The radius of the circle is 4 units.
Given to us:
[tex]x^2 + y^2 - 10x + 6y + 18 = 0[/tex]
The generalized format for radius of a circle is given by:
[tex]\\(x - h)^2 + (x - k)^2 = a^2\\where,\\h, k= coordinate\ of\ the\ center\ of\ the\ circle\\a= radius\ of\ the\ circle[/tex]
therefore after rearrangement of the equation we get,
[tex]x^2 + y^2 - 10x + 6y + 18 = 0,\\x^2 - 10x + y^2 + 6y =- 18,\\[/tex]
adding 25 and 9 on both the sides to bring it in the generalized format for radius of a circle,we get
[tex]x^2 - 10x+25 + y^2+ 6y+9 =-18+25+9,\\[/tex]
[tex](x - 5)^2 + (y + 3)^2 = 16\\(x - 5)^2 + (y + 3)^2 = 4^2\\[/tex]
Hence, the coordinate for this circle are x=5 and y=-3. And the radius of the circle is 4 units.
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If f(x) = x2 + 3x and g(x) = x + 2, find (f ∘ g)(x) and (g ∘ f)(x).
Answer:
(f ∘ g)(x) = x²+7x+10
(g ∘ f)(x) = x²+3x+2
Step-by-step explanation:
(f ∘ g)(x) = f(g(x)) = f(x+2) = (x+2)² + 3(x+2) = x² + 4x + 4 + 3x + 6 = x² + 7x + 10
(g ∘ f)(x) = g(f(x)) = g(x²+3x) = (x²+3x) + 2 = x² + 3x + 2
Make sure to review composite functions
) Are 9:6 and 18: 12 equivalent?
Answer:
Yes
Step-by-step explanation:
9 18
_ = _
6 12
9*2=18
6*2=12
2=2 TRUE
What does R represent?
A. a line segment
B. a point
C. a line
D. a rat
Answer:
B
Step-by-step explanation:
1/5 divided by 2/15 as a mixed number
Answer: 1 1/2
Step-by-step explanation:
Step One: 3 / 2 = 1.5000 = 1
Step Two: 3 - (2 x 1) = 1
Step Three: 1 1/2
Please mark me branliest
What is the simplified form of the expression? HELP ASAP
Answer:
[tex]360[/tex]
Step-by-step explanation:
[tex] \frac{5(14 - 2)^{2} }{2} = \frac{5 {(12)}^{2} }{2} = \frac{5(144)}{2} \\ \\ \frac{720}{2} = 360[/tex]
Answer:
The answer is option (d) 360.
Step-by-step explanation:
Solution :[tex]\implies{\tt{\dfrac{5(14 - 2)^{2} }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5(12)^{2} }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5(12 \times 12) }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5(144) }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5 \times 144 }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5 \times \cancel{144}}{ \cancel{2}}}}[/tex]
[tex]\implies{\tt{5 \times 72}}[/tex]
[tex]\implies{\tt{360}}[/tex]
[tex]\dag{\underline{\boxed{\sf{\red{360}}}}}[/tex]
Hence, the answer is 360.
[tex]\rule{300}{1.5}[/tex]
Learn More :✧ BODMAS :
↝ BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.
It stands for :-
⠀ ⇝ B - Brackets,
⠀ ⇝ O - Order of powers or roots,
⠀ ⇝ D - Division,
⠀ ⇝ M - Multiplication
⠀ ⇝ A - Addition
⠀ ⇝ S - Subtraction.
↝ It means that expressions having multiple operators need to be simplified from left to right in this order only.
✧ BODMAS RULE :
↝ First, we solve brackets, then powers or roots,then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.
⠀ ↠ Addition (+)
⠀ ↠ Subtraction (-)
⠀ ↠ Multiplication (×)
⠀ ↠ Division (÷)
⠀ ↠ Brackets ( )
[tex]\rule{300}{1.5}[/tex]
Identify the horizontal asymptote of f(x) =4x/7
y = 0
y = 2/3
y=1
No horizontal asymptote
Answer:
y = 1
Step-by-step explanation:
To find the Horizontal Asymptote, you have to look at the degree of the numerator and denominator.
[tex]h(x) = \frac{x^n}{x^m}[/tex]
If n < m, then y = 0If n = m, y = coefficient of [tex]x^n[/tex] divided by the coefficient of [tex]x^m[/tex]If n > m, then there is no Horizontal AsymptoteMarco is five years less then twice hi sister Leah's age. Their mother is 14 years older than Marco and Leah's combined ages. If their mother is 48 years old, how old is Marco?
Answer:
Marco is 21
Step-by-step explanation:
Let the sister's age = x
Marco's age = 2*x - 5
x + 2x - 5 + 14 = 48 Combine the left side of the equation.
3x + 9 = 48 Subtract 9 from both sides
3x = 48 - 9
3x = 39 Divide by 3
x = 39/3
x = 13
So the sister is 13
Marco = 2x - 5 = 2*13 - 5
Marco = 21
PLEASE PLEASE HELP ME
Answer:
Assuming that it ends at 9.5. The domain is (-8 , 9.5). However, assuming it continues further to the right, it could be (-8 , ∞)
Range is the area covered vertically. Assuming it ends at 9.5 it would be (4 , -4) However, assuming it continues further down vertically, it would/could be (4 , -∞)
Neither.
Step-by-step explanation:
Domain is the area covered horizontally. Assuming that it ends at 9.5. The domain is (-8 , 9.5). However, assuming it continues further to the right, it could be (-8 , ∞)
Range is the area covered vertically. Assuming it ends at 9.5 it would be (4 , -4) However, assuming it continues further down vertically, it would/could be (4 , -∞)
It is neither because it is on the x-axis.
What is the answer to -3x + 7y = -16 and -3x + 7y = -16
Answer:
-16-7y/3
Step-by-step explanation:
-3x+7y=-16
Subtract 7y from both sides
-3x=-16-7y
Divide both sides by -3
x=-16-7y/3
Consider the line y=-5x+3. Find the equation of the line that is parallel to this line and passes through the point (3,4). Find the equation of the line that is perpendicular to this line and passes through the point (3, 4).
Answer:
parallel
y= -5x + 19
perpendicular
y= (1/5)x + 17/5
Step-by-step explanation:
yeah-ya......... right?
do you use multiplication at all when solving for x
if silas sandwich measures, 3 yards 2 feets 3 inches, How many inches in total does silas sandwich measure
========================================================
Work Shown:
1 yard = 3 feet
3 yards = 9 feet (multiply both sides by 3)
3 yards + 2 feet = 9 feet + 2 feet = 11 feet
1 foot = 12 inches
11 feet = 132 inches (multiply both sides by 11)
11 feet + 3 inches = 132 inches + 3 inches = 135 inches
A bottle of juice costs $1.85, and a pack of 6 bottles of lemonade costs $5.40. If Jimmy
buys 3 bottles of juice and a dozen bottles of lemonade, how much money should he
spend in all?
Answer:
Step-by-step explanation:
+
1.85
5.40
_____
6. 2 5
How to write a line segment
Answer:
In geometry, you will write a line segment using the letters for each of the end points and a line over the top of the letters.
Please help worth 20 points
Answer:
Try going on D.e.s.m.o.s.c.o.m it worked for me when I had something like this
Step-by-step explanation:
GURL POWER
A restaurant is considering reducing its meal sizes, because it noticed many of its customers cannot finish their meals. The manager decided to weigh the left-over portion of the meals before putting them in to-go containers. The line plot displays the weights of the left-over portions of the meals. If the left-over portions are divided equally among the customers, how much food would each customer take home? Weight of Left-over Meals A. B. C. D.
Answer:
1/2
Step-by-step explanation:
You need to add all the fractions up to get 1/2 is what food the costumers brought home
Answer:
1/2
Step-by-step explanation:
i got it correct!!
Find the value of two numbers if their sum is 147 and their difference is 51
No links
Answer:
99 and 48
Step-by-step explanation:
99+48=147
99-48=51
Jayden purchases a television when his local electronics store had a sale. The television was 40% off its original price of $672. What was the sale price that jayden paid?
Answer:
The sale price he paid for the TV was $403.20
Step-by-step explanation:
You multiply the original price by .4 (40%). Then, you subtract that number from $672 to find the price Jayden paid! :)
30 POINTS!
Find the gravitational force between Earth (5.97 x 1024 kg) and the Sun (1.99 x 1030 kg) knowing they are 1.48 x 1011 m apart.
Answer:
The correct answare would be 3.54 x 10^22 N
PERIMETER PLEASE HELP
Answer:
164 round = 160
your answer now can you please help me
Step-by-step explanation:
Help?please rnnnn………
Answer:
8,176
Step-by-step explanation:
You have to first do 8 × 5110 = 40,880
Then you divide 40,880 by 5
40,800 ÷ 5 = 8,176
If x is not equal to zero, what is the value of [tex]\frac{4(3x)^2}{(2x)^2}[/tex]
Answer:
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex]
General Formulas and Concepts:
Pre-Algebra
Evaluations
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Distributive Property
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2}[/tex]
Step 2: Simplify:
Rewrite [Exponential Distributive Property]: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(3^2x^2)}{2^2x^2}[/tex][Order of Operations] Evaluate exponents: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(9x^2)}{4x^2}[/tex][Order of Operations] Multiply: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36x^2}{4x^2}[/tex]Simplify: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36}{4} ,\ x \neq 0[/tex][Order of Operations] Divide: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex][tex]\\ \sf\longmapsto \dfrac{4(3x)^2}{(2x)^2}[/tex]
[tex]\\ \sf\longmapsto\dfrac{ 4(9x^2)}{4x^2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{36x^2}{4x^2}[/tex]
Take x^2 common and cancel.[tex]\\ \sf\longmapsto \dfrac{x^2}{x^2}\left(\dfrac{36}{4}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto 9[/tex]
this is the next question
Solve: 1/2÷0.2
Answer:
2.5
Step-by-step explanation:
What is the product?
it tells you the answer..
The product of matries [tex]\left[\begin{array}{cc}5&-2\\-6&2\end{array}\right][/tex] and [tex]\left[\begin{array}{c}-1\\-1\end{array}\right][/tex]is option c. [tex]\left[\begin{array}{c}-3\\4\end{array}\right].[/tex] By perform matrix multiplication of 2x2 matrix with 2x1 matrix.
Given the matrices:
[tex]A = \left[\begin{array}{cc}5&-2\\-6&5\end{array}\right][/tex]
[tex]B = \left[\begin{array}{c}-1\\-1\end{array}\right][/tex]
To find the product, perform matrix multiplication.
Using the given matrices, the multiplication can be done as follows:
[tex]\left[\begin{array}{cc}5&-2\\-6&2\end{array}\right] \times \left[\begin{array}{c}-1\\-1\end{array}\right][/tex]
Multiply each element in the corresponding row of the first matrix by the corresponding column of the second matrix and summing the products.
[tex]=\left[\begin{array}{cc}(5\times-1)+(-2\times-1)\\(-6\times-1)+(2\times-1)\end{array}\right][/tex]
On multiplying the term in brackets gives:
[tex]=\left[\begin{array}{cc}-5+2\\6-2\end{array}\right][/tex]
On performing the algebraic sum gives:
[tex]=\left[\begin{array}{cc}-3\\4\end{array}\right][/tex]
Therefore, the product of the matrices is [tex]\left[\begin{array}{cc}-3\\4\end{array}\right].[/tex]
Matrix multiplication is an important operation in linear algebra and has applications in various fields, including physics, computer science, and engineering.
It allows us to perform transformations, solve systems of equations, and represent linear relationships between variables.
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What is the answer to 3(y - 1 + 2y)
Answer:
Collect like terms.
3((y+2y)-1)
3((y+2y)−1)
2 Simplify (y+2y)-1(y+2y)−1 to 3y-13y−1.
3(3y-1)
3(3y−1)
Solve using substitution.
=
10x + 4y = -14
X = 1
-
Submit
Answer:
-6
Step-by-step explanation:
10x1 + 4y = -14
10+4y=-14
4y=-14-10
4y = -24
y = -24/4
y = -6
out of 300 students at rsm summer camp 180 are boys what fraction of all students are boys
Answer:
3/5
Step-by-step explanation:
so first of all...
out of
300
students,
180
are boys.
180/300
which, simply by 60
3/5
so.. 3/5 of the people at rsm (whatever that is) summer camp are boys! Explanation isn't good, but you didn't really ask for it so i think you're ok... I guess. Now i just need an answer to my problem...
In rsm summer camp, fraction of boys is 3/5.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total number of students at rsm summer camp = 300.
Total number of boys at rsm summer camp = 180.
To find the fraction of boys to all students.
Fraction of boys = number of boys / total number of students
= 180 / 300
= 18 / 30
= 3 / 5
The required fraction of boys is 3/5.
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if r and s represent the solutions of the equation below and r>s, what is the value of the difference r-s?
(3x+14)x=5
Answer:
16/3
Step-by-step explanation:
(3x + 14)x = 5
3x² + 14x = 5
3x² + 14x - 5 = 0
3x² + 15x - x - 5 = 0
3x(x + 5) - 1(x + 5) = 0
(3x - 1)(x + 5) = 0
x = 1/3 & -5
Here,
r = 1/3
s = -5
r - s
1/3 - (-5)
1/3 + 5
1 + 15/3
16/3
the value of the difference r-s is [tex]\bold{\frac{16}{3}}[/tex]
Answer:
Solution given:
(3x+14)x=5
opening bracket
3x²+14x=5
3x²+14x-5=0
Doing middle term factorisation
3x²+(15-1)x-5=0
3x²+15x-x-5=0
3x(x+5)-1(x+5)=0
(3x-1)(x+5)=0
either
x=-5
or
3x-1=0
3x=1
x=⅓
According to question value of x is r>s
so
⅓>-5
so
r=⅓
and
s=-5
Now
r-s=⅓-(-5)=[tex]\frac{1+5*3}{3}=\frac{16}{3}[/tex]
initial value on this table
Answer:correct me if I’m wrong but it’s 0.
Step-by-step explanation:
85-51=34. 34
—————=. —————=17
5-3. 2
And once 17 is the slope/rate of change,you can either go back 17 each time or….do an equation : f(x)=17(x-3)+51
can someone please help me with this? pls & thank you!
Answer:
see explanation
Step-by-step explanation:
Equation for Fast Internet is
45 + 50.45x
Equation for Quick Internet is
57.95x
To find when they cost the same , equate the 2 equations
45 + 50.45x = 57.95x ← required equation
Solve the equation by subtracting 50.45x from both sides
45 = 7.5x ( divide both sides by 7.5 )
6 = x
Both services would cost the same after 6 months