The line of equation that passes through (5,2) and (6,4) is 4x+y=22.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given points are (5,2) and (6,4)
The equation that passes from two points (x₁,y₁) and (x₂,y₂) is,
y-y₁=m.(x-x₁)
Where m=(y₂-y₁)/(x₂-x₁)
Then linear equation,
y-y₁=(y₂-y₁)/(x₂-x₁)×(x-x₁)
Substitute the values here,
y-2=(6-2)/(4-5) ×(x-5)
y-2=4/(-1)(x-5)
y-2=20-4x
4x+y=22
So the required linear Equation is 4x+y=22.
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A flagpole casts a shadow 18m long when the athlete of the sun is 54°. What is the height of the flagpole.
If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
In the question ,
it is given that ,
the length of the shadow of the flag pole = 18m
the angle of "elevation" of the sun = 54°
let the height of the flagpole be = "x" ,
The flagpole and the shadow form a right triangle ,
So , tan(54°) = (height of flag pole)/(shadow of flagpole)
Substituting the values from above ,
we get ,
tan(54°) = x/18
on cross multiplication ,
x = 18 × tan(54°)
x = 18 × 1.3763
x = 24.7734
x ≈ 24.8
Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
The given question is incomplete , the complete question is
A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?
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Evaluate. Write your anwer a a whole number or a a implified fraction.
5 –1
·
8 –2
=
Answer:
Step-by-step explanation:
so basically 2+2=3
What is -4 (3-1) +2 simplified?
Answer: [tex]-4(3-1)+2=-4(2)+2=-8+2=-6[/tex]
I Need help for this one is about linear equations
Answer:
not sure what the question is but if you look for the equation
it's
1/4 * x + 1
or in decimal
0.25x + 1
A swimming pool is being filled with a hose. The hose fills the pool at a constant rate. The pool’s water level rises 30 inches in 15 hours.
What was the rate per hour of the water level change?
How long will it take for the water level to rise 4 feet?
Answer:
1. 2 inches per hr
2. 24 hrs
Step-by-step explanation:
30/15=2/1
4ft=48in
48/2=24
hope it helps
what is 1/3 plus 4.1 in simplest form written as a mixed number
what's 33 ÷ 33 × 33 - 33 + 33
Answer:
33
Step-by-step explanation:
first we divide 33 by 33 then we have 1 now we have times 33 which is 33 now 33-33 is 0 not we add 33 to 0 now we have 33
Kyle has 80 potatoes he multiples them by 1900 than adds 100000 then he divides them by 53727282 then subtracts 1.5. How many potatoes does Kyle have?
Answer:
-1.49530965
Step-by-step explanation:
The circumference of a circle is 47 cm. Find its radius, in centimeters.
Answer:
The radius (in centimeters) is 18.9999, or roughly 19 centimeters.
Step-by-step explanation:
If you need a step-by-step explanation, please let me know and I will help you. Thanks!
What is the independent variable
Answer:
Your answer is correct.
Step-by-step explanation:
Answer:
p
Step-by-step explanation:
when p changes, it causes the equation to change
a conical tank has height 3 m and radius 2 m at the base. water flows in at a rate of 2 m3/min. cone with bottom radius 2 meters and height 3 meters. how fast is the water level rising when the level is 1 m and when the level is 1.8 m? (use decimal notation. give your answers to four decimal places.)
The speed at which conical tank water will rise is 9/8[tex]\pi[/tex] m/min.
What is cone?
A cone could be a three-dimensional geometric type with a flat base and a sleek tapering apex or vertex.
Main body:
The quick way of solving this is simply to consider the horizontal cross sectional area of the tank at the 2m water depth. This is 2/3 of the way up a tank having radius increasing linearly with depth, and so the radius is 2/3 of the 2m at the top, i.e: 4/3 m. So the area is:
πr²=π(4/3)2=16/9π
Now water having this cross section filling at 2 m³ per minute would fill a cylinder having this volume and cross section each minute. A cylinder has volume equal to cross section times length, so the cylinder would have a height of:
2/(16/9π)=9/8π metres
Therefore the water at this depth is rising at a rate of 9/8π meters per minute.
