3 hours = 8/3 hours = 2 2/3 hours
The reduced the time it takes to build 1 guitar by 2 2/3 hours.
Shota is a dangerous fellow who likes to go rock climbing in active volcanoes. One time, when he was 303030 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. He climbed up at a constant rate. After 4.54.54, point, 5 seconds, he was 7.57.57, point, 5 meters below the edge of the volcano How fast did Shota climb? In total, how long did it take Shota to reach the edge of the volcano?
Answer:
Speed = 5m/s
Total time taken = 6 seconds
Step-by-step explanation:
Shota's initial position = 30 metres below the edge of a volcano
If Shota climbed at a constant rate:
Shota's position after 4.5 seconds = 7.5meters below the edge of the volcano
Shota's climbing speed :
Distance covered / time taken
Distance covered = (30 - 7.5) = 22.5 meters
Hence, speed = (22.5 / 4.5) = 5m/s
Time taken to reach edge of volcano:
Time left to reach edge = (distance left to cover / speed)
Time left to reach edge = (7.5 / 5) = 1.5 seconds
Total time taken: (4.5 + 1.5) = 6 seconds
Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 37 x2 − 6x
Answer:
[tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]
Step-by-step explanation:
Given the function [tex]\dfrac{37}{x(x-6)}[/tex], to write the form of its partial fraction on decomposition, we will separate the two functions separated by an addition sign. The numerator of each function will be constants A and b and the denominator will be the individual factors of each function at the denominator. The partial fraction of the rational function is as shown below.
[tex]= \dfrac{37}{x(x-6)}\\\\= \dfrac{A}{x}+\dfrac{B}{x-6}[/tex]
Since we are not to solve for the constants, hence the partial fraction is [tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]