Given:
Center of the circle P = (-4,7)
Point on the circle = (-1,9).
To find:
The equation of the circle P.
Solution:
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, (h,k) is the center and r is the radius of the circle.
Center of the circle is at point (-4,7). So, [tex]h=-4,k=7[/tex].
The center passes through the point (-1,9). So, the distance between the point (-1,9) and the center (-4,7) is the radius.
Distance formula:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the distance formula, we get
[tex]r=\sqrt{(-4-(-1))^2+(7-9)^2}[/tex]
[tex]r=\sqrt{(-3)^2+(-2)^2}[/tex]
[tex]r=\sqrt{9+4}[/tex]
[tex]r=\sqrt{13}[/tex]
Substituting [tex]h=-4,k=7[/tex] and [tex]r=\sqrt{13}[/tex] in (i), we get
[tex](x-(-4))^2+(y-7)^2=(\sqrt{13})^2[/tex]
[tex](x+4)^2+(y-7)^2=13[/tex]
Therefore, the equation of the circle P is [tex](x+4)^2+(y-7)^2=13[/tex].
The equation of the circle P is (x +4)² + (y-7)² = 13
What is the standard equation for a circle ?The standard equation for a circle is
(x - h)² +(y-k)² = r²
here the centre of the circle is (h,k) and r is the radius
It is given that
Circle P is graphed in the coordinate plane with centre (- 4, 7)
The equation can be written as
(x +4)² + (y-7)² = r²
It is also given that
Circle P contains the point (-1,9)
Therefore
( -1 +4)² + (9-7)² = r²
3² + 2² = r²
r² = 9+4 = 13
r = √13
Therefore the equation of the circle P is
(x +4)² + (y-7)² = 13
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true or false : A triangle can have interior angles of 50 degrees, 70 degrees, and 68 degrees
Answer:
it is false as the sum of the degrees of the triangle should be 180 but here it is 188 so it is false
Let R(x)=3x3+2x2+x and S(x)=4x2+1. Find R(x)−S(x).
Answer:
hope it will help u......................
The function R(x) - S(x) is [tex]3x^{3} -2x^{2} +x-1[/tex].
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.
According to the given question.
We have two functions
[tex]R(x) = 3x^{3} +2x^{2} +x[/tex]
And, [tex]S(x) = 4x^{2} + 1[/tex]
Therefore, the function R(x) - S(x) is given by
[tex]R(x) - S(x) = 3x^{3} +2x^{2} +x-(4x^{2} +1)[/tex]
[tex]\implies R(x) - S(x) = 3x^{3} +2x^{2} +x - 4x^{2} -1[/tex]
[tex]\implies R(x) - S(x) = 3x^{3} -2x^{2} +x-1[/tex]
Hence, function R(x) - S(x) is [tex]3x^{3} -2x^{2} +x-1[/tex].
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A company is testing and comparing two hair spray formulas. The box plots show the number of hours each hair spray lasts before reapplication is necessary. Which statement is best supported by the information in the plots?
1.Hair spray B will always last two hours longer than hair spray A.
2.Hair spray A will likely last longer than hair spray B.
3.Hair spray B will likely last longer than hair spray A.
4.Hair spray B will always last longer than hair spray A.
Answer:
Foundations of Financial Management with Time Value of Money card (15th Edition) Edit edition Solutions for Chapter 4 Problem 9P: Vitale Hair Spray had sales of 13,000 units in March. A 70 percent increase is expected in April. The company will maintain 30 percent of expected unit sales for April in ending inventory.
Step-by-step explanation:
Can somebody pls help me!!?
Answer:
$ 7.29
Step-by-step explanation:
bill = $40.50
tip = 18%
tip amount = tip% of bill
=18/100 * $40.50
=729/100
=$ 7.29
Answer:
7.29 DOLLARS IS THE ANSWER
may anyone help me please and thank you so much !
Answer:
8
Step-by-step explanation:
Which expression represents the situation below?
14 times the sum of 8 and 7, divided by 6.
Answer:
option 1
Step-by-step explanation:
Sum of 8 and 7 = 8 + 7
14 times sum of 8 and 7 = 14 x (8 + 7)
Divided by 6 = 14 × (8 + 7) ÷ 6
Answer:
1.) 14 × ( 8 + 7 ) ÷ 6
Step-by-step explanation:
Sum of 8 and 7 = 8 + 7
14 times of sum of 8 and 7 = 14 × ( 8 + 7 )
And it Divided by 6 = 14 × ( 8 + 7 ) ÷ 6
Find the average of the numbers 8, 13,15
Answer:
average = 12
Step-by-step explanation:
average = sum of numbers/no. of numbers
=8 + 13 + 15 /3
=36/3
=12
A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?
Answer:
30 inches
Step-by-step explanation:
f(x) = –2(x)(x – 8)
x = 3
f(3) = -2(3)(3 - 8)
f(3) = -2(3)(-5)
f(3) = 30
30 inches
Answer:
30 inches
Step-by-step explanation:
When a hockey team gets possession of the puck, the following probabilities have been
estimated:
They carry the puck over the opposing blue line 0.6.
• They get a shot on net 0.3.
• They get a shot and score 0.01
• They cross the blue line and score 0.005.
Determine the probability that they score given that they get a shot.
Answer: p(a given b) = p(a and b) / p(b)
a is the probability that they score.
b is the probability that they cross the blue line.
p(a and b) is given as .005
this is the probability that they cross the blue line and score.
p(b is given as .6
that's the probability that they cross the opposing blue line.
the formula becomes:
p(a given b) = .005 / .6 = .0083333333.....
that's what i get using the p(a given b) formula.
Step-by-step explanation:
Which linear inequality is represented by the graph?
plz help
what equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number"?
Answer:
6+2(n+4) = (3-n)÷2
Step-by-step explanation:
6 + 2n + 8 = (3-n)/2
14 + 2n = (3-n)/2
multiply through by 2 to eliminate the denominator
28 + 4n = 3 - n
25 + 4n = -n
25 = -5n
n = -5
EASYY ASAPPP!!!!!!
Include 3 examples of each vertical, horizontal, and oblique lines of symmetry that you can find in your house. List them below
Answer:
fridge. door. cabinet. Each line goes from bottom right to top left
Step-by-step explanation:
ANSWERS:
positive linear
negative linear
nonlinear
no relationship
Answer:
Step-by-step explanation:
No relationship i belive
help me with these!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Hope this helps u!!
Given
f (x) = x3 + 1
and
g(x) = x – 1
find the composition
f(g(x))
Answer:
(x-1)³+1
is correct option
simplify 3^3 - 2x(5x-5) + √25
............................
Answer:
8.63
Step-by-step explanation:
It ends in a one and it has to end in the 100ths place sooo.... yeah
Hope this helps!
please help me i don’t know how to solve this
Answer:
welp good luck ha
Step-by-step explanation:
For the image below, state the line of reflection:
4
***
O
y=-x
o
yx
o
X-axis
y-axis
State the line of reflection of this pre-image and image
HELP ME PLZ!!!!! Plz!!!
Answer:
hi the right answer is option C.112
here's why:
[tex] \frac{14}{50} \times 400 = 112[/tex]
what is the slope of the line y = 8x - 10
Answer:
slope is 8
Step-by-step explanation:
y=Mx+c
m is the slope therefore the slope is equal to 8
The slope of the line y = 8x - 10 is 8.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
Given line is y = 8x - 10
Equation of a line in slope intercept form is given by,
y = mx + c
Here, m is the slope and c is the y intercept.
The given equation is in the slope intercept form.
y = 8x - 10
The coefficient of x is the slope.
So slope of the given line = 8
Hence the slope of the line y = 8x - 10 is 8..
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8 steps ----> 20 ft
6 steps -----> 15 ft
4a. Is this a proportional relationship?
yes
no
14b. If no, explain. If yes, find constant of proportionality. *
Answer:
It is a proportional relationship. 1 step/2.5 Feet.
Step-by-step explanation:
First of all, you need to find out what a single step equals to feet.
If 6 steps is 15 feet, and 8 is 20, then 2.5 feet is the transition of proportional relationship. (15, 17.5, 20)
This means that the proportional relation ship is that every 1 step is equal to 2.5 feet.
In the first quadrant you start at 2, 6 and move 2 units right and 3 units down what point will you end up on?
Answer:
(4, 3)
Step-by-step explanation:
(2+2 , 6-3) = (4 , 3)
Hello I need the answer fast plssssss
Answer:
32
Step-by-step explanation:
8x6=48
2x4=8
48-16=32
Answer:
[tex]area = 2(area \: of \: trapezium) - 2(area \: of \: triangle) \\ = 2( \frac{1}{2} h(a + b)) - 2( \frac{1}{2} bh) \\ = 4(4 + 6) - (4 \times 2) \\ = 40 - 8 \\ = 32 \: {ft}^{2} [/tex]
I will give brianliest!! 20 points. Look at the picture for the question…
the answer is B. A translation 1 unit to the right followed by 180-degree counterclockwise rotation about the origin.
15. What is the equation of the line that contains the point (3,-1) and is perpendicular to the line whose
equation is 6x + 2 y = 4?
Answer:
2y=-2x
Step-by-step explanation:
2y=4-6x
2y=-2x
y=-1
On a spelling quiz lily got 16 out of 20 questions correct which radio shows represents the number of that response to the total number of questions
The question is in the screenshot. ( I really need help in this one)
Answer:
V=A*L
V=72*6
V=432 in cube
i need help and it would be great if someone could answer most of them please
Answer:
[tex]h=6\\k=2.5\\n=3\sqrt{10}\\m=\sqrt{21}\\p=\sqrt{17}[/tex]
Step-by-step explanation:
All of the triangles in this problem are right triangles. This means that all of them contain a right angle, this is indicated by the box around one of the angles. The Pythagorean theorem is a property of the sides of a right triangle, this property, in the form of an equation, is as follows,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs, that is, the sides that are adjacent to the right angle of a right triangle. The parameter (c) represents the hypotenuse, the side opposite the right angle of a right triangle. For each triangle, substitute the given side lengths, simplify, and solve for the unknown side.
[tex](h)^2+(8)^2=(10)^2\\h^2+64 = 100\\h^2=36\\h=6[/tex]
[tex](k)^2+(6)^2=(6.5)^2\\k^2+36=42.25\\k^2=6.25\\k=2.5[/tex]
[tex](n)^2+(\sqrt{10})^2=(10)^2\\n^2+10=100\\n^2=90\\n=\sqrt{90}\\n=3\sqrt{10}[/tex]
[tex](m)^2+(2)^2=(5)^2\\m^2+4=25\\m^2=21\\m=\sqrt{21}[/tex]
[tex](p)^2+(\sqrt{68})^2=(\sqrt{85})^2\\p^2+68=85\\p^2=17\\p=\sqrt{17}[/tex]
2. A stack of 500 sheets of paper is 2.5 inches high. Each sheet of paper is 8.5 inches wide and 11 inches long. A person places more sheets onto the stack, making the total volume of the stack 561 cubic inches. Approximately how many more sheets of paper were added to the original stack of paper?
1) 200
2) 700
3) 1,200
4) 1,700
