Given:
The point (7, 4) lies on a circle centered at the origin.
To find:
The equation of the circle and the radius of the circle.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The point (7, 4) lies on a circle centered at the origin. So, the distance between the points (7,4) and (0,0) is equal to the radius of the circle.
[tex]r=\sqrt{(0-7)^2+(0-4)^2}[/tex]
[tex]r=\sqrt{(-7)^2+(-4)^2}[/tex]
[tex]r=\sqrt{49+16}[/tex]
[tex]r=\sqrt{65}[/tex]
The standard form of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, (h,k) is the center of the circle and r is the radius of the circle.
Putting h=0, k=0 and [tex]r=\sqrt{65}[/tex] in (ii), we get
[tex](x-0)^2+(y-0)^2=(\sqrt{65})^2[/tex]
[tex]x^2+y^2=65[/tex]
Therefore, the equation of the circle is [tex]x^2+y^2=65[/tex] and its radius is [tex]r=\sqrt{65}[/tex].
Bill is 6 years older than Mary. The sum of their ages is 48. What are the equations used to find their ages?
Step-by-step explanation:
Mary's age = x
Billi's age = x+6
So, Mary age + Billi age = x + (x + 6)
Sum of their ages = 2x + 6
So, 2x + 6= 48
2x = 48 - 6
2x = 42
x = 42/2
Mary age = x = 21
And Billi age = x +6= 21 + 6 = 27
So Mary = 21
And Billi = 27
Lets check!
21 + 27 = 48
So therefore their ages add up to 48
So the answer is correct!
24 pack of mountain dew for 9.99 or a pack if mountain dew for 5.99 find the unit number
Answer:
24 pack of mountain dew=9.99
1 pack of mountain dew=9.99/24=0.41625
Consider the number line graph of x > 28. Which numbers are solutions for the inequality?
A)
0
B)
21
C)
28
D)
30
E)
45
Answer:
D and E
Step-by-step explanation:
X is any number GREATER THAN 28, but it is not greater than or equal to so it is not C. A and B are less than 28, so those cannot be answers. D and E are both larger than 28, therefore those are correct.
Answer:
D and E
Step-by-step explanation:
X is any number GREATER THAN 28, but it is not greater than or equal to so it is not C. A and B are less than 2
Step-by-step explanation:
Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have?
a.
$50,000
b.
$70,000
c.
$90,000
d.
$120,000
Answer:
The answer is 70,000 sales.
Bob gets paid an annual salary of $30,000, which means that monthly he gets:
$30,000 : 12 months = $2,500 per month
x - number of sales
Bob earns 5% commission on all sales he makes: x * 5% = x * 0.05 = 0.05x
The function is:
f(x) = 2,500 + 0.05x
Bob wants to make $6,000 this month: f(x) = 6,000
2500 + 0.05x = 6000
0.05x = 6000 - 2500
0.05x = 3500
x = 3500 : 0.05
x = 70000 sales
Step-by-step explanation:
Sales for the month should amount to $70,000
Annual salary = $30,000
Commission on sales = 5%
To make 6000 in a month :
Monthly salary = $30000 / 12 = $2500
Month earning = $2500 + 5% × (monthly sales)
Month earning = $6000
Let month sales = m
6000 = 2500 + 0.05m
6000 - 2500 = 0.05m
3500 = 0.05m
m = 3500 / 0.05
m = 70,000
Sales for the month should be 70,000
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volume of rectangular prism with length of 9in and width of 1 1/3in and height of 4 2/3in
Answer:
V≈55.98
Step-by-step explanation:
V=WHL=1.33x4.67x9≈55.978
A rectangular painting is bordered on all sides by a frame. Write an
expression to describe the area of the frame.
A. 6x + 4
B. 4x2 + 3
C. 5x + 3
D. 4x2 + 5x + 3
I think it is a 6x+4
The required area of the frame shown is 5x + 3. Option C is correct.
What is surface area?The surface area of any shape is the area of the shape that is faced or the surface area is the amount of area covering the exterior of a 3D shape.
Here,
The area of the picture is given as,
= 2x × x
= 2x²
The area of the whole painting with frame.
