Calculate 6+9i/-1+4i
Multiply the numerator and denominator by the conjugate of the denominator:
[tex]\dfrac{6+9i}{-1+4i} \times \dfrac{-1-4i}{-1-4i} = \dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2}[/tex]
Simplify:
[tex]\dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2} = \dfrac{-6-9i-24i-36i^2}{1-16i^2} = \dfrac{-6-33i-36i^2}{1-16i^2} = \dfrac{-6-33i+36}{1+16} = \boxed{\dfrac{30-33i}{17}}[/tex]
I need help to find Y =
Answer:
3
Step-by-step explanation:
1.2 m
1.2 m
Susie is 1.13 metres tall
She has a play tent in the shape of a triangular prism.
The diagram shows the front view of the tent.
The front of the tent has been drawn to scale below.
a) Complete the scale drawing.
1.5m
Not drawn accurately
b) Can Susie stand up in the
middle of the tent?
1.5m
Scale: 1 cm represents 60 cm
Split the triangle into 2 right in the middle so you have 2 identical right triangles. The base on one would be half the base of the triangle shown so, the base would be: 1.5/2 = 0.75 m.
Now using the Pythagorean theorem you can find the height:
Height - sqrt(1.2^2 - 0.75^2)
Height = sqrt(1.44 - 0.5625)
Height = sqrt(0.8775)
Height = 0.93675 meters
The height of the tent is smaller than the height of Suzie so she cannot stand up.
Select the expression that represents the following statement: find the sum of 6 and 14 and divide by 4.
a (6 + 14) ÷ 4
b 14 ÷ 4 + 6
c 4 x 4 – 6
d 14 x 6 ÷ 4
Answer:
A
Step-by-step explanation:
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
A. 11.7
B. 11.9
C. 11.4
D. 14.4
Answer:
Option A, 11.7
Step-by-step explanation:
To find height,
tan 68 = 26/h
h = 26/tan(68)
to find x
tan(42) = h/x
x = h/tan(42)
x = 11.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
cosec^2θ-1/cosec^2θ=cos^2θ
cosec(2t)=1/sin(2t) ==> 1/(2×cos(t)×sin(t))
cos(2t)= 1-2sin²t
or 2cos²t-1
or cos²t - sin²t
after we knew this informations we have to write it in the question
1/2×sint×cost-1/1/2×sint×cost=cos2t
-2×sint×cost+1/2sint×cost/1/2sint×cost=cos2t
the 2sint×cost will gone
-2×sint×cost+1=cos2t
lets take cos2t =1-2sin²t
-2×sint×cost+1=1-2sin²t
-2sint×cost=-2sin²t
cost=sint
that means the t is equal to 45 because sin45 and cos45 equal to √2/2
hopefully i didn't waste your time by reading and not understanding my English is not that good sorry
Answer:
see explanation
Step-by-step explanation:
Using the identities
cosec x = [tex]\frac{1}{sinx}[/tex] , 1 - sin²θ = 1
Consider the left side
[tex]\frac{cosec^20-1}{cosec^20}[/tex]
= [tex]\frac{\frac{1}{sin^20}-\frac{sin^20}{sin^20} }{\frac{1}{sin^20} }[/tex]
= ( [tex]\frac{1}{sin^20}-\frac{sin^20}{sin^20}[/tex] ) × [tex]\frac{sin^20}{1}[/tex] ← distribute parenthesis by sin²θ
= 1 - sin²θ
= cos²θ
= right side, thus proven
Factor completely 3x - 15.
O 3(x - 5)
O 3(x + 5)
O 3x(-15)
O Prime
Answer: First Choice. 3 ( x - 5 )
Step-by-step explanation:
Concept:
When we are doing factoring, we should try to find any Greatest Common Factor (GCF) of all constants in the given expression.
The Greatest Common factor is the largest value of the values you have, that multiplied by the whole number is able to "step onto both".
Solve:
Factors of 3: 1, 3
Factors of 15: 1, 3, 5, 15
As we can see from the list above, 3 appears in both lists of factors and is the greatest for 3. Therefore, [3] is the GCF of 3 and 15
Divide 3 for both numbers to find the remaining.
3x / 3 - 15 / 3x - 5Check whether or not the remaining can be divisible
Ans: NOPut the factored out 3 and remaining together
3 ( x - 5)Hope this helps!! :)
Please let me know if you have any questions
Find the volume and surface area of the composite figure. Give four answer in terms of pi
Answer:
B
Step-by-step explanation:
Volume = Volume of cylinder + Volume of semi sphere
= pi*r^2*h+(2/3)*pi*r^3
=pi*(4*12+16/3)=pi*53.3
SOMEBODY GET IT RIGHT FOR ME PLS I NEED HELP ITS PYTHAGOREAN THEOREM
Answer:
a^2+b^2=c^2
a^2=c^2-b^2
a^2=10^2-5^2
a^2=100-25
a^2=75
a=7.7cm
Step-by-step explanation:
what is the height of the water prism
Answer:
32 because I Don't know please vote my answer please
Answer:
12 (10) cm 937 637 = hafe 2929888389292822
20 points lovelys <3
Answer:
A) 2 cm
Step-by-step explanation:
By definition, regular polygons have equal sides and angles. Therefore, each side of the regular hexagon must be equal. Since one side is marked as 2 cm, the length of PQ must also be 2 cm.
23. (04.05)
Which statement best describes the effect of replacing the function f(x) = 2 ^x-2 with the function g(x) = 2 ^x+3
The graph shifts 1 units left.
The graph shifts 5 units left.
The graph shifts 1 unit right.
The graph shifts 3 units right.
Answer:
The graph shifts 5 units left
Step-by-step explanation:
The given functions are;
f(x) = [tex]2^{x - 2}[/tex], g(x) = [tex]2^{x + 3}[/tex]
Therefore, we have;
When x = 2, f(2) = [tex]2^{2 - 2}[/tex] = 1 and g(2) = [tex]2^{2 + 3}[/tex] = 32
When x = 3, f(3) = [tex]2^{3 - 2}[/tex] = 2 and g(3) = [tex]2^{3 + 3}[/tex] = 64
When x = 6, f(6) = [tex]2^{6 - 2}[/tex] = 16 and g(6) = [tex]2^{6 + 3}[/tex] = 512
When x = 7, f(7) = [tex]2^{7 - 2}[/tex] = 32 and g(7) = [tex]2^{7 + 3}[/tex] = 1024
When x = 8, f(8) = [tex]2^{8 - 2}[/tex] = 64 and g(8) = [tex]2^{8 + 3}[/tex] = 2,048
Therefore, the y-value of f(x) obtained at x = 8, is obtained by g(x) at x = 3, and the graph is shifts(ed) 5 units left.
What is his weekly allowance if he ended with $15?
Determine the measure of the interior angle at vertex E.
A. 135
B. 45
C. 225
D. 75
Answer:
135
Step-by-step explanation:
The sum of the interior angles of a pentagon is 540
3x+3x+2x+2x+2x = 540
12x = 540
Divide by 12
12x/12 = 540/12
x = 45
E = 3x = 3*45 = 135
Answer:
135
Step-by-step explanation:
a sequence starts 2,-1,-4,-7 what is the 25th term
Answer:
-70
Step-by-step explanation:
They have a common difference of -3
2). 2, x, 14 are in Arithmetic progression, then the value of x is :
A. 28
B. 16
C. 7
D. 8
G is related to one of its parent function g(x)=2√x. a) find the f function b) using the function notation write g interns of f
Answer:
Here we have:
g(x) = 2*√x
And we know that it is related to a parent function, where the parent functions are:
Linear Function: f(x)=x.
Quadratic Function: ݂f(x)=x^2.
Square Root function: f(x)= √x.
Absolute Value function: f(x)=|x|
Cubic function: f(x)=x^3.
Cube Root function: f(x) = ∛x
Logarithmic function: f(x)=log x or f(x)=In x.
Exponential function: f(x) = a^x.
a) Because g(x) = 2*√x
We can see that it is related to the square root function, then the parent function is:
f(x) = √x
b) now we want to write g(x) in terms of f(x)
we have:
g(x) = 2*√x
we can replace √x by f(x)
then we get:
g(x) = 2*f(x)
Now we have g(x) in terms of f(x)
Find he probability of no more than 35 defective CD's in a batch of 80 CD's if the probablility of any one CD being defective is 0.1.
Answer:
0.999999
Step-by-step explanation:
Given that :
Probability of CD being defective, p = 0.1
q = 1 - p = 1 - 0.1 = 0.9
Total number of CD's = number of trials = 80
Probability, that no more than 35 CD's are defective ;
The question satisfied the requirements for a binomial probability problem ;
Recall :
P(x = x) = nCx * p^x * q^(n-x)
Hence,
P(x ≤ 35) = 80C35 * 0.1^35 * 0.9^(45)
Using calculator to save computation time :
P(x ≤ 35) = 0.999999
Please help!!!......
Answer:
12*12=144
8*10=80
80+144=224
224*2=448
10*4=40
8*10=80
80*2=160
40+160=200
12*10=120
120+200=320
20*10=200
320+200=520
448+520=968
Hope This Helps!!!
Given the radius and area of the circle, calculate the angle at the centre of the circle.
Radius : 21 m
Area of the circle : 27.72 m^2
Answer:
[tex] \theta = 7 .2\degree [/tex]
Step-by-step explanation:
[tex]area = \frac{\theta}{360} \times \pi {r}^{2} \\ 27.72 = \frac{\theta}{360} \times \pi \times {21}^{2} \\ 27.72 = \frac{\theta}{360} \times \pi \times 441 \\ \frac{27.72 \times 360}{441\pi} = \theta \\ \frac{9979.2}{1385.4} = \theta \\ \\ 7 .2\degree = \theta[/tex]
I am struggling with this question anyone help
9514 1404 393
Answer:
b, c
Step-by-step explanation:
The factor (x+7) is common to both numerator and denominator. The function can be simplified by cancelling that factor.
y = (x -3)/(x -9) . . . . . . x ≠ -7
The restriction x ≠ -7 is put on the simplified function because the original function is undefined there. The denominator factor x+7 makes the denominator 0 at that point.
The point at x=-7 is called "hole" in the graph. A properly drawn graph will show the function is undefined there (has a hole).
__
The denominator of the simplified function is zero when x=9. This means there is a vertical asymptote at x=9.
__
The ratio of the highest-degree terms of the numerator and denominator will tell you the end behavior of the function — its value when x is large. Here, that ratio is y = x/x = 1. This represents a horizontal asymptote at y=1. The function approaches this line as x gets large, but never reaches it.
The appropriate descriptors are ...
Asymptote: x=9, y=1Hole: x=-7Can I please get help with these 2 questions about polygons
Answer:
a)139°
Step-by-step explanation:
two co interior angles make one opposite exterior angle
49+90=139°
For which of following equations is (-2,-3) not a solution (Will give brainlest plus 33 points)
Answer:
[tex] - 3x = 4y - 6[/tex]
[tex] - 3( - 2) = 4( - 3) - 6[/tex]
[tex]6 = - 12 - 6[/tex]
[tex]6 = - 18[/tex]
What are the first 5 terms?
Answer:
please can you specify which topic exactly is it on Arithmetric or Geometric Progression or on another topic
please kindly specify and send the question back
Thank you
Step-by-step explanation:
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
Mrs Dlamini bought a 10kg bag of rice. She cooks 500g of rice per day. How many days will the bag of rice last her family
Answer:
20 days
Step-by-step explanation:
10kg= 10,000g
10,000g/500g= 20 days
Answer:
20 days
Step-by-step explanation:
1 kg=1000 grams
10 kg=10000 grams
10000÷500
=20 days
Hamid had gained weight he is now 88k which is 10% more then he uses to be what was his original weight
Answer:
80k
Step-by-step explanation:
let the previous weight be x
88=x + 10%of x
88=x+(10/100)of x
8800=110x
8800/110=x
x=80k
Answer: Original weight = 80 kg
Step-by-step explanation:
Given:
Current weight = 88 Kg
Gain weight rate = 10%
Solve:
Original weight = Current weight / Gain rate
Original weight = (88) / (1 + 10%)
Original weight = 80 Kg
Hope this helps!! :)
Please let me know if you have any questions
_(9)=(2(1-2(2)^(9)))/(1-2(2))
PLEASE HELP ME OUT.
Answer:
the answer = um ok
Step-by-step explanation:
Please hurry I will mark you brainliest
Step-by-step explanation:
I think you first have to calculate a°,this can be done by first finding c°
c°=180-125
=55°
opposite angles in a quadrilateral add up to 180
therefore a°=180-55
=125
therefore angle d
180-125
=55
I hope this helps
please help fast!! geometry
Answer:
512 inches ^2
Step-by-step explanation:
The surface area is found by
SA = 2(lw+wh+hl) where l is the length h is the height and w is the width
SA = 2( 8*8 + 8*12 + 12 * 8)
= 2(64+ 96+96)
= 2 ( 256)
= 512 inches ^2
Answer:
512 square inches
Step-by-step explanation:
8 x 8 = 64
12 x 8 = 96
64 x 2 = 128
96 x 4 = 384
128 + 384 = 512 in^2
Which statement is true? O A. The number 23 is prime, but 36 is composite. B. The number 33 is prime, but 42 is composite. OC. The number 21 is prime, but 25 is composite. D. The number 27 is prime, but 39 is composite.
Answer: A. The number 23 is prime, but 36 is composite.
=====================================================
Explanation:
Let's go through the possible answer choices
A) This is true because 23 only has the factors 1 and 23. So that's why 23 is prime. We can say 36 is composite since 2 is a factor, ie 36 = 2*18.B) This is false because 33 is not prime. Note how 33 = 3*11, showing that 3 is a factor of 33.C) Similar to B, the statement "21 is prime" is false. Note how 21 = 3*7.D) Like the other false statements, 27 is not prime because 27 = 3*9.23 is indeed prime, and 36 is indeed composite.
33 is composite, and 42 is indeed composite.
21 is composite, and 25 is composite as well
27 is not prime, and 39 is composite.
Primes have only 2 factors: 1 and themselves.
And 33, 21 and 27 definitely have more than 2 factors. Hope this helps!
~Just a joyful teen
[tex]GraceRosalia[/tex]
