Step-by-step explanation:
1
[tex] \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{3 - 4i}{25} = \frac{ 3}{25} - \frac{4i}{25} [/tex]
2)
[tex] \frac{1}{3 - 4i} \times \frac{3 + 4i}{3 + 4i} = \frac{3 + 4i}{25} = \frac{ 3}{25} + \frac{4i}{25} [/tex]
3)
1+0i
4)
[tex] \frac{3 - 4i}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{ - 7 - 24i}{25} = - \frac{7}{25} - \frac{24i}{25} [/tex]
5)
3 - 4i
6)
[tex] \frac{3 + 4i}{3 - 4i} \times \frac{3 + 4i}{3 + 4i} = \frac{ - 7 + 24i}{25} = - \frac{7}{25} + \frac{24i}{25} [/tex]
Find the gradient of the curve y= x^2 - 5x + 6 at x=1
Answer:
Gradient or slope at x=1 is -3
Step-by-step explanation:
[tex]y=x^2-5x+6\\\frac{dy}{dx} =2x-5\\at ~x=1\\\frac{dy}{dx} =2(1)-5=-3[/tex]
What value of x will make the equation true?
(Square Root of 5) (square root of 5)=x
Answer:
(2.236067978)(2.236067978)
=5 ans.
If this is incorrect forgive me
I hope this will help you
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Help me plsss! Thank you
Answer:
45/139 green or 20/139 yellow
Step-by-step explanation:
1. Add up total number of candles- thats your denominator
2. The total number of green or yellow candles is your numerator
3. Simplify your fractions if you have to
The measure of BAC is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?
Bob placed a 17- foot ramp against the side of a house so the ramp rested on a ledge that is 8 feet above the ground. How far was the base of the ramp from the house?
the system of equations y =-3x+2 and y =1/2 x -6 is shown on the graph below. What is a reasonable estimate for the solution>
The reasonable estimate for the solution is (2.29, -4.87)
The reasonable estimate for the solution is the point where the two lines intersect each other.
To get the point where they intersect, we will simply equate the system of equations given as shown:
[tex]-3x+2=\frac{1}{2}x-6\\Collect \ the \ like \ terms\\-3x-\frac{1}{2}x=-6-2\\\frac{-7x}{2}=-8\\-7x=-16\\x=\frac{16}{7} \\x=2.29[/tex]
Substitute x = 2.29 into any of the equation
Using the equation y = -3x+2
y = -3(2.29)+2
y = -6.87+2
y =-4.87
This shows that the reasonable estimate for the solution is (2.29, -4.87)
Further explanation about the system of equations can be found here https://brainly.com/question/19713330
The point of intersection of the linear equations is approximately [tex](x,y) = (2.286, -4.857)[/tex].
The most quickest approach that offers a reasonable solution consist in representing both linear functions graphically by means of a graphing tool (i.e. Desmos). As there is a system of two equation and two variables, the system can be represented by 2D-graphing tool.
The solution of this system is represented by the point, in which both lines intercepts each other. Let be the following two linear functions:
[tex]y = 3\cdot x + 2[/tex] (1)
[tex]y = \frac{1}{2}\cdot x - 6[/tex] (2)
The result from graphic tool is presented below and the point of intersection is approximately [tex](x,y) = (2.286, -4.857)[/tex].
Now graph the points C(2, 8) and D(8, 7). (Try entering the coordinates through the input window.) Measure the lengths of and . Do the points C and D lie on the circle? How do you know? Take a screenshot showing the points and their distances from the center, and paste it below.
Answer:
this was from plato
Step-by-step explanation:
Answer:
Any point on the circle must be at a distance from the center equal to the length of the circle’s radius. In this example, the radius is 3.61 units, AC = 4.24, and AD = 3.61. Point D, which lies on the circle, has the same distance from the center as the length of the radius. Point C, which lies outside the circle, is at a different distance from the center than the length of the radius.
What is the product of the polynomials below?
(5x2 - x-3)(2x+6)
[tex]\bf \rightarrow \:(5 {x}^{2} - x - 3) \: \: (2x + 6) \\ \\ \bf \small \rightarrow \:10 {x}^{3} - 2 {x}^{2} - 6x + 30 {x}^{2} - 6x - 18 \\ \\ \bf \rightarrow \:10 {x}^{3} + 28 {x}^{2} - 12x - 18[/tex]
༆ Option D is the correct answer༆
26)
A pile of bricks has 93 bricks in the first row, 89 bricks in the second row, 85 bricks in the third row, and so on.
How many bricks are there in the 12th row?
OA) 49 bricks
OB) 69 bricks
Answer:
49 bricks
Step-by-step explanation:
because it's getting smaller my 4
A circle has a radius of 3. An arc in this circle has a central angle of 20°. What is the length of the arc? Either enter an exact answer in terms of or use 3.14 for 1 and enter your answer as a decimal.
Answer:
[tex]\frac{\pi }{3}[/tex]
[tex]2 * \pi * 3 * \frac{20}{360}[/tex]
120[tex]\pi[/tex]/360 = [tex]\frac{\pi }{3}[/tex]
Step-by-step explanation:
Which expression is equivalent to ((2x²) (3x) (4x)??
A.24x7
B.48x?
C.9677
D.576x12
Answer:
24x^4
Step-by-step explanation:
((2x²) (3x) (4x)
Add the exponents when multiplying
2*3*4 x^(2+1+1)
24x^4
please answer all the questions above.
Answer:
hope it was helpful!! You are welcome to ask any question
Answer:
Step-by-step explanation:
1) 7 - ( 3+4) = 7 + [- (3+ 4)] = 7 + (-3) + (-4)
(-) is distributed to 3 and 4
A
2) C
I (-3) - 4 I
3) 5 + 3 = 8 miles
B
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest
form.
Answer:
x = 40
y= 20
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 20 sqrt(3)/ x
x sin 60 = 20 sqrt(3)
x = 20 sqrt(3)/ sin 60
x = 20 sqrt(3)/ sqrt(3)/2
x = 20 *2
x = 40
tan theta = opp /adj
tan 60 = 20 sqrt(3)/y
y = 20 sqrt(3)/ tan 60
y = 20 sqrt(3) / sqrt(3)
y = 20
What is the area of polygon
For what value of k are the roots of the quadratic
equation kx²+ 4x+ 1=0 equals and reals."
Answer:
k ≥ 4
Step-by-step explanation:
A Quadratic equation is given to us and we need to find out the value of k for which the equation has real roots. The given equation is ,
[tex]\rm\implies kx^2 +4x +1=0[/tex]
With respect to Standard form of Quadratic equation :-
[tex]\rm\implies ax^+bx+c=0[/tex]
For real roots ,
[tex]\rm\implies Discriminant = b^2-4ac\geq 0[/tex]
Substitute the respective values ,
[tex]\rm\implies b^2-4ac \geq 0\\[/tex]
[tex]\rm\implies 4^2 - 4(k)(1) \geq 0 \\[/tex]
Simplify the LHS ,
[tex]\rm\implies 16 - 4k \geq 0 \\[/tex]
Add 4k both sides ,
[tex]\rm\implies 4k\geq 16 [/tex]
Divide both sides by 4 ,
[tex]\rm\implies \boxed{\blue{\rm k \geq 4}}[/tex]
please explain this to me.
Answer:
Equation of line:- y=2x-7
slope(m)=2
slope of parallel line (m)=2
∴ Equation of parallel line:- y=2x+b
it passes through the point (-3,6)
6=2(-3)+b 6+6=b
b=12
∴ y=2x+12
OAmalOHopeO
Find the height of a rectangular prism with a 3 in by 4 in base and a volume of 20 cubic inches
Answer:
1 2/3 inches.
Step-by-step explanation:
Volume = area of the base * height so:
20 = 3*4 * h
h = 20/12
h = 1 2/3 inches.
Student Council members are designing a large poster that will tell people who each member is and what position each person holds. Each member gets a triangle piece of paper to decorate, then all the pieces will be fitted together to form the final display. The triangles are identical and fit together to form a regular polygon. It will look similar to the shape below:
A) If there are 8 council members, what type of polygon will be formed?
B) To achieve this shape, what type of triangles will the individual pieces be? What will be the measures of each of the three angles in each of the triangles?
C) What will be the sum of the measures of the internal angles of the final shape?
D) Redo parts (b) and (c) if the Council decides to include triangles for the two staff advisors, assuming the poster will still form a regular polygon, but now with 10 triangles.
A) With 8 council members, the polygon formed with the triangles will be an octagon.
A polygon formed with a set of isosceles triangles will have as many sides as triangles you are using. An octagon is a geometric figure that has 8 equal sides to it.The final shape should look just like the one you posted with your question.
B) The individual pieces should be isosceles triangles. The three angles of each triangle should measure 45°, 67.5° and 67.5°.
An isosceles triangle is the one that has two sides of the same length and one side with a different length.We need two sides of the triangles to be the same. The base of the triangle's length will depend on the number of triangles we are using to form the final polygon.
The number of triangles will define the angle between the two sides of equal length. You can find this by dividing 360° into the number of triangles:
[tex]\frac{360^{o}}{8}=45^{o}[/tex]
The other two angles should measure the same, so we can find them by subtracting the 45° from 180° (which is what we get when adding the three angles of any triangle) and then dividing the answer into 2.
180°-45°=135°
[tex]\frac{135^{o}}{2}=67.5^{o}[/tex]
C) The sum of the measures of the internal angles of the final shape should add up to 360°, that way we can guarantee that the figure is closed:
45°+45°+45°+45°+45°+45°+45°+45°=360°
D)
D.B) The individual pieces should be isosceles triangles. The three angles of each triangle should measure 36°, 72° and 72°.
The number of triangles will define the angle between the two sides of equal length. You can find this by dividing 360° into the number of triangles:
[tex]\frac{360^{o}}{10}=36^{o}[/tex]
The other two angles should measure the same, so we can find them by subtracting the 36° from 180° (which is what we get when adding the three angles of any triangle) and then dividing the answer into 2.
180°-36°=144°
[tex]\frac{144^{o}}{2}=72^{o}[/tex]
C) The sum of the measures of the internal angles of the final shape should add up to 360°, that way we can guarantee that the figure is closed:
36°+36°+36°+36°+36°+36°+36°+36°+36°+36°=360°
You can find further information on the following links:
https://brainly.ph/question/6658482
The median house price in Waterloo Region increased by 3.6% from Jan 1, 2018 to Jan 1, 2019. A home
was purchased in Waterloo Region on April 1, 2019 for $600,000.
(a) Assume this trend continues, write an exponential equation that models the Resale Value of this
home over time.
(b) At this rate, determine the date of the resale price of the home would reach $1 million (Show your
work to accurate to the nearest month)
(c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.
Answer:
The right answer is:
(a) [tex]P(t) = P_o \ e^{0.03536t}[/tex]
(b) [tex]t = 14 \ years \ 6 \ months[/tex]
(c) [tex]P(t) = =621,595.6[/tex] ($)
Step-by-step explanation:
Given:
House price increment rate,
= 3.6% annually
(a)
Let the exponential equation will be:
⇒ [tex]P(t) = P_o e^{Kt}[/tex]
here,
t = 0
P = P₀
t = 1 yr
then,
[tex]P(1) = P_o +3.6 \ persent \ P_o[/tex]
[tex]=1.036 \ P_o[/tex]
now,
⇒ [tex]1.036 P_o = P_o \ e^{K.1}[/tex]
[tex]ln(1.036) = K[/tex]
[tex]K = 0.03536[/tex]
Thus, the exponential equation will be "[tex]P(t) = P_o \ e^{0.03536t}[/tex]".
(b)
We know,
[tex]P_o = 600,000[/tex] ($)
[tex]P(t) = 10,00,000[/tex] ($)
∵ [tex]P(t) = P_o \ e^{0.03536t}[/tex]
[tex]1000000=600000 \ e^{0.03536 t}[/tex]
[tex]\frac{5}{3}= e^{0.03536 t}[/tex]
[tex]ln(\frac{5}{3} )=0.03536 t[/tex]
[tex]\frac{\frac{0.5}{0825} }{0.03536} =t[/tex]
[tex]t = 14.45 \ years[/tex]
or,
[tex]t = 14 \ years \ 6 \ months[/tex]
(c)
[tex]P_o=600,000[/tex] ($)
[tex]t = 1 year[/tex]
Now,
⇒ [tex]P(t) = P_o \ e^{0.03536 t}[/tex]
[tex]=600000 \ e^{ 0.03536\times 1}[/tex]
[tex]=621,595.6[/tex] ($)
You are riding your bike. At 8:00am you have ridden your bike 23 miles. By 9:00pm you have ridden 179 miles. Find the rate of change in miles per hour. If needed, round your answer to the nearest whole number.
Answer:
12 miles/hour
Step-by-step explanation:
8am to 9pm = 13 hours
in that time we were driving 179-23 = 156 miles.
so, our speed was 156 miles / 13 hours.
now simplify it to our standard miles/hour format :
156/13 = 12
therefore, or standardized speed was
12 miles/hour
need help with this!!
Answer:
{ 1,3,4,6,7}
Step-by-step explanation:
Do B∩C first
This is B intersect C which means what they have in common
B∩C = {3,6,7}
Then A∪(B∩C)
A union {3,6,7} which means join together ( combine with no duplicates) the two sets
{ 1,3,4,6,7}
Which expressions are equivalent to the given expression?
Answer:
The answers are option B and E.
Can someone please help?
Will mark brainliest!
Answer:
108 degrees
Step-by-step explanation:
an arithmetic progression means that there is a constant inbetween all of the angles. Since the smallest angle is 12 degrees, ( i just guessed and checked) and came up with the angles :
12, 60, 108
these have a constant of 48
Answer:
108°
Step-by-step explanation:
Since the angles are in arithmetic progression , then the angles are
a + a + d + a + 2d
a is the first term and d the common difference
Sum the angles and equate to 180 with a = 12
a + a + d + a + 2d = 180
12 + 12 + d + 12 + 2d = 180 , that is
36 + 3d = 180 ( subtract 36 from both sides )
3d = 144 ( divide both sides by 3 )
d = 48
Then the largest angle is
a + 2d = 12 + 2(48) = 12 + 96 = 108°
“The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct?
Answer:
b is the answer
Step-by-step explanation:
This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?
Given:
The table that shows the relationship of the total number of pieces of fruit to the number of bananas.
To find:
Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].
Solution:
If a, b, c are real numbers, then
[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]
The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:
[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]
The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].
Therefore, the correct option is A.
Can someone help me with this math homework please!
Answer:
(6,1)
Step-by-step explanation:
Find sin 0
A. 16/20
B. 12/16
C. 12/20
D. 16/12
Answer:
16/20
Step-by-step explanation:
Since this is a right triangle
sin theta = opp side / hypotenuse
sin theta = 16/20
Answer:
A.
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
What could be the coefficient of x once the variable term is isolated on one side of the equation? Check all that apply.
3x - 6(5x + 3) = 9x + 6
1. Distribute: 3x - 30x - 18 = 9x + 6
2. Combine like terms: -27x - 18 = 9x + 6
–36
–27
–24
24
27
36
Answer:
-36,36
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6
Distribute:
3x - 30x - 18 = 9x + 6
Combine like terms:
-27x - 18 = 9x + 6
There are two possible ways to isolate x
On the left
Subtract 9x from each side
-27x - 18 -9x = 9x-9x + 6
-36x -18 = 6
On the right
Add 27x from each side
-27x - 18 +27x = 9x+27x + 6
-18 =36x+ 6
