Answer:
d = -12
Step-by-step explanation:
[tex]3i-4-di = -4-11i+2i\\3i-4-di = -4-9i\\3i-\left(4-di\right)-3i = -4-9i-3i\\-\left(4-di\right)=-4-12i\\\frac{- 4 - di}{-1} = -\frac{4}{-1}-\frac{12i}{-1}\\\frac{-\left(4-di\right)}{-1}\\= \frac{\left(4-di\right)}{1}\\=4-id\\=\frac{- 4 - 12i}{-1}\\=-\frac{- 4-12i}{1}\\=-( - 4)-( - 12i)\\=-\left(-4\right)-\left(-12i\right)\\= 4 + 12i\\4-(id) = 4 + 12i\\4 - id - 4 = 4 + 12i - 4\\- id=12i\\\frac{-id}{-i} = \frac{12i}{-i}\\\frac{id}{i}\\= d\\- \frac{12i}{i}\\= - 12[/tex]
Alan thinks of a number. He squares it, then takes away 5, next multiplies it by 4, takes away 7, divides it by 3 and finally adds 6. His answer is 9. What number did Alan start with?
Answer: [tex]\pm3[/tex]
Step-by-step explanation:
[tex][(4(x^{2} -5)-7)/3]+6=9[/tex]
[tex]((4x^{2} -20)-7)/3=9-6[/tex]
[tex]4x^{2} -27=3*3[/tex]
[tex]4x^{2} =9+27[/tex]
[tex]x^{2}=36/4=9[/tex]
[tex]x=\sqrt{9} =\pm3[/tex]
[tex]x = 3[/tex]
please help DUE TODAY. I WILL GIVE 35 POINTS!!!!!!
Shureka Washburn has scores of 79, 69, 61, and 91 on her algebra tests. a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 75 or higher, given that the final exam counts as two tests. b. Explain the meaning of the answer to part (a).
She must have a score greater than the average of 75 on her final exam.
What is arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
Let the required score be x
Mean = 79 + 69 + 61 + 91 + x/5
⇒ 79 + 69 + 61 + 91 + x/5 > 75
⇒ 300 + x/5 > 75
⇒ 300 + x > 375
⇒ x > 375 - 300
⇒ x > 75
This implies that she needed a score on her final exams that were higher than the average of 75.
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The heights of women aged 20–29 in the United States are approximately Normal with mean 64.1 inches and standard deviation 3.7 inches. Men the same age have mean height 69.4 inches, with standard deviation 3.1 inches.
Using the normal distribution, it is found that the z-score of the height of a women 5.5 feet tall is 0.51.
What is the missing information?The problem asks for the z-score of the height of a women 5.5 feet tall.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Considering that each feet has 12 inches, the parameters are given as follows:
[tex]X = 5.5 \times 12 = 66, \mu = 64.1, \sigma = 3.7[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (66 - 64.1)/3.7
Z = 0.51.
The z-score of the height of a women 5.5 feet tall is 0.51.
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what are least common multiple and greatest common factor of the numbers 9 and 6
Answer:
LCM=18 and GCF = 3
Step-by-step explanation:
Multiples of 9: 9, 18, 27
Multiples of 6: 6, 12, 18
LCM = 18
Factors of 9: 1, 3, 9
Factors of 6: 1, 2, 3, 6
GCF = 3
I need to answer this is something like a test but it is not just help me please
Perpendicular lines from angles that measure (90) degrees
What is the best estimate of the area of the figure if each square has a side length of 1 mm?
27 square millimeters
36 square millimeters
39 square millimeters
46 square millimeters
Answer:
(c) 39 mm²
Step-by-step explanation:
You want to know an estimate of the area of the irregular figure.
DecompositionThe areas of irregular figures are often easily computed by decomposing the figure into shapes whose areas have formulas. Here, we can draw a vertical line from the upper left vertex to divide the figure into a triangle on the left and a trapezoid on the right.
TriangleThe triangle has a base of 3 squares and a height of 6 squares, so an area of ...
A = 1/2bh = 1/2(3)(6) = 9 . . . . square mm
TrapezoidThe trapezoid has vertical parallel bases of 6 and 7 squares, and a width of 5 squares. Its area is ...
