Answer:
A
Step-by-step explanation:
Work with the two points
Formula
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = 1
x2 = - 2
x1 = - 5
Solution
m = (3 - 1) / (-2 - - 5)
m = 2 / (-2 + 5)
m = 2 / 3
Answer: A
Answer:
[tex]\large\boxed{\text{A.}\,2/3}[/tex]
Step-by-step explanation:
In this question ,we're trying to find the slope with the given points.
We would use the slope-formula to find the slope.
Slope-formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
We would plug in the numbers to their right spots in the formula. The second y-coordinate going to y2, the second x coordinate going to x2, and etc.
Your equation should look like this:
[tex]m=\frac{3-1}{-2-(-5)}[/tex]
Now we solve:
[tex]m=\frac{3-1}{-2-(-5)} \\\\m=\frac{2}{-2-(-5)}\\\\\text{Carry the negative over to the 5, turning it to a positive 5}\\\\m=\frac{2}{-2+5}\\\\\text{Add the denominators}\\\\m=\frac{2}{3}[/tex]
When you're done solving, you should get 2/3
This means that the slope is 2/3
I hope this helped you out.Good luck on your academics.Have a fantastic day!What is the measure of PQR
Answer:
C. 86°
Step-by-step explanation:
I just did it on A p 3 x
which of the following correctly describes the end behavior of the polynomial function f(x)=-x^3+x^2-4x+2
Answer:
The left end goes up and the right end goes down.
Step-by-step explanation:
Lets solve the function first and then find out the end behavior of the polynomial:
The given function is f(x)=-x^3+x^2-4x+2
First step is: Identify the degree of the polynomial. For this we have to find out the variable with the largest exponent.
The variable with the largest exponent in the given function is -x³
The degree of the polynomial is the largest exponent on the variable.
3 is the degree of the polynomial.
Since the degree is Odd, the ends of the function will point in the opposite direction.
Now find out the leading coefficient of the polynomial which is -1.
Since the leading coefficient is negative the graph falls to the right.
To find the behavior we have to use the degree of the polynomial as well as the sign of leading coefficient.
If it is ODD and NEGATIVE then the the left end goes up and the right end goes down.
Therefore the end behavior of the given function will be described as "the the left end goes up and the right end goes down"....
what is the first term of the sequence below? ___1, 5,25,125
Answer:
The first term of the sequence is 1/5
Step-by-step explanation:
The first term is 1/5.
The reason is that there is a common ratio between each term. In this case multiplying the previous term in the sequence by 5 would give the next term.
So in this case 1/5 is the first term.
If we multiply 1/5 by 5, it will give the next term which is 1.
1/5*5=1
Thus the first term in the sequence = 1/5....
PLEASE HELP!!!!!!!!!!!!!!Given that B, C, and D are the midpoints of AZYA, find the perimeter of AZYA.
A. 70.6
B. 72.6
C. 76.6
77.6
simplify 3 divided by 5-6i
Answer:
[tex]\frac{15}{61}+\frac{18}{61}i[/tex]
Step-by-step explanation:
[tex]\frac{3}{5-6i}[/tex]
To simplify or to write in the form a+bi, you will need multiply the top and bottom by the bottom's conjugate like so:
[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}[/tex]
Keep in mind when multiplying conjugates you only have to multiply first and last.
That is the product of (a+b) and (a-b) is (a+b)(a-b)=a^2-b^2.
(a+b) and (a-b) are conjugates
Let's multiply now:
[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}=\frac{3(5+6i)}{25-36i^2}[/tex]
i^2=-1
[tex]\frac{15+18i}{25-36(-1)}[/tex]
[tex]\frac{15+18i}{25+36}[/tex]
[tex]\frac{15+18i}{61}[/tex]
[tex]\frac{15}{61}+\frac{18}{61}i[/tex]
For this case we must simplify the following expression:
[tex]\frac {3} {5-6i}[/tex]
We multiply by:
[tex]\frac {5 + 6i} {5 + 6i}\\\frac {3} {5-6i} * \frac {5 + 6i} {5 + 6i} =\\\frac {3 (5 + 6i)} {(5-6i) (5 + 6i)} =\\\frac {3 (5 + 6i)} {5 * 5 + 5 * 6i-6i * 5- (6i) ^ 2} =\\\frac {3 (5 + 6i)} {25-36i ^ 2} =\\\frac {3 (5 + 6i)} {25-36 (-1)} =\\\frac {3 (5 + 6i)} {25 + 36} =\\\frac {3 (5 + 6i)} {61} =\\\frac {15 + 18i} {61}[/tex]
Answer:
[tex]\frac {15 + 18i} {61}[/tex]
Question 1 of 10
2 Points
If F(x) = x- 5 and G(x) = x?, what is G(F(x))?
O A. x2(x-5)
O B. x2 + x-5
O C. (X - 5)2
O D. x2.5
SUBMIT
Answer:[tex]\large\boxed{C.\ (x-5)^2}[/tex]Step-by-step explanation:
[tex]f(x)=x-5,\ g(x)=x^2\\\\g\bigg(f(x)\bigg)-\text{put}\ x-5\ \text{expression instead of}\ x\ \text{in}\ g(x):\\\\g\bigg(f(x)\bigg)=(x-5)^2[/tex]
Find the exact value of sec30º.
Answer:
2 /√3 or 2√3 / 3.
Step-by-step explanation:
Referring to the 30-60-90 triangle: hypotenuse = 2 , smaller leg = 1 and longer leg = √3 and the shorter side is opposite the 30 degree angle.
So cos 30 = √3/2
Sec 30 = 1 / cos 30
= 2 /√3
or 2√3 / 3.
The exact value of sec(30º) using trigonometric identity for secant is 2.
To find the exact value of sec(30º), use the trigonometric identity for secant:
sec(θ) = 1/cos(θ)
Using the special right triangle with angles 30º, 60º, and 90º, it is known that the side lengths are in the ratio 1:√3:2.
The cosine is defined as the adjacent side divided by the hypotenuse.
For a 30º angle, the adjacent side = 1 and the hypotenuse = 2.
So, cos(30º) = 1/2
Substituting this into the formula for secant:
sec(30º) = 1/cos(30º)
= 1/(1/2)
= 2
Therefore, the exact value of sec(30º) is 2.
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The width of a soccer field should be 60% of its length. Write and simplify an expression for the perimeter of a soccer field with a length of x feet.
Answer:
here you go
Step-by-step explanation:
W = (0.6) L
P = 2 ( L + W )
P = 2 [ L + (0.6) L ]
P = 2 ( 1.6 L )
P = (3.2) L
P = (3.2) x
The perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to
[tex]3.2x[/tex] feet.
What is the perimeter?" Perimeter is defined as the total length around the given geometrical shape."
Formula used
Perimeter of the soccer field [tex]= 2 ( L + W)[/tex]
[tex]L=[/tex] length of the soccer field
[tex]W =[/tex] width of the soccer field
According to the question,
Given,
[tex]'x'[/tex] represents the length of the soccer field
As per the given condition,
Width = [tex]60\%[/tex] of length
[tex]= \frac{60}{100} \times x\\\\= 0.6x[/tex]
Substitute the value in the formula to get the perimeter,
Perimeter of the soccer field [tex]= 2 ( x+ 0.6x)[/tex]
[tex]= 2(1.6x)\\\\= (3.2x) feet[/tex]
Hence, the perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to [tex]3.2x[/tex] feet.
Learn more about the perimeter here
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construct a difference table to predict the next term of the sequence -1,3,18,47,93,159,248
Answer:
362
Step-by-step explanation:
-1,3,18,47,93,159,248
First difference (just do term minus previous term):
4, 15, 29, 46, 66 ,89
The first differences are not common.
Second difference (doing term minus previous term)
11, 14, 17, 20, 23
Third difference:
3 ,3 ,3, 3
So it is a cubic because the third differences are the same.
Anyways we don't have to find the explicit form of this sequence. We just have to find the next term.
Let's go back through starting with second difference:
11 , 14, 17, 20, 23 , (25)
(25) would be next term here.
Let's go back to first difference:
4, 15, 29, 46, 66 ,89 , (89+25)
4, 15 ,29, 46, 66, 89 , (114)
Now let's go back to original sequence:
We want 114+248 to be the next term.
That equals 362.
Men and women (ages 22–40) were surveyed to choose a favorite free-time activity: playing sports, dancing, or watching movies/TV. The survey showed the following frequencies: Men—playing sports: 11; dancing: 3; watching movies/TV: 6 Women—playing sports: 5; dancing: 16; watching movies/TV: 9 Which of the following is a correct two-way frequency table for the data?
can you please add the answers to choose from? I'd like to help
Answer:
B. The second graph displayed.
Step-by-step explanation:
Recieved an 100% on my test with this question!!
Hope I could help! (´⊙◞⊱◟⊙｀)
7z-[(2z+y)-(-5y+3z)+9]-12z
Answer:
-4z-6y-9
Step-by-step explanation:
7z-[(2z+y)-(-5y+3z)+9]-12z
=7z-[2z+y+5y-3z+9]-12z
=7z-2z-y-5y+3z-9-12z
=7z-2z-12z+3z-y-5y-9
=-4z-6y-9
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f - g)(x).
O A. (f- g)(x) = x+15
O B. (f- g)(x) = -x+3
OC. (f- g)(x) = -x - 15
O D. (f- g)(x) = 5x + 3
[tex](f-g)(x)=2x-6-(3x+9)=2x-6-3x-9=-x-15[/tex]
Answer:
The correct option is C.
Step-by-step explanation:
The correct option is C.
We have given:
f(x) = 2x - 6 and g(x) = 3x + 9
Now we have to find (f-g)(x)
(f-g)(x) = f(x)- g(x)
Now subtract g(x) from f(x)
(2x - 6) - (3x + 9)
Open the parenthesis. When we open the parenthesis the signs of second bracket will become negative because there is a negative sign outside the bracket.
(f-g)(x)= 2x-6-3x-9
Now solve the like terms:
(f-g)(x)= -x-15
Thus the correct option is C....
Suppose that g(x) = f(x) - 3. Which statement best compares the graph of
g(x) with the graph of Rx)?
Answer:
The graph of g(x) is a translation of f(x) 3 units down.
Step-by-step explanation:
The given function is
[tex]g(x) = f(x) - 3[/tex]
The parent function now is f(x).
The -3 tells us that there is a vertical translation of the parent function 3 units down.
Therefore the graph of g(x) is obtained by translating the graph of f(x) down by 3 units.
Sheila is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of the obstacle, while the y-coordinate is the average time to complete the obstacle, measured in minutes. (1, 8.25), (2, 9.075), (3, 9.9825), (4, 10.98075) Help Sheila use an explicit formula to find the average time she will need for the 8th obstacle.
A. f(8) = 8.25(1.1)^8; f(8) = 17.685
B. f(8) = 8.25(1.1)^7; f(8) = 16.077
C. f(8) = 1.1(8.25)^7; f(8) = 2861345
D. f(8) = 1.1(8.25)^8; f(8) = 23606102
Answer:
f(8) = 8.25(1.1)^7 ; f(8) = 16.077 ⇒ answer B
Step-by-step explanation:
* Lets explain how to solve the problem
∵ The x-coordinate is the number of the obstacle
∵ The y-coordinate is the average time to complete the obstacle
∵ The order pairs of function are (1 , 8.25) , (2 , 9.075) , (3 , 9.9825) ,
(4 , 10.98075)
- From these order pairs
# The time to finish the 1st obstacle is 8.25 minutes
# The time to finish the 2nd obstacle is 9.075 minutes
# The time to finish the 3rd obstacle is 9.9825 minutes
# The time to finish the 4th obstacle is 10.98075 minutes
∵ 2nd ÷ 1st = 9.075/8.25 = 1.1
∵ 3rd ÷ 2nd = 9.9825/9.075 = 1.1
∵ 4th ÷ 3rd = 10.98075/9.9825 = 1.1
∴ There is a constant ratio 1.1 between each 2 consecutive terms
∴ The order pairs formed a geometric series
- Any term in the geometric series Un = a r^(n - 1) , where a is the 1st
term in the series , r is the constant ratio and n is the position of the
term in the series
∵ a = 8.25 ⇒ the time of the first obstacle
∵ r = 1.1
- Sheila wants to find the average time she will need for the 8th
obstacle
∴ n = 8
∵ The explicit formula is f(x) = a r^(n - 1)
∴ f(8) = 8.25 (1.1)^(8 - 1)
∴ f(8) = 8.25(1.1)^7
∴ f(8) = 16.076916 ≅ 16.077
* f(8) = 8.25(1.1)^7 ; f(8) = 16.077
Answer:
Option) BEE is the correct answer!
Step-by-step explanation:
factor this polynomial expression 10x^2-7x-12
[tex]10x^2-7x-12=\\10x^2-15x+8x-12=\\5x(2x-3)+4(2x-3)=\\(5x+4)(2x-3)[/tex]
Answer:
(2x - 3)(5x + 4)
Step-by-step explanation:
Given
10x² - 7x - 12
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 10 × - 12 = - 120 and sum = - 7
The factors are - 15 and + 8
Use these factors to split the x- term
10x² - 15x + 8x - 12 ( factor the first/second and third/fourth terms )
= 5x(2x - 3) + 4(2x - 3) ← factor out (2x - 3) from each term
= (2x - 3)(5x + 4) ← in factored form
find the distance between the points (5, -3) and (0, 2).
Answer:
Distance between points (5, -3) and (0, 2) is √50 or 7.07
Step-by-step explanation:
We need to find distance between two points (5,-3) and (0,2)
The distance formula used is:
[tex]d= \sqrt {\left( { x_2-x_1 } \right)^2 + \left( {y_2-y_1} \right)^2 }[/tex]
here
x₁= 5, y₁=-3, x₂=0 and y₂=2
Putting values in the formula:
[tex]d= \sqrt {\left( {x_2-x_1} \right)^2 + \left( {y_2-y_1} \right)^2 }\\d= \sqrt {\left( {0-5} \right)^2 + \left( {2-(-3)} \right)^2 }\\d= \sqrt {\left( {-5} \right)^2 + \left( {2+3} \right)^2 }\\d= \sqrt {25+25}\\d= \sqrt {50}\\d= 7.07[/tex]
So, distance between points (5, -3) and (0, 2) is √50 or 7.07
How can x^2+3x+1=2x^2+2x+3 be set up as a system of equations?
Answer:
System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.
Step-by-step explanation:
We need to make system of equations of:
x^2+3x+1=2x^2+2x+3
Solving,
Adding -2x^2 on both sides
x^2+3x+1-2x^2=2x^2+2x+3-2x^2
-x^2+3x+1=2x+3
Adding -2x on both sides
-x^2+3x+1-2x=2x+3-2x
-x^2+x+1=3
Adding -3 on both sides
-x^2+x+1-3=3-3
-x^2+x-2=0
Multiplying with -1
x^2-x+2=0
System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.
hey, need some help with this
Step-by-step explanation:
simplify the equation
5-x(2)-3x(4x-7)/(5-x)(3x)
=10-2x-12x²+21x/15x-3x²
=-12x²-23x+10/15x-3x³
the answer is B
yes, Robot is correct but Irum is not
Answer:
simplify the equation first
5-x(2)-3x(4x-7)/(5-x)(3x)
=10-2x-12x²+21x/15x-3x²
=-12x²-23x+10/15x-3x³
the answer is B
Step-by-step explanation:
:)
what expression is equivalent to (3x^2+4x-7)(x-3)
Answer:
[tex]\arge\boxed{B.\ (3x^2+4x-7)(x)+(3x^2+4x-7)(-3)}[/tex]
Step-by-step explanation:
[tex]\text{The distributive property:}\ a(b+c)=ab+ac.\\\\(3x^2+4x-7)(x-3)=(3x^2+4x-7)(x)+(3x^2+4x-7)(-3)[/tex]
Kinley bought 3 notebooks that cost the same and a poster that cost $6. She spent $20.40 in all. What was the cost of each notebook?
