Answer:
[tex](x-5)^2+(y-7)^2=50[/tex]
Step-by-step explanation:
Hi there!
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at [tex](h,k)[/tex] and r is the radius
Plug in the center (5,7)
[tex](x-5)^2+(y-7)^2=r^2[/tex]
Plug in the given point (-2,8) to solve for r²
[tex](-2-5)^2+(8-7)^2=r^2\\(-7)^2+(1)^2=r^2\\49+1=r^2\\50=r^2[/tex]
Therefore, r² is equal to 50. Plug this back into [tex](x-5)^2+(y-7)^2=r^2[/tex]
[tex](x-5)^2+(y-7)^2=50[/tex]
I hope this helps!
need some help with question 20
Answer:
l = 420 cm
Step-by-step explanation:
20.
Central angle = 60°
The radius of circle, r = 7 cm
We need to find the length of the arc. We can find it as follows :
[tex]l=r\times \theta\\\\l=7\times 60\\\\l=420\ cm[/tex]
So, the length of the arc is equal to 420 cm.
Round-Off 12579,18375 To The Nearest 10
Answer:
12579 nearest ten = 12580
18375 nearest ten = 18370
Given two similar cones, if cone A has a base area of 9π and cone B has a base area of 25π, and the volume of cone A is 60π, what is the approximate volume of cone B?
Answer:
bro its D and your taking your math finals lol
Step-by-step explanation:
This reduction was drawn at a scale of 1 inch scaled to 4 feet actual. What is the actual height of the giraffe?
Answer:
5 inches tall i think
Step-by-step explanation:
sorry if its wrong
A watermelon that weighs 9 pounds costs $4.50.
What is the price per pound?
Answer:
0.5 cents per pound.
4.50/9 = 0.5
Please mark me brainliest! I hope this helps!
Confused on both any help for either?
Answer:
y = 5/4 x + 9
y = -5x+4
Step-by-step explanation:
a)The equation of the line in slope intercept form is expressed as y = mx+b
m is the slope
b is the intercept
Given
Slope m = 5/4
y-intercpet = 9
Substitute
y = mx+b
y = 5/4 x + 9
b) Given the coordinates (0,4) and (2, -6)
Slope m = -6-4/2-0
m = -10/2
m = -5
Since the y intercept of the line is (0, 4), hence b = 4
Get the equation
Recall
y = mx+b
y = -5x +4
This gives the required equation
The point (6, n) lies on the circle whose equation is (x − 1)2 + (y − 5)2 = 50. Find the values of n
Answer:
n = 0 or 10
Step-by-step explanation:
From the question,
Equation of the circle = (x-1)²+(y-5)² = 50 ............... Equation 1
Coordinate of the circle = (6,n)
From the question
x = 6, y = n
Substitute the value of x and y into equation 1
(6-1)²+(n-5)² = 50
5²+(n-5)² = 50
25+(n-5)² = 50
(n-5)² = 50-25
(n-5)² = 25.
Solving for n
n-5 = √(25
n-5 = ±5
Either,
n-5 = -5
n = -5+5
n = 0
or
n-5 = +5
n = 5+5
n = 10
Answer:
n = 3.16
Step-by-step explanation:
Since the point (6, n) lies on the circle then the coordinates of the point make the equation true.
Substitute x = 6 and y = n into the equation
(6 - 1)² + (n - 5)² = 50, that is, expanding using FOIL
5² + n² - 10n + 25= 50 by simplifying
25 + n² - 10n = 50 ( subtracting 50 from both sides and rearrange )
n² - 10n = 0 ← in standard form
n²=10
n = √10
The values of n is 3.16
Principle = 30,000
Time = 4 years
Rate = 30
Then find the simple interest ?
Answer:
[tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline\color{brown}{Given:}}}}}}\end{gathered}[/tex]
[tex]{\dashrightarrow \sf{Principle = Rs.30000}}[/tex][tex]{\dashrightarrow \sf {Time = 4 \: years}}[/tex][tex]\dashrightarrow \sf{Rate = 30\%}[/tex][tex]\begin{gathered}\end{gathered}[/tex][tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline\color{brown}{To Find:}}}}}}\end{gathered}[/tex]
[tex]\dashrightarrow{\sf{Simple \: Interest }}[/tex][tex]\begin{gathered}\end{gathered}[/tex]
[tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline\color{brown}{Using Formula:}}}}}}\end{gathered}[/tex]
[tex] \dag{\underline{\boxed{\sf{ S.I = \dfrac{P \times R \times T}{100}}}}}[/tex]
Where
[tex]\dashrightarrow{\sf{S.I = Simple \: Interest }}[/tex][tex]{\dashrightarrow{\sf{P = Principle }}}[/tex][tex]{\dashrightarrow{\sf{ R = Rate }}}[/tex][tex] {\dashrightarrow{\sf{T = Time}}}[/tex][tex]\begin{gathered}\end{gathered}[/tex]
[tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline\color{brown}{Solution:}}}}}}\end{gathered}[/tex]
[tex]{\quad {: \implies{\sf{ S.I = \bf{\dfrac{P \times R \times T}{100}}}}}}[/tex]
Substituting the values
[tex]{\quad {: \implies{\sf{ S.I = \bf{\dfrac{30000 \times 30\times 4}{100}}}}}}[/tex]
[tex]{\quad {: \implies{\sf{ S.I = \bf{\dfrac{30000 \times 120}{100}}}}}}[/tex]
[tex]{\quad {: \implies{\sf{ S.I = \bf{\dfrac{3600000}{100}}}}}}[/tex]
[tex]{\quad {: \implies{\sf{ S.I = \bf{\cancel{\dfrac{3600000}{100}}}}}}}[/tex]
[tex]{\quad {: \implies{\sf{ S.I = \bf{Rs.36000}}}}}[/tex]
[tex]{\dag{\underline{\boxed{\sf{ S.I ={Rs.36000}}}}}}[/tex]
Henceforth,The Simple Interest is Rs.36000..[tex]\begin{gathered}\end{gathered}[/tex]
[tex]\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline\color{brown}{Learn More:}}}}}}\end{gathered}[/tex]
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \dag \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Amount = Principle + Interest}} \\ \\ \dashrightarrow \sf{ P=Amount - Interest }\\ \\ \dashrightarrow \sf{ S.I = \dfrac{P \times R \times T}{100}} \\ \\ \dashrightarrow \sf{P = \dfrac{Interest \times 100 }{Time \times Rate}} \\ \\ \dashrightarrow \sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}} \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]
Answer:
INTEREST=P*T*R/100
=30000*4*30/100
=3600000/100
=36000
Step-by-step explanation:
Therefore ,simple interest is 36000
which equivalent form of g(x)=2x^2-12x-54 is the best form to find the zeros of the function?
a) g(x)=2(x-3)^2-72
b) g(x)=2(x^2-6x-27)
c) g(x)=2(x-9)(x-3)
d) g(x)=2x^2-18x+6x-54
Answer:
g(x)=2(x-9)(x+3)
Step-by-step explanation:
Given GH with endpoints (-7,3) andH (7. - 11), what are the coordinates of the
mielpoint of GH?
Answer:
Midpoint is (0, -4)
Step-by-step explanation:
x-coordinate of midpoint = (-7 + 7)/2 = 0/2 = 0
y-coordinate of midpoint = (3 - 11)/2 = -8/2 = -4
Midpoint is (0, -4)
Answer:
(0,-4)
Step-by-step explanation:
(x1 + x2/2, y1 + y2/2)
(-7 + 7/2 , 3 + -11/2)
(0/2, -8/2)
(0,-4)
50 POINTS FOR THIS MATH QUESTION
Answer:
B; 1
Step-by-step explanation:
Firstly, we need to find the inverse of the given function
Let us have f(x) as y
To find the inverse, we set out to make x the formula subject
Thus;
y = √(3x + 6)
square both sides
y^2 = 3x + 6
3x = y^2 - 6
x = (y^2 - 6)/3
To write the inverse, replace y by x
So we have the inverse of the function as ;
(x^2 - 6)/3
So what we have to do here is to substitute 3 for x in the inverse
We have this as;
(3^2 -6)/3
(9-6)/3
= 3/3 = 1
Answer:
1 ( option B )
Step-by-step explanation:
The given equation is ,
[tex]\implies f(x) =\sqrt{ 3x + 6 }[/tex]
Now substituting y = f(x) , we have ,
[tex]\implies y=\sqrt{ 3x + 6 }[/tex]
For finding the inverse , Interchange x and y , we have ,
[tex]\implies x =\sqrt{ 3y + 6 }[/tex]
Now solve for y , we have ,
[tex]\implies x ^2=3y + 6 \\\\\implies 3y = x^2-6 \\\\\implies y =\dfrac{x^2-6}{3} [/tex]
Now replace y with f-¹(x) , we have ,
[tex]\implies f^{-1}(x) =\dfrac{x^2-6}{3} [/tex]
Now put x = 3 , we have ,
[tex]\implies f^{-1}(3) =\dfrac{3^2-6}{3}\\\\\implies f^{-1}(3) = \dfrac{9-6}{3}\\\\\implies \underline{\underline{ f^{-1}(3) = 1 }} [/tex]
4 + 8x = -12
what is X?
Answer:
x=-2
Step-by-step explanation:
4+8x=-12
-4 -4
8x = -16
/8 /8
x = -2
Answer:
X=(-2)
Step-by-step explanation:
8(-2)=(-16)
so -16+4=(-12)
What is the surface area of the cube shown below
Answer:
90
Step-by-step explanation:
What is the volume of the rectangular prism?
3 cm
3 cm
3 cm
Answer:
Step-by-step explanation:
9
As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?
5x + 6y = 18
2x – 3y = 12
Answer:
3
Step-by-step explanation:
First, we can start by multiplying the equation 2x - 3y = 12 by six to see where that gets us,
2x - 3y = 12 --> 12x - 18y = 72
12x - 18y = 72
5x + 6y = 18 (other equation)
We can notice that eliminating the y term would be the easiest to go about, so we want to find the number that we can multiply 6 by to get 18. That number is 3, so the factor is 3.
You can use the fact that non of 2 times 6 doesn't include 5 as factor.
There are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.
Those values of the factor are [tex]3[/tex] (for elimination of y) or [tex]-\dfrac{12}{5}[/tex] (for elimination of x)
How to find by what factor should we multiply the equations to eliminate a variable in a system of linear equations of two or more variables?Our aim in doing so is to make the coefficients of same variable equal and with opposite signs so that when we add the equations, that variable gets eliminated because of coefficient becoming zero.
For example, take the given equations and the factor by which Yumiko multiplied the second equation.
5x + 6y = 18
2x – 3y = 12 => 12x - 18y = 72 (since she multiplied this with 6)
Let she multiply the first equation with factor "p"
Then we will have the system as;
[tex]p \times 5x + p \times 6y = p \times 18\\12x - 18y = 72[/tex]
Adding both the equations, we get:
[tex](5p + 12)x + (6p - 18)y = 18p + 72[/tex]
Since there are two variables and since any one of them can be eliminated depending on the value of p, thus we have two cases:
Case 1: Eliminated variable is xThen we have coefficient of x = 0
or
[tex]5p + 12 = 0\\5p = -12\\p = -\dfrac{12}{5}\\[/tex]
Case 2: Eliminated variable is yThen we have coefficient of y = 0
or
[tex]6p - 18 = 0\\6p = 18\\p = \dfrac{18}{6} = 3[/tex]
Thus, there are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.
Those values of the factor are [tex]3[/tex] or [tex]-\dfrac{12}{5}[/tex]
Learn more about system of linear equations here:
https://brainly.com/question/13722693
The Surface are of a cylinder is 325 inches. The Lateral area is 200 in. What is radius of each base?
Answer:
The radius of each base is 4.46 inches.
Step-by-step explanation:
The surface area (SA) of a cylinder is given by:
[tex]SA = 2\pi rh + 2\pi r^{2} = 325[/tex] (1)
Where:
r: is the radius of each base
h: is the height of the cylinder
Now, the lateral area (LA) is:
[tex]LA = 2\pi rh = 200[/tex] (2)
Hence, by entering equation (2) into equation (1) we have:
[tex] SA = LA + 2\pi r^{2} [/tex]
[tex] 325 = 200 + 2\pi r^{2} [/tex]
[tex] r = \sqrt{\frac{325 - 200}{2\pi}} = 4.46 in [/tex]
Therefore, the radius of each base is 4.46 inches.
I hope it helps you!
Simplify
[tex]\frac{4\sqrt{6} }{\sqrt{30} }[/tex] by rationalizing the denominator. Show your work.
Answer:
[tex]\frac{4\sqrt{5} }{5}[/tex]
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Help ..................
Answer:
rang is 31
Step-by-step explanation:
Please do it step by step!
9514 1404 393
Answer:
80 in^3
Step-by-step explanation:
The volume of a pyramid is given by the formula ...
V = 1/3Bh
where B is the area of the base, and h is the height of the pyramid. Here, h=8 in.
__
Here, the base is a triangle. The formula for its area is ...
A = 1/2bh
where b is the base segment of the triangle, and h is the height of the triangle perpendicular to the base segment. Here, b=10 in, and h = 6 in.
The triangular base area is ...
A = 1/2(10 in)(6 in) = 30 in^2 . . . . base area "B"
__
Using the above base area and pyramid height, we find the volume of the pyramid is ...
V = 1/3(30 in^2)(8 in) = 80 in^3
The volume of the pyramid is 80 cubic inches.
HELP IT'S DUE IN 2 MINUTES
Answer:
D) 2² × 3³ × 7
Step-by-step explanation:
Hope this helps! Have a nice day :)
Toda expresión de la forma xn + yn tiene un factor con los signos alter nados, uno positivo y uno negativo.
????????????
Step-by-step explanation:
?????????
Please help me!! Please!
Answer:
Step-by-step explanation:
The first answer choice is correct i ma 100% sure
Answer:
(-1.2,0.3)
Step-by-step explanation:
does this help you
A three dimensional object has?
Answer:
3
Step-by-step explanation:
length
width
height
What is an equation of the form a b = c d b a = d c stating that two ratios are equivalent?
Answer:
true proportion
A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio.
hope it helps ya.
Can you give me brainliest? please?.ت︎
OK BESTIES I NEED SOME HELP ASAP!!!
A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can be the three-dimensional object?
A. Cone
B. Cylinder
C. Pyramid
D. Rectangular prism
Answer: C. Pyramid
Step-by-step explanation:
A cylinder is kind of like a paper towel roll.
A Rectangular prism is more like a cube.
A cone has a round part on the bottom.
And a Pyramid is this ...
The area of a rectangle is represented by the expression 2x2 + 10x + 12. Daniel is convinced that the dimensions of this rectangle could be (2x + 4) and (x + 3) or (x + 2) and (2x + 6). Do you agree or disagree with Daniel? Use words to justify your opinion.
Answer:
I agree with daniel
Step-by-step explanation:
Given the area of a rectangle expressed as;
A(x) = 2x²+10x+12
On factorizing;
A(x) = 2x²+6x+4x+12
A(x) = 2x(x+3)+4(x+3)
A(x) = (x+3)(2x+4)
since A(x) = l(x)w(x)
Hence the legnth and width of the rectangle are 2x+4 and x+3.
Also A(x) = 2x²+6x+4x+12 can be factorized as;
A(x) = 2x²+4x+6x+12
A(x) = 2x(x+2) + 6(x+2)
A(x) = 2x+6(x+2)
Therefore I agree with Daniel. The factor differs due to the difference in arrangement of 4x and 6x in the expression. Precedence of values affects the final factors
Can someone please help with this ASAP thank you
Answer:
2.7, 3, 6
Step-by-step explanation:
Abby earned $600 this past
summer babysitting. She decided
to put this money in a bank that
earns a 5% simple interest rate.
How many years will it take to
double her initial deposit?
do step my step equation or your answer gets reported for false info THANKSSS. I'll mark brainlist
Answer:
2 years
Step-by-step explanation:
5%× 600= $30
$30×2=$60
not sure if you will get what I mean but that's how I worked it out.
Answer:
[tex]I = \frac{PRT}{100}[/tex]
P= $600
R= 5%
[tex]I = \frac{600 \times \ 5 \times T}{100} = 30T\\\\[/tex]
A = double the deposit =2 600= $1200
[tex]A = I + P \\1200 = 30T + 600\\30T = 600\\T = 20[/tex]
the mean of 4 8 9 x and 2x is 6 calculate the value of x
Answer:
x = 3
Step-by-step explanation:
Mathematically, the mean is the sum of the numbers divided by the count of the numbers
The count of the numbers is 5
Thus;
( 4 + 8 + 9 + x + 2x)/5 = 6
(21 + 3x)/5 = 6
21 + 3x = 6(5)
21 + 3x = 30
3x = 30-21
3x = 9
x = 9/3
x = 3
anwers :
a. dotted
b. y=-x+4
c. y=x-4
d. y=x+1
e. solid
f. yes
g. no
Answer:
Those answers are correct