\( \frac{8}{5} \times \frac{4}{3} = \frac{32}{15} = 2 \frac{2}{15} \\ \)
So the correct answer is D
find the general equation of the ellipse passing though points A and B, center at C.
The general equation of an ellipse is
\(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\)Where (h, k) are the coordinates of the center.
For our ellipse, we already have the center (2, 1), then, our equation will be
\(\frac{(x-2)^2}{a^2}+\frac{(y-1)^2}{b^2}=1\)Using the points that belong to this ellipse, we can substitute them on this equation to find the coefficients a and b.
First, let's use the point (4, 1). Doing the substitution, we have
\(\begin{gathered} \frac{(4-2)^2}{a^2}+\frac{(1-1)^2}{b^2}=1 \\ \frac{(2)^2}{a^2}=1 \\ a=2 \end{gathered}\)Using the other point, we can calculate the other coefficient.
\(\begin{gathered} \frac{(1-2)^2}{4}+\frac{(1+2\sqrt[]{3}-1)^2}{b^2}=1 \\ \frac{(-1)^2}{4}+\frac{(2\sqrt[]{3})^2}{b^2}=1 \\ \frac{1}{4}+\frac{12^{}}{b^2}=1 \\ \frac{12^{}}{b^2}=\frac{3}{4} \\ 4\cdot12=3\cdot b^2 \\ b^2=16 \\ b=4 \end{gathered}\)And then, we have our ellipse equation.
\(\frac{(x-2)^2}{4}+\frac{(y-1)^2}{16}=1\)Please I really need help with this
Answer:
(-20x -25)/(x^2-x-30)
Step-by-step explanation:
You want to simplify the rational expression (3x²)/(x²-x-30) -(3x+5)/(x-6).
Use a common denominatorUsually these problems are constructed so that the higher-degree polynomial denominator has the lower degree denominator as a factor. That is the case here.
\(\dfrac{3x^2}{x^2-x-30}-\dfrac{3x+5}{x-6}=\dfrac{3x^2}{(x+5)(x-6)}-\dfrac{(x+5)(3x+5)}{(x+5)(x-6)}\\\\=\dfrac{3x^2-(3x^2+20x+25)}{x^2-x-30}\)
Simplify\(=\boxed{\dfrac{-20x-25}{x^2-x-30}}\)
question on picture
Step-by-step explanation:
i hope this helps ! :) this is all i.could find
Use the fact that the sum of the 3 angles in a triangle is 180° to answer this question.One angle in a triangle has a measure that is three times as large as the smallest angle. Themeasure of the third angle is 20° more than that of the smallest angle. Find the measure of the eachof the angles.nsOThe SMALLEST angle has a measure of
Let us call the angles x, y , and z. We know that these three angles must add up to 180; therefore,
\(x+y+z=180\)If x is the smallest angle, we know that one of the angles (call it y) is 3 times this angle; therefore,
\(y=3x\)And the other angle z is 20 more than the smallest angle x; therefore, we have
\(z=20+x\)Putting the last two equations into the very first equation gives us
\(x+3x+20+x=180\)\(5x+20=180\)\(\textcolor{#FF7968}{\therefore x=32}\)which is the measure of the smallest angle.
The other two angles are
\(y=3x=3(32)\)\(\textcolor{#FF7968}{y=96}\)and
\(z=20+x=20+32\)\(\textcolor{#FF7968}{z=52.}\)Hence, the measure of the smallest angle is 32,
The measure of the middle angle is 52
And the measure of the largest angle is 96.
Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist. how many miles does the second cyclist bike in 45 mins?
Answer:
Step-by-step explanation:
45 minutes is 3/4 hr.
(3/4)(12 + b) = 9 + 3b/4 miles
A class contains 5 girls and 7 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.
Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.
Determine the total number of students in the class. That is 5 + 7 = 12.
Determine the number of ways to select two students from the class.
Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.
In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).
C(12, 2) = 12! / (2!(12-2)!) = 66.
Determine the number of favorable outcomes.
In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.
To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):
Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.
So, the probability of selecting a girl and a boy for the class committee is 5/6.
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Does anyone know the answer?
Answer:
lx-3l
Step-by-step explanation:
negative in the abs means moving to the right
=========================================================
Explanation:
We start with the parent function y = |x|
Shifting it 3 units to the right will make the equation y = |x-3| and that's the equation of the green curve shown.
The x-3 is because each input is 3 units smaller than it used to be. Imagine the xy axis moved 3 units to the left while the V shaped graph stayed fixed in place. It would give the illusion the V shape moved while the xy axis stay fixed.
The graph doesn't shift up or down, so k = 0
The value of 'a' stays the same at a = 1.
What type of angle is this
b) In 3x?, the 3 is called the____
please help
Answer:
3 is the coefficient
Step-by-step explanation:
The number in front of the variable is called the coefficient
3x
3 is the coefficient
x is the variable
The general form of the equation of a circle is a X squared plus BY squared plus 3X plus 3Y plus Z equals zero wear a equals B does not equal zero is the circle has a radius of three units in the center lies on the Y axis, which set of values of a B C,D and E my correspond to the circle
The set of values that corresponds to the circle with a radius of three units and the center lying on the Y axis is:
A = 1, B = 1, C = 0, D = 3, E = 0.
The general equation of a circle is given by:
x^2 + y^2 + 2gx + 2fy + c = 0
In this case, since the circle has a radius of three units and the center lies on the Y axis, we can deduce the following information:
The center of the circle lies on the Y axis, which means the x-coordinate of the center is zero.
The radius of the circle is three units, which means the distance from the center to any point on the circle is three units.
Using the information above, we can substitute the values into the general equation to solve for the corresponding values:
Substituting the x-coordinate of the center (zero) into the equation, we have:
0^2 + y^2 + 2g(0) + 2fy + c = 0
y^2 + 2fy + c = 0
Since the center lies on the Y axis, the x-coordinate is zero, so the term with x (2gx) becomes zero.
Substituting the radius of the circle (three) into the equation, we have:
(3)^2 = 9
Therefore, the equation becomes:
y^2 + 2fy + c = 9
Comparing this equation with the general form of the circle equation, we can deduce the values of A, B, C, D, and E as follows:
A = 1 (coefficient of x^2)
B = 1 (coefficient of y^2)
C = 0 (constant term)
D = 3 (coefficient of x)
E = 0 (coefficient of y)
Hence, the set of values that corresponds to the circle is A = 1, B = 1, C = 0, D = 3, and E = 0.
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Which is the value of this expression when m-3 and n=-5
Answer:
1/8
Step-by-step explanation:
(6m^-1n^0)^-3 =
= (6 × 1/3 × (-5)^0)^-3
= (6/3)^-3
= 2^-3
= 1/2^3
= 1/8
help me on this plz and thank you
By solving for x you get x=6
Answer:
x = 6
Step-by-step explanation:
12x = 72
72/12 = 6
x = 6
HELP PLZ THANK U VERY MUCH
Answer: 0.28 is the answer i believe
Step-by-step explanation:
I hope this helps! :)
Solve 5(3+0.5) distributive
Answer:
17.5
Step-by-step explanation:
Answer:
17.5
Step-by-step explanation:
Alex created a new game. Please HELP!
Answer:
64
Step-by-step explanation:
What was yesterday? Or tim
Answer:
Tuesday may 18 2020
Step-by-step explanation:
Which real-world problem correctly involves dividing a decimal by a decimal?
a
Michael has 162.4 feet of wood to make birdhouses. If each birdhouse uses 2 feet of wood, how many birdhouses can he make? 81 birdhouses
b
Michael has 162 feet of wood to make birdhouses. If each birdhouse uses 2 feet of wood, how many birdhouses can he make? 81 birdhouses
c
Michael has 162 feet of wood to make birdhouses. If each birdhouse uses 1.4 feet of wood, how many birdhouses can he make? 115 birdhouses
d
Michael has 162.4 feet of wood to make birdhouses. If each birdhouse uses 1.4 feet of wood, how many birdhouses can he make? 116 birdhouses
Answer:
b
Step-by-step explanation:
parking garage a charge A charge $3 per hour for parking. parking garage B charges of a fee of $ 2 pkus $ 2 per hour for parking
you good itStep-by-step explanation:
Solve for x and graph the solution on the number line below.
The solution of the inequality is 8 ≥ x or x > 10. The graph of the solution is attached
How to solve for x and graph the solution on the number line?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.
Solving for x:
11≥ 2x - 5 or 2x - 5 > 15
Collect like terms:
11 + 5 ≥ 2x or 2x > 15 + 5
16 ≥ 2x or 2x > 20
8 ≥ x or x > 10
Note: 8 ≥ x can also be written as x ≤ 8
We can combine the two as follow:
Inequality notation: 8 ≥ x > 10
The graph of the solution is attached
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Find the sum of the following finite geometric series.
The sum of the geometric sequence in this problem is given as follows:
5.77.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.
The first term, the common ratio and the number of terms for this problem are given as follows:
\(a_1 = 10, q = -\frac{2}{3}, k = 8\)
The formula for the sum of the first n terms is given as follows:
\(S_n = a_1\frac{1 - r^n}{1 - r}\)
Hence the sum for this problem is given as follows:
\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)
\(S_8 = 5.77\)
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which ordered pair represents a solution to both equations? A - (-5,5) B - (-2,1) C - (1, -2) D - (-4,0)
Answer:
B-(-2,1)
THIS ONE X=-2 Y=1. ALL THE POINTS CROOS HERE
Examine the following typical corporate bond listing:
In the name column, NYTel is the abbreviated name of the company (New York Telephone) issuing the bond. What was the closing price of the bond? What was the dollar amount? (See attachments)
a. 101 3/4; $101,750
b. 7 1/4; $7250
c. 101 3/4; $1017.50
d. 107 1/4; $1072.50
Answer:
C. 101 3/4; $1017.50
Step-by-step explanation:
Correct on E2020!
Find the slope of the line that passes through the points (1.9) and (2, 5).
AV
Answer:
-2 is the slope
Step-by-step explanation:
Slope=Rise/Run=(y2-y1)/(x2-x1)=(5-9)/(2-1)=-4/2=-2, therefore the slope is -2
HELP QUICK
For each statement about owners of equity in a business, select True or False.
Solve each system of linear equations below, then check your work.
A. 3x−y=−11 −x+y=5
B -2y+3= 4x + 2 6x + 4y=1
C. 32y- x= -25 5x= 100 + x - 8Y
D. 2y + 3x = 6 4x + 5y +20 = 0
A. The solution of linear equation is (x, y) = (-3, 8).
B. The solution is (x, y) = (3/4, -1).
C. The solution is (x, y) = (-31/8, 3/8).
D. The solution is (x, y) = (55/7, -117/14).
A. 3x - y = -11 --- (1)
-x + y = 5 --- (2)
From equation (2), we can write y = x + 5, and substitute it in equation (1):
3x - (x + 5) = -11
2x = -6
x = -3
Substituting x in equation (2):
-y = -8
y = 8
Therefore, the solution of the system is (x, y) = (-3, 8).
To check the solution, we substitute the values of x and y in the original equations:
3(-3) - 8 = -11 (True)
-(-3) + 8 = 5 (True)
So, the solution is correct.
B. -2y + 3 = 4x + 2 --- (1)
6x + 4y = 1 --- (2)
From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):
6x + 4y = 1
6x - 4y = 8 (rearranging)
12x = 9
x = 3/4
Substituting x in equation (1):
-2y + 3 = 4(3/4) + 2
-2y + 3 = 5
-2y = 2
y = -1
Therefore, the solution of the system is (x, y) = (3/4, -1).
To check the solution, we substitute the values of x and y in the original equations:
-2(-1) + 3 = 4(3/4) + 2 (True)
6(3/4) + 4(-1) = 1 (True)
So, the solution is correct.
C. 32y - x = -25 --- (1)
5x = 100 + x - 8y --- (2)
From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):
32y - x = -25
32y - (100 - 8y) = -25
40y = 75
y = 3/8
Substituting y in equation (1):
32(3/8) - x = -25
x = -31/8.
Therefore, the solution of the system is (x, y) = (-31/8, 3/8).
To check the solution, we substitute the values of x and y in the original equations:
32(3/8) - (-31/8) = -25 (True)
5(-31/8) = 100 + (-31/8) - 8(3/8) (True)
So, the solution is correct.
D. To solve the system of equations:
2y + 3x = 6 --- (1)
4x + 5y + 20 = 0 --- (2)
We can rearrange equation (2) to isolate one of the variables:
4x + 5y = -20 (subtracting 20 from both sides)
5y = -4x - 20 (subtracting 4x from both sides)
y = (-4/5)x - 4 (dividing both sides by 5)
Substituting this value of y in equation (1):
2((-4/5)x - 4) + 3x = 6
(-8/5)x - 8 + 3x = 6
(-8/5)x + 3x = 14
(-8/5 + 3)x = 14
(-8/5 + 15/5)x = 14
(7/5)x = 14
x = 10
Substituting this value of x in the equation for y:
y = (-4/5)(10) - 4
y = -12.
Therefore, the solution of the system is (x, y) = (10, -12).
To check the solution, we substitute the values of x and y in the original equations:
2(-12) + 3(10) = 6 (True)
4(10) + 5(-12) + 20 = 0 (True)
So, the solution is correct.
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I am so confused right now. will give brainlest to anyone how can solve this chicken scratch lol
1. Write an equation representing this hanger
2. find the value (or "weight) of one circle (w).
3. Explain how you found the value of one circle (w)
I really have no idea what any of this is
Answer:
1. 25÷4w
2. w=6.25
3.I divided 25 by 4 to find w
Step-by-step explanation:
kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail. imagine an angle with its vertex at the center of the circular ski trail that subtends kelsey's path.
a) How many radians has the angle swept out since kelsey started skiing?
b) How many km has kelsey skied since she started skiing?
a) The angle swept out since kelsey started skiing: 1.1498 radians
b) The distance Kelsey skied: 3.334 km
In this question, we have been given Kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail.
Consider the following figure for reference.
We need to find the angle θ and the distance kelsey skied (i.e., the arc length)
Here, the horizontal distance x = 1.185 km and the vertical distance y = 2.647 km
a. the tangent of angle θ would be,
tan(θ) = y/x
tan(θ) = 2.647/1.185
tan(θ) = 2.2337
θ = arctan(2.2337)
θ = 65.88°
θ = 1.1498 radians
b. The length of the arc is:
s = rθ
s = 2.9 * 1.1498
s = 3.334 km
Therefore, a) the angle swept out : 1.1498 radians
b) the distance Kelsey skied: 3.334 km
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Subtract 38¢ from $5.60. Include the dollar sign and no spaces in your answer.
Answer:
5.22
Step-by-step explanation:
Answer:
its easy, just subtract 50 - 38 = 22 so its $5.60
(your welcome and math makes me notalisgica :) )
Step-by-step explanation:
For the equation f(x) = 1.1 * (0.44) ^ x state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x
c = (Type an integer or a decimal)
a = (Type an integer or a decimal)
R = % (Simplify your answer. Type an integer or a decimal)
The parameters of the exponential function in this problem are given as follows:
c = 1.1.a = 0.56.R = -56%.What is an exponential function?The standard format of an exponential function is given as follows:
y = c(1 - a)^t.
This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:
c is the initial value, value assumed by y when t = 0.a is the decay rate.In this problem, the function is given as follows:
f(x) = 1.1(0.44)^x.
Hence the values for the parameters are given as follows:
c = 1.1, which is the initial value.a = 0.56, as 1 - a = 0.44 -> a = 0.56.Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.
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Write the sentence as a proportion: $3.50 for 9 bottles is equivalent to $31.50 for 81 bottles.
Answer:
$0.39:1
Step-by-step explanation:
$0.39:1
Dividing the amount by the cost of the bottles.