Answer:
(x - 1)² + (y - 2)² = 20
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given the endpoints, then the centre is at the midpoint
C = [ [tex]\frac{-3+5}{2}[/tex], [tex]\frac{0+4}{2}[/tex] ] = (1, 2 )
The radius is the distance from the centre to either of the 2 endpoints.
Use the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)
r = [tex]\sqrt{(-3-1)^2+(0-2)^2}[/tex]
= [tex]\sqrt{(-4)^2+(-2)^2}[/tex]
= [tex]\sqrt{16+4}[/tex]
= [tex]\sqrt{20}[/tex]
Thus equation of circle is
(x - 1)² + (y - 2)² = ([tex]\sqrt{20}[/tex] )² , that is
(x - 1)² + (y - 2)² = 20
A wheel rolling at a constant speed has a radius of 15 inches and takes 30
seconds to roll 100 feet along the ground. What is its angular velocity? Use
3.14 for (pie) , and solve to two decimal places
Answer:
152.87 degree/seconds
Step-by-step explanation:
1 rotation = Circumference of a circle = 2πr
r = 15 inches
1 rotation = 2 × 3.14 × 15
94.2 inches.
We are told in the question that it takes 30 seconds to roll 100 feet along the ground
Convert feet to inches
1 feet = 12 inches
100 feet =
100 × 12 = 1200 inches.
Hence, if
94.2 inches = 1 rotation
1200 inches = X
Cross multiply
94.2 × X = 1200 × 1
94.2X = 1200
X = 1200/94.2
X = 12.738853503 rotations
Formula for Angular velocity = Number of rotations × 2π/time in seconds
Time = 30 seconds
12.738853503 × 2 × 3.14/30
= 2.6666666667 rotations per second
Converting Angular velocity to degree per second
= 2.6666666667 × 180/ π
= 2.6666666667 × 180/3.14
= 152.86624204 degree/seconds
Approximately to 2 decimal places
= 152.87 degree/seconds
The equal sides of isosceles triangle are 10 cm and perimeter is 28 cm. The area of this triangle is?
Answer:
A=24 CM²
Step-by-step explanation:
10 x 2 + x=28
20+x=28
x=8
a=b x h/2
a=6 x 8 / 2
a=24CM²
What the correct answer now
Answer:
[tex] Area = 1,309.0 in^2 [/tex]
Step-by-step explanation:
Given:
∆TUV
m < U = 22°
TV = u = 47 in
m < V = 125°
Required:
Area of ∆TUV
Solution:
Find the length of UV using the Law of Sines
[tex] \frac{t}{sin(T)} = \frac{u}{sin(U)} [/tex]
U = 22°
u = TV = 47 in
T = 180 - (125 + 22) = 33°
t = UV = ?
[tex] \frac{t}{sin(33)} = \frac{47}{sin(22)} [/tex]
Multiply both sides by sin(33)
[tex] \frac{t}{sin(33)}*sin(33) = \frac{47}{sin(22)}*sin(33) [/tex]
[tex] t = \frac{47*sin(33)}{sin(22)} [/tex]
[tex] t = 68 in [/tex] (approximated)
[tex] t = UV = 68 in [/tex]
Find the area of ∆TUV
[tex] area = \frac{1}{2}*t*u*sin(V) [/tex]
[tex] = \frac{1}{2}*68*47*sin(125) [/tex]
[tex] = \frac{68*47*sin(125)}{2} [/tex]
[tex] Area = 1,309.0 in^2 [/tex] (to nearest tenth).
Urgent help I need it right now!!!!
Answer:
[tex]\boxed{\sf 30 \ bean \ cans}[/tex]
Step-by-step explanation:
The ratio of bean cans to corn cans is 6 : 7
Given that Corn cans = 35
Let the bean can be x
So,
The proportion for it will be:
6 : 7 = x : 35
Product of Means = Product of Extremes
7 * x = 6 * 35
7x = 210
Dividing both sides by 7
x = 30
So, 30 bean cans have to be put on the table to hold the needed ratio
Rearrange the following formula to solve for p: wa+3p=q
Answer:
wa + 3p = q
3p = q - wa -- Subtract wa
p = (q - wa) / 3 -- Divide by 3
Answer:
[tex] \boxed{\sf p = \frac{1}{3} (p - wa)} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: p: \\ \sf \implies wa + 3p = q \\ \\ \sf Subtract \: wa \: from \: both \: sides: \\ \sf 3p = q - wa \\ \\ \sf Divide \: both \: sides \: by \: 3: \\ \sf \implies p = \frac{1}{3} (q- wa)[/tex]
Need help i dont understand
Answer:
The answer is d
Step-by-step explanation:
Mrs.joshi bought a saree for Rs 1750.she sold it at a profit of 4%.what would be her profit or loss percent ?
Answer: Rs 1820
Step-by-step explanation:
This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750. Thus, simply do 1.04*1750 to get 1820.
Hope it helps <3
On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points, P and Q
Answer:
[tex]d = \sqrt{85}[/tex] or d ≈ 9.22
Step-by-step explanation:
Distance formula:
[tex]d = \sqrt{(2 - (-4))^2 + (-3- 4)^2} \\d = \sqrt{36+ 49}\\d = \sqrt{85} \\[/tex]
Find the angle θ between the two sides of a triangle whose lengths are 5cm and 4cm , if its area is 5cm²
[tex] \Delta = \frac 1 2 a b \sin C[/tex]
[tex]\Delta=5, \quad a=5, \quad b=4[/tex]
[tex]\sin C = \dfrac{2 \Delta}{ab} = \dfrac{2 (5)}{5(4) } = \dfrac 1 2[/tex]
[tex]C=30^\circ \textrm{ or } C=150^\circ[/tex]
Answer: two possibilities, θ=30° or 150°
Evaluate 3x2 - 4 when x = 2.
A. 12
B. 32
c. 2
D. 8
Answer:
8
Step-by-step explanation:
3x^2 - 4
Let x = 2
3 * 2^2 -4
Exponents first
3 *4 -4
Then multiply
12 -4
Now subtract
8
[tex]\text{Plug in and solve:}\\\\3(2)^2-4\\\\3(4)-4\\\\12-4\\\\8\\\\\boxed{\text{D). 8}}[/tex]
Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?
Answer:
here is your answer
Answer:hey guys just saying its 1/52
Step-by-step explanation:
Wally rides his bicycle at an average speed of 13 miles per hour. How many miles will he travel in 4 1/2 hours? Please answer this quickly!
Answer:
58.5
Step-by-step explanation:
Distance = rate * time
so if it's 4.5 hours:
Distance = 13 mph* 4.5 hours
= 58.5 miles
Simplify the following v^4*v^5*v
Answer:
v^10
Step-by-step explanation:
For this, we need to understand one important rule of exponents. For powers of like bases, you add the exponents when they are being multiplied. With this in mind let's continue.
In this problem, the base is v, each multiplied with different powers. So:
v^4 * v^5 * v = v^(4+5+1) = v^10
So the solution will be v^10.
An additional example would be 2^2 * 2^3.
For this we know it would be 2^2 * 2^3 = 2^(2+3) = 2^5 = 32.
We can verify by simply doing 2 * 2 * 2 * 2 * 2 = 32. Note both are 32, and this example shows the usefulness of exponent rules.
Hope this helps. Cheers.
Answer:
v10
Step-by-step explanation:
v^4*v^5*v=v^10
add exponents when multiplying since we have exponents 4,5, and 1
4+5+1=10
The two lines graphed below are not parallel. How many solutions are
there to the system of equations?
Answer:
Step-by-step explanation:
Any non-parallel lines in the plane must intersect in one place; thus, there is one solution to the system of equations.
What the answer question
Answer:
TW = 3.18 yd (Approx)
Step-by-step explanation:
Given:
TV = 6 yd
∠TYW = 32°
∠TWV = 90°
Find:
TW
Computation:
Using trigonometry application.
TW / TV = Sin 32°
TW / 6 = 0.53
TW = 3.18 yd (Approx)
the point slope form of the equation of the line that passes through (-5,1 ) and (10,-7) is y +7= - 1/2 (x-10) what is the standard form of the equation for this line ?
Answer:
The standard form of the equation is y = -x/2 -2
Step-by-step explanation:
The standard form of equation of this line is expressing the line in the form;
y = mx + c
So let’s make a rearrangement to what we have at hand;
y + 7 = -1/2(x-10)
2(y + 7) = -1(x-10)
2y + 14 = -x + 10
2y = -x + 10 -14
2y = -x -4
divide through by 2
y = -x/2 -2
36 моля колкото по бързо може формулата е (X÷2)÷(x×3)=305,4
Answer:
Step-by-step explanation:
The quotient of two numbers is 305.4. Find the quotient if the divisor decreases 2 times and the divisor increases 3 times
x/y = 305.4
3x/(y/2) = 6x/y = 6*305.4 = 1832.4
Note that the question will be deleted soon because it is posted in a language other than English.
Обратите внимание, что вопрос будет удален в ближайшее время, потому что он размещен на языке, отличном от английского.
simplify. Remove all perfect squares from inside the square root. V180=
Answer:
6√5
Step-by-step explanation:
We have to solve the expression [tex]\sqrt{180}[/tex]
Break 180 into its factors which are in the perfect square form.
Since, 180 = 9 × 4 × 5
= 3² × 2² × 5
Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]
= [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]
= 3 × 2 × √5
= 6√5
Therefore, solution of the given square root will be 6√5.
Indicate, in standard form, the equation or inequality that is shown by the graph.
Answer:
The equation is y = -x + 4
Step-by-step explanation:
This is a very trivial exercise:
The general equation of a line is given by:
y - y₁ = m(x - x₁)
where m = slope of the linear graph
From the given graph, it can be observed that the coordinate (x₁, y₁) and (x₂, y₂) are (0, 4) and (4, 0)
The slope, m = (y₂ - y₁)/(x₂ - x₁)
m = (0 - 4)/(4 - 0)
m = -4/4
m = -1
Substituting the values of (x₁, y₁) = (0, 4) and m = -1 into the general equation:
y - y₁ = m(x - x₁)
y - 4 = -1 (x - 0)
y - 4 = -x
y = -x + 4
Evaluate the expression. Assume that all the angles are in Quadrant I. (cos (arctan √3/7))
Answer:
0.971
Step-by-step explanation:
Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.
From the expression given
(cos (arctan √3/7)), we need to get the expression in parenthesis first.
Let y = (cos (arctan √3/7))
If u = arctan √3/7
Then y = cos(u) .... 1
Let's get the value of u first
u = arctan √3/7
u = arctan(0.2474)
u = 13.896°
Substituting u = 13.896° into equation 1, we will have;
y = cos(u)
y = cos13.896°
y = 0.971.
Hence the expression (cos(arctan√3/7)) is equivalent to 0.971
Answer:
y = 0.971.
Step-by-step explanation:
Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.
From the expression given
(cos (arctan √3/7)), we need to get the expression in parenthesis first.
Let y = (cos (arctan √3/7))
If u = arctan √3/7
Then y = cos(u) .... 1
Let's get the value of u first
u = arctan √3/7
u = arctan(0.2474)
u = 13.896°
Substituting u = 13.896° into equation 1, we will have;
y = cos(u)
y = cos13.896°
y = 0.971.
Which of these functions could have the graph shown below?
y
80
70-
60
50+
40+
30+
20
10
-5
-4 -3
-2 -1 0
1
2
3
4
х
O A. f(x) = 20e
O B. f(x) = 2020
O C. f(x) = 20%
O D. f(x) = e20x
Answer:
A
Step-by-step explanation:
[tex]f(x) = 20 {e}^{x} [/tex]
The function that could have the graph shown is:
f(x) = 20[tex]e^x[/tex]
Option A is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The function:
f(x) = 20[tex]e^x[/tex]
If we graph this function we get a similar graph that is shown.
The coordinates of f(x) = 20 [tex]e^x[/tex] are:
To find the coordinates, we need to plug in different values of x into the function and calculate the corresponding y-values.
For example, when x = 0, we have:
f(0) = 20e^0 = 20(1) = 20
So one coordinate on the graph is (0, 20).
Similarly, when x = 1, we have:
f(1) = 20e^1 = 20e = 20(2.71828) ≈ 54.6
So another coordinate on the graph is (1, 54.6).
We can find more coordinates by plugging in other values of x and calculating the corresponding y-values.
Now,
As x increases, the function f(x) grows exponentially, meaning the y-values will increase very rapidly.
Thus,
The function f(x) = 20[tex]e^x[/tex] could have the graph shown.
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how many ways can you order a hot dog with the choices below?
Answer:
8
Step-by-step explanation:
2 x 2 x 2 = 8
you have 2 choices each time, with or without
Expand. Your answer should be a polynomial in standard form. (6x+1)(1-3x)
Answer:
3x-18x^2+1
Step-by-step explanation:
(6x+1)(1-3x)
6x-18x^2+1-3x
6x-3x-18x^2+1
3x-18x^2+1
Hope this helps :)
Answer:
[tex]-18x^2+3x+1[/tex]
Step-by-step explanation:
[tex]6x *1=6x\\6x*-3x=-18x^2\\1*1=1\\1*-3x=-3x\\[/tex]
Add all the like terms
[tex]-9x^2+3x+1[/tex]
WILL GIVE BRAINLEST ANSWER IF ANSWERED IN THE NEXT 24 HRS Express the complex number in trigonometric form. -5i
Answer:
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Step-by-step explanation:
If a complex number is z=a+ib, then the trigonometric form of complex number is
[tex]z=r(\cos \theta +i\sin \theta)[/tex]
where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].
The given complex number is -5i.
It can be rewritten as
[tex]z=0-5i[/tex]
Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.
[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]
[tex]\tan \theta=\dfrac{-5}{0}[/tex]
[tex]\tan \theta=\infty[/tex]
[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex] [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]
[tex]\theta=\dfrac{3\pi}{2}[/tex]
So, the trigonometric form is
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Answer:
in degrees the answer is 5 (cos 270 + i sin 270)
in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))
Step-by-step explanation:
The temperature in Chicago when the plane left was 22°F. When the plane arrived in Atlanta it was 46°F. What was the difference in temperature?
Answer:
24
Step-by-step explanation:
46 - 22 = 24
What’s the perimeter and surface area of this shape?
Please also show working out.
Answer: Perimeter = 8π ≈ 25.12
Area = 12π ≈ 37.68
Step-by-step explanation:
This is a composite of two figures.
The bigger figure is a quarter-circle with radius (r) = 8 cm
The smaller figure is a quarter-circle with diameter = 8 cm --> r = 4
Perimeter of a quarter-circle = [tex]\dfrac{1}{4}(2\pi r)[/tex] = [tex]\dfrac{\pi r}{2}[/tex]
Perimeter of composite figure = bigger - smaller figure
[tex]P_{bigger}=2\pi(8)\quad = 16\pi\\P_{smaller}=2\pi(4)\quad =8\pi\\P_{composite}=16\pi-8\pi \\.\qquad \qquad = \large\boxed{8\pi}[/tex]
Area of a quarter-circle = [tex]\dfrac{1}{4}\pi r^2[/tex]
[tex]A_{bigger}=\dfrac{1}{4}\pi (8)^2\quad =16\pi\\\\A_{smaller}=\dfrac{1}{4}\pi (4)^2\quad =4\pi\\\\A_{composite}=16\pi-4\pi\\.\qquad \qquad = \large\boxed{12\pi}[/tex]
Help please!! Thanks
Answer:
A
Step-by-step explanation:
First, let's label the variables:
[tex]\text{Let }x \text{ represent Kaylee's number of pens,}\\\text{Let }L \text{ represent Lou's number of pens,}\\\text{And let }I \text{ represent Ilene's number of pens.}[/tex]
The first and second sentence, Kaylee at the start has x pens. She gave half to Lou, who started out with two fewer than Kaylee.
In other words, the total Lou now has is:
[tex]L=(\frac{1}{2}x )+(x-2)[/tex]
The first term represents what Kaylee gave to Lou. The second term represents what Lou had originally (two fewer than Kaylee [x]).
Simplifying, we get:
[tex]L=\frac{3}{2}x-2[/tex]
Third sentence. Lou give half of his new total to Ilene, who started out with three fewer pens than Lou. Lou, remember, started with three fewer than Kaylee (x-2). In other words:
[tex]I=(\frac{1}{2}(\frac{3}{2}x-2) )+((x-2)-3)[/tex]
The left represents what is given to Ilene: one-third of Lou's new total. The right represents Ilene's original total: three fewer than Lou: or five fewer than Kaylee. Simplifying gives:
[tex]I=(\frac{3}{4} x-1)+(x-5)\\I=\frac{7}{4}x-6[/tex]
Finally, Ilene gives a third of this new amount to Kaylee, and Kaylee's final amount is 37. Thus:
[tex]37=x-\frac{1}{2}x+\frac{1}{3}(\frac{7}{4}x-6)[/tex]
The first term represents what Kaylee originally started with. The second term represents what she gave to Lou. And the third term represents what Ilene gave to Kaylee. Simplify:
[tex]37=\frac{1}{2}x+\frac{7}{12}x-2\\39=\frac{6}{12}x+\frac{7}{12}x \\39=\frac{13}{12}x\\ 468=13x\\x=36[/tex]
Each day that a Redbox movie is kept past its due date, a $1.50 fee is charged at midnight.
What is the ordered pair it a movie is kept for 5 days?
Let x represents the number of days that a movie is late and y represents the total fee
Answer:
(5, 7.5)
Step-by-step explanation:
Each day the movie is late adds $1.50 for late fees.Then, after 5 days of past due, the total late fee would be: 5 * $1.50 = $7.50
Then the coordinate pair representing this would be: (5, 7.5)
An economist is studying the linear relationship between the selling price p, of a
mobile phone and the number of persons buying the phone x. The table of values
illustrates her findings. Write the equation that represents the relationship between the
number of persons buying the phone and the price of the phone.
Answer:
The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60
Step-by-step explanation:
The given data are as follows
x, p($)
10, 52.5
25, 41.25
40, 30
60, 15
We note that a plot of the given points give a straight line graph indicating a linear relationship
The rate of change of p($) with x is given by slope, m in the following relation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Which gives;
[tex]Slope, \, m =\dfrac{41.25-52.5}{25-10} = \dfrac{30-41.25}{40-25} = \dfrac{15-30}{40-60} =-0.75[/tex]
Therefore, to write the equation in slope and intercept form, we have;
From the first point with coordinates (52.5, 10), we have
y - 52.5 = -0.75×(x - 10)
y = -0.75·x + 7.5 + 52.5 = -0.75·x + 60
The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60.
On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]
[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
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