a) 3 - 8 + 2i - (-5i) = -5 + 2i +5i = -5 + 7i
b) 4 - 20i - 2i + 10i² = 4 - 22i + 10([tex]\sqrt{-1}[/tex])² = 4 - 22i + 10(-1) = 4 - 10 -22i
= -6 -22i
c) Multiply both numerator and denominator by i
[tex]\frac{i(-2-4i)}{i^{2} }[/tex] = [tex]\frac{-2i - 4i^{2} }{i^{2} }[/tex] = [tex]\frac{-2i - 4(\sqrt{-1})^{2} }{(\sqrt{-1})^{2}}[/tex] = [tex]\frac{-2i - 4(-1)}{-1}[/tex] = [tex]\frac{-2i+4}{-1}[/tex] = 2i - 4 = -4 + 2i
d) Multiply both numerator and denominator by (3+6i)
[tex]\frac{(3+6i)(-3+2i)}{(3+6i)(3-6i)}[/tex] = [tex]\frac{-9+6i-18i+12i^{2} }{9-36i^{2} }[/tex] = [tex]\frac{-9-12i+12(\sqrt{-1} )^{2} }{9-36(\sqrt{-1} )^{2} }[/tex] = [tex]\frac{-9-12i+12(-1)}{9-36(-1)}[/tex] = [tex]\frac{-9-12-12i}{9+36}[/tex]
= [tex]\frac{-21-12i}{45}[/tex] = [tex]-\frac{21}{45} - \frac{12}{45}i[/tex]
please help question is in the image!
x1 = 4 x2 = -4
substitute the values into the given equations!!
(4 + (-4)) / 2 = (0 / 2) = 0
y1 = -5 y2 = 5
(-5 + 5) / 2 = (0 / 2) = 0
midpoint = (0, 0)
bold values - box answers :D
Can someone help me
Answer: well look you can fid live tutors
Step-by-step explanation:
n vcxvbnm
What is the area, in square meters, of the shape below? Express your answer as a fraction in simplest form.
Area = 5/12 m².
For image see the attachment below-
Area of Triangle - A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC. Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.
The basic formula to find the area of a triangle is,
Area of triangle = 1/2 (b × h);
where b = base and
h = height of the triangle.
Now , we have been given that -
Base =5/3 m
Height = 1/2 m
Find out area of the triangle .
The area of a triangle = 1/2 x base x height
Put the values in formula
area of a triangle = 1/2 x 5/3 x 1/2
area of a triangle = (1x5x1)/ (2x3x2)
area of a triangle = 5/12 m².
Hence, the area in square meters of the given shape is 5/12 .
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Solve the literal equation for x.
13. x + 5y = 2
14. 2x + 5 = 12y + 9
Answer:
x=2
Step-by-step explanation:
You would use substitution. In which x =-5y +2 and x = 6y+2. -5y + 2 = 6y + 2. So would solve for y value then plug it into the equation to solve x.
Write and solve a system of equations for each problem situation. Interpret the solution in terms of context.
Pedro has 97 athlete cards. In his collection, he has 39 more baseball player cards than football player cards. How many of each type of card does Pedro have?
Number of each type of cards after solving system of equations for given situation of Pedro cards are 29 and68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
As given,
Total number of cards=97
Let y=football cards
x=baseball cards
System of equations are
x + y=97 __(1)
x=y +39 __(2)
Substitute (2) in (1)
y+ 39 +y=97
⇒2y=58
⇒y=29
Substitute y=29 in (2),
x=29 +39
=68
Therefore, number of each type of cards after solving system of equations are football cards 29 and baseball cards 68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
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Say you are given the graph of the line y = -x. Write the equation of the line that is perpendicular to the given line and goes through the point (-8, 2).
Linear equations are often organized in slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptTo find a linear equation, we often first solve for the slope, and then solve for the y-intercept algebraically.
To find the slope of a perpendicular line, we must find the negative reciprocal of the slope of the reference line.
Solving the Question
We're given:
Reference line is [tex]y=-x[/tex]Perpendicular line passes through [tex](-8,2)[/tex]1) Find the slope of the reference line
We can rewrite the reference line to be clearer in slope-intercept form:
[tex]y=-1x+0[/tex]
This means that -1 is the slope.
2) Find the slope of the perpendicular line
The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular line is 1. Plug this into slope-intercept form:
[tex]y=x+b[/tex]
3) Solve for the y-intercept of the perpendicular line
[tex]y=x+b[/tex]
Plug in the given point (-8,2) and solve for b:
[tex]2=-8+b\\b=2+8\\b=10[/tex]
Therefore, the y-intercept of the perpendicular line is 10. Plug this back into our original equation:
[tex]y=x+10[/tex]
Answer[tex]y=x+10[/tex]
Which algebraic expression is equivalent to the expression below?
4(4x + 5) + 4(11 - x)
A.
20x + 64
B.
12x + 24
C.
12x - 64
D.
12x + 64
Answer:
D. 12X + 64
Step-by-step explanation:
4(4x+5)+4(11-x)
4(4x+5)+4(11−x)
4(4x + 5) + 4(11 - x)
1 Expand by distributing terms.
16x+20+4(11-x)
16x+20+4(11−x)
2 Expand by distributing terms.
16x+20+44-4x
16x+20+44−4x
3 Collect like terms.
(16x-4x)+(20+44)
(16x−4x)+(20+44)
4 Simplify.
12x+64
12x+64
Answer:
D. 12x + 64
Step-by-step explanation:
expand the brackets by multiplying:
= 16x + 20 + 44 - 4x
= 12x + 64
brainliest pls :,)
The square below represents one whole. What percent is represented by the shaded area?
Answer:
29%
Step-by-step explanation:
There are 100 boxes. 29 of them are shaded in, so we can divide that by 100.
29/100=0.29
0.29 is equal to 29%
Write 6.42 as a mixed number in simplest form.
6.42=
Answer:
6 [tex]\frac{21}{50}[/tex]
laura runs a 100 m race in 20.0 s. what is her time in kiloseconds ? how long is the race in kilometers
Laura runs for 0.02 kiloseconds
The race is 0.1 kilometers
How to convert to kiloseconds and kilometers ?The first step is to convert 20 seconds to kiloseconds
= 20/1000
= 0.02 kiloseconds
The next step is to calculate the distance in kilometers
Convert 100 meters to kilometer
= 100/1000
= 0.1 km
Hence the race is 0.1 kilometers
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Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
Can someone please help I will be giving Brainliest to whoever can answer :)
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1}
The questions are matched with the graphs that are labeled A-H. (
1. A = {(x, y): y > x^2} Matching answer D2. B = {(x, y): y ≥ x^2+ 3} Matching answer G3. C = {(x, y): y ≤ 3x^2 + 2} Matching answer C4. D = {(x, y): y ≥ 2x^2- 5x + 1} Matching answer A5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25} Matching answer F6. x^2- 3x ≥ 0 Matching answer J (the curve should be solid line)7. x^2- 3x + 2 ≤ 0 Matching answer E8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1} Matching answer BHow to find the matching graphThe graph has some rules for matching them to the equation some of the rules are:
finding the rootsusing solid lineusing broken lineknowing about circlelearning about straight lineRead more on graphs here: https://brainly.com/question/19040584
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Which algebraic expression represents each verbal expression?
a. the product of five and a number, decreased by eleven
b. the sum of a number and five less than eleven
c. five times a number fewer than eleven
d. the quantity of a number minus eleven, multiplied by five
Answer:
A) 5n − 11
B) 11 − (n + 5)
C) 11 − 5n
D) 5(n − 11)
Your Welcome ;)
The required verbal algebraic expressions are given as ,
(a) 5x - 11 (b) (x + 5) - 11
(c) 5x - 11 (d) (x - 11)×5
What is an algebraic expression?The algebraic expression consists of constants and variables. eg x, y, z etc.
Here,
Let the number x,
a. The product of five and a number, decreased by eleven
⇒ 5x - 11
b. The sum of a number and five less than eleven
⇒ (x + 5) - 11
c. Five times a number fewer than eleven
⇒5x - 11
d. The quantity of a number minus eleven, multiplied by five
⇒(x - 11)×5
Thus, the required expression is shown above
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a quarry needs to ship a marble block weighing 10000 pounds. if the cost of shipping is 110 per ton, how much will shipping cost?
The cost of shipping the marble block is 550.
The total weight of the marble block is 10,000 pounds.We need to convert the weight from pounds to tons.Unit conversion is the process of converting various units of measurement for the same amount, often using multiplicative conversion factors that modify the measured quantity value without affecting its effects.1 ton equals 2000 pounds.The total weight of the marble block in tons is 10000/2000.The total weight of the marble block is 5 tons.The cost of shipping is 110 per ton.The total cost of shipping the marble block = 5 * 110.The total cost of shipping the marble block is 550.To learn more about unit conversion, visit :
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Which of the following ordered triples is the solution to the system of equations?
2x − y − z = −1
3x + y − z = 2
x + y − 5z = −8
Answer:
1,1,2
Step-by-step explanation:
The solution to the given system of equations are:{ x = 1, y = 1, z = 2} which is the corrrect answer would be option (A).
What is an equation?The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.
We have been given the system of equations as:
2x − y − z = −1
3x + y − z = 2
x + y − 5z = −8
Isolate the term of x in the equation 2x − y − z = −1, and we get
x = (- 1 + y +z)/2
Substitute the value of x = (- 1 + y +z)/2 in the above both equations,
3(- 1 + y +z)/2 + y − z = 2
(- 1 + y +z)/2 + y − 5z = −8
Simplify the equation to you get,
(5y + z - 3) / 2 = 2
(3y - 9z - 1) / 2 = -8
Isolate the term of y : (5y + z - 3) / 2 = 2 ⇒ y = (-z +7 )/5
Substitute the value of y = (-z +7 )/5 in the equation (3y - 9z - 1) / 2 = -8
(3(-z +7 )/5 - 9z - 1) / 2 = -8
Simplify the equation to you get,
8(-3z + 1)/d = -8
Isolate the term of z : 8(-3z + 1)/d = -8 ⇒ z = 2
Substitute the value of z = 2 in the equation y = (-z + 7) / 5 to simplify to get
⇒ y = 1
Substitute the values of y = 1 and z = 2 in the equation x = (-1 + y + z) / 2 to simplify to get
⇒ x = 1
The solution to the given system of equations are:
{ x = 1, y = 1, z = 2}
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24-{[16-(8-1)]×2 please answer
Answer:
4
Step-by-step explanation:
It look like your are missing a bracket.
Do the inner most parentheses first.
24 -(16 -(7))x2
24 - 9 x 2
24 -18
4
work out the value of (3.5 x 10^6) ÷ (5 x 10^-3) give your answer in standard form.
The standard form of (3.5 x 10^6) ÷ (5 x 10^-3) is 7*10^8
What is standard form?Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.
Given:
(3.5 x 10^6) ÷ (5 x 10^-3)
On further solving
3.5 * 10^(6 -(-3)) / 5
3.5* 10^9 /5
0.7 * 10^9
7*10^8
Hence, the standard form is 7*10^8.
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WILL GIVE YOU BRAINILEST or however you spell it
BIRDHOUSES Ebony can build 0.7 birdhouse in 1 day. How many birdhouses can she build in 10 weeks?
Step-by-step explanation:
0.7 birdhouses in 1 day.
how many in 10 weeks ?
for that we need to know how many days are in 10 weeks.
1 week = 7 days
assuming that she is working on the birdhouses also on weekends, that means 10 weeks = 10×7 = 70 days.
and that means she can build
0.7 × 70 = 49 birdhouses in 10 weeks.
now, if she works only Monday to Friday on the birdhouses, then that means
1 week = 5 days
and 10 weeks = 10×5 = 50 days.
and that means she can build
0.7 × 50 = 35 birdhouses in 10 weeks.
if there is really no other information about that, I would use the usual 7 days per week and the first solution (49).
please solve this question step by step
Answer:
Step-by-step explanation: The given question is wrong. To be a valid question, there must be "-9" in place of "-7" in the second given matrix.
heidi was able to walk 2/3 of a mile in 12 minutes how far could heidi walk in 1 hour
Heidi is able to walk 10/3 miles in 1 hour (60 min).
What is described as unitary method?It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.
The value of many items is given in the unitary method, and we must either determine the worth of more or fewer items. To do so, we must first determine the value of one item by division and then determine the value of more as well as fewer items by multiplication.Now, for the given question;
It takes Heidi 12 minutes to walk 2/3 miles.
Applying the unitary method.
Then, for in 1 minutes Heidi will walk = 2/(3×12).
For walking in 1 hour or 60 min = (2×60)/(3×12).
Further simplifying;
In 1 hour = 10/3 miles.
Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.
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Find the distance between the two points on the graph.
Answer:
[tex]3 \sqrt{5} [/tex]
Step-by-step explanation:
See attached for details. Basically finding the distance between 2 points requires creating a right angle triangle. And we are looking for the hypotenuse.
The pythagorean theorem is used.
Please help - thanks
Insert parentheses in the appropriate places:
8+ 3-2 ×9 =17
28 ÷ 4+3 × 4+3 =28
5× 3+2 ×6 ÷3 =50
6× 9-4 +3-3 ×4=30
5 ×3+2× 6÷3 =19
5× 3+2×6 ÷3 =25
Answer:
the answer is 27
Step-by-step explanation:
. The oxygen saturation of a lake is found by dividing the
amount of dissolved oxygen the lake water currently has
per liter by the dissolved oxygen capacity per liter of the
water, and then converting that number into a percent.
If the lake currently has 6.4 milligrams of dissolved oxy-
gen per liter of water and the dissolved oxygen capacity
is 9.5 milligrams per liter, what is the oxygen saturation
level of the lake, to the nearest percent?
A. 64%
B. 67%
C. 70%
D. 89%
E. 95%
Answer:
70% i think
Step-by-step explanation:
Can someone help me out
Answer:
I believe its graph 4 (not sure though, you can plug in some values to make sure)
Step-by-step explanation:
Which numbers are a distance of 3 units from 12 on a number line?
Select each correct answer.
Answer:
9 and 15
Step-by-step explanation:
ans should be 9 and 15
i dun really understand what this qns wants u to find really bad qns to test
2. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
How to state the additional information required?The congruence postulate is given as:
SSS Triangle Congruence Postulate
The above means that the three sides of the triangles are congruent.
From the figure, the following side lengths are said to be congruent
UV and FV
TV and TV
For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent
This is represented as:
UT = T F
Hence, the additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
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Describe at least two differences between constructing an inscribed regular hexagon and constructing an inscribed square.
100 points and brainliest
There are some differences in the process of constructing a inscribed square and a hexagon inside a circle.
When constructing a square, we start with a circle. Then draw its diameter through the center of the circle. Now putting compass on end points of this diameter, measuring more than half the length of diameter on the compass, draw 4 arcs above and below the diameter. So we get a perpendicular bisector of the diameter. In total, we get 4 points on the circle. Joining the adjacent points, we get the inscribed square.
When constructing the regular hexagon, start drawing a circle. Put the compass on a point on the circle and measure the radius on it. Now draw an arc on the circle. Putting compass on this new point on the circle draw another arc. Continuing like this, we get a total of 6 arcs giving 6 points on the circle. Join the adjacent points to get an inscribed regular hexagon.
So the differences in constructing the square and the regular hexagon are:
Diameter is used in square whereas radius is enough for the regular hexagonPerpendicular bisector is constructed for square while regular hexagon does not need one.For a square,4 arcs giving 4 points on the circle are needed. But for a regular hexagon 6 arcs giving 6 points are there.Learn more about inscribed shapes at https://brainly.com/question/21502832
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The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (1 point)
a
A 180 degree counterclockwise rotation about the origin followed by a translation 5 units up
b
A 270 degree counterclockwise rotation about the origin followed by a translation 5 units up
c
A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin
d
A translation 5 units to the left followed by a 270 degree counterclockwise rotation about the origin
The set of transformations that is performed on triangle ABC to form triangle A′B′C′ is C. A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin.
What is a translation?A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the coordinate system's origin or as adding a constant vector to each point.
In this case, it can be seen that the shape was rotated counterclockwise twice. That's 90° × 2 = 180°
Therefore, the transformation that is performed on triangle ABC to form triangle A′B′C′ is a translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin.
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b.a slug takes 4.25 minutes to travel 11.2 centimeters. what is the speed of the slug in meters per second? predicted number of significant digits in answer: 2 or 3 answer value: actual number of significant digits:
Answer:
0.00375 meters per second,
Step-by-step explanation:
0.00375 meters per second, we know this is the answer because, 4.25*60=255 and 255/11.2=0.00375
russell runs 9/10 miles in 5 minutes. at this rate how many miles can he run in one mintue?
Answer:
1.8 miles
Step-by-step explanation: