what are the coordinates of the vertex of the function f(x) = x2 -12x +5?
Answer:
[tex]\huge\boxed{(6;\ -31)}[/tex]
Step-by-step explanation:
METHOD 1:Let: [tex]f(x)=ax^2+bx+c[/tex].
The coordinates of the vertex:
[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have
[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]
Substitute:
[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]
METHOD 2:The vertex form of an equation of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
We have:
[tex]f(x)=x^2-12x+5\to a=1[/tex]
Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]
1. Find the Product of 8.02 and 6.1 and correct your answer to the highest whole number. 2. How many pieces of ribbon each 6cm long can be cut from a roll of ribbon 24m long?
A total of 32/3 strips can be derived from the ribbon.
What is quotients?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, we have,
to determine the number of strips:
From the question, we have the following parameters
Length of a roll of ribbon = 4 meters
Also, from the question;
We have
Length of a piece of ribbon = 5/12 meter
The number of strips of ribbon is the quotient of the Length of a roll of ribbon and the Length of a piece of ribbon
This is represented as
Number of strips = Length of a roll of ribbon/Length of a piece of ribbon
So, we have
Number of strips = (4 )/(5/12)
Evaluate the quotient
Number of strips = 32/3
Hence, the number of strips is 32/3
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complete question:
How many strips of a ribbon can be cut from a roll of ribbon that is 4 4/9 meters long if each piece is 5/12 meters long
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on a graph, he notices that his classmates’ times are distributed symmetrically along the x-axis. Which component of data analysis is Ralph observing
Answer:
The overall shape of the data
Step-by-step explanation:
For us to know what shape a data is, it must fulfil 4 conditions
is it symmetrical?the amount of peaks available in the data set.is it uniform? Is it rightly or leftly skewed?From the question, Ralph observed that the classmates time are symmetrical along the x-axis.
Therefore he is observing the shape of the data since one of the conditions have been fulfilled.
Thank you!
Use this scenario for questions 16-20: A city council begins hosting music nights in the park. They want to understand the success of the program, so they record attendance on 4 different nights (n = 4). On average, the city saw an average attendance of 47 (s = 4.7). Other cities that have launched a similar program and have seen an average attendance of μ = 53 (σ = 4.2). Is the city attendance different from other cities that have launched these music programs (alpha = .05)? What would be the hypotheses for this test? (HINT: remember one-tailed and two-tailed tests!).
Answer:
Step-by-step explanation:
To identify the null hypothesis, the null hypothesis is the default statement while the alternative hypothesis is the opposite of the null and always tested against the null hypothesis.
The alternative hypothesis depending on the case study can give rise to a one-tailed or a two-tailed test. The one tailed test includes either less than or greater than option and not both while the two tailed test involves both.
In this case study,
the null hypothesis is u1 (representing the city in particular) = u2 (representing other cities)
The alternative hypothesis is u1 (representing the city in particular) =/ u2 (representing other cities).
This, this test due to its not equal to sign is a two tailed test, the two results might differ maybe with one higher than the other, or lower than the other.
A wire that is 76 feet long needs to be divided into lengths using the ratio 1 to 13. What is the longer length? Round your answer to two decimal places if necessary.
Answer:
70.59 feet
Step-by-step explanation:
There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.
1. Divide 76 by 14
76 ÷ 14 = 5.43
2. Multiply the longer length of 13 parts
5.43 · 13 = 70.59
The longer length of the wire 70.59 feet
There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.
1. Divide 76 by 14
76 ÷ 14 = 5.43
2. Multiply the longer length of 13 parts
5.43 · 13 = 70.59
What is a decimal in numbers?In algebra, a decimal number can be defined as a range whose entire number part and the fractional element are separated by means of a decimal point. The dot in a decimal range is referred to as a decimal point. The digits following the decimal factor show a price smaller than one.
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Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
Which of the following is the standard form of y =3/7 x-1 a)3/7x-y=1 b) y-3/7x= - 1 c) 7y-3x= -7 d) 3x - 7y= 7
Answer:
d)
Step-by-step explanation:
the general form is ax + by = c
Based on historical data, an insurance company estimates that a particular customer has a 2.6% likelihood of having an accident in the next year, with the average insurance payout being $1600.
If the company charges this customer an annual premium of $110, what is the company's expected value of this insurance policy?
Answer: $68.4
Step-by-step explanation:
Given: Annual Premium = $110
Average insurance payout = $1600
Likelihood of having an accident= 2.6% = 0.026 [we divide perecnt by 100 to convert it into decimal]
Then, Expected value = (Annual Premium) - (Likelihood of having an accident) x (Average insurance payout )
= $110 - (0.026) x ($1600)
= $(110-41.6)
= $68.4
Hence, the company's expected value of this insurance policy : $68.4
A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?
Answer:-95 1/7 feet
Step-by-step explanation:
-120 4/7+25 3/7=-95 1/7 feet
The difference between seven times a number and 9 is equal to three times the sum of the number and 2. Find the number If x represents the number, which equation is correct for solving this problem?
Answer:
[tex]\large \boxed{\bf \sf \ \ \ 7x-9 = 3(x+2) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
x represents this number and we know that
the difference between seven times this number and 9
7*x - 9
is equal to three times the sum of this number and 2
3(x+2)
So we can write
[tex]7x-9 =3(x+2) \\\\7x-9 =3x+6 \ \ \text{distributive law} \\\\7x-9-3x=3x+6-3x =6 \ \ \text{subtract 3x} \\\\4x-9+9=6+9 \ \text{add 9} \\\\4x=15 \ \ \text{divide by 4} \\\\ \boxed{x=\dfrac{15}{4}}\\[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A land owner is planning to build a fenced-in, rectangular patio behind his garage, using his garage as one of the "walls." He wants to maximize the area using 80 feet of fencing. The quadratic function A(x)=x(80−2x) gives the area of the patio, where x is the width of one side. Find the maximum area of the patio.
Answer: 800 feet²
Step-by-step explanation:
Lets remove the brackets from the function's expression
A(x) = -2x²+80x
So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max
As we know Xmax= (X1+X2)/2 , where X1 and X2 are the roots of the function A(x)
Lets find X1 and X2
x(80-2x)=0
x1=0 80-2*X2=0
x2=40
So Xmax= (0+40)/2=20
So Amax= A(20)= 20*(80-2*20)=20*40=800 feet²
1. 2x-y≤-6
2. 5x+4y ≥20
Answer
2x-y <or =-6
2x<or=-6+y
divide both sides by 2
x<or=1/2y+3
5(1/2y+3)+4y>or=20
5/2y+15+4y>or=20
5/2y+4y>or=20-15
13/2y>or=5
divide both sides by 2/13
y>or=10/13
2x-10/13<or=-6
2x<or=-6+10/13
2x<or=-68/13
divide both sides by 2
x< or =-34/13
According to medical data, the ages at which patients have their first knee replacement surgery
follows a normal distribution. The average age for a first knee replacement is 58 years of age, with a
standard deviation of 8.25 years. Therefore, doctors can expect the middle 68% of their knee
replacement surgery patients to be between what ages?
Answer:
The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
Step-by-step explanation:
68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years
So, the ages lies between x₀ + σ and x₀ - σ
So, the ages lie between 58 - 8.25 = 49.75 years
and 58 + 8.25 = 66.25 years
So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
1. A mortgage of $200,000 requires payments of $1395.40 per month at 5.7%
compounded quarterly. How long will it take to repay the loan? What amount of interest
does the purchase pay?
Answer:
a) How long will it take to repay the loan?
20 years
b) What amount of interest does the purchase pay?
$134,896
Step-by-step explanation:
a) How long will it take to repay the loan?
In the above question, they are asking you for the Loan duration
The Formula for Loan duration(T) =
ln (- m/(r÷n) × C - m)/In (1 + r/n)
Where:
m = monthly payments = $1395.40
C = Amount of mortgage =$200,000
r = Interest rate = 5.7% = 0.57
n = compounded quarterly = 4
T = ln (- 1395.40/(0.57÷4) × 200,000 - 1395.40)/In (1 + 0.57/4)
T = 20 years.
Therefore, it will take 20 years to repay the Loan.
b) What amount of interest does the purchase pay?
The total number of payments =
Loan duration × Number of months
Number of months = 12 months( because it is monthly payment)
Loan duration = 20 years
Total number of payments = 240 payments.
In the question, we are given the amount paid monthly payment as
$1,395.40
Total amount paid = Monthly payments × Total number of payments
= $1,395.40 × 240
= $334,896
The amount of Interest the purchase pay = $334,896 - $200,000
= $134,896
Choose the correct equation for the parabola based on the given information. Given: Focus:(2,8) Directrix: y = 4 a. 2(y-2)= (x- 6)^2 b. 8(x -2) = (y -6)^2 c. 8(y - 6)= (x-2)^2 d. 2(x-2)= (y-8)^2
Explanation:
The directrix is horizontal, so the axis of symmetry is vertical. We'll have an x^2 term. The vertical distance from y = 4 to y = 8 is 4 units. Cut this in half to get 2, which is the focal distance p = 2.
The point (2,4) is directly below (2,8), and the point is on the directrix. The midpoint between (2,4) and (2,8) is (2,6). This is the vertex.
(h,k) = (2,6)
4p(y-k) = (x-h)^2
4*2(y-6) = (x-2)^2
8(y-6) = (x-2)^2
Water leaking from a local reservior at the rate of 500 gallons per hour. A. none of these B. quadratic C. exponential D. linear
Answer:
Linear
The 500 hundred gallons is adding up by the hours. Linear- first difference.
Y is directly proportional to x. Create an equation using k as the constant of proportionality.
Answer:
[tex]y = kx[/tex]
Step-by-step explanation:
y is directly proportional to x.
[tex]y \propto x[/tex]
[tex]y = kx[/tex]
Where k is as the constant of proportionality.
Answer:
y = kx
Step-by-step explanation:
Y is directly proportional to x which means that
=> y ∝ x
=> y = kx
Where k is the constant of proportionality.
Which equation represents the function graphed
coordinate plane?
Answer:
b. y = |x+4| - 10
Step-by-step explanation:
When you see a v-shaped graph, it could very well relate to an absolute-value function.
The value of the absolute value function has the vertex at x= -4, meaning that it has a minimum value when x=-4, which means that the absolute value function is of the form |x+4| giving a zero when x= -4.
Also, the minimum of the function occurs at y = -10, meaning that the function has been translated by -10.
Therefore the function is
y = |x+4| - 10
Answer:
B
Step-by-step explanation:
EDGE unit review
What are the solutions to the system of equations graphed attached pic
Answer: C
Step-by-step explanation:
For system of equations, the solution is the point or points where the equations intersect. The point they meet signifies that they are the same at the x and y point.
Looking at the graph, we see 2 intersection points. They are (0,-8) and (4,8). Therefore, C is the correct answer.
James is measuring the temperature (1) of a plate left sitting in the sun fort
hours. Which of the following is the most appropriate domain for h(0?
O A. All positive numbers
O B. Positive integers only
O C. All real numbers
O D. All integers
Answer:
O B. Positive integers only
Step-by-step explanation:
You have that the temperature of a plate is measured respect to the number of hours that the plate has been left in the sun.
In this case you have that the independent variable is the number of hours and the dependent variable is the temperature.
Due to James would like to know how is changing the temperature of the plate, per hour, the best domain for the function, that is, the best available values for the time on which the temperature of the plate is measured, are the positive integers only.
O B. Positive integers only
If f (x) = -9x - 9 and g (x) = Vx - 9, what is (f ° g) (10)?
Answer: [tex](f \circ g) (10)= -18\ .[/tex]
Step-by-step explanation:
Given: [tex]f (x) = -9x - 9[/tex] and [tex]g (x) = \sqrt{x - 9}[/tex]
To find : (f o g) (10)
For this we first find (f o g) (x)= [tex]f(g(x))[/tex]
[tex]=f(\sqrt{x-9})\\\\=-9(\sqrt{x-9})-9[/tex]
Now,
[tex](f \circ g) (10)=-9(\sqrt{10-9})-9\\\\=-9\sqrt{1}-9\\\\=-9-9=-18[/tex]
Hence, the value of [tex](f \circ g) (10)= -18\ .[/tex]
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes. Y
Answer:
yyy = xxx + 151515
Step-by-step explanation:
Since you want to swim 151515 minutes longer one day at practice (note this time is actually 105 days), you simply need to swim the same amount of time as your friend, plus the extra time. Hence, your time will be equal to your friends time plus the extra time you plan to swim.
CAN I GET SOME HELP OVER HERE? Ina Crespo rowed 12 miles down the Habashabee River in 2 hours, but the return trip took her 3 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current. Ina can row ? mph in still water
Answer: The speed of Ina in still water is 5mph
Step-by-step explanation:
If the speed of Ina on still water is x, and the speed of the river is y:
The total speed of Ina when she goes along with the current is:
S = x + y
when she goes against the current we have:
St = x - y.
Now we can use the relation:
speed = time/velocity.
along with the current, we have:
x + y = 12mi/2h = 6mi/h
against the current we have:
x - y = 12mi/3h = 4mi/h
So we have the equations
x + y = 6mi/h
x - y = 4mi/h
in the first equation we can isolate x
x = 6mi/h - y
now we replace this in the second equation:
(6mi/h - y) - y = 4mi/h
6mi/h - 2y = 4mi/h
-2*y = 4mi/h - 6mi/h = -2mi/h
y = 1mi/h
now we replace this in the first equation:
x + 1mi/h = 6mi/h
x = 5mi/h.
The speed of Ina in still water is 5mph
Write an expression with four terms. Include at least one term with an exponent, one term with a coefficient of 5, one term with three factors, and one constant. Make two of the terms like terms. Include a brief description of each term in the expression.
Answer:
4x^2 + 5x^2 + 4xy
Explanation
You need 2 like terms this could be of the form:
ax^2 + bx^2 + c
1 term with a coefficient of 5, sub in b = 5
ax^2 + 5x^2 + c
1 term with 3 factors, c = 4xy
This would mean it has a factor of 4,x and y.
So final equation is (a could be any value I give it a value of 4 for convenience)
4x^2 + 5x^2 + 4xy
Step-by-step explanation:
Evelyn is shopping for laundry detergent, and she prefers to get the best unit price she can. At the store, brand A is priced at $54 for 6 loads of laundry and brand B is priced at $63 for 9 loads of laundry
The unit cost of Brand B is less than Brand A, Evelyn for shop for Brand B.
What is the meaning of Unit Price ?Unit price is the price of one(unit) quantity of any substance.
The Brand A detergent costs $54 for 6 loads of laundry
Brand B detergent costs $63 for 9 loads of laundry
The unit price of both the detergent has to be compared to find the best among both
Unit cost for Brand A = 54/6 = $9
1 load of Brand A costs $9
Unit cost of Brand B = $63/9 = $7
1 load of Brand B costs $7
As, the unit cost of Brand B is less than Brand A, Evelyn for shop for Brand B.
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1. Which of the following ordered pairs are solutions to the system of equations below?
4x + 4y = -9
Y = 2x - 13
A : (-3, -7)
B : (3-7)
C : (3,7)
D : (-3,7)
Answer:
43\ 12 , 35/ 6
Step-by-step explanation:
43\ 12 , 35/ 6
Answer: B: (3, -7)
Step-by-step explanation:
4x + 4y = -9
y = 2x - 13
Use Substitution:
4x + 4(2x - 13) = -9
4x + 8x - 52 = -9
12x - 52 = -9
12x = 43
[tex]x=\dfrac{43}{12}[/tex]
None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.
Plan B: Input the choices into the equation to see which one makes a true statement.
4x + 4y = -9
A) (x, y) = (-3, -7)
4(-3) + 4(-7) = -9
-12 + -28 = -9
-40 ≠ -9
B) (x, y) = (3, -7)
4(3) + 4(-7) = -9
12 + -28 = -9
-16 ≠ -9
C) (x, y) = (3, 7)
4(3) + 4(7) = -9
12 + 28 = -9
40 ≠ -9
D) (x, y) = (-3, 7)
4(-3) + 4(7) = -9
-12 + 28 = -9
16 ≠ -9
Obviously there is something wrong with the first equation because none of the options provide a true statement.
y = 2x - 13
A) (x, y) = (-3, -7)
-7 = 2(-3) - 13
-7 = -6 -13
-7 ≠ -19
B) (x, y) = (3, -7)
-7 = 2(3) - 13
-7 = 6 -13
-7 = -7 this works!!!
C) (x, y) = (3, 7)
7 = 2(3) - 13
7 = 6 -13
7 ≠ -7
D) (x, y) = (-3, 7)
7 = 2(-3) - 13
7 = -6 -13
7 ≠ -19
Option B is the only one that provides a true statement so this must be the answer.
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Answer: A. A=(1000-2w)*w B. 250 feet
C. 125 000 square feet
Step-by-step explanation:
The area of rectangular is A=l*w (1)
From another hand the length of the fence is 2*w+l=1000 (2)
L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.
Express l from (2):
l=1000-2w
Substitude l in (1) by 1000-2w
A=(1000-2w)*w (3) ( Part A. is done !)
Part B.
To find the width w (Wmax) that corresponds to max of area A we have to dind the roots of equation (1000-2w)w=0 ( we get it from (3))
w1=0 1000-2*w2=0
w2=500
Wmax= (w1+w2)/2=(0+500)/2=250 feet
The width that maximize area A is Wmax=250 feet
Part C. Using (3) and the value of Wmax=250 we can write the following:
A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets
Solve for X. Pls help asap
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{12}}}}}[/tex]
Step-by-step explanation:
hypotenuse ( h ) = x
Peendicular ( p ) = 10
base ( b ) = 22
Using the Pythagoras theorem
[tex] \boxed{ \sf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{2} = {10 }^{2} + {22}^{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{2} = 100 + 44}}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{2} = 144}}[/tex]
[tex] \dashrightarrow{ \sf{ \sqrt{ {x}^{2} } = \sqrt{144}}} [/tex]
[tex] \dashrightarrow{ \sf{x = 12}}[/tex]
Hope I helped!
Best regards! :D
Se golpea (chuta) un balón sobre el piso y sale dando botes parabólicos cada vez menores. Si se lanzo inicialmente con una velocidad de 32m/s, y un ángulo de 60º y se sabe que en cada bote pierde un cuarto de su velocidad y el ángulo se reduce en 10º, determinar el alcance total logrado al termino del tercer bote y el tiempo empleado en ello Gracias a la persona Desconocida
Answer:
a)d = 180,91 m
b)t = 11,76 seg
Step-by-step explanation:
Para el lanzamiento de proyectil, la ecuación que nos da la velocidad en V(y) es:
V(y) = Voy - g*t
en donde Voy = Vo * senα ( donde Vo es la velocidad inicial, α el angulo del disparo.
Si en esta ecuación hacemos V(y) = 0 estamos en el punto donde el componente en el eje y de la velocidad del proyectil es cero, ese punto es el punto medio del recorrido.
0 = Vo*sen 60⁰ - g*t
g*t = Vo* √3/2
t = { 32 [m/s] * √3 }2*9,8 [m/s²]
t = 16*√3 / 9,8
t = 2,8278 seg
El tiempo total del primer recorrido es entonces por simetría
t₁ = 2 * 2,8278 t₁ = 5,6556 seg
La distancia del primer impacto al suelo es:
x = Vox * t₁ ( Vox es constante Vx = Vo*cos 60⁰ )
x = 32 * (1/2) * 5,6556
x₁ = 90,49 m
Aplicando los mismos criterios ahora para el segundo bote
Ahora Vo = 32 - 32*(1/4)
V = 24 m/s
g*t = 24 * sen 50⁰
t = 24* 0,7660/ 9,8
t = 1,8759
2*t = 2*1,8759
t₂ = 3,7518 seg
x₂ = Vox * t₂
x₂ = 24* 0,6428*3,7518
x₂ = 57,88 m
Y para el tercer bote Vo = 24 - 24(1/4) Vo = 18 m/s α = 40⁰
t = 18 *0,6428/9,8
t = 1,18
2t = t₃ = 2*1,18
t₃ = 2,36 seg
x₃ = Vox * 2,36 Vox = Vo*cos 40 Vox = 18*0,7660
Vox = 13,79
x₃ = 13,79*2,36
x₃ = 32,54 m
La distancia total será
d = x₁ + x₂ + x₃
d = 90,49 + 57,88 + 32,54
d = 180,91 m
y el tiempo total será la suma de los tiempos
t = t₁ + t₂ + t₃
t = 5,65 + 3,75 + 2,36
t = 11,76 seg
please please please help me. i need to pass, will do anything. ANYTHING!
Answer:
[tex]d \approx 5.8[/tex]
Step-by-step explanation:
Just use the distance formula.
[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]
[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]
[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]
[tex]d=\sqrt{9+25}[/tex]
[tex]d=\sqrt{34[/tex]
[tex]d \approx 5.8[/tex]