A = 1/2(b1 +b2)h = 1/2(6 +7)(5) = 65/2 = 32 1/2 . . . . square mm
Total areaThen the total area of the figure shown is ...
area = triangle area + trapezoid area
area = 9 mm² +32.5 mm² = 41.5 mm²
The closest estimate of those offered is 39 square mm.
Solve for x. Figures are not necessarily drawn to scale.
N
32
40
59⁰
45
P
X
59⁰
M
The value of x is 81 since similar triangles have equal ratios of corresponding sides.
Given:
PQ ǁ MN
OQP= N
QPO= M
ΔOQP=ΔONM
OP/OM=OQ/ON
45/X=40/72
X= (72×45)/40
X=81
If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name of this usual ratio.
Therefore, the value of X is calculated as 81.
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The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion
s = 5 sin(t) + 5 cos(t),
where t is measured in seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period.
(1)[1,2]? cm/s
(2)[1,1.1]? cm/s
(3)[1,.101]? cm/s
(4)[1,1.001]? cm/s
(b) estimate the instantaneous velocity of the particle when t = 1? cm/s
a) the average velocity during each time period.
(1) 4.87 cm/s(2) 4.90 cm/s(3) 4.95 cm/s(4) 4.91 cm/s(b) 0.08 cm/s is the instantaneous velocity of the particle when t = 1.
Step-by-step explanation:
Given that
the equation of motions = 5 sin(t) + 5 cos(t),
To find
a) The average velocity during each time period.(1)[1,2]? cm/s
(2)[1,1.1]? cm/s
(3)[1,.101]? cm/s
(4)[1,1.001]? cm/s
b) The instantaneous velocity of the particle when t = 1? cm/sSo, according to the question
a) The average velocity during each time period.
(1)[1,2]? cm/s
(2)[1,1.1]? cm/s
(3)[1,.101]? cm/s
(4)[1,1.001]? cm/s
We have the displacement equation at time t :
s = 5 sin(t) + 5 cos(t)
Now differentiate it by t to get velocity.
v(t) = ds/dt
[tex]= \frac{d}{dt} (5sint+5cost)\\= 5(\frac{d}{dt} sint+\frac{d}{dt}cost)\\\\[/tex]
v(t) [tex]= 5( cost - sint)[/tex]
velocity at t = 1,
v(1) = 5 { cos(1)- sin(1) } = 5( 0.99-0.017) = 5 x 0.982 = 4.91 cm/s
velocity at t = 2,
v(2) = 5 { cos(2)- sin(2) } = 5( 0.999 - 0.0348) = 4.82 cm/s
velocity at t = 1.1,
v(1.1) = 5 { cos(1.1)- sin(1.1) } = 5( 0.999 - 0.0191) = 4.90 cm/s
velocity at t = 0.101,
v(0.101) = 5 { cos(0.101)- sin(0.101) } = 5( 0.999 - 0.0176) = 4.99 cm/s
velocity at t = 1.001,
v(1.001) = 5 { cos(1.001)- sin(1.001) } = 5( 0.999 - 0.0174) = 4.911 cm/s
Now,
The average velocity at [1,2]
= (4.91+4.82)/2 = 4.87 cm/s
The average velocity at [1,1.1]
= (4.91+4.90)/2 = 4.90 cm/s
The average velocity at [1,0.101]
= (4.91+4.99)/2 = 4.95 cm/s
The average velocity at [1,1.001]
= (4.91+4.911)/2 = 4.91 cm/s
b) instantaneous velocity at 1s.
instantaneous velocity[tex]= \frac{instantaneous\; displacement }{instantaneous\; time}[/tex]
v(1) = [tex]\frac{s(1)-s(0)}{1-0}[/tex]
s(1) = 5 {sin(1) + cos(1)} = 5 (0.017 + 0.999) = 5.08 cm
s(0) = 5 {sin(0) + cos(0)} = 5 (0 + 1) = 5.0 cm
Now, putting the all values
v(1) = (5.08 - 5.0)/1 = 0.08 cm/s
Answer:
a) the average velocity during each time period.
