[tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]
solve cosx = 0
x = [tex]cos^{-1}[/tex](0) = [tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]
The solutions to the trigonometric equation: 0.5π radians, 1.5π radians.
How to solve a trigonometric equation
In this question we find the case of a trigonometric equation whose solution must be found:
cos (2π · x / T) = 0
Solution:
2π · x / T = cos⁻¹ 0
2π · x / T = 0.5π + i · π, where i is an integer.
2π · x = π · T · (0.5 + i)
[tex]x = \frac{T\cdot (0.5 + i)}{2}[/tex]
Where T is the period of the trigonometric equation.
If we know that T = 2π, then the solutions to the trigonometric equations are:
x = π · (0.5 + i)
x₁ = 0.5π, x₂ = 1.5π
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Find the value of b if the graph the equation y=−3x+b goes through the given points. A,(-2,4) | B,(5, 2)
A(,-2,4)=b= -2
B,(5,2)= b=17
The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
(−2,−3)
(3, 1)
(1, 3)
(3, 2)
pleaseeeee help i will give brainliest
Answer:
(1, 3)
Step-by-step explanation:
The first number of each pair is the x-coordinate, the horizontal location of the point.
The end points of the graphed line segment are (1, 3) and (-3, -2). It looks like the answer choices are intended to see if you can tell what order the coordinates are expressed in.
The appropriate choice is (1, 3), the upper right end point.
6.
2.Find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin
We need to find the triangle bounded by the y-axis the line [tex]f(x)=9-\frac{6}{7}x[/tex] and the line perpendicular to it that passes through the origin.
This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:
Therefore, this line is the blue one and is written as:
[tex]f(x)=\frac{7}{6}x[/tex]
To find [tex]y(t)[/tex] we need to find the slope and y-intercept. So, taking two points:
[tex]P_{1}(15,150) \ and \ P_{2}(25,450) \\ \\m=\frac{450-150}{25-15}=30[/tex]
So:
[tex]Using \ P_{1}(15,150) \\\\y=30t+b\\\\150=30(15)+b \therefore b=-300 \\\\\boxed{y(t)=30t-300}[/tex]
The y-intercept is [tex]b=-300[/tex] and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.
The x-intercept can be found when y=0 (year 1980), that is:
[tex]y(t)=30t-300 \\\\0=30t-300 \therefore t=10[/tex]
This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.
The slope of this function is [tex]m=30[/tex]
This value tells you that the profit increases $30.000 each year.
Hello,
Please, see the attached files.
Thanks.
during a 500-meter race, a runner ran the first 400 meters in 1 minute and 25 seconds.she finished the race i 2 minutes and 15 seconds. what was her average rate of change during the last 100 meters of the race as a decimal
She ran the last 100 meters in 2:15 -1:25 = 0:50, so her average speed was
... (100 m)/(50 s) = 2.0 m/s
How can you tell by looking at the coordinates of the two triangles that Δ A'B'C' is a 180° rotation of Δ ABC? A) The coordinates cannot prove a 180° rotation. B) The y-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. C) The x-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. D) Both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC.
under a rotation about the origin of 180°
a point (x, y ) → (- x, - y )
hence D is correct, both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC
Answer:
Its D
Step-by-step explanation:
Both coordinates have opposite signs.
Jared has taken out a loan for his car. His monthly payments amount to $650. If his loan is for 36 months, and he paid a down payment of $400, what is the total cost of the car for Jared? A. $15,050 B. $23,800 C. $28,300
B! 650 x 36 +400 = 23,800!
Answer:
$23800.
Step-by-step explanation:
Monthly payment of loan of a car = $650
His loan is for 36 months
So, Total payment of 36 months = [tex]36 \times 650[/tex]
= [tex]23400[/tex]
He paid the down payment of amount $400
So, Total cost of the car = [tex]23400+400[/tex]
= [tex]23800[/tex]
Hence the total cost of the car for Jared is $23800.
So, Option B is correct.
An employment agency specializing in temporary construction help pays heavy equipment operators $ 122 per day and general laborers $ 93 per day. If thirty dash four people were hired and the payroll was $ 3771 comma how many heavy equipment operators were employed? How many laborers?
If all were general laborers, the payroll would be 93·34 = 3162 per day. The payroll is actually 3771 -3162 = 609 more than that.
Each equipment operator makes 29 more than a laborer, so there must be ...
... 609/29 = 21 heavy equipment operators
and 34 -21 = 13 general laborers
_____
If you write an equation for the number of heavy equipment operators (h), you get the same result in the same way. 34-h is the number of laborers
... 122h + 93(34 -h) = 3771 . . . equation for total daily payroll
... 29h + 3162 = 3771 . . . . . . simplify
... 29h = 609 . . . . . . . . . . . . . subtract 3162
... h = 609/29 = 21 . . . . . . . . divide by 29
please help, need answer fast!
What is the simplified expression for -3(2x - y) + 2y + 2(x + y)
a. 8x + y
b. y - 4x
c. 7y - 4x
d. -4x - y
Hey there!!!
Given equation :
... - 3 ( 2x - y ) + 2y + 2 ( x + y )
... -6x + 3y + 2y + 2x + 2y
... -6x + 5y + 2x + 2y
... -4x + 7y
( or )
... 7y - 4x
Hope helps!
Please help!!! The last one. Word answer
Often, variability is most usefully expressed in the same units as the original data. That's what standard deviation (square root of variance) does. In situations where that is the case, the variance is useful only for getting to the value of standard deviation.
I could REALLY use some help on this. I just cant seem to get it.(please help me)
Write an equation for the line parallel to the given line that contains C.
C (3, 6); y= -2 x + 7
y = - 2x + 12
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - 2x + 7 is in this form with slope m = - 2
Parallel lines have equal slopes, thus
y = - 2x + c is the partial equation.
To find c, substitute (3, 6 ) into the partial equation
6 = - 6 + c ⇒ c = 6 + 6 = 12
y = - 2x + 12 ← equation of parallel line
find the sum of (2x^2 +4x-9) +(3x^2-2x+10) please show work
You can eliminate parentheses and combine like terms.
(2x^2 +4x-9) +(3x^2-2x+10)
= 2x^2 +4x-9 +3x^2-2x+10 . . . . . nothing needs to be distributed, so we can simply drop the parentheses
= x^2(2 +3) +x(4 -2) +(-9 +10) . . . group like terms
= 5x^2 +2x +1
Evaluate -a^n when a=3 and n=2,3,4, and 5. Now evaluate (-a)^n when a=3 and n=2,3,4, and 5. Based on the sample, does it appear that -a^n = (-a)^n? If not, state the relationships,if any, between the two.
The attachment shows the requested evaluations.
-a^n ≠ (-a)^n . . . . except when n is an odd integer
a mattress store charges 7% sales tax and a $50 delivery fee. The delivery fee is not subject to sales tax. The following functions represent the situation F(a)=1.07a and g (b)= b+50
Solve for g (f (a)).
Answer: [tex]g(f(a))=1.07a+50[/tex]
Step-by-step explanation:
The given functions are: [tex]f(a)=1.07a[/tex] and [tex]g(b)= b+50[/tex]
[tex]g(f(a))[/tex] means [tex]f(a)[/tex] is the input of the function [tex]g[/tex].
Thus, [tex]g(f(a))= g(1.07a)[/tex]
Now replacing [tex]b[/tex] as [tex]1.07a[/tex] into the given function of [tex]g(b)[/tex], we will get......
[tex]g(1.07a)= 1.07a+50[/tex]
So, [tex]g(f(a))=1.07a+50[/tex]
which of the following demonstrate closure in a polynomial? Select all that apply: A.(x^2+2) (x-1) B.(x^2+2) over (X -1) C.(x+1) plus (X^2-3X -2) D.(X +5)-(3X +6) E.4/8x
Any arithmetic operation on polynomials except division* will result in a polynomial. Appropriate choices are ...
A. (x^2+2) (x-1)
C. (x+1) plus (X^2-3X -2)
D. (X +5)-(3X +6)
E. (4/8)x . . . . . but not if you mean 4/(8x)
_____
* For division, the result may be a polynomial. In the specific example given here for B, it is not.
The term closure in mathematics refers to the property of a set, in this case, polynomials, where doing certain operations (addition, subtraction, multiplication) with any numbers from the set always yields a number within the set. The options demonstrating closure in a polynomial are A, C, D, E, all but option B, which implies division.
Explanation:The term 'closure' in mathematics refers to the property of a set under an operation where the operation performed on any numbers in the set always produces a number that is also in that set. In the case of polynomials, the operations could be addition, subtraction, or multiplication.
The expressions that demonstrate closure in a polynomial for addition, subtraction, and multiplication are all but option B. Option B, '(x^2+2) over (X -1)', isn't representative of closure in a polynomial as it implies a division operation. Polynomial closure doesn't include division because it can produce numbers outside the original set.
So, the correct answers are A.(x^2+2) (x-1), C.(x+1) plus (X^2-3X -2), D.(X +5)-(3X +6) and E.4/8x as they illustrate closure by either multiplication of two polynomials, addition of two polynomials, or subtraction of two polynomials.
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What is the solution of sqrt1-3x=x+3
x = - 1
given [tex]\sqrt{(1-3x)}[/tex] = x + 3
square both sides
1 - 3x = (x + 3 )² ( expand right side using FOIL )
1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )
0 = x² + 9x + 8
0 = ( x + 1)(x + 8)
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = -1
x + 8 = 0 ⇒ x = - 8
As a check
substitute these values into the equation and if both sides are equal then they are the solutions
x = - 1 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true
x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
Solve |P| > 3. a{-3, 3}
b.{P|-3 < P < 3}
c.{P|P < -3 or P > 3}
(c)
given the inequality | P | > a then the solution is always of the form
P < - a or P > a
for | P | > 3 , then
P < - 3 or P > 3
In LaToya’s school
3
8
of the students have a blood type of O+, and
1
12
of the students have a blood type of O–. What fraction of the students in LaToya’s school has a blood type of O+ or O–?
[tex]\frac{11}{24}[/tex]
combine the fractions of each type by adding them
[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{12}[/tex]
Before we can add the fractions we require them to have the same denominator
To achieve this we require the lowest common multiple (LCM ) of 8 and 12
The LCM of 8 and 12 is 24
To change the denominators , multiply the numerator/ denominator by the appropriate value
[tex]\frac{3}{8}[/tex] = [tex]\frac{3(3)}{8(3)}[/tex] = [tex]\frac{9}{24}[/tex]
[tex]\frac{1}{12}[/tex] = [tex]\frac{1(2)}{12(2)}[/tex] = [tex]\frac{2}{24}[/tex]
Add the numerators leaving the denominator as it is
= [tex]\frac{9+2}{24}[/tex] = [tex]\frac{11}{24}[/tex]
Answer:111/24
Step-by-step explanation:
Solve the equation. -3x + 1 + 10x = x + 4
Answer:
[tex]x=[tex]\frac{1}{2}[/tex][/tex]
Step-by-step explanation:
Solving the equation mean finding the value of x
Equation given is:
[tex]-3x+1+10x=x+4[/tex]
Now what we need to do is take the values with x in it to the left side of the equation and the other numbers to the right side of the equation.
[tex]-3x+10x-x=4-1[/tex]
Now simplify values with x and the numbers.
[tex]6x=3[/tex]
[tex]x=[tex]\frac{1}{2}[/tex][/tex]
Therefore [tex]x=[tex]\frac{1}{2}[/tex][/tex]
x = [tex]\frac{1}{2}[/tex]
simplify the left side by collecting like terms
7x + 1 = x + 4 ( subtract x from both sides )
6x + 1 = 4 ( subtract 1 from both sides )
6x = 3 ( divide both sides by 6 )
x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Need some help please.
In the smaller triangle, the corresponding side is 3 times the base length. Since these triangles are similar, the same ratio holds.
... n = 3×5
... n = 15
Jacob tapes down a piece of red tape on a basketball court. The piece of tape is 3/5 yard long. He wants to divide it into sections that are each 1/10 yard long. How many sections will the piece of tape be divided into? 30 points if u answer
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Answer:
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Step-by-step explanation:
!HELP!
Three is a zero of the equation x^3−4x^2−3x+18=0.
Which factored form is equivalent to the equation?
A (x+2)(x−3)^2=0
B (x−2)(x−3)^2=0
C (x+2)(x−√3)(x+√3)=0
D (x−2)(x−3)(x+3)=0
x^3−4x^2−3x+18=0
(x - 3)^2 (x + 2) = 0
Choice B
A
since x = 3 is a zero then (x - 3) is a factor
dividing x³ - 4x² - 3x + 18 by (x - 3) gives
x³ - 4x² - 3x + 18 = (x - 3)(x² - x - 6 ) = 0,
(x - 3)(x - 3 )(x + 2 ) = 0
(x + 2 )(x - 3)² = 0 → A
Two large topping pizzas cost $25.00. what is the constant of proportionality (k)?
E-mails do not require professionalism; it's acceptable to be informal. True False
Write the equation of line in slope-intercept form. Line parallel to y=0.5x+3 that passes through the point (−9,12)
My answer was: y=0.5x+16.5
The math test scores of Mrs. Hunter's class are shown below. 48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100 What is the median of the data? A)80 B) 82 C) 84 D) 88
The median is "B) 82". The word "median" means middle so you have to find the number in the middle. If you cross out the corner numbers and keep doing that until you have one number left, you get the answer.
Answer:
Step-by-step explanation:
A
Explain why P(A|D) and P(D|A) from the table below are not equal.
Answer:
Step-by-step explanation:
Recall the definition for conditional probability.
We have P(A/D) = P(A and D)/P(D)
P(AD) = 2/17
P(A) = 8/17 and P(D) = 10/17
From the definition of conditional probability,
P(A/D) = P(AD)/P(D) = 2/17 divided by 10/17 = 1/5
But P(D/A) = P(AD)/P(A) = 2/17 divided by 8/17 = 1/4
Hence the two are not equal.
This is because there is a difference in the denominators
P(A|D) and P(D|A) from the table are not equal because the total number of A and D are not equal
From the table, we have the following parameters:
n(A) = 8n(D) = 10n(A and D) = 2P(A|D) and P(D|A) are both conditional probabilities, and they are calculated using:
[tex]P(A|D) = \frac{n(A\ and\ D)}{n(D)}[/tex]
[tex]P(D|A) = \frac{n(A\ and\ D)}{n(A)}[/tex]
So, we have:
[tex]P(A|D) = \frac{2}{10}[/tex]
[tex]P(A|D) = 0.2[/tex]
[tex]P(D|A) = \frac{2}{8}[/tex]
[tex]P(D|A) = 0.25[/tex]
From the above computations, we have:
[tex]P(D|A) \ne P(A|D)[/tex]
This is so, because:
The total number of A and D are not equal
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the x-axis on a graph represents the number of identical items purchased. the y-axis represents the total cost in dollars. what does the slope of the graph represent?
the unit cost per item
the number of items per dollar
the total cost for all the items
the total number of items bought
Answer:
the unit cost per item
Step-by-step explanation:
The description of the graph tells you what the slope means. The slope is the (change in) y-value (cost) per (change in) x-value (item), thus is cost per item.
The slope of the line from the origin to a point is the average cost for that number of items. The slope of a tangent line at a point on the curve is the marginal cost for that number of items.
When the curve is linear and goes through the origin, the slope is the same everywhere and is the cost per item. (It is also the average cost and the marginal cost, where that is of interest.)
The slope of the graph, which represents the rate of change between the number of identical items purchased and the total cost, means the unit cost per item.
Explanation:In the given context of a graph where the x-axis represents the number of identical items purchased and the y-axis represents the total cost in dollars, the slope of the graph represents the unit cost per item. This is because the slope of a line is a measure that describes the rate of change between the independent and dependent variables. It tells us how the dependent variable (in this case, total cost, represented by 'y') changes for every one-unit increase in the independent variable (in this case, number of items purchased, represented by 'x'), on average.
Therefore, when you buy more items (increase in 'x'), the total cost ('y') increases. Hence, the rate at which 'y' is increasing per unit 'x' is actually the cost per item. This concept is fundamental in understanding how variations in quantity purchased impact the total cost, applicable in contexts from shopping to major business transactions.
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Which of the following statements are true?
All square matrices are diagonal matrices.
All diagonal matrices are square matrices.
The size of any square matrix is m x m, where m is a positive integer.
All coefficient matrices are square matrices.
The statements that are true are:
All diagonal matrices are square matrices. The size of any square matrix is m x m, where m is a positive integer.The following information should be considered;
All square matrices should not be diagonal matrices. All coefficient matrices should not be square matrices.Therefore, the above two options should be considered true statement.Learn more: https://brainly.com/question/1301963?referrer=searchResults
Answer: B & C
Step-by-step explanation:
on edge
The expression 20L + 25G – 10 calculates the number of dollars that the ABC Lawn Company makes from mowing L lawns and raking G gardens. How many dollars does the company make from raking 444 gardens and mowing 333 lawns?
Put the numbers where the corresponding variables are, then do the arithmetic.
... 20·3 + 25·4 -10 = 60 +100 -10 = 150
Bill draws a regular octagon with the perimeter of 32 units.He picks a vertex of the octagon and draws two line segments through the interior of the octagon on each different opposite vertex.His line segments divide the octagon into three quadrilaterals.what does the shape look like ?
The quadrilaterals are two congruent isosceles trap ezoids and a kite.