What is the slope of the line that passes through the points (4,1) and (6, 2)?
Answer:
1-2
Step-by-step explanation:
honestly idek what this stuff is I just need points
6+√27/4-√3 can be written in the form r +s√3/13
where are both r and s integers
what are the values of r and s
[tex]r = \left(\dfrac{33}{13}\right)[/tex]
[tex]s = \left(\dfrac{10}{13}\right)[/tex]
Step-by-step explanation:
Let's multiply and divide the given fraction by the conjugate of the denominator:
[tex]\dfrac{6+\sqrt{27}}{4-\sqrt{3}}×\dfrac{4+\sqrt{3}}{4+\sqrt{3}}[/tex]
[tex]\;\;\;\;= \dfrac{24 + 6\sqrt{3} + 4\sqrt{3} + \sqrt{27}\sqrt{3}}{13}[/tex]
[tex]\;\;\;\;=\frac{1}{13}(24 + 10\sqrt{3} + \sqrt{81})[/tex]
[tex]\;\;\;\;=\frac{1}{13}(33 + 10\sqrt{3})[/tex]
[tex]\;\;\;\;=\left(\dfrac{33}{13}\right) + \left(\dfrac{10}{13}\right)\dfrac{\sqrt{3}}{13}[/tex]
We can see here that
[tex]r = \left(\dfrac{33}{13}\right)[/tex]
[tex]s = \left(\dfrac{10}{13}\right)[/tex]
The value of the variable 'r' and 's' will be 33 and 18, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The two equations are given below.
(6 + √27) / (4 - √3) and (r + s√3) / 13
Simplify the expression (6 + √27) / (4 - √3), then we have
[tex]\rightarrow \dfrac{6 + \sqrt{27}} { 4 - \sqrt3} \times \dfrac{4 + \sqrt3} { 4 + \sqrt3} \\\\[/tex]
⇒ [(6 + 3√3)(4 + √3)] / (4² - 3)
⇒ [(24 + 6√3 + 12√3 + 9)] / (16 - 3)
⇒ (33 + 18√3) / 13
Compare the expression (33 + 18√3) / 13 with (r + s√3) / 13, then the value of r and s will be given as,
r = 33
s = 18
The value of the variable 'r' and 's' will be 33 and 18, respectively.
More about the Algebra link is given below.
https://brainly.com/question/953809
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Millie has a bank account balance of $1200. Each week, her balance changes by
-$72.50.
She wants to keep the balance
above $620.
How many weeks will Millie's balance remain above $620?
Select from the drop-down menu to correctly complete the statement.
Answer:
at least 8
Step-by-step explanation:
Answer:
At least 8
Step-by-step explanation:
I took the test
3. West Fremont is a community consisting of 3,000 homes. A small coal-burning power plant currently supplies electricity for the town. The capacity of the power plant is 12 megawatts
(MW) and the average household consumes 8,000 kilowatt hours (kWh) of electrical energy each year. The price paid to the electric utility by West Fremont residents for this energy is $0.10 per kWh. The town leaders are considering a plan, the West Fremont Wind Project (WFWP), to generate their own electricity using 10 wind turbines that would be located on the wooded ridges surrounds the town. Each wind turbine would have a capacity of 1.2 MW and each would cost the town $3 million to purchase, finance, and operate for 25 years.
(a) Assuming that the existing power plant can operate at full capacity for 8,000 hrs/yr, how many kWh of electricity can be produced by the plant in a year?
(b) At the current rate of electrical energy use per household, how many kWh of electrical energy does the community consume in one year?
(c) Assuming that the electrical energy needs of the community do not change during the 25-year lifetime of the wind turbines, what would be the cost to the community of the electricity supplied by the WFEP over 25 years? Express your answer in dollars/kWh.
Power is the rate of doing work, and the power of the generating plant or
turbine and the duration of generation, gives the energy generated.