(1) 4.87 cm/s(2) 4.90 cm/s(3) 4.95 cm/s(4) 4.91 cm/s(b) 0.08 cm/s is the instantaneous velocity of the particle when t = 1.
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A survey of 65 customers was taken at a bookstore regarding the types of books purchased. The survey found that 41 customers purchased mysteries, 33 purchased science fiction, 25 purchased romance novels, 19 purchased mysteries and science fiction, 15 purchased mysteries and romance novels, 10 purchased science fiction and romance novels, and 5 purchased all three types of books.
a) How many of the customers surveyed purchased only mysteries?
b) How many purchased mysteries and science fiction, but not romance novels?
c) How many purchased mysteries or science fiction?
d) How many purchased mysteries or science fiction, but not romance novels?
e) How many purchased exactly two types of books?
Answer:
a) 41 customers purchased only mysteries.
b) 19 customers purchased mysteries and science fiction, but not romance novels.
c) 19 customers purchased mysteries and science fiction.
d) 19 customers purchased mysteries and science fiction, but not romance novels.
e) 15 and 10 customer purchased mysteries
The following graph represents the results of a survey, in which a random sample of adults in a certain country was asked if a certain action was morally wrong in general. Complete parts (a) through (c) below. A bar graph titled "Opinion Regarding an Action" with a horizontal axis titled "Percentage of respondents" and labeled from 0 to 100 in increments of 10 contains three horizontal bars. The labels and approximate values of the horizontal bars from top to bottom are as follows: Depends on situation, 7; Morally wrong, 18; Morally acceptable, 75. Opinion Regarding an Action 0 20 40 60 80 100 Depends on situation Morally wrong Morally acceptable Percentage of respondents Question content area bottom Part 1 (a) What percent of the respondents believe the action is morally acceptable? About 75% of the respondents (Round to the nearest whole number as needed.) Part 2 (b) If there are million adults in the country, how many believe that the action is morally wrong
Using proportions, it is found that:
a) 75% of the respondents believe the action is morally acceptable.
b) Supposing there are 217 million adults, 39.06 million believe that the action is morally wrong.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
In item a, 75 out of 7 + 18 + 75 = 100 adults believe that the action is morally acceptable, hence the percentage is:
75/100 x 100% = 75%
75% of the respondents believe the action is morally acceptable.
In item b, we suppose that there are 217 million adults, hence the amount that believe the action is morally wrong is:
0.18 x 217 = 39.06.
Supposing there are 217 million adults, 39.06 million believe that the action is morally wrong.
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Covert 3/7 into percent
The percentage of fraction 3/7 is 42.8571%.
what is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given fraction:
3/7
To convert the fraction into percentage we have multiply 100
3/7*100
=300/7
= 42.8571%
Hence, the percentage of fraction 3/7 is 42.8571%.
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what is the sum?
2x+4/x+1 + -x+5/x+1
Answer:
x + 9
------------
x + 1
Step-by-step explanation:
2x + 4 -x + 5 x + 9
------------ + ------------ = -----------
x + 1 x + 1 x + 1
I hope this helps!
B.5 Additive property of length 7RA
If KL = 5x, LM = = 6, and KM = x + 10, what is KL?
K
5x
Submit
L
x + 10
6
M
Simplify your answer and write it as a proper fraction, mixed number, or integer.
The length of the KL by additive property is 5 units.
The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.
An example of the additive property is :
If A=B then A+n=B+n where n∈R.
Now the given line segment is KM is x+10
And KL=5x and LM=6
Now using additive property we can say that
KL+LM=KM
Substituting the values in the equations we get:
5x+6=x+10
or, 4x=4
or, x=1
Now using this value of x we can find the length of KL.
Therefore KL=5x=5×1=5
Hence the length of the KL by additive property is 5 units.
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Estimate each product 13.92*2.7???
Answer
Estimate each product 13.92*2.7
37.584
(
2) a) If the function f(x) = |x| is changed to g(x) = 3|x-1| +3,
how is the graph transformed? (left, right, up, down? By how much?)
b) On the blank graph, graph the function g(x) = 3|x-1| +6
The required transformation of graphs are represented and attached below.
Given:
(a) function f(x) = |x| transformed to g(x) = 3 |x ₋ 1 | ₊ 3
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function : f(x) = |x|
Horizontal Shift: Right 1 Units
Vertical Shift: Up 3 Units
Reflection about the x-axis: None
Vertical Stretch: Stretched
(b) If there is a horizontal or vertical shift, reflection around the x-axis or y-axis, or vertical stretch, the function has undergone transformation. To identify the transformation, compare the function to the parent function.
Parent Function : f(x) = |x|
Horizontal Shift: Right 1 Units
Vertical Shift: Up 6 Units
Reflection about the x-axis: None
Vertical Stretch: Stretched
Hence the required graphs are plotted.
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3x³ = -16x² - 21x
Solve for x
Answer:
x=0, x=-7/3, x=-3
Step-by-step explanation:
Which of the following would you not expect to find in the study design section of the research protocol
A description of primary and secondary endpoints
A schematic diagram of the study design
The methods of recording and analyzing the effectiveness criteria
The expected duration of participant participation
Answer:
im not to sure but i think its this
Step-by-step explanation:
The expected duration of participant participation
3x-1=2x-3+3x
Solve for x
Step-by-step explanation:
MAR ME AS A BRAINLIST
THANKS
a family paid $25,200 as a down payment for a home. if this represents 14% of the price of the home, find the price of the home
Answer:
$178571.43
Step-by-step explanation:
14% of a number is 25000
multiply 25000 by 100 and divide the product by 14
you will get 178571.428571
round up the 100ths place and it's 178571.43
Two brothers, Rick and Charles, each inherit $38000. Rick invests his inheritance in a savings account with an annual return of 1.7%, while Charles invests his inheritance in a CD paying 5.4% annually. How much more money than Rick does Charles have after 1 year?
Answer:
Rick will have in interest 646.00 for a total of 38646. Charles will have 2052.00 interest for a total of 40052. Charles has a total of 1406.00 more than Rick.
Solve equation by factoring.
2x^2=10x
Answer:
x = 0, x = 5
Step-by-step explanation:
2x² = 10x ( subtract 10x from both sides )
2x² - 10x = 0 ← factor out 2x from each term on the left side
2x(x - 5) = 0
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x - 5 = 0 ⇒ x = 5
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of d feet
below the surface, is given by the following equation:
P = 13+
5d
13
< >
If a scientific team uses special equipment to measures the pressure under water and finds it to be 308 pounds
per square foot, at what depth is the team making their measurements?
Answer: Depth d = 767 feet.
Step-by-step explanation:
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of D feet below the surface, is given by the following equation:
P= 13+ 5d/13
If a scientific team uses special equipment to measures the pressure under water and finds it to be 308 pounds per square foot, at what depth is the team making their measurements?
Given data,
The relationship between the pressure, p of sea water in certain deep parts of oceans is and the distance, d below the surface is given by the following equation,
P= 13+ 5d/13
Where,
p is in pounds per square foot.
d is in feet
The pressure of seawater is 308 pounds per square foot at a depth
308 = 13+ 5d/13 (eq-1)
308 - 13 = 5d/13
Cross multiplying, it becomes
295 = 5d/13
295 * 13 = 5d
3,835 = 5d
3,835/5 = d
d = 767 feet
At a depth of 308 feet below the surface of the water, the pressure of seawater is,
Substitute d value in equation 1,
So, we can write,
P= 13+ 5d/13
P = 13+ 5 (767) /13
P = 13 + 3835/13
P = 13 + 295
P = 308 pounds per square foot.
Therefore,
Depth d = 767 feet.
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The eighth-grade math class keeps a flower garden in the front of the building. The garden is in the
shape of a right triangle. The two smaller sides measure 9 feet and 12 feet. The class wants to install a
3-foot-high picket fence around the garden to keep students from stepping onto the flowers. The picket
fence they need costs $5 per foot. How much will the fence cost? Do not calculate sales tax. Show your
work and justify your solution.
Answer: $180
Step-by-step explanation:
a right triangle has three sides: the two smaller ones and the big one. the two smaller ones squared add up to the bigger one squared.
this is the pythagorean theorem, a^2 + b^2 = c^2.
in this case, it would be 9 squared + 12 squared = c squared.
81 + 144 = 225
225 is the square of 15, so the third side is 15.
now, solve for the perimeter.
the perimeter is the 3 sides added up, so 9+12+15 = 36 feet of perimeter.
each foot costs $5, so 36x5= 180.
$180 is the answer.
Consider the following conditional statement and scenario. Is the conditional statement true or false?
Conditional Statement: If I had set my alarm clock, I would have woken up on time.
Scenario: The power went out and reset all the clocks in the house.
We can actually deduce here that considering the conditional statement and scenario, the conditional statement is false.
What is conditional statement?Conditional statement is actually known to be an if-then statement. It is usually used to show and emphasizes the relationship that exists between two ideas. This means that one idea comes as a result of the other.
Conditional statements actually helps one to make proper deductions in a clear and rigorous way.
We see here that considering the scenario that "the power went out and reset all the clocks in the house", even if alarm was set, it wouldn't ring out because all the clocks in the house were reset when the power out.
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C
E
O
(5x - 21)°
(4x)⁰
B
What is the value of
x if mZDBC is 105°?
Please show work
Answer:
x = 14
Step-by-step explanation:
m<DBC = m<DBE + m<EBC
105 = 4x + 5x - 21
105 = 9x - 21
126 = 9x
9x = 126
x = 126/9
x = 14
A line with a slope of 14/3 passes through the point (0,8). What is the equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of slope-intercept form of the line is y = 14/3x + 8.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.Given,
m = 14/3
the point = ( 0,8 )
A line with a slope of 14/3 passes through the point (0,8).
y - y₁ = m ( x- x₁)
y - 8 = 14/3 ( x - 0 )
3(y - 8 ) = 14x
3y - 24 = 14x
3y = 14x + 24
y = 14/3x + 8
Finally, the equation of the line is
y = 14/3x + 8
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You have a gift card for your favorite clothing store for the amount of $60. You found a shirt you want to buy that costs $15. If you don't want to spend more than the amount of the gift card, which of the following inequalities could be used to determine the amount you have left to spend?
The inequalities could be used to determine the amount you have left to spend will be 60 - 15.
How to calculate the inequality?From the information, the person have a gift card for your favorite clothing store for the amount of $60 and found a shirt you want to buy that costs $15.
The inequalities could be used to determine the amount you have left to spend will be:
= Total amount - Shirt
= 60 - 15
Therefore, inequalities could be used to determine the amount you have left to spend will be 60 - 15.
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Value of sin if csc=13/9 and 0° < theta < 90°
Answer: 9/13 ==> A
Step-by-step explanation:
sin is between 0 and 1 if 0° < theta < 180° ==> sin is positive when y is positive
sin is between -1 and 0 is 180° < theta < 360° ==> sin is negative when y is negative
sin theta * csc theta = 1
sin theta * 13/9=1
sin theta * 13/9 * 9/13 = 1 * 9/13
sin theta = 9/13 ==> A
Tony rounded each of the numbers and to the nearest hundred. Which choice correctly compares the rounded numbers?
Tony rounded each of the numbers and to the nearest hundred. Which choice correctly compares the rounded numbers?
Tony rounded each of the numbers 1183 and1145 to the nearest hundred. Which choice correctly compares the rounded numbers?
The rounded numbers are 1200 and 1100
The two numbers that we have been given are 1183 and 1145.
We have been asked to round of each number to the nearest hundred.
Note that when we are rounding of number to the nearest hundred then we have to check the tens place.
If it is greater than or equal to 5 then we will increase the hundred place number by 1
And if it is less than 5 then we will not change anything in the hundreds place.
And after the required changes in the hundred place number, the numbers after that will convert into zero.
Therefore,
1183 is rounded of to = 1200 as 8 which is in the tens place is greater than 5, we will add 1 to 1 in the hundreds place
1145 is rounded of to = 1100 as 4 is less than 5, 1 will not change
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2. Choose one of the factors of 6x3 + 6
Answer:
24 is the answer to the Equation