The longer way around is to calculate the water volume for a given depth and differentiate. We know that the volume of a cone is a third that of a cylinder with the same dimensions, ie: 1/3πr²h . So if our tank has radius R and height H, then the radius of the surface of the water at depth h is (R/H)h , and so the water volume having this depth is:
v=1/3π(R/H)h)²h=[tex]\frac{\pi r^{2} }{3H^3} h^2[/tex]
We’re interested in rate of change with respect to time, so let’s try differentiating this formula with respect to time, remembering that h is changing with time and so we need to use the chain rule:
[tex]\frac{dv}{dt}[/tex]=[tex]\frac{\pi r^{2} }{3H^2} 3h^2[/tex][tex]\frac{dh}{dt}[/tex]=[tex]\frac{\pi r^{2} }{H^2} h^2[/tex][tex]\frac{dh}{dt}[/tex]
Notice that we can solve this for [tex]\frac{dh}{dt}[/tex] , which is the rate of water height change, i.e: the value that we want:
[tex]\frac{dh}{dt}[/tex]= [tex]\frac{H^2 }{\pi r^{2}} h^2[/tex][tex]\frac{dh}{dt}[/tex]
The rate of change of water volume dv/dt is just the rate that water flows in, so now all we need to do is slot the given numbers into the equation:
dh/dt=2(3²/π2²2²)=9/8π meters per minute
Hence the answer is 9/8[tex]\pi[/tex] m/min.
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Puja Limbu did 8 out of 10 math problem and Raju Lama did 11 out of 15 imilar math problem. Expre the number of problem olved by each of them in fraction and identify who did better performance.
The person that has a better performance is Puja Limbu.
How to illustrate the information?From the information, Puja Limbu did 8 out of 10 math problem. This can be converted to percentage as:
= 8/10 × 100
= 80%
Raju Lama did 11 out of 15 similar math problem. This will be:
= 11/15 × 100
= 73%
Therefore, Puja has a better performance.
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Simplify the expression below as a simplified fraction.
(1+1/3)²−2/9
(1 + 1/3)^2 - 2/9
= (3/3 + 1/3)^2 - 2/9
= (4/3)^2 - 2/9
= 16/9 - 2/9
= 14/9
QUESTION 10/10 HELP ASAPP
!WILL GIVE BRAINLIEST TO WHOEVER ANSWERS THE OTHER 9 TOO.!
Answer: tyhe image / screenshot
Step-by-step explanation:
For a project in her Geometry cla, Violet ue a mirror on the ground to meaure the height of her chool’ football goalpot. She walk a ditance of 12. 75 meter from the goalpot, then place a mirror flat on the ground, marked with an X at the center. She then walk 6. 55 more meter pat the mirror, o that when he turn around and look down at the mirror, he can ee the top of the goalpot clearly marked in the X. Her partner meaure the ditance from her eye to the ground to be 1. 75 meter. How tall i the goalpot? Round your anwer to the nearet hundredth of a meter
3.406 tall is the goalpost
given that
she walk a distance of 12.75 meters from the goalpost, then place a mirror flat on the ground, marked with an X at the center. She then walks 6. 55 more meters past the mirror
Her partner measures the distance from her eye to the ground to be 1. 75 meters.
based on the given condition [tex]\frac{1.75}{6.55}[/tex] = [tex]\frac{x}{12.75}[/tex]
x = [tex]\frac{1.75}{6.55}[/tex] ×12.75
x = 3.406
Therefore, 3.406 tall is the goalpost
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Vickie Ewing deposits her savings of $2800 in an investment paying 6% ompounded quarterly and she leaves it there for 5 years. Find (a) the compound amount nd (b) the interest.
The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $2800
Rate of interest = 6% = 0.06
Compound quarterly n = 4
Time period T = 5 yeras
a)
Total amount = P(1 + R/n)^(nT)
Total amount = 2800(1 + 0.06/4)^(4 x 5)
Total amount = 2800(1.015)^20
Total amount = $3771.19
b)
Let's say the equivalent annual interest rate is r.
n = 1
3771.19 = 2800(1 + r/1)^(1 x 5)
3771.19 = 2800(1 + r)^5
1.061 = 1 + r
r = 0.06136 = 6.136%
Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".
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Fourteen more than the product of x and y
Answer:
14+(x*y)
Step-by-step explanation:
for a random sample of 65 overweight men, the mean of the number of pounds that they were overweight was 29. the standard deviation of the population is 4.3 pounds.
The best point estimate of the mean is 29 pounds.
Sample size n =65; sample means (X) =29; population std (s) =4.3
Since the sample size is more than 30 we can use the central limit theorem. Hence population means estimate is equal to the sample mean which is 29.
At 90% confidence z value = 1.645
Lower limit = X -z * s/[tex]n^{0.5}[/tex]= 29 -1.645 * 4.3/[tex]65^{0.5}[/tex] = 28.1
Upper limit = X -z * s/[tex]n^{0.5}[/tex] = 29 +1.645 * 4.3/[tex]65^{0.5}[/tex] = 29.9
At 95% confidence z = 1.96
Lower limit = X -z * s/[tex]n^{0.5}[/tex] = 29 -1.96 * 4.3/[tex]65^{0.5}[/tex] = 27.9
Upper limit = X -z * s/[tex]n^{0.5}[/tex] = 29 +1.96 * 4.3/[tex]65^{0.5}[/tex]= 30.1
95% confidence interval is larger. It has a wider range of values than 90% confidence. This is because we are covering more area on a normal curve with a higher confidence interval. So mean value is more likely to fall in the 95% range than the 90% range.
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i have no clue what this is can someone help me
Step-by-step explanation:
you have to transform the equations, so that in the end you have only x on one side, and everything else on the other.
and that is the solution.
remember, when doing such transformations, we have to do every change to both sides at the same time.
a)
x/5 = 3 | multiply both sides by 5
x = 3×5 = 15
b)
x/2 = 8.5 | multiply both sides by 2
x = 8.5×2 = 17
Answer:
a=15 b=17
Step-by-step explanation:
since we know x divided by something is 3 we do the inverse method so it's going to b 15. The same thing happened with b.
I hope this helps!!
Zola took a picture of Greg standing next to a building. Greg is 5 feet tall. The picture Zola took
shows Greg as ½ inch tall. If the building is 25 feet tall in real life, how tall should the building be
in the picture? Explain.
Answer
2inch tall
Explanation
let the height of the building in the picture = y
5ft -––- ½ inch
20 ft -––- y inch
Cross multiply ✖️
20 × ½ = 5 × y
10 = 5y
10/5 = y
y = 2
A chool will only accept tudent who core in the top 2 %of an admiion tet. If the normal ditribution with a mean of 70 %and a tandard deviation 5%. What i the minimum grade that a tudent mut core in order to be accepted?
Ninety-five percent of people have IQs between 70 and 130.99.7 percent of people have IQ scores between 55 and 145.With IQ scores between 55 and 145, only 0.3% of the population falls outside this range.
How likely is it that a student chosen at random will have an IQ of 115 or higher?
Since half should be over the normal of 100 (by evenness), this implies 50 - 34.13 = 15.87 (%) has an intelligence level score over 115.
Which level of understudies might have scored either higher than 90 or lower than 70?
That always prompts the same response: 95%!Since we are aware that one standard deviation equals five points, two standard deviations equal two x 5.As a result, 95% of scores fall between 70 and 90, which is 10 points above the mean of 80.
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Please help!!!!! ASAP, thank you :)) I’ll give the right answers brainliest
Answer:
Step-by-step explanation:
ok
Leah makes $3.25 per hour. Lois makes $8.64 per hour. How much more does Lois make per hour than Leah
Answer:
$11.89 is the answer
Step-by-step explanation:
because $3.25 + $8.64 is $11.89
Hope this helps
What is the equation of this line?
Responses
y=12x−3
y equals fraction 1 half end fraction x minus 3
y=−12x−3
y equals negative fraction 1 half end fraction x minus 3
y=−2x−3
y equals negative 2 x minus 3
y=2x−3
y equals 2 x minus 3
Number graph ranging from negative 5 to 5 on both the x and y axis. A line passes through the point begin ordered pair 0 comma negative 3 end ordered pair and the point begin ordered pair 4 comma negative 1 end ordered pair
The equation of the line in slope-intercept forms expressed as: y = y = 1x + 3
How to Write the Equation of a Line?
To wrote the equation of a line in slope-intercept form, first, find the slope (m) of the line, determine the y-intercept (b) of the line, then substitute the values into y = mx + b (equation in slope-intercept form).
Using two points on the line, (0, 3) and (4, -1):
Slope (m) = change in y / change in x = (3 - -1)/(0 - 4)
Slope (m) = 4/-4
Slope (m) = -1
The slope of the line is m = -1.
Find the y-intercept (b) by substituting one point, (x, y) = (0, 3), and m = -1 into y = mx + b and solve for b:
3 = 1(0) + b
3 = 0 + b
b = 3
Write the equation of the line by substituting b = 3 and m = -1 into y = mx + b:
y = 1x + 3
Thus, the equation in slope-intercept form of the line is expressed as: y = 1x + 3
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Cross multiply the numbers
Answer:
2m/4m = 9m/xm
2m(xm) = 4m(9m)
2xm = 36m
You work a basic week of 40 hours and your basic rate is $19.50 per hour. What is your basic wage for the week and showing working for this question.
If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer
19.50 x 40 = $ 780 a week.
I hope this helps!
Alex has drawn two circles, A and B.
Circle A has a diameter of 18 cm and
circle B has a diameter of 16 cm.
How much wider was the pair of
compasses when Alex drew circle A than
when he drew circle B?
Answer:
Circle B and 3.14 cm
Step-by-step explanation:
Not 100% sure but good luck :)
The length 1 cm wider was the pair of compasses when Alex drew circle A than when he drew circle B.
What is a diameter?A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.
Given:
Alex has drawn two circles, A and B.
Circle A has a diameter of 18 cm.
So, the radius is 18/2 = 9 cm.
And circle B has a diameter of 16 cm.
So, the radius is 16/2 = 8 cm.
To find how much wider was the pair of compasses when Alex drew circle A than when he drew circle B:
The difference in the radius,
= 9-8
= 1 cm
Therefore, when Alex drew circle A than when he drew circle B, the compass was wider 1 cm.
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HELP! PLEASE! I WILL NAME YOU THE BRAINLIEST!
Solve the system by graphing.
y = 1/3x - 1
x - 3y = 3
(6, 1)
(0, −1)
This system has no solutions.
This system has infinitely many solutions.
Answer:
This system has infinitely many solutions.
Step-by-step explanation:
The graphic in both functions is the same line, which means the system has many solutions
What is the sum?
- 1 1/8 + (-1/2) = -1 1/8 + ( - 4/8) = ?
Answer:
[tex]-1\frac{5}{8}[/tex]
Step-by-step explanation:
-1 1/8 - 1/2 =- 1 1/8 -4/8
= -9/8-4/8
=-13/8
=-1 5/8
Hopes this helps please mark brainliest
College freshmen were asked if they were currently enrolled in Composition I. The results are shown in the table.
How many females are currently enrolled in Composition I?
A) 46
B) 73
C) 75
D) 119
There are 73 females currently involved in the competition.
What is arithmetical operation?The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')
Given that, there is a table of male and female involved and not involved in a competition,
Female column total = 103
103-57 = 46
Female row total = 119
119-46 = 73
Hence, There are 73 females currently involved in the competition.
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