Step-by-step explanation:
125 -30 = 95..
125 - 60 = 65
If a line has a midpoint at (2,5), and the endpoints are (0,0) and (4,y), what is the value of y? Please explain each step for a better understanding:)
Answer:
y = 10
Step-by-step explanation:
To find the y coordinate of the midpoint, take the y coordinates of the endpoints and average
(0+y)/2 = 5
Multiply each die by 2
0+y = 10
y = 10
Hi please answer ASAP please and thank you
Answer:
1 1/4
Step-by-step explanation:
2 3/4 - 1 1/2
3 3/4 - 1 2/4
1 1/4
What is the volume of a sphere with a diameter of 7.7 ft, rounded to the nearest tenth
of a cubic foot?
Step-by-step explanation:
V=4/3πr^3
V=4/3π(3.85)^3
V=4/3π(57.066625)
V=4/3 (179.280089865)
V=239.04011982
V=239 ft^3
What is the range of the absolute value function shown in the graph?
A. 3 ≤ y < ∞
B. -∞ < y ≤ 3
C. -6 ≤ y < ∞
D. -∞ < y < ∞
Answer:
C
Step-by-step explanation:
as we can see on the graph, the lowest y value is the vertex/corner at x=3, y=-6.
all other y values are above (=are larger) that level.
and it goes up without appearant limit, so up to infinity.
Ray is making his reward winning lemonade recipe for a party he is comparison shopping for lemons at super pioneer supermarket he can buy 4 lemons for 1.60 ray visits keyfood and found 3 lemons cost 1.80 use the table below to compare the values
Answer:
classified info jk juss use a mf calculater
Step-by-step explanation:
Write the equation of the sinusoidal function shown?
A) y = cos x + 2
B) y = cos(3x) + 2
C) y = sin x + 2
D) y = sin(3x) + 2
Answer:
günah(3x) + 2
Step-by-step explanation:
Gösterilen sinüzoidal fonksiyonun denklemini yazınız? A) y = cos x + 2 B) y = cos(3x) + 2 C) y = günah x + 2 D) y =
Answer:
y = sin(3x) + 2
Where did term “infinity” come from
Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
Answer:
1320
Step-by-step explanation:
Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)
The terms increase by 6, so d is 6
a is the first term, -56
n is the terms you want to find, 33
Plug in the numbers, 33/2 (2(-56)+(32)6)
Simplify into 33(80)/2 and you get 1320
Rationalise the denominator
Answer:
sqrt(3) /3
Step-by-step explanation:
1 / sqrt(3)
Multiply the top and bottom by sqrt(3)
1/ sqrt(3) * sqrt(3)/ sqrt(3)
sqrt(3) / sqrt(3)*sqrt(3)
sqrt(3) /3
Answer:
[tex] = { \sf{ \frac{1}{ \sqrt{3} } }} \\ \\ { \sf{ = \frac{1}{ \sqrt{3} } . \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ = { \sf{ \frac{ \sqrt{3} }{ {( \sqrt{3}) }^{2} } = \frac{ \sqrt{3} }{3} }} [/tex]
(√0,04-√(-1,2)²+√121)×√81
Answer: 90
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{} (\sqrt{0,04}-\sqrt{(-1,2)^2}+\sqrt{121 } ) \cdot \sqrt{81} = \\\\\\(0,2-1,2+11)\cdot 9=(11-1)\cdot 9=90[/tex]
To purchase a car costing $10,000, the buyer bor-
rowed part of the money from the bank at 9% sim-
ple interest and the rest from her mother-in-law at
12% simple interest. If her total interest for the year
was $1080, how much did she borrow from the
bank?
Answer:
She borrowed 4000 from bank.
Step-by-step explanation:
Let 'y' be the amount borrowed from bank. Then 10000-y is the amount borrowed from her mother-in-law.
Let x= interest amount gained by bank . Then 1080- x = interest gained by mother-in-law
I1= interest rate by bank= 9%
I2= interest rate by mother-in-law=12%
Time(T) = 1 year
Now, By Simple Interest formula:
x=PTR/100
Or, x=(y*1*9)/100
Or,100x=9y
or,9y-100x=0...........................Equation (i)
Again 1080-x= ((10000-y)*1*12)/100
Or, 108000-100x=120000-12y
Or, 12y-100x=12000.................Equation(ii)
Solving equation (i) and (ii), we get
y= 4000, which the amount borrowed from bank.
convert 10.09% to a decimal
Answer:
0.1009
Step-by-step explanation:
To convert percentage into decimal, you need to divide the percentage by 100
10.09/100
= 0.1009
what does this equal 2^3 + 6^5=
[tex]\\ \sf\longmapsto 2^3+6^5[/tex]
[tex]\\ \sf\longmapsto 2^3+(2\times 3)^5[/tex]
[tex]\\ \sf\longmapsto 8+2^5\times 3^5[/tex]
[tex]\\ \sf\longmapsto 8+32\times 243[/tex]
[tex]\\ \sf\longmapsto 40+7776[/tex]
[tex]\\ \sf\longmapsto 7784[/tex]
Answer:
2*2*2= 8
6*6*6*6*6= 7,776
7,776+8=
7,784
→
If u vector= a vector-b vector and v vector= a vector+b vector and magnitude of a = b = 2, then magnitude of u vector multiply v vector =???
Answer:
zero
Step-by-step explanation:
[tex]\overrightarrow{u} = \overrightarrow{a} - \overrightarrow{b}\\\\\overrightarrow{v}= \overrightarrow{a} + \overrightarrow{b}\\\\\overrightarrow{u} . \overrightarrow{v} = a^2 - b^2 \\\\\overrightarrow{u} . \overrightarrow{v} = 2^2 - 2^2 = 0[/tex]
So, vector u and vector v are perpendicular to each other.
help me pls??????? :)
Answer:4 in each bad 2 left over
Step-by-step explanation:
Answer:
4 in each bag and 2 left over
Step-by-step explanation:
divide 14 by 3
3 goes into 14, 4 times
14 - 12 = 2
4 in each bag and then 2 left over
Answer ASAP
Given that the point X(3, -2) is rotated 90° counterclockwise about the point (-1, 4).
What are the coordinates of X', the image of X? (1 point) *
1) X'(5,8)
2) X'(-7, 8)
3) X'(4,1)
4) X'(-2, -3)
Answer:
4) x -2,-3 hope it helps to you
Determine three consecutive odd integers whose sum is 2097.
Answer:
first odd integer=x
second odd integer=x+2
third odd integer=x+4
x+x+2+x+4=2097
x+x+x+2+4=2097
3x+6=2097
3x=2097-6
3x=2091
3x/3=2091/3
x=697
therefore, x=697
x+2=697+2=699
x+4=697+4=701
Please help I’ll mark as brainlist
Answer:
Ekta and Preyal
Step-by-step explanation:
−30=5(x+1)
what is x?
[tex]\\ \rm\Rrightarrow -30=5(x+1)[/tex]
[tex]\\ \rm\Rrightarrow -30=5x+5[/tex]
[tex]\\ \rm\Rrightarrow 5x=-30-5[/tex]
[tex]\\ \rm\Rrightarrow 5x=-35[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-35}{-5}[/tex]
[tex]\\ \rm\Rrightarrow x=7[/tex]
Answer:
x = -7
Step-by-step explanation:
-30 = 5 (x -1 )
5 ( x + 1 ) =-30
5 (x + 1 ) = - 30
5 5
x + 1 = -6
x + 1 -1 = -6 -1
x = - 7
help help help help
Answer:
abc is a triangle so ,
a is ( 9,6 )
b is ( 9,3 )
and c is ( 3,3 )
If Sin x = -¼, where π < x < 3π∕2 , find the value of Cos 2x
Answer: 7/8
Cos2x has 3 formulas, Sinx is given in the question, we should use the formula with sinus. I guess that's the solution.
What is the perimeter of a square which has the same area as a circle with circumfrence of 4π
Answer:
Perimeter square = 8 sqrt(pi)
Step-by-step explanation:
The perimeter of a square is 4*s
The area of a circle is Area = pi * r^2
The circumference of a circle is C = 2*pi * r
C = 4 pi
4pi = 2*pi * r
r = 2
So the area of the circle is pi * r^2 = pi * 2^2 = 4pi
The square has the same area
Area = 4*pi
Square = 4*pi
s^2 = 4*pi
s = sqrt(4*pi)
s = 2*sqrt(pi)
The perimeter = 4 * 2 * sqrt(pi)
The perimeter = 8 * sqrt(pi)
100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT
a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal
places.
Answer:
See Below (Boxed Solutions).
Step-by-step explanation:
We are given the two complex numbers:
[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]
First, convert z to polar form. Recall that polar form of a complex number is:
[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]
We will first find its modulus r, which is given by:
[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]
In this case, a = √3 and b = -1. Thus, the modulus is:
[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]
Next, find the argument θ in [0, 2π). Recall that:
[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]
Therefore:
[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]
Evaluate:
[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]
Since z must be in QIV, using reference angles, the argument will be:
[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]
Therefore, z in polar form is:
[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]
Part A)
Recall that when multiplying two complex numbers z and w:
[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]
To find the complex form, evaluate:
[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]
Part B)
Recall that when raising a complex number to an exponent n:
[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]
Therefore:
[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]
Substitute:
[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]
Simplify:
[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]Simplify using coterminal angles. Thus, the polar form is:
[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]
And the complex form is:
[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]
Part C)
Recall that:
[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]
And the complex form is:
[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]
Part D)
Let a be a cube root of z. Then by definition:
[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
From the property in Part B, we know that:
[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]
Therefore:
[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:
[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]
The first equation can be easily solved:
[tex]r=\sqrt[3]{2}[/tex]
For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:
[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]
Solve for the argument:
[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]
There are three distinct solutions within [0, 2π):
[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]
Hence, the three roots are:
[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]
Or, approximately:
[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]
Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene.
9514 1404 393
Answer:
(d) Right, scalene
Step-by-step explanation:
The little square in the upper left corner tells you that is a right angle. Any triangle with a right angle is a right triangle. This one is scalene, because the sides are all different lengths.
__
Additional comment
An obtuse triangle cannot be equilateral, and vice versa.
An equilateral triangle has all sides the same length, and all angles the same measure: 60°. It is an acute triangle.
Julie assembles shelves for a department store and gets paid $3.25 per shelf. She can assemble 5 per hour and works 8 hours per day. Determine Julie’s gross pay for 1 week
Pay per shelf = $3.25
No of shelfs per hour = 5
Total hours per day = 8
Total days to find pay of = 7
= 3.25×5×8×7
= 910
Therefore she is paid $910 after 1 week.
Must click thanks and mark brainliest
result of 5 and 75 with dividid by 3
Answer:
your answer is 30
Step-by-step explanation:
I hope this help
Find the value of the sum 219+226+233+⋯+2018.
Assume that the terms of the sum form an arithmetic series.
Give the exact value as your answer, do not round.
Answer:
228573
Step-by-step explanation:
a = 219 (first term)
an = 2018 (last term)
Sn->Sum of n terms
Sn=n/2(a + an) [Where n is no. of terms] -> eq 1
To find number of terms,
an = a + (n-1)d [d->Common Difference] -> eq 2
d= 226-219 = 7
=> d=7
Substituting in eq 2,
2018 = 219 + (n-1)(7)
1799 = (n-1)(7)
1799 = 7n-7
1799 = 7(n-1)
1799/7 = n-1
257 = n-1
n=258
Substituting values in eq 1,
Sn = 258/2(219+2018)
= 129(2237)
= 228573
How do we derive the sum rule in differentiation? (ie. (u+v)' = u' + v')
It follows from the definition of the derivative and basic properties of arithmetic. Let f(x) and g(x) be functions. Their derivatives, if the following limits exist, are
[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h\text{ and }g'(x)\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]
The derivative of f(x) + g(x) is then
[tex]\displaystyle \big(f(x)+g(x)\big)' = \lim_{h\to0}\big(f(x)+g(x)\big) \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)+g(x+h)\big)-\big(f(x)+g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)-f(x)\big)+\big(g(x+h)-g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{f(x+h)-f(x)}h+\lim_{h\to0}\frac{g(x+h)-g(x)}h \\\\ \big(f(x)+g(x)\big)' = f'(x) + g'(x)[/tex]
PLEASE HELP I WILL GIVE BRAINLIEST
Step-by-step explanation:
A natural number is a positive whole number.
A whole number is a positive number with no fractions or decimals.
A interger is a whole number negative or positive.
A rational number is a number that terminates or continue with repeating digits.
A irrational number is a number that doesn't terminate or continue with repeating digits.
1. Rational Number
2. Natural,Whole,Interger,Rational
3. Whole,Rational,Interger
4. Rational
5.Irrational
6.Rational
7.Natural,Whole,Interger,Rational
8.Interger,Rational
9.Irrational
ASAP I NEED HELP WITH THIS!!!
Find the area the sector.
A.1083pi/4in
B.38pi in
C. 57/4pi
D.1083/8pi in
Answer:
D
Step-by-step explanation:
Sector of Area=(theta/360)*pi*r^2
Sector of area=(135/360)*pi*19^2=(1083)/8 pi