Answer:
a= 2/5
b= -3/5
Step-by-step explanation:
We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator
\(\frac{(3+2i)(-i)}{5i(-i)}\)
This simplifies to:
\(\frac{-3i+-2i^{2} }{-5i^{2} }\)
This further simplifies to:
\(\frac{-3i +2}{5}\)
Can be rewritten as:
\(\frac{2}{5} +-\frac{3}{5} i\)
a = 2/5
b = -3/5
Find the distance between the points (-3,-1) and (2, 3)
Check the attached image.
Answer = √41 = 6.403
____
RainbowSalt2222 ☔
Solve 5(x − 8) = 50.
Answer:
x = 18
Step-by-step explanation:
5(x - 8) = 50
Divide both sides by 5.
x - 8 = 10
Add 8 to both sides.
x = 18
Answer:
x=18
Step-by-step explanation:
5(x − 8) = 50.
5x-40=50
+40 +40
5x/5=90/5
x=18
What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (-6, 9)?
y=-1/3x+3
y=-1/3x+7
y=3x-33
y = 3x + 27
Answer:
y = - \(\frac{1}{3}\) x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 3 ← is in slope- intercept form
with slope m = 3
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then
y = - \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 6, 9 ) into the partial equation
9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )
7 = c
y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line
Why should we wear rubber gloves on our hands while working with electricity?
Answer:
a simple answer would be that rubber doesnt conduct electricity, so by wearing it you are at a substantially lower risk of being insured by electricity. This is also why people who work with electricity wear rubber soled boots.. to prevent grounding and ultimately, to prevent getting electrocuted. hope this helps :)
Answer:
if you don't wear rubber gloves, there will be a chance of you being electrocuted. Rubber gloves don't let any electricity to go through, so your body can stay safe.
Hope this helps.
Step-by-step explanation:
) Find the average gold medal winnings of those NOCs who have been
awarded fewer than ten bronze medals.
Count the number of those NOCs that have been awarded ten or more
silver medals.
This question requires the construction and interpretation of a pie chart based
on the data throughout this task.
a) Create a suitable and fully labelled pie chart to show the total medal
winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games.
Interpret the pie chart produced in Question 8a). Discuss two probable
justifications for the behaviour of the data.
a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:
Obtain the data for the medal winnings of the Top 10 NOCs
Find the average gold medal winnings of those NOCs who have beenawarded fewer than ten bronze medals.?Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)
Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option
Add a title and labels to the chart to show the NOCs and their corresponding medal winnings
b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:
Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.
Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.
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Jason plotted points on a number line at the four values below.
0.27,- 1. 3. -T
Which of these values is farthest from zero?
Answer:
Point 5/3 is the farthest from 0
Step-by-step explanation:
Given
Points: 0.27, -1/4, 1.1, 5/3
Required
The farthest from zero
The first step is to convert all points to decimal;
Points: 0.27, -1/4, 1.1, 5/3
This becomes
Points: 0.27, -0.25, 1.1, 1.67
The next step is to calculate the absolute difference of each point from 0;
The farthest from 0 is the point with highest absolute difference
For 0.27
Absolute Difference = |0.27 - 0| = |0.27| = 0.27
For -0.25
Absolute Difference = |-0.25 - 0| = |-0.25| = 0.25
For 1.1
Absolute Difference = |1.1 - 0| = |1.1| = 1.1
For 1.67
Absolute Difference = |-1.67 - 0| = |-1.67| = 1.67
From the above calculations; point 1.67 or 5/3 is the farthest from 0
Hello could you please help me with question number 9?
Given:
Brooke is saving money
she puts $150 into a savings account
The interest = r = 7.25% = 0.0725
Compounded quarterly, n = 4
We will find the balance after 4 years
So, t = 4
We will use the following formula:
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P=150,r=0.0725,n=4,t=4 \end{gathered}\)Substitute and simplify
\(A=150\cdot(1+\frac{0.0725}{4})^{4\cdot4}=150\cdot1.018125^{16}\approx199.94\)Compare the result with the cost to Bahamas ($295.99)
So, it will be less than the cost
so, the answer will be
After 4 years, she will not have enough money.
A one-way trolley ticket to Old Town costs 3.50. How much will it cost for Ahyeon and three friends to ride to Old Town and home again?
Answer:
$28
Step-by-step explanation:
Each round trip will be double the price of a one-way trip, so will be ...
2 × $3.50 = $7.00
Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...
4 × $7.00 = $28.00
HELP! WILL GIVE BRANLIEST!
Answer: I believe it is 108 good luck girl
A prism and two nets are shown below: Prism 1 E 3 Net A Net Part A: Which is the correct net for the prism? Explain your answer. (2 points) Part B: Write the measurements of Sides AB. BC, and CD of the correct net. (4 points) Part C: What is the surface area of the prism? Show your work. (4 points)
Answer:
A) Net A (see explanation)
B) AB = 3 in. | BC = 5 in. | CD = 7.2 in.
C) SA = 98.4 in²
Step-by-step explanation:
Part A
Net A is the correct net for the prism. If you look at the way the folds are, the flaps on the top and bottom would fold up to make the side of the prism. On net B, the flaps wouldn’t fit the shape correctly.
Part B
AB = This is the height of the prism.
= 3 in.
BC = This is the slant on the front of the prism.
= 5 in.
CD = This is the length of the prism.
= 7.2 in.
Part C
* First we’ll solve for the two triangles. They are the same shape and size, so we just need to solve one then duplicate it.
One triangle:
A = 1/2bh
= 1/2 (4) (3)
= 6 in²
Back rectangle:
A = bh
= 7.2 (3)
= 21.6 in²
Front rectangle:
A = bh
= 7.2 (5)
= 36 in²
Bottom rectangle:
A = bh
= 7.2 (4)
= 28.8 in²
Total:
A = 6 + 6 + 21.6 + 36 + 28.8
= 98.4 in²
Find the domain and range of the relation of 6,5, -13, 1, -4,2, -5, 23, -10, -5
Answer:
\(Range = \{5,1,2,23,-5\}\)
\(Domain = \{6,-13,-4,-5,-10\}\)
Step-by-step explanation:
Given
\((6,5)\ (-13, 1)\ (-4,2)\ (-5, 23)\ (-10, -5)\)
Required
Determine the domain and range
A relation has the following format:
\(\{(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)........(x_n,y_n)\}\)
The range of the relation are:
\(\{y_1,y_2,y_3,y_4........y_n\}\)
While the domain are:
\(\{x_1,x_2,x_3,x_4........x_n\}\)
Using this analysis, the domain of the relation is:
\(Domain = \{6,-13,-4,-5,-10\}\)
and the Range is
\(Range = \{5,1,2,23,-5\}\)
a quadratic function is defined by f(x) = x*2 - 8x - 4.
Which expression also defines f and best reveals the max and mini of the function?
a) (x-4)*2 - 20
B) (x-4)*2 + 12
c) x(x-8) -4
d) (x-4)*2 + 20
The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.\) Option A
How to find the expressionThe vertex form of a quadratic function is given by\(f(x) = a(x - h)^2 + k\) where (h, k) represents the coordinates of the vertex.
In the given quadratic function \(f(x) = x^2 - 8x - 4\), we can rewrite it in the vertex form by completing the square:
\(f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20\)
From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).
The term\((x - 4)^2\) tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.
The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4\) is \((x - 4)^2 - 20.\)
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the rule for being the nth item in a certain sequence is n(n+1)/2. what is the 4th term in this sequence ?
a.) 4
b.)10
c.)16
d.)20
Answer:
a.) 4
Step-by-step explanation:
a.)4
Are these questions different at all? And if so whats the answer to them?
Answer:
i think u got it
Step-by-step explanation:
The owner of an appliance store bought 15 washers at $279 each and 18 dryers at $229 each. How much did the dealer spend in all?
Answer:
8307 dhdhdhsjs
Step-by-step explanation:
vahahahwhahehe
Answer: 8,307$
Step-by-step explanation:
279$ x 15 = 4185$
229$ x 18 = 4122$
4185$ + 4122$ = 8,307$
Find the magnitude and direction of the vector using the given information. V=<6,7>
Answer:
The magnitude of the vector is 9.165 and it's direction is 40.6°
Step-by-step explanation:
Vector Quantities:A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.
Magnitude of vector v is given by
|v| = √6²+7²
= √36+49
= √84
= 9.165
Direction of vector v is obtained by:
\( \tan( \theta) = \frac{x}{y} \)
\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)
\(\theta = {40.6°}\)
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Keith is playing a game. He needs at least 500 points to win the high score. He has 240 points now and 8 rounds to go. How many points does he need per round to get the high score?
Answer:
280
Step-by-step explanation:
He is gaining points during the 8 courses are there
Evaluate 8 ÷ -2 · 42 + 9. -100 -55 73 -23
Steps to solve:
8 / -2 * 42 + 9
~Divide
-4 * 42 + 9
~Multiply
-168 + 9
~Add
177
Best of Luck!
The simplified expression is equivalent to -159.
Given is an expression 8 ÷ -2 · 42 + 9, we need to simplify it,
To evaluate the expression 8 ÷ -2 · 42 + 9, we need to follow the order of operations, which is typically remembered using the acronym PEMDAS.
In this case, we should first perform the multiplication and division, and then the addition.
Starting with the multiplication and division:
8 ÷ -2 = -4
-4 · 42 = -168
Now we can add the result to 9:
-168 + 9 = -159
Therefore, the evaluation of 8 ÷ -2 · 42 + 9 is -159.
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The radius of a circle is 19 cm. Find the area
Answer: 1134.11
A=3.14*r^2
Step-by-step explanation:
Answer:
a ≈ 1134.11 cm2
Step-by-step explanation:
The formula:
\(a=\pi r^{2}\)
\(a=\pi (19)^{2} =361\pi\)
\(a=1134.11cm^{2}\)
Hope this helps
six compared to 11 is the same as 84 compared to what number A.154 B.155 C. 145 D. 146
HELP ME PLEASE
Answer:
A
Step-by-step explanation:
\( \frac{6}{11} = \frac{84}{?} \\ = 154\)
find the x and y intercepts of the following linear function and draw the graph: 2x-8y=-18
Answer:
Step-by-step explanation:
2x - 8y = - 18
- 8y = - 2x - 18
y = ¼x + 2¼
y intercept occurs when x = 0, so b = 2¼ (0, 2¼)
x intercept occurs when y = 0
0 = ¼x + 2¼
¼x = - 2¼
x = -9 (-9, 0)
Multiply
(9.4 x 10^6)(3.2 x 10^5)
PLZZZZ
Answer:3.008x10^12
Step-by-step explanation:
Answer:
3008000000000 or 3.008×10^12
Step-by-step explanation:
(9.4×3.2)×(10^6×10^5) use communitive property to reorder terms
30.08×10^6+5 multiply the numbers
30.08×10^11 add your exponents to equal 10^11
3.008×10^12 put in scientific notation
hope this helped!
Fixed expenses are defined as those that do not very with changed in volume. Examples include:
A( direct staffing costs
B( lease costs and taxes
C( utilities and supplies utilized in production of service or product
D( utilities, rent, lease, depreciation
Answer:
B (lease costs and taxes) and D (utilities, rent, lease, depreciation) are examples of fixed expenses as they typically do not vary with changes in volume.
Direct staffing costs (A) and utilities and supplies utilized in the production of service or product (C) are generally considered variable expenses as they tend to vary based on the volume of production or sales. For example, if a business produces more goods or provides more services, it will typically need to hire more staff and use more supplies, leading to an increase in expenses.
Step-by-step explanation:
The area of the base of a cylinder is 75 square ft and the height is 20 ft. Calculate the volume and surface
area.
Answer:
volume: 1500 , surface area: 764
Step-by-step explanation:
formula of circle's area
\(\pi \: r {}^{2} \)
formula of cylinder's surfaces area
\(2\pi \: r {}^{2} + 2\pi \: rh\)
The temperature of a person has a normal distribution. What is the probability that the temperature of a randomly selected person will be within 2.42 standard deviations of its mean? Provide answer with 4 or more decimal places.
Answer:
Step-by-step explanation:
If the temperature of a person follows a normal distribution, we know that approximately 95% of the observations fall within 2 standard deviations of the mean. Since we are given that we want to find the probability of the temperature being within 2.42 standard deviations of its mean, we can use the standard normal distribution and the z-score formula.
The z-score formula is given by:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation. In this case, we want to find the probability that the temperature is within 2.42 standard deviations of the mean, so we can set:
z = 2.42
Since the normal distribution is symmetric, we can find the area to the right of the mean (z = 0) and double it to get the total probability. Using a standard normal distribution table or calculator, we find that the area to the right of z = 2.42 is approximately 0.0074. So the area to the left of z = 2.42 is approximately 0.9926.
Doubling this area gives us the total probability:
P(z < 2.42 or z > -2.42) = 2 * P(z < 2.42) = 2 * 0.9926 = 0.9852
Therefore, the probability that the temperature of a randomly selected person will be within 2.42 standard deviations of its mean is 0.9852, or approximately 0.9852 with four decimal places.
The point K lies on the segment JL. Find the coordinates of K so that the ratio of JK to KL is 5 to 4.J(-19,12)K(?,?)L(8,-6)
The Solution:
Step 1:
We shall find the distance between point J an
Solve these please!!!
The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;
1. The area is about 15.16 units²
2. The coordinates of the points are;
(i) B(5, 8)
(ii) C(8.58, 4)
(ii) D(8,58, 1.21)
What is a quadrilateral?A quadrilateral is a four sided polygon.
1. The coordinate of the point C can be found as follows;
Let (x, y) represent the coordinates of the C, we get;
(x + 8)/2 = 5
x = 2 × 5 - 8 = 2
(y + 8)/2 = 6
y = 2 × 6 - 8 = 4
The coordinates ot the point C (2, 4)
The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)
Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)
The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13
CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;
(4 - y)/(2 - x) = -(5 - x)/(6 - y)
y - 4 = (-4/7)(x - 2)
y - 6 = (7/4)(x - 5)
(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6
x = (17/5) = 3.4
y = (7/4)((17/5) - 5) + 6 = 3.2
The coordinates of the point E is (3.4, 3.2)
The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)
Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)
Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)
Area of the figure is therefore;
13 + (1/2) × √(10.4) × √(1.8) ≈ 15.16 square units2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))
y - 6 = (1/3)·(x + 1)
y = (1/3)·(x + 1) + 6
The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2
Slope of the segment BE = -1/(-1/2) = 2
Equation of BE is; y - 4 = 2·(x - 3)
y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6
Therefore, x = 5
y = (1/3)·(5 + 1) + 6 = 8
The coordinates of the point B is (5, 8)(ii) Area of the triangle EBC = 24 unit²
EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20
Therefore;
BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)
(x - 5)² + (y - 8)² = 28.8
y = 4, therefore;
(x - 5)² + (4 - 8)² = 28.8
(x - 5)² = 28.8 - (4 - 8)² = 12.8
x = √(12.8) + 5
The coordinates of the point C is C(√(12.8) + 5, 4) ≈ (8.58, 4)(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)
x = √(12.8) + 5
Therefore;
y - 4 = (-1/2)((√(12.8) + 5) - 3)
y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21
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the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?
A rectangle has an area of 40 square meters. If the length is 8 m, what is the width?
Answer:
5 m
Step-by-step explanation:
The area of a rectangle is found by doing length times width. To find a side length, or the width, do area divided by the length. In this case, it would be 40 divided by 8. 40/8 is 5 so the width is 5 m.
The width is 5 m.
Slope 3/5 yintercept2 write an equation slope-intercept form
The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.
To write the equation of a line in slope-intercept form, we use the formula:y = mx + b
where:
- y represents the dependent variable (the vertical axis)
- x represents the independent variable (the horizontal axis)
- m represents the slope of the line
- b represents the y-intercept, the point where the line intersects the y-axis.
In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:
y = (3/5)x + 2
This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).
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