If we were to denote the counterclockwise rotation by θ, then the angle would be measured around the origin, starting from the positive x-axis and proceeding in a counterclockwise direction.
Which axis are angles measured?In 2D space, angles are measured around the origin and are referred to as the angle of rotation. This is measured in degrees or radians and can be calculated using trigonometry.
In 2D space, angles are measured about the origin. In other words, the point (0,0) is used as a reference point. In addition, the standard position of an angle is a unit vector along the positive x-axis that has been rotated counterclockwise by the angle in question.
If we were to denote the counterclockwise rotation by θ, then the angle would be measured around the origin, starting from the positive x-axis and proceeding in a counterclockwise direction.
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Factorize:
(3a-3) / ( 9a²-9a)
Answer: 1 / (3a+3)
Step-by-step explanation:
9a^2 - 9a is (3a-3) x (3a+3) so when
3a-3 is divided by (3a-3)x (3a+3) you can cancel the 3a-3 and you are left with (1 / 3a+3)
Round 68.5719758824 to 4 decimal places.'
Answer:68.57
Step-by-step explanation:
If the last number is less than 5 (1,2,3,4) no round is needed.
If the last number is greater than 4 (5,6,7,8,9) round up and add 1.
I think that is how you do it (try it first) then ask parents
ABC and XYZ are similar triangles with right angles at B and Y. AC=13 cm,
BC=5 cm. Find AB and XZ. (No links pls...)
Answer:
See belowStep-by-step explanation:
Since B is the right angle, AC is the opposite side - hypotenuse.
Use Pythagorean and find the missing side, AB:
\(AB = \sqrt{AC^2-BC^2} = \sqrt{13^2-5^2} =\sqrt{144} =12cm\)There is no info given to link the triangles ABC and XYZ and hence can't provide solution to any dimension of XYZ.
If the scale factor was given as k, then XZ would be:
XZ = k*BC = 5kPlease help its a grade!!! appreciate the help
maria's age multiplied by six is forty-two?
four times a number equals two hundred?
twice as old as vinnie is fifty?
the quotient of 48 and the number of hours worked is six?
Maria's age is 7 years.
The number is 50.
Vinnie's age is 25 years
The number of hours worked is 8 hours.
Let Maria's age be m years.
It is given that,
m*6 = 42
6m = 42
m = \(\frac{42}{6}=7 years\)
Let the number be n.
It is given that,
4*n = 200
4n = 200
\(n=\frac{200}{4}=50 years\)
Let Vinnie's age be v years.
It is given that,
2*v = 50
\(v=\frac{50}{2}=25 years\)
Let the number of hours worked be h hours.
It is given that,
\(\frac{48}{n}=6\)
Hence,
\(\frac{48}{6}=8 years\)
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After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.
The slope of the line is
.
The y-intercept of the line is
.
The linear function is
.
The slope of the line is -300
The y-intercept of the line is 2000
The linear function is f(x) = -300x + 2000.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
we have,
Let x be the time passed, in hours.
Let y be the amount of fluid left in the IV, in mL.
If fluid drips at a rate of 300 ml per hour.
And 1400 ml of fluid remain after 2 hours.
The linear function can be modeled as:
f(x) = y = -300x + 2000 _____(1)
Put x = 2 in (1)
f(2) = -300 x 2 + 2000 = -600 + 2000 = 1400
The linear function is in the form of an equation of a line with slope m and y-intercept c:
y = mx + c
So,
Slope of the line = m = -300
The y-intercept = c = 2000
Thus,
The slope of the line is -300
The y-intercept of the line is 2000
The linear function is f(x) = -300x + 2000.
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r² +2r³=
(what is r squared plus two r cubed?)
Answer:
\( { \tt{ {r}^{2} + 2 {r}^{3} = {r}^{2} (1 + 2r) }}\)
Answer:
We can't add these two terms since they're not like terms
Step-by-step explanation:
We cannot add variables if they have different exponents
Write the equation for the linear function that goes through –3 on the y-axis and has a slope of 0.5.
y= ????
Answer: y = \(\frac{1}{2} x\) - 3
Step-by-step explanation:
The equation for a line is in the form y = mx + b, where "m" is the slope and "b" is the y-intercept.Since the slope is 0.5 (which is \(\frac{1}{2}\)), we can plug that value in for "m": y = \(\frac{1}{2} x\) + bSince the line goes through -3 on the y-axis, that is the y-intercept. So, we can just plug in that value for "b": y = \(\frac{1}{2} x\) - 3And there's your answer: y = \(\frac{1}{2} x\)-3what are the three main components of the data model structure in sap s/4hana? configuration data 2) master data 3) quantitative data 4) transaction data 1, 2, 4 1, 3, 4 2, 3, 4 1, 2, 3
By using the concept of data structure, it can be concluded that-
First option is correct
What is data structure?
Data structure is a group of elements that provides an efficient way of storing and organizing data so that the data can be accessed and used efficiently. Data structure is a very important tool for computer science and computer engineer and especially in IT industry. Nowadays, lots of research work is being done on data structure.
The three main components of data model structure in SAP S/4HANA are,
configuration data, master data and transaction data
First option is correct
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I will give brainliest to whoever gets this correct.
Answer:
0
Step-by-step explanation:
I'll comment if you need an explanation! Hope this helps! :)
The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold?
The income that's made based on the equation when 1 comb is sold is $0.5.
How to calculate the price?From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.
Therefore, the income by selling 1 comb will be:
y = 1/2
y = $0.5
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Identify the interval(s) on which each quadratic function is positive.
1. y= x^2 + 2x - 8
2. y= -x^2 +4x +12
3. y= 5x^2 - 3x - 8
Help on these three problems above would be greatly appreciated, thanks! ☜(ˆ▿ˆc)
Answer:
\(\textsf{1. \quad $x < -4$ or $x > 2$}\)
\(\textsf{2. \quad $-2 < x < 6$}\)
\(\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}\)\(\textsf{3. \quad $x < -1$ or $x > \dfrac{8}[5}$}\)\(\textsf{3. \quad $x < -1$ or $x > \dfrac{8}{5}$}\)
Step-by-step explanation:
The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.
The zeros of the quadratic function are the points at which the parabola crosses the x-axis.
If the leading coefficient of a quadratic function is positive, the parabola opens upwards.
If the leading coefficient of a quadratic function is negative, the parabola opens downwards.
Therefore, to find the intervals on which each quadratic function is positive:
Calculate the zeros.Determine if the parabola opens upwards or downwards.If the parabola opens upwards, the intervals are less than the smaller zero and greater than the larger zero.If the parabola opens downwards, the interval is between the zeros.Question 1Given function:
\(y=x^2+2x-8\)
Factor the given function:
\(\implies y= x^2+4x-2x-8\)
\(\implies y=x(x+4)-2(x+4)\)
\(\implies y=(x-2)(x+4)\)
Substitute y = 0 to find the zeros:
\(\implies (x-2)(x+4)=0\)
\(\implies x-2=0 \implies x=2\)
\(\implies x+4=0 \implies x=-4\)
The leading coefficient is positive, so the parabola opens upwards.
Therefore, the interval on which the function is positive is:
Solution: x < -4 or x > 2Interval notation: (-∞, -4) ∪ (2, ∞)Question 2Given function:
\(y=-x^2+4x+12\)
Factor the given function:
\(\implies y=-(x^2-4x-12)\)
\(\implies y=-(x^2-6x+2x-12)\)
\(\implies y=-(x(x-6)+2(x-6))\)
\(\implies y=-(x+2)(x-6)\)
Substitute y = 0 to find the zeros:
\(\implies -(x+2)(x-6)=0\)
\(\implies (x+2)(x-6)=0\)
\(\implies x+2=0 \implies x=-2\)
\(\implies x-6=0 \implies x=6\)
The leading coefficient is negative, so the parabola opens downwards.
Therefore, the interval on which the function is positive is:
Solution: -2 < x < 6Interval notation: (-2, 6)Question 3Given function:
\(y=5x^2-3x-8\)
Factor the given function:
\(\implies y=5x^2-8x+5x-8\)
\(\implies y=x(5x-8)+1(5x-8)\)
\(\implies y=(x+1)(5x-8)\)
Substitute y = 0 to find the zeros:
\(\implies (x+1)(5x-8)=0\)
\(\implies x+1=0 \implies x=-1\)
\(\implies 5x-8=0 \implies x=\dfrac{8}{5}\)
The leading coefficient is positive, so the parabola opens upwards.
Therefore, the interval on which the function is positive is:
Solution: x < -1 or x > ⁸/₅Interval notation: (-∞, -1) ∪ (⁸/₅, ∞)can someone help me with this please ?
Answer:
Step-by-step explanation:
∠EMC = ∠EMD + ∠DMC
∠EMC = 90
∠EMD + ∠DMC = 90
∠EMD + 20 =90
∠EMD = 90 - 20
∠EMD = 70
∠FMD + ∠DMB = 180 {Linear pair}
90 + ∠DMB = 180
∠DMB = 180 - 90
∠DMB = 90
Plsss help… it’s imagine math
Answer:
it is b
bcs
a>b<c
.........
Answer:
hii the answer is B.
What is the answer to this please help me cause I’m new to all of this kind of math and I’m not really the type of person to like math.
Answer:
12/16 then we have to simplify by finding the largest number that goes into both so from looking i can see that its 4
3/4
Hope This Helps!!!
Solve each equation. Write The properties that justify each step in the solution method
a. 3x - 8 = -7x + 18
Answer: I’m not sure how to explain so you look at what I did and if it is an equation then I did solve it but if I should did the two separately then tell me so I can do it , have a great and funny day :)
Step-by-step explanation:
plz simplify and answer 3x+7x−28+31−8x for x=2043
Answer:
4091
Step-by-step explanation:
Given the equation;
3x + 7x − 28 + 31 − 8x
First, we would collect like terms;
3x + 7x − 8x − 28 + 31
Simplifying, we have;
\( 2x + 5\)
For x = 2043;
2(2043) + 5 = 4086 + 5 = 4091.
What is the diameter of a circle whose area is 28.3 cm^2
I don't understand this question can someone help me with the answer
The approximate diameter of the circle is 5.77 cm
Given that :
area of circle = 28.3 cm²
How is Area of circle is calculated ?
Area of circle is calculated using formula :
A= πr²
where "π" represents 3.14 and r is radius. So now, according to given information,
Where Pi = 3.14
Hence,
A= πr²
Substitution the value of A in above formula :
28.3 = πr²
28.3 = 3.14r²
r² =28.3/3.14
r² =8.323
√r²=√8.323
r = 2.885
r = 2.885 cm Approximately.
d = 2r
d = 5.77 Approximately.
Therefore, the diameter of the circle is 5.77 cm
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calculate result of matrix equation suppose that a real, symmetric matrix has two distinct eigenvalues and such that . calculate . hint: what do we know about eigenvectors of real, symmetric matrices with distinct eigenvalues?
The result of the matrix equation is not specified in the given problem statement. Instead, we are given some information about a real, symmetric matrix with two distinct eigenvalues and are asked to calculate a certain expression involving this matrix.
For real, symmetric matrices with distinct eigenvalues, it is known that the eigenvectors corresponding to these eigenvalues are orthogonal. This means that if we let v1 and v2 be the eigenvectors corresponding to the two distinct eigenvalues of our matrix A, then v1 and v2 are orthogonal (i.e., their dot product is zero).
To calculate the expression , we need to find the dot product of the two vectors A^(-1)v1 and v2. Using the fact that A is symmetric and has distinct eigenvalues, we can show that A is diagonalizable. That is, there exists an invertible matrix P such that P^(-1)AP = D, where D is a diagonal matrix with the eigenvalues of A on the diagonal. Multiplying both sides of this equation by P^(-1), we get AP^(-1) = P^(-1)DP, which shows that the columns of P^(-1) are the eigenvectors of A. Therefore, we can find v1 and v2 by computing the first and second columns of P^(-1), respectively. Once we have v1 and v2, we can compute A^(-1)v1 and take the dot product with v2 to get our answer.
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Solve 1/2x−5=10−3/4x . Check your solution.
x=___
Answer
The answer is 12 for sure
Step-by-step explanation:
i just solved it like any other equation
1 i added 3/4 on both sides
2 then i added 5 on both sides
3 after you equation should look like 1 1/4x = 15
4 then i divided and it should be x = 12
pls mark brainliest
The value of x is "12".
Calculating the value of x:\(\to \frac{1}{2}x-5=10-\frac{3}{4}x \\\\\to \frac{1}{2}x+ \frac{3}{4}x=10+5 \\\\\to \frac{2+3}{4}x=15 \\\\\to \frac{5}{4}x=15 \\\\\to x=15 \times \frac{4}{5}\\\\\to x=3 \times 4\\\\\to x=12\)
Therefore, the final value of x is "12".
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Which angles are vertical to each other? Select all that apply.
The option 2 and 4 is correct ∠IAH = ∠EAD and ∠EDG = ∠FDA these angle are vertical to each other
What do you mean by Vertically opposite angle ?Vertically opposite angles are a pair of angles formed by the intersection of two straight lines. When two lines intersect, four angles are formed at the point of intersection. Vertically opposite angles are formed by two non-adjacent angles that lie across from each other and share the same vertex, or corner point, at the intersection of the two lines.
Line IC and Line GH intersect each other at A
∴ ∠IAH = ∠EAD (vertacally opposite angle)
Similarly, Line FB and Line GH intersect each other at D
∴ ∠EDG = ∠FDA (vertacally opposite angle)
Hence,∠IAH = ∠EAD and ∠EDG = ∠FDA are vertical to each other
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true or false: in a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.
True. This is because a two-tailed test evaluates both the extreme lower and upper ends of the distribution, allowing for the possibility of a significant difference in either direction.
In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.
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hotel pool a hotel owner is trying to calculate how many square feet of fabric he will need to make a pool covering for winter. if the pool is in the shape of a regular hexagon with a side-to-side length of 30 feet, how many square feet of fabric will the owner need to construct the cover? round to the nearest square foot.
The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.
To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:
apothem = 30 × √3/2 = 25.980762
The area of a regular hexagon is given by the formula:
area = 3 × √3/2 × apothem^2
Substituting the value of the apothem, we get:
area = 3 × √3/2 × 25.980762^2 = 2247.72
Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.
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1-What is 30% of 45?
2-What is 5%of 55.2
Answer:
13.5 and 2.76
Step-by-step explanation:
Help this is due today
The weight of the fish tank when it is empty, given the the dimensions of the water, is 44 pounds.
How to find the weight of the fish tank ?First, let's find the weight of the water in the fish tank.
Convert the dimensions of the water inside the fish tank from inches to feet:
34 inches = 34/12 = 2.83 feet
13 inches = 13/12 = 1.08 feet
Calculate the volume of the water in cubic feet:
Volume = length × width × height
Volume = 2.83 ft × 1.08 ft × 1.08 ft = 3.3 cubic feet
Calculate the weight of the water in the fish tank using the given weight of 1 cubic foot of water (62.4 pounds):
Weight of water = Volume × Weight per cubic foot
Weight of water = 3.3 cubic feet × 62.4 pounds/cubic foot = 206 pounds
Now that we have the weight of the water, we can find the weight of the empty fish tank.
Weight = Weight of tank + Weight of water
Weight of tank = Weight - Weight of water
Weight = 250 pounds - 206 pounds
Weight = 44 pounds
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How to find the length of the segment indicated?
Answer:
Step-by-step explanation:
it is 2x
Combine the like terms to create an equivalent expression for 4z−(−3z)
Answer:
7z
Step-by-step explanation:
Answer: 7z
Step-by-step explanation:
two negatives cancel into a positive, so -(-3z) is +3z. 4z + 3z = 7z
A survey was given to a random sample of 1350 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 64% of the people said they were in favor of the plan. At the 95% confidence level, what is the margin of error for this survey expressed as a percentage to the nearest tenth?
The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.
To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.
The formula for calculating the standard error is:
Standard Error = sqrt((p * (1 - p)) / n)
where p is the sample proportion and n is the sample size.
In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.
Plugging in the values:
Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)
\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)
≈ 0.0131
Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.
Margin of Error = z * Standard Error
= 1.96 * 0.0131
≈ 0.0257
Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:
Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100
= (0.0257 / 0.64) * 100
≈ 4.0%
Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.
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15% of what number is 15? write the answer answer in the simplified form HELP PLEASEEEE ASAP
Answer:
Hi! The answer to your question is 100
Step-by-step explanation:
☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
Answer:
100
Step-by-step explanation:
.15x = 15
x = 15/.15
x = 100
The applet below allows you to view three different angles. Use the slider at the top-left of the applet to switch the angle that is shown. Each angle has a radian measure that is a whole number. Angle A a. Use the slider to view Angle A. What is the radian measure of Angle A? radians b. Use the slider to view Angle B. What is the radian measure of Angle B? radians c. Use the slider to view Angle C. What is the radian measure of Angle C? radians Submit\
The values of all sub-parts have been obtained.
(a). The radian measure of angle A is 6 radians.
(b). The radian measure of angle B is 3 radians.
(c). The radian measure of angle C is 2 radians.
What is relation between radian and degree?
A circle's whole angle is 360 degrees and two radians. This serves as the foundation for converting angles' measurements between different units. This means that a circle contains an angle whose radian measure is 2 and whose central degree measure is 360. This can be written as:
2π radian = 360° or
π radian = 180°
(a). Evaluate the radian measure of angle A:
Near to 360° and radians measure whole number, so we get,
A = 6 radian {1 radian = 57.296°}.
(b). Evaluate the radian measure of angle B:
Near to 180°, and radian measure whole number, so we get,
B = 3 radian
(c). Evaluate the radian measure of angle C:
Near to 90 and radian measure whole number, so we get,
C = 2 radian.
Hence, the values of all sub-parts have been obtained.
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which equation has the same solution as 2x^2+-16x10=0
Answer:
Your answer (x + 4)2 =-11 x + 4)2 13 x + 4)221 Correct answer.