Step-by-step explanation:
A you see here, we have 3 different shapes. a Triangle, a big and small rectangle. Lets start with the triangle.
between the 8 in's, theres a gap. 5+4=9,
9+8+8=25. we have the length of the triangle.
9*25 divided by 2= 112.5. thats are area of the triangle.
for the bigger rectangle, 20*9=180, the area of the rectangle, and the smaller rectangle at the bottom is 16.
Now we add:
112.5+180+16=308.5
hope this helps!
result of 5 and 75 with dividid by 3
Answer:
your answer is 30
Step-by-step explanation:
I hope this help
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
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 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
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]
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
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
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
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
help help help help
Answer:
abc is a triangle so ,
a is ( 9,6 )
b is ( 9,3 )
and c is ( 3,3 )
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
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]
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.
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]
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
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
Please help me solve this problem guys
Answer:
17%
Step-by-step explanation:
Again, as the amount of years increase, the population of bees gets multiplied by 0.83. We can rewrite this to 83%, and then again rewrite this to 100%-17%. We can see now that the population of bees decreases by 17% each year.
plzzzz heeeeeeellllllllppppppppp again...
ANS=40
hope this help you
bye have a great day :)
Pls help it’s due in the morning ;(
[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1-3}{-4-3}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-2}{-7}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{2}{7}[/tex]
10:-Points are (-7,6),(11,-4)
[tex]\boxed{\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-4-6}{11+7}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-10}{18}[/tex]
[tex]\\ \sf\longmapsto m=-\dfrac{5}{9}[/tex]
Answer:
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
9) Mark any two point on the line
(x₁ , y₁) = (3 , 3) ; (x₂, y₂) = (-4 ,1)
[tex]Slope =\frac{1-3}{-4-3}\\\\=\frac{-2}{-7}\\\\=\frac{2}{7}[/tex]
10) (x₁ , y₁) = ( -7 , 6) ; (x₂, y₂) = (11 ,-4)
[tex]Slope =\frac{-4-6}{11-[-7]}\\\\ =\frac{-4-6}{11+7}\\\\=\frac{-10}{18}\\\\=\frac{-5}{9}[/tex]
The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?
Answer:
9 years older
Step-by-step explanation:
The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )
In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so
[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides
40x + 150 = 30x + 180 ( subtract 30x from both sides )
10x + 150 = 180 ( subtract 150 from both sides )
10x = 30 ( divide both sides by 10 )
x = 3
Then
Michell is 8x = 8 × 3 = 24 years old
Connor is 5x = 5 × 3 = 15 years old
Mitchell is 24 - 15 = 9 years older than Connor
help pleasseeeeeeeee
Answer:
-1
Step-by-step explanation:
I know that i^4 = 1
i^10 = i^4 * i^4 * i^2
= 1 * 1 * i^2
We know that i^2 = -1
=1 *1 *-1
= -1
s the function represented by the table non-linear?
x
y
6
4
7
2
8
0
9
–2
On a map, 1 in represents 420 miles. How much does 3/4 in represent?
Answer:
315
Step-by-step explanation:
420 x 3/4 = 315
Answer:
315 miles
Step-by-step explanation:
We can write a ratio to solve
1 inch 3/4 inches
------------ = ---------------
420 miles x miles
Using cross products
1 * x = 420 * 3/4
x=315
Factorize this and solve no p, q, s, t, w
explanation:
all the questions are solved
in question no. s and t u need to divide the number in two different parts to slove
for no. w we can get two type of solution.
p and q u need to give the power of whole .
Write and solve a word problem that can be modeled by addition of two negative integers.
Answer:
Step-by-step explanation:
Question:
Max needs to purchase a car and withdraws $100 from his bank. In a few days he withdraws another $50 to make same repairs. In total what is the change in his bank balance from theese two costs?
Solution:
(-100) + (-50) =
-150
Answered by G a u t h m a t h
solue for &
X(3 + X) = 3x + x²
3x+x^2=3x+x^2
3x-3x=x^2-x^2
which means x=0
PLSSS HELPPPP AYUDA PLSSS URGENT AS WELL PLSS PSL PSL evaluate this expression “(-7x^3 + 9x^2 - 3) x (-2x^2 - 5x + 6)???
Answer: 14x^5 + 17x^4 - 87x^3 + 60x^2 + 15x - 18
Step-by-step explanation: You would need to simplify the expression by using distributive property.
Translate this phrase into an algebraic expression.
the sum of 4 and twice a number is 12
Answer:
4+2x = 12
Step-by-step explanation:
sum means add an is means equal
4+2x = 12
Step-by-step explanation:
the sum of 4 and twice a number is 12:
Have a great day! I hope this helps!! :)