Answer:
a = 3 , b = - 18
Step-by-step explanation:
2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]
express as a fraction with common denominator (x - 2)(x + 2)
= [tex]\frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}[/tex]
= [tex]\frac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}[/tex]
= [tex]\frac{2x^2-8-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]
= [tex]\frac{3x-18}{x^2-4}[/tex]
compare to [tex]\frac{ax+b}{x^2-4}[/tex]
with a = 3 and b = - 18
Answer the 2 question in the photo for EASY points ( 20 points )
Answer:
the answer is 29
Easton is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. easton will earn $40 every time one of his songs is played in a commercial and he will earn $110 every time one of his songs is played in a movie. easton's songs were played on 6 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $840. determine the number of commercials and the number of movies on which easton's songs were played.
The number of time Easton's song was played on commercials is 10 times.
The number of time Easton's song was played during a movie is 4 times.
How many times was the song played in commercials and during movies?The first step is to form a system of equations:
40c + 110m = 840 equation 1
c - m = 6
c = 6 + m equation 2
Where:
c = number of times the songs was played in commercials.m = number of times the songs was played in moviesThe system of equations would be solved using the substitution method.
Substitute for c in equation 1 using equation 2
40(6 + m) + 110m = 840
240 + 40m + 110m = 840
40m + 110m = 840 - 240
150m = 600
m = 600 / 150
m = 4
Substitute for m in equation 2.
c = 6 + 4
c = 10
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An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 30x + 56 = 0, and tunnel B is modeled by x2 – 30x + 16y – 95 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work.
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work.
Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work.
The tunnel A will be damaged and truck can pass through tunnel B.
Given that, tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² – 30x + 16y – 95 = 0.
What is the standard form of parabola equation?The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y²= = 4ax.
Part A: x²+y²+30x+56=0
Add 15² on both the sides of a equation
That is, x²+30x+15²+y²=-56+15²
⇒ (x+15)²+y²=169
⇒ (x+15)²+y²=13²
Divide 13² on both the sides of the equation
⇒ (x+15)²/13² + y²/13² =1
Part B:
x²-30x+16y-95=0
Now, x²-30x+16y=95
Add 15² on both the sides of a equation
That is, x²-30x+15²+16y=95+15²
⇒ (x-15)²=320-16y
⇒ (x-15)²=16(20-y)
Part C:
Maximum height:
A: 13 feet
B: 20 feet
Width = 8 feet
A: x+15=8/2=4 y=12.37<13.5
B: x-15=8/2=4 y=19>13.5
Hence, the tunnel A will be damaged and truck can pass through tunnel B.
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A 10 inch-candle burns at a linear rate. It measures 9 inches two hours after it was lit. Which equation can be used to find the length of the candle, y, in inches after x hours it was lit?
1. y = 10 - 0.5x
2. y = 10 - 4.5x
3. y = 10 - 9x
4. y = 10 - 2x
Answer:
1. y = 10 - 0.5xStep-by-step explanation:
Find the burning rate of candle per hour:
(10 - 9)/2 = 1/2 = 0.5 inThe rate is the slope of the linear function and the initial length of the candle is the y-intercept:
m = - 0.5,b = 10.The equation is:
y = -0.5x + 10 ory = 10 - 0.5xCorrect choice is the first one.
Explain how to use a graph of the function f(x) to
find f(3).
By focusing on x- axis we can get value of f(3).
What is function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
We have a function f(x).
Now, we have to find the value of f(3) from the graph
So, If we had the graph of f(x) and wanted to find f(3), we would look for the location on the graph where x = 3, then determine its y-value.
The response to f(3) is that y-value.
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An elementary school wants to purchase a new swing set. The table shows the selling price of the swing sets they are interested in buying.
Swing Set Wholesale Price ($)
Adventurers 3,056
Thunder Ridge 4,125
The markup for both swing sets is
20
1
4
%
. The school decides to buy the Adventurers swing set. What is the selling price of the swing set they are buying? Round to the nearest cent if necessary.
The selling price of the adventurers swing set given the wholesale price and the mark-up price is $3,674.84.
What is the selling price?The selling price of the adventurers swing set is the sum of the wholesale price and the percentage mark-up. Mark-up is the rate at which the selling price of an item is increased.
Percentage is the rate of an amount expressed as a number out of hundred. The sign that is used to represent percentages is %.
Selling price = wholesale price x (1 + mark-up price)
3,056 x (1 + 0.2025)
3056 x 1.2025 = $3,674.84
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HELP ME PLEASE AND HURRY :[ From a lamp post four feet away from her, Sandra looks up to the sky and sees a bird that is five feet away from her. How high up is the bird? Show all of your steps in answering the question
Answer:
3 feet
Step-by-step explanation:
s= sandra
L= Lamp
if you know that the lamp is four feet away, and the bird is five feet away. go vertically up from the lamp until the distance from the lamp vertically equals five feet back to sandra.
I WILL MARK BRAINLIEST!!
What does y equal in the solution of the system below:
x/2 + y/3 = 1
x/5 + y/2 = 1
A. 2/11
B. 42/19
C. 18/11
D. 2/19
Please work it out/explain!!!
Answer:
C
Step-by-step explanation:
I'm to lazy to type it out so...I took a photo
I hope this helps :D
and I need brainiliest so bad...
The area of the entire figure below is 1 square unit.
What is the area of the stripped rectangle??
Rewrite as a simplified fraction.
3.8333333333333=?
Answer:
38333333333333/10000000000000
Step-by-step explanation:
Nick has 32 nickels and quarters.
The total value of Nick's coins is
$4.60. How many nickels does he
have?
A. 15
B. 16
c. 17
D. 18
Gabriel tiene el doble de dinero que Daniel y tiene cinco veces lo que Edgar. Si Gabriel regalara Q14 a Daniel y Q33 a Edgar, los tres quedarían con igual cantidad. ¿Cuánto dinero tiene cada uno?
Using a system of equations, it is found that the amounts of money that each of Gabriel, Daniel and Edgar have are given as follows:
Gabriel: Q122.Daniel: Q61.Edgar: Q42.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.
In the context of this problem, the variables are given as follows:
Variable x: Amount of money that Gabriel has.Variable y: Amount of money that Daniel has.Variable z: Amount of money that Edgar has.Gabriel has double the amount of Daniel, hence:
x = 2y.
Gabriel has five times the amount of Edgar, hence:
x = 5z.
If Gabriel loans Q14 to Daniel and Q33 to Edgar, they will have the same amount, hence:
x - 47 = y + 14 = z + 33.
Since x = 2y, we can replace into the first two sides of the equality above and solve for y as follows:
2y - 47 = y + 14
y = 61. (Daniel's amount).
The solution for x is given as follows:
x = 2y = 2(161) = 122 (Gabriel's amount).
The solution for z is given as follows:
x - 47 = z + 33
122 - 47 = z + 33
75 = z + 33
z = 75 - 33
z = 42 (Edgar's amount).
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help need help i give 26 pointes
According to the given line, the points are L and M and the segment is LM.
Lines:
The line is defined as the one-dimensional figure, which has length but no width. It is made of a set of points which is extended in opposite directions infinitely.
Given,
Here we have the diagram.
Through the given diagram we have to identify the points and segments from it.
We know that, the points refers the is a dimensionless shape, since it represents a dot only, whereas a line is a one-dimensional shape.
Based on this definition , we have two points that L and M in the given diagram.
Next one we have to identify from the graph is segment,
Segment means the part of the line that connects two points.
So, LM is the segment of the line.
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What are all of the solutions to the trigonometric equation 2 times cosine squared theta minus 2 times sine squared theta equals radical 2 question mark
Explanation
Given the trigonometric expression
[tex]2cos^2\theta-2sin^2\theta=\sqrt{2}[/tex]We can find the solutions below;
From trigonometry identities;
[tex]cos^2\theta-sin^2\theta=cos2\theta[/tex]Therefore; we will have;
[tex]\begin{gathered} 2cos^2\theta-2s\imaginaryI n^2\theta=\sqrt{2} \\ 2(cos^2\theta-sin^2\theta)=\sqrt{2} \\ 2cos2\theta=\sqrt{2} \\ Divide\text{ both sides by 2} \\ \frac{\begin{equation*}2cos2\theta\end{equation*}}{2}=\frac{\sqrt{2}}{2} \\ cos2\theta=\frac{\sqrt{2}}{2} \end{gathered}[/tex]Therefore, the general solutions for the above is given as;
[tex]\begin{gathered} 2θ=\frac{\pi}{4}+2\pi n,\:2θ=\frac{7\pi}{4}+2\pi n \\ therefore; \\ \theta=\frac{\frac{\pi}{4}+2\pi n}{2},\theta=\frac{\frac{7\pi}{4}+2\pi n}{2} \\ \theta=\frac{\pi}{8}=\pi n,\theta=\frac{7\pi}{8}+\pi n \end{gathered}[/tex]Answer:
[tex]\theta=\frac{\pi}{8}+\pi n,\theta=\frac{7\pi}{8}+\pi n[/tex]Graph the following set of points: A B C (1,3), (-3, -3), (5,2). Find the area and perimeter of ∆ABC . Leave answer in two decimal places.
The perimeter of the triangle is 29.31 units and the area of the triangle is 38.87 units^2
Distance Between Points
To find the perimeter and area of the triangle, we have to use the formula of distance between two points.
A = (1, 3)B = (-3, -3)C = (5, 2)Distance between AB
[tex]d_a_b = \sqrt{(a_1+a_2)^2 + (b_1 + b_2)^2} \\d_a_b = \sqrt{(3+1)^2 + (-3-3)^2}\\ d_a_b = \sqrt{4^2 + 9^2} \\d_a_b = 9.85 units[/tex]
Distance between BC
[tex]d_b_c = \sqrt{(b_1+b_2)^2 + (c_1+c_2)^2}\\d_b_c = \sqrt{(-9)^2 + (7)^2}\\d_b_c = \sqrt{130} \\d_b_c = 11.40 units[/tex]
Distance between AC
[tex]d_a_c = \sqrt{(a+1_a_2)^2 + (c_1+c_2)^2} \\d_a_c = 8.06 units[/tex]
The perimeter of the triangle is equal to
[tex]p = 9.85 + 11.40 + 8.06 = 29.31 units[/tex]
The area of the triangle is 38.87 units^2
Kindly find the attached graph below;
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What is the slope
y = 8x - 15
Answer: the slope of this equation is 8
Step-by-step explanation: y = 8x - 15, the 8x represents the slope of this equation
Victoria is older than Tyee. Their ages are consecutive even integers. Find Victoria's
age if the product of their ages is 80.
The ages of Victoria and tyee are 72 and 74.
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b that only contains a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables. Ax+By=C is the accepted form for two-variable linear equations. Finding both intercepts of an equation in this form is rather simple (x and y). If an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is said to be linear. The point-slope form, standard form, and slope-intercept form are the three primary types of linear equations.
As given
ages are consecutive even integers
Victoria > Tyee
So
Victoria's age = x
Tyee's age = x + 2
x(x + 2) = 80
= x² + 2x - 80
= x² + 8x - 10x - 80
Hence , the ages are 72 and 74.
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A tree branch is observed to bend as the fruit growing on it increase in size. By estimating the mass of the developing fruit and plotting the data over time, a student finds that the height h in metres of the branch end above the ground is closely approximated by the function h=2-0.2×1.60.2m where m is the estimated mass, in kilograms, of fruit on the branch.
(a) Sketch the graph of h against m.
The graph of h against m is plotted in form of a curve.
Given:
A tree branch is observed to bend as the fruit growing on it increases in size.
The height h in metres of the branch end above the ground is closely approximated by the function [tex]h=2-0.2*1.60^{0.2m}[/tex] where m is the estimated mass, in kilograms, of fruit on the branch.
We have to sketch the graph of h against m.
The x-axis represents the mass in kg while the y-axis represents the height of the branch above the ground in metres.
Hence a curved graph is obtained by plotting the function.
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Two numbers add up to $23$ and their difference is $27$. How far apart are the two numbers
Answer:
27
Step-by-step explanation:
x + y = 23
x - y = 27
(x + y) + (x - y) = 23 + 27
2x = 50
x = 25
y = - 2
How to find distance:
|25 -(-2)| = |27| = 27
Answer:-4+27
Step-by-step explanation:
A waterwheel has a radius of 4 feet, and the center of the wheel is 1 foot under the waterline. You notice a yellow mark at the top of the wheel. If the wheel rotates StartFraction pi Over 3 EndFraction radians, how far above the water is the yellow mark? 1 foot 2 feet 3 feet 4 feet
The height of the yellow mark above the water is 1 foot.
This is further explained below.
How far above the water is the yellow mark?Generally, The radius of a waterwheel is 4 feet, and its center is 1 foot below the waterline.
Estimation of feet:
cos π/3 = OB/OA
1/2 = OB/4
OB = 2
t
In conclusion,A yellow mark should be placed above the water
= OB - OD
= 2 - 1
= 1 foot
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Answer:
the other answer is correct is A. 1 foot
Step-by-step explanation:
Got it right on edge
men versus women: the average 20- to 29-year-old man is 69.9 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year-old woman is 64.1 inches tall, with standard deviation of 3.8 inches. a. find the z scores for a 67-inch- man and a 62-inch woman.
The z-scores for a 67-inch- man and a 62-inch woman are -0.9667 and -0.5526, respectively.
