Answer:
3i
Step-by-step explanation:
3i x 3i = -9
-3i x -3i = -9
Therefore the square root of -9 is 3i or -3i
The simplified radical expression ±√(-9) is ±3i
The expression ±√(-9) involves finding the square root of a negative number. In the real number system, this is not possible, as no real number multiplied by itself will result in a negative value. To overcome this limitation, mathematicians introduced the concept of imaginary numbers. The imaginary unit, denoted by 'i,' is defined as √(-1).
Now, let's simplify the expression ±√(-9) step by step:
Step 1: Begin by recognizing that √(-9) is the square root of -9.
Step 2: Since √(-1) is 'i,' we can rewrite √(-9) as √(9) * √(-1).
Step 3: The square root of 9 (√9) is 3.
Step 4: Replace √(-1) with 'i.'
Step 5: The final result is 3i.
Therefore, the simplified form of ±√(-9) is ±3i.
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Pls help I need a good grade
Answer:
y=4/7x
Step-by-step explanation:
Graph the point (4,7) and (0,0) because x is pint and y is servings
The equation is y=4/7 x because the slope is 4/7 and it starts at the origin.
William was parasailing at about 900 feet in the air while a shark swam
directly below him at 30 feet below the surface of the ocean. How far is
William from the shark?*
Answer:
930m
Step-by-step explanation:
It says they were 900 feet in the air below him is the ocean so thats 900 meters away from him and the shark is 30 feat below the surface of the ocean so you would do 900+30=930m so the shark is 930m away from him
• 6 mystery books
5 science books
• 4 history books
3 adventure books
.
Robero will randomly choose 1 book to read. What is the probability that he will
choose an adventure book?
Answer:
Step-by-step explanation:
How many books are there?
6+5+4+3 = 18 books total
How many are adventure books?
3
3 out of 18 books are adventure books
Robero has a 3/18 probability of choosing an adventure book.
Your teacher might want that probability in the lowest possible form. That is because it is the easiest to use and to understand.
You can do this by dividing both numbers by the "numerator" which is the first number in the fraction, (the adventure book count).
3/3 = 1
18/3 = 6
So the fraction can be reduced to 1/6.
Robero has a 1/6 chance of choosing an adventure book.
I need help! I have an idea of which pick.
Answer: ok so I am bad at this but i would pick.....the top one
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
1 mi 1927 ft
Step-by-step explanation:
Turn everything into feet:
5mi x 5280 ft/1 mi = 26,400ft + 1,348 ft = 27, 748 ft
3mi x 5280 ft/1 mi = 15,840ft + 4,701 ft = 20,541 ft
Do the subtration that the problem wants you to do:
27, 748 ft - 20,541 ft = 7,207 ft
Turn the answer into mi & ft:
7,207 ft - 5280 ft = 1927 ft
=
1 mi 1927 ft
A bacteria culture grows with constant relative growth rate. The bacteria count was 1296 after 2 hours and 531441 after 6 hours. Answer the following questions. 1. What is the relative growth rate
Answer:
1)k=1.50408
2)=64
3)P(t)=64e^(1.50408t)
4)=118098
5)t=6.42 hrs
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW
A bacteria culture grows with constant relative growth rate. The bacteria count was 1296 after 2 hours and 531441 after 6 hours. Answer the following questions.
1. What is the relative growth rate?
2. What was the initial size of the culture?
3. Find an expression for the number of bacteria after t hours.
4. Find the number of cells after 5 hours.
5. When will the population reach 1000000?
To find relative growth rate, expression below can be used
P(t)= Po*e^(kt)
Where k= growth rate
Po= initial amount
t= time in hours
We were given The bacteria count as 1296 after 2 hours and 531441 after 6 hours. This can be expressed below as
P(2)= P(o)e^(2k)= 1296.........eqn(1)
P(6)= P(o)e^(6k)= 531441........eqn(2)
If we find the ratio of the two eqn we have
531441/1296 =[P(o)e^(6k)]/[P(o)e^(2k)]
410.0625= e^(4k)
If we take Ln of both side
ln 410.0625=ln(e^4k)
k=1.50408
1)= k=1.50408
2)
From P(2)= Po*e^(2k)= 1296
1296=Po × e^(2×1.50408)
1296= Po × e^(3.00816)
Po=1296/e^(3.00816)
=64
3) the expression is P(t)=64e^(1.50408t)
4). P(5)=64e^(1.50408×5)
=118098
5) P(t)= 1,000,000
1000000=64e^(1.50408t)
1000000/64 = 64e^(1.50408t)
Ln(15625)=ln[e^(1.50408t)]
9.657=e^(1.50408t)
t=6.42 hrs
Solve for x (round to the nearest thousandth)
to
FREE
HEALTH
le
110
CA
65
40°
х
Answer:
x = 79.799
Step-by-step explanation:
Apply trigonometric ratio formula to find x.
Thus, find the adjacent side of each triangle using 40° and 65° as reference angles respectively.
✔️Adjacent length of the triangle with reference angle 40°:
tan (40) = 110/adj
adj*tan(40) = 110
Adjacent length = 110/tan(40)
Adjacent length = 131.093 (nearest thousandth)
✔️Adjacent length of the triangle with reference angle 65°:
tan (65) = 110/adj
adj*tan(65) = 110
Adjacent length = 110/tan(65)
Adjacent length = 51.294 (nearest thousandth)
✔️Find x:
x = 131.093 - 51.294
x = 79.799
Helppppppppp plzzzzz
Answer:
1) 25, 2) 6
Step-by-step explanation:
how to graph f(x)=7|x -4|-1
Answer:
here I drew it digitally Hope it helps
Step-by-step explanation:
The graph of the function is a V-shaped curve.
Given that we need to determine the graph of the function f(x) = 7|x - 4| - 1.
To graph the function f(x) = 7|x - 4| - 1, you can follow these steps:
Start by identifying the key points of the function. In this case, the function involves an absolute value, which means it may change direction at the point inside the absolute value.
Set the expression inside the absolute value equal to zero and solve for x to find this critical point:
|x - 4| = 0
x - 4 = 0
x = 4
So, the critical point is x = 4.
Next, consider the behavior of the function on each side of the critical point.
Choose some values of x less than and greater than 4 and substitute them into the function to determine the corresponding y-values.
Let's choose x = 2:
f(2) = 7|2 - 4| - 1
f(2) = 7|-2| - 1
f(2) = 7(2) - 1
f(2) = 14 - 1
f(2) = 13
Let's choose x = 6:
f(6) = 7|6 - 4| - 1
f(6) = 7|2| - 1
f(6) = 7(2) - 1
f(6) = 14 - 1
f(6) = 13
Therefore, we have the points (2, 13) and (6, 13) on the graph.
Plot the critical point and the points you found on the coordinate plane. Mark them on the x-axis and y-axis.
To graph the absolute value part of the function, draw a V-shaped curve with the vertex at the critical point (4, 0).
The arms of the V-shaped curve will pass through the plotted points (2, 13) and (6, 13).
Extend the arms of the V-shaped curve indefinitely in both directions.
Finally, add the constant term (-1) by shifting the entire graph down by 1 unit. This means that every y-value on the graph should be reduced by 1 unit.
Your completed graph of the function f(x) = 7|x - 4| - 1 should resemble a V-shaped curve with its vertex at (4, -1), passing through the points (2, 12) and (6, 12), and extending infinitely in both directions.
The graph of the function is attached.
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WORTH 20 POINTS PLS HELP!!!
On a windy morning, a hot air balloon starts rising and flying away from the top of a hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the hill, can be modeled by the function:
Part B: There is a positive and negative x intercept for this function. What is the positive x-intercept?
Explain what this x-intercept represents in the given situation.
h(x)=-16x2+64x+80
Here the positive intercept should be considered as the -1 and 5.
Calculation of the positive intercept:Since X-Intercept shows the landing point i.e. bottom of the cliff since all x intercepts contains a y value of 0.
In this case it would be 0 feet.
So,
[tex]h(x)= -16x^2-16x+80x+80[/tex]
h(x)= -x(16x-16) +5(16x+16)
h(x)= (-x+5)(16x+16)
x intercepts = -1 and 5
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O will give te brainliest plz help
Answer:
B
Hope it helps uwu
An automobile manufacturer claims that its van has a 59.1 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 160 vans, they found a mean MPG of 59.5. Assume the variance is known to be 2.89. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.
Answer:
Test statistic Z = 1.8099
Step-by-step explanation:
Step(i):-
Given that mean of the Population (μ) = 59.1 miles/gallon
Mean of the sample (x⁻ ) = 59.5
The standard deviation of the Population = 2.89
mean of the sample (n) = 160
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{59.5-59.1 }{\frac{2.89}{\sqrt{160} } }[/tex]
Z = 1.8099
Test statistic = 1.8099
7. A bag of M&Ms dumped on the table and you court 91 blue pieces Approximately how many
M&ms do you expect to be in the entire bag based on the proportions of the entire class?
Answer:
i would think that there would be at least 100 m&m in the bag
Step-by-step explanation:
i might be wrong a hven't had m&m in about 10 years
An oak tree is planted when it is 650 centimeters tall. What is this height in meters?
The height of the oak tree is
meters.
Answer:
The answer is 6.5 meters tall
Step-by-step explanation:
650 divided by 100
do your 2 loops to the left and you get 6.5
I need help plzzzzzzzz
Answer:
B and 7
Step-by-step explanation:
because 9 minus 2 is 7
at 6:00 a.m., the temperature is 58°. At 2:00 p.m., temperature is 76°. Find the rate of change in degrees per hour during this time.
Answer:
The rate of change is of 2.25 degrees per hour.
Step-by-step explanation:
The rate of change in degrees per hour is given by by the change in temperature divided by the change in time(by number of hours).
In this question:
From 6 am to 2 pm, there are 12 - 6 + 2 - 0 = 6 + 2 = 8 hours
The change in temperature was of 76 - 58 = 18º
Rate of change:
18º/8 = 2.25º
The rate of change is of 2.25 degrees per hour.
Carlos tried to find a fraction equivalent to 2/3. Below is his work. Which
statement describes Carlos' error?
2/3=2/3 x 1/4=2/12
He should have divided by 1/4.
He incorrectly multiplied 2/3 and 1/4.
It is impossible to find a fraction equivalent to 2/3.
He did not multiply 2/3 by a fraction equal to 1.
Answer:
He did not multiply 2/3 by a fraction equal to 1.
Step-by-step explanation:
For example he could have multiplied 2/3 by 4/4
= 2*4/3*4 = 8/12,
write in standard form: eight and twenty nine hundredths
Answer:
8 hundred 29 thousand
Step-by-step explanation:
No explanation for this question.
8.29dbyevsvegehehshhs
Find the measure of<1
What's equivalent to 2/5?
Answer: 4/10 , 6/15, 8/20,
Step-by-step explanation:
Answer: Equivalent fractions of 2/5 : 4/10 , 6/15 , 8/20 , 10/ Equivalent fractions of 3/5 : 6/10 , 9/15 , 12/20 , 15/
Step-by-step explanation:
The distribution of the heights of students in a large class is roughly Normal. Moreover, the mean height is 68 inches, and approximately 95% of the heights are between 62 and 74inches. Thus, the standard deviation of the height distribution is approximately equal to
Answer:
Probably equal to 6 or 7.
Step-by-step explanation:
A baby elephant weighs 200 pounds at birth. It gains 3 pounds every day. Write an equation that represents this situation.
Answer:
y=200+3x
Step-by-step explanation:
I hope that this helps you
on selling a fan for rupees 4700 A shopkeeper loses 6% at what price must he sell it to gain 6 percentage
Given:
Selling price of a fan = Rs.4700
Loss percent = 6%
To find:
The price at which he must sell it to gain 6 percentage.
Solution:
Let x be the cost price of the fan.
Loss percent = 6%
Selling price = Cost price - 6% of cost price
[tex]S.P.=x-\dfrac{6}{100}x[/tex]
[tex]S.P.=x-0.06x[/tex]
[tex]S.P.=0.94x[/tex]
Selling price of a fan = Rs.4700
[tex]4700=0.94x[/tex]
[tex]\dfrac{4700}{0.94}=x[/tex]
[tex]5000=x[/tex]
So, the cost price of the fan is Rs.5000.
Now, he need to sell this fan in 6% gain.
Selling price = Cost price + 6% of cost price
[tex]S.P.=5000+\dfrac{6}{100}\times 5000[/tex]
[tex]S.P.=5000+300[/tex]
[tex]S.P.=5300[/tex]
Therefore, he must sell it for Rs.5300 to gain 6 percentage.
Explain what is the difference between the solutions to 2x=10 and 2x > 10
Answer:
See explanation below
Step-by-step explanation:
Explain what is the difference between the solutions to 2x=10 and 2x > 10
Given the equations;
2x = 10
x = 10/2
x = 5
For the equation 2x > 10
x > 10/2
x > 5
The first equation has only one solution which is 5 while the second equation has infinite number of solutions since the values of x can take any value that is greater than 5
Damon's father pays him one dollar to start the work and
doubles his pay for each hour of work. Write a function that
models this situation.
Answer: p(x) = $1*(2)^x
Step-by-step explanation:
First, the father pays him $1 for only starting the work, and for each hour, the payment is doubled.
So after the first hour, the payment wil be 2*$1 = $2.
After the second hour, the payment will be 2*(2*$1) = $1*(2)^2
After another hour, the payment will be 2*($1*(2)^2) = $1*(2)^3
We already can see the pattern here, after x hours, the payment will be:
p(x) = $1*(2)^x
This is the function that models this situation.
1. Evaluate when y=3. 3y + 2 (2y+6)
33
27
3y+12
Answer:
33
Step-by-step explanation:
3(3) + 2 (2(3)+6)
=9 + 2 (12)
=9 + 24
=33
QUESTION 7
Solve for x.
(3x + 32)
(5x-8)
O a. 3
b. 12
O c. 20
O d. 19.5
Answer:
The answer is x = 20
Step-by-step explanation:
If you set both equations equal to each other and solve for x, you will get 20.
3x+32 = 5x-8 add 8 to both sides
3x+40 = 5x subtract 3x from both sides
40 = 2x divide by 2 on both sides
20 = x
Becca has 115 students. Susana has 8 fewer students than Becca. Erika has 25 more students than Susana. How many students does Susana have? *
Answer:
Susana will have 107 students.
Step-by-step explanation:
Becca have students = 115
Susana has 8 fewer students than Becca.We can write its as:
Becca has 115 students, so Susana will have 115-8 = 107 students
Because fewer means less than so, 8 less than 115 is 115-8
Erika has 25 more students than Susana.We can write it as:
Susana has 107 students, so Erika will have: 107+25 = 132 students.
because more means we need to add 25 students with number of students in Susana class.
So, Susana will have 107 students.
helppppppppppppppppppppp
Answer:
$7.20
Step-by-step explanation:
60% of 4.5 = 2.7
4.5+2.7 = $7.2
Answer:
7.2
Step-by-step explanation:
So u do 60% of 4.5 and add ur answer to 4.5
What is the domain of the function y=2./X-6?
O 0x
O 3x<0
O 6x<0
Answer:
because this is a positive root function, domain is positive so
0<=x<infinity
Step-by-step explanation: