Answers
PQ is the diameter so the midpoint of PQ is the center of the circle. if we suppose the center point of the circle called o then ;
[tex]o = \frac{pq}{2} \\ [/tex]
[tex]pq = \sqrt{ { (- 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]o = \frac{( -10 ,10) + (6 , - 2) }{2} \\ [/tex]
[tex]o = \frac{( - 10 +6 ,10 - 2)}{2} \\ [/tex]
[tex]o = ( \frac{ - 4}{2} , \frac{8}{2} ) \\ [/tex]
[tex]o = ( - 2,4)[/tex]
For the second step we need to find the radius of the circle which has the half the PQ distance measure, so we have to find the the PQ distance and divide it by 2 :
_____________________________________________
As u know the distance between 2 point is going to find by following formula :
[tex]pq = \sqrt{ {(x(p) - x(q)})^{2} + {(y(p) - y(q)})^{2} } \\ [/tex]
[tex]pq = \sqrt{ ({ - 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]pq = \sqrt{ ({ - 16})^{2} + ({12})^{2} } [/tex]
[tex]pq = \sqrt{256 + 144} [/tex]
[tex]pq = \sqrt{400} [/tex]
[tex]pq = 20[/tex]
Thus :
[tex]radius = \frac{pq}{2} \\ [/tex]
[tex]radius = \frac{20}{2} \\ [/tex]
[tex]radius = 10[/tex]
_____________________________________________
Ok we're almost done cuz we have what we needed:
If we suppose that the first coordinate of the center is a and the second coordinate of the center is b and the radius shown by r then :
[tex] ({x -a})^{2} + ( {y - b})^{2} = {r}^{2} [/tex]
Is the equation of the circle in the standar form thus :
[tex] ({x - ( - 2)})^{2} + ({y - 4})^{2} = {10}^{2} \\ [/tex]
[tex] ({x + 2})^{2} + ({y - 4})^{2} = 100[/tex]
As u can see option B is the correct answer.
And we're done ...
Have a great day ♡♡♡♡♡Related Questions
Which function has a range of {y|y ≤ 5}? f(x) = (x – 4)2 5 f(x) = –(x – 4)2 5 f(x) = (x – 5)2 4 f(x) = –(x – 5)2 4
Answers
The function range of {y|y ≤ 5} is f(x)=-(x-4)^4+5.
Since the range has less than a sign, this means that the parabola is
facing downwards and it means that a is negative.
The range is given by
[tex]{y|y \leq k}[/tex]
What is the vertex form of a quadratic equation?[tex]f(x)=a(x-h)^2+K[/tex]
Since the range is
[tex]{y|y \leq 5},[/tex]
This means that k = 5 , and since a is negative
The correct function is
[tex]f(x)=-(x-4)^4+5[/tex]
To learn more about the range visit:
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Answer: B: (f(x) = –(x – 4)2 + 5)
Step-by-step explanation:
is y=x^3 a linear equation
Answers
Answer:
No
Step-by-step explanation:
Linear equations, when graphed, look like straight lines.
Examples include:
y= mx + b
y = 3
x + 2 = 0
y + 6 = 0
y = 7x +2
Please help me. I’m not so familiar with graphing.
Answers
Answer:
Hey i believe this is the answer
Step-by-step explanation:
Take a look at the screenshot
Also Desmos graphing calculator is a big help :) It might make you a little more confident
I can’t solve this can someone help me
Answers
Answer:
[tex]\textsf{D.}\quad\dfrac{b}{\sqrt{a^2+b^2}}[/tex]
Step-by-step explanation:
Tan trig ratio
[tex]\tan(x)=\sf \dfrac{O}{A}[/tex]
where:
[tex]x[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleUsing the given information:
[tex]\implies x=\tan^{-1}\left(\dfrac{a}{b}\right)[/tex]
[tex]\implies \tan(x)=\tan\left(\tan^{-1}\left(\dfrac{a}{b}\right)\right)[/tex]
[tex]\implies \tan(x)=\left(\dfrac{a}{b}\right)[/tex]
Comparing this with the trig ratio, we can say that:
[tex]x[/tex] is the angle opposite side [tex]a[/tex]
Cos trig ratio
[tex]\cos(x)=\sf \dfrac{A}{H}[/tex]
where:
[tex]x[/tex] is the angleA is the side adjacent the angleH is the hypotenuseTherefore:
A = side [tex]b[/tex]H = side [tex]\sqrt{a^2+b^2}[/tex][tex]\implies \cos\left(\tan^{-1}\left(\dfrac{a}{b}\right)\right)=\cos(x)= \dfrac{b}{\sqrt{a^2+b^2}}[/tex]
Answer number 17 please
Answers
Answer:
Ava
Step-by-step explanation:
Ava's = 100/10 = 10
Ian's = 110/20 = 5.5
A roof is constructed as shown. What is the length of the slope of the roof? Round to the nearest 10th
Answers
Answer:
Length of slope = 15.8 yd
Step-by-step explanation:
using Pythagoras theorem,
?² = 13² + 9²
?² = 169 + 81
? = √250
? = 15.8 yd
Step-by-step explanation:
According to Pythagoras theorem ,
Hypotenuse ² = Perpendicular ² + base ²
Here , we have to find the hypotenuse
perpendicular = 13ydbase = 9ydputting the known values ,
Hypotenuse² = (13yd)²+ (9yd)²
Hypotenuse² = 169+81
Hypotenuse² = 250 yd
Hypotenuse = √250 yd
Hypotenuse = 15.8 yd
Which equations represent nonlinear functions?
y= 2x + 7
y= 6(x-1)
y= x2+ 2
y=-5/x
Answers
Answer:
y = x² + 2
y = -5/x
Step-by-step explanation:
Linear & Nonlinear Definition:
Linear is something that is associated with a straight line such as linear equation or function. That means the highest degree of equation has to be 1 or only x.Nonlinear is something that does not form a line graph such as parabola, cubic, exponential, etc.From choices:
Both y = 2x+7 and y = 6(x-1) are linear because they have highest degree as 1 which is only x and these equations are known as linear function.However, both y = x²+2 and y = -5/x are nonlinear because y = x²+2 forms parabola which is a curve graph and also has highest degree of 2. As for y = -5/x, this is called fractional function which also forms curve graph and the degree of this equation is -1 via law of exponent.Therefore, y = x²+2 and y = -5/x are nonlinear.
Mark bought a drink for $2. 39 and chips for $1. 89. If he pays with a $20 bill, how much change will he receive?
Answers
Explanation:
This is because you add $2.39 and $1.89. Then you subtract the total from $20.00.
20.00 - 4.28 = 15.72
solving quadratic inequalities
Answers
Answer:
[tex]\boxed{\sf x < -3\quad \mathrm{or}\quad \:x > -1}[/tex]
Step-by-step explanation:
[tex]\sf x^2+4x+3 > \:0[/tex]
In order to solve inequality, we need to factor the left hand side. we can use the transformation [tex]ax^2+bx+c=a(x-x_1)(x-x_2)[/tex] to factor quadratic polynomials. where x(1) & x(2) are the solutions of the quadratic equation ax²+bx+c=0 .
[tex]\sf x^2+4x+3=0[/tex]
Quadratic formula:-
[tex]\boxed{\sf x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\sf a=1\\b=4\\c=3[/tex]
[tex]\sf \cfrac{-4\pm \sqrt{4^2-4\times \:1\times \:3}}{2\times \:1}[/tex] ← Calculate
[tex]\sf \sqrt{4^2-4\times \:1\times \:3}=\boxed{2}[/tex]
[tex]\sf \cfrac{-4\pm \:2}{2\times \:1}[/tex]
Now, let's Separate the solutions,
[tex]\sf x_1=\cfrac{-4+2}{2\times \:1},\:x_2=\cfrac{-4-2}{2\times \:1}[/tex]
Do the calculations,
[tex]\sf x_1=\cfrac{-4+2}{2\times \:1}=\boxed{-1}[/tex]
[tex]\sf x_2=\cfrac{-4-2}{2\times \:1}=\boxed{-3}[/tex]
[tex]\boxed{\sf x < -1\quad \mathrm{or}\quad \:x > -3}[/tex]
Miguel has a kite shaped like a rhombus. The two diagonals measure 10 inches and 3 inches. What is the area of the kite?
Answers
Answer:
15
Step-by-step explanation:
26 Inches!
10 + 3 = 13
13 + 13 = 26 (10 + 10 + 3 + 3)
Jake's net pay is $160.65 after deductions of $68.85. He makes $8.50 per hour. how many hours did he work?
Answers
Answer:
27 hours
Step-by-step explanation:
160.65 = 8.50x-68.85
x=27
Mr. Fowler's science class grew two different varieties of plants as part of an
experiment. When the plant samples were fully grown, the students
compared their heights.
Plant
variety
Mean Mean absolute deviation
(inches)
Helght of plant
(inches)
20, 17, 19, 18, 21
13, 18, 11,9,14
19
1.2
Variety A
Variety B
13
2.4
Based on these data, which statement is true?
O A. The height of a plant from variety B is likely to be closer to the
mean
B. Plants from variety A always grow taller than plants from variety B.
C. The maximum height for plants from variety B is greater than for
variety A
O D. The height of a plant from variety A is likely to be closer to the
mean
Please help who ever answers first and the answer is correct will get brainlist please help fast!!!!
Answers
Answer:
B. plant from variety Always grow taller than plant from variety B
Anybody knows 3x^2+6x-10 + 3x+5
Answers
solution:
3x^2+9x-5
i hope this helps
:)
It takes 12 hours to make a trip going 50 mph. How fast would you need to go to make it in 10 hours?
Answers
Answer:
10 hours = 60 mph
you will need to go 60 mph to make the trip 10 hours
explaination:
Multiplying the amount of hours and the mph, 12 times 50 is 600 miles.
10 times 60 is 600 miles. They both have the same answer, but 60 mph is the fastest. 60 mph is how fast you would need to go to make it in 10 hours.
I dont know if i explained it good.
A total of 392 were sold for the school play. They were either adult tickets or student tickets. The number of students sold was three times the number of adult tickets sold. How many adult tickets were sold?
Answers
The claim being assessed in a hypothesis test is called.
Answers
Explain how this shows that you can multiply numbers in any order and get the same answer.
Answers
Answer:
i dont see the problem but lets say you have 19*8*15
Step-by-step explanation:
19*8=152*15=2280
8*15=120*19=2280
any way you multiply them their always gonna add up to the same thing
Which statement is true?
Answers
We will see that the fourth statement:
"-0.3*|3 + 8x| = 0.9 has no solutions."
Is the true statement.
Which statement is true?Here we need to see which statement regarding absolute value equations is true.
Here you can see that the fourth statement is:
-0.3*|3 + 8x| = 0.9 has no solutions.
Now, if you look at the left side of the above equation, the left side will always be negative, while the right side is positive, then the equation can't have a solution.
There is no value of x that makes that equation true, so it is true that the given equation has no solutions. This is the correct statement.
If you want to learn more about absolute values, you can read:
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What is the value of x?
Answers
Answer:
Step-by-step explanation:
Sum of all angles of triangle = 180
17x + 10x -5 + 50 = 180
Combine like terms
27x + 45 = 180
To find the valu of x, we have to isolate x. To isloate x
Step 1: Subtract 45 from both sides
27x = 180 - 45
27x = 135
Step 2: Divide both sides by 27
x = 135/27
x = 5
$21.46 Divided By 37 I want the solution and the answer
Answers
Answer:
[tex] \frac{21.46}{37} = 0.58[/tex]
[tex]answer:$0.58[/tex]
The two cones below have the same radius, height, and volume. are the two cones congruent? explain and include details to support your claim.
Answers
The cones are not congruent because one cone is oblique, which makes the length of the slant heights different.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
The two cones below have the same radius, height, and volume.
One cone is oblique.
The cones have different slant heights.
The lengths of all corresponding edges are not equal.
Since, Congruent cones must have congruent corresponding measures, including slant height.
The cones are not congruent because one cone is oblique, which makes the length of the slant heights different.
Learn more about congruent;
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Answer:
Sample Response: The cones are not congruent because one cone is oblique, which makes the length of the slant heights different. Having the same radius, height, and volume does not make the cones congruent when the corresponding slant heights are not equal. Congruent cones must have congruent corresponding slant heights, with all other corresponding parts being congruent.
What did you include in your response? Check all that apply.
One cone is oblique.
The cones have different slant heights.
The lengths of all corresponding edges are not equal.
Congruent cones must have congruent corresponding measures, including slant height.
question b only please
b) A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line : cost of one arc = 2 : 3
Work out the total cost of metal in the pattern.
Answers
Answer:
total cost= 24.6
Step-by-step explanation:
12 ÷ 20 = 0.6 per straight line
arc 0.6 × 3/2 = 0.9
12 + 0.9 × 14
12 + 12.6 = 24.6
The required cost of the metal used in the pattern is £24.6.
Given that,
A different pattern is made using 20 straight lines and 14 arcs.
The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line is cost one arc = 2 : 3.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the cost of the total arcs be x,
As per the given condition,
The cost of the one straight line is 12/20 and cos if the one arc is x/14,
According to the question,
[12/20]/[x/14] = 2/3
12×14/20 = 2x / 3
x = £12.6
The total cost of a metal arc is £12.6
And the total cost of the metal line in the pattern is = £12.
Total cost of metal = 12 + 12.6 = £24.6
Thus, the required cost of the metal used in the pattern is £24.6.
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ5
Which comparison is correct?
Answers
Answer:
B
Step-by-step explanation:
-5 is less than -4 is true. it cannot be the first one because they are equal. It cannot be the third one because the absolute value of 5 (which is 5) is not greater than 7. And, it cannot be the last on because the absolute value of -5 (which is also 5) is not less than -4.
Which of the following is true? (8th Math)
Answers
This is true because when simplifying the two equations you end up with 0=0 making all real numbers a solution to the equation
Lines l and m are parallel lines cut by the transversal line t. Which angle is congruent to ∠7
Answers
congruent angles are of similar measures
congruent angles that are congruent to ∠7:
∠6 ( vertically opposite angles )∠3 ( corresponding angles )∠2 ( alternate interior angles )See how
<7+<5 are linear pairs<5+<3 are also linear pairsFrom both
<7 and <3 are equal(Corresponding angles)Similarly
<7 nd <6 are equal (Opposite angles)And
<6 and <2 are corresponding and equal so
<7 and <2 are equalWhich function represents the graph
Answers
The absolute value function represented by the graph is:
y = -3*|x|
So the correct option is B.
Which function represents the graph?
In the graph, we can see a "V" shape, which belongs to the absolute value functions, but this graph opens down, so our function will be something like:
y = -a*|x - b|
The value of b is the value of x where we have the vertex, in this case, is at x = 0, so b = 0
y = -a*|x|
To get the value of 1, we ise one of the points that we can see on the graph. For example, for x = 1, we have y = -3, replacing that we get:
-3 = -a*|1| = -a
3 = a
So we can conclude that our function is:
y = -3*|x|
So the correct option is B.
If you want to learn more about absolute value functions, you can read:
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A quarter of a circle has a radius of 7cm. What is is the area of the shaded part
Answers
Answer:
14
Step-by-step explanation:
using the formula:
(theta/360 pi r^2)-(1/2ab(the radius)sin theta)
theta is obtained by multiplying 1/4 and 360 therfore theta is 90°
Derek lives in canada and enjoys herb gardening. his american friend sent him a guidebook for growing fresh herbs. the book says that it is best to cut bay shoots when they are 3.25 in long. if 1 mm is equivalent to 0.03937 in, how many millimeters long should the bay shoots be when derek cuts them? a. 8.26 mm b. 12.80 mm c. 82.55 mm d. 95.67 mm
Answers
When the bay shoots are 82.55 mm, Derek should cut them according to the guidebook for growing fresh herbs option (c) is correct.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.
The book says that it is best to cut bay shoots when they are 3.25 in long.
As it is given that the:
1 mm = 0.03937 in
To find how many millimeters long should the bay shoots be when Derek cuts them, we must convert 3.25 in to mm
From the 1 mm = 0.03937 in, we can find how many mm is there in 1 in;
[tex]\rm 1 \ in= \frac{1}{0.03937} \ mm[/tex]
To convert 3.25 in into mm, we must multiply it by 1/0.03937
= 3.25×(1/0.03937)
= 82.55 mm
Thus, when the bay shoots are 82.55 mm, Derek should cut them according to the guidebook for growing fresh herbs option (c) is correct.
Learn more about the unit conversion here:
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Which word in this excerpt from "Places" by Sara Teasdale connotes a soothing feeling?
1. Hush
2. Flaming
3. Fired
4. Desired
Answers
Answer:
1. Hush
Step-by-step explanation:
Answer:
The answer should be D.) Desired.
Step-by-step explanation:
The definition of soothing is "having a gently calming effect",
A.) Hush, which in most cases is negative,
B.) Flaming, does not sound gentle OR calming,
B.) Fired usually comes from a negative impact, so your answer MUST and SHOULD be, D.) Desired.
How many outcomes are possible when you roll 3 regular six-sides dice ?
Answers
Answer:
216 outcomes.
Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes