Answer:
x = -9, y = -13 or x = 13, y = 9 or x = -13, y = -9 or x = 9, y = 13Step-by-step explanation:
[tex]x^2+y^2=250\\\\x^2-2xy+y^2+2xy=250\\\\(x-y)^2=250-2xy\\\\(x-y)^2=250-2\cdot117\\\\ (x-y)^2=16\\\\x-y=4\qquad\qquad\vee\qquad \qquad x-y=-4\\\\x=4+y \qquad\qquad \vee\qquad\qquad x=-4+y\\\\(y+4)y=117\qquad\vee\qquad\quad (y-4)y=117\\\\y^2+4y-117=0\qquad\vee\qquad y^2-4y-117=0\\\\y=\dfrac{-4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\qquad\vee\qquad y=\dfrac{4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\\\\y=\dfrac{-4\pm\sqrt{16+468}}{2}\qquad\ \ \vee\qquad y=\dfrac{4\pm\sqrt{16+468}}{2}[/tex]
[tex]y_1=\dfrac{-4-22}{2}\ ,\quad y_2=\dfrac{-4+22}{2}\ ,\quad y_3=\dfrac{4-22}{2}\ ,\quad y_4=\dfrac{4+22}{2}\\\\y_1=-13\ ,\qquad y_2=9\ ,\qquad\quad\qquad\ y_3=-9\ ,\qquad y_4=13\\\\x_{1,2}=4+y_{1,2}\qquad\qquad\qquad\qquad\qquad x_{3,4}=-4+y_{3,4}\\\\x_1=-9\ ,\qquad x_2=13\ ,\qquad\quad\qquad x_3=-13\ ,\qquad x_4=9[/tex]
Which of the following relation is correct
Answer:
Both the equation and its inverse are functions.
Step-by-step explanation:
In order to solve this problem lets first find the inverse of this function. This is done below:
[tex]y = x^2 + 8\\[/tex]
We first swap x and y.
[tex]x = y^2 + 8[/tex]
We now isolate y.
[tex]y^2 = x - 8\\y = \sqrt{x - 8}\\f^{-1}(x) = \sqrt{x - 8}[/tex]
Functions are relations between two groups of numbers, in such a way that one number on the input group must generate a singular answer from the output group. This holds true for both f(x) and its inverse, therefore both are functions.
The weight of an object on the moon is
5 of its weight on Earth. If a moon rock
weighs 202 lb on Earth, how much did
the moon rock weigh on the moon?
Give your answer as a simplified mixed number.
Enter the number that belongs in the green box.
Answer:
40 2/5Ibs or [tex]40\frac{2}{5}[/tex] lbs
Step-by-step explanation:
Let weight of object on the moon be represented = Wm
weight of object on the Earth = We
In the above question, we are told:
The weight of an object on the moon is
5 of its weight on Earth.
Hence, mathematically, this is represented as:
5Wm = We
If a moon rock weighs 202 lbs on Earth
5Wm = 202lbs
Wm = 202lbs/5
Wm = [tex]40\frac{2}{5}[/tex]Ibs
Therefore, the moon rock weighs [tex]40\frac{2}{5}[/tex]Ibs on the moon.
How do you factor this expression: x^3 + 9x^2 + 27x + 27. Thanks! :)
Answer:
(x + 3)³
Step-by-step explanation:
Use rational root test to check for possible rational roots.
Factors of 27 are 1, 3, 9, and 27.
Factors of 1 are 1.
Possible rational roots are:
±1/1, ±3/1, ±9/1, ±27/1
Checking each one, we find that -3 is a root. So x + 3 is a factor.
Knowing that, we can use grouping to factor.
x³ + 9x² + 27x + 27
x³ + 9x² + 18x + 9x + 27
x (x² + 9x + 18) + 9 (x + 3)
x (x + 6) (x + 3) + 9 (x + 3)
(x + 3) (x (x + 6) + 9)
(x + 3) (x² + 6x + 9)
(x + 3) (x + 3)²
(x + 3)³
An observer on the top of a lighthouse observes the angles of depression of two ship at anchor to be 75 and 45 respectively. Find the distance between the two ships if the line joining them points to the base of the light house which is 100 meters high. (use tan 15 = 0.27) Answer should be 73 meter.
Answer:
Distance between two ships = 73 units
Step-by-step explanation:
Note:
tangent = opposite / hypotenuse
Referring to diagram,
Distance of ship A from tower = 100 tan(90-45) = 100 units
Distance of ship B from tower = 100 tan(90-75) = 100 tan (27) = 27 units
Distance between two ships = 100-27 = 73 units
Brenda has three times more quarters
than Lisa has. Brenda gives 20% of her
quarters to Lisa, but she still has $1
more. How many quarters does Lisa
have in the beginning?
