8 A circle passes through the points (0, 2) and (0,8) and its centre lies on the line
x=4.
Draw a sketch and find the equation of the circle.
Answers
Step-by-step explanation:
A circle that passes through point 0,2 and (0,8) and has a center that lies on x=4 is what given.
So we know is center (4,p) for some number p,
Since the points on circumference of the circle have the same x value, then we know that the y coordinate of the center must be the midpoint of the circumferences' y coordinates.
Why?
A circle is not a function since it doesn't pass the vertical line test. And the standard form of a circle is
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
With center (0,0).
Consider the equation
[tex] {x}^{2} + {y}^{2} = 9[/tex]
The radius is 3 so two points with x coordinate 0 is
(0,3) and (0,-3). And the midpoint of them is (0,0) which is the center. Which is the defining trait of all circles.
Now, back on hand, our the midpoint of 2 and 8 is 5 so our center is
(4,5).
Now, we must find the radius. We use distance formula.
For (4,5) and (0,8).
[tex]d = \sqrt{(8 - 5) {}^{2} + ({0 - 4) {}^{2} } } [/tex]
[tex]d = \sqrt{3 {}^{2} + {4}^{2} } [/tex]
[tex]d = \sqrt{25} [/tex]
[tex]d = 5[/tex]
So our radius is 5.
So now we use the equation of center h,k.
[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
H is 4
K is 5
[tex](x - 4) {}^{2} + (y - 5) {}^{2} = 25[/tex]
Above is sketch of graph.
Related Questions
A line passes through the point (-9,-4) and has a slope of -2/3 . write an equation in slope intercept form for this line
Answers
Answer:
[tex]y=-0.667x+-10[/tex]
Step-by-step explanation:
Given the following question:
Point A = (-9, -4), (x1, y1)
Point B = (-6, -6), (x2, y2)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-6--4}{-6--9} =\frac{-2}{3}[/tex]
[tex]m=\frac{-2}{3}[/tex]
Write in slope intercept form:
[tex]y=mx+b[/tex]
[tex]m=\frac{-2}{3}=-2\div3=-0.667[/tex]
[tex]y=-4[/tex]
[tex]x=-9[/tex]
[tex]-4=-0.667\times-9+b[/tex]
[tex]-0.667\times-9=6[/tex]
[tex]b=-10[/tex]
[tex]y=-0.667x+-10[/tex]
Hope this helps.
(3.4 x 10^-15) +(8.1 x 10^-14) help please, show work thank you
Answers
Answer:
see below
Step-by-step explanation:
1) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex].
[tex]3.4x*\frac{1}{10^{15} } +8.1*x*10^{-14}[/tex]
2) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex].
[tex]3.4x*\frac{1}{10^{15} } +8.1*x*\frac{1}{10^{14} }[/tex]
3) Use this rule: [tex]\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd} .[/tex]
[tex]\frac{3.4x*1}{10^{15} }+8.1*x*\frac{1}{10^{14} }[/tex]
4) Simplify [tex]3.4x*1[/tex] to [tex](3.4)x[/tex].
[tex]\frac{3.4x}{10^{15} } +8.1*x*\frac{1}{10^{14} } }[/tex]
5) Use this rule: [tex]\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd} .[/tex]
[tex]\frac{3.4x}{10^{15} } +\frac{8.1*x*1}{10^{14} }[/tex]
6) Simplify [tex]8.1*x*1[/tex] to [tex]8.1(x)[/tex].
[tex]\frac{3.4x}{10^{15} } *\frac{8.1*x}{10^{14} }[/tex]
find the domain of
- y/(y-6) +15/(y+6)
- y-10/y^2+3
Answers
Answer:
Step-by-step explanation:
Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.
Given function is,
If Domain (input values) of this function is,
{-12, -6, 3, 15}
Table for the input-output values of this function,
x -6 3 15 -12
y 11 5 -3 15
PLS HELP 30 POINTS
Find the area of the composite figure.
Answers
Answer:
104 m²
Step-by-step explanation:
From inspection of the diagram, we can see that the composite figure is made up of a triangle and a rectangle.
Triangle
If you turn the figure 90° clockwise, you will see that the base of the triangle = 8m and the height of the triangle = 6m.
Area of a triangle = 1/2 x base x height
⇒ area of the triangle = 1/2 x 8 x 6 = 24 m²
Rectangle
From inspection, the length of the rectangle = 10m and the width = 8m
Area of a rectangle = length x width
⇒ area of the rectangle = 10 x 8 = 80 m²
Composite figure area
Therefore the total area of the figure = area of triangle + area of rectangle
⇒ total area = 24 + 80 = 104 m²
Answer:
104 m^2
Step-by-step explanation:
See attached image.
Laurie is trying to stay within 10 feet of her current diving depth of -30 feet (with regard to sea level) so that the light
is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the
minimum and maximum depths Laurie wants to stay between?
-30 - x = 10 and -30 - x = -10
-30 + x = 10 and -30 + x = -10
x + 10 = 30 and x + 10 = -30
O X - 10 - 30 and x - 10 = -30
Answers
Answer:
I believe it's the 1st one.
HOPE IT HELPS! BE SAFE :3
Answer:
A
Step-by-step explanation:
find the radius of a cylinder with a volume 686mm2 and a height of 14mm
Answers
Answer:
r = 3.95 mm (nearest hundredth)
Step-by-step explanation:
[tex]\textsf{volume of a cylinder} = \pi r^2h[/tex]
(where r = radius and h = height)
Given, volume = 686 mm² and height = 14 mm:
[tex]686=\pi r^2\times14[/tex]
[tex]\implies\pi r^2=686 \div14=49[/tex]
[tex]\implies r^2=49 \div \pi[/tex]
[tex]\implies r=\sqrt{49 \div \pi }=3.949327085...[/tex]
[tex]\implies r=3.95 \ \textsf{mm}[/tex]
A tray of cake samples contains a variety of flavors.
vanilla 25
strawberry 1
lemon 2
red velvet 3
chocolate 2
What is the probability that a randomly selected piece of cake will be red velvet?
Write your answer as a fraction or whole number.
Answers
Answer: 1/11
Step-by-step explanation:
The probability that the selected piece will be red velvet is equal to the amount of red velvet cake divided by the total amount of cake.
Therefore, it would be 3/(25+1+2+3+2)
= 3/33
= 1/11 when simplified
What is the value of x in the figure below? In this diagram, ABD similar to CAD.
Answers
Answer:
x = [tex]\frac{25}{4}[/tex] so the answer is B
Step-by-step explanation:
11. An astronaut travels 32 million miles to Mars, turns around and comes back the same way, ending up exactly where he started his trip. What is his displacement?
Answers
Answer:
0
Step-by-step explanation:
Since displacement is the distance between the journey starting point and the final point if they both are the same the difference becomes zero and hence the displacement.
Displacement = final point - initial point
(both are same)
= same - same
= 0
What is the value of x?
Answers
If I’m correct, could you please give me brainliest?
Is (-3-2c)/(-3) the same as (2c+3)/(3)??
(I believe they are the same, but just checking.)
Answers
Answer:
Yes, they're the same.
Step-by-step explanation:
-3-2c can be re-written as -1(2c+3) and -3 can be re-written as -1(3). So you can rewrite the fraction as -1(2c+3)/-1(3). The -1's go away and the new fraction is (2c+3)/3.
HELP Solve for w x and y
Answers
Answer:
x = 24
PS = 45
Step-by-step explanation:
Perimeter of P Q R S is :
( 4x + 1 ) + ( 2x - 3 ) + ( 2x - 3 ) + 4 + ( 4x + 1 )
4x + 1 + 2x - 3 + 2x - 3 + 4 + 4x + 1
And in the question , given that the perimeter of this figure is 288.
Now let us find the value of x.
4x + 1 + 2x - 3 + 2x - 3 + 4 + 4x + 1 = 288
4x + 2x + 2x + 4x + 1 - 3 - 3 + 4 + 1 = 288
12x + 0 = 288
12x = 288
Divide both sides by 12
x = 24
And now let us find the value of PS
PS = 2x - 3
PS = 2× 24 - 3
PS = 48 - 3
PS = 45
Hope this helps you :-)
3 rhombi are connected at a point, side by side. All sides are congruent. Juan is making a model out of rhombi. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide. How much paper does he need for each rhombus? square inches If his wall is 11 feet long, how much paper does he use? square inches.
Answers
Rhombus has all sides equal. The total amount of paper that will be needed to cover the wall is 396 in².
Given to us
Each rhombus will be 6 inches tall and 4 inches wide.
A.)
The area of each rhombus can be found using the formula,
[tex]Area = \dfrac{1}{2} \times d_1 \times d_2[/tex]
We know that diagonals of the rhombus are of length 6 in and 4 in. therefore,
[tex]Area = \dfrac{1}{2} \times 6 \times 4\\\\Area = 12\ in^2[/tex]
Hence, the area of the single rhombus is 12 in².
We know that the wall is 11 feet long, also, 1 foot = 12 inches, therefore,
11 feet = 132 in.
Now, since the wall is 132 in long and the width of the rhombus is 4 in, therefore, the number of rhombi that will be needed,
[tex]\dfrac{132}{4} =33[/tex]
Hence, the number of rhombi that will be needed is 33.
We know the area of each paper rhombus, also, we know the number of rhombi that will be needed. Therefore,
[tex]33 \times 12 = 396\ in^2[/tex]
Hence, the total amount of paper that will be needed to cover the wall is 396 in².
Learn more about Rhombus:
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Answer:
3 rhombi are connected at a point, side by side. All sides are congruent.
Juan is making a model out of rhombi. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide.
How much paper does he need for each rhombus?
✔ 12
square inches
If his wall is 11 feet long, how much paper does he use?
✔ 396
square inches
Step-by-step explanation:
egd
TOSSING A NUMBER cube numbered from 1 to 6 and getting and even number that is greater that or equal to 2
Answers
Answer:
the probability is 3/5
Step-by-step explanation:
you have the numbers 2, 4, 6
and the numbers 3, 5
the 1 doesn't count, the question says numbers greater than or equal to 2
so, the remaining numbers add up to 3/5
If each side of a square grows 6 mm, the area of the square is multiplied by 16. How long are the sides of the original square?
Answers
Answer:
2 mm
Step-by-step explanation:
Let x be the sides of the original square,
then the area of the original square is x^2
The sides of the new square is x + 6
The area is (x + 6)^2
Then (x + 6)^2 = 16*x^2
Take square root on both sides and get
x + 6 = 4x,
3x = 6
so x = 2 mm
5. Rewrite the following equation in standard form.
2y=-3/4x-2/3
Answers
Answer:
9x +24y = -8
Step-by-step explanation:
2y + 3/4 x = -2/3 ( multiple by 4)
24y + 9 x = -8 (move x to the front)
9x + 24y = -8
identify the trinomial that is not a perfect square
Answers
Answer: To test whether the given trinomial is a perfect square, we should try to write the trinomial in the form of a² + 2ab + b² (or) a² - 2ab + b² If we are able to write the given trinomial in the above form, then it is perfect square. Otherwise the given trinomial is not a perfect square.
Step-by-step explanation:
0 = 5² - 2х + 6
a) x = 1 ± 3i / 2
b) x = 1 ± √11 / 5
c) x = 1 ± i √29 / 5
Answers
Answer:
c) x = 1 ± i √29 / 5
Step-by-step explanation:
assuming we are solving for x we can use the quadratic formula
quadratic formula : [tex]\frac{-b+or-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]
where the values of a,b and c are derived from the equation
the equation is put in quadratic form : ax² + bx + c
so in 5x² -2x + 6 a = 5 , b = - 2 and c = 6
we then plug these values of a, b and c into the quadratic formula
recall quadratic formula [tex]\frac{-b+or-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]
a = 5 , b = - 2 , c = 6
[tex]\frac{-(-2)+or-\sqrt{(-2)^2-4(5)(6)} }{2(5)}[/tex]
remove parenthesis at -(-2) to get positive 2 because the negative signs cancel out
[tex]\frac{2+or-\sqrt{(-2)^2-4(5)(6)} }{2(5)}[/tex]
evaluate exponent
[tex]\frac{2+or-\sqrt{4-4(5)(6)} }{2(5)}[/tex]
multiply -4(5)(6)
[tex]\frac{2+or-\sqrt{4-120} }{2(5)}[/tex]
subtract 120 from 4
[tex]\frac{2+or-\sqrt{-116} }{2(5)}[/tex]
multiply 2 and 5
[tex]\frac{2+or-\sqrt{-116} }{10}[/tex]
because we cant have a negative square root we replace the negative sign with i (which equals -1 ) and add it to the outside of the square root
[tex]\frac{2+or-i\sqrt{116} }{10}[/tex]
we then simplify the radical
[tex]\frac{2+or-2i\sqrt{29} }{10}[/tex]
we then simplify the fraction
2/10 = 1/5 so both 2's cancel out
[tex]\frac{1+or-i\sqrt{29} }{10}[/tex]
the answer is C
Three friends each bought matching necklaces and one pair of earrings. The necklaces were priced at $30.00. If the total bill for all 3 friends was $180.00, what was the price of one pair of earrings?
Answers
the sum of ten times a number and 12
Answers
Answer:it’s 10x + 12
Step-by-step explanation:
your welcome
The sum of ten times a number and 12 can be written as 10x + 12.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The expression "ten times a number" can be represented as 10x, where x is the number.
So, "the sum of ten times a number and 12" can be written as:
10x + 12
This expression represents a mathematical operation where 10 times the number is added to 12.
Thus,
The sum of ten times a number and 12 can be written as 10x + 12.
Learn more about expressions here:
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IM MARKING BRAINLEIST SO PLS BE QUICK IS DUE IN MINS
Answers
Answer:
x^2y−7xy+10xy^2
Step-by-step explanation:
(the first y isn't up but I tried)
anyways, hope this helped! :)
Answer:
[tex]4x^2y-7xy+10xy^2[/tex]
Step-by-step explanation:
We have [tex]\left(6x^2y-8xy+7xy^2\right)+\left(3xy^2-2x^2y+xy\right)[/tex] and need to add them together.
Though complicated at first, we can simplify by taking out the parenthesis and making this whole question into one equation.
[tex]\left6x^2y-8xy+7xy^2\right+\left3xy^2-2x^2y+xy\right[/tex]
Now combine like terms, meaning you can only add the terms that have the same ending, in math, you cannot add numbers that have different exponents or variables.
Therefore:
[tex]\left6x^2y-8xy+7xy^2\right+\left3xy^2-2x^2y+xy\right[/tex]
[tex]6x^2y-2x^2y-8xy+xy+7xy^2+3xy^2[/tex]
[tex]4x^2y-7xy+10xy^2[/tex]
if the average speed is 2.6km per hour and distance is 55km.What is the time?
Answers
Answer:
21.15 hrs
Step-by-step explanation:
I divided 55 by 2.6 to get the 21.15.
Have a good day!
A rational number between 11 and 12
Answers
Answer:
it would be 23/2
Step-by-step explanation:
Answer:
11.5
Step-by-step explanation:
A rational number is one that does not repeat.
2) Choose the best answer.
Find the volume of this terrarium. You may use a calculator to find the answer.
l = 5 m, w = 1 m, h = 3 m
A. 30 m2
B. 15 m3
C. 5 m2
D. 7.5 m3
E. 9 m3
p
Pelz I really really need help:(
Answers
Answer:
B. 15 m^3
Step-by-step explanation:
The volume of a rectangular prism is the product ...
V = lwh
For the given values of l, w, h, the volume is ...
V = (5 m)(1 m)(3 m) = 15 m^3
Does the point (-2,-3) lie in the graph of y>2x+1?
Answers
Answer:
Yes.
Step-by-step explanation:
Replace x with -2 and y with -3.
-3 = 2(-2) + 1
-3 = -4 + 1
Is -3 = -4 + 1?
Yes, so the answer is yes.
Use the distributive property to remove the parentheses.
(v + 10)7
Answers
Answer:
7v+70
1v x 7=7v
10 x 7=70
Step-by-step explanation:
Sorry if wrong!
Answer:
the answer is
7v + 70
I need help with these inequalities
Answers
when a number is increased by 9.5% the result is 58 what is the original number to the nearest tenth?
Answers
Answer:
53 i think
Step-by-step explanation:
What is the volume of the sphere in cubic centimeters?
Possible answers:
A. 201
B. Not enough information is given to calculate this volume
C. 1608
D. 2144
Answers
Answer:
D. 2144.6
Step-by-step explanation:
volume of a sphere is 4/3 * pi * r^3
we've been given the value of our radius as 8 and also the value for pi is 3.142 so in you solve using the formula you get 2144
[tex]\\ \rm\Rrightarrow V=4/3\pi r^3[/tex]
[tex]\\ \rm\Rrightarrow V=4/3\pi (8)^3[/tex]
[tex]\\ \rm\Rrightarrow V=4/3\pi 512[/tex]
[tex]\\ \rm\Rrightarrow V=170.6(4)\pi[/tex]
[tex]\\ \rm\Rrightarrow V=682.4cm^3[/tex]
The balance after the grace period is $25,000. A payment of $5,000 is made on the 10th day. A payment of $5,000 is made on the 20th day. What is the average daily balance?
Answers
The average daily balance after 20 days is; $1750
Average BalanceThe initial balance after grace period is; $25,000
Afterwards, A payment of $5,000 each is made on the 10th and 20th day.
Hence, the total balance after 20 days is;
= $25,000 + $5000 + $5000= $35,000.The average daily balance is therefore the quotient of $35,000 and 20 days
The average daily balance = $35,000/20Average daily balance = $1750Read more on average;
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