Answer:
[tex]\displaystyle z=\frac{5}{2}\biggr(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\biggr)[/tex]
Step-by-step explanation:
A complex number in polar form is [tex]z=r(\cos\theta+i\sin\theta)[/tex] where [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)[/tex], thus:
[tex]r=\sqrt{x^2+y^2}=\sqrt{(\frac{5\sqrt{3}}{4})^2+(-\frac{5}{4})^2}=\sqrt{\frac{75}{16}+\frac{25}{16}}=\sqrt{\frac{100}{16}}=\frac{10}{4}=\frac{5}{2}[/tex]
[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)=\tan^{-1}\biggr(\frac{-\frac{5}{4}}{\frac{5\sqrt{3}}{4}}\biggr)=\tan^{-1}\biggr(-\frac{\sqrt{3}}{3}\biggr)=\frac{11\pi}{6}[/tex]
Thus, the complex number in polar form is [tex]\displaystyle z=\frac{5}{2}\biggr(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\biggr)[/tex]
Choose the histogram that has the smallest variance.
The histogram first represents the smallest variance option first is correct.
What is a histogram?It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.
We have four histograms shown in the picture.
As we know in a histogram, the curves that resemble hills show groupings of statistics that are close collectively, leading to low variation.
Whenever the taller bars are farther away from the mean in a histogram, the variability is greater, and when the taller bars are closer to the mean, the variability is less.
In the histogram first, there is very less variability.
Thus, the histogram first represents the smallest variance option first is correct.
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Based on the information in the two-way table, what is the probability that a person selected at random is Ages 16-18 and has prepared a meal for their family? Round your answer to the nearest tenth of a percent.
The probability that a person selected at random is Ages 16-18 and has prepared a meal for their family
How to determine the experimental probability?From the table of values, we have:
Age 16 - 18 that has performed meal = 8
Total = 30
The probability is then calculated using:
P(16 - 18) = n(16 - 18)/Total
This gives
P(16 - 18) = 8/30
Simplify
P(16 - 18) = 4/15
Hence, the probability is 4/15
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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°
find the value of x.....
The food store sold 88 ice cream cakes in June. If it would sell 25% more ice cream cakes in July, how many more ice cream cakes would they sell in July than in June?
Caroline's favorite animal is the dolphin. One of the dolphins in the tank is 4 meters long. What is its length in centimeters?
Answer:
400 centimeters
Step-by-step explanation:
hope this helps. have a nice day
Please Help Giving Brainlist!!!!! Given that the area of rectangle IJKL is 490 units^2, what are its length and width?
Answer:
Option 4
Step-by-step explanation:
Equating given length and width to the area :
8x(5x) = 49040x² = 490x² = 490/40x² = 12.25x = 3.5Finding the dimensions :
length = 8x = 8(3.5) = 28 unitswidth = 5x = 5(3.5) = 17.5 unitsfind the value of each of the lettered angles in the diagram below
Answer:
Angle a = 114 Angle b = 114 Angle c = 66 Angle d = 66
Step-by-step explanation:
180 - 48 = 132
132/2= 66
180 - 66 = 114
!!!!!!ANSWER!!!!!!
An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of
alues for the third side, s?
2< s < 18
!!!!!!! 6
Os<2 ors > 18
s< 6 or s> 12.8
Answer:
1st option
Step-by-step explanation:
given 2 sides of a triangle then the third side s is in the range
difference of 2 sides < s < sum of 2 sides , that is
10 - 8 < s < 10 + 8
2 < s < 18
To which of the following situations can the function y=5x+10 best be applied?
A. The number of miles a person walks if he walks for 5 hours at the rate of 10 miles per hour
B. The total weight on a scale if 5 pounds is placed there initially and a series of 10-pound weights are added to it
C. The total wages earned by a waiter who is paid $5 per hour and earns $10 in tips
D. The combined length of 5 boards, each 10 feet longer than the width of a doorway
The situation in which the linear function y = 5x + 10 can be applied is given by:
C. The total wages earned by a waiter who is paid $5 per hour and earns $10 in tips.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we want a function with a slope of 5(rate of change), and an y-intercept of 10(initial quantity), hence option C is correct.
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Please help me and hurry
Answer:
1.5 x 10 ^4
Step-by-step explanation:
Answer:
1.5 x 10 ^4
Step-by-step explanation:
hello hope this helps
The parent cosine function is transformed to create the function . which graphed function has the same amplitude as function m?
Based on the graph given, the option that will show the same amplitude as function m is graph D.
Which graphed function is this about?The cosine function is seen as:
f(x) = A*cos(kx) + M
And the functions are:
A stands for amplitude, k is angular frequency,M is the midline.When the function is m(x) = -2*cos(x+π).
The absolute value of the amplitude will be 2*|-2| = 4
Therefore, the option that can have the requirement above is graph D.
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Please help me with Proportions
Answer:
Step-by-step explanation:
7. Hours Money earned
4 34
8 68
10 85
14 119
8. Seconds yards
1 9
3 27
6 54
10 90
9. Minutes Cost
5 $1.50
12 $3.60
24 $7.20
30 $9.00
19. Solve the following inequality.
Answer:
c
Step-by-step explanation:
(5y - 1) = 4y + (9y - 4) = 5y
2y > .75
Answer:
C. The solution set is {y|y > 0.75}.
Step-by-step explanation:
Given :
5y - 1 < 9y - 4Add 4 to each side.
5y - 1 + 4 < 9y - 4 + 45y + 3 < 9ySubtract 5y from each side.
5y + 3 - 5y < 9y - 5y4y > 3y > 3/4y > 0.75Solution set
C. The solution set is {y|y > 0.75}.
Someone help me.............asap
Answer:
11 h
Step-by-step explanation:
1/2 h
11h 1/2 will be need for a bike
What is the surface area for a rectangular prism with the height of 6 inches, width of 8 inches, and the length of 4 inches
Answer:
Using the formula, we can find that the surface area is 208 in².
Step-by-step explanation:
To find the surface area (SA) for a rectangular prism, substitute its dimensions into the formula and solve.
DimensionsDimensions mean the side lengths of the shape, the height, width and length. We know the dimensions from the question.
Height: h = 6 in
Width: w = 8 in
Length: l = 4 in
FormulaWe will need the formula to find the surface area for rectangular prisms. Note that different shapes have a different formula for finding surface area.
[tex]SA= 2(lw + lh + hw)[/tex]
Substitute the dimensions h = 6in, w = 8in and l = 4in into the formula.
[tex]SA= 2((4\ in)(8\ in) + (4\ in)(6\ in) + (6\ in)(8\ in))[/tex]
Remember order of operations (BEDMAS) when solving. Multiply within the brackets first.
[tex]SA= 2(32\ in^{2} + 24\ in^{2} + 48\ in^{2})[/tex] Add within the brackets.
[tex]SA= 2(104\ in^{2})[/tex] Multiply.
[tex]SA= 208\ in^{2}[/tex] Final answer
Tip: The final answer for area will always have squared units.
∴ The surface area (SA) of the rectangular prism with a height of 6 inches, width of 8 inches, and length of 4 inches is 208 squared inches.
PLEASE HELP!!! NEED QUICKLY!!! WILL GIVE EXTRA POINTS AND WILL MARK BRAINLIEST!!! NEED ANSWERS TO ALL
Answer:
B and D have a horizontal line of symmetry ( their top and bottom parts match ) Some letters like X, H, and O, have vertical and horizontal lines of symmetry. some like P, R, and N have no lines of symmetry.
Step-by-step explanation:
A,. C,. D,. E,. H,. I,. M,. O,. T,. U,. V,. W,. X,. and Y have lines of reflective symmetry. Some of them have more than one.
'O' has an infinity of them.
There is no way for you to give extra points.
What is the solution to this equation?
log4(x^2+1)= log4 (-2x)
A.no solution
B.x = 1
C.x = -1
D. X=2
Answer:
C. x = -1
Step-by-step explanation:
Here :
log 4 (x² + 1) = log 4 (-2x)
Then :
x² + 1 = -2x
x² + 2x + 1 = 0
(x + 1)² = 0
x + 1 = 0
x = -1
25. Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not
drawn to scale.
12 cm
6 cm
45
2 cm
084 cm²
96 cm²
72 cm²
108 cm²
The area of a the trapezoid given in the diagram is calculated as: B. 96 cm².
What is the Area of a Trapezoid?Area of trapezoid = 1/2(a + b)h
Given the following:
a = 12 cmb = 12 + 2 + (6/tan 45) = 20 cmh = 6 cmArea of the trapezoid = 1/2(12 + 20)6
Area of the trapezoid = 96 cm²
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Multiply.
[tex]\frac{\sqrt{2}}{6}cis (\frac{3\pi }{5})[/tex]·[tex]\frac{\sqrt{6}}{4}cis (\frac{2\pi }{3})[/tex]
A.[tex]\frac{\sqrt{3}}{12}cis(\frac{19\pi }{15})[/tex]
B. [tex]\frac{\sqrt{3}}{12}cis(\frac{2\pi }{5})[/tex]
C. [tex]\frac{\sqrt{2}}{8}cis(\frac{2\pi }{5})[/tex]
D. [tex]\frac{\sqrt{2}}{8}cis(\frac{19\pi }{15})[/tex]
Multiply the moduli and add the arguments:
√2/6 cis(3π/5) × √6/4 cis(2π/3)
= (√2/6 × √6/4) cis(3π/5 + 2π/3)
= √3/12 cis(19π/15) … [A]
(9x^2+5x^2+11x)+(-2x^3+9x-8x^2)
Answer:
First step is to remove those unnecessary brackets :[tex] \longrightarrow\tt \: 9 {x}^{3} + 5 {x}^{2} + 11x - 2 {x}^{3} + 9x - 8 {x}^{2} [/tex]
Combine the like terms :[tex] \longrightarrow \tt \: 9 {x}^{3} - 2 {x}^{3} + 5 {x}^{2} - 8 {x}^{2} + 11x + 9x[/tex]
[tex] \longrightarrow \boxed{\tt \: 7 {x}^{3} - 3 {x}^{2} + 20x}[/tex]
Our final answer is 7x^3 - 3x^2 + 20x .--------- HappY LearninG <3 --------
Which triangle congurence theorem proves that ABD ≈ CBD?
AAS
SAS
HL
CPCTC
Answer:
AAS
Step-by-step explanation:
the ansewer
4. At a local print shop, 25 copies cost $1.50. At this rate, how much would 60 copies cost?
Answer:
60 copies would cost 3.60
Step-by-step explanation:
-(6)³;(-6)³
what is the answer to this?
Answer:
Step-by-step explanation:
-(6)³=-6×6×6=-216
(-6)³=(-6)×(-6)×(-6)=-216
Find the surface area and lateral area of the following three prisms. Be sure to show all of your work.
Problem 1
L = 10 = length
W = 5 = width
H = 4 = height
SA = surface area of a rectangular prism, aka block or box
SA = 2*(LW+LH+WH)
SA = 2*(10*5+10*4+5*4)
SA = 220
--------------------
LA = lateral area, aka wall area
LA = (perimeter of the base)*(height)
LA = (2L+2W)*H
LA = (2*10+2*5)*4
LA = 120
or
LA = SA - (floor area) - (ceiling area)
LA = SA - 2*(area of the floor)
LA = 220 - 2*(LW)
LA = 220 - 2*(10*5)
LA = 220 - 100
LA = 120
--------------------
Answers:
Surface Area = 220 square feet
Lateral Area = 120 square feet
==========================================================
Problem 2
Imagine rotating the object so that the triangular face is resting on the flat ground. This means the triangular faces are the floor and ceiling. The walls of any prism are always rectangles.
Focus on the right triangle with leg b = 4 and hypotenuse c = 5.
Use the pythagorean theorem to find that a = 3 is the missing leg length.
The triangle has base = 4 and height = 3, so its area is base*height/2 = 4*3/2 = 6 square inches. This is the area of the floor and ceiling each.
--------------------
This is the summary so far
base or floor area = 6 square inchesdepth of the prism = 8 inches(a,b,c) = (3,4,5) are the sides of the right triangleThose values are then plugged into the formulas below.
SA = surface area of a triangular prism
SA = 2*(base area) + depth*(a+b+c)
SA = 2*(6) + 8*(3+4+5)
SA = 108
LA = lateral area
LA = depth*(a+b+c)
LA = 8*(3+4+5)
LA = 96
or
LA = SA - 2*(floor area)
LA = 108 - 2*(6)
LA = 96
Note that a+b+c = perimeter of the triangular base.
--------------------
Answers:
Surface Area = 108 square inches
Lateral Area = 96 square inches
==========================================================
Problem 3
Imagine rotating the figure so that the octagon is resting on the flat ground.
Refer to the screenshot below to see the steps on computing the area of the regular octagon, aka the floor area.
The floor area is approximately 120.710678 square cm. The same goes with the ceiling because the floor and ceiling are congruent regular octagons that are parallel.
Each rectangular wall has an area of 5*22 = 110 square cm. Eight identical walls give a total lateral area of 8*110 = 880 square cm.
Add the floor and ceiling area to the wall area to get the total surface area
floor + ceiling + walls = 120.710678 + 120.710678 + 880 = 1121.421356
--------------------
Answers:
Surface Area = 1121.421356 square cm (approximate)
Lateral Area = 880 square cm
A wire of length 4x is bent into the shape of a circle. A. Express the circumference of the circle as a function of 4x. B. Express the area of the circle as a function of 4x.
The circumference of the wire is 4x and the area of the circle is 4x^2/π
How to determine the circumference?The length of the wire is given as;
Length = 4x
This represents the circumference.
Hence, the circumference of the wire is 4x
How to determine the area?In (a), we have:
Circumference = 4x
Calculate the radius using:
2πr = 4x
Divide through by 2π
r = 2x/π
The area is:
Area = πr^2
This gives
Area = π(2x/π)^2
Evaluate
Area = 4x^2/π
Hence, the area of the circle is 4x^2/π
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For his phone service, Omar pays a monthly fee of $26, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is
$108.74
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
D
>
DO
20
х
5
?
Answer: m ≥ 1,379
Step-by-step explanation:
$26 monthly fee
$0.06/minute of use
$108.74 (least charged in a month)
m = number of minutes
26 + 0.06m ≥ 108.74
0.06m ≥ 108.74 - 26
0.06m ≥ 82.74
[tex]\frac{0.06m}{0.06}[/tex] ≥ [tex]\frac{82.74}{0.06}[/tex]
m ≥ 1,379
Will mark brainliest for right answer
Tasha has foam blocks stored in a box that measures 214 ft long by 2 ft wide by 2 ft tall.
Each foam block is a cube with 12ft edge length.
How many blocks can fit into the box?
Which is wrong? Question is below in link.
In simplifying the given expression, the error made was in Step 4. 7c - 41 is wrong. The correct answer should be -c - 59.
How to Simplify Expressions?In simplifying expressions, like the one given, first apply the distributive property to clear out the bracket.
Next is to combine like terms. In step 4, there was an error in the calculation while combining like terms.
-6c - 3c + 10c should give us -c NOT 7c.
Also, 3 - 12 - 50 should give us -59 not -41.
Therefore, the correct answer should be:
-c - 59.
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