This relation is a function because a function, in fact this is a linear function. We have that:
[tex]\left[\begin{array}{cc}x & y\\2 & 3\\4 & 4\\6 & 5\\8 & 6\end{array}\right][/tex]
As you can see below, all the points have been plotted an this is a linear function. Therefore, with two points we can get the equation, so:
[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-3=\frac{4-3}{4-2}(x-2) \\ \\ \\ y-3=\frac{1}{2}(x-2) \\ \\ y=\frac{1}{2}x-1+3 \\ \\ y=\frac{1}{2}x+2 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(2,3) \\ \\ (x_{2},y_{2})=(4,4)[/tex]
Finally, the equation is:
[tex]\boxed{y=\frac{1}{2}x+2}[/tex]
Answer:
y=0.5x +2
Step-by-step explanation:
Simplify this expression 13+(-12)-(-5)
The answer is 6
Explaination:
Step-by-step explanation:
(-)(-) = (+)(+) = (+)
(-)(+) = (+)(-) = (-)
13 + (-12) - (-5) = 13 - 12 + 5 = 1 + 5 = 6
How do I factor out the coefficient of the variable -3/5k-3/10?
Answer:
make all the numbers have the same denominator, then simply see what multiplies to equal both fractions. your answer should be -3/10(1/5k+1)
Step-by-step explanation:
What’s the answer to this please ?
Answer:
YesStep-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
ΔABC:
A(2, 5), B(5, 5), C(5, 9)
[tex]AB=\sqrt{(5-2)^2+(5-5)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\AC=\sqrt{(5-2)^2+(9-5)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\BC=\sqrt{(5-5)^2+(9-5)^2}=\sqrt{0^2+4^2}=\sqrt{0+16}=\sqrt{16}=4[/tex]
ΔDEF:
D(-7, 8), E(-4, 8), F(-4, 4)
[tex]DE=\sqrt{-4-(-7))^2+(8-8)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\DF=\sqrt{(-4-(-7))^2+(4-8)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\EF=\sqrt{(-4-(-4))^2+(4-8)^2}=\sqrt{0^2+(-4)^2}=\sqrt0+16}=\sqrt{16}=4[/tex]
AB ≅ DE
AC ≅ DF
BC ≅ EF
Therefore ΔABC ≅ ΔDEF
The value of Greta's rolls of coins is $121.00. If pennies and dimes come in
rolls of 50 coins each, and nickels and quarters come in rolls of 40 coins
each, which of these combinations could Greta have?
Answer:
There are a lot of combinations possible
Step-by-step explanation:
One of them would be that each roll of quarters is $10 and each roll of pennies is 50cents so she could have 12 rolls of quarters and 2 rolls of pennies
One of the possible combinations that Greta can have is 12 rolls of quarters and 2 rolls of pennies.
What are the values of coins in USA?A penny is worth 1 cent.One nickel is equal to 5 centsOne dime is equal to 10 centsOne quarter is worth 25 centsNo. of quarters required to make $1 = 4 quarters
No. of coins in 1 roll of quarter = 40 coins = $10
If one roll of quarter is $10, then we can have 12 rolls which will give us $120.
Now we reached $120, we need $1 more to reach $121
No. of pennies to make $1 = 100 pennies
No. of coins in 1 roll of pennies = 50
So we need 2 rolls of pennies to make $1.
Hence, we need 12 rolls of quarters and 2 rolls of pennies to make $121.
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Which polynomial represents a sum of cubes
x^3-64
8x^3 +125
16x^3+1
26x^3+4
Answer:
B
Step-by-step explanation:
A sum of cubes has the form
a³ + b³
8x³ = (2x)³ and 125 = 5³
Hence
8x³ + 125 = (2x)³ + 5³ ← a sum of cubes
Plz help me with this
The answer is B. Since there are no parenthesis around pi/2, it stating that the graph shifts up pi/2 units - which is incorrect. It is a phase shift of pi/2 units (not a vertical shift).
Answer: [tex]\bold{B)\quad y=2\ sin2x+\dfrac{\pi}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the given graph,
A (amplitude) = 2 Phase Shift [tex]\bigg(\dfrac{C}{B}\bigg)[/tex] = [tex]\dfrac{\pi}{2}[/tex] to the left P (period) = π --> B = 2 D (vertical shift) = 0Option B shows the value of D as [tex]\dfrac{\pi}{2}[/tex], which is incorrect since there is no vertical shift up. If the parenthesis included that value, like Option C, then it would have been correct.
A college track team scout watched a 100-meter dash event at a countywide school district track meet. The college offers a track scholarship to applicants who run the 100-meter dash in less than 10 seconds. How many potential scholarship candidates ran in this event?
A. 6
B. 8
C. 4
D. 2
Answer to this is 8. Letter B
Determine the domain of the function h=9x/x(x^2-49)
ANSWER
[tex]( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )[/tex]
EXPLANATION
The given function is
[tex]h(x) = \frac{9x}{x( {x}^{2} - 49) } [/tex]
This function is defined for values where the denominator is not equal to zero.
[tex]x( {x}^{2} - 49) \ne0[/tex]
[tex]x(x - 7)(x + 7) = 0[/tex]
The domain is
[tex] x \ne - 7, x \ne0, \: and \: x \ne 7,[/tex]
Or
[tex]( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )[/tex]
The domain of the function h=9x/x(x^2-49) is x = -7, x = 7.
Explanation:The domain of the function h = 9x/(x(x^{2}-49)) can be determined by considering the values of x that make the denominator non-zero. Since division by zero is undefined, we need to find the values that would make the denominator equal to zero. In this case, the denominator is x(x^{2}-49), which factorizes to x(x+7)(x-7). So, the values of x that make the denominator equal to zero are x=0, x=-7, and x=7.
However, we also need to consider that the function is undefined when cancelling out those values of x that would also make the numerator zero. In this case, x=0 would make the numerator zero, so it cannot be a part of the domain.
Therefore, the domain of the function h = 9x/(x(x^{2}-49)) is given by x = -7, x = 7.
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at midnight, the temperature was -8 F. at noon, the temperature was 23 F. Write an expression to represent the increase in temperature.
A) -8 - 23
B) |-8| - 23
C) -8 - |23|
D) |-8 - 23|
Answer:
Option D
Step-by-step explanation:
we now that
The increase of the temperature is equal to the absolute value of the difference of the temperatures
Let
x-----> the increase of the temperature
[tex]x=\left|-8-23\right|=31\°F[/tex]
or
[tex]x=\left|23-(-8)\right|=31\°F[/tex]
The expression to represent the increase in temperature is 23 - (-8). To find the increase in temperature, we subtract the initial temperature (-8) from the final temperature (23).
Explanation:The expression to represent the increase in temperature is 23 - (-8).
To find the increase in temperature, we subtract the initial temperature (-8) from the final temperature (23).
Therefore, the correct expression is 23 - (-8).
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plz help me brainliest to whoever answers first.
Answer:
Second is the answer
Step-by-step explanation:
Slope = rise/run = y /x = m
Solve y to get y = mx
The slope of a line is rise over run, which would be Y over X.
The second answer is the correct one.
witch expression is equivalent to 2(6y-4)
Answer:
12y-8
Step-by-step explanation:
so what you do is to distribute the 2 to both 6y and -4 so 2 times 6y is 12y and 2 times -4 equals -8
The equivalent expression for the given expression is 12y-8.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 2(6y-4)
= 12y-8
Therefore, the expression is equivalent to 2(6y-4) is 12y-8.
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Christina and Sarah went on a fishing trip and caught 31 fish. Christina caught one less than three times as many fish as Sarah got. Can you help me set up a 5D table to figure out how many fish each girl caught?
Answer:
I think Christina caught 23 fish and Sarah caught 8 fish.
Step-by-step explanation:
If I did this right, we have to find the equation to represent this situation. Christina caught one less than 3 times as many as Sarah caught. Since we do not know how many Sarah has, we have to use a variable so let's go with x. One less than 3 times as many would be 3x - 1 because one less means subtracting 1 and 3 times means multiply by three. So we have x for Sarah and 3x - 1 for Christina. We add those together to get x + 3x - 1 = 31 (since they caught 31 fish, the total would be 31). We simplify it down to 4x - 1 = 31. Add one to both sides to cancel it out and we get 4x = 32. Divide by 4 on both sides and we get x = 8. Since Sarah was x, Sarah caught 8 fish. To find Christina we just plug in the 8. 3(8) -1. 3 times 8 is 24 and 24 minus 1 is 23. To check our answers we add 8 and 23 together which comes out to be 31.
Please correct me if I'm wrong! (Now I'm not sure what you mean by a 5D table but if this is right I hope it helps)
The number of fish caught by Sarah = 8
And, The number of fish caught by Christina = 23
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Christina and Sarah went on a fishing trip and caught 31 fish.
Now,
Let number of fish caught by Sarah = x
So, The number of fish caught by Christina = 3x - 1
Here, Christina and Sarah went on a fishing trip and caught 31 fish.
Hence, We get;
⇒ x + (3x - 1) = 31
⇒ 4x - 1 = 31
⇒ 4x = 31 + 1
⇒ 4x = 32
⇒ x= 8
Thus, The number of fish caught by Sarah = x
= 8
So, The number of fish caught by Christina = 3x - 1
= 3×8 - 1
= 23
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Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation , where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
Answer:
168
Step-by-step explanation:
you would times 3.75 by 82 and subtract the answer from 2071.50 and get 1764 then divide 1764 by 10.50 and get 168
Answer:
168 adult adult ticket were sold
Step-by-step explanation:
Hello
The tickets cost for adults is $10.50
The tickets cost for students is $3.75
number of adult ticket sold: A
number of student ticket sold: B
10.50A+3.75B=2071.50 Equation 1
B=82 Equation 2
replacing equation 2 in equation 1
10.50A+3.75(82)=2071.50
10.50A=2071.50-307.50
[tex]A=\frac{1764}{10.50} \\\\A=168\\\\\\[/tex]
168 adult adult ticket were sold
Have a great day.
Solve this system of linear equations.separate the x- and y-value with a comma. -6x=-4-y -7x=-22+y.
Answer:
(2,8)
Step-by-step explanation:
Add them together to get rid of the y.
-6x = -4 - y
-7x = -22 + y
=
-13x = -26
Then solve for x.
-13x/-13 = -26/-13
x = 2
Now plug in the x value into either equation and solve for y.
-7(2) = -22 + y
-14 = -22 + y
-14 + 22 = -22 + 22 + y
8 = y
So...
x = 2
y = 8
(2,8)
Answer:
The solution is (-2, -16).
Step-by-step explanation:
-6x = -4-y can be solved for y: y = 6x - 4
-7x = -22 + y
In the second equation, substitute 6x - 4 for y:
-7x = -22 + 6x - 4
Grouping like terms: 0 = -22 + 6x + 7x - 4, or
-26 = 13x
So x = -2. If x = -2, we can obtain the value of y from y = 6x - 4 (see above).
y = 6(-2) - 4 = -16
The solution is (-2, -16).
Ratio of a to c
Please answer
Answer:
Step-by-step explanation:
a/b=4/5 b/c=2/9
Ration of a to c is
a/c=4/9
Answer:
[tex]\frac{8}{45}[/tex]
Step-by-step explanation:
[tex]\frac{a}{c}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{b}{c}[/tex]
= [tex]\frac{4}{5}[/tex] × [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{45}[/tex]
I need help please.
Answer:
56 oz
Step-by-step explanation:
1 pound = 16 ounces
16 * 3.5 = 56
3.5 pounds = 56 ounces
I hope I helped!
Let me know if you need anything else!
~ Zoe
16x3=48 half of 16 is 8 so 48+8=56 :)
Find the distance between the two points.
(-1, -3), (1, 3)
the distance between the two points is ____ units.
[tex]2\sqrt{10}[/tex]
Explanation1. Use Distance formula
Important to use distance formula in such problems, so keep this formula memorized for future use.
The formula to find distance amongst two points is
[tex]\sqrt{(x^2-x^1)^2 + (y^2 - y1)^2}[/tex]
2. Plug in the numbers into the formula:
1 -(-1)^2 + 3 - (-3)^2
[tex]2^2=4[/tex]
[tex]6^2 = 36[/tex]
36 + 4 = 40
3. Find the square root of 40.
[tex]\sqrt{40}[/tex]
Simplify further:
[tex]2\sqrt{10}[/tex]
The distance between two points (-1, -3) and (1, 3) in a 2-dimensional Cartesian system is √40 units or approximately 6.32 units.
Explanation:The subject of this question relates to finding the distance between two points in a 2-dimensional Cartesian system. This can be done using the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. That is the square root of the sum of the squares of the differences of the x-coordinates and the y-coordinates of the two points respectively.
Here, we have points (-1, -3) and (1, 3). Substituting into the distance formula, we get:
d = √[(1--1)² + (3--3)²]
= √[(2)² + (6)²] = √[4 + 36] = √40
So the distance between the points (-1, -3) and (1, 3) is √40 units, which is approximately 6.32 units.
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What are the solutions of x^2-2x+26=0?
Answer:
x = 1 + (i)5 and x = 1 - (i)5
Step-by-step explanation:
x^2-2x+26=0 can be rewritten by completing the square of x^2-2x, as follows:
x^2-2x+26=0
x^2-2x+ 1 - 1 +26=0 (this 1 comes from halving the coefficient of x (which is -2), obtaining -1, squaring the result, and then adding this 1 to and subtracting this 1 from x^2-2x) → x^2-2x+ 1 - 1 +26=0
Rewriting x^2-2x+ 1 as the square of a binomial, we get:
(x - 1)² - 1 +26=0, or (x - 1)² - 1 +26=0, or (x - 1)² = -25
Taking the square root of both sides yields x - 1 = ±(i)5.
Thus, the roots are x = 1 + (i)5 and x = 1 - (i)5 (Answer C)
A car stuck in traffic travels 75 feet in one minute. In each subsequent minute, the car travels three-fourths the distance it traveled in the previous minute. How far does this car travel in 6 minutes?
Answer:
246.61 feet (rounded to 2 decimal places)
Step-by-step explanation:
We multiply 3/4 with previous minute traveling.
Minute #1: travels 75 feet
Minute #2: travels (3/4)*75 = 56.25 ft
Minute #3: travels (3/4)(56.25) = 42.19 ft
Minute #4: travels (3/4)(42.1875) = 31.64 ft
Minute #5: travels (3/4)(31.64) = 23.73 ft
Minute #6: travels (3/4)(23.73) = 17.80 ft
So, in 6 minutes, the car travels 75 + 56.25 + 42.19 + 31.64 +23.73 + 17.80 = 246.61 feet.
(Tn) is an arithmetic sequence in which T3-T5=6, T4= 16 , find the (n)th term and find the order and the value of the first negative term in this sequence . Please help
Since [tex]T_n[/tex] is arithmetic, it's given recursively by
[tex]T_n=T_{n-1}+c[/tex]
where [tex]c[/tex] is a fixed number and [tex]T_1[/tex] is the starting term in the sequence. We have
[tex]T_n=T_{n-2}+2c[/tex]
[tex]T_n=T_{n-3}+3c[/tex]
and so on, so that
[tex]T_n=T_1+(n-1)c[/tex]
We're told that [tex]T_4=16[/tex], so
[tex]16=T_3+c[/tex]
and
[tex]T_5=16+c[/tex]
so that
[tex]T_3-T_5=(16-c)-(16+c)=-2c=6\implies c=-3[/tex]
Then the first term in the sequence is [tex]T_1[/tex]:
[tex]T_4=T_1+3(-3)\implies T_1=25[/tex]
and the sequence has general formula
[tex]T_n=25-3(n-1)\implies\boxed{T_n=28-3n}[/tex]
The first negative term occurs for
[tex]28-3n<0\implies28<3n\implies n>\dfrac{28}3[/tex]
[tex]\implies n=10[/tex]
The first negative term in the sequence is [tex]T_{10}=28-3\cdot10=\boxed{T_{10}=-2}[/tex].
Write 40/32 in simplest form
The required fraction 40/32 simplifies to 5/4.
To simplify the fraction 40/32, we can find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.
The prime factorization of 40 is 2³ * 5, and the prime factorization of 32 is 2⁵. The common factors between 40 and 32 are 2³, so the GCD is 2³ = 8.
Dividing both the numerator and denominator by 8, we get:
40/32 = (40 ÷ 8) / (32 ÷ 8) = 5/4
Therefore, 40/32 simplifies to 5/4.
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To simplify 40/32, find the greatest common divisor (GCD) of 40 and 32, which is 8. Divide both the numerator and the denominator by 8 to get the simplest form 5/4.
To simplify the fraction 40/32, we need to find the greatest common divisor (GCD) of the numerator (40) and the denominator (32). The GCD is the largest number that can evenly divide both the numerator and the denominator.
List out the factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.List out the factors of 32: 1, 2, 4, 8, 16, 32.The greatest common factor is 8.Divide both the numerator and the denominator by the GCD (8):40 ÷ 8 = 532 ÷ 8 = 4Thus, 40/32 simplified is 5/4.
Suppose f(x) = x^2. what is the graph of g(x) = f(2x)?
Answer:
C
Step-by-step explanation:
Substitute 2x into the equation where x is located. G(x)= (2x)^2=4x^2. This will be a graph which has been vertically stretched has a very steep curve to it facing up. It is C.
Answer:
C
Step-by-step explanation:
if John has 5 apples and gives away 3 how many apples does he have?
if this is some kind of riddle then i think its 5
Kyle is practicing for a 3-mile race. His normal time is 23 minutes 25 seconds. Yesterday it took him only 21 minutes 38 seconds. How much faster was Kyle's time yesterday than his normal time?
Kyle was 1 minute and 47 seconds faster in a 3-mile race yesterday compared to his normal running time.
Kyle's normal time is 23 minutes and 25 seconds, which is (23 * 60) + 25 = 1405 seconds. Yesterday, Kyle's time was 21 minutes and 38 seconds, which is (21 * 60) + 38 = 1298 seconds.
Now, we subtract the faster time from the normal time: 1405 seconds - 1298 seconds = 107 seconds.
Thus, Kyle was 107 seconds faster yesterday than his normal time. To put it back into minutes and seconds, we divide by 60: 107 \ 60 = 1 minute and 47 seconds.
So, Kyle was 1 minute and 47 seconds faster yesterday.
What is the solution of 9x-8=34x-12
The equation 9x-8=34x-12 is a linear equation which is solved by moving variables and numerals at the opposite sides of the equation. This simplifies to -25x = 4 and by dividing both sides by -25, the answer x=-0.16 is obtained.
Explanation:The subject of your question is a linear equation, more specifically, the solution to the equation 9x-8=34x-12. To find the solution, firstly bring variables to one side and numerals to the other side of the equation. So, it becomes 9x - 34x = 12 - 8, which simplifies to -25x = 4.
Then, solve for 'x' by dividing both sides by -25. This yields x = -4/25 or x = -0.16. So, x=-0.16 is the solution to the original equation 9x-8=34x-12.
Such questions involve understanding the principles of algebraic manipulation and the resolution of linear equations, which are fundamental concepts in mathematics.
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PLEASE HELP ASAP !!
-
A right triangle has an angle of 38 degrees and an opposite leg of 12 yards. Solve the right triangle. Label each of your solutions. Round to two decimals.
ANSWER
See below
EXPLANATION
To solve the triangle means to find all sides and angles.
The right triangle has an angle of 38 degrees and an opposite leg of 12 yards
The third angle is 90-38=52°
We use the sine ratio to find the hypotenuse, h.
[tex] \sin(38 \degree) = \frac{opposite}{hypotenuse} [/tex]
[tex] \sin(38 \degree) = \frac{12}{h} [/tex]
[tex]h = \frac{12}{ \sin(38) } [/tex]
[tex]h = 19.49[/tex]
The hypotenuse is 19.49 yards to the nearest hundredth.
We can find the adjacent leg using the cosine ratio.
[tex] \cos(38) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(38) = \frac{a}{19.49} [/tex]
[tex]a = 19.49 \cos(39) [/tex]
[tex]a = 15.36[/tex]
to the nearest hundredth.