= (x + 1)(2x+ 3)
= 2x² + 5x + 3
The area of the frame is given as,
= area of picture with frame - an area of the picture,
= 2x² + 5x + 3 - 2x²
= 5x + 3
Thus, the required area of the frame shown is 5x + 3. Option C is correct.
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x to the second power is 49 what is x?
Answer:
7 or -7
Step-by-step explanation:
the question is asking for x to to the second power which is x squared or x^2
so setting x^2=49
square root both sides of the equation so that x is by itself and the other side is just ±√(49). which ±√49 is just 7 or -7
Hope that helps :)
Please gve brainliest
Help Me Please.................
Answer:
[tex]x=-15.8994[/tex]
Step-by-step explanation:
Skills needed: Solving one variable equations, Multiplication
1) We are given: [tex]-11.818=-7+\frac{x}{3.3}[/tex], and we need to solve for "[tex]x[/tex]"
2) In order to do this, you need to isolate the variable. In other words, you need to make sure the term involving "[tex]x[/tex]" is on one side of the equation, while everything else is on the other side.
In this case, the term involving "[tex]x[/tex]" is: [tex]\frac{x}{3.3}[/tex] In order to isolate [tex]\frac{x}{3.3}[/tex], you need to get rid of the "-7" on the right side. To get rid of it, we can add 7 to both sides.3) [tex]-11.818+7 = -7+\frac{x}{3.3} +7[/tex]
[tex]-11.818+7=-4.818[/tex]
-7 and 7 on the right side cancel out.
4) So you are left with: [tex]-4.818=\frac{x}{3.3}[/tex]
To get "[tex]x[/tex]", you need to multiply both sides by 3.3If you do this, the denominator will get cancelled out, leaving us with "[tex]x[/tex]" equaling a value.5) So then: [tex]-4.818 * 3.3 = x[/tex] (that star sign in between -4.818 and 3.3 is a multiplication sign)
[tex]-4.818*3.3 = -15.8994[/tex], so [tex]x = -15.8994[/tex]
Hope this helps and have a nice day!! :] :) :D
Decide if the function is an exponential function. If it is, state the intial value and the base. y = 5 ^ x
Answer:
B
Step-by-step explanation:
7/10 - ___ + 3/2 = 6/5. I want to know the blank and how you did it so I can solve it on my own! Thank you!
the probability that it will rain tomorrow is 0.85what is the probability that it will not rain tomorrow
Answer:
.15
Step-by-step explanation:
Probability of Rain = x
Probabiliy of No Rain = y
Y=1-X
Y=1-0.85
Y=.15
Question 4
(05.05)What is the rate of change for the linear relationship modeled in the table
Answer:
-1/2
Step-by-step explanation:
Simplify the following expression:
6b + 3ab + 4b + 3
O 2b
O 10b + 3ab + 3
O 13b + 3
06b + 3ab + 4b + 3
Answer:
6b+4b first because you have to combine like terms so 10b and the others aren't like terms so you just plug them in so 10b+3ab+3
the price of a stereo system is $627.50 the sales tax is 6% find the amount of the tax and the total cost
Mean and standard deviation of sample proportions
Suppose that 35% of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 30 students from the population of 750 students at the school and finds that 40% of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this. Let p represent the proportion of a sample of 30 students in the school who can sing their national anthem correctly. What are the mean and standard deviation of the sampling distribution of p?
Answer: D
Suppose that 35\%35%35, percent of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 303030 students from the population of 750750750 students at the school and finds that 40\%40%40, percent of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this.
Step-by-step explanation: Khan Academy Explanation
The mean and standard deviation is given by -
μ = 0.35 and σ = 0.09.
What is mean, median and mode in statistics?Mean : The "average" number; found by adding all data points and dividing by the number of data points.Median : The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).Mode : The most frequent number—that is, the number that occurs the highest number of times.Given is that suppose that 35% of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 30 students from the population of 750 students at the school and finds that 40% of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this. Let {p} represent the proportion of a sample of 30 students in the school who can sing their national anthem correctly.
The standard deviation is given by → [tex]$\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]where -
{σ} = population standard deviation
{N} = the size of the population
x{i} = each value from the population
{μ} = the population mean
The mean and standard deviation is given by -
μ = 0.35
σ = √(0.35)(0.65)/(30) = 0.48/5.5 = 0.09
σ = 0.09
Therefore, the mean and standard deviation is given by -
μ = 0.35 and σ = 0.09
To solve more questions on statistics, visit the link below -
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I need help please?
Answer:
B
Step-by-step explanation:
the blue parabola shows (1/4x)^2, the red shoes x^2, you can see the horizontal stretch, hope this helps :)
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer: im in 100% sure but i think its yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
I used photomath
4. Bobby is 12 years old. His grandfather is 60 years old, what percent of Bobby's
grandfather's age is Bobby's age?
Show your work
Somebody please help me I'm confused on this question and this is our last day to do this test and it's most of our grade
Answer: 12/60 as a percentage is 20%
Step-by-step explanation: boby is 12 and his grandfather is 60 so Bobby’s age is 12/60 of his grandfather and as a percentage it’s 20%
Answer:
5% maybe....
Step-by-step explanation:
Tyrone used 15 centimeters of tape to wrap 5 presents. How many presents did Tyrone wrap if he used 42 centimeters of tape? Assume the relationship is directly proportional.
Answer: 14 presents
Step-by-step explanation:
5 presents 42 cm tape
——————I-———————.
15 cm tape 1
= (5x42) /15 = 14 presents
Find the value of y. *
40
80
140
100+2y = 180
2y=180-100
2y=80
y=40
Name two pairs of adjacent angles and two pairs of vertical angles in
the figure.
Can anyone help with 1 and 2?
Answers are
1.
∠ABC and ∠EBD are vertical angles.
∠ABE and ∠CBD are vertical angles.
∠ABE and ∠DBE are adjacent angles.
∠ABC and CBD are adjacent angles.
2.
∠LMN and <RMQ are vertical angles.
∠SML and ∠QMP are vertical angles.
∠LMN and ∠PMN are adjacent angles.
∠NMP and ∠PMQ are adjacent angles.
Adjacent and vertical angles:
Adjacent angles: Two angles with a common arm and vertex are called adjacent angles.
They share a common arm and common vertex.
Adjacent angles are not always equal in measure
Vertical angles: When two lines intersect each other, then the pair of opposite angles formed at the vertex are called vertical angles.
They share a common vertex, but no common arm.
Vertically opposite angles are equal in measure.
(Here)
For question - 1,
∠ABC and ∠EBD are vertical angles.
∠ABE and ∠CBD are vertical angles.
∠ABE and ∠DBE are adjacent angles.
∠ABC and CBD are adjacent angles.
For question - 2,
∠LMN and <RMQ are vertical angles.
∠SML and ∠QMP are vertical angles.
∠LMN and ∠PMN are adjacent angles.
∠NMP and ∠PMQ are adjacent angles.
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Match the tangent and sine angles to their expressions.
Answer:
1) [tex]sin \left(\dfrac{- \pi}{12} \right) = \dfrac{(\sqrt{2} - \sqrt{6} }{4}[/tex]
2) [tex]tan\left(\dfrac{ \pi}{12} \right) = 2 - \sqrt{3}[/tex]
3) [tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = 2 + \sqrt{3}[/tex]
Step-by-step explanation:
1) [tex]sin \left(\dfrac{- \pi}{12} \right) = sin(-15^{\circ})[/tex]
sin(-15°) = sin(30° + (- 45°)) = sin(30°)cos(-45°) + cos(30°)sin(-45°)
sin(30°)cos(-45°) + cos(30°)sin(-45°) = 1/2 × (√2)/2 + (√3)/2 × (-√2)/2
1/2 × √2/2 + √3/2 × -√2/2 = (√2)/4 - (√6)/4 = ((√2) - (√6))/4
sin(-15°) = ((√2) - (√6))/4
[tex]sin \left(\dfrac{- \pi}{12} \right) = sin(-15^{\circ}) = \dfrac{(\sqrt{2} - \sqrt{6} }{4}[/tex]
2) [tex]tan\left(\dfrac{ \pi}{12} \right) = tan(15^{\circ})[/tex]
tan(15°) = tan(45° + (-30°)) = (tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°))
(tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°)) = ((-1/√3) + 1)/(1 - (-1/√3))
((-1/√3) + 1)/(1 - (-1/√3)) = (3 - √3)/(3 + √3) = (3 - √3)·(3 -√3)/((3 - √3)·(3 + √3))
(3 - √3)·(3 -√3/((3 - √3)·(3 + √3)) = (9 - 6·√3 + 3)/(9 - 3) = (12 - 6·√3)/6
(2 - √3)
[tex]tan\left(\dfrac{ \pi}{12} \right) = tan(15^{\circ}) = 2 - \sqrt{3}[/tex]
3) [tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = tan(75^{\circ})[/tex]
tan(75°) = tan(30° + 45°) = (tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°))
(tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°)) = ((1/√3) + 1)/(1 - 1/√3)
((1/√3) + 1)/(1 - 1/√3) = (3 + √3)/(3 - √3) = (3 + √3)·(3 +√3/((3 - √3)·(3 + √3))
(3 + √3)·(3 +√3/((3 - √3)·(3 + √3)) = (9 + 6·√3 + 3)/(9 - 3) = (12 + 6·√3)/6
(12 + 6·√3)/6 = 2 + √3
[tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = tan(75^{\circ}) = 2 + \sqrt{3}[/tex]
A system of equations is shown below,
y = 5x + 2
10x - 2y = 12
what is the solution to the system of equations?
The governor's approval rating dropped by 40% to 18%. What was his approval rating before?
Answer:
58%
Step-by-step explanation:
58 cuz 40+18=58
A weather station on the top of a mountain reports that the temperature is currently 14°C and has been falling at a constant rate of 9°C per hour. If it continues to fall at this rate, find each indicated temperature. What will the temperature be in 2 hours? What will the temperature be in 5 hours? What will the temperature be in half an hour?
Answer: 2 hours=6 degrees C
5 hours=-31 degrees C
Half an hour=9.5 degrees C
I hope this helps. Sorry if I made a mistake. Good luck!
Step-by-step explanation:
9 x 2 hours = 18 C 14-8= 6 degrees C
9 x 5 hours = 45 C 14-45= -31 degrees C
9 x 0.5 = 4.5 C 14-4.5= 9.5 degrees C
A boat travels 187 miles in 10
hours (with a constant speed).
How far can it travel in 14 hours
(with the same speed)?
Answer:
grufhvdyfvgysgddgfvsygujsbchusb
Step-by-step explanation:
The measurements of a rectangular room, in a scale drawing, are 2 inches by 3
inches. The scale is inch = 3 feet. If carpet costs $1.75 per square foot, how much will
it cost to put carpet in this room?
Answer:
so,
the room (2×3) × (3×3) feet, or 6x9 feet.
6x9= 54square feet
54 x 1.75= $94.50
m(x)=x(x+6)
p(x)=x(x+3)²-9
Show that m(x) and p(x) are equivalent
Answer:
m=x+6
Step-by-step explanation:
Let's solve for m.
mx=x(x+6)
Step 1: Divide both sides by x.
2x/x= x²+6x/x
m=x+6
Hope this helps :)
PLS BRAINLIEST
What does 15+5= 18 +
Answer:
2
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
Determine which lines, if any, are parallel or perpendicular. Explain
Line a: 2x-7y=14
Line b: y=7/2x-8
Line c: 2x+7y=21
Answer:
line b and c are perpendicular because the product of their slope is -1
Step-by-step explanation:
For two lines to be parallel they must have the same slope
For two line to be perpendicular, the product of their slope must be -1
Line a: 2x-7y=14
Rewrite in the form y = mx+c
-7y = -2x + 14
y = -2/-7 x + 14/-2
y = 2/7x - 7
The slope of line a is 2/7
Line b: y=7/2x-8
This is already in standard format
mx = 7/2 x
m = 7/2
The slope of line b is 7/2
Line c: 2x+7y=21
Rewrite in standard form
7y = -2x + 21
y = -2/7 x + 21/7
y = -2/7 x + 3
The slope of line c is -2/7
Take the product of line b and c
mb * mc = 7/2 * -2/7
mb * mc = -1
Hence line b and c are perpendicular because the product of their slope is -1