Simplifying and expressing each term in standard and polar form are respectively; 49/2 and -512 - 512i√3
How to express an equation in polar form?
1) We are given the expression;
[7 cos (45)]²
We know that cos (45) in standard form is 1/√2. Thus;
[7 cos (45)]² = (7 * 1/√2)² = 49/2
2) We are given the expression;
(-2 + 2i√3)⁵
Using binomial theorem, we have;
(−2)⁵ + 5(−2)⁴ (2i√3) + 10(−2)³(2i√3)² + 10(−2)²(2i√3)³ + 5 * −2(2i√3)⁴ + (2i√3)⁵
Simplifying each term gives;
−32 + 160i√3 + 960 − 960i√3 −1440 + 288i√3
⇒ -512 - 512i√3
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can you submit a picture of the question
A three dimensional object is created by rotating a circle about one of its diameters.
What is the shape of the resulting object?
O A Cone
OB Disc
OC. Sphere
OD. Cylinder
Answer:
C. Sphere
Step-by-step explanation:
If you rotate a circle about one of its diameters, it produces the three dimensional shape of a sphere.
See attached diagram.
Estimate the product of 2.28 × 5.59 using compatible numbers.
The quotient of 2.28 × 5.59 using compatible numbers is approximately 12.75
What are products?Quotients are result derived from the multiplication of two rational or integers. Given the expression
2.28 × 5.59
Convert to fraction
2.28 × 5.59 = 228/100 ÷ 559/100
2.28 × 5.59= 127452/10000
2.28 × 5.59= 12.75
Hence the quotient of 2.28 × 5.59 using compatible numbers is approximately 12.75
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Huw has a maths test. the second question is:
here is huw's working. 9 days is incorrect. work out the correct answer.
Huw's answer of 9 days is incorrect because more guests would finish the food in less time so the number of days for 30 guests is less than 6 days.
The number of days that the food can last 30 guests is 4 days.
How long will Seaview Hotel's food feed 30 guests?More guests would eat the food faster which means that it would be finished in less days than the 6 days used by 20 guests.
To find the days the food would last 30 guests, use the inverse proportion formula:
= (Number of guests x Number of days food lasts for guests) / New number of guests
= (20 x 6) / 30
= 4 days
Full question is:
The only food provided for guests at Seaview Hotel is breakfast. The hotel has enough food to make breakfast for 20 guests for 6 days. How long would the food last 30 guests? You may assume each guest eats the same amount of food for breakfast.
Without working out the correct answer, explain why Huw’s answer of 9 days is incorrect.
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Write a recursive formula for a_na n , the n^{\text{th}}n th term of the sequence 50, -10, 2, ...50,−10,2,....
The recursive formula of the sequence is [tex]a_n = -\frac{a_{n-1} }{5}[/tex] where a1 = 50
How to determine the recursive sequence?The sequence is given as:
50,−10,2,....
The above sequence is a geometric sequence, and it has the following parameters:
First term, a = 50Common ratio, r = -1/5 i.e. -10/50 = 5This means that the product of the current term and -1/5 gives the next term.
i.e.
[tex]a_n = -\frac{a_{n-1} }{5}[/tex]
Hence, the recursive formula of the sequence is [tex]a_n = -\frac{a_{n-1} }{5}[/tex] where a1 = 50
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Use the function to predict the minimum target heart rate for a person 20 years old. beats per minute
The minimum target heart rate for a person 20 years old is 120 beats per minute
How to predict the minimum target heart rate?The equation of the function is given as:
y = -0.6x + 132
Where x represents the age, and y represents the minimum target heart rate
From the question, we have:
x = 20
Substitute x = 20 in y = -0.6x + 132
This gives
y = -0.6 *20 + 132
Evaluate
y = 120
Hence, the minimum target heart rate for a person 20 years old is 120 beats per minute
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Answer:
Answer is 120 !!
Step-by-step explanation:
~Hope this helps! :)
100 POINTS AND BRAINLIST
The answer could be c
Because the title of the table says the dollar sales and how much it's increasing so my answer is c
Hope I helped!
TheOneAndOnlyLara~
Answer:
C.
Step-by-step explanation:
Hope it helped!
SUPER EASY 9TH GRADE GEOMETRY
- find the area
using the diagonal: area = 1/2 x diagonal^2
the full diagonal is 20 x 2 = 40 cm
area = 1/2 x 40^2 = 800
answer: 800 cm^2
Hailey's laundry basket contains 777 socks. These 777 socks account for approximately 21\!!, percent of Hailey's socks. How many socks does Hailey have in total
The number of socks for Hailey will be 163.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Hailey's laundry basket contains 777 socks. These 777 socks account for approximately 21, per cent of Hailey's socks.The number of Haley's socks will be calculated as=
Socks = 777 x 21/100
Socks = 777 x 0.21
Socks = 163
Therefore the number of socks for Hailey will be 163.
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Keno and Angelita will randomly select from a treat bag containing 6 lollipops and 4 gum balls. -Keno will select a treat, replace it, and then select a second treat. -Angelita will select a treat, not replace it, and then select a second treat. Who has the greater probability of select 1 lollipop and then 1 gumball?
Keno
[tex]|\Omega|=10^2=100\\|A|=6\cdot4=24\\\\P(A)=\dfrac{24}{100}=\dfrac{6}{25}=24\%[/tex]
Angelita
[tex]|\Omega|=10\cdot9=90\\|A|=6\cdot4=24\\\\P(A)=\dfrac{24}{90}=\dfrac{4}{15}\approx26,7\%[/tex]
Therefore, the answer is Angelita.
Show ALL work and calculations. Max needs to choose an outfit. He has three sweaters: red, blue and pink; two pants: yellow and black; and two kinds of shoes: dress shoes and running shoes.Draw a probability tree diagram to show all his combinations to choose from.
Answer:
- Red
- Yellow
- Dress
- Running
- Black
- Dress
- Running
- Blue
- Yellow
- Dress
- Running
- Black
- Dress
- Running
- Pink
- Yellow
- Dress
- Running
- Black
- Dress
- Running
If JL = 30, JK = 18, and LM = 6, then the value of LN is:
Answer: LN = 15
Make a proportional relationship:
[tex]\sf \dfrac{LN}{JL} = \dfrac{LM}{KL}[/tex]
Insert the values:
[tex]\rightarrow \sf \dfrac{LN}{30} = \dfrac{6}{30-18}[/tex]
cross multiply:
[tex]\rightarrow \sf LN = \dfrac{30(6)}{12}[/tex]
Simplify:
[tex]\sf LN =15[/tex]Answer:
LN = 15
Step-by-step explanation:
The arrows on the line segments indicate they are parallel.
[tex]\implies \overline{KM} \parallel \overline{JN}[/tex]
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then it divides these two sides proportionally.
[tex]\textsf{If }\overline{KM} \parallel \overline{JN}, \textsf{ then }\dfrac{LK}{LJ}=\dfrac{LM}{LN}[/tex]
Given:
LM = 6JL = 30JK = 18⇒ LK = JL - JK = 30 - 18 = 12
Substituting the values into the equation and solving for LN:
[tex]\begin{aligned}\implies \dfrac{LK}{LJ} & = \dfrac{LM}{LN}\\\\\dfrac{12}{30} & = \dfrac{6}{LN}\\\\12LN & = 30 \cdot 6\\\\LN & = \dfrac{180}{12}\\\\LN & = 15\end{aligned}[/tex]
I don’t understand this whatsoever
Answer:
7
Step-by-step explanation:
4*(x-2)^2 - 9
replace x with 4; 4*(4-2)^2-9
solve inside parenthesis; 4*(2)^2-9
order of operations; 4*4 - 9 becomes 16-9=7
Grayson is preheating his oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 15° per minute after being turned on. What is the temperature of the oven 6 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answer:
155 Degrees
Step-by-step :
(Time x Rate of Temp) + Initial Temp = Final Temperature
Ex. (6 * 15) + 65 = 155 Degrees
Answer:
The temperature of the oven 6 minutes after being turned on is 155°
The temperature of the oven t minutes after being turned on is 15t + 65
Step-by-step explanation:
y=mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The y intercept is when x = 0, so the initial temperature
b = 65°
The slope is increase at a rate of per minute after being turned on.
m = 15°
The y coordinate will represent the temperature of the oven after a certain amount of minutes after being turned on
y
The x coordinate will represent the amount of minutes after the oven being turn on
x = t
combine:
What is the temperature of the oven tt minutes after being turned on?
y = 15t + 65
What is the temperature of the oven 6 minutes after being turned on?
t = 6 minutes
y = 15t + 65
y = 15(6) + 65
y = 90 + 65
y = 155
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The box-and-whisker plot represents a data set. Which statements are never true for this data set?
The statement that can never be true is the data set contains a value of 3.
What is box plot?A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
minimum number = 8
maximum number = 22
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what would i put in, in the blanks? please help, i don’t get this
Answer:
Parent function
[tex]f(x)=\log_2(x)[/tex]
Since we cannot take logs of zero or negative numbers, the domain is [tex](0, \infty)[/tex] and there is a vertical asymptote at [tex]x=0[/tex].
There are no horizontal asymptotes and the range is [tex](- \infty,\infty)[/tex].
The end behaviors of the parent function are:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow - \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]
To determine the attributes of the given function, compare the given function with the parent function.
Given function
[tex]f(x)=- \log_2(x)+5[/tex]
The given function is reflected in the x-axis. Therefore, the end behaviors are a reflection of those of the parent function:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow - \infty[/tex]
As the given function is translated vertically (5 units up) only, the domain, range and asymptote will not change, since the function has not been translated horizontally.
[tex]\textsf{Domain}: \quad (0, \infty)[/tex]
[tex]\textsf{Range}: \quad (- \infty, \infty)[/tex]
[tex]\textsf{Asymptote}: \quad x=0[/tex]
Conclusion
The function f(x) is a [tex]\boxed{\sf logarithmic}}[/tex] function with a [tex]\boxed{\sf vertical}}[/tex] asymptote of [tex]\boxed{x = 0}[/tex].
The range of the function is [tex]\boxed{(- \infty, \infty)}[/tex], and it is [tex]\boxed{\sf decreasing}[/tex] on its domain of [tex]\boxed{(0, \infty)}[/tex].
The end behavior on the LEFT side is as [tex]\boxed{x \rightarrow 0^+}[/tex], [tex]\boxed{f(x) \rightarrow \infty}[/tex], and the end behavior of the RIGHT side is [tex]\boxed{x \rightarrow \infty}[/tex], [tex]\boxed{f(x) \rightarrow -\infty}[/tex].
Solve the following equation for x.
(5/6)x + 10 = 30
x = 24
x = 20
x = 20/6
x = 25/6
Answer:
x=24
Step-by-step explanation:
6×(5/6)x +6(10)=6(30)
5x +60=180
5x +60-60=180 - 60
5x=180 -60
5x=120
5x/5 =120/5
x=24
Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
5, 5, 5
5, 1, 5
1, 5, 5
1, 1, 5
A triangle is a three-edged polygon with three vertices. The length of the sides of the triangle is 5, 5, and 5√2.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Since the two angles are equal, therefore, the length of the two legs of the isosceles right triangle will be equal and will be less than the hypothenuse.
Hence, the length of the sides of the triangle is 5, 5, and 5√2.
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How large the size of a sample needs to be if we want to a 90% confidence level with a margin of error no more than 1.5%
Answer:
A 90 percent level can be obtained with a smaller sample, which usually translates into a less expensive survey. To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000.
helpppp please and quick
Answer:
The way is in the steps.
Step-by-step explanation:
y = sin(x) has a period of 2π and amplitude of 1.
a) y = a * sin b(x - c) - d
y = 7/2 * sin 2/3(x - π/4) - 2
[tex]a=\frac{7}{2}[/tex][tex]b=\frac{2}{3}[/tex][tex]c = \frac{\pi }{4}[/tex][tex]d=-2[/tex]b) amplitude is affected by a = 7/2 , so the amplitude is 7/2.
The range is (-5.5 , 1.5) because looking at the graph, but also by making a table to help find the range.
c) Period = 2π/b
Period = 2π/2/3 = 3π
d) Horizontal Shift left/right is dependent on c.
c = π/4 , so Horizontal Shift to the Right by π/4
Vertical Shift up/down is dependent on d.
d = -2 , so Vertical down shift by 2.
The nature of the roots of 3x^2+4x-5=0
Answer:
Imaginary Roots
Step-by-step explanation:
The quadratic equation ax^2 + bx + c = 0 is written in standard form, and the formula is
x = [-b ± √(b^2 - 4ac)]/ 2a
Given:
3x2 - 4x + 5 = 0'
Here a = 3, b = -4 and c = 5
Substituting:
x = [-(-4) ± √((-4)2 - 4 × 3 × 5)]/ (2 × 3)
Further Simplification:
x = [4 ± √(16 - 60)]/6 ----> Discriminant: b^2 - 4ac = -44 < 0.
x = [4 ± √-44]/ 6
Now, we get:
x = [4 ± 2√-11]/ 6
x = [2 ± i √11]/ 3
Therefore, The best description of the roots of the equation 3x2 - 4x + 5 = 0 is imaginary roots.
Vertical angles are equal in measure.
Osometimes
Onever
O always
The vertical angles are always equal in measure.
What is Vertical Angle?Vertical angles are angles opposite each other where two lines cross.
Here, As given in definition
All the vertical angles are always equal with each other.
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Seleccione el número que se puede
describir mejor como enteros.
the second one
Step-by-step explanation:
What is the equation for this graph?
Answer:
hmm try multiplying every number at the top and then put them all together
then divide the answer u got and u have ur answer :)
Step-by-step explanation:
Abcd is a trapezoid. = 1 cm and = 5 cm, and the area = 7.5 cm2. what is the altitude of the trapezoid? 1.5 cm 2.5 cm 3 cm 2 cm
Answer:
2.5cm
Step-by-step explanation:
hope it helps. if there's any question feel free to ask me I be ready to respond appropriately bye.
The altitude of the trapezoid is approximately 2.5 cm.
Here, we have,
To find the altitude of the trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) * (sum of the bases) * altitude
Given that
one base (a) is 1 cm, the other base (b) is 5 cm, and the area is 7.5 cm², we can plug these values into the formula and solve for the altitude:
7.5 cm² = (1/2) * (1 cm + 5 cm) * altitude
Simplifying:
7.5 cm² = (1/2) * 6 cm * altitude
7.5 cm² = 3 cm * altitude
Now, we can isolate the altitude by dividing both sides of the equation by 3 cm:
altitude = 7.5 cm² / 3 cm
altitude ≈ 2.5 cm
Therefore, the altitude of the trapezoid is approximately 2.5 cm.
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Isabel says that 0.02 can be expressed as 20%. Is she correct? Explain why or why not.
[tex]\text{She is not correct because}\\\\20\% = \dfrac{20}{100} = \dfrac 2{10} = 0.2 \neq 0.02[/tex]
Find all the missing angles and side lengths
use pythagoras theorem to find the missing side, then find the an angle using the sine rule. at this point you will only have one angle left. using the law that sum of all angles of a triangle add up to 180⁰, you can do 180⁰- ( [the angle you found by the sine rule] + 90⁰) hope this wasn't too complicated :)
i did (b) as an example attatched (2 photos bc it couldn't fit it all)
Emergency answer now I will make it brainliest!!!!
are there any answer choices?????
Step-by-step explanation:
If .111... = 1/x, what is x?
Correct answer will get brainliest
Answer:
x = 9
Step-by-step explanation:
When 1 is divided by 9, we understand it is a non-terminating decimal number because the denominator consists of other number other than 2 and 5.
Now, let's get into how to solve for x :
Divide both sides by .111... :
1/.111... x .111... = 1/.111 x 1/x
1 = 1/(x)(.111....)
Multiply both sides by x :
1(x) = (x)/(x)(.111...)
x = 1/.111...
x = 9 (nearest whole number)
Answer:
[tex]\sf 0.\dot{1}=\dfrac{1}{9}[/tex]
Therefore, x = 9
Step-by-step explanation:
To convert 0.11111... to a fraction:
Equation 1
Let: y = 0.11111...
Equation 2
Multiply both sides by 10:
⇒ y · 10 = 0.11111... · 10
⇒ 10y = 1.11111...
Subtract Equation 1 from Equation 2 to eliminate the recurring digits after the decimal:
⇒ 10y - y = 1.1111... - 0.11111...
⇒ 9y = 1
Divide both sides by 9
[tex]\implies \sf y=\dfrac{1}{9}[/tex]
Therefore,
[tex]\sf 0.\dot{1}=\dfrac{1}{9}[/tex]
So if:
[tex]\sf 0.\dot{1}=\dfrac{1}{x}[/tex]
Then x = 9
Find the sum of the first 7 terms of the following series, to the nearest integer. 150,60,24...
Answer:
250
Step-by-step explanation:
The sum of the terms of a geometric series is given by the formula ...
Sn = a1×(1 -r^n)/(1 -r)
sum of n terms for first term a1 and common ratio r.
__
series sumThe given series has first term a1 = 150, and common ratio r = 60/150 = 2/5. Putting these values into the formula gives a sum of 7 terms that is ...
S7 = 150×(1 -(2/5)^7)/(1 -2/5) = 150((77997/78125)/(3/5))
S7 = 150×(25999/15625) = 249.5904
Rounded to the nearest integer, the sum of the first 7 terms is 250.