Solve the equation. 6(2x - 3) + 4 = 16 - (-18)
6(2x-3)+4 = 16-(-18)
(6)(2x)+(6)(-3)+4 = 16+18
12+ -18+4 = 16+18
(12x)+(-18+4) = (16+18)
12x+ -14 = 34
12x-14 = 34
12x-14+14 = 34+14
12x = 48
12x/12 = 48/12
x = 4
2. There are some benches in a classroom. If 4 students sit on each bench then 3 benches
remains empty and if 3 students sit on each bench then 3 students remain standing.
Find the number of students in the class.
I will surely give 10 points.
Answer: There are 48 students in the class.
Step-by-step explanation:
Let the number of students = S
Let the number of benches = B
If 4 students sit on each bench, 3 benches are left vacant.
S = 4(B - 3)
S = 4·B - 12 } Equation 1
If 3 students sit on each bench, 3 students still standing.
S = 3·B + 3 } Equation 2
We can match the two equations because they both indicate the same number of students.
4B - 12 = 3·B + 3
on solving this
4·B - 3·B = 3 + 12
B = 15 → number of benches
That is the number of benches, therefore substituting the value for B in equation 1
S = 4·B - 12 Equation 1
S = 4·15 -12
S = 60 - 12 = 48 → number of students
Answer: There are 48 students in the class.
VerificationThere are 48 students and 15 benches.
If 4 students sit on each bench, 3 benches are left vacant.
48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.
If 3 students sit on each bench, 3 students still standing.
15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.
Checked!![tex]\textit{\textbf{Spymore}}[/tex]
Final answer:
By creating a system of equations from the given conditions, the number of students in the class is calculated to be 48.
Explanation:
To find the number of students in the class based on the provided scenario, we can set up a system of equations based on the given conditions:
If 4 students sit on each bench, 3 benches remain empty.
If 3 students sit on each bench, 3 students remain standing.
Let's use B to represent the total number of benches and S to represent the total number of students. The first condition tells us that when 4 students sit on each bench, there are B - 3 benches filled, which means 4(B - 3) students are seated. The second condition implies that if 3 students sit on each bench, all the benches are filled, and 3 more students are still standing, which can be represented by 3B + 3.
Therefore, we can write two equations as follows:
4(B - 3) = S
3B + 3 = S
Since both expressions equal S, we can set them equal to each other:
4(B - 3) = 3B + 3
Simplifying this equation, we can find the number of benches (B), and then substitute back to find the number of students (S).
4B - 12 = 3B + 3
B = 3 + 12 = 15 benches
Now we substitute B into one of our original equations to find S:
S = 4(B - 3)
S = 4(15 - 3)
S = 4 × 12
S = 48 students
Therefore, there are 48 students in the class.
What is f(g(x)) for x > 5?
f(g(x)) (you plug/substitute g(x) into x)
f(x) = 4x - √x
f(g(x)) = 4(g(x)) - √(g(x)) since g(x) = (x - 5)², you can do:
f(g(x)) = 4(x - 5)² - √(x - 5)² The ² and √ cancel each other, leaving
f(g(x)) = 4(x - 5)² - (x - 5) Next factor out (x - 5)² or (x - 5)(x - 5)
f(g(x)) = 4(x² - 10x + 25) - (x - 5) Now distribute the 4 and the -
f(g(x)) = 4x² - 40x + 100 - x + 5 Simplify
f(g(x)) = 4x² - 41x + 105 Your answer is B
ANSWER
[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 4x - \sqrt{x} [/tex]
and
[tex]g(x) = {(x - 5)}^{2} [/tex]
To find
[tex]f(g(x)) = f( {(x - 5)}^{2} )[/tex]
[tex]f(g(x)) =4 {(x - 5)}^{2} - \sqrt{{(x - 5)}^{2} } [/tex]
We expand and simplify to obtain,
[tex]f(g(x)) =4 {( {x}^{2} - 10x + 25)} - (x - 5)[/tex]
[tex]f(g(x)) =4{x}^{2} - 40x + 100 - x + 5[/tex]
Combine similar terms to get;
[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]
The correct choice is B.
Using the linear equation 3x+2y=6, express x in terms of y
Answer:
2-2/3y
Step-by-step explanation:
First, you rearrange the equation, to get 3x=6-2y.
Then, you would divide all of the terms by 3, in order to get the value of x
x=2-2/3y