Answer:
n^2/4
Step-by-step explanation:
If n is the number, squared is n^2
Quotient if this number and four is
n^2/4
The quotient of a number squared and four will be n² / 4.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Division means the separation of something into different parts, sharing of something among different people, places, etc.
The square of a number is the multiplication of that number with itself.
Let the number be n.
Then the square of the number n will be given as,
⇒ n²
The quotient of a number squared and four will be given as,
⇒ n² / 4
Thus, the quotient of a number squared and four will be n² / 4.
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Find the equation of the tangent line to the curve at the given point?
y = x cot(x) at the point with x-coordinate= π/4
Answer:
The equation of the tangent line
[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]
Step-by-step explanation:
Step(i):-
Given function y = x cot (x) ....(i)
Differentiating equation (i) with respective to 'x' , we get
[tex]\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)[/tex]
Step(ii):-
The slope of the tangent line
[tex]\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x[/tex]
[tex](\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}[/tex]
We will use trigonometry formulas
[tex]Cosec(\frac{\pi }{4} ) = \sqrt{2}[/tex]
[tex]sec(\frac{\pi }{4} ) = \sqrt{2}[/tex]
[tex]Cot(\frac{\pi }{4} ) = 1[/tex]
Now the slope of the tangent
[tex]\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1[/tex]
[tex]\frac{dy}{dx} =-\frac{\pi }{2} +1[/tex]
Step(iii):-
Given
Substitute [tex]x=\frac{\pi }{4}[/tex] in y = x cot (x)
[tex]y = \frac{\pi }{4} cot (\frac{\pi }{4} )[/tex]
[tex]y = \frac{\pi }{4}[/tex]
The point of the tangent line [tex](x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )[/tex]
The equation of the tangent line
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]
Simplify 0.5x-2y > 3
I will assume you want it in the form of y>mx+b
0.5x-2y>3
0.5x-3>2y
0.25x-1.5>y
Answer:
[tex]x>4y+6[/tex]
Step-by-step explanation:
[tex]0.5x-2y>3[/tex]
First, we will have to add 2 to both sides.
[tex]0.5x-2y+2y>3+2y[/tex]
This equals to
[tex]0.5x>2y+3[/tex]
Now, we will make this into a fraction and divide. We will divide by 0.5.
[tex]\frac{0.5x}{0.5} >\frac{2y+3}{0.5}[/tex]
Now that we divided, we got our answer!
[tex]x>4y+6[/tex]
Hope this helps!
4(2x+6)=5(x+5)+2 Infinite solutions Infinite solutions No solution No solution One solution; x=0One solution; x is equal to 0 One solution; x=1
Answer:
x = 1
Step-by-step explanation:
Solve for x:
4 (2 x + 6) = 5 (x + 5) + 2
Hint: | Distribute 5 over x + 5.
5 (x + 5) = 5 x + 25:
4 (2 x + 6) = 5 x + 25 + 2
Hint: | Group like terms in 5 x + 2 + 25.
Grouping like terms, 5 x + 2 + 25 = 5 x + (25 + 2):
4 (2 x + 6) = 5 x + (25 + 2)
Hint: | Evaluate 25 + 2.
25 + 2 = 27:
4 (2 x + 6) = 5 x + 27
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
8 x + 24 = 5 x + 27
Hint: | Move terms with x to the left hand side.
Subtract 5 x from both sides:
(8 x - 5 x) + 24 = (5 x - 5 x) + 27
Hint: | Combine like terms in 8 x - 5 x.
8 x - 5 x = 3 x:
3 x + 24 = (5 x - 5 x) + 27
Hint: | Look for the difference of two identical terms.
5 x - 5 x = 0:
3 x + 24 = 27
Hint: | Isolate terms with x to the left hand side.
Subtract 24 from both sides:
3 x + (24 - 24) = 27 - 24
Hint: | Look for the difference of two identical terms.
24 - 24 = 0:
3 x = 27 - 24
Hint: | Evaluate 27 - 24.
27 - 24 = 3:
3 x = 3
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 3 x = 3 by 3:
(3 x)/3 = 3/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
x = 3/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
Answer: x = 1
A normal population has the mean of 10 and the variance of 25 . A random sample of size n-28 is selected.
(a) Find the standard deviation of the sample mean. Round your answer to two decimal places (e.g. 98.76)
(b) How large must the sample be if you want to halve the standard deviation of the sample mean?
Answer:
Step-by-step explanation:
Given that:
population mean = 10
variance [tex]\sigma^2[/tex] = 25 ; [tex]\sigma[/tex] =[tex]\sqrt{ 25}[/tex] = 5
sample size n = 28
The standard deviation of the sample mean:
= [tex]{\dfrac{5}{\sqrt{28}}[/tex]
= 0.95
To halve the standard deviation of the sample mean, the size of how large the sample will be can be computed as follows:
[tex]\dfrac{sd_1}{sd_2} = \dfrac{\dfrac{\sigma}{\sqrt{n}} }{\dfrac{\sigma}{\sqrt{n}} }[/tex]
[tex]\implies \dfrac{\dfrac{5}{\sqrt{28}} }{\dfrac{5}{\sqrt{28}} }[/tex]
[tex]= \dfrac{5}{\sqrt{28}} \times \dfrac{\sqrt{28}}{5}[/tex]
= 2
n = 4 × 28
n = 112
The standard deviation is 0.95 and if the standard deviation is halved then the sample mean is 112.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
A normal population has a mean of 10 and a variance of 25.
A random sample of sizes n-28 is selected.
A. The standard deviation will be
[tex]\sigma = \dfrac{\sqrt{Var(x)}}{n} \\\\\sigma = \dfrac{\sqrt{25}}{\sqrt{28}} \\\\\sigma = 0.95[/tex]
B. The sample be if you want to halve the standard deviation of the sample mean
[tex]\rm \dfrac{SD_1}{SD_2} = 2 = \dfrac{\sqrt{n}}{\sqrt{28}}\\\\n = 4*28 \\\\n= 112[/tex]
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Which of the following sets are equal? A = {2, 3, 4} n B = {XER 1 4 x < 5} n C = { ERI 1 < x < 5} n D = {xEZ| 1 < x < 59} n E = {xez | 1 < x < 59} n
Answer:
Step-by-step explanation:
The question is not too clear. check the attachment for better view of the question.
From the options The set A = {2, 3, 4} will be compared to other options to determine which of the remaining set is equivalent to the set A.
x e R means the values in the set are real numbers and real numbers can either be rational or irrational. R= Hence the real numbers between 1 and 5 are not restricted to only positive integer values but also decimal numbers. and since set A does nit contain ant rational number, hence both set B and C are not equivalent to set A.
Also, set B is not equivalent to set C even though the values in both sets are integers. They are not equal because 1 is included in set B but not in set C.
Set D and E are equivalent because they both contains integers between 1 and 5. Integers are positive whole numbers between 1 and 5 since the both sets doesn't contain any negative value. Hence the set A = set D = set E
Find the product of -3/5 • -1.5.
Answer:
0.9
Step-by-step explanation:
I am not sure how to really explain but the 2 negatives equal a positive. So if there is 2 Negatives also know as - = a positive. And a positive is just the the opposite of a negative
The product of the given fractions is 3/25.
The given fractions are -3/5 and -1/5.
What is the product of fractions?The product of two fractions can often be expressed by an equivalent fraction where the numerator and denominator have been divided by a common factor. The product of two fractions is the product of the numerators and the product of the denominators.
Now, multiply the given fractions
-3/5 × -1/5
Multiply numerators and write the result in numerator and multiply denominators and write the result in denominator.
That is, -3/5 × -1/5 = 3/25
Therefore, the product of the given fractions is 3/25.
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Identify the line(s) of symmetry for kite ABCD.
les )
A)line BD
B)line AC
C)line EF
D)no line of symmetry
Answer:Line BD
Step-by-step explanation:
The top is shorter than the bottom, so it can't be AC. EF will only have about half of the section covered. BD is symmetrical so it can't be no lines. So it must be BD.
Which set of numbers could be the side lengths of a right triangle?
A. 3,4,6
B.4,5,7
C. 5, 12, 13
D. 7. 20, 21
E. 8, 15, 16
Why did I get this question wrong?
Answer:
9.25
Step-by-step explanation:
M₄ means the area using 4 rectangles with heights equal to the function evaluated at the midpoints.
The width of each rectangle is (4−0)/4 = 1.
The area of each rectangle is:
M₁ = (1) (1.12) = 1.12
M₂ = (1) (1.80) = 1.80
M₃ = (1) (2.69) = 2.69
M₄ = (1) (3.64) = 3.64
The total area is therefore:
M = 1.12 + 1.80 + 2.69 + 3.64
M = 9.25
Find the slope of the given line, if it is defined. 2x + 1 = 0
Given :
A line 2x + 1 =0 .
To Find :
The slope of the given line .
Solution :
We know , slope of line is given by the tangent of the angle between the x-axis and the line .
Now, for line 2x + 1 =0 i.e [tex]x=\dfrac{-1}{2}[/tex] .
The line is perpendicular to x-axis and cuts the x-axis at [tex]\dfrac{-1}{2}[/tex] .
Therefore , the angle between the line and x-axis is [tex]90^o[/tex] .
So , slope [tex]m=\tan\ 90^o[/tex] i.e undefined .
Therefore , the slope of given line is not defined .
Hence , this is the required solution .
help please
pleaseeee i dont understand
:(
Derive the positive square root of 982081
Answer: 991
square root of 982081 hope this helps
Divide rs 21000 between Nisha and Nishan so that Nisha gets double than Nishan
let the nisha be x and nishan be y
Step-by-step explanation:
ATQ
your statement is x=2y
I get paid $40 a month. If i want 5 less each month, how much should i get paid every week?
Answer:
$5 each week
Step-by-step explanation:
$40 a month
$10 a week
$10-$5 is $5 each week
If you want to be paid $5 less, then every month you will be paid $35
There the amount that you get paid every week will be:
35 ÷ 4 ( 1 month have 4 weeks )
= $8.75
67.9 is ten times as much as what number?
A. 6.79
B. 6,790
C. 607.9
D. 6.7
Answer:
6.79
Step-by-step explanation:
6.79 x 10 = 67.9
The unknown number z would be 6.79
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that 67.9 is ten times as much as unknown number;
Let the unknown number be z;
Z x 10 = 67.9
Now divide by 10 on both sides, we get;
Z = 67.9/10
Z = 6.79
Therefore,
6.79 x 10 = 67.9
Hence, the unknown number z would be 6.79
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I need help with d ASAP plz explain
Answer:
a. g(0)= 1
b. f(-2)= 0
d. g(x-2)= 5x-9
Step-by-step explanation:
a. g(x)=5x+1 *substitute 0 for x*
g(0)= 5(0)+1
g(0)= 1
b. f(-2)= [tex](-2)^2-4[/tex] *substitute -2 for x*
f(-2)= 4-4 =0
c. g(x-2)= 5(x-2)+1 *substitute x-2 for x*
g(x-2)= 5x-10+1 *distributive property*
g(x-2)=5x-9 *simplify*
c
Which equation could you use to solve for x in the proportion 5
- 2
Vx
4X= 14
4x=45
5x= 13
5x = 36
ANSWER QUICK!!
Answer:
4x= 14
Step-by-step explanation:
What number should be placed in the box to help complete the division calculation?
(Long division setup showing an incomplete calculation). 13 is in the divisor, 4231 is in the dividend, and 3 hundreds and 2 tens is written in the quotient. 3900 is subtracted from 4231 to give 331. An unknown value represented by a box is being subtracted from 331.
Answer:
299
Step-by-step explanation:
Solve for y. 6 x + 2y = z
Answer:
[tex]y = \frac{z}{2} -3x[/tex]
Step-by-step explanation:
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents & roots
Multiplication
Division
Addition
Subtraction
& is the order of operation.
First, subtract 6x from both sides:
6x (-6x) + 2y = z (-6x)
2y = z - 6x
Next, divide 2 from both sides:
(2y)/2 = (z - 6x)/2
y = (z - 6x)/2
y = (z/2) - 3x
[tex]y = \frac{z}{2} -3x[/tex] is your answer.
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Lydia owns a food truck that sells tacos and burritos. She only has enough supplies to make 115 tacos or burritos. She sells each taco for $4 and each burrito for $6.75. Lydia must sell at least $680 worth of tacos and burritos each day. If 32 tacos were sold, determine the minimum number of burritos that the Lydia must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.
Answer:
Lydia must sell 552 burritos
Step-by-step explanation:
Name 3 rays in this geometric construction
E
A
D
B
Your answer
Twice a number increased by three times the number?
this is the answer
Step-by-step explanation:
2x+3
Answer:
2x+3x
Step-by-step explanation:
Select all that apply.
Which expressions are equivalent to 6x +18?
6(2+3)
3(2x + 6)
2 (32 +9)
6(x + 18)
3(x+6)
The expression equivalent to 6x + 18 is 3(2x + 6) thus option (B) is correct.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that are all constrained and create an equation.
Expression is very useful to determine the end or root value of constraint.
As per the given,
6x + 18
Take 3 as common,
3(2x + 6)
Hence "The expression equivalent to 6x + 18 is 3(2x + 6)".
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Nick's mom gave him $10 allowance. His little sister was given $4 less than Nick. Write an expression for the amount that Nick's little sister was given
Answer:
Let x be the amount Nick's little sister is given.
x = 10 - 4
The sphere weighs 4 pounds. sorry no picture but you can ask me for it in the comments What is the weight of the cylinder? What is the weight of the cube?
Answer:
The weight is 4 pounds :D
Step-by-step explanation:
Select all that apply which expressions are equivalent to 6X +12
(A) 6(x+12)
(B) x(6+12)
(C) 3(2x+4)
(D) 2(3x+6)
(E) 6(x + 2)
3(2x+4), 2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 6X +12
We have to find the equivalent expressions of 6x+12
Let us take 6 as a common factor we get
6(x+2)
so 6(x+2) is equivalent expression of 6X +12
Now let us take 3 as common factor
3(2x+4)
so 3(2x+4) is equivalent expression of 6X +12
Now let us take 2 as common factor
2(3x+6)
so 2(3x+6) is equivalent expression of 6X +12
Hence, 3(2x+4), 2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12
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answer reeeeeeeeeeeeeeeeeeeeeeeee
Answer:
36 and 49
Step-by-step explanation:
6x6 and 7x7
(30 points) the line contains the point (5,-7) and is parallel to 4x+ 3y =-9 The equation of the line is:
Answer:
4x +3y = -1
Step-by-step explanation:
To find the new constant for the equation, use the given x- and y-values:
4(5) +3(-7) = 20 -21 = -1
The equation of the parallel line in standard form is ...
4x +3y = -1
46 winners divided $33 equally. what decimal is equivalent to the fraction of a dollar that each winner received? round to the nearest hundredths.
Answer:
1.39
Step-by-step explanation:
Which of the following would be considered the most conservative alpha level?
a. .01
b. .05
c. .10
d. .15
Answer:
C.0.1
Step-by-step explanation:
Because this is 10% confidence confirmed