The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
A circle can be modelled after a expression of the form:
[tex]A\cdot x + B\cdot y + C =-x^{2}-y^{2}[/tex] (1)
We can determine all coefficients by knowing three distinct points on plane.
If we know that [tex](x_{1}, y_{1}) = (2, 8)[/tex], [tex](x_{2}, y_{2}) = (0, 8)[/tex] and [tex](x_{3}, y_{3}) = (2, 2)[/tex], then the solution of the system of linear equations is:
[tex]2\cdot A + 8\cdot B + C = -68[/tex] (2)
[tex]8\cdot B + C = -64[/tex] (3)
[tex]2\cdot A + 2\cdot B + C = -8[/tex] (4)
[tex]A = -2, B = -10, C = 16[/tex]
Now we proceed to complete squares and factor each resulting perfect square trinomial in order to determine the coordinates of the center of the circle:
[tex]x^{2}+y^{2}-2\cdot x -10\cdot y +16 = 0[/tex]
[tex](x^{2}-2\cdot x +1)-1+(y^{2}-10\cdot y +25)-25 +16 = 0[/tex]
[tex](x-1)^{2}+(y-5)^{2}= 10[/tex]
The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
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James is planning to spend $425 on food for his vacation this summer. This is 34% of his total vacation budget. How much is James' total vacation budget?
1250$,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
What us y+3=-2 (6x-1)
Answer:
y=-12x-1
Step-by-step explanation:
1+12-9+23409-1238 -12313+122321
What is the equation of the line in slope-intercept form?
The equation of the line is
Answer:
y=mx+b
Step-by-step explanation:
The slope-intercepts formula, the y = y coordinate, m = slope, x = x coordinate, b = y intercept
Graph y= 0.5x^2 - 4x +6 on the coordinate plane.
Vertex:
Is this considered a minimum or maximum point?
Axis of symmetry: x=
Roots: x= and x=
Answer:
V: (4, -2), min, Axis: x = 4, Roots 2 and 6
Step-by-step explanation:
Multiply everything x 2 to get rid of the decimal in front of x^2
2y = x^2 - 8x + 12
Factor
2y = (x - 6)(x - 2)
The roots are at 2 and 6.
The axis of symmetry is in the center between the roots, so it is x = 4.
Put 4 into the original equation to find y
y = 0.5(4*2) - 4(4) + 6
y = 8 - 16 + 6, y = -2
Vertex is at (4, -2). It is a minimum because the graph opens up since x*2 is positive.
Marcus has $15.00 to spend on fruit. He buys 3 mangoes and spends the rest of the money on grapes. The store charges $0.75 for each mango and $2.50 per pound for grapes. Which equation represents the number of pounds of grapes, x, Marcus bought and how many pounds of grapes did he buy?
Answer:
It equals to $13.25
Step-by-step explanation:
PLEASE PLEASE HELP!!! i’m struggglingggg
Given g(r) = 3 – 8r, find g (–3).
Answer: R = 3/5
Step-by-step explanation:
i think
add: 8x^2+7xy-6y^2, 4x^2-3xy+2y^2 and -4x^2+xy-y^2
Answer:
8x² - 5y² + 5xy
Step-by-step explanation:
8x² + 7xy - 6y² + 4x² - 3xy + 2y² - 4x² + xy - y² = (8x² + 4x² -4x²) + (-6y² + 2y² - y²) + (7xy - 3xy + xy) = 8x² - 5y² + 5xy
f(x)=-x^2-7x+9 find 7f(x)
Answer:
do it got a picture
on the edge
Step-by-step explanation:
question 4. Write an equation of the line that passes through (1, 2) and (3,-2).
Answer in slope-intercept form
O
Answer:
y=-2x+4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-2-2)/(3-1)
m=-4/(2)
m=-4/2
m=-2
y-y1=m(x-x1)
y-2=-2(x-1)
y-2=-2x+2
y=-2x+2+2
y=-2x+4
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Mr Page uses oil to heat his home.
