Answers
Answer:
see explanation
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( where r is the radius )
x² + y² = 49 ← is in this form with
r² = 49 ( take square root of both sides )
r = [tex]\sqrt{49}[/tex] = 7
Thus A = (7, 0 ) and B = (0, 7 )
To find M use the midpoint formula
M = ( [tex]\frac{7+0}{2}[/tex], [tex]\frac{0+7}{2}[/tex] ) = (3.5, 3.5 )
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (3.5, 3.5 )
m = [tex]\frac{3.5-0}{3.5-0}[/tex] = [tex]\frac{3.5}{3.5}[/tex] = 1
y = x ← equation of line passing through O and M
Answer:
Below in bold.
Step-by-step explanation:
(a)
At point A, y = 0 so the coordinates of A are found as follows:
x^2+ 0^2 = 49
x^2 = 49
x = 7 so A is (7, 0).
In a similar way, by putting x = 0 in the equation, we can show that
B = (0, 7).
(b)
M is the midpoint of the line AB so its coordinates are:
(7+ 0)/2, (0 + 7) /2 = (3.5, 3.5).
So the slope of OM which also passes through the origin (0,0) is:
(3.5 - 0) /(3.5 - 0) = 1.
y - y1 = m (x - x1)
y - 3.5 = 1(x - 3.5)
y = x - 3.5 + 3.5
y = x is the required equation.
Related Questions
The bumper car ride at the state fair has 2 red cars, 3 green cars, and 3 blue cars. Janet is first in line for the ride and is assigned a car at random. Sarah is next in line and is randomly assigned a car. What is the probability that both Janet and Sarah will drive a red bumper car? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
96.4%
25%
6.3%
3.6%
Answers
The probability (in percentage form) is 3.6%, so the correct option is the last one.
How to find the probability?First, Janet is assigned to a car. We want to find the probability that it is a red car. All the cars have the same probability of being assigned, then the probability of getting a red car is equal to the quotient between the number of red cars and the total number of cars:
p = 2/(8) = 1/4
Now there is 1 red car left and 7 cars in total left.
Sarah is next on line, the probability that she gets a red car will be:
q = 1/7
The joint probability (the probability of both of these events happening) is given by the product of the two individual probabilities, so we get:
P = (1/4)*(1/7) = 0.036
If we multiply this by 100%, we get:
P = 100%*0.036 = 3.6%
So the correct option is the last one.
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
Please help me ASAP!!!!!
Answers
Answer:
Since
x=−5 is a vertical line, there is no y-intercept and the slope is undefined.
Slope: Undefined
y-intercept: No y-intercept
Step-by-step explanation:
Simplify -|-5 + 2|.
7
3
-7
-3
Answers
Answer:
-3
Step-by-step explanation:
-|-5+2|
= -|-3|
= - 3
Hope it helps
Answer:
-3
Step-by-step explanation:
-|-5+2|
-|-3| absolute value of -3 is 3
-3
If the slope of a line is 7/10, how much vertical change will be present for a
horizontal change of 63 ft?
Answers
If the slope of the line is 7 /10, the vertical change that will be present for a horizontal change of 63 ft is 44.1 ft
What is a slope?The slope of a line is the measure of its steepness. Therefore,
slope = change in y(vertical) / change in x(horizontal)
slope = y₂ - y₁ / x₂ - x₁
slope = 7 / 10
Therefore,
7 / 10 = y / 63
cross multiply
441 = 10y
divide both sides by 10
y = 441 / 10
y = 44.1 ft
learn more on slope here: https://brainly.com/question/18555739
A large container holds 7 gallons of water. It begins leaking at a
constant rate. After 8 minutes, the container has 5 gallons of
water left.
At what rate is the water leaking and After how many minutes will the container be empty?
Answers
Answer:
The container will take 25 minutes to go from full to empty.
Step-by-step explanation:
In 15 minutes, the container has lost 3 gallons of water (
5
−
2
=
3
).
Since the leak is at a constant rate, we can determine that every five minutes the container loses one gallon.
So for the container to lose the full 5 gallons will take 25 minutes (
5
×
5
=
25
Question 2 of 10
In the diagram below, BD is parallel to XY. What is the value of x?
*
A. 120
B. 60
ОООО
D. 40
Answers
Answer:
Step-by-step explanation:
It’s 60 baka
A guy wire supports a cell-phone tower. The guy wire makes a 55° angle with the ground and touches the ground 34 ft from the base of the tower. What is the length of the guy wire, rounded to the nearest foot? 20 ft 28 ft 49 ft 59 ft A right triangle. The base is labeled 34 feet. The angle made between the base and the hypotenuse is labeled 55 degrees. The angle made between the base and the perpendicular is marked as a right angle.
Answers
The length of the guy wire (rounded to the nearest foot) is 20 ft. Then the correct option is A.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
A guy wire supports a cell phone tower.
The guy wire makes a 55° angle with the ground and touches the ground 34 ft from the base of the tower.
Base = 34 ft.
The length of the wire will be given as
[tex]\rm Wire \ length = 34 * cos\ 55^o\\\\Wire \ length = 19.5 \approx 20 \ ft[/tex]
The length of the wire is 20 ft. Then the correct option is A.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
Answer:
is 59ft
Step-by-step explanation:
just took the test
a2 - b2 - 2a + 1 plss give me answer fast
Answers
Answer:
( a − 1 + b )( a − 1 − b )
.
Answer:
(a−1+b)(a-1−b)
Step-by-step explanation:
A truck driver averages 45 miles per hour while delivering freight and 60 miles per hour on the return
trip. The total drive time is 7 hours. How long does each trip take?
pls send help a girl is struggling
Answers
Answer:
Delivery Trip: 3 hours
Return Trip: 4 hours
Step-by-step explanation:
d/60 + d/45 = 7
45d/2700 + 60d/2700 = 7
105d/2700 = 7
105d = 18900
d = 180
180/60 = 3
180/45 = 4
Answer:
delivering 180/45 = 4 hours and return trip 180/60 = 3 hours
Step-by-step explanation:
d = unknown number to calculate each trip
[tex]\frac{d}{45}[/tex] + [tex]\frac{d}{60}[/tex] = 7
find common denominator (45 * 60 = 2700)
([tex]\frac{60}{60}[/tex])*([tex]\frac{d}{45}[/tex]) +( [tex]\frac{45}{45}[/tex])*([tex]\frac{d}{60}[/tex]) =7
[tex]\frac{60d}{2700}[/tex] + [tex]\frac{45d}{2700}[/tex] =7
[tex]\frac{60d + 45d}{2700}[/tex] =7
[tex]\frac{105d}{2700}[/tex] = 7
105d = 7 * 2700
105d = 18,900
d = 18900/105
d = 180
delivering 180/45 = 4 hours
return trip 180/60 = 3 hours
[tex] \sf \large \: If \: y = Sin x \: * Cos \: 2x \: Find \frac{dy}{dx} [/tex]
Thanku!
Answers
Answer:
cos (x) cos (2x) - 2sin(x) sin(2x)Solution:
(See the solution in the photo)
Answer:
[tex]\sf -5\cos \left(x\right)+6\cos ^3\left(x\right)[/tex]
explanation:
[tex]\sf y = sin(x) * cos(2x)[/tex]
[tex]\rightarrow \sf \frac{d}{dx}\left(sin\left(x\right)\ * \:\:cos\left(2x\right)\right)[/tex]
[tex]\sf \bold {Apply\:the\:Product\:Rule}:\quad \left(f\cdot g\right)'=f\:'\cdot g+f\cdot g'[/tex]
[tex]\rightarrow \sf \frac{d}{dx}\left(\sin \left(x\right)\right)\cos \left(2x\right)+\frac{d}{dx}\left(\cos \left(2x\right)\right)\sin \left(x\right)[/tex]
[tex]\sf \bold{ Apply \ differentiation \ rule \ \ \ : } \ \ \ sin(x) = cos(x) \ \ and \ \ cos(x) = -sin(x)[/tex]
[tex]\rightarrow \sf \cos \left(x\right)\cos \left(2x\right)+\left(-\sin \left(2x\right)\ * \:2\right)\sin \left(x\right)[/tex]
[tex]\rightarrow \sf \cos \left(x\right)\cos \left(2x\right)\left-2\sin \left(2x\right)\sin \left(x\right)[/tex]
[tex]\sf \bold {use \ the \ formulae \ : \ cos(2x) = 2cos^2(x) - 1} \ {and} \ \ \sf \bold{sin(x) = 2 sin x cos x}[/tex]
[tex]\rightarrow \sf cos(x) (2cos^2 (x) -1) -2(2sin(x)cos(x)sin(x))[/tex]
[tex]\rightarrow \sf 2cos^3 (x) - cos(x) - 4sin^2(x) cos(x)[/tex]
[tex]\rightarrow \sf -5\cos \left(x\right)+6\cos ^3\left(x\right)[/tex]
Convert 2.19 liters to milliliters.
Enter your answer in the box.
Answers
Hey there!
1 litres = 1000 milliliters
To find the value we multiply litres × 1000
=> 2.19 × 1000
=> 2190
Therefore, 2.19 to milliliters is 2190 millilitres
Which best describes the graph of the cubic function f(x) = x3 x2 x 1?.
Answers
Graph of a function is plotting of its input and corresponding output. The graph of the considered cubic function is attached below.
How do we make graph of a function?Suppose the considered function whose graph is to be made is [tex]f(x)[/tex]
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values [tex]f(x)[/tex]
are plotted on the vertical axis.
They are together plotted on the point
[tex](x,y) = (x, f(x))[/tex]
This is why we usually write the functions as:
[tex]y = f(x)[/tex]
For the considered function [tex]f(x) = x^3 +x^2 +x + 1[/tex] is attached below.
Learn more about graphing functions here:
https://brainly.com/question/10166124
The revenue function for a bicycle shop is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=800−0.5x is the unit price. Find the maximum revenue.
Answers
Answer:
The maximum revenue is $320,000
Step-by-step explanation:
To find the maximum of a function f, the procedure is as follows:
Find the first derivative of f.Equate the derivative to 0. Solve the resulting equation to get the critical points.Try all the critical points in the original function and select the one that maximizes it.The revenue function for a bicycle shop is
R(x)=xp(x), where p(x)=800-0.5x. Substituting:
[tex]R(x)=x(800-0.5x)=800x-0.5x^2[/tex]
Find the first derivative of R:
R'(x)=800-x
Equate to 0:
800-x=0
Solve:
x=800
There is only one critical point. Substitute it into the revenue function:
[tex]R(800)=800(800)-0.5(800)^2=320,000[/tex]
The maximum revenue is $320,000
Solve for x + 5 = 30
Answers
Answer:
25
Step-by-step explanation:
A farmer had 3,000 acres of land. He planted 30% of it with wheat, 45% of it with corn, and the rest with oats.
Find how many acres he planted with each kind of grain
Answers
Answer:
900 acres of wheat
1350 acres of corn
750 acres of oats
Step-by-step explanation:
3000 = 100%
÷ 10 both sides
300 = 10%
× 3
900 = 30%
300 = 10%
× 4
1200 = 40%
300 ÷ 2 = 150 (5%)
1200 + 150 = 1350
1350 + 900 = 2250
3000 - 2250 = 750
The number of siblings each student at a softball game has is recorded. The graph below shows the probability distribution of having any number of siblings, X, for a randomly selected student. Which number of siblings is least likely?.
Answers
The number 4 siblings are least likely to be selected
What is the number of a sibling to be selected?Probability is the likelihood of an event occurring or not. Probability value ranges from impossibility(0) to certainty(1).
The lower the value, the less likely the event is bound to occur.
From the probability distribution table, the probability of having 4 siblings at the game is 0.
This is the lowest out of all the given values in the probability distribution table. Therefore, it is the least likely event.
Thus the number 4 siblings are least likely to be selected
To know more about probability follow
https://brainly.com/question/24756209
42 + (-31) + (-12) =
Answers
Answer:
-1
Step-by-step explanation:
I used a calculator :)
The answer is -1
Because if you do all the math you will find that the answer is -1.
Anita needs to build a house for a school project. The base of the house is a rectangle where the length of a rectangle is 8 more than the width. Its area is 240 ft sq
Answers
L = lengh
W = width
french reasoning ( hello from France ) !
The base of the house is a rectangle where the length of a rectangle is 8 more than the width.
=> L = W + 8
and
Its area is 240 ft sq
W x L = 240
L = W + 8
W x L = 240
=> W x (W+8) = 240
W² + 8W - 240 = 0
Δ = 8² - 4*1*(-240) = 32²
W' = (-8 + 32) / 2 = 12 ft
W'' = (-8 - 32) / 2 = impossible
at the end
W the width = 12 ft
and then the lengh = 12 + 8 = 20
area = 12 x 20 = 240 ft²
The graph shows information about the costs of taxi journeys in France.
For each journey, there is a fixed charge plus a charge for the distance travelled.
a) How much is the fixed charge?
Jean makes two journeys by taxi.
One journey is 6km more than the other journey.
b) Work out the difference between the costs of these two journeys.
Answers
The fixed charge is about 5 pound. For extra 6 km, extra cost is about 9 pound
What is a linear equation?A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value of y.
From the graph:
The fixed charge is about 5 pound.
Using the point (0, 5) and (20, 35)
Charge per mile = (35 - 5) / (20 - 0) = 1.5 pound per mile
For extra 6 km, extra cost = 1.5 * 6 km = 9 pound
Find out more on linear equation at: https://brainly.com/question/2972832
(;-;) I NEED HELP W THIS PLSSS HELP WILL MARK BRAINLIEST
Answers
Answer:
With respect to angle A, a is opposite, b is adjacent, c is the hypotenuse
With respect to angle B, b is opposite, a adjacent, and c is the hypotenuse.
Step-by-step explaination:
To find the opposite side of an angle of a right triangle - look at the side that is directly across from that angle. For example, angle A shows that the side directly across from it is side a.
To find the adjacent side of an angle of a right triangle - look at the side that is right next to it and connected to the 90 degree angle. For example, angle B shows that the side that is next to it and connected to the 90 degree angle is side b.
The hypotenuse will always be the longest side opposite the 90 degree angle.
Four people each deliver food to people’s homes. Curtis charges a flat flee of $2.50 for each delivery plus $0.20 per mile for each mile he drives. For one delivery, Curtis drives 6 miles. How much does Curtis charge to deliver the food?
Please show your work
Answers
So, if x=6, then its 2.5+0.2(6)=2.5+1.2=3.70, therefore the final answer is $3.70
Answer:
$3.70
Step-by-step explanation:
0.2 x 6 = 1.2
1.2 + 2.5 = 3.7
can some one help me please
Answers
Answer:
Step-by-step explanation:
i think it is reflection in the line y=-1
[tex]\sqrt{54y^{11}z^{5} }[/tex]
Answers
What, do you want that thing to be answered? There is a app that does your math for you in a few seconds i hope ya know. I dont think anyone here could figure that out either.
Solve the two-step equation and identify the steps.
1.4x + 6.1 = –7.9
1. The first step is to
on both sides.
2. The second step is to
on both sides.
The solution is x =
.
Answers
Answer:
x = -10
Step-by-step explanation:
1.4x = -7.9 -6.1
1.4x = -14
x = -14÷1.4
x= -10
Answer:
x = -10
Step-by-step explanation:
What is the volume of a sphere with a radius of 2.5 units?
Answers
Answer: A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a geometrical object that is a three-dimensional analog to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.
Step-by-step explanation: The formula used to calculate the sphere radius is: r = ∛((3/4) · V / π) Symbols. r = Sphere radius; V = Sphere volume; π = Pi = 3.14159… The volume of Sphere. Enter the volume contained within a sphere. The radius of Sphere. This is the radius of a sphere that corresponds to the specified volume.
Find the measure of angle c in the triangle below. Then find the length of segment BC
Answers
Answer:
Step-by-step explanation:
when 8 is added to 1/3 of a number, the result is 23 find the number
Answers
Answer:
The number would be 5!
Step-by-step explanation:
23-8=15
15/3=5
Have a wonderful day!! :)
Answer:
8+x/3=23
Step-by-step explanation:
x/3=15
x=15x3=45
The price of a new car was £12500It is reduced to 11625Work out the percentage reduction
Answers
Answer:
The percentage reduction is 7%
Which shows one way to determine the factors of 12x3 – 2x2 18x – 3 by grouping?.
Answers
The equation which shows the one way to determine the factors of provided equation by grouping is,
[tex]2x^2(6x-1)+3(6x-1)[/tex]
What is a factor of polynomial?Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
Factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.
The provided polynomial equation is,
[tex]12x^3 - 2x^2 +18x - 3[/tex]
To factorize the above polynomial equation, make the groups, by taking out the greatest common factor.
[tex]12x^3 - 2x^2 +18x - 3\\2x^2(6x-1)+3(6x-1)\\(6x-1)(2x^2+3)[/tex]
Hence, the equation which shows the one way to determine the factors of provided equation by grouping is,
[tex]2x^2(6x-1)+3(6x-1)[/tex]
Learn more about factor of polynomial here;
https://brainly.com/question/24380382
Give the coordinates of each vertex (D, E and F) and explain how you found the coordinates using the transformation rules.
Answers
Step-by-step explanation:
We have that the vertices of triangle ABC are:
A(4, 2)
B(7, 9)
C(7, 2)
First, we are reflecting over the y axis, which makes (x,y) map onto (-x, y). This gives us:
A'(-4, 2)
B'(-7, 9)
C'(-7, 2)
Then, we translate 5 units down, meaning we subtract 5 from each of the y coordinates. This gives us a final answer of:
D(-4, -3)
E(-7, 4)
F(-7, -3)