Answer:
the cost of each notebook is $4.8
Step-by-step explanation:
Cost of each notebook= ?
Cost of a poster = $6
Total amount she spent = $20.40
If we subtract the cost of poster from total amount we get the cost of 3 notebooks.
$20.40-$6
=$ 14.4
It means the cost of 3 notebooks = $14.4
To find the cost of each notebook divide the cost of 3 notebooks by the number of books.
=14.4/3
=$4.8
Thus the cost of each notebook is $4.8....
The average (arithmetic mean) of k scores
is 20. The average of 10 of these scores
is 15. Find the average of the remaining
scores in terms of k.
(A) 20k +150/10
(B) 20k -150/10
(C) 150-20k/10
(D) 150 - 20k/k-10
(E) 20k -150/k-10
Answer:
(E) (20k - 150)/(k - 10)
Step-by-step explanation:
Sum of all scores = average × number of scores = 20 × k = 20k
Sum of 10 scores = 15 × 10 =150
Sum of remaining scores = 20k - 150
Number of remaining scores = k -10
Average of remaining scores = sum of remaining/no. remaining
= (20 k -150)/(k-10)
use a graphing calculator to solve the equation 3tan1/3theta=8 in the interval 0 to 2pi round your answers to the nearest hundredth
A. 1.21,4.35
B. 3.64
C. 1.21, 2.26, 3.31, 4.35, 5.40
D. .404, 1452.5, 3.55, 4.59, 5.64
Answer:
B. 3.64 to the nearest hundredth.
Step-by-step explanation:
3tan1/3theta=8
tan1/3theta = 8/3
1/3 theta = 1.212 radians, 1.212 + π radians.
theta = 1.212 * 3 = 3.636 radians, 3(1.212 + π) radians.
The second value is greater than 2π radians.
The correct answer is C. 1.21, 2.26, 3.31, 4.35, 5.40.
To solve the equation [tex]\( 3 \tan \frac{1}{3}\theta = 8 \)[/tex] in the interval[tex]\( 0 \) to \( 2\pi \)[/tex], we first isolate [tex]\( \tan \frac{1}{3}\theta \):[/tex]
[tex]\[ \tan \frac{1}{3}\theta = \frac{8}{3} \][/tex]
Next, we take the inverse tangent (arctan) of both sides to solve for
[tex]\[ \frac{1}{3}\theta = \arctan\left(\frac{8}{3}\right) \][/tex]
Now, we multiply both sides by 3 to solve for [tex]\( \theta \)[/tex]:
[tex]\[ \theta = 3 \cdot \arctan\left(\frac{8}{3}\right) \][/tex]
Using a graphing calculator, we find the values of [tex]\( \theta \)[/tex] that satisfy the equation within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \)[/tex]. The calculator will give us the principal value and we need to consider all solutions within the given interval, taking into account the periodicity of the tangent function.
The principal value for [tex]\( \arctan\left(\frac{8}{3}\right) \)[/tex] is approximately[tex]\( 1.21 \)[/tex] radians. Since the tangent function has a period of[tex]\( \pi \)[/tex], we add multiples of[tex]\( \pi \)[/tex] to find other solutions within the interval [tex]\( 0 \)[/tex] to [tex]\( 2\pi \).[/tex]
[tex]\[ \theta \approx 1.21 + k\pi \][/tex]
where [tex]\( k \)[/tex] is an integer such that[tex]\( \theta \)[/tex] remains within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \).[/tex]
For[tex]\( k = 0 \):[/tex]
[tex]\[ \theta \approx 1.21 \][/tex]
For [tex]\( k = 1 \):[/tex]
[tex]\[ \theta \approx 1.21 + \pi \approx 4.35 \][/tex]
For[tex]\( k = 2 \):[/tex]
[tex]\[ \theta \approx 1.21 + 2\pi \approx 7.49 \][/tex]
However, this value is outside our interval, so we do not include it.
For[tex]\( k = 3 \):[/tex]
[tex]\[ \theta \approx 1.21 + 3\pi \approx 10.63 \[/tex]]
This value is also outside our interval, so we do not include it.
Since the tangent function is periodic with a period of [tex]\( \pi \),[/tex] we also need to consider the solutions in the second half of the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \),[/tex] which are obtained by subtracting the principal value from[tex]\( 2\pi \):[/tex]
[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]
[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]
For [tex]\( k = 0 \)[/tex]:
[tex]\[ \theta \approx 2\pi - 1.21 \approx 5.40 \][/tex]
For [tex]\( k = 1 \)[/tex]:
[tex]\[ \theta \approx 2\pi - 1.21 + \pi \approx 8.54 \][/tex]
This value is outside our interval, so we do not include it.
Therefore, the solutions within the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], rounded to the nearest hundredth, are: [tex]\[ \boxed{1.21, 2.26, 3.31, 4.35, 5.40} \][/tex]
Note that [tex]\( 2.26 \)[/tex] and [tex]\( 3.31 \)[/tex] are obtained by adding [tex]\( \pi \) to \( 1.21 \)[/tex] and [tex]\( 2.26 \)[/tex]respectively, which are the first two solutions in the first half of the interval. These values are within the interval [tex]\( 0 \) to \( 2\pi \)[/tex] and are also solutions to the original equation.
What percent is 48cm of 1.5 m
First of all, recall that 1.5m is the same as 150cm.
Now, we simply build a proportion where we consider 48 to be 100, and wonder what 150 will be:
[tex]48\div 100 = 150 \div x[/tex]
Solving for x, we have
[tex]x = \dfrac{150\cdot 100}{48}=\dfrac{15000}{48} = 312.5[/tex]
Which actually makes sense, because we're stating that 1.5m is about 300% of 48cm, which means three times as much. Which is true, because three times 48cm means 144cm, which is about 1.5m
Answer:
32%Step-by-step explanation:
To solve this problem, you must first have the numbers in the same units, that is, convert the meters to centimeters and operate with them or transform to meters and work with them, therefore, I decide to work with centimeters, like this:
1.5 meters = 150 centimeters (each meter equals 100 centimeters)Then, you can make a simple rule of three, where 150 centimeters corresponds to 100% and you look for the percentage of 48 centimeters:
150 cm = 100% 48 cm = XSo:
X = (48 * 100) / 150 X = 4800/150 X = 32Therefore, the percentage of 48 centimeters is equal to 32%.
If the figure below is rotated 90degrees clockwise about the origin, what is the new location? the options are:
A’ (0, 8), B’ (6, 0), C’ (0, -8), D’ (0, -6)A’ (-8, 0), B’ (0, 6), C’ (8, 0), D’ (0, -6)A’ (0, 8), B’ (6, 0), C’ (0, -8), D’ (-6, 0)A’ (0, -8), B’ (6, 0), C’ (0, 8), D’ (-6, 0)
Answer:
A'(0, -8), B'(6, 0), C'(0, 8), D'(-6, 0)
Step-by-step explanation:
Whenever you are doing a 90° clockwise rotation ABOUT THE ORIGIN, it is in the form of [y, -x], meaning you take the y and make it your x, then take your original x and put its OPPOSITE.
90° counterclockwise rotation → [-y, x]
90° clockwise rotation → [y, -x]
I hope this helps, and as always, I am joyous to assist anyone at any time.
The picture shows the arrangement of balls in a game of boccie. The object of the game is to throw your ball closest to the small, white ball, which is called the pallino The green ball is the midpoint between the red ball and the pallino. The distance between the green ball and the red ball is 10 inches. The distance between the yellow
ball and the pallino is 8 inches. Which ball is closer to the pallino, the green ball or the yellow ball? Explain.
Answer:
Step-by-step explanation:
Distance of yellow to white = 8 inches which is given
The green ball is at the midpoint of red to white.
Since the green ball is 10 inches to the red ball, the green ball is also 10 inches from the white ball. That's what a midpoint is.
The yellow ball is closer.
find the real numbers that satisfy the equation
x=35.3
Answer:
35.3
Step-by-step explanation:
Actually, there are none but 35.3. Here you have already defined x as 35.3. 35.3 satisfies the given equation.
The solution to the given equation x = 35.3 is simply x equals 35.3. There are no further calculations required for this straightforward linear equation.
Explanation:The equation given, x = 35.3, is a simple linear equation where the variable x is already isolated on one side of the equation. The solution to this equation is straightforward: x equals 35.3. There is no need for further calculation or iterative numerical methods, as this is not a quadratic equation nor does it require techniques such as least squares to find a solution. The equation simply states that x is equal to the real number 35.3.
However, if you are given a quadratic equation or more complex equations, there can be different methods to solve for x. For example, the quadratic formula, iterative methods, or writing computer programs for finding least squares solutions in systems of equations with multiple variables.
Which of the following data sets has the mean, median, and mode as the same number?
A. 10,10,12,12,13,13
B. 2,3,4,4,5,7
C. 4,7,11,11,16,17
D. 1,2,3,3,5,6
Answer:
C. 4, 7, 11, 11, 16, 17
Step-by-step explanation:
The mean is the average of the numbers'
The median is the middle number
The mode is the number that occurs most often.
Let's look at each data set I turn.
A. 10, 10, 12, 12, 13, 13
Mean = 11. 7; Median: = 12; Modes: 10, 12, 13
All three measures are different.
B. 2, 3, 4, 4, 5, 7
Mean = 4.2; median = 4; mode = 4
Median and mode are the same, but the mean is different.
C. 4, 7, 11, 11, 16, 17
Mean = 11; median = 11; mode = 11
All three measures are the same.
D. 1, 2, 3, 3, 5, 6
Mean = 3.3; median = 3; mode = 3
Median and mode are the same, but the mean is different.
Make n the subject of the formula t= square root of n+3/n
Step-by-step explanation:
hi I have answered ur question
To make n the subject of the formula t = square root of n+3/n, we can isolate the square root term by squaring both sides of the equation and rearranging the equation to make n the subject.
Explanation:To make n the subject of the formula t = √(n+3)/n, we can start by isolating the square root term. To do this, we square both sides of the equation:
t2 = √(n+3)/n2
Next, we can multiply both sides by n2 to get rid of the denominator:
t2n2 = n + 3
Finally, we can rearrange the equation to make n the subject:
n = (t2n2 - 3)/t2
Learn more about Making n the subject of a formula here:https://brainly.com/question/32039678
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There are 9 students in a class. The teacher chooses 2 students to go to the
library. The order in which they are chosen does not matter. How many ways
are there to choose the students?
Answer: 72
Step-by-step explanation:
There are 9 students to choose from to go the library. After that person is chosen there are 8 students remaining.
First student and Second student
9 x 8 = 72
There are 36 ways for a teacher to choose 2 students out of 9 to go to the library, using combinations where the order of selection is not important.
The student is asking how many ways there are to choose 2 students out of 9 to go to the library, with the order of selection being irrelevant. This is a classic combinatorics problem that involves calculating combinations. Combinations are used in mathematics to count selections where order does not matter.
To find the number of combinations, denoted as C(n, k), where n is the total number of available options and k is the number of selections made, you can use the formula C(n, k) = n! / (k! * (n - k)!), where ! denotes a factorial. For this specific problem, the formula becomes C(9, 2) = 9! / (2! * (9 - 2)!), which simplifies to C(9, 2) = 9 * 8 / (2 * 1) = 36 ways to choose 2 students out of 9.
State the degree: 11m^3n^2p
Explanation:
Using the rule that x = x^1, we can rewrite the p as p^1
So 11m^3n^2p is the same as 11m^3n^2p^1
The exponents are: 3, 2, 1
Those exponents add up to 3+2+1 = 6
The degree of a monomial like this is simply equal to the sum of the exponents.
Answer:
6
Step-by-step explanation: