Answer:
3
Step-by-step explanation:
[tex]\frac{y+x}{xy} =3\\x+y=3xy\\xy+x+y=4\\xy+3xy=4\\4xy=4\\xy=1\\x^2y+xy^2=xy(x+y)=xy(3xy)=3(xy)^2=3(1)^2=3[/tex]
Answer:
3
Step-by-step explanation:
So we're given: [tex]\frac{1}{x} + \frac{1}{y} = 3[/tex] and that: [tex]xy+x+y=4[/tex]. And now we need to solve for: [tex]x^2y+xy^2[/tex].
Original equation:
[tex]\frac{1}{x} + \frac{1}{y} = 3[/tex]
Multiply both sides by xy
[tex]y+x=3xy[/tex]
Now take this and plug it as x+y into the second equation:
Original equation:
[tex]xy+x+y=4[/tex]
Substitute 3xy as x+y
[tex]xy + 3xy = 4[/tex]
Combine like terms:
[tex]4xy = 4[/tex]
Divide both sides by 4
[tex]xy=1[/tex]
Divide both sides by x:
[tex]y=\frac{1}{x}[/tex]
Original equation:
[tex]x^2y+xy^2[/tex]
Substitute 1/x as y
[tex]x^2(\frac{1}{x})+x(\frac{1}{x})^2[/tex]
Multiply values:
[tex]\frac{x^2}{x}+\frac{x}{x^2}[/tex]
Simplify:
[tex]x+\frac{1}{x}[/tex]
Substitute y as 1/x back into the equation:
[tex]x+y[/tex]
so now we just need to solve for x+y
Look back in steps to see how I got this:
[tex]y+x=3xy[/tex]
Divide both sides by 3
[tex]\frac{x+y}{3}=xy[/tex]
Original equation:
[tex]xy+x+y=4[/tex]
Substitute
[tex]\frac{x+y}{3}+x+y=4[/tex]
Multiply both sides by 3
[tex]x+y+3x+3y=12[/tex]
Combine like terms:
[tex]4x+4y=12[/tex]
Divide both sides by 4
[tex]x+y=3[/tex]
So now we finally arrive to our solution 3!!!!! I swear I felt like I was going in circles, and I was about to just stop trying to solve, because I had no idea what I was doing, sorry if I made some unnecessary intermediate steps.
Prove: The product of the slopes of lines AC and BC is -1.
Given that the AC and BC are perpendicular, their slopes are the negative inverse of each other which gives that the product of the slopes of AC and BC is -1
How can the prove that the product of the slopes is -1 be found?The completed proof is presented as follows;
The slope of AC or GC is GF/FC by definition of slope. The slope of BC or CE is DE/CD by definition of slope.
<FCD = <FCG + <GCE + <ECD by angle addition property <FCD = 180° by the definition of a straight angle, and <GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = <FCG + 90° + <ECD. Therefore 90° - <FCG = <ECD, by the subtraction property of equality . We also know that 180° = <FCG + 90° + <CGF by the triangle sum theorem and by the subtraction property of equality 90° - <FCG = <CGF, therefore <ECD = <CGF by the substitution property of equality. Then <ECD ≈ <CGF by the definition of congruent angles. <GFC ≈ <CDE because all right angles are congruent. So by AA ∆GFC ~ ∆CDE. Since the ratio of corresponding sides of similar triangles are equal then GF/CD = FC/DE or GF•DE = CD•FC by cross product. Finally, by the division property of equality GF/FC = CD/DE. We can multiply both sides using the slope of using the multiplication property of equality to get GF/FC × -DE/CD = CD/DE × -DE/CD. Simplify so that GF/FC × -DE/CD = -1. This shows that the product of the slopes of AC and BC is -1.
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If one angle is 8 less than four times th of its complementary angle find both angle
Answer:
Let the angle be x
∘
. Then it's complement = (4x)
∘
.
We know that if the sum of two angles is equal to 90
∘
then the angles are said to be complementary.
Step-by-step explanation:
4x+x=90°
5x=90°
x=90°/5
x=18
4×18=72°
This is the complete solution!
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Gabrielle is 15years older than mik. The sum of their ages is 103.what is mik age?
Answer:
Mikhail is 44 years old.
Step-by-step explanation:
Set both Gabrielle and Mikhail's age to a variable.
Gabrielle is x, Mikhail is also x.
Now create an equation using the variables with the sum.
Age1 + Age2 + 15 = 103
x + x + 15 = 103
Now we solve.
1. Combine like terms
2x + 15 = 103
2. Make all the numbers on one side of the equation, and the variables of the other, so subtract.
2x + 15 - 15 = 103 - 15
2x = 88
3. Simplify further by dividing.
x = 44
Mikhail is 44 years old.
Check your work:
44 + (x + 15) = 103
x + 15 = 59
x = 44
Answer:
Step-by-step explanation:
Let Gabrielle's age be x.
The age of the milk will be x - 15.
x + (x - 15) = 103.
2x - 15 = 103
2x = 118
x = 59
The milk's age = x - 15 = 59 - 15 = 44.
Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answer:
(x-{-2})^2+(y-{4})^2={36}
Equation:
x^2+y^2=r^2
r=radius
Blank following x/y is flipped center(of circle) coordinate for x/y
5 coins worth 17 cents
Answer:
3 nikels and 2 cents
Step-by-step explanation:
1 niquel = 5 cents
5+5+5= 15
15+ 2= 17
Cube A and cube B are similar solids. The volume of cube A is 27 cubic inches, and the volume of cube B is 125 cubic inches. How many times larger is the base area of cube B than the base area of cube A? A small cube labeled cube A has points K, L, M, and N on the top face and O, P, Q, and R on the bottom face. A large cube labeled cube B has points A, B, C, and D on the top face and E, F, G, and H on the bottom face. A. B. C. D.
The area of the base of cube B is 25/9 times larger than the area of the base of cube A.
How many times larger is the base area of cube B than the base area of cube A?Because the cubes are similar, then we know that the dimensions of cube B are a dilation of scale factor K of the dimensions of cube A.
Then, the volume of cube B is K³ times the volume of cube A.
The area of any face of cube B is K² times the area of any face of cube A
From this we can write:
125 in³ = K³*27in³
(125/27) = K³
If we apply the cubic root in both sides, we get:
∛(125/27) = K = 5/3
Then the relation between the areas is equal to:
K² = (5/3)^2 = 25/9
The area of the base of cube B is 25/9 times larger than the area of the base of cube A.
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Answer:
25/9
Step-by-step explanation:
I Just Took the Test.
A couple decides that sophia will drive the first 3/5 of a trip and toby the last 2/5. the entire trip is 500 miles long. how far will sophia drive?
The miles Sophia drove is 60 miles
The distance Sophia drove is represented in fractions.
What is a Fraction?A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.
A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.
In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.
Miles Sophia drove = 3/5 x 100
= 60 miles
So sophia drove 60 miles in 500 miles.
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PLEASE I NEED THIS ASAP PLEASE
The correct option is the second one:
i) right, right, left.ii) Undefined.What can we say about the calculation?We know that:
x > 0z > 0y < 0We have the operation:
x - y + (-z)
Notice that because y is negative, then -y is positive.
Because z is positive, -z is negative.
Then we have:
positive + positive + negative
Or, in the number line:
right, right, left.
Second question:
Can we conclude the sign of the outcome?
No, we can't, the sign will depend on the values of x, y, and z.
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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.
Step-by-step explanation:
the graph below shows the quadratic function of f and the table below shows the quadratic function of g -1 0.75 2 2.75 3 2.75
The correct information based on the equation is that the functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
How to illustrate the information?From the graph of f(x):
⇒ Axis of symmetry will be at x = 2
⇒ The maximum value of f(x) = 4
From the table of g(x):
⇒ Axis of symmetry will be at x = 2
⇒ The maximum value of g(x) = 3
The graph is attached.
The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
Here is the other part of the question:
Which statement is true?
The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.
The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
The functions f and g have different axes of symmetry and different maximum values.
The functions f and g have the same axis of symmetry and the same maximum values.
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Find the measure of an interior angle of a regular nonagon (9-sided polygon).
Hint: (n-2)180
x=[?] degrees
The measure of an interior angle of a regular nonagon (9-sided polygon) is 140°
How to determine the angle
The formula for sum of interior angles of a polygon is given as;
= ( n -2) × 180
Recall that a nonagon has nine sides, so , n = 9
Substitute the value into the formula
= ( 9 -2) × 180
= 7× 180
= 1260°
Since the sum of the angles = 1260°
One of the angles = 1260/ 9 = 140°
Therefore, the measure of an interior angle of a regular nonagon (9-sided polygon) is 140°
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what’s the slope of the line
Answer:
90
Step-by-step explanation:
slope
Answer:
formula is equal to rice run is equal to y 2 -y 1 X2 minus X1
The z-score with a two-tail probability of 0.55 is
Answer:
-0.61
Step-by-step explanation:
0.55/2=0.275
Read 0.275 from normal distribution tables
Gives -0.61
help me please i need help
Answer:
B
Step-by-step explanation:
[tex](f-g)(x)=4x^2+5x-3-(4x^3-3x^2+5)\\\\=-4x^3+7x^2+5x-8[/tex]
Hence B is correct.
Unknown to a medical researcher, 6 out of 25 patients have a heart problem that will result in death if they receive the test drug. 8 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that exactly 6 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places.
Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of the parameters for this problem are:
N = 25, k = 6, n = 8.
