ANSWER
[tex]2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]
EXPLANATION
The complex number given to us is in the polar form,
32(cos 280° + i sin 280°)
The fifth root is
[tex] {32}^{ \frac{1}{5} } ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]
This is equal to:
[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]
According to the DeMoivre's Theorem,
[tex]( { \cos \theta \: \degree + i \sin\theta \degree) }^{ \frac{p}{q} } = ( { \cos \frac{p}{q} \theta \degree + i \sin \frac{p}{q} \theta \degree) }[/tex]
We now use the DeMoivre's Theorem to obtain:
[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: \frac{1}{5} \times 280 \degree + i \sin \:\frac{1}{5} \times 280 \degree) }[/tex]
[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]
Gigi makes a scale drawing of a patio. The drawing below shows the two scales use she used to plan two patios of different sizes. Which shows the correct dimensions of the rectangle in both scales?
Answer:
Scale 1 35 ft by 25 ft and Scale 2 56 ft by 40 ft
Step-by-step explanation:
step 1
Find the actual dimensions of a patio with the scale 1
The scale 1 is equal to
1 cm/5 ft
Length=7 cm=7*5=35 ft
Width=5 cm=5*5=25 ft
therefore
The dimensions are 35 ft by 25 ft
step 2
Find the actual dimensions of a patio with the scale 2
The scale 2 is equal to
1 cm/8 ft
Length=7 cm=7*8=56 ft
Width=5 cm=5*8=40 ft
therefore
The dimensions are 56 ft by 40 ft
Answer:
C
Step-by-step explanation:
If Scale 1 is 1 cm:5 ft, multiply 5 and 7 by 5 to get the correct dimensions. 7×5=35 and 5×5=25. If Scale 2 is 1 cm: 8 ft, multiply 5 and 7 by 8 to get the correct dimensions. 7×8=56 and 5×8=40. The answer is: Scale 1: 35 ft by 25 ft; Scale 2: 56 ft by 40 ft.
Hope this helps!
Find p(A|A^c)
A.1
B.0
C.1/2
D. Unknown
If [tex]A^C[/tex] has occurred, then [tex]A[/tex] cannot occur, so the probability is 0.
This follow directly from the definition of conditional probability:
[tex]P(A\mid A^C)=\dfrac{P(A\cap A^C)}{P(A^C)}[/tex]
but [tex]A[/tex] and [tex]A^C[/tex] are disjoint, so the probability of their intersection is 0.
Answer:
B.
Step-by-step explanation:
For the bar graph, what is the total population surveyed?
A) 303
B) 3,030
C) 3,030,000
D) 303,000
Answer:A
Step-by-step explanation:
80+141+74+4+3+1=303
Answer:A) 303
Step-by-step explanation:
Please help will give brainliest
If we have two functions [tex]f \ and \ g[/tex] such that [tex]f(g(x))=x[/tex] for every [tex]x[/tex] in the domain of [tex]g[/tex], and [tex]g(f(x))=x[/tex] for every for every [tex]x[/tex]in the domain of [tex]f[/tex]. If we prove this, then [tex]g[/tex] is the invers function of [tex]f[/tex] and denoted by [tex]f^{-1}[/tex]
1. We need to prove whether [tex]f(g(x))=x[/tex]. So:
[tex]f(x)=\frac{4}{5}x+1 \\ \\ g(x)=\frac{5x-5}{4} \\ \\ So: \\ \\ f(g(x))=\frac{4}{5}\left(\frac{5x-5}{4})+1 \therefore f(g(x))=\frac{4}{5}\left(\frac{5x-5}{4})+1[/tex]
[tex]\therefore f(g(x))=x-1+1 \\ \\ \boxed{f(g(x))=x}[/tex]
2. We need to prove whether [tex]g(f(x))=x[/tex]. So:
[tex]g(f(x))=\frac{5(\frac{4x}{5}+1)-5}{4} \\ \\ \\ g(f(x))=\frac{4x+5-5}{4} \\ \\ \\ g(f(x))=\frac{4x}{4} \\ \\ \\ g(f(x))=x[/tex]
Since [tex]f(g(x))=g(f(x))=x[/tex], then:
[tex]f(x) \ and \ g(x)[/tex] are inverses to each other.
Which step is part of a proof showing the opposite sides of parallelogram ABCD are congruent?
A) show that AC is congruent to BD
B) show that AD is congruent to AB
C) show that angles A and D are supplementary
D) show that triangle ADB is congruent to triangle CBD
I think it’s D. Because A) and B) are not true and im pretty sure that C) is also false
Answer:
its d
Step-by-step explanation:
Match the expression 7x^2-5x+9
A. Cubic trinomial
B. Constant monomial
C. Quadratic trinomial
D. Not a polynomial
it it c becauee I had already learned this
Suppose h(t)= -0.2t^2+2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds.
After how many seconds does the ball reach its maximum height?
What is the maximum height of the ball?
After how many seconds does the ball reach the ground?
Answer:
Step-by-step explanation:
Height: h(t)= -0.2t^2+2t = 2t(-0.1t + 1)
-0.2t^2+2t is a quadratic expression with a = -0.2 and b = 2.
The ball reaches its max height at t = -b/(2a).
Here, t = -2 / (2·[-0.2] ), or t = 2/0.4 = 5 (sec)
The ball reaches its max height at at 5 sec.
The max ht. of the ball is h(5) = -0.2(5 sec)^2 + 2(5 sec) = (-5 + 10) sec, or 5 ft.
To determine after how many sec the ball reaches the ground, we set h(t) = 0 and solve for t:
h(t)= -0.2t^2+2t = 0 = 2t(-0.1t + 1). Thus, t = 0 sec or t = 10 sec
The ball reaches the ground again after 10 sec.
If p varies directly as r and p=4,r=2,what the value of r when p=12
Answer:
r = 6
Step-by-step explanation:
Given that p varies directly as r, then the equation relating them is
p = kr ← k is the constant of variation
To find k use the condition p = 4, r = 2
k = [tex]\frac{p}{r}[/tex] = [tex]\frac{4}{2}[/tex] = 2
p = 2r ← equation of variation
When p = 12
12 = 2r ( divide both sides by 2 )
hence r = 6
WORTH 98 POINTS
The number of horses occupying stalls at the county fairgrounds can be modeled by the following function, where x represents the number of days since the first of June.
h(x)=-3x^2+30+225
Rewrite this function in the form that reveals when there are no horses occupying stalls at the fairgrounds
Answer:
The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.
Step-by-step explanation:
I assume an x is missing, and the function is h(x) = -3x^2 + 30x + 225
You want to know the number of days in which the function value is zero.
-3x^2 + 30x + 225 = 0
Divide both sides by -3.
x^2 - 10x - 75 = 0
(x - 15)(x + 5) = 0
x - 15 = 0 or x + 5 = 0
x = 15 or x = -5
We discard the negative solution.
Answer: The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.
Answer:
h(x) = -3 (x + 5) (x - 15)
Step-by-step explanation:
h(x) = -3x^2 + 30 + 225
= -3(x^2 - 10x - 75)
= -3(x + 5)(x - 15)
x = -5 x = 15
e
| 2.
Solve this system of two linear equations using the
linear combination method.
2x - 5y = 18
y-x=-10
Answer:
[tex]x=\frac{32}{3}, y=\frac{2}{3}[/tex]
Step-by-step explanation:
We can multiply the second equation by 2 to eliminate.
[tex]2(y-x)=2(-10) \\ \\ 2y-2x=-20[/tex]
Let's eliminate.
[tex]2x-5y=18 \\ -2x+2y=-20 \\ -3y=-2 \\ y=\frac{2}{3}[/tex]
Now we can substitute back into the equation to find the value of [tex]x[/tex].
[tex]\frac{2}{3}-x=-10 \\ \\ \frac{2}{3}-x=-\frac{30}{3} \\ \\ -x=-\frac{32}{3} \\ \\ x=\frac{32}{3}[/tex]
plss help will give brainliest and thx and 5star
Answer:
12. Heptagon
13. 14 cm
14. 50°
Step-by-step explanation:
12.
A polygon containing
3 sides is a triangle
4 sides is Quadrilateral
5 Sides is a Pentagon
6 sides is a Hexagon
7 sides is a Heptagon
Our polygon contains seven sides, it is hence a Heptagon
13. RST = ?
S is the mid point of RT
Hence RS = ST
ST = 7 given
Hence RS = 7
RT = RST = RS + ST
= 7 + 7
= 14 cms
14.
∠RSQ = ∠QST = 25°
∠RST=∠RSQ + ∠QST = 25°+ 25° = 50°
choose the correct expression to represent the piecewise-defined function?
Answer:
-3 5 2
Step-by-step explanation:
trust
The circumference of a circle is 9 pi.What is the area,in square inches,of a circle?Express your answer in terms of pi.
Answer:
20.25π
Step-by-step explanation:
The circumference (C) of a circle is calculated using the formula
C = 2πr ← r is the radius
given C = 9π, then
2πr = 9π ( divide both sides by 2π )
r = [tex]\frac{9\pi }{2\pi }[/tex] ( cancel the π on numerator/denominator )
= 4.5
The area (A) of a circle is calculated using the formula
A = πr² = π × 4.5² = 20.25π
A fair die with sides 1, 2, 3, 4, 5, and 6 is rolled. Find the probability of showing a number less than 5. Enter your answer in decimal form, rounded to two decimal places.
Answer:
0.25
Step-by-step explanation:
there are 4 numbers that are less than 5.
1,2,3,4 make a fraction 1/4
which equals 0.25
sorry if this wasn't a good explanation..
Answer:
4/6 = 0.67
Step-by-step explanation:
3w - 4z = 8 what is w
Final answer:
To solve the equation 3w - 4z = 8 for w, add 4z to both sides and then divide by 3, resulting in the expression w = (4z + 8) / 3.
Explanation:
The student's equation, 3w - 4z = 8, involves algebraic manipulation to solve for the variable w. To isolate w, we rearrange the equation to get w by itself on one side of the equation:
Add 4z to both sides to get: 3w = 4z + 8
Divide both sides by 3 to solve for w: w = (4z + 8) / 3
Now we have w expressed in terms of z. This is the solution for w assuming you have a specific value for z you can substitute into this expression.
Final answer:
To find w, isolate it by adding 4z to both sides and then dividing by 3, resulting in w = (8 + 4z) / 3.
Explanation:
To solve for w in the equation 3w - 4z = 8, you would isolate w on one side of the equation. First, add 4z to both sides of the equation so that you have 3w = 8 + 4z. Then, divide both sides by 3 to get w by itself. The final equation representing w would be w = (8 + 4z) / 3. This doesn't directly correspond to the provided physics equations; however, we can apply a similar method of isolating the unknown in those as well.
In 18 years time Halley will be five times as old as she was two years ago. Write this information in the form of an equation involving Halley's present age, a years How old is Halley now?
To solve any questions relating to ages, I find it easier to make a table, like in the picture below.
See picture for answer and clear diagram.
-----------------------------------------------------------------
Notes/Explanations + answer in written form
Let's say that Halley's age now is: x
That means that her age in 18 years is: x + 18
It also means that her age 2 years ago is: x - 2
In the question, we are told that when Halley is 18 years older that her current age, she will be 5 times the age she was when she was 2 years younger than her current age
That means:
Halley's current age + 18 years = 5 times (Halley's current age - 2 years)
So we get this equation (which we solve to get the answer) :
x + 18 = 5 * (x -2) ( expand the brackets)
x + 18 = 5x - 10 (subtract x from both sides)
18 = 4x - 10 (add 10 to both sides)
28 = 4x (now divide both sides by 4)
7 = x
Therefore, Halley's current age is 7 years
What is the next term in -2, -5, -9, -14, -20.
And why
The next term would be -27
Lets pretend that all the negative signs went away, that way you have the data:
2, 5, 9, 14, 20
^^^In my opinion it just makes it easier because I don't like negative numbers. Keep in mind that the negatives are still there but I just made them "Invisible"
The pic below is how I found the pattern. If you can't tell by the picture from 2 to 5 it increases by 3. From 5 to 9 it increases by 4. From 9 to 14 it increases by 5. From 14 to 20 it increases by 6.
This means the pattern is to increase the number 1 more then the amount the previous number was increased (keep in mind this is the pattern for the positive version and therefore the original pattern would be decreasing (since the bigger a number that is negative is, the farther away it gets from zero, therefor getting smaller.) For the original version the rule would be: it would decrease the number 1 more then the amount the previous number was decreased) <<<Hope that makes sense
That means that 20 will be increased by 7 ( 6+ 1 = 7). Which equals 27. Make the negative sign visible again and your answer is -27.
Let me know if this made sense and if it was helpful!
What’s the difference between ratio and proportion? Do they go under the same category?
Answer:
Step-by-step explanation:
Ratio is a relationship between two numbers indicating how many times the first number contains the the second.
Proportion is a part or share or number considered in comparative relation to whole.
So Ratio and Proportion wouldn't go under the same category.
I hope this would help you!!
The moon has a radius of about 939 leagues long. What is the total surface area of the moon? Rounded to the nearest whole number. (Ex. 3244.55 rounds up to 3245.) *
Radius, r = 939 ft
Then:
Diameter, d = 1878 ft
Circumference, C = 5899.9110034416 ft
Area, A = 2770008.2161158 ft^2
AREA = 2770 if you're shortening.
For this case we assume that the moon is spherical. For definition, the surface area of a sphere is given by:
[tex]S = 4 \pi*r ^ 2[/tex]
Where:
A: It is the radius of the sphere
We have that the radius is 939 leagues.
by definition, 1 league is equivalent to 4.82803 kilometers.
ENtonces 939 leagues represent 4533.52 km.
Substituting:[tex]S = 4 \pi * (4533.52) ^ 2\\S = 20552803.5904 * 4 * \pi\\S = 258,274,147.081[/tex]
It has a surface area of 258,274,147 km
ANswer:
258,274.147 km
Find the value of term a14 in the sequence.
6, 5, 4, 3, 2, . . .
Answer:
[tex]a_{14}=-7[/tex]
Step-by-step explanation:
The given sequence is:
6, 5, 4, 3, 2, . . .
The first term of the sequence is:
[tex]a_1=6[/tex]
The common difference is
d=5-6=-1
The nth term of the sequence:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=6-1(n-1)[/tex]
[tex]a_n=6-n+1[/tex]
[tex]a_n=7-n[/tex]
When n=14
[tex]a_{14}=7-14=-7[/tex]
The quadratic function h(t)=-16.1t^2+150 models a balls height in feet over time in seconds after it is dropped from a 15 story building
someone please answer
Answer:
A
Step-by-step explanation:
I did the same test
Find the measure of angle 2
I would say 45 degrees
The whole square is 360 degrees because each corner is a 90 degree angle
Which means each triangle section would be 90 degrees but angle 2 is cut in half, so half of 90 is 45
Hope this helps :)
Miss Clark’s farm has chickens and pigs. There are a total of 26 animal feet and 8 animal heads on her farm. If 20 feet belong to the pigs and 6 feet belong to the chickens, the ratio of the number of pigs to the number of chickens is
Answer:
5 : 3
Step-by-step explanation:
Given in the question that,
total number of animal feet = 26
number of pig's feet = 20
number of chicken's feet = 6
As we know that pig have four legs and chicken have 2 legs so,
number of pigs in the farm = 20/4 = 5
number of chickens in the farm = 6/2 = 3
Questions says that there are 8 heads so we can confirm our calculations as
5 + 3 = 8The ratio of the number of pigs to the number of chickens is
5 : 3
By visual inspection, determine the best fitting regression model for the data below
Answer:
A) Quadratic
Step-by-step explanation: It has the U shape of a parabola which a quadratic equation has.
Answer:
The correct option is A.
Step-by-step explanation:
In a scatter plot the best fit curve in known as regression curve. Types of regression curves are
1. Linear regression line : If the best fit of a data is a straight line, then it is known as linear regression line.
2. Quadratic regression : If the best fit of a data is a U-shape curve, then it is known as quadratic regression.
3. Exponential regression : If the best fit of a data is an exponential curve, then it is known as exponential regression.
From the given graph it is clear that scatter data forms a U-shaped curve. Since the best fit of a data is a U-shape curve, therefore the quadratic regression model is best for the data.
Thus, option A is correct.
Pls help me with my math brainliest and 20 points!!
Answer:
23 miles
Step-by-step explanation:
Substitute into the formula d = 3 s + 5
We know s = 6 so
d = 3 s + 5
d = ( 3 × 6 ) + 5
d = ( 18 ) + 5
d = 23
Hope this helps :)
Have a great day !
5INGH
Answer:
23 miles
Step-by-step explanation:
Substitute the numbers into d=3s+5.
d=(3×6)+ 5 (d=18+5)
18+5=23
Find the area of a circle with a diameter of \color{green}{6}6start color green, 6, end color green.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
units^2
2
start superscript, 2, end superscript
Answer:
9pi
Step-by-step explanation:
Tell whether the System has one solution infinite solution many solutions or no solutions 5x-3y=10 10x+6y=20
ANSWER
The system has one solution.
EXPLANATION
The given system is
1st: 5x-3y=10
2nd: 10x+6y=20
Make y the subject in the first equation to get:
[tex]y = \frac{5}{3} x + \frac{10}{3} [/tex]
Solve for y in the second equationquation to get;
[tex]y = - \frac{5}{3} x + \frac{10}{3} [/tex]
The slope of the two equations are not the same.
The two lines will intersect at exactly one point.
.The system has one solution.
Answer:
One solution
Step-by-step explanation:
We are given the following system of equations and we are to tell if the system has one solution, infinite solution, many solutions or no solutions:
[tex]5x-3y=10[/tex] --- (1)
[tex]10x+6y=20[/tex] --- (2)
If we take the common out from (2), we get:
[tex]2(5x+3y) = 20 [/tex]
[tex]5x+3y = 10 [/tex] --- (3)
So adding the two equations (1) and (3) gives 10x=20 ⇒ x=2.
Therefore, this system of equations has one solution.
Find the first four iterates of the function f(x) = 2x with an initial value of x0 = 2.
a.
4, 6, 8 ,10
c.
2, 4, 8, 16
b.
2, 4, 6, 8
d.
4, 8, 16, 32
Please select the best answer from the choices provided
Answer:
d. 4, 8, 16, 32
Step-by-step explanation:
We'll use the formula f(x) = 2x for each iteration. The output of the first iteration will be come the input of the second iteration, and so on.
So, we start with x0 = 2 and we plug that into the base equation:
x0 = 2 ==> f(x) = 2(2) = 4
x1 = 4 ==> f(x) = 2(4) = 8
x2 = 8 ==> f(x) = 2(2) = 16
x3 = 16 ==> f(x) = 2(2) = 32
x4 = 32 ==> f(x) = 2(2) = 64
Madison currently has a balance of 5503.51 ina an account earning simple interest. 19 years ago she opend up an account with an intial deposit of 3196. What is the interest rate on the account o
Answer:
The simple interest is 3.80% per year.
Step-by-step explanation:
We are presented with a simple interest problem and the following information has been availed;
Accumulated amount = 5503.51
Time = 19 years
Principal = 3196
The first step is to determine the total interest earned over the entire time period;
Interest = Amount - Principal
= 5503.51 - 3196
= 2307.51
The simple interest formula states the total interest earned is equal to the product of the principal, the interest rate and the time;
[tex]I=\frac{P*R*T}{100}[/tex]
Making R the subject of the formula yields;
[tex]R=\frac{100*I}{P*T}[/tex]
Substituting the values we have and simplifying;
[tex]R=\frac{100*2307.51}{3196*19}=3.80[/tex]
The simple interest is thus 3.80% per year.
Kathy designed a square patio. She made the sides of the patio 15 feet. What is the area of the patio?
Answer:
225 feet.
Step-by-step explanation:
15 X 15