The correct responses are;
(a) 96 × 10⁶ kWh(b) 24 × 10⁶ kWh(c) 0.05 dollars/kWhReasons:
Number of homes in the town = 3,000 homes
The given capacity of the power plant = 12 MW = 12,000 kW
Power consumed by a household = 8,000 kWh per year
The price for electrical energy = $0.10 per kWh
Number of wind turbines = 10
WFWP = The West Fremont Wind Project
Capacity of each wind turbine = 1.2 MW
Cost of each wind turbine for 25 years = $3 million
(a) Number of hours of operation of the power plant = 8,000 hrs/yr
Required:
The amount of kWh of electricity produced in a year by the plant.
Solution:
The energy produced = Power × Time
∴ The energy produced = 12,000 kW × 8000 hr = 96,000,000 kWh
Therefore;
The energy produced by the plant in a year, E = 96 × 10⁶ kWh
(b) Energy consumed = Energy consumed per home × Number of homes
Therefore;
Energy consumed = 8,000 kWh/home × 3,000 homes = 24,000,000 kWh
The energy the community consumes in one year = 24 × 10⁶ kWh
(c) The cost per kWh = $0.10
The cost, C, of the energy per year is therefore
C = 24,000,000 kWh × $0.10/kWh = $2,400,000
The cost for 25 years = 25 × C = 25 × $2,400,000 = $60,000,000
The number of wind turbines = 10
Cost per wind turbine = $3 million
Total cost to operate the 10 wind turbine = $3 million × 10 = $30 million
Energy consumed = 24,000,000 kWh
Therefore;
24,000,000 kWh × 25 = $30 million
[tex]\displaystyle 1 \ kWh = \frac{\$ 30 \ million}{25 \times 24,000,000 \ kWh} = \mathbf{\$0.05/kWh}[/tex]
The cost to the community of the electricity supplied by WFWP over 25 years is $0.05/kWh.
Learn more about energy and power here:
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Math isn't really my thing, so if you could help I would really, really appreciate!!
Answer:
1. 0.25
2. 105-40
3. 0.375
4. 0.5
5. 0.4 same as the number 6
Step-by-step explanation:
i hope it helpful i guess?
Find the perimeter of a regular polygon with an interior angle of 90° and side length 3.5 ft.
Please be accurate and explain.
Answer:
p=14 ft
Step-by-step explanation:
The figure that meets these conditions is the square
The perimeter:
4(3.5) = 14 ft.
Hope this helps
divide g by 9, then triple the result
Answer:
nose que dice no hablo inglesh :v
Trigonometry I need help please
Answer:
10.7°
Step-by-step explanation:
SOH CAH TOA
Tan(BCA) = x/y
= 4/21
BCA= Tan`¹(4/21)
= 10.7856
to 3SF = 10.7°
Help help help help math math
Answer:
y = -2x - 1
See image
Step-by-step explanation:
The "slope-intercept" form of the equation is the
y = mx + b form
So you need to find the slope (m) and the y-intercept (b), which you are able to find on the image in the question.
Slope (m) tells how steep a line is and whether it goes up or down from left to right. It also works just like directions, from any point on the line to any other point on the line.
The y-intercept (b) is the point on the line where the line crosses the y-axis.
The slope is -2 and the y-intercept is -1
So the equation is
y = -2x - 1
See image
6(25-8w)+20w for w=2
150−28w
i think i dont know
-6x+6y=9 (1/2,2) please helppppp
Answer:
Not a solution.
Step-by-step explanation:
[tex]-6x + 6y = - 9\\\rule{150}{0.5}\\-6(\frac{1}{2}) + 6(2) = -9\\\\-3 + 12 = -9\\\\9 =-9[/tex]
The final result is a contradiction. It is not a solution to the equation, and therefore, will not be on the line.
Which of the following is a proper fraction? A7001/6 B 9/4 C 31/99 D3/2
Answer:
31/99
Step-by-step explanation:
Becuase the numerator is lesser than the denominator
Answer:
C. 31/99
Step-by-step explanation:
It's C because a proper fraction is a fraction with a numerator that is less that it's denominator in its lowest terms
Help pleaseee????????
it will be equal to the photo
median 5
lowerWhich of the following equations describes the graph shown above
Answer: D
Step-by-step explanation:
this is in y=Mx+ b form. M stands for the slope and b stands for the y intercept, or where the line intersects with the y-axis.
Going left to right, the line slopes downwards, therefore it is a negative Slope. This narrows down your answer to either a or d. the slope is -1 because you can only ever write x by itself if it means 1x. In this case it is negative so it would look like this: -x
for the y-intercept, simply look at where the line passes through the y-axis. In this case, it is positive 2.
your finished equation would be: y=-x+2
i hope this is helpful
here are vaccinations for all of the following except __________
Question 10 options:
hepatitis C.
chicken pox.
tuberculosis.
mumps.
Answer:
Hepatitis C.
Step-by-step explanation:
Write the phrase "one more than the product of six and nine" as a mathematical expression.
Answer:
6.9+1
Step-by-step explanation:
hope it helps
[tex]\huge\mathfrak\blue{ ☃ }[/tex]
Answer:
the product of six and nine is fifty five
Help help help help math
Please answer this question IT IS NOT AVTEST DONT TRY TO DELETE IT.
Find the disFind the distance between the points P and Q shown.
tance between the points P and Q shown below
Step-by-step explanation:
I am sorry but please give detailed question
The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.
Enter a number answer only.
Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
Solve for the Width (W)P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]
[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]
Substitute the value of the Perimeter and the length (L) into the formula:
[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
Double-check:Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
Write an equation in standard form for the line that passes through (-1, -2) and (3, 0).
Find m
∠
F
E
D
∠FED. This question is going to be 20 points
Answer:
the answer is : 180° - (61° +61°) = 58°
Help help math math math
Answer:
10
Step-by-step explanation:
substitute -8 into x.
f(-8)=-8+18=10
Answer:
10
Step-by-step explanation:
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value?
You have to add.
Step-by-step explanation:
I'm trash at math.
the product of two factors is 4200.if one of the factors is 60.what is the other factor?
Answer:
Other factor is 70
Step-by-step explanation:
Let,
Other factor = x
Then,
x × 60 = 4200
x = 4200/60
x = 420/6
x = 70
∴Another factor is 70.
Answer:
Solution given
let two factor be a and b.
if one factor a=60, then b=?
we have
product of factor=4200
a*b=4200
60*b=4200
b=[tex]\frac{4200}{60}=70[/tex]
Step-by-step explanation:
A horse gallops 200ft, turns and trots 350ft, turns again and travels 410ft to return to the point he started from.
What is the area of the triangle formed by his path?
round to the nearest hundredth.
for Acellus!!!
Answer:
I think it's 28,700,000 feet
Step-by-step explanation:
Answer:
34,971.99
Step-by-step explanation:
Solve each inequality 3+1/2(3-x)<_7
Answer:
x > 5
Step-by-step explanation:
multiply the fractions, break up the fraction, group like terms, convert integer into a fraction, combine the fraction, combine the numerator, etc. hope this helps.
Helppp! I dont completly get the conceptttt
Sin(180-A)/tan(180-A) × cot(90-A)/tan(90+A) × cos(-A)/ cos(270-A) Please solve
so tan = me sun bathing for 2.5 second
Aline that includes the point 5. 10) has a siope of 1. What is its equation in siope-intercept
te your answer using integers, proper fractions, and improper fractions in simplest for
Step-by-step explanation:
a lot of typos in the problem description.
if I understand correctly, the line contains the point (5, 10) and has a slope of 1.
and we need to give the line equation in slope-intercept form.
that means it has to look like
y = ax + b
a is the slope and b is the y-intercept (hence the name of the form).
we know a = 1.
we can use use the point-slope form to start and then transform it into the slope-intercept form.
point-slope means
y - y1 = a(x - x1)
a is again the slope, and (x1, y1) is a point on the line.
so,
y - 10 = 1(x - 5) = x - 5
now we transform it (adding 10 on both sides)
y = x + 5
and that's it.