Answer:
The right answer is figure B
Step-by-step explanation:
* Lets talk about the complex number
- The complex number z = a + bi consists of two part:
# a is the real part and represented graphically by the x-axis
# b is the imaginary part and represented graphically by the y-axis
- We can add and subtract them by adding or subtracting the real parts
together and the imaginary parts together
# Ex: if z1 = 2 + 3i and z2 = -1 - i
∴ z1 + z2 = (2 + -1) + (3 + -1)i = 1 + 2i
∴ z1 - z2 = (2 - -1) + (3 - -1)i = (2 + 1) + (3 + 1)i = 3 + 4i
* Now lets solve the problem
- Let find from the graph z1 , z2 and point A
- Look to the any graph and find z1 through the axes
- We moved 6 units on the x-axis (real part) and 7 units up
(imaginary part)
∴ z1 = 6 + 7i
- Similarly find z2 through the axes
- We moved 5 units on the x-axis (real part) and 2 units down
(imaginary part)
∴ z2 = 5 - 2i
* Now lets solve z1 - z2
∵ z1 = 6 + 7i and z2 = 5 - 2i
∴ z1 - z2 = (6 + 7i) - (5 - 2i) = (6 - 5) + (7 - -2)i = 1 + 9i
* Lets find in which figure the coordinates of A are (1 , 9)
∵ In figure A point A is (1 , 6)
∵ In figure B point A is (1 , 9)
∵ In figure C point A is (11 , 5)
∵ In figure D point A is (11 , 9)
∴ The right answer is figure B
What segment is the projection of QT on RT?
A) RS
B) ST
C) UT
Answer:
The correct answer option is ST.
Step-by-step explanation:
We are given a figure of a right angled triangle and we are to determine whether which of the given segments is the projection of QT on RT.
We know that:
QT = QS + ST
Therefore, on RT, ST is the projection of QT since it comes mid way from Q to T.
So the correct answer option is ST.
Answer:
ST is the projection of QT on RT
Step-by-step explanation:
To Find : What segment is the projection of QT on RT?
Solution:
We are supposed to find the projection of QT
In the projection
We draw a perpendicular on RT with point Q
So, Perpendicular on RT is QS
So, ST is the projection of QT on RT
So, Option B is true
Hence ST is the projection of QT on RT
The current flowing through an electric circuit is the derivative of the charge as a function of time. If the charge q is given by the equation q(t)=3t^2+2t-5 what is the current at t = 0?
Answer:
The current at t = 0 is
[tex]I (0) = 2[/tex] units of current
Step-by-step explanation:
If the current flowing through an electric circuit is defined as the derivative of the charge as a function of time and we have the equation of the charge as a function of time, then, to find the equation of the current, we derive the equation of the charge.
[tex]q (t) = 3t ^ 2 + 2t-5[/tex]
[tex]\frac{dq(t)}{dt} = 3 (2) t ^ {2-1} +2t ^ {1-1} -0[/tex]
Simplifying the expression we have:
[tex]\frac{dq(t)}{dt} = 6t + 2t ^0\\\\\frac{dq(t)}{dt} = 6t + 2 = I (t)[/tex]
Finally, the equation that defines the current of this circuit as a function of time is:
[tex]I (t) = 6t +2[/tex]
Now to find the current at t = 0 we make [tex]I (t = 0)[/tex]
[tex]I (0) = 6 * 0 +2[/tex]
[tex]I (0) = 2[/tex] units of current
Jamie tried to solve an equation step by step.
2/5n+7=12
2/5n=5 (Step 1)
n=2 (Step 2)
Find Jamie's Mistake
A: Step 1
B:Step 2
C: Jamie did not make a mistake
THIS IS FOR 10 POINTS AND I WILL BE GIVING OUT THANK YOUS AND BRAINLY CROWNS!!!!
Answer:
Step 2
Step-by-step explanation:
Jaime did not multiply by the reciprocal of 2/5 which is 5/2 on both sides.
5*5/2=25/2
The solution to the equation 2/5n+7=12 is n = 25/2
The mistake in Jamie's simplification of the equation is in Step 2.
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is 2/5n + 7 = 12
On simplifying the equation , we get
2/5n + 7 = 12
Subtracting by 7 on both sides of the equation , we get
2/5n = 12 - 7
2/5n = 5
Now , Multiplying by 5/2 on both sides of the equation , we get
n = ( 5/2 ) x 5
The value of n = 25/2
Therefore , the value of n is 25/2
Jamie made a mistake in step 2 while simplifying the equation by cross multiplying
Hence , The solution to the equation 2/5n+7=12 is n = 25/2
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WILL MARK BRAINLIEST!
find the solution of this system of equations.
2x+6y=4
8x-5y=45
Answer:
x= -1, y= 1
Step-by-step explanation:
2x + 6y = 4.........(1)
8x - 5y = 45........(2)
multiply equation (1) by 4
8x + 24y = 16......(3)
subtract equation (3) by (2)
29y = 29
y = 1
then substitute y=1 in equation (1)
2x + 6(1) = 4
solving for x
x = -2/2 = -1
The solution to the system of equations 2x + 6y = 4 and 8x - 5y = 45 is x = 5 and y = -1, found by using the method of elimination.
To find the solution of the system of equations containing 2x + 6y = 4 and 8x - 5y = 45, we will use the method of elimination.
First, we will manipulate the first equation to line up with the second equation regarding the x coefficient. We do this by multiplying the entire first equation by 4, giving us 8x + 24y = 16 which we will call equation (3).
Next, we subtract equation (2) from equation (3) to eliminate the x variable: (8x + 24y) - (8x - 5y) = 16 - 45, leading to 29y = -29.
Dividing both sides by 29 gives us the value of y: y = -1.
To find x, substitute y = -1 back into the original equation (1): 2x + 6(-1) = 4. Solving for x we get 2x - 6 = 4, therefore 2x = 10 and x = 5.
We can conclude that the solution to the system of equations is x = 5 and y = -1.
What is the area of the triangle
ANSWER
B. 24 sq. units.
EXPLANATION
The area of a triangle is calculated using the formula:
[tex]Area = \frac{1}{2} \times AB \times BC[/tex]
From the graph ,
AB=3--3=6 units.
BC=3--5=8 units
We substitute the values into the formula to get,
[tex]Area = \frac{1}{2} \times 6 \times 8 = 24sq. \: units[/tex]
The correct answer is B
Need help asap! Thank you in advanced!
Answer:
b
Step-by-step explanation:
The i is is square root of -1, which can be factored out from under the square root.
Please answer this question only if you know it! 25 points and brainliest!
Answer:
[tex]\boxed{70^\circ}[/tex]
Step-by-step explanation:
Step 1. Calculate θ
[tex]\begin{array}{rcll}70^{\circ} + \theta + 60^{\circ} & = & 180^{\circ} & \text{Angles of straight line}\\130^{^{\circ}} + \theta & = & 180^{\circ}} & \\\theta & = & 50^{\circ} & \\\end{array}[/tex]
Step 2. Calculate x
[tex]\begin{array}{rcll}60^{\circ} + \theta + x & = & 180^{\circ} & \text{Interior angles of triangle}\\60^{\circ} + 50^{\circ} + x & = & 180^{\circ} &\\110^{^{\circ}} + x& = & 180^{\circ} & \\\\x & = & \boxed{70^\circ} & \\\end{array}[/tex]
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Answer:
okay
Step-by-step explanation:
Choose all correct statements concerning roots of unity.
Answer:
all but the second statement are correct
Step-by-step explanation:
The n roots of unity are evenly spaced around a circle of radius 1 in the complex plane. One of the roots is always 1. If n is even, -1 will also be a root.
Please help me out if possible:)
Answer:
False
Step-by-step explanation:
The angle between a tangent and radius is right.
Use the converse theorem of Pythagoras to determine.
If the square on the longest side is equal to the sum of the squares on the other two sides then the triangle is right and the segment is a tangent.
longest side = 13.1 ⇒ 13.1² = 171.61
11.3² + 6.65² = 127.69 + 44.2225 = 171.9125
Since 171.61 ≠ 171.9125 the line is not a tangent
The play cost $2,600.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 741 people attend the play's opening night, what will the balance of the bank account be? A. $7,410 B. $10,010 C. - $2,526 D. $4,810
Answer:
4,810
Step-by-step explanation:
$10 per ticket times 741 people (10 * 741) is 7,410, then subtract the cost to produce the play, 7,410 - 2600 = 4,810.
Please please help me
Answer:
[tex]\large\boxed{\dfrac{\boxed{8}}{81}}[/tex]
Step-by-step explanation:
[tex]\text{If}\ a_1,\ a_2,\ a_3,\ a_4,\ ...,\ a_n\ \text{is the geometric sequence, then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=constant=r-\text{common ration}.\\\\\text{We have}\ \dfrac{1}{2},\ \dfrac{1}{3},\ \dfrac{2}{9},\ \dfrac{4}{27},\ ...\\\\\dfrac{\frac{1}{3}}{\frac{1}{2}}=\dfrac{1}{3}\cdot\dfrac{2}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{2}{9}}{\frac{1}{3}}=\dfrac{2}{9}\cdot\dfrac{3}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{4}{27}}{\frac{2}{9}}=\dfrac{4}{27}\cdot\dfrac{9}{2}=\dfrac{2}{3}[/tex]
[tex]\bold{CORRECT}\\\\\dfrac{x}{\frac{4}{27}}=\dfrac{2}{3}\qquad\text{multiply both sides by}\ \dfrac{4}{27}\\\\x=\dfrac{2}{3}\cdot\dfrac{4}{27}\\\\x=\dfrac{8}{81}[/tex]
The ratio in lowest terms of length to width for a rectangle with length 10 and width 4 is 5/2 .
True False
Find the area of the following figure drawn from the side of length eight to the side of length 2 is 8 unit long
Answer:
(52) is the homogeneous mixture
George is reading a book that is 420 pages long. He reads 45 pages on the first day. He will read the remaining pages in the book 15 more days. During that time he will read an equal number of pages each day. How many pages will he read each day.
Answer:
25
Step-by-step explanation:
The book is 420 pages long and he reads 45 pages so he has 375 pages left.
The will read equal amounts during the next 15 days so 375 ÷ 15 = 25
George reads 45 pages each day
How to find out how many pages will he read each day ?According to the problem,
George is reading a book that is 420 pages long.He reads 45 pages on the first day.He will read the remaining pages in the book 15 more days.Number of pages left after reading 45 pages = (420 - 45) = 375
Now, George completes the remaining pages in 15 days reading equal number of pages everyday.So number of pages he read per day = 375/15 = 25
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What is the correlation coefficient r for the data set? Enter your answer to the nearest hundredth in the box. r =
x y
0 8
1 7.5
2 6
2 5.5
3 5.5
3 4
4 3
5 3
6 2.5
Answer:
-0.00348
Step-by-step explanation:
x y xy [tex]x^2[/tex] [tex]y^2[/tex]
0 8 0 0 64
1 7.5 7.5 1 56.25
2 6 12 4 36
2 5.5 11 4 30.25
3 5.5 16.5 9 30.25
3 4 12 9 16
4 3 12 16 9
5 3 15 25 9
6 2.5 15 36 6.25
Now [tex]\sum x=0+1+2+2+3+3+4+5+6=26[/tex]
[tex]\sum y=8+7.5+6+5.5+5.5+4+3+3+2.5=45[/tex]
[tex]\sum (xy)=0+7.5+12+11+16.5+12+12+15+15=101[/tex]
[tex]\sum x^2=0+1+4+4+9+9+16+25+36=104[/tex]
[tex]\sum y^2=64+56.25+36+30.25+30.25+16+9+9+6.25=257[/tex]
N = number of pairs of scores = 9
Formula :[tex]r =\frac{N\sum(xy)-\sum x \sum y}{(N \sum x^2 -(\sum x)^2)(N \sum y^2 -(\sum y)^2)}[/tex]
Substitute the values.
[tex]r =\frac{9(101)-(26 \times 45)}{(9 (104) -(26)^2)(9(257) -(45)^2)}[/tex]
[tex]r =-0.00348[/tex]
Hence the correlation coefficient is -0.00348
The value of Correlation coefficient is -0.00348.
What is a Correlation Coefficient?A correlation coefficient denotes the strength of the relation between two variables of a function.
The formula for correlation coefficient is
[tex]\rm r = \dfrac{ N \sum (xy) - \sum x \sum y}{(N \sum x^2- (\sum x)^2)(N\sum y^2 - (\sum y)^2}[/tex]
The data is
x y
0 8
1 7.5
2 6
2 5.5
3 5.5
3 4
4 3
5 3
6 2.5
the value of ∑x = 26
∑y = 45
∑(xy) = 101
∑x² = 104
∑y² = 257
N = Total frequency = 9
The value of r is obtained by substitution of value in the equation.
r = -0.00348
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50 points!!! Please help!!!
Two variables are correlated with r=−0.31.
Which answer best describes the strength and direction of the association between the variables?
weak positive
weak negative
strong negative
strong positive
The r value is a number between -1 and +1.
For a negative value, the closer to -1 it would be a strong negative, if it is closer to 0, it would be a strong negative.
-0.31 is closer to 0 than -1, so it would have a strong negative association.
Lines m and n are parallel. What is the measure of angle 4?
Answer:
132 deg
Step-by-step explanation:
from diagram, if lines m and n are parallel, then angle 3 = angle 7 and angle 4 = 132deg
The measure of angle 4 depends on its relationship to other angles in the diagram. If angle 4 is an alternate interior angle to another angle whose measure we know, it would share that measure.
Explanation:To find the measure of angle 4 given that lines m and n are parallel, we need to understand a concept in geometry called alternate interior angles. According to this concept, when a line (called a transversal) intersects two parallel lines, the pairs of alternate interior angles it forms are equal. So, if angle 4 is an alternate interior angle to another angle whose measure we know, we can say that the measure of angle 4 is equal to that angle. Therefore, without knowing the measure of the corresponding angle, we can't provide a definitive measure for angle 4.
To make this more concrete, let's imagine we have a situation where lines m and n are parallel and line t is a transversal. We know the measure of angle 3 (on line m and intersected by t) is 75 degrees. If angle 4 is on line n and forms a Z shape with angle 3 (making them alternate interior angles), the measure of angle 4 would also be 75 degrees.
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Page 2
7. Donald has 6 unit cubes. How many
different rectangular prisms can he
make using all 6 unit cubes?
Answer:
Step-by-step explanation:
2
With 6 unit cubes, it is possible to form 4 distinct rectangular prisms: 1x1x6, 1x2x3, 1x3x2, and 2x3x1.
Explanation:The subject here is combinatorial mathematics focusing specifically on the construction of geometric shapes with a limited number of unit cubes. With 6 unit cubes, Donald can make 4 different rectangular prisms:1x1x6, 1x2x3, 1x3x2, and 2x3x1, each dimension representing length, width, and height in units. Here, the number of ways to arrange the cubes depends on unique combination of dimensions that respect the given total volume (i.e., number of unit cubes), which is 6 in this case.
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*20 POINTS PLEASE HELP ME!!!!!!!!*
Answer:
helloooooooooooooooooooo
Please help me. I really need help with this proof.
Usually you prove the medians are concurrent way before you get the Ceva's Theorem. But we do the problem as given. Next time try to include the whole problem in the photo.
FA=FB, BE=EC, CG=GA
Answer: C. Definition of median
The medians go to the midpoints of the sides, so we have congruent segments from the foot.
FA/FB=1, BE/EC=1, CG/GA=1
Answer: A. Division of equal segment lengths yields 1
This one is cut off so we can't read the full justification, but we have equal segments so their ratio is 1.
(FA/FB)(BE/EC)(CG/GA)=1
Answer: E. Substitution property
Again the justification is cut off, but we have three things equal to 1, when we multiply them together we still get 1.
Medians are Concurrent
Answer: B. Ceva's Theorem
This is really the converse of Ceva's Theorem; we have the required ratio product equal to 1, so we know the medians are concurrent. Technically they might be parallel (which is concurrent in the projective sense, meeting at infinity). So we really need to show they're not parallel as well, which they can't be, but they left that part out.
I don't like this proof very much.
Please please help me
Answer:
x = 4.1
Step-by-step explanation:
The line segment from the centre to the chord is a perpendicular bisector Thus one half of the chord = 15.6 ÷ 2 = 7.8
Consider the right triangle formed with legs x and 7.8 and hypotenuse 8.8
Using Pythagoras' identity on the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other two sides, then
x² + 7.8² = 8.8²
x² + 60.84 = 77.44 ( subtract 60.84 from both sides )
x² = 16.6 ( take the square root of both sides )
x = [tex]\sqrt{16.6}[/tex] ≈ 4.1
Sophie was mixing her favorite shade of purple paint. The paint requires 1/3 cup of blue for every 1/2 cup of red paint
Which property is shown in the matrix addition below?
| 6
lo
-8
2
1 0
-19] [
0
0
0
0
6
0
-8
2
1
-19)
inverse property
identity property
commutative property
associative property
Answer:
Identity Property
Step-by-step explanation:
The property shown in the given matrix addition is identity property (of addition)
Let's define additive identity first,
For all real numbers there is exists a number zero which is when added to any real number, the number remains the same. The number is called additive identity.
Similarly, for matrices, there exists a matrix of same dimensions that is when added to the matrix, gives the same result as the original matrix.
The matrix is denoted by O and it only contains zeros..
Answer:
Identity property
Step-by-step explanation:
Select all the lines that represent functions
Answer:
B, C, D are functions
Step-by-step explanation:
Functions are those that do not share an x value. Look at A. x-values are used twice everywhere except the vertex. This is not a function, it is just a relation. B does not at any time share x-values, so this is a function. C is also a function, and so is D. F is a vertical line that shares the same x value throughout the whole line, so this is definitely not a function.
Answer:
bcd
Step-by-step explanation:
i got it right
SOMEONE PLS HELP PLS PLS PLS PLS I DONT UNDERSTAND ANYTHING AND I WANT TO SCREAM THIS IS SO DIFFICULT ILL GIVE BRAINLIEST AND ALL THAT STUFF PLS HELP.
Answer:
[tex]\sqrt{5}[/tex]
Step-by-step explanation:
in this exercise, when asking you to simplify the fraction, you are actually asking to rationalize the denominator, that is, you operate the fraction until any square root of the denominator disappears
In order to do that, the first thing to do is multiply both the denominator and the numerator by the root that you want to eliminate, that is, by [tex]\sqrt{5}[/tex] :
[tex]\frac{5}{\sqrt{5}}*\frac{\sqrt{5} }{\sqrt{5} } =\frac{5*\sqrt{5} }{\sqrt{5} *\sqrt{5} } = \frac{5\sqrt{5} }{\sqrt{5} ^{2} } =\frac{5\sqrt{5} }{5} =\sqrt{5}[/tex]
Answer:
the answer is 7.2
Step-by-step explanation:
the square root of 5 is 2.2 that plus 5 is 7.2
Can I get brainliest
Write an equation of the line passing through point P(0,-1) that is parallel to the line y=-2x+3
Y = __
The answer to this question is:
y = -2x - 1
Please help me out with this please
The area of a circle is
[tex]a = r {}^{2} \pi[/tex]
So we get
[tex]a = 2.5 {}^{2} \pi[/tex]
so we get 19.6 rounded to the nearest tenth
Now we subtract that from the area of the square which is 25
We get 5.4
So the answer shoild be 5.4ft
Hopefully this is correct and helps you!
Answer:
5.4 ft²
Step-by-step explanation:
The area of the yellow region = area of square - area of circle
area of square = 5² = 25
note that the diameter of the circle = 5, thus radius = 2.5
area of circle = π × 2.5² = 6.25π
yellow region = 25 - 6.25π ≈ 5.4 ft²
Which equation most closely represents the line of best fit for the scatter plot below?
I think that the first choice is the correct one
Ricardo is factoring the polynomial, which has four terms.
5x3 + 20x2 + 2x + 8
5x2(x + 4) + 2(x + 4)
Which is the completely factored form of his polynomial?
The first step of factorization is done for you. All that is needed to be done is a simplification of the factored polynomial.
5x^2(x+4)+2(x+4)
*Factor out an (x+4)*
(x+4)(5x^2+2)
Hope this helps!!