Answer:
[tex]r^2=4\sec 2\theta}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^2-y^2=4[/tex]
We substitute [tex]x=r\cos (\theta)[/tex] and [tex]y=r\sin (\theta)[/tex] to obtain:
[tex]r^2\cos^2\theta-r^2\sin^2\theta=4[/tex]
This implies that:
[tex]r^2(\cos^2\theta-\sin^2\theta)=4[/tex]
Apply double angle identity to obtain:
[tex]r^2\cos 2\theta=4[/tex]
This implies that:
[tex]r^2=\frac{4}{\cos 2\theta}[/tex]
This simplifies to:
[tex]r^2=4\sec 2\theta}[/tex]
i need to find the sum of this equation
Answer:
[tex]\large\boxed{\dfrac{3s^2+19s-4}{(s-1)^2(s+5)}=\dfrac{3s^2+19s-4}{s^3+3s^2-9s+5}}[/tex]
Step-by-step explanation:
[tex]s^2-2s+1=s^2-s-s+1=s(s-1)-1(s-1)=(s-1)(s-1)=(s-1)^2\\\\s^2+4s-5=s^2+5s-s-5=s(s+5)-1(s+5)=(s+5)(s-1)\\\\\text{Therefore}\ LCD\ \text{is}\ (s-1)^2(s+5).[/tex]
[tex]\dfrac{3s}{s^2-2s+1}+\dfrac{4}{s^2+4s-5}=\dfrac{3s(s+5)}{(s-1)^2(s+5)}+\dfrac{4(s-1)}{(s-1)^2(s+5)}\\\\\text{use the distributive property}\\\\=\dfrac{(3s)(s)+(3s)(5)+(4)(s)+(4)(-1)}{(s-1)^2+(s+5)}=\dfrac{3s^2+15s+4s-4}{(s-1)^2(s+5)}\\\\=\dfrac{3s^2+19s-4}{(s-1)^2(s+5)}[/tex]
if Angela's house is assessed valuation of $61,200 and the tax rate per 100 is $3.78 what will she pay in annual real estate tax to the nearest tenth
Answer:
[tex]\boxed{\text{\$2313.40}}[/tex]
Step-by-step explanation:
The tax rate is $3.78/$100 assessed
[tex]\text{Tax} = \text{\$61 200 assessed} \times \dfrac{\text{\$3.78}}{\text{\$100 assessed}}[/tex]
Cancel the $100 assessed.
612 × $3.78 = $2313.40
Angela's real estate tax will be [tex]\boxed{ \textbf{\$2313.40}}[/tex]
x^16/x^3
a. 16/x^3
b. x^48
c. x^19
d. x^13
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^{16}}{x^3}\implies \cfrac{x^{16}}{1}\cdot \cfrac{1}{x^3}\implies x^{16}\cdot x^{-3}\implies x^{16-3}\implies x^{13}[/tex]
Answer:
x^13
Step-by-step explanation:
when you divide variables with exponents you subtract them. So x^16-3 = x^13
The students in Mr. Robertson's class recorded the number of siblings that each student has. The results are shown here.
How many students have fewer than 3 siblings?
A) 1
B) 5
C) 7
D) 19
What is the probability of you picking a weekend day from the days of the week?
Answer:
3/7
Step-by-step explanation:
its 3/7 because there are 3 weekend days and there are 7 days in total in one week, so out of the week there is 3 weekend days.
i hope this helps :)
The probability will be "[tex]\frac{1}{7}[/tex]". A further solution is below.
According to the question,
Number of days in a week,
7Number of weekend,
1Now,
The probability of you picking weekend day from the days of the week will be:
= [tex]\frac{Number \ of \ weekend}{Number \ of \ days \ in \ week}[/tex]
By substituting the values, we get
= [tex]\frac{1}{7}[/tex]
Thus the response above is appropriate.
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The formula for the volume of a cylinder is V=\pi r^2 h,V=πr2h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
Answer:
[tex]h=V/(\pi r^{2})[/tex]
Step-by-step explanation:
we know that
The formula for the volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
where
r is the radius
h is the height of the cylinder
Solve for h
That means -----> isolate the variable h
Divide by πr² both sides
[tex]V/(\pi r^{2})=h[/tex]
Rewrite
[tex]h=V/(\pi r^{2})[/tex]
Answer:
The formula for the Volume of a cylinder [note: area of circle times height]:
V = Πr2h
Solve for r in terms of h
r2 = V / (Πh)
For this cylinder, V=539.
r2 = 539 / (Πh)
r = √(539/(Πh))
This is also:
r = 23.1 / √(Πh)
r = 13.1 / √h
which number is rational?
a. 16/6 sqrt
b. 6 sqrt
c. 36/6 sqrt
d. 36/16 sqrt
D.
36/16 sqrt = 6/4, since the square root applies to denominator and numerator.
A rational number is a number that can be expressed as the quotient or fraction of two integers. None of the given options are rational in the provided question.
Explanation:A rational number is a number that can be expressed as the quotient or fraction of two integers. In this question, we need to determine which of the given options is rational.
To identify a rational number, we need to check if the number can be written in the form a/b, where a and b are integers. Let's analyse each option:
16/6 sqrt: This option can be written as 16/(6 sqrt). The denominator contains a square root, which means it is not rational. 6 sqrt: This option cannot be written as the quotient of two integers since it contains a square root. 36/6 sqrt: This option can be simplified to 6/(sqrt 6). Once again, the denominator contains a square root, making it irrational. 36/16 sqrt: This option simplifies to 9/(4 sqrt). The denominator contains a square root, so it is not rational.
From the analysis, we can see that none of the given options is rational.
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Simplify 6P2.
A. 30
B. 15
C. 12
D. 720
could i also have an explanation so i can understand better?
The answer would be A
The solution of ⁶P₂ would be,
⇒ ⁶P₂ = 30
We have to given that,
An expression to solve,
⇒ ⁶P₂
Now, By definition of permutation, we get;
⇒ ⁶P₂
⇒ 6! / (6 - 2)!
⇒ 6! / 4!
⇒ 6 × 5
⇒ 30
Therefore, The solution of ⁶P₂ would be,
⇒ ⁶P₂ = 30
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What is the domain and range for the following function and it’s inverse ? Help needed !!!
ANSWER
f(x)
Domain:(-∞,∞)
Range:(-∞,∞)
[tex] {f}^{ - 1} (x)[/tex]
Domain:(-∞,∞)
Range:(-∞,∞)
The given function is
[tex]f(x) = \frac{3x - 1}{2} [/tex]
This is a polynomial function.
All polynomial functions are defined everywhere.
The domain is all real numbers.
Or
(-∞,∞).
The range is also all real numbers.
(-∞,∞).
The domain of the inverse function equals the range of the function.
(-∞,∞).
The range of the inverse function equals the domain of the function.
(-∞,∞).
find the equation ....
Answer:
[tex]y=-\frac{1}{16}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,-4)
and the directrix is y=4.
The equation of this parabola is given by:
[tex]x^2=-4py[/tex]
The vertex of this parabola is at the origin.
The value of p is the distance from the vertex to the focus.
p=0--4=4
The equation of the parabola is
[tex]x^2=-4(4)y[/tex]
[tex]x^2=-16y[/tex]
Or
[tex]y=-\frac{1}{16}x^2[/tex]
what is the complete factorization of the polynomial below
Answer:
B
Step-by-step explanation:
(x+2)(x^2+1)
=(x+2)(x+1)(x+1)
Answer:
( x + i)(x -i) ( x +2).
Step-by-step explanation:
Given : x³ + 2x² +x +2.
To find : complete factorization of the polynomial below.
Solution : We have given x³ + 2x² +x +2.
On taking common x² from first two terms and 1 from last two terms .
x² ( x +2) +1 (x +2).
On grouping
(x² +1) ( x +2).
Now factor of (x² +1) become ( x + i)(x -i) in complex form .
Factors are ( x + i)(x -i) ( x +2).
Therefore, ( x + i)(x -i) ( x +2).
Cross multiplication
Answer:
7. 5/6 8. 3/12
Step-by-step explanation:
-4h - 6 + 15 = 17 ( I don’t understand the concept.)
the concept is to find the value of h
Answer:
it is an algebraic expression (answer is h = -2 )
Simplify the expression
−4h−6 + 15 = 17
(Combine Like Terms)
(−4h)+(−6+15)=17
−4h + 9 = 17
Step 2: Subtract 9 from both sides.
−4h + 9 − 9 = 17 − 9
−4h=8
Step 3: Divide both sides by -4.
[tex]\frac{-4h}{-4}[/tex] = [tex]\frac{8}{-4}[/tex]
h = -2
Step-by-step explanation:
Solve the proportion 5/25= x/20
5/25 = x/20
To solve a proportion cross multiply:
(5 * 20) = (25 * x)
Simplify:
100 = 25x
Divide both sides by 25:
x = 100/25
x = 4
richard wants to paint the top sides of the block column. what is the surface area he needs to cover?
First of all, you have to send the measurements; otherwise, there would not be an answer
What value must be defined for to remove the discontinuity of this function at ?
Answer:
Option D. 8
Step-by-step explanation:
we have
[tex]f(x)=\frac{x^{2}-16 }{x-4}[/tex]
Remember that
[tex]x^{2}-16 =(x+4)(x-4)[/tex]
substitute
[tex]f(x)=\frac{(x+4)(x-4)}{x-4}[/tex]
Remove the discontinuity at x=4
Simplify
[tex]f(x)=(x+4)[/tex]
so
Find the value of f(4)
For x=4
[tex]f(4)=(4+4)=8[/tex]
Answer:
8
Step-by-step explanation:
I have the plato platform
What is the approximate area of the triangle below?
a)72.8
b)111.9
c)142.0
d)164.7
all in sq. cm.
I believe it’s B of joy them A
Answer:
A
Step-by-step explanation:
Got a 100
Solve the equation.
5х + 8 – 3x = -10
Answer:
x=-9
Step-by-step explanation:
5x+8-3x=-10
2x+8=-10
2x=-18
Divide both sides by 2 to get
Answer is -9
Geometry, Triangle in a circle. Find X show work and explain please
Answer: [tex]x=7[/tex]
Step-by-step explanation:
By the Intersecting Secants Theorem, we know that:
[tex](5)(x+5)=(6)(6+4)[/tex]
Having this, we can find the value of "x" by solving for "x":
Applying Distributive property:
[tex](5)(x+5)=(6)(24)\\5x+25=60[/tex]
Subtract 25 from both sides of the equation:
[tex]5x+25-25=60-25\\5x=35[/tex]
And finally dviding both sides of the equation by 5, we get:
[tex]\frac{5x}{5}=\frac{35}{5}\\x=7[/tex]
Answer:
35/5 it would be 35 over 5
Step-by-step explanation:
Solve 7x - 4 = 5x + 15 for x.
11/2
19/2
19/12
[tex]
7x-4=5x+15 \\
2x=11
x=\boxed{\frac{11}{2}}
[/tex]
Hope this helps.
r3t40
which of the following properties can be used to show that the expression?
Answer:
1 3 5set/dhzhhhhhhhhhhhhhhhhhhh
The expression [tex]\(4^5/3\)[/tex] is indeed equivalent to[tex]\(\sqrt[3]{4^5}\)[/tex].
The correct option is (a).
To demonstrate that the expression[tex]\(4^5/3\) is equivalent to \(\sqrt[3]{4^5}\)[/tex], we can apply the following properties:
1. Radical to Exponent Property:
- The expression [tex]\(\sqrt[3]{4^5}\) can be rewritten as \(4^{5/3}\)[/tex].
- This property allows us to convert a radical expression to an exponent expression by raising the base to the reciprocal of the index of the radical.
2. Exponent to Radical Change Property:
- The fraction exponent [tex]\(5/3\)[/tex] can be expressed as a radical: [tex]\(\sqrt[3]{4^5}\)[/tex].
down step-by-step:
1. Start with the given expression: [tex]\(4^5/3\)[/tex].
2. Apply the **Radical to Exponent Property: [tex]\[4^5/3 = 4^{5/3}\][/tex]
3. Now, express the fraction exponent as a radical:
[tex]\[4^{5/3} = \sqrt[3]{4^5}\][/tex]
Therefore, the expression [tex]\(4^5/3\)[/tex] is indeed equivalent to[tex]\(\sqrt[3]{4^5}\)[/tex].
The circle below is centered at (-1, 1) and has a radius of 3. What is its
equation?
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{3}{ r}\\[2em] [x-(-1)]^2+[y-1]^2=3^2\implies (x+1)^2+(y-1)^2=9[/tex]
The equation of the circle will be ( x + 1 )² + ( y - 1 )² = 9.
What is the equation of circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle can be written as,
( x - h)² + ( y - k )² = r².
Given that the circle below is centered at (-1, 1) and has a radius of 3. The equation of the circle will be written as,
( x - h)² + ( y - k )² = r².
( x + 1 )² + ( y - 1 )² = 9.
Hence, the equation can be written as ( x + 1 )² + ( y - 1 )² = 9.
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The expression below is a sum of cubes. True or false
64x^3+ 125
A. True
B. False
Answer:
True
Step-by-step explanation:
64x³ + 125
64x³ = (4x)³ ← a perfect cube
125 = 5³ ← a perfect cube
Thus 64x³ + 125 ← is a sum of cubes
It is true that the expression which is given below is a sum of cubes.
The given expression is:
[tex]64x^{3} +125[/tex]
As we can see that there are two terms in it:
one is [tex]64x^{3}[/tex] and the second one is [tex]125[/tex].
So, at first, we will see [tex]64x^{3}[/tex]
[tex]64x^{3}=4^{3} *x^{3}[/tex]
from the above, we can state that [tex]64x^{3}[/tex] is a cube of [tex]4x[/tex].
Now, we will look at [tex]125[/tex].
So, [tex]125=5^{3}[/tex]
Therefore, we can also state that [tex]125[/tex] is a cube of [tex]5[/tex].
Hence, the given statement is true.
What is sum of cubes formula?The sum of cubes (a3 + b3) formula is expressed as a3 + b3 = (a + b) (a2 - ab + b2).
What is the rule for cubing a sum?Sum of cubes:The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.
What is the sum of cubes of n terms?The formula to find the sum of cubes of n natural numbers is S = [n2 (n + 1)2]/4, where n is the count of natural numbers that we take.
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NEED HELP FAST!!!!!!!!
i need a life fast plz
Answer:
[tex]m=0.002kg[/tex]
Step-by-step explanation:
The given formula is:
[tex]E=mc^2[/tex]
Divide both sides by [tex]c^2[/tex].
[tex]\implies \frac{E}{c^2}=\frac{mc^2}{c^2}[/tex]
Cancel out the common factors to get;
[tex]\implies \frac{E}{c^2}=m[/tex]
[tex]m=\frac{E}{c^2}[/tex]
When [tex]E=1.8\times10^{14}J[/tex] and [tex]c=300,000,000ms^{-1}[/tex], then
[tex]m=\frac{1.8\times10^{14}}{300,000,000^2}[/tex]
This simplifies to
[tex]m=0.002kg[/tex]
Identify the domain for the function !!! 10 points. Help needed!!
The answer is:
The domain for the function is:
Domain:(-∞,-3)∪(-3,∞)
Why?Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.
We are given the function:
[tex]f(x)=\frac{x^3} +27}{x+3}[/tex]
We have two expressions:
The first expression (numerator) has no restriction, however, we can find a restriction at the second expression (denominator) because when a fraction has a denominator equal to 0, the function does not exist on the real numbers.
For the denominator, we have that it tends to 0 at:
[tex]x=-3[/tex]
So, the domain for the given function will be:
Domain:(-∞,-3)∪(-3,∞)
Hence, the answer is the second option, the domain for the function is:
Domain:(-∞,-3)∪(-3,∞)
Have a nice day!
20) Which rule yields the dilation of the figure RSTU centered at the origin?
A)
(x, y) → (4x, 4y)
B)
(x, y) → (0.25x, 0.25y)
C)
(x, y) → (x + 4, y + 4)
D)
(x, y) → (x + 0.25, y + 0.25)
Answer: A) [tex](x,y)\to(4x,4y)[/tex]
Step-by-step explanation:
The rule of dilating a shape by scale factor k centered at the origin is given by :-
[tex](x,y)\rightarrow (kx,ky)[/tex] [We multiply k to the coordinates of pre-image ]
It means Option C) and D) is incorrect.
From the given graph , it can be observe that quadrilateral R'S'T'U' (image) is larger than the RSTU (pre-image) .
It means the scale factor should be greater than 1. [∵ Scale factor for enlargement is k>1]
Then, Option B is also incorrect.
Hence, the rule yields the dilation of the figure RSTU centered at the origin is given by option A)
i.e. [tex](x,y)\to(4x,4y)[/tex]
NEED HELP URGENTLY!!
how do you solve this?
u can see the solution in pic
Find the greatest common factor 5x^5y^2+15x^2y^3+x^3y^5
5x^5•y^2 + 15x^2•y^3 + x^3•y^5
GCF = (x^2)(y^2)
The greatest common factor of the given polynomial is x²y².
What is the greatest common factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.
The given expression is 5x⁵y²+15x²y³+x³y⁵.
In the given expression, there are three terms 5x⁵y², 15x²y³ and x³y⁵
5x⁵y²=5×x×x×x×x×x×y×y
15x²y³=3×5×x×x×y×y×y
x³y⁵ =x×x×x×y×y×y×y×y
So, the common factor = x×x×y×y
= x²y²
Therefore, the greatest common factor is x²y².
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Question 1(Multiple Choice Worth 5 points)
(8.01 LC)
Two lines, A and B, are represented by the equations given below:
Line A: x + y = 2
Line B: 2x + y = 4
Which statement is true about the solution to the set of equations?
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.
Question 7(Multiple Choice Worth 5 points)
(8.02 MC)
Which of the following graphs shows a pair of lines that represent the equations with a solution (−5, 2)?
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 2 units to the right and 5 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 5 units to the right and 2 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 5 units to the left and 2 units up.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 2 units to the left and 5 units up.
Question 9(Multiple Choice Worth 5 points)
(8.03 LC)
A set of equations is given below:
Equation C: y = 2x + 6
Equation D: y = 2x + 2
Which of the following best describes the solution to the given set of equations?
One solution
Two solutions
No solution
Infinitely many solutions
Question 11(Multiple Choice Worth 5 points)
(8.01 MC)
Two lines, C and D, are represented by the equations given below:
Line C: y = x + 12
Line D: y = 3x + 2
Which of the following shows the solution to the system of equations and explains why?
(4, 14), because one of the lines passes through this point
(4, 14), because the point lies between the two axes
(5, 17), because both lines pass through this point
(5, 17), because the point does not lie on any axis
Question 1:
Substitution.
x+y=2
y=-x+2
2x+(-x+2)=4
x=2
(2)+y=2
y=0
Solution: (2,0)
There is one solution
Question 7 is too confusing, just find where the points intersect at (-5,2).
Question 9:
Elimination.
(-1)y=2x+6
y=2x+2
New: -y=-2x-6
0=-4
No Solution
Question 11:
Just look at explanations.
It's (5,17) both lines etc..
Final answer:
The set of equations for Line A and Line B has one solution. The graph correctly represents the solution (-5, 2) if the lines intersect 5 units to the left and 2 units up. Equations C and D have no solution since the lines are parallel, and the solution to Lines C and D is (5, 17), with both lines passing through this point.
Explanation:
Question 1: To determine the relationship between Line A: x + y = 2 and Line B: 2x + y = 4, we can solve for y in both equations.
For Line A, y = 2 - x.
For Line B, y = 4 - 2x.
Since the coefficients of x are different in the two equations, and the y-intercepts are also different, the lines are not parallel nor identical. Therefore, they intersect at exactly one point, which means there is one solution to the set of equations.
Question 7: The coordinates of the solution is given as (-5, 2). Among the options, the one showing the lines intersecting at the point 5 units to the left and 2 units up represents the correct set of lines, so the graph that corresponds to this description contains the solution.
Question 9: Comparing the two equations: Equation C: y = 2x + 6 and Equation D: y = 2x + 2, we see that both have the same slope but different y-intercepts. Because they have the same slope but different y-intercepts, these lines are parallel and never intersect. Hence, there is no solution to this set of equations.
Question 11: To find the intersection point, we set the equations of Line C: y = x + 12 and Line D: y = 3x + 2 equal to each other and solve for x:
x + 12 = 3x + 2
Subtract x from both sides: 12 = 2x + 2
Subtract 2 from both sides: 10 = 2x
Divide by 2: x = 5
We then substitute x = 5 into one of the equations to find y:
For Line C: y = 5 + 12 = 17.
Hence, the solution to the set of equations is (5, 17), and both lines pass through this point, which lies between the two axes, but that is irrelevant to why it is the solution.
a bag with 10 marbles is shown below. a marble is chosen from the bag at random. what are odds in favor of choosing a black marble
Divide the number of black marbles by 10, the total number of marbles. If there is one black marble, the chances of choosing a black marble is 1/10.