E. 5
F. 10
G. 15
H. 20
Answer:
5
Step-by-step explanation:
If Lisa has x quarters and Brenda has 3x quarters, we can write:
80% * 3x = 4 + (20% * 3x + x) -- We write 4 because 1 dollar = 4 quarters
0.8 * 3x = 4 + (0.2 * 3x + x)
2.4x = 4 + 1.6x
0.8x = 4
x = 5
Determine which one of the following statements is true.
A. Linear growth will always exceed exponential growth.
B. Linear growth will always exceed quadratic growth.
C. Quadratic growth will always exceed exponential growth.
D. Exponential growth will always exceed linear growth.
Answer:
D. Exponential growth will always exceed linear growth.
Step-by-step explanation:
An "exponential growth function" would always exceed the "linear growth function" in the end because the "x-values" tends to get larger in continuation, so the change rate associated with the "exponential function" also increases in continuation whereas the "linear functions' change rate is considered as constant.
In the question above, option D is correct.
PLEASE HELP The equation of the line below is: y = -4x + 4. y = -2x + 4. y = 2x + 4. None of these choices are correct.
Answer:
y = 2x+4
Step-by-step explanation:
The y intercept ( where it crosses the y axis ) is 4
The slope is positive because the line goes up from the bottom left to top right
We pick two point ( -2,0) and ( 0,4)
The slope is found by
m= (y2-y1)/(x2-x1)
= ( 4-0)/(0- -2)
= 4/ (0+2)
= 4/2
= 2
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
Answer:
The equation to this line is y=-4x+4
Step-by-step explanation:
If you look at the graph you can see that the y intercept is 4.
To find the slope take two points on the graph and plug it into be y2-y1/x2-x1
I chose (0,-2) and (-1,2) So 2+2=4 and -1-0= -1 so 4/-1= -4
What is the average length of a side in the shape made from the file datatest1.txt whose contents are shown below (just give to two decimal places)? -3,3 -4,-3 4,-2 6,5
Answer:
0.75
Step-by-step explanation:
The average length is given as the sum of all the lengths given divided by the number of lengths (frequency).
Mathematically:
Average = (Sum of lengths) / frequency
The lengths given are -3, 3, -4, -3, 4, -2, 6, 5. There are 8 lengths there.
The average is therefore:
Average = (-3 + 3 + (-4) + (-3) + 4 + (-2) + 6 + 5) / 8
Average = 0.75
Last week Lisa had a gross earning of $1441.30. Cathy receives a base salary of $375 and a commission on sales exceeding her quota of $5000. What is her rate of commission if her sales were $6560?
Answer:
4.25%
Step-by-step explanation:
Commision = 441.30 - 375 = 66.30
Commision is based on = 6560-5000 = 1560
Rate of Commision = (in decimal) 66.30/1560 = 0.0425
Rate of Commision = 0.0425 * 100 = 4.25 %
Another one omg this is annoying
Answer:
Correct option: first one
Step-by-step explanation:
The equation f(x) = 5x + 1 is a function, because each value of x gives only one value of y.
Now let's find the inverse by switching f(x) by x and x by f'(x), then isolating f'(x):
[tex]x = 5f'(x) + 1[/tex]
[tex]5f'(x) = x - 1[/tex]
[tex]f'(x) = \frac{x - 1}{5}[/tex]
The inverse f'(x) is also a function, because each value of x gives only one value of x.
So we have that both the equation and its inverse are function, therefore the correct answer is the first option.
dentify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A researcher selects every 890 th social security number and researcher selects every 890th social security number and surveys surveys that the corresponding corresponding person.person. nothing nothing nothing Which type of sampling did the researcher researcher use
Complete Question:
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below;
A researcher selects every 890th social security number and surveys the corresponding person. Which type of sampling did the researcher use?
Answer:
Systematic sampling.
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Random sampling.
2. Convenience sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Systematic sampling.
A systematic sampling is a type of probability sampling method which involves the researcher selecting or collecting data from a larger population.
Under systematic sampling method, samples are selected from an ordered (fixed) sample population at periodic interval. Therefore, numbers are assigned to every member of the population and then, the "nth" member are selected by the researcher after choosing a fixed starting point.
In this scenario, the researcher selects every 890th social security number and surveys the corresponding person.
Hence, the type of sampling used by the researcher is systematic sampling.
Find the value of X and Y in the following parallelogram.AD =X+8 D=2y +13 C=16-x CB=5y+4 AB=o
Answer:
The answer is below
Step-by-step explanation:
AD = X + 8 ∠D = 2y +13 ∠C = 16 - x CB = 5y+4
In a parallelogram, consecutive angles are supplementary and opposite sides are equal.
Therefore for parallelogram ABCD, AB = CD, CB = AD
Since AD = CB (opposite sides of a parallelogram are equal):
x + 8 = 5y + 4
5y - x = 8 - 4
5y - x = 4 (1)
∠C + ∠D= 180° (consecutive angles of a parallelogram are supplementary). Therefore:
16 - x + 2y + 13 = 180
2y - x + 29 = 180
2y - x = 180 -29
2y - x = 151 (2)
To find x and y, subtract equation 1 from equation 2:
3y = -147
y = -49
Put y = -49 in equation 2
2(-49) - x = 151
x = -98 - 151
x = -249
I need the answers to B and C as (as fractions please)
Answer:
1/12 and 1/3
Step-by-step explanation:
There are 2 choices for flipping a coin (heads or tails) and 6 choices for rolling the die (1 - 6) so the total possible outcomes are 2 * 6 = 12. Of these, there's only one possibility where we get a tail and a 5 so the answer to b is 1/12. For c, there's only one head but there are 4 numbers less than 5 (1 - 4) so the total number of outcomes that satisfy our condition is 1 * 4 = 4 which makes the probability 4/12 = 1/3.
Answer:
Step-by-step explanation:
The probable results are:
Head + 1/2/3/4/5/6
Tail + 1/2/3/4/5/6.
B. This gives 12 results and tail + 5 is one of them, so the probability of getting that is 1/12.
C. A result with a head and a number less than 5 is available 4 times, making the fraction 4/12 or 3/4
Hope this helps
2) Jeremy needs to build a fence around his pool. The pool and the sidewalk around it have
a distance around 300 feet, so the perimeter of the fence needs to be at least 300 feet. The
length of the fence is four more than two times the width. What is the length and width?
Answer:
length = 26.6
width = 11.3
Step-by-step explanation:
1. Set up the equation
(2x + 4)(x) = 300
2. Simplify
2x² + 4x = 300
3. Solve by completing the square
Divide by 2 to make "a" equal to 1
x² + 2x = 150
Find term to complete the square by squaring half of "b"
(2/2)² = 1
x² + 2x + 1 = 150 + 1
Factor perfect square trinomial
√x² + 2x + √1 = 151
(x+1)² = 151
Square root each side
x + 1 = ±12.3
Set up two possibilities and solve
x + 1 = 12.3
x = 11.3
x + 1 = -12.3
x = -13.3
The measurement cannot be negative so width is equal to 11.3
4. Use the width to solve for the length
11.3(2) + 4 = 26.6
The length and width is 26.6 and 11.3.
Calculation of the length and width:Since The length of the fence is four more than two times the width.
So here the equation should be
(2x + 4)(x) = 300
[tex]2x^2 + 4x = 300[/tex]
Now
Here we divided by 2
So,
[tex]x^2 + 2x = 150[/tex]
Now we determine the term
[tex](2/2)^2 = 1\\\\x^2 + 2x + 1 = 150 + 1[/tex]
Now applied the Factor perfect square trinomial
[tex]\sqrt x^2 + 2x + \sqrt1 = 151\\\(x+1)^2 = 151[/tex]
Now do the Square root each side
x + 1 = ±12.3
Here we required to set up two possibilities and solve
x + 1 = 12.3
x = 11.3
And,
x + 1 = -12.3
x = -13.3
The measurement should not be negative so the width is equal to 11.3
Now the width is
= 11.3(2) + 4
= 26.6
Therefore, The length and width is 26.6 and 11.3.
Learn more about length here: https://brainly.com/question/4979629
PLEASE HELP!!!!!Using the following image, solve for the trigonometry ratios of ∠D and ∠F.
Answer:
Here we have a triangle rectangle, where the length of one of the cathetus is: 15 (the one at the top)
And the length of the other cathetus is 8 units (i think, i can not see well the image)
Now, if we want to find the angle D.
In this case, the adjacent cathetus is the one of 15 units, and the opposite cathetus is the one of 8 units.
Then we can use the relation:
Tg(A) = (opposite cathetus)/(adjacent cathetus)
So:
Tg(D) = 8/15
D = ATg(8/15) = 28.1°
Now, for the angle F, the adjacent cathetus is the one of 8 units, and the opposite cathetus is the one of 15 units:
F = ATg(15/8) = 61.9°
Answer:
x= 17
Next, find the trigonometry ratios of ∠D.
sin∠D= 8/17
cos∠D= 15/17
tan∠D= 8/15
Finally, find the trigonometry ratios of ∠F.
sin∠F=15/17
cos∠F= 8/17
tan∠F=15/8
To obtain a Class E license, you don’t need to
Answer:
provide a valid passport
Step-by-step explanation:
Answer:
be a us citizen
Step-by-step explanation:
Which is the graph of f(x) = /x?
Answer:
neither on of those. I can't see the the other answers so your best bet is to look on m-a-t-h-w-a-y. (had to spell out with hyphens but remove them and go to that)
Step-by-step explanation:
Select the number of solutions for each system of two linear equations.
Answer:
work is shown and pictured
C, infinitely many solutions.
B, one solution.
C, infinitely many solution.
A system of linear equations:A system of linear equations is a collection of one or more linear equations involving the same variables.
A system of linear equation has
one solution when the graph intersect at a point.no solution when the graphs are parallel.infinitely many solutions when the graphs are exact same line.According to the given questions
the given system of equations
(1). 2x+2y=3 and 4x+4y=6
if we see the graph of the above system of linear equations, the graphs are the" exact at same line".
Hence, they have infinitely many solution.
(2). 7x+5y=8 and 7x+7y =8
if we see the graph of the above system of linear equations, the graphs are intersecting at a single point.
Hence, there is only one solution.
(3). -2x+3y=7 and 2x-3y=-7
if we see the graph of the above system of linear equations, the graphs are exact at same line.
Hence, there is infinitely many solutions.
Learn more about the system of linear equations here:https://brainly.in/question/5130012
#SPJ2
3m-(m + 5) when m = 11 help
Answer:
17
Step-by-step explanation:
3m-(m + 5)
Distribute the minus sign
3m -m -5
Combine like terms
2m -5
Let m =11
2*11 -5
22-5
17
Answer:
[tex]17[/tex]
Step-by-step explanation:
[tex]3m-(m + 5)[/tex]
[tex]m= 11[/tex]
Plug m as 11 in the expression.
[tex]3(11)-(11+5)[/tex]
Evaluate.
[tex]33-16[/tex]
[tex]=17[/tex]
Three years after a company was founded, its assets were $11,283,500. Ten years after being founded, its assets had grown to $21,794,600. During that period of time, at what rate did the company's assets grow per year?
Answer:
$1,051,110Step-by-step explanation:
Given
Step one:
Company's initial asset value = $11,283,500
Company's final asset value = $21,794,600
Step two
we can calculate the company's asset appreciation after 10 years as
$21,794,600- $11,283,500= $10,511,100
Step three
Hence, the growth rate of the company's asset value per year can be expressed as = $10,511,100/10= $1,051,110
Please answer quickly I am unsure what to do
Answer:
Investment B is £97 more than investment A
Step-by-step explanation:
For investment A
£160is saved for 2 years every month
Total amount at the end of the two years= 2*160*12= £3840
The the percentage interest added is
=2.5/100*3840
= £96
Total amount= 3840+96
Total amount=£ 3936
For investment B
£3800 is compounded every year for two years at 3%
Total amount= 3800(1+0.03/2)^(2*2)
Total amount= 3800(1+0.015)^4
Total amount= 3800(1.015)^4
Total amount= 3800(1.061363551)
Total amount= 4033.18
Total amount= £4033
The difference between the two investment= 4033-3936
= £97
Find the value of this expression if x = 3
and y = -1.
xy²
5
Answer:
0.6 = 6/10 = 3/5 is the answer.Step-by-step explanation:
0.6 = 6/10 = 3/5
is the answer
This is because you have to substitute.
Given:
x = 3
y = -1
Unknown:
Final Answer
(x*y^2)/5
((3)(-1*-1)/5
= (3*1)/5
= 3/5= 6/10= 0.6Hope this helped,
Kavitha
HELP PLEASE!!
Below is the graph of f(x)=2ln(x). How would you describe the graph of g(x)=4ln(x)?
Reasoning:
g(x) = 4*ln(x)
g(x) = 2*2ln(x)
g(x) = 2*f(x)
Whatever the output f(x) is, it is doubled to get g(x). Recall that y = f(x), so we're really doubling the y values to visually stretch it vertically by a factor of 2. In short, g(x) is twice as tall compared to f(x).
Answer:
C. g(x) stretches f(x) vertically by a factor of 2.
Step-by-step explanation:
a p e x
Use the ratio of a 30-60-90 triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form. u= n=_____square root________
Answer:
A. v = 19√3.
B. u = 38.
Step-by-step explanation:
The following data were obtained from the question:
Angle θ = 60°
Adjacent = 19
Opposite = v
Hypothenus = u
A. Determination of the value of 'v'
The value of v can be obtained by using Tan ratio as shown below:
Angle θ = 60°
Adjacent = 19
Opposite = v
Tan θ = Opposite /Adjacent
Tan 60 = v/19
Cross multiply
v = 19 × Tan 60
Tan 60 = √3
v = 19 × √3
v = 19√3
Therefore, the value of v is 19√3
B. Determination of the value of 'u'
The value of u can be obtained by using cosine ratio as shown below:
Angle θ = 60°
Adjacent = 19
Hypothenus = u
Cos θ = Adjacent /Hypothenus
Cos 60 = 19/u
Cos 60 = 1/2
1/2 = 19/u
Cross multiply
u = 2 × 19
u = 38
Therefore, the value of u is 38.
CAN ANYONE HELP IM VERY CLUELESS
Answer:
51°
Step-by-step explanation:
A circle has a total of 360 degrees. So,
360 = 62 + 66 + x + 73 + x + 57
Next, combine like terms:
360 = 2x + 258
Next, isolate your variable by subtracting 258 from both sides:
102 = 2x
Finally, divide both sides by 2 to get x:
x = 51
Answer:
x = 51
Step-by-step explanation:
x + 73 + x + 57 + 62 + 66 = 360
2x + 258 = 360
2x = 360 - 258
2x = 102
[tex]\frac{x}{2} =\frac{102}{2}[/tex]
x = 51
x over 4 + 3/5 is equal to 3x over 5 - 2
Answer:
[tex]\huge\boxed{x=\dfrac{52}{7}=7\dfrac{3}{7}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x}{4}+\dfrac{3}{5}=\dfrac{3x}{5}-2\qquad\text{multiply both sides by}\ LCD=20\\\\20\cdot\dfrac{x}{4}+20\cdot\dfrac{3}{5}=20\cdot\dfrac{3x}{5}-20\cdot2\\\\5\cdot x+4\cdot3=4\cdot3x-40\\\\5x+12=12x-40\qquad\text{subtract 12 from both sides}\\\\5x+12-12=12x-40-12\\\\5x=12x-52\qquad\text{subtract}\ 12x\ \text{from both sides}\\\\5x-12x=12x-12x-52\\\\-7x=-52\qquad\text{divide botgh sides by (-7)}\\\\\dfrac{-7x}{-7}=\dfrac{-52}{-7}\\\\x=\dfrac{52}{7}[/tex]
? Given: All US area codes are three-digit numbers that use the numerals 0 to 9. Step 1: How many area codes are possible if the first digit can't be 0? Use your keyboard and the keypad to enter your answer. Then click Done.
Answer:
1-9, 1929
Step-by-step explanation:
You do the arithmetic and then study the us government postal codes and then you do kid behavior with my names. So, you get 1929 basically, in a nutshell, forever incessantly. thank yopu
Answer ill mark the brainliest please help
Answer:
42
Step-by-step explanation:
You can get this right from the table. 42 females had a positive opinion about the campus.
Answer:
42
Step-by-step explanation:
Let's look at the intersection of the "positive opinion" column and "female" row, the number we see at the intersection is 42.
Find the y-intercept and the axis of symmetry of f(x)=ax2+2ax+3.
Answer:
[tex] y= cx^2 +dx +e[/tex]
We see that:
[tex] c = a, d= 2a , e= 3[/tex]
The axis of symmetry is defined by this formula:
[tex] X= - \frac{d}{2c}[/tex]
And replacing we got:
[tex] X= -\frac{2a}{2a}= -1[/tex]
Thn the axis of symmetry would be X=-1
Step-by-step explanation:
For this case we have the following function:
[tex] y = ax^2 +2ax +3[/tex]
If we compare this function with the general expression of a quadratic formula given by:
[tex] y= cx^2 +dx +e[/tex]
We see that:
[tex] c = a, d= 2a , e= 3[/tex]
The axis of symmetry is defined by this formula:
[tex] X= - \frac{d}{2c}[/tex]
And replacing we got:
[tex] X= -\frac{2a}{2a}= -1[/tex]
Thn the axis of symmetry would be X=-1
[tex] - x - 2 \div x(x {}^{2} - 4)[/tex]
Answer:
Step-by-step explanation:
Hello,
First of all we will take any real number x different from 0, -2, +2 as dividing by 0 is not allowed and then we can write
[tex]\dfrac{( - x - 2)}{x(x^2 - 4)}=-\dfrac{x+2}{x(x-2)(x+2)}=\large \boxed{ -\dfrac{1}{x(x-2)}}[/tex]
because we know that
[tex]x^2-4=x^2-2^2=(x-2)(x+2)[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you