At the beginning of November there were 1000 litres of oil in his oil tank.
Mr Page bought enough oil to fill the tank completely.
He paid 50p per litre for this oil.
He paid a total amount of £750
At the end of February Mr Page had 600 litres of oil in the tank.
He bought enough oil to fill the tank completely.
The cost of oil had increased by 4%.
Work out the total amount Mr Page paid for the oil he bought in February.
The total amount Mr Page paid for the oil he bought in February was $21,580.
Since Mr Page uses oil to heat his home, and at the beginning of November there were 1000 liters of oil in his oil tank, and Mr Page bought enough oil to fill the tank completely, and he has paid $50 per liter for this oil, and he has paid a total amount of $750, while at the end of February Mr Page had 600 liters of oil in the tank, and he has bought enough oil to fill the tank completely, and the cost of oil had increased by 4%, to determine the total amount Mr Page paid for the oil he bought in February, the following calculation must be performed:
1000 + (750 / 50) = X1000 + 15 = X1015 = X1015 - 600 = 415415 x (50 x 1.04) = X415 x 52 = X21,580 = XTherefore, the total amount Mr Page paid for the oil he bought in February was $21,580.
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Need help please if anyone one can help me now I will like that
Answer:
.
Step-by-step explanation:
PLEASE HELP QUESTION IN PICTURE
Find three consecutive even numbers such that the difference
between the square of the third and twice the square of the first is 32
Find the value of x in the solution of the system y = -4x + 48
Answer:
x = 12
Step-by-step explanation:
y= -4x+48
0=-4x+48
4x=48
x=12
Daniel has 7 photo books. Each book has 5 pages with 1 photo on each page. He gets 2 more pages with 1 photo on each page.
How many total photos does Daniel have? Enter the answer in the box
help please i’m doing homework and i can’t fail this lesson.
Answer: y = 3x +1
Step-by-step explanation:
How do you turn 48% in to a decimal?
Answer:
0.48
Step-by-step explanation:
Since a percent is ALWAYS a part of the number 1, this makes it to where you must multiply by 100 in order to convert a percent into a decimal. In this case, 48%(100) is 0.48.
I need help I have a test...!
Find the value of x in the figure:
Answer:
In first situation= =given angle + x=sum of angle of triangle. =110°+x=180°=70° X=70° Similarly, 2. condition can be solved i.e-x=144°
Step-by-step explanation:
help me out plzzzzzz
Answer:
A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Step-by-step explanation:
To factor this, you are looking for factors of 8×21 = 168 that have a sum of 34.
168 = 1×168 = 2×84 = 3×56 = 4×42 = 6×28 = 7×24 = 8×21 = 12×14
The sums of these factor pairs are 169, 86, 59, 46, 34, 31, 29, 26. The factor pair whose sum is 34 is 6×28. This means we can rewrite the expression as ...
8x² +28x +6x +21
Factoring by pairs gives ...
4x(2x +7) +3(2x +7)
(4x +3)(2x +7) ⇒ A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Answer:
......................
A community hall is in the shape of a cuboid.
The hall is 20m long, 15m wide, and 4m high.
Answer:
The total paint cost is £380. The total tiles cost is £1800. The total cost is £2180.
Step-by-step explanation:
To know the cost, you need to calculate the area of the community hall.
Area of the ceiling/floor: 40m x 15m = 600m2So together, their area is 1200m2.
Area of the small walls of the community hall: 15m x 3m = 45m2/each wallTogether the two walls have an area of 90m2
Area of the big walls of the community hall: 40m x 3m = 120mTogether the two big walls have an area of 240m2
So, therefore, the total area of the community hall: 1530m2Painting:
They are going to paint the walls and the ceiling and each 10L tin covers 25m2 so:
Area of the walls and ceiling = 600m2 + 90m2 + 240m2 = 930m2
930m2 ÷ 25m2 = 37.5 tins. Since you can't have half a tin, they will need 38 10L tins.
38 x £10 = £380
Floor:
1m2 floor tiles costs £3 so 600m2 x £3 = £1800
Total:
£1800 + £380 = £2180
(This is easy, but confusing) What is 1+ 2+ 3+ 4+ 5 -6 divided by 7 times 8 - 9???
Answer:
=-0.8
Step-by-step explanation:
1+2+3+4+5-6÷7×8-9
15-6÷7×8-9
15-0.85×8- 9
15-6.8-9
=-0.8
Write an equation of a line that is perpendicular to y = 2/3 x + 8 and has a y-intercept of
2.
Answer in slope-intercept form
Answer:
y = -3/2x + 2
Step-by-step explanation:
Since you know it has a point at (0, 2) - the y intercept, put those values into the equation and solve. To be perpendicular it seems the reciprocal of the slope with the opposite sign, so 2/3 is the original slope, and -3/2 becomes the new slope.
y = 2/3x + 8 becomes
2 = -3/2(0) + b We substitute in the x and y values, but we have to figure out what the last number will be.
2 = 0 + b
b = 2
So put the whole equation together
y = -3/2x + 2
what does the point (60,20) mean in the graph math
• The outside temperature changes -4.8°F in 4 hours. What is the average change in temperature each hour?
-19.2°F
-12.2°F
-1.8°F
-1.2°F
Answer:
-1.2°F
Step-by-step explanation:
-4.8F = 4 hours
Divide both sides by 4 to get one side to 1 hour
-4.8F/4 = 4 hours / 4
-1.2F = 1 hour
The average change in temperature each hour is -1.2°F
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that the outside temperature changes -4.8°F in 4 hours
We need to find the average change in temperature each hour
To find this we need to use division.
We need to divide -4.8 by 4
-4.8/4
Minus four point eight divided by 4
-1.2
Hence, the average change in temperature each hour is -1.2°F
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what is the set of all the output values in a function called?
Answer:
Set Y I’m pretty sure
Step-by-step explanation:
Question 1
On page 179 of your textbook, what percent of group A are Blue squares? What percent of group B are Blue squares? What percent of group C are Blue squares?
The Percent of Blue sqaures out of the total for Group A is _ %.
The Percent of Blue sqaures out of the total for Group B is _ %.
The Percent of Blue sqaures out of the total for Group C is _ %.
Answer:
The Percent of Blue sqaures out of the total for Group A is 75%.
The Percent of Blue sqaures out of the total for Group B is 60%.
The Percent of Blue sqaures out of the total for Group C is 66.66666%.
A cylinder has a height of 18 feet.
Its volume is 16,334.28 cubic feet.
What is the radius of the cylinder?
The answer is 17, Volume = h × π×r^2
Divide by known height from both sides
Divide by pi
square root
Please help I will give good points! Fake answers=report
Answer:
159
Step-by-step explanation:
10^2+(3+5)^2-5
First do the parentheses: 3+5 is 8
Now the equation is
10^2+8^2-5
Exponents:
10^2 is 100
8^2 is 64
100+64-5
Simplify and you would get 159
Thus the answer is 159
Hope this helps!
First thing we want to know is what it is asking us.
So, it is asking us to evaluate this expression. Which means to find the answer to it.
Second thing is the order of Operations.
P- (Parentheses)
E-Exponents
M Multiplication
D Division
A Add
S Sub
Now that we know what that means, we may now solve it.
you see a parenthesis, right? Do what is inside first
1.3+5=8
Now there is a exponent by the parentheses. We do that next
(Exponent means we times that number by the number. Like 4 to the power of 3 is really just 4x4x4)
2.8 to the power of 2 is 8x8 which is 64.
So, we got 64 down let's see our equation now.
10^2+64-5
Now, the next step in PEMDAS Is to do the exponents. 10 to the power of 2 is really just 10x10.
(A trick is that if you see the little number beside the 10, it means how many zeros there are like 10to the power of 2 is 100)
So, our new equation is
100+64-5.
Now all we have to do it add and sub right to left
100+64=164
Our new equation is 164-5 which is 159.
I hope this helps! If it's wrong blame me..