The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that
z-score = (x – μ) / σ
where x = sample data value
μ = mean
σ = standard deviation
For a 67-inch- man, use the formula to solve for the z-score.
x = 67
μ = 69.9
σ = 3.0
z-score = (x – μ) / σ
z-score = (67 - 69.9) / 3.0
z-score = -0.9667
Do the same for a 62-inch- man, use the formula to solve for the z-score.
x = 62
μ = 64.1
σ = 3.8
z-score = (x – μ) / σ
z-score = (62 - 64.1) / 3.8
z-score = -0.5526
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Write a ratio for the following situation.
For every one year, there are twelve months.
A flight from sydney to auckland takes 3 hours and 12 minutes. auckland time is 2 hours ahead of sydney's. if the flight departed at sydney 10:10am at what time did it arrive at auckland
suppose m<7 = 96 find m<2 and m< 4
Answer:
Answer down below!
Step-by-step explanation:
If we draw this out, we already know that m<7 = 96
Using what we already know, we can figure out the rest
m<6 also equals 96 because m<7 and m<6 are verticle angles
m<3 also equals 96 because m<6 and m<3 are opposite interior angles
m<2 also equals 96 because m<3 and m<2 are verticle angles
Now, to find m<4, simply subtract 96 from 180. That should give you 84
Thus, m<2 = 96 and m<4 = 84
Congruent triangle
Please answers the following question…
The picture is attached below
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1600 after 1 day, what is the size of the colony after 4 days? How long is it until there are 70,000 mosquitoes?
The number of mosquitoes on the colony after 4 days is 2800.
The number of days that there are 70,000 mosquitoes will be 114 dad.
How to illustrate the population?The population of a colony of mosquitoes obeys the law of uninhibited growth and there are 1000 mosquitoes initially and there are 1600 after 1 day. The common difference will be:
= 1600 - 1000
= 600
The formula for the arithmetic sequence will be:
= a + (n - 1)d
a = 1000
d = 600
n = 4
The colony after 4 days will be:
= a + (n - 1)d
= 1000 + (4 - 1)600
= 1000 + 1800
= 2800
The number of days that there are 70,000 mosquitoes will be:
a + (n - 1)d = 70000
1000 + 600(n - 1) = 70000
1000 + 600n - 600 = 70000
Collect like terms
600n = 70000 - 1000 + 600
600n = 68400
n = 68400/600
n = 114 days
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Write an equation of the line in point-slope form that passes through the given points.
(3,4) and (4,7)
Answer:
y - 4 = 3(x - 3) or y - 7 = 3(x - 4)
Step-by-step explanation:
y1 = mx1 + b
y2 = mx2 + b
(3, 4) = (x1, y1)
(4, 7) = (x2, y2)
4 = 3m + b
7 = 4m + b
-3 = -m
m = 3
y - y1 = m(x - x1)
y - 4 = 3(x - 3)
The area of a circle is 9π cm². What is the circumference, in centimeters? Express your answer in terms of
π
The circumference of a circle whose area is 9π cm² in terms of pi is 6π centimeters.
What is the circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed mathematically as;
C = 2πr
Given that the area of the circle is 9πcm², we determine the radius of the circle.
A = πr²
9πcm² = π × r²
r² = 9πcm² / π
r² = 9cm²
r = √9cm²
r = 3cm
Now, we determine the circumference of the circle.
C = 2πr
C = 2 × π × 3cm
C = 6cm × π
C = 6π cm
Therefore, the circumference of the circle is 6π centimeters.
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The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 23 fl oz per hour. How fast was the pipe leaking in gallons per day
The pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.
The Janitor find the leakage in the pipe at a rate of [tex]23[/tex] fl oz per hour.
We have to find how fast was the pipe leaking in gallons per day.
To find the leaking in gallons per day we have to convert [tex]23[/tex] fl oz per hour into gallons per day.
As we know that
[tex]1[/tex] gallon[tex]=128[/tex] fl oz
So [tex]1[/tex] fl oz[tex]=\frac{1}{128}[/tex] gallons
There are [tex]24[/tex] hours in a day so we multiply with [tex]24[/tex] to convert in day.
So the expression should be
[tex]=23[/tex] fl oz/hours[tex]\times\frac{1}{128}[/tex] gallons/fl oz[tex]\times24[/tex] hours/day
[tex]=\frac{23\times24}{128}[/tex] gallons/day
[tex]=\frac{23\times3}{16}\\[/tex] gallons/day
[tex]=\frac{69}{16}[/tex] gallons/day
Hence, the pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.
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-2
What is the Domain:
What is the Range:
Answer:
The set of all the first element of the ordered pairs of R is called domain and the set of all the second element of the ordered pairs of R is called range .