9514 1404 393
Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
_____
Additional comments
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
__
At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
The height of a triangle is 3 cm more than the length of the base. If the area of the triangle is 119cm^2 find the height and the length of the base.
Answer:
[tex]base = 14cm \\ height = 17cm[/tex]
Step-by-step explanation:
Let the length of the base be x
So length of the base = x
height = x +3
[tex]area \: \: of \: \: a \: \: triangle = \frac{1}{2} \times b\times h \\ 119 = \frac{1}{2} \times x \times (x + 3) \\119 = \frac{ {x}^{2} + 3x }{2} \\ 119 \times 2 = {x}^{2} + 3x \\ 238 = {x}^{2} + 3x \\ 0 = {x}^{2} + 3x - 238 \\ {x}^{2} + 3x - 238 = 0 \\ {x}^{2} + 17x - 14x - 238 = 0 \\ x(x + 17) - 14(x + 17) = 0 \\ (x - 14)(x + 17) = 0 \\ \\ x - 14 = 0 \\ x = 14 \\ \\ or \\ x + 17 = 0 \\ x = - 17 \\ \\ length \: \: cannot \: \: be \: \: given \: \: as \: \: a \: \: negative \: \: number \: \: \\ \\ so \\ \: \: base \: = 14cm \\ height = x + 3 \\ = 14 + 3 \\ = 17cm[/tex]
please hello :(
The Venn diagram below shows the type of crops planted by 50 farmers in a particular area.
If a farmer is chosen at random, what is the probability that the farmer planted corn OR lettuce?
Answer:
D ( It may be because I think other two are non relative )
Answer:
b) 1\2
Step-by-step explanation:
I need help with both questions.
Answer:
y = 17x
$595
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{85 - 51}{5 - 3}[/tex] = [tex]\frac{34}{2}[/tex] = 17 (find the slope, gradient or rate of change)
The y intercept is 0. Zero hours = 0 charge.
y = 17(35)
y = 595
The annual membership fee at a local club is $100. After each year of membership, the fee is lowered by $8 a year. The
arithmetic sequence {100, 92, 84,...) models this situation.
Write an explicit function that describes the fee at the club after n years of membership. Then rewrite your function in the
slope-intercept form.
Answer:
y = 100 - 8(n - 1)
Step-by-step explanation:
I. if n = 1 or 1st year = 100 - 8(1-1) is 100
if n = 2 or 2nd year = 100 - 8(2-1) is 92
if n = 3 or 3rd year = 100 -8(3-1) is 84
Hope it'll help.
An election ballot asks voters to select two city commissioners from a group of six candidates. In how many ways can this be done?
Answer:
15 ways
Step-by-step explanation:
There are 6 choices available for the first seat
There are 5 remaining choices for the second seat.
6(5) = 30 possible combinations
however, as the two seats are of equal power, the combination of AB is equal the the combination of BA etc, This eliminates half of the options.
When taking a measurement with a pH meter, keep the instrument in the Choose... until it is needed. Rinse the pH meter with Choose... and gently pat dry. Place the meter in the sample solution, and record the measurement when the
Answer:
Storage solution; deionized water; stabilizes
Step-by-step explanation:
A pH scale measures the concentration of hydrogen ions in acidic and alkaline solutions.
In chemistry, pH literally means the power of hydrogen ions and it is a measure of the molar concentration of hydrogen ions in a particular solution; thus, specifying the acidity, neutrality or basicity of any chemical solution.
Mathematically, the pH of a solution is given by the formula;
[tex] pH = -log_{10}(H^{+}) [/tex]
On a pH scale, a solution with a pH of 7 is neutral, a solution with a pH below 7 is acidic and it's basic (alkaline) when it's pH is above 7.
A pH meter can be defined as a scientific instrument or device designed and developed for the measurement of the hydrogen-ion concentration in water-based solutions, in order to determine their level of acidity or alkanility.
As a general rule, when using a pH meter to take a measurement, you should keep it in a storage solution until it is needed. Also, a deionized water should be used to rinse the pH meter and gently pat dry.
Furthermore, the pH meter should be placed in a given sample solution and a reading of the measurement taken when the pH of the solution stabilizes
When taking a measurement with a pH meter, keep the instrument in the storage solution until it is needed. Rinse the pH meter with distilled water and gently pat dry.
The pH meter has been the instrument used for the measurement of the hydrogen ion concentration in a sample. The instrument has consisted of a probe that has been placed in the storage medium when it is not in use.
The working procedure of the pH meter has required the washing of pH meter with the distilled water and properly removing the excess water from the probe by pat dry.
The probe has been immersed in the sample and the pH has been recorded. After the experiment, the instrument has been again washed with the distilled water and get stored in the storage solution.
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I need Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
150.72 cm³314 cm³160 cm³48 cm³Step-by-step explanation:
Put the given numbers in the relevant formula and do the arithmetic.
right cylinder
V = πr²h = 3.14(4 cm)²(3 cm) = 3.14×48 cm³ = 150.72 cm³
cone
V = 1/3πr²h = 1/3(3.14)(5 cm)²(12 cm) = 3.14×100 cm³ = 314 cm³
pyramid of unknown shape
V = 1/3Bh = 1/3(16 cm²)(30 cm) = 160 cm³
square pyramid
V = 1/3s²h = 1/3(3 cm)²(16 cm) = 48 cm³
whats the common difference of p+q, p , p-q
Answer:
- q
Step-by-step explanation:
p - ( p + q )
= p - p - q
= - q
p - q - p
= p - p - q
= - q
Common difference is - q.
What are the solutions to the quadratic equation x^2-16=0
Answer:
x = ±4
Step-by-step explanation:
Hi there!
[tex]x^2-16=0[/tex]
Move 16 to the other side
[tex]x^2=16[/tex]
Take the square root of both sides
[tex]\sqrt{x^2}=\sqrt{16}\\x=\pm4[/tex]
I hope this helps!
Q2 (a). Workout the value of each expression:
i)
X-y when x =
10 and y = 15
n when m
10 and n= = 2
iii) f+2g when f= 5 and g = 10
30
m
Step-by-step explanation:
x=10, y=15
x-y = -5
n=10, m=2
n-m= 8
f=5, g=10
f+2g
5+2(10)
=25
Point J is the midpoint of the line segment KI Find the length of JI.
Answer:
I belive i is 5
Step-by-step explanation:
yannie read 24 pages of a book. one fourth of the book is unread.how many pages are there?
Answer:
32
Step-by-step explanation:
24/3=8, 24+8=32
that's how I think of it
Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?\
Answer:
The directrix is y=6 and focus is (0,4)
The equation of the parabola is,
20-4y=x²
What is the reason for each step in the solution of the equation?
-5(x - 6) = 10x
Drag and drop the reasons into the boxes to correctly complete the table.
–5(x – 6) = 10x
Given
-5x + 30 = 10x
30 = 15x
2 = x
Division Property of Equality
Commutative Property
Addition Property of Equality
Given
Distributive Property
Answer:
Distributive property (-5 is being multiplied to x and - 6)
Addition property of equality (5x is being added in both side of the equation)
Division property of equality (15 is being devided in both side of the equation)
Brainliest please~
The reason for each step will be
Distributive property (-5 is being multiplied to x and - 6)
Addition property of equality (5x is being added in both sides of the equation)
Division property of equality (15 is being divided into both sides of the equation)
What are algebraic properties?
We can solve mathematical equations thanks to algebra's inherent characteristics. The algebraic properties are distributive property, addition property of equality, and division property of equality.
Given expressions are:-
-5x + 30 = 10x
30 = 15x
2 = x
-5x + 30 = 10x ⇒ Distributive property (-5 is being multiplied to x and - 6)
30 = 15x ⇒ Addition property of equality (5x is being added in both sides of the equation)
30 = 15x ⇒ Division property of equality (15 is being divided into both sides of the equation)
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The scores for a particular examination are normally distributed with a mean of 68.5% and a standard deviation of 8.2%. What is the probability that a student who wrote the examination had a mark between 80% and 100%? Give your answer to the nearest hundredth.
Answer:
[tex]P(80/100<x<100/100)=0.08[/tex]
Step-by-step explanation:
We are given that
Mean,[tex]\mu=68.5[/tex]%=68.5/100
Standard deviation, [tex]\sigma=8.2[/tex]%=8.2/100
We have to find the probability that a student who wrote the examination had a mark between 80% and 100%.
[tex]P(80/100<x<100/100)=P(\frac{80/100-68.5/100}{8.2/100}<\frac{x-\mu}{\sigma}<\frac{100/100-68.5/100}{8.2/100})[/tex]
[tex]P(80/100<x<100/100)=P(1.40<Z<3.84)[/tex]
We know that
[tex]P(a<Z<b)=P(Z<b)-P(Z<a)[/tex]
Using the formula
[tex]P(80/100<x<100/100)=P(Z<3.84)-P(Z<1.40)[/tex]
[tex]P(80/100<x<100/100)=0.99994-0.91924[/tex]
[tex]P(80/100<x<100/100)=0.0807\approx 0.08[/tex]
Given that f(x)=x^2 and g(x)=5x+2 , find (f-g)(2), if it exists.
Answer:
(f - g)(2) = -8
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x²
g(x) = 5x + 2
Step 2: Find
Substitute in functions: (f - g)(x) = x² - (5x + 2)[Distributive Property] Distribute negative: (f - g)(x) = x² - 5x - 2Substitute in x [Function (f - g)(x)]: (f - g)(2) = 2² - 5(2) - 2Evaluate: (f - g)(2) = -8Module 8: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Describe how to eliminate the parameter to change from parametric to rectangular form. How does this ability help us with graphing parametric equations?
Answer:
rectangular equation, or an equation in rectangular form is an equation composed of variables like xx and yy which can be graphed on a regular Cartesian plane. For example y=4x+3y=4x+3 is a rectangular equation.
A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y)(x,y) , are represented as functions of a variable tt .
x=f(t)y=g(t)x=f(t)y=g(t)
These equations may or may not be graphed on Cartesian plane.
Step-by-step explanation:
I hope this helps
In 1995 the U.S. federal government debt totaled 5 trillion dollars. In 2008 the total debt reached 10 trillion dollars. Which of the following statements about the doubling time of the U.S. federal debt is true based on this information?
Where are the statements?
3x-2=2(x-5)
find the value of x
Now we have to,
find the required value of x.
Let's begin,
→ 3x-2 = 2(x-5)
→ 3x-2 = 2x-10
→ 3x-2x = -10+2
→ x = -8
Hence, value of x is -8.
Answer:
x = -8
Step-by-step explanation:
3x - 2 = 2 ( x + 5
Solve for x.
Let's solve,
3x - 2 = 2 ( x + 5 )
Step 1:- Distribute 2.
3x - 2 = 2 × x + 2 × 5
3x - 2 = 2x - 10
Step 2 :- Move constant to the right-hand and change their sign.
3x = 2x - 10 + 2
Step 3:- Add -10 and 2.
3x = 2x - 8
Step 4 :- Move variable to the left-hand side and change their sign.
3x - 2x = -8
Step 5 :- Subtract 2x from 2x.
x = -8
Hence, value of x = -8.
Which of the following is true about congruent figures?
Write an expression representing the unknown quantity.
There are 5,682,953 fewer men than women on a particular social media site. If x represents the number of women using that site, write an expression for the number of men using that site.
The expression for the number of men is
.
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Answer:
x - 5,682,953
Step-by-step explanation:
If x is the number of women, and the number of men is 5,682,953 less, then the number of men is x -5,682,953
Please help, I will give brainliest if you answer.
An angle measures 78.6° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
so required angles are 50.7°and 129.3°
Step-by-step explanation:
Let the angle be x
another angle = x + 78.6°
so,
x + x + 78.6° = 180° {being sum of supplementary angle}
so, 2x + 78.6° = 180°
or, 2x = 180° - 78.6°
or, x = 101.4/2
so, x = 50.7°
so another angle = x + 78.6°
= 50.7° + 78.6°
= 129.3°
1/2 litre of kerosene costs $1.50what is the cost ofn2 litre of kerosene
Answer:
$6
Step-by-step explanation:
1.5 × 2 = 3
1 liter = $3
3 × 2 = 6
2 liters of kerosene is $6
An object is dropped from 24 feet below the tip of the pinnacle atop a 1468-ft tall building. The height h of the object after t seconds is given by the equatior h= - 16t2 + 1444. Find how many seconds pass before the object reaches the ground. seconds pass before the object reaches the ground. (Type an integer or a decimal.)
Answer:
9.5 seconds pass before the object reaches the ground.
Step-by-step explanation:
Height of the ball:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -16t^2 + 1444[/tex]
Find how many seconds pass before the object reaches the ground.
This is t for which h(t) = 0. So
[tex]h(t) = -16t^2 + 1444[/tex]
[tex]-16t^2 + 1444 = 0[/tex]
[tex]16t^2 = 1444[/tex]
[tex]t^2 = \frac{1444}{16}[/tex]
[tex]t^2 = 90.25[/tex]
[tex]t = \pm \sqrt{90.25}[/tex]
Since it is time, we only take the positive value.
[tex]t = 9.5[/tex]
9.5 seconds pass before the object reaches the ground.
A store offers different brands of a product. It decides to eliminate the brand
that is most likely to be returned. The table shows the number of items of
each brand that were returned over the past year and the total sold.
Retums
Total sold
Brand A
40
913
Brand B
38
792
Brand C
21
626
Brand D
15
451
Which brand should the store eliminate?
Answer:
In my points of view brand D should elimininate.In table have show the brand of D.If I am wrong I am sorry for talking 5pbt
The brand B must be eliminated since it has highest percentage 4.79%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here,
Brand A percentage = 40/913 ×100
= 4.38%
Brand B percentage = 38/792 ×100
= 4.79%
Brand C percentage = 21/626 ×100
= 3.35%
Brand D percentage = 15/451 ×100
= 3.32%
Therefore, brand B must be eliminated since it has highest percentage 4.79%.
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Find the sum of the series if possible, if not possible explain why:
1+(−2/5)+(−2/5)^2+(−2/5)^3+⋯
Answer:
Step-by-step explanation:
5/7
Sum of a geometric series is a/(1-r) = 1/(1-(-2/5)) = 5/7
When male workers were asked how many hours they worked in the previous week, the mean was with a standard deviation of . Does this suggest that the population mean work week for men exceeds hours
Answer:
We can conclude that the population mean work week for men exceed 40 hours.
Step-by-step explanation:
Given that :
Mean, xbar = 45.6
Standard deviation, s = 14.6
Sample size, n = 893
x = 40
Hypothesis :
H0 : μ = 40
H1 : μ > 40
Using test statistic for one sample t test :
Test statistic = (xbar - μ) ÷ (s/√(n))
Test statistic = (45.6 - 40) ÷ (14.6/√(893))
T = (5.6 / 0.4885703)
Test statistic = 11.46
Using the Pvalue approach :
Reject H0 : if Pvalue < α
Pvalue for test statistic of 11.46 will be approximately 0 (Extremely low)
Hence, Pvalue < α ; We reject H0 ; and conclude that population mean work week for men exceed 40 hours
2. What polygon is formed if you divide this figure into three equal parts? A squares B. triangles C. rhombuses D. kites
Answer: C
Step-by-step explanation:
Use the distributive property to remove parentheses.
-8(x-3w-2)
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Answer:
= -8x +24w +16
Step-by-step explanation:
The factor outside multiplies each term inside parentheses.
-8(x -3w -2) = (-8)(x) +(-8)(-3w) +(-8)(-2)
= -8x +24w +16
Multiply (8 + 3i)(3 + 5i).
39 + 491
9+ 491
24 + 152
24 + 491 + 15/2
(8+3)(3+5)=88
88+(39+491)= 618.
88+(9+491)= 588
88+(24+152)= 264.
sorry could not find the last ansswer..
