Step-by-step explanation:
[tex] = 6 \times \frac{4}{15} \\ [/tex]
[tex] = \frac{6}{1} \times \frac{4}{15} \\ [/tex]
[tex] = \frac{24}{15} \\ [/tex]
Change into lowest term ....
[tex] = \frac{8}{5} \\ [/tex]
Change into mixed....
[tex] = 1 \ \frac{3}{5} \\ [/tex]
if you were asked to convert the complex number, -6 + 8i, into polar form, what values of “r” and “0” would be in polar form?
Answer:
10∠126.87°
r = 10; θ = 126.87°
Step-by-step explanation:
The coordinate conversion from (x, y) or (x +yi) to (r; θ) can be done using the relations ...
r = √(x² +y²)
θ = arctan(y/x) . . . . paying attention to quadrant
__
For the given complex number, we have ...
r = √((-6)² +8²) = √(36 +64) = √100 = 10
θ = arctan(8/(-6)) = arctan(-4/3) . . . . in the 2nd quadrant
θ ≈ -53.13° +180° = 126.87°
The equivalence is ...
-6 +8i ⇔ 10∠126.87° . . . . . in the form r∠θ
_____
Additional comment
Many scientific and graphing calculators are equipped to work with complex numbers, including their conversion to or from polar form.
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NEED HELP ASAP!!! 50 POINTS Match the following items by evaluating the expression for x = -6.
x^-2
x^-1
x^0
x^1
x^2
Answer:
x^-2 = 1/36
x^-1 = 1/6
x^0 = 1
x^1 = -6
x^2 = 36
#1
(-6)^-21/(-6)²1/36#2
(-6)^(-1)1/(-6)#3
x^0(-6)⁰1#4
(-6)¹(-6)#5
(-6)²36The terminal arm of an angle drawn in standard position rotates in a positive direction through two quadrants of the coordinate plane, and then rotates an additional 25 degrees. What is the measure of the angle?
A. 205°
B. 215°
C. 155°
D. 25°
HELP!!
The measure of the angle is 205°. Then the correct option is A.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
There are 4 quadrants and each quadrant has a measure of 90° angle.
The fact that the orientation is positive indicates that the arm is moving from the first to the second quadrant.
90° + 90° = 180°
The arm has been in the third quadrant due to the additional 25° rotation.
180° + 25° = 205°
The measure of the angle is 205°.
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Solve the system of equations.
5x−4y=−10
−4x+5y=8
Answer:
(- 2, 0 )
Step-by-step explanation:
5x - 4y = - 10 → (1)
- 4x + 5y = 8 → (2)
multiplying (1) by 4 and (2) by 5 and adding result will eliminate x
20x - 16y = - 40 → (3)
- 20x + 25y = 40 → (4)
add (3) and (4) term by term to eliminate x
9y = 0 , thus
y = 0
substitute y = 0 into either of the 2 equations and solve for x
substituting into (1)
5x - 4(0) = - 10
5x - 0 = - 10
5x = - 10 ( divide both sides by 5 )
x = - 2
solution is (- 2, 0 )
Which of the following graphs could be the graph of the function f(x)=0.003x^2(x^2-25)?
Answer:
See below
Step-by-step explanation:
You don't give any options, but here's the information you can get from just the equation itself:
Since your polynomial is a 4th-degree polynomial, I would expect to see 3 turning points at most. I would also expect to see zeroes at x=0, x=5, and x=-5Look for these characteristics and find the appropriate graph.
The number of bacteria, B left parenthesis d right parenthesis, in a certain population increases according to the following function, where time, d, is measured in days:
B(d)= 2425e to the power of 0.15 d
How many days will it take for the bacteria to reach 3,700?
The time taken by the bacterias to reach 3,700 will be 2.81 days.
What will be the time?
It is given in the question that:-The the number of bacteria, B left parenthesis d right parenthesis, in a certain population increases according to the following function, where time, d, is measured in days:
[tex]B(d)=2425\ e^{0.15d[/tex]
[tex]3700= 2425\ e^{0.15d}\\\\\\e^{0.15d}=\dfrac{3700}{2425}\\\\\\0.15d=ln\dfrac{3700}{2425}\\\\\\[/tex]
d = 2.81 days
Hence the time taken by the bacteria to reach 3,700 will be 2.81 days.
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math hw 1
The Normal Distribution
pls help me with my homework!!
thanks,
Using the normal distribution, it is found that the desired measures are given by:
a. Z = -0.67.
b. X = 2.2.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In item a, we have that [tex]X = 36, \mu = 40, \sigma = 6[/tex], and want to find Z, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 40}{6}[/tex]
Z = -0.67.
In item b, we have that [tex]\mu = 1.3, \sigma = 0.6, Z = 1.5[/tex], and want to find X, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.5 = \frac{X - 1.3}{0.6}[/tex]
X - 1.3 = 0.6 x 1.5
X = 2.2.
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PLEASE HELP I BEG YOU! IF I DONT FINISH MY CLASS TODAY I HAVE TO MOVE SCHOOLS
A printing service charges a set-up fee of $11.00 for each order and 15 cents more for each copy. The total cost, c (in dollars), for an order of x copies is given by the following function.
C(x)=11.00+0.15x
What is the total cost for an order of 40 copies?
Answer:
$17 ( 17 USD )
Step-by-step explanation:
C(x)=11.00+0.15x
40 copies:
C(40) = 11+0.15(40)
C(40) = 11+6
C(40) = $17
Therefore, the total cost for an order of 40 copies is $17.
Hope this helps!!!
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P.S. I guess you don't have to change schools now?
write an inequality to represent the situation:the temperature stayed above -15
Answer:
temperature > -15
a girl saved $13.50 in 6 weeks. at that rate, how long will it take to save $108?
Answer:
48 weeks to save $108
Step-by-step explanation:
$13.50 = 6 weeks so dividing both sides by 6 would find out how much each week
$13.50 / 6 = 6 / 6 weeks
$2.25 = per week
so $2.25 times _____ = $108
2.25x = 108 divided both side by 2.25 to get x alone
x is defined by the number of weeks
2.25x / 2.25 = 108 / 2.25
x = 48 $2.25 times 48 = $108
Angles around a point
Grade 8
Answer:
x=45, y=45, z= 131
Step-by-step explanation:
x and y makes up a right angle (90). You can even;y split them in half, which is 45 degrees. Therefore, x= 45 and y also = 45.
Now that there are 2 right angles, that makes up 180. 180+49=229
A full rotation is 360, so you subtract that. 360-229=131
z=131.
Answer:
x = 41°y = 49°z = 131°Step-by-step explanation:
The relevant relations are ...
a straight angle measures 180°a right angle measures 90°vertical angles have the same measure__
The angle marked 49° and the one marked "y" are vertical angles, so have the same measure.
y = 49°
The angle marked "x" and the angle marked "y" together make up a right angle, so total 90°.
x + y = 90°
x + 49° = 90°
x = 41° . . . . . . . . . subtract 49°
The angle marked z and the one marked 49° together make up a straight angle, so total 180°. (They are a "linear pair.")
49° +z = 180°
z = 131° . . . . . . . subtract 49°
The measures of the marked angles are ...
x = 41°
y = 49°
z = 131°
True or False: A sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.
O True
O False
Question 1 True or False: A sector of a circle with a measure of 72 and radius of 12 cm has an arc length of about 15cm. True O False
Step-by-step explanation:
its false
The given statement about the sector of the circle is true.
What is a circle?A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the centre. A circle is also the set of all points that are equidistant from the centre.
Given that we need to check whether a sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm, or not,
Arc length = central angle / 360° × 2π × radius
= 72/ 360° × 2(3.14) × 12
= 0.2 × 6.28 × 12
= 15.072
≈ 15
Therefore, yes the sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.
Hence, the given statement about the sector of the circle is true.
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What is the rage of the data?
Answer
the range is the spread of your data from the lowest to the highest value in the distribution
Answer:
9
Step-by-step explanation:
To find the range, subtract the biggest number (here it's 9) and the smallest number (here it's 0).
9 - 0 = 9
In the diagram, the length of segment AB is 10 units and the radius of the circle centered at A is 4 units. Use this to create two unique triangles, each with a side of length 10 and a side of length 4. Label the sides that have lengths 10 and 4.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.
The two triangles can be made as shown below, the bigger triangle will be an equilateral triangle with each side measuring 10 units, while the smaller triangle will be an isosceles triangle and the measure of the same length side will be equal to the radius of the circle.
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P(Head, Diamond AND Head, Heart) = ?
Using it's concept, it is found that the desired probability is given as follows:
P(Head, Diamond AND Head, Heart) = 1/64.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, for each trial, there are 8 equally as likely outcomes, hence:
P(Head, Diamond) = 1/8.P(Head, Heart) = 1/8.Hence the probability of both outcomes is given by:
P(Head, Diamond AND Head, Heart) = 1/8 x 1/8 = 1/64.
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The graph shows triangle A B C is congruent to triangle D E F by S A S, where segment C A is congruent to segment F D, segment C B is congruent to segment F E, and angle C is congruent to angle F
Move the statements to the table to create a series of transformations that will map triangle A B C onto triangle D E F to show that the two triangles are congruent.
What is Transformation 1 and. Transformation 2
reflection on x-axis
then translations right 3 units & down 2 units
need help asap please
Answer:
The radius of the circle r=12.
The area of a circle is 144π.
Step-by-step explanation:
The radius of the circle is r where 2πr=24π, r=12.
The area of a circle with radius 12 is
A=πr², A=π12², A=144π.
A, B and C lie on a straight line.
Given that angle
y
= 135° and angle
z
= 103°, work out
x
.
Answer:
x = 42
Step-by-step explanation:
a striaght line = 180°
z + y + x = 180
103 + 135 + x = 180
138 + x = 180
subtract 138 from both sides
138 - 138 + x = 180 - 138
x = 42
Answer:
what shape it is
Step-by-step explanation:
wat is the shape
the value of y is directly proportional to the value of x .If y = 124 when x = 8 , what is the value of y when x= - 1/2
Answer:
-7.75
Step-by-step explanation:
[tex]\text{if}\ x = 8 \rightarrow y = 124\\y \propto x\\y = kx\\\\124 = k \times 8 = 8k\\\frac{124}{8} = \frac{8k}{8}\\15.5 = k\\\\\text{We've now found the formula}\\y \propto x\\y = kx = 15.5x\\\\x = -\frac{1}{2} \rightarrow y = ?\\y = 15.5x = 15.5 \times -\frac{1}{2} = -7.75[/tex]
A rectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 x)(9 x) = 88. what does the value of x in her solutions represent? one possible length and one possible width two possible amounts for the widths two possible amounts for the lengths two possible amounts by which the dimensions were changed
The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft
How to determine the value of x?The equation is given as:
(6 + x) * (9 + x) = 88
Express 88 as a product of two factors
(6 + x) * (9 + x) = 8 * 11
Express 8 and 11 as a sum
(6 + x) * (9 + x) = (6 + 2) * (9 + 2)
By comparison, we have:
6 + x = 6 + 2
9 + x = 9 + 2
This means that
x = 2
So, we have:
The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft
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Answer: D) two possible amounts by which the dimensions were changed
Step-by-step explanation:
Edg 2022
I need help answering this question please!
Answer:
p(x) = x⁴ -7x³ +59x² -343x +490
Step-by-step explanation:
Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.
__
The given roots mean the polynomial can be written in factored form as ...
p(x) = (x -2)(x -5)(x -7i)(x -(-7i))
We can combine multiply these factors together to simplify the polynomial.
p(x) = (x² -7x +10)(x² +49)
p(x) = x⁴ -7x³ +59x² -343x +490
_____
Additional comment
Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.
a² -b² = (a -b)(a +b)
(x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)
what is the probability tho computer will select a point in the shaded region?
Need help asap, will give brainliest
Ailsa is twice as old as Barbara. Ailsa is 5 years younger the candy. the average age of candy ailsa and Barbara is 15. determine candys age
Answer:
Candy is 21 years old
Step-by-step explanation:
If Alisa is 16 years old, that would mean that Barbara would be 8, since she is half of Alisa's age.
If we add 5 to Alisa's age, we get 21. To find the average of their ages, we add them all up, and divide by how many people there are (3).
16+8+21=45
45÷3=15
Hope this helps!
Age of Ailsa is 20 years. Then Candy's age will be 15 years.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Ailsa is twice as old as Barbara. Ailsa is 5 years younger than Candy. The average age of Candy, Ailsa, and Barbara is 15.
Let 'x' be the age of Ailsa, 'y' be the age of Barbara, and 'z' be the age of Candy. Then the equations are given as,
x = 2y ...(1)
x - 5 = z ...(2)
(x + y + z) / 3 = 15 ...(3)
From equations (1), (2), and (3), then
x + x / 2 + x - 5 = 45
(5/2) x = 50
x = 20
Then the age Candy is calculated as,
z = 20 - 5
z = 15
Age of Ailsa is 20 years. Then Candy's age will be 15 years.
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What is the best estimate of the area of the figure on the grid if each square has an area of 1 square inch?
O3 square inches
O 5 square inches
O 7 square inches
O9 square inches
Answer: 3 square inches
Step-by-step explanation:
See attached for how I broke the shape up. Since each square is equal to 1 square inch, and the shape is about 3 squares, the answer should be;
O 3 square inches
Please note that different people may estimate differently.
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Jonah is attending a school orchestra concert. He sees his math teacher seated 6 meters ahead of him and his science teacher seated 7 meters to his right. How far apart are the two teachers? If necessary, round to the nearest tenth.
Answer:
42 meters
Step-by-step explanation:
if his math teacher is 6 meters ahead of him and his science teacher is 7 meters to the right of him than you multiply to get the area of distance from each other.
6 x 7 = 42
the teachers are 42 area meters away from each other
A game has a spinner with 15 equal sectors labeled 1 through 15. what is p(multiple of 4 or multiple of 7)? 215 15 25 13
The probability that the spinner is multiple of 4 or multiple of 7 is 1/3
What is probability?Probability is the likelihood or chance that an event will occur, Mathematically;
Probability = expected/total
If a game has a spinner with 15 equal sectors labeled 1 through 15, the total outcome is 15
P(multiple of 4) = 3/15 =1/5
Pr(multiple of 7 )= 2/15
p(multiple of 4 or multiple of 7) = 1/5 + 2/15
p(multiple of 4 or multiple of 7) = 5/15 =1 /3
Hence the probability that the spinner is multiple of 4 or multiple of 7 is 1/3
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how do u solve this equation? ↓
10 = 7 - m
thanksss
Answer:
17
Step-by-step explanation:
10=7-m
m=???
so if you do 10+7 which equal 17 and then do 17-7 you will get ten
m=17
have a good day
Answer:
the answer is -3
Step-by-step explanation:
10 = 7 -m
swap sides so that all the variable terms are on the left hand side
7 - m =10
subtract 7 from both sides
-m + 10 - 7
subtract 7 from 10 to get 3
multiply both sides by -1
m = -3
Convert the angle to radians. leave as a multiple of pi.
324 degrees
a.
startfraction 8 pi over 5 endfraction
c.
startfraction 18 pi over 5 endfraction
b.
startfraction 9 pi over 5 endfraction
d.
startfraction 9 pi over 10 endfraction