The probability that exactly 6 patients will die is P(X = 6), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002[/tex]
0.0002 = 0.02% probability that exactly 6 patients will die.
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Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?
The type of transformation that preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x) is vertical translation.
What is vertical translation?Vertical translation of a graph is done by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.
The vertical translation is the movement of the curve along the y-axis by a certain number of units without altering the function's shape or domain.
The function's form is preserved in the case of vertical translation.
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When graphing the function f(x)=x^2-81/x^2-11x 18 on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?
An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.
We have been given a rational function:
[tex]f(x)=\frac{x^{2} -81}{x^{2} -11x+18}[/tex]
And we are required to determine an appropriate viewing rectangle for the graphing calculator.
Hence, An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.
For the given function, an appropriate viewing rectangle will be [-20,20,2] by [-20,20,2].
This function, when graphed using a graphing calculator on the said viewing rectangle, it appears as attached.
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2) Which statement about the radius of a circle is true?
A. The radius is the boundary of a
circle.
B. The radius is the distance around a portion of a circle's boundary.
C. The length of a radius is always the same for a given circle.
D. The radius is a line segment passing through a circle's center, with endpoints on the boundary.
Answer:
C.
Step-by-step explanation:
The boundary of a circle is the circle itself.
The radius of a circle is a segment from the center of the circle to any point of the circle.
In a circle, every radius has the same length.
Answer: C.
David and Lacey are 2000 feet apart on a coastline. They each look at the same boat in the water. The angle between the coastline and the line from David to the boat is 70%. The line between the coastline
and the line from Lacey to the boat is 32.
Part A: How far is the boat from David?
Part B: How far is the boat from Lacey?
Part C: If David moved so that his distance from the boat is 1200 feet, what would the angle be between the coast and his view of the boat?
By using the given distances and directions, we have;
Part A: 1083.5 feet
Part B: 1921.37 feet
Part C: 58.05°
How can the distances and directions be calculated?The distance between David and Lacey = 2000 feet
David's angle to the boat = 70°
Lacey's angle to the boat = 32°
Part A
The distance of the boat from David is found as follows;
Imaginary lines drawn from the boat to David and then to Lacey form a triangle.
In the triangle, let A = 70°
B = 32°
Therefore by the sum of angles in a triangle, we have;
C = 180° - (70° + 32°) = 78°
By using sine rule we have;
[tex] \frac{a}{sin(A)} = \frac{b}{sin( B )} = \frac{c}{sin(C)}[/tex]
David's distance from the boat, b, is therefore;
[tex] \frac{b}{sin( 32 )} = \frac{2000}{sin(78)}[/tex]
The angle subtended by the coastline, C, is therefore;
[tex] b = \frac{2000}{sin(78)} \times sin( 32 ) = 1083.5 [/tex]
David's distance from the boat is 1083.5 feetPart B
The distance between the boat and Lacey is found as follows;
[tex] \mathbf{ \frac{a}{sin( 70)} }= \frac{2000}{sin(78)}[/tex]
[tex] a = \frac{2000}{sin(78)} \times sin( 70 ) = 1921.37 [/tex]
Lacey's distance from the boat is 1921.37 feetPart C
When b = 1200 feet, we have;
Finding the vertical distance of the boat from the coastline, we have;
1083.5 × sin(70) = 1018.17
We have;
[tex] \frac{1200}{sin(90)} = \frac{1018.17}{sin( B' )} [/tex]
[tex] {sin( B' )} = \frac{sin(90)}{1200} \times 1018.17 [/tex]
The angle between the coastline and his view to the boat, B', is therefore;
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Write a formula for the following:
The amount in an account at the end of a year, if simple interest is paid at
the rate of 16%, and the account contains d dollars at the beginning of the year.
Answer:
A = 1.16d
Step-by-step explanation:
Multiplying by 1 + the percentage value is equivalent to adding the percentage.
The price of a CD decreased from $18 to$12 . What is the percent of decrease? 6% 25% 33% 60%
A percentage is a way to describe a part of a whole. The percetage decrease in the price of CD is 33.33%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The price of the CD decreases from $18 to $12. Therefore, the percentage decrease is,
Percentage Decrease = ($18-$12)/$18 × 100% = 33.33%
Hence, the percetage decrease in the price of CD is 33.33%.
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Express the number as a ratio of integers.
0.16 = 0.16161616...
0.16 = 0.16161616... as a ratio of integers is 16 : 99
How to express as a ratio?The equation is given as:
0.16 = 0.16161616...
The above is a non-terminating decimal.
It can be represented as:
a/b - 1
Where
a = 16
b = 100
So, we have:
16/100 - 1
Evaluate the difference
16/99
Express as ratio
16 : 99
Hence, 0.16 = 0.16161616... as a ratio of integers is 16 : 99
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Please HELP!!!!!
The domain (input values) of the cosine function is:
A. angle measures less than 2π radians.
B. angle measures between 0 and π radians.
C. angle measures less than 90°.
D. all negative and positive angle measures.
SUBMIT
Answer: D. all negative and positive angle measures.
The expression √5x is equivalent to the expression x√5.
O A. True
OB. False
Answer: False
Step-by-step explanation:
[tex]\sqrt{5x}=\sqrt{x} \sqrt{5} \neq x\sqrt{5}[/tex]
Carla Vista Co. has delivery equipment that cost $49,600 and has been depreciated $24,600.
Prepare a tabular summary to record the disposal under the following assumptions.
It was sold for $37,900
was sold for 19100
a)
Gain on disposal=$12,900
b)
Loss on disposal=$5,900
Prepare a tabular summary to show the cost of equipment disposed of, the accumulated depreciation, and gain or loss recorded on disposal?
Note that initially when the equipment was purchased, it would be debited to an asset account, whereas, it would be credited upon disposal since the company no longer owns it.
The accumulated depreciation was originally a credit entry in the balance sheet and needs to be debited now that the equipment has been sold.
Note that the excess of the sum of the accumulated depreciation and the cash received over the initial cost of the equipment is a gain and the reverse means a loss was recorded on disposal.
Account DR CR
Asset $49,600
Gain on disposal $12,900
Accumulated depreciation $24,600
Cash received $37,900
gain on disposal=$24,600+$37,900-$49,600
gain on disposal=$12,900
Account DR CR
Asset $49,600
Accumulated depreciation $24,600
Cash received $19,100
Loss on disposal $5,900
Loss on disposal=$49,600-$24600-$19,100
Loss on disposal=$5,900
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What is the length of DE ?
Answer:
option D. DE = 11
Step-by-step explanation:
The line DF is equivalent in length to the blue line,
(x + 7) + 7 = 4x + 2
Solve:
x + 14 = 4x + 2
subtract 14 from both sided to get x alone,
x + 14 - 14 = 4x + 2 - 14
x = 4x - 12
subtract 4x from both sided,
x - 4x = 4x - 4x - 12
-3x = -12
divided both sides by -3,
-3x / 3 = -12 / -3
x = 4
Plug in x into DE equation:
x + 7: (4) + 7 = 11
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A normal population has a mean of 20.0 and a standard deviation of 4.0.
a. Compute the z value associated with 25.0.
b. What proportion of the population is between 20.0 and 25.0?
c. What proportion of the population is less than 18.0?
Calculations:
Normal pop has mean of 20.0
standard deviation = 4.0
XNN(20.0, 4.0)
a).
[tex]z=\frac{x-h}{z}[/tex]
[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]
Z = 1.25
b).
The proportion between 20 and 25 is P(20 <x<25.0)
[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]
[tex]=P(0 < z < 1.25)[/tex]
[tex]=P(Z < 1.25)-P(z < 0)[/tex]
[tex]=0.8944-0.5000[/tex]
P(20 < x < 25)=0.3944
c).
The proportion value is less than 18 when
[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]
[tex]=P(z < \frac{-2}{4})[/tex]
[tex]=P(z < -0.5)[/tex]
P(x<18) = 0.3085
What percent of 5280 feet is 880 yards
Answer:16.67
Step-by-step explanation:
880 of 5280 can be written as:
880
5280
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
880
5280
×
100
100
= (
880 × 100
5280
) ×
1
100
=
16.67
100
Therefore, the answer is 16.67%
If you are using a calculator, simply enter 880÷5280×100 which will give you 16.67 as the answer.
G(X) IS A TRANSFORMATION OF F(X) WHAT IS G(X) IN TERMS OF F(X)
This is a very simple transformation problem and can be solved by observation. The correct answer is Option D where g(x) = f(x-3) + 6. See the attached graph for the full question.
What is a transformation?
In mathematics, transformation is the process of converting one figure, expression, or function into another of equivalent value.
What is the explanation for the above problem?Note that on an x-axis, moving past zero to the left gets you into the negative, and vice versa.
On the y-axis moving upwards past zero gets you into the positive.
Recall that g(x) is a transformation of f(x). This means that the original image is f(x).
Notice that F(x) is transformed three degree beyond 0 on the -axis and 6 degrees beyond zero on the y-axis. Hence the correct equation is:
g(x) = f(x-3) + 6.
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Use the function below to find F(4)
Answer:
A 256/3
Step-by-step explanation:
1/3 * 4^4 =
1/3 * (4*4*4*4) =
1/3 * 256 = 256/3
Answer:
A = 256/3
Step-by-step explanation:
F(x) = 1/3 × 4ˣ = 4ˣ/3
F(4) = 4⁴/3 = 256/3
Formulate the quadratic function that contains the points (-2,1), (0,1) and (1,4).
Answer:
Step-by-step explanation: