The statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number:
= 6 + 4i
Multiplied by 3:
= 18 + 12i
If we plot on the coordinate plane there will be no rotation the scalar has changed by multiplying with a real number.
Thus, the statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.
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2^x - 3^x = √(6^x - 9^x)
[tex]2^x-3^x=\sqrt{6^x-9^x}\\\\D:6^x-9^x\geq0 \wedge 2^x-3^x\geq0\\D: 6^x\geq 9^x \wedge 2^x\geq3^x\\D:x\leq0 \wedge x\leq 0\qquad(\text{if }a < b \text{ then } a^x < b^x\text{ for } x > 0 \text{ and } a^x > b^x \text{ for } x < 0 )\\D:x\leq 0\\\\(2^x-3^x)^2=6^x-9^x\\(2^x-3^x)^2=3^x(2^x-3^x)\\\\\text{We divide both sides by } 2^x-3^x \text{ assuming }2^x-3^x\not=0\Leftrightarrow x\not=0.\\\\2^x-3^x=3^x\\2^x=2\cdot3^x\\\ln 2^x=\ln (2\cdot3^x )\\x\ln 2=\ln 2+\ln 3^x\\x\ln 2=\ln 2+x\ln 3[/tex]
[tex]x\ln 2-x\ln 3=\ln 2\\x(\ln 2-\ln 3)=\ln 2\\x=\dfrac{\ln 2}{\ln 2-\ln 3}=-\dfrac{\ln 2}{\ln 3-\ln 2}=-\dfrac{\ln 2}{\ln \frac{3}{2}}\approx-1.7[/tex]
For [tex]x=0[/tex], our initial equation is obviously true.
Therefore [tex]x\in\left\{-\dfrac{\ln 2}{\ln \frac{3}{2}},0\right\}[/tex].
Answer to the miscellaneous equation, is x=0 and x=-1.71
Miscellaneous equation are the equations which are not polynomial
The question can be solved by:
Factorising Splitting the terms to find the required solution
Completing the squares, etc
2ˣ - 3ˣ = √(6ˣ - 9ˣ)
Squaring both sides,
2²ˣ+3²ˣ -2.2ˣ.3ˣ=2ˣ.3ˣ - 3²ˣ
2²ˣ+2.3²ˣ -3.2ˣ.3ˣ=0
Factorising the terms,
2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0
(2ˣ-3ˣ)(2ˣ-2.3ˣ)=0
Equating the braces to zero,
Either,
2ˣ=3ˣ
x=0
or
2ˣ=2.3ˣ
Taking log on both sides
xln2=ln2+xln3
x=ln2/(ln2-ln3)
=-1.71
Therefore, x=0 and x=-1.71 is the only solution
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copy machine can make 250 copies in 4 minutes. Represent
rate of change in copies per minute.
Answer:
62.5 copies per minute
Step-by-step explanation:
Note that the word "per" means divide. So, a rate of change in "copies per minute", means a number of copies divided by a number of minutes
If the copy machine can make 250 copies in 4 minutes, then the number of copies is 250 copies, and the number of minutes is 4 minutes:
[tex]\text{rate of change in copies per minute}=\dfrac{\text{number of copies}}{\text{number of minutes}}[/tex]
[tex]\text{rate of change in copies per minute}=\dfrac{\text{250 copies}}{\text{4 minutes}}[/tex]
[tex]\text{rate of change in copies per minute}=62.5\dfrac{\text{copies}}{\text{minute}}[/tex]
write an equation in slope intercept form of the line with the given characteristics: a) passes through (-3,0) and (-5,-3)
The equation of the line in slope-intercept form is [tex]\bf{y= \frac{3}{2} x + \frac{9}{4}} [/tex].
What is slope-intercept form?y=mx +c, where m is the slope and c is the y-interceptStepsFind the slopeSubstitute value of the slope into the equationSubstitute a pair of coordinatesSolve for cRewrite equation with value of m and cWorkingThe first step is to calculate the slope of the line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope
[tex] = \frac{ - 3 - 0}{ - 5 -( - 3)} [/tex]
[tex] = \frac{ - 3}{ - 5 + 3} [/tex]
[tex] = \frac{ - 3}{ - 2} [/tex]
[tex] = \frac{3}{2} [/tex]
Substitute the value of m into y= mx +c:
[tex]y = \frac{3}{2} x + c[/tex]
Next, substitute a pair of coordinates that the line passes through. Here, I will substitute (-3, 0) into the equation.
When x= -3, y= 0,
[tex]0 = \frac{3}{2} ( - 3) + c[/tex]
Find the value of c:
[tex]0 = - \frac{9}{2} + c[/tex]
[tex]c = \frac{9}{2} [/tex]
Substitute the value of c into the equation:
Thus, the equation of the line is [tex]y = \frac{3}{2} x + \frac{9}{2} [/tex].
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Unit 8:Right triangles & Trigonometry
Answer:
[tex]24\sqrt{5}[/tex]
Step-by-step explanation:
So for this problem you can use the law of sines which states
[tex]\frac{a}{sin A} = \frac{b}{sin B}\\[/tex]
Since the angle is a right triangle we can find the hypotenuse by plugging in the values.
[tex]\frac{4\sqrt{15}}{sin 60} = \frac{hypotenuse}{sin 90}\\\\\frac{4\sqrt{15}}{sin 60} = hypotenuse\\hypotenuse = \frac{4\sqrt{15}}{\frac{\sqrt{3}}{2}} = \frac{8\sqrt{15}}{\sqrt{3}}\\hypotenuse = \frac{8\sqrt{45}}{3} = \frac{24\sqrt{5}}{3}\\[/tex]
we now just multiply that side by 3since all the sides should be equal since all the angles are equal and we get the length of 24sqrt(5)
divided it by 7 and added 25. the result was 34 what was my number?
25. the result was 34 what was my number?
Answer:63
Step-by-step explanation:
63/7+25=34
Answer:
x = 63
Step-by-step explanation:
we know that...
(x will be the stand-in for "your number")
x ÷ 7 + 25 = 34
(x ÷ 7) + 25 = 34
To find x, we have to isolate x
first, we can subtract 25 from both sides (remember, if you do an action on one side, you must do the same action on the other side)
{why are we subtracting? we need to do the opposite of a sign to get rid of it. By subtracting, we are undoing addition; by multiplying we are undoing division (and vice versa) }
(x ÷ 7) + 25 = 34
- 25 - 25 (subtract 25)
x ÷ 7 = 9
× 7 ×7 (multiplying by 7 to get rid of the "÷7")
x = 63
now, we can test out our x-value:
(63 ÷ 7) +25 = 34
( 9 ) + 25 = 34
34 = 34
because this equation is true, we can be certain that x = 63
hope this helps!
Please help! I'm not quite understanding this.
Answer:
d.) 21
Explanation:
Rules:
-|a| = -a|-a| = ax = |a| then x = ±aSolve:
[tex]\rightarrow \sf \dfrac{4|a|}{2} + |a-3|[/tex]
[insert a = -6]
[tex]\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|[/tex]
[simplify the following]
[tex]\sf\rightarrow \dfrac{4(6)}{2} + 9[/tex]
[tex]\sf\rightarrow 12 + 9[/tex]
[tex]\sf\rightarrow 21[/tex]
Area of a triangular prism
Answer:
if you mean the formula it is (1/2) · b · (6 · h + sqrt(3) · b)
Step-by-step explanation:
A building 190 feet tall casts a 90 foot long shadow. if a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building
Answer:
About 64.65 degrees
Step-by-step explanation:
[tex] \tan(x) = \frac{190}{90} [/tex]
[tex]x = { \tan}^{ - 1} \frac{190}{90} = 64.65[/tex]
Make sure your calculator is in degree mode.
vincent mows 8 lawns in 2 hours. how many lawns are mowed in 5 hours .
Answer:
20 lawns
Step-by-step explanation:
City worker drain a community pool that contains 403,920 gallons of water. The pump they use removes water at a rate of 40 cubic feet per minute. One cubic foot of water contains 7.48 gallons how long in hours will it take to remove all the water from the pool
Answer:
22.5 hours
Step-by-step explanation:
One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have
299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours
A=(3+[tex]\frac{a+\sqrt{a} }{\sqrt{a}+1 }[/tex])(3-[tex]\frac{a-5\sqrt{a} }{\sqrt{5}-5 }[/tex])
The simplification of the given algebra we see is; 9 + 3((a√a + a - a + √a)/(a - 1)) - ³/₂₀((√5 - 5)(a - 5√a)) - (a² - 4a√a - 5a)/((√a + 1)*√5 + 5))
How to Simplify Algebra?We are given the algebra expression;
A = [3 + ((a + √a)/(√a + 1))][3 - ((a - 5√a)/(√5 + 5))]
When we multiply out, we will get;
9 + 3((a + √a)/(√a + 1)) - 3((a - 5√a)/(√5 + 5)) - [((a + √a)/(√a + 1)) * ((a - 5√a)/(√5 + 5))]
⇒ 9 + 3((a√a + a - a + √a)/(a - 1)) - ³/₂₀((√5 - 5)(a - 5√a)) - (a² - 4a√a - 5a)/((√a + 1)*√5 + 5))
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he height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent?
the number of seconds after the rocket is released
the initial height of the rocket
the initial velocity of the rocket
the height of the rocket after t seconds
Answer: the number of seconds after the rocket is released
The function f(x) = x² has been translated 9 units up and 4 units to the right to form the function g(x). Which represents
g(x)?
O g(x) = (x + 9)² + 4
O g(x) = (x + 9)²-4
Og(x)=(x-4)² +9
Og(x) = (x+4)² +9
Answer:
g(x) = (x-4)² +9
Step-by-step explanation:
If f(x) is moved up 9 units, it becomes x² + 9, as only the 'y' value is changed by 9. Then, if it is moved 4 units to the right, it becomes (x+4)² +9, as only the 'x' value is changed by -4.
The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,
⇒ g(x) = (x-4)² + 9.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Now, To translate the function f(x) = x² with 9 units up and 4 units to the right, we need to use the following formula:
⇒ g(x) = f (x - 4) + 9
Substituting f(x) with its equivalent form:
⇒ g(x) = ( x - 4 )² + 9
Therefore, The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,
⇒ g(x) = (x-4)² + 9.
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7 is what percent of 154?
Answer: 10.78
Step-by-step explanation:
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
1 European euro = 1.3687 US dollars
Answer:
44.70 US dollars
Step-by-step explanation:
Begin by converting the Euros to US dollars by dividing 250 by 1.3687
250/1.3687=182.655
Then subtract 150
182.655-150=32.655
Multiply by 1.3687 to convert back to US dollars
32.655x1.3687=44.70
18 A student has 273 matchsticks with which to make a pattern of nested triangles. Fig. 18.9 shows the first three triangles. Fig. 18.9 If all the matchsticks are used, how many matchsticks will each side of the biggest triangle contain? 18 A student has 273 matchsticks with which to make a pattern of nested triangles . Fig . 18.9 shows the first three triangles . Fig . 18.9 If all the matchsticks are used , how many matchsticks will each side of the biggest triangle contain ?
The number of matchsticks that each side of the biggest triangle contains is; 137 matchsticks
How to find the biggest side of a triangle?We know that for a diagram to be a triangle, then two smallest sides must not be greater than the third side.
Now, if there are 273 matchsticks, then the greatest side of the triangle must not be less than 273/2 = 136.5 ≈ 137
Thus, the largest side will have at least 137 matchsticks
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Using the following image, solve for JI.
J
2x + 28
x + 22
5
H
In the given image, the length of JI is 6
Solving linear equationsFrom the question, we are to solve for JI
From the given image, we can write that
JI + IH = JH
Then,
2x + 28 + 5 = x + 22
Solving for x
2x + 28 + 5 = x + 22
First, collect like terms
2x - x = 22 - 28 - 5
Simplifying
x = -11
But,
JI = 2x + 28
∴ JI = 2(-11) + 28
JI = -22 + 28
JI = 6
Hence, the length of JI is 6
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Help please answer this point an brainlist
The tables represent the functions f(x) and g(x). f(x) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g(x) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions? x = -3 O x = -1 x = 0 Ox=1 The tables represent the functions f ( x ) and g ( x ) . f ( x ) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g ( x ) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions ? x = -3 O x = -1 x = 0 Ox = 1
Answer:
x=1
Step-by-step explanation:
There are two functions (f & g), each of which have a table of inputs and outputs. The same list of inputs is given to both functions, but the outputs are different.
Imagine that you asked your Father 6 questions, (weirdly instead of numbered 1 through 6, numbered -3 through 2), and that he gave you a list of answers.
Imagine that you asked your Grandfather the same 6 questions, and you got a list of answers from him.
On which question did they give the same answer?
It was on question number "1", (really the 5th question, but as we've numbered things from -3 to 2, it's question "1").
Since the "questions" were the input, "x", x=1.
how many eggs are in 2 3/4 dozen?
please answer this one...i need it today
Step-by-step explanation:
please mark me as brainlest
Answer:
33 eggs
Step-by-step explanation:
1 Dozen = 12 units
2 dozen = 2*12 = 24 units
3/4 dozen = 12*3/4 = 36/4 = 9 units
2 3/4 = 2 + 3/4 = 24 + 9 = 33 units
For the graph below, what should the domain be so that the function is at least 300? (1 point) graph of y equals minus 2 times the square of x plus 50 times x plus 300 a x ≥ 0 b −5 ≤ x ≤ 30 c 0 ≤ x ≤ 25 d all real numbers
The function is a quadratic function, then the domain will be all real numbers. Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = -2x² + 50x + 300
Then the function is a quadratic function, then the domain will be all real numbers.
Then the correct option is D.
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Practice A
Get a coin and toss it five times. Record the outcomes on the table below. Then, answer the questions that follow.
Head
Tail
1st toss
2nd toss
3rd toss
4th toss
5th toss
Total
Answer:
You can just flip a coin five times either with a real one (heads being a face or a picture and tails being the other side) or online, then put a tick on either heads or tails depending on what you got on that toss. Then just put how many times you got heads in the first question.
Hope this helps I guess.
(Giving 45 points, and brainly if correct! Please hurry!)
Point A is on point −6 and Point B is on point 0. Let's use the Ruler Postulate to find the length of AB¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯ is 6. We can also write this as AB=6 or mAB¯¯=6.
Find the Length of CD¯¯
Now, let's find the length of CD¯¯. Point C is on point 4 and Point D is on point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯ is 4. We can also write this as CD=4 or mCD¯¯=4
Your Turn
1. What is the length of BC¯¯?
2. What is the length of AC¯¯?
3. What is the length of AD¯¯?
The length of BC , AC and AD is 4 , 10 , 14.
What is Length ?Length is the distance between two points , It is measured in cm , m , km etc.
It is asked to calculate the length of BC , AC , AD
For BC
Point B is on point 0 and Point C is on point 4.
BC=|b−c|
BC=|0−4|
BC=4
For AC
Point A is on point -6 and Point C is on point 4.
AC=|a−c|
AC=|-6−4|
AC= 10
For AD
For AC
Point A is on point -6 and Point D is on point 8.
AD=|a−c|
AD=|-6−8|
AD= 14
Therefore the length of BC , AC and AD is 4 , 10 , 14.
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Use the given graph to determine the limit, if it exists.
The limit in the given graph [tex]\lim_{x \to \ 2^{-} } f(x)[/tex] is 3 and [tex]\lim_{x \to \ 2^{+} } f(x)[/tex] is -2
Given graph of a function and we have to determine the limits when x tends to 2 minus and when x tends to 2 plus.
When we see the graph we can find that the graph is not of the linear function because it is not straight line.
From x=2 and onwards it gives values values of only -2 because it is parallel to x-axis at y=-2.From x=2 and leftwards it gives values values of only 3 because it is parallel to x-axis at y=3.
Hence the limit of the function whose graph is shown is 3 and -2.
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Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.
{(-3, 7.5) , (-2, 10) , (-1, 12.5)}
Write the equation of the graph for the set of ordered pairs.
{(1, 150) , (2, 112.5) , (3, 84.375)}
Write the equation of the graph for the set of ordered pairs.
12. Last month, a store sold a total of 182 pairs of jeans and shorts. The
number of shorts sold was 28 fewer than twice the number of jeans sold.
How many pairs of jeans were sold?
C. 105
A 51
D. 112
B. 70
Answer:
B. 70
Explanation:
A total of 182 pairs of jeans and shorts were sold and the number of shorts sold was 28 fewer than twice the number of jeans. This can be expressed with j being the number of jeans as:
j2 - 28 = number of shorts
As the number of shorts is 28 lower than twice the number of jeans, this means it can not be C or D, as these numbers are larger than 182 when doubled. The process of elimination can be done with the remaining using our equation.
51(2) - 28 = 102 - 28 = 74
70(2) - 28 = 140 - 28 = 112
Now that we have the number of shorts sold by using the equation, we can add them with what number was used as their number of jeans.
74 + 51 = 125
112 + 70 = 182
So the number of jeans sold is B. 70.
Luis and Raul are playing Odds or Evens. Both friends flip a coin. If both coins land on heads or if both coins land on tails, then Luis wins both coins. If one coin lands on hea
No, the game is not fair because Raul has a higher probability of winning than Luis.
Yes, the game is fair because both friends have an equal probability of winning.
No, the game is not fair because Luis has a higher probability of winning than Raul.
Yes, the game is fair because the friends do not have an equal probability of winning.
Answer:
B
they both have equal probability of winning as both of them have a 50/50 chance of winning
Step-by-step explanation:
Yes, the game is fair because both friends have an equal probability of winning.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The game of Odds or Evens is not fair because Raul has a higher probability of winning than Luis.
In this game, the probability of both coins landing on heads or both coins landing on tails is 1/2 * 1/2 = 1/4.
Therefore, there is a 1/4 probability that Luis will win both coins.
However, there is a 1/2 probability that one coin will land on heads and the other will land on tails. In this case, Raul will win both coins because he chose "evens" and the sum of the numbers is even.
The sum of two random coin flips has an equal probability of being even or odd, so the probability of Raul winning both coins is 1/2.
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Tomas learned that the product of the polynomials
(a + b)(a ab + bf) was a special pattern that would
result in a sum of cubes, a3 + b3. His teacher
put four
products on the board and asked the class to identify
which product would result in a sum of cubes if a =
2x and b = y
The product that would result in a sum of cubes if a =2x and b = y is: (2x + y)(4x² – 2xy + y²).
Product that would result in a sum of cubesGiven:
Product of polynomials=(a + b)(a²- ab + b²)
Sum of cubes=a³+ b³
Hence,
a³+ b³ = (a + b) (a²-ab + b²)
When:
a=2x
y=b
So,
a³+ b³= (2x + y ) [ (2)² - (2x) (y) + y²)
a³+ b³= (2x + y ) [ 4x² - 2xy + y²]
a³+ b³ = (2x + y)(4x² – 2xy + y²)
Therefore the product that would result in a sum of cubes if a =2x and b = y is: (2x + y)(4x² – 2xy + y²).
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Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answer:
| x - 57 | = 3
Step-by-step explanation:
Since the house is on the 57th block, Jamaal must stop walking on the 54th block or the 60th block.
i do not now these questions
Using proportions, it is found that:
a) 5 people are needed.
b) Yes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Item a:
Each person works for 32 hours, and 150 hours are needed, hence the number of people needed is given by:
150/32 = 4.6875.
However, an integer number is needed, hence 5 people are needed.
Item b:
With 30 hours, the number of people needed is given by:
150/30 = 5.
Which remains the same.
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