Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6 end quantity question mark
\(6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}\)
Pythagorean triples are given by these formulas:
(2²-37, 2zy, z²+37²)
The hypotenuse of a right triangle is 29. The lengths of the legs are whole numbers. List your answers in increasing
order.
The lengths of the two legs are
and
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
We have,
The formula given is incorrect.
The correct formula for Pythagorean triples with a given integer z is:
(z² - 1², 2z, z² + 1²)
Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:
z² + 1² = 29²
z² + 1 = 29²
z² = 29² - 1
z² = 840
z = √840
z = 28.98
Since z must be an integer, we can try integer values close to 28.98 to find one that works.
Trying z = 29,
a = z² - 1² = 840 - 1 = 839
b = 2z = 58
c = z² + 1² = 840 + 1 = 841
Therefore,
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
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Given z=f(x,y),x=x(u,v),y=y(u,v), with x(1,3)=2 and y(1,3)=2, calculate zu(1,3) in terms of some of the values given in the table below.
The value of zu(1,3) using the data elements represented on the table of values is q + p
How to solve the calculus expression?The given parameters are:
z = f(x, y)
x = x(u, v)
y = y(u, v)
Where
x(1, 3) = 2 and y(1, 3) = 2
To calculate zu(1,3), we make use of:
\(z_u(1,3) = f_x(x,y) * x_u(1,3) + f_y(x,y) * y_u(1,3)\)
The values x(1, 3) = 2 and y(1, 3) = 2 mean that:
(x,y) = (2,2).
So, we have:
\(z_u(1,3) = f_x(2,2) * x_u(1,3) + f_y(2,2) * y_u(1,3)\)
From the table of values, we have:
\(f_x(2,2) = q\)
\(x_u(1,3) = 1\)
\(f_y(2,2) = 1\)
\(y_u(1,3) = p\)
So, the equation becomes
\(z_u(1,3) = q * 1 + 1 * p\)
Evaluate the product
\(z_u(1,3) = q + p\)
Hence, the value of zu(1,3) is q + p
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pablo drove 240 mies using 9 gallons of gas. At this rate how many gallons of gas would he need to drive 216 miles?
Which rational number also belongs to the set of whole numbers?
Answer:
Answer: A) 15
A natural number is basically a counting number {1, 2, 3, 4, 5, ...} so any positive whole number. That is why 15 is the answer. Choices B and D are fractional values, so we can rule them out. We can rule out choice C because this value is negative.
Step-by-step explanation:
what are the answers for the table
Answer:
X-intercepts: -1 and 3
Y-intercepts: 3
Vertex: (1, 4)
Axis of Symmetry: y= -1x + 3x + 4 (I think this is right it might not be and im sorry if it isnt).
Step-by-step explanation: Hope this helps even a little bit <33
Bryan invests $6500 in two different accounts. The first account paid 11 %, the second account paid 7 % in interest. At the end of the first year he had earned $519 in interest. How much was in each account?
$ at 11 %
$ at 7 %
Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.
The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).
According to the problem, the total interest earned after one year is $519. So we can set up the equation:
0.11x + 0.07(6500 - x) = 519
Simplifying the equation:
0.11x + 455 - 0.07x = 519
0.04x + 455 = 519
0.04x = 64
x = 64 / 0.04
x = 1600
Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
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What is a to the power of 1?
The number itself equals any integer raised to the power of one.
What is Exponent?
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
What is integer?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.
Any number that is multiplied by one has the same value as the original number, according to the exponent rule.
Take this as an example:
You can write x to the power of 1 as x and 100 to the power of 1 as 100.
Therefore, anything raised to the power of one equals that number.
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Laurel divided 2/3 of a gallon of paint into 4 containers. How much of the of the
paint was put into each container?
Answer: 1/6 of the paint went to each container
Step-by-step explanation: Since we know he had 2/3 of a gallon of paint and they were divided into 4 containers, we have to divide 2/3 by 4 and when you do that you get 0.16666 continuous but in fraction for you arrive at 1/6 of a gallon of paint
what is Bethany's score on the test if she answered 23 out of 30 right?
part:
whole:
percent:
Answer: 76.67%
Step-by-step explanation:
Simplify the expression by combining like terms.
16z + 5z
16z + 5z
(16+5)z
Solution = 21z
Answer:
21z
Step-by-step explanation:
1. Find Like terms (z)
2. 16z and 5z are both like terms so you add them together
3. 16+5 = 21
4. Final Answer is 21z
Consider the function f(x)=2x−−√−8. If f−1(x) is the inverse function of f(x), find f−1(2)
\(f^(-1)(2) = 6\), which is consistent with our earlier result.
What is inverse function?A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.
Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?
Solution:
To find f^(-1)(2), we need to find the value of x such that \(f(x) = 2\) . We can set up an equation:
\(f(x) = \sqrt(2x - 8) = 2\)
Squaring both sides, we get:
\(2x - 8 = 4\)
\(2x = 12\)
\(x = 6\)
Therefore, \(f^(-1)(2) = 6.\)
We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:
\(f(f^(-1)(x)) = x\)
We can substitute x = 2 and solve for f^(-1)(2):
\(f(f^(-1)(2)) = 2\)
\(f^(-1)(2) = (f(6))^(-1)\)
f(6) = √(2(6) - 8) = √4 = 2
Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.
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Which of the following are possible
side lengths for a triangle?
A. 9, 4,8
B. 14, 7,6
C. 3, 8, 1
The only set of side lengths that can form a triangle is 9, 4, 8.
Option A is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check if each of the given sets of side lengths satisfies this condition:
A.
9, 4, 8
9 + 4 > 8 ✓
9 + 8 > 4 ✓
4 + 8 > 9 ✓
All three inequalities are true, so these side lengths can form a triangle.
B.
14, 7, 6
14 + 7 > 6 ✓
14 + 6 > 7 ✓
7 + 6 > 14 ✗
The last inequality is false, so these side lengths cannot form a triangle.
C.
3, 8, 1
3 + 8 > 1 ✓
3 + 1 > 8 ✗
8 + 1 > 3 ✓
The second inequality is false, so these side lengths cannot form a triangle.
Therefore,
The only set of side lengths that can form a triangle is A. 9, 4, 8.
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1/2b-7=5.5 slove for b
Answer:
b = 25
Step-by-step explanation:
Given
\(\frac{1}{2}\) b - 7 = 5.5 ( multiply through by 2 to clear the fraction )
b - 14 = 11 ( add 14 to both sides )
b = 25
Answer:
B=25
Explanation1
1/2b−7=5.5
Add 7 to both sides.
1/2b=5.5+7
b=5.5+7
Add 5.5 and 7 to get 12.5.
1/2 b=12.5
Multiply both sides by 2, the reciprocal of 1/2.
b=12.5×2
Multiply 12.5 and 2 to get 25.
b=25
Half a number plus 5 is
11. What is the number?
Answer:
x = 12
Step-by-step explanation:
Let the number be x
Condition:
=> \(\frac{1}{2} x+5 = 11\)
=> \(\frac{x}{2} = 11-5\)
=> \(\frac{x}{2} = 6\)
Multiplying both sides by 2
=> x = 6* 2
=> x = 12
If you double a number and then subtract eight the result is 18. Which equation below could be used to represent the situation?
Answer: 2x - 8= 18
2x - 8=18
2x=26
x= 13
The photo is kinda blurry but please help me with it
The perimeter of rectangle M'N'O'P' is given as follows:
54 cm.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The ratio between the areas is given as follows:
126/14 = 9.
The area is measure in square units, while the perimeter is measured in units, hence the ratio of the perimeters is the square root of the ratio of the areas, that is:
3.
Hence the perimeter of rectangle M'N'O'P' is given as follows:
3 x 18 = 54 cm.
Missing InformationThe complete problem is:
Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm2. After rectangle MNOP is dilated, rectangle M'N'O'P' has an area of 126 cm2. What is the perimeter of rectangle M'N'O'P'?
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What is 8 3/5 graphed on a number line
PLZ I NEED HELP ASAP CUZ IM ON A TIMER!
Answer:
Step-by-step explanation:
8 3/5 on a number line is between 8 and nine
idk how to draw a number line on a computer so ill just tell you how
1. divided the spaces between 8 and 9 into 5 sections ( 3/5 )
2. then mark 3 of those 5 spaces and put a dot or a line at where the 3rd space ends
There were five football games at school. The number of hotdogs sold at the first four games were 523 604 544 596
The mean number of hotdogs sold at five games was 573.
How many hotdogs were sold at the fifth football game?
Total sold at 4 games: 523 + 604 + 544 + 596 = 2,267
Mean is the average, multiply mean by total games to find total sold:
573 x = 5 = 2,865 total
Now subtract for the amount sold at the 5th game:
2865 - 2267 = 598 hotdogs sold at 5th game.
write an equation in slope intercept form that passes through the given point and is perpendicular to the graph of given equation (1,-2) y=5x+4
The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.
The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.
To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.
The negative reciprocal of 5 is -1/5.
Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values:
y - (-2) = (-1/5)(x - 1)
Simplifying:
y + 2 = (-1/5)(x - 1)
To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:
y + 2 = (-1/5)x + 1/5
Subtracting 2 from both sides:
y = (-1/5)x + 1/5 - 2
Combining the constants:
y = (-1/5)x - 9/5
Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
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How many different strings can be made from the letters in HAPPINESS, using all the letters?
Answer:
20 different strings
Step-by-step explanation:
Let the lines in the alphabets be the strings. So, each alphabet has many strings. Counting them would make them 20 strings.
Find all the measures
Answer:
Step-by-step explanation:
A person places $7120 in an investment account earning an annual rate of 7.4%, compounded continuously. Using the formula V = Pe^rt where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 11 years.
Answer:
16069.25
Just know that
P=Is the first number in the word prob.
R=the second number (percentage one) which you get into decimal form
T=the last number in the word problem
Identify the proof to show that △ABD≅△CBD
, where ∠BDA≅∠BDC
are right angles, D
is the midpoint of AC¯¯¯¯¯
, AB¯¯¯¯¯≅BC¯¯¯¯¯
, and BD¯¯¯¯¯
bisects ∠B
.
The figure shows two triangles A B D and C B D with a common side B D. Points A, D, C lie on one line.
We have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.
To prove that △ABD ≅ △CBD, we can use the SAS (Side-Angle-Side) congruence criterion.
Given:
∠BDA ≅ ∠BDC (Both are right angles)
D is the midpoint of AC¯¯¯¯¯
AB¯¯¯¯¯ ≅ BC¯¯¯¯¯
BD¯¯¯¯¯ bisects ∠B
Proof:
Since D is the midpoint of AC¯¯¯¯¯, we have AD ≅ CD by the definition of a midpoint.
AB¯¯¯¯¯ ≅ BC¯¯¯¯¯ (Given)
BD¯¯¯¯¯ is a common side for both triangles.
∠BDA ≅ ∠BDC (Given)
To apply the SAS congruence criterion, we need to show that one pair of corresponding sides and the included angle are congruent in both triangles.
AD ≅ CD (Side) - This is true as D is the midpoint of AC¯¯¯¯¯.
∠BDA ≅ ∠BDC (Included Angle) - Both are right angles.
By the SAS congruence criterion, we can conclude that △ABD ≅ △CBD.
Therefore, we have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.
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The table below shows the number of seats in a theater based on the number of rows.
a
b.
C
Row, n
1
2
d.
3
4
5
70
Which function represents the number of seats in a theater with n rows?
Number of Seats, S
18
31
44
57
S(n)= 18+ 13(n-1)
S(n)= 13 + 18(n-1)
S(n) = 5n + 13
S(n) = 13n+ 18
The function S(n) = 18 + 13 (n - 1) represents the number of seats in a theater with n rows.
What is a function?
A function is a mathematical expression, rule, or law that explains how one independent variable and one dependent variable relate to one another.
We are given a table which shows the number of seats in a theater based on the number of rows.
Now, in order to find the function, we will put n = 5 in the functions
So,
⇒S(n) = 18 + 13 (n - 1)
⇒S(5) = 18 + 13 (5 - 1)
⇒S(5) = 18 + 13 * 4
⇒S(5) = 18 + 52
⇒S(5) = 70
Since, n = 5 satisfies the equation so, it correctly represents the number of seats in the theater.
Hence, the function S(n) = 18 + 13 (n - 1) represents the number of seats in a theater with n rows.
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The complete question has been attached below.
a cylinder can has a radius of 4.4 centimeters and a height of 3.3 centimeters, what is the volume in cub is centimeters of the can? round it to the nearest tenth
Answer:
The volume is 200.7 cm^3
Step-by-step explanation:
The volume of a cylinder is:
Vol = pi•r^2•h
The radius and height were given, so fill them in.
V = pi • (4.4)^2 • 3.3
V = 200.710071
This is the answer you get if you use the pi key on the calculator.
Round to the nearest tenth.
V = 200.7
The volume is 200.7cm^3.
***(If your teacher/class/text/program says to use 3.14 for pi, the answer will come out as 200.6)
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Will give brainliest
Answer:
First Gardener.
Step-by-step explanation:
1st gardener= 56 divided by 8= 7 bushes <---
2nd gardener= 45 divided by 5= 9 bushes
3rd gardener= 80 divided by 10= 8
3+3=???
A: 3113
B: 33
C. 6 ( I did the math and never got this answer)
D. 9
please help !!!!!
Answer:
D
Step-by-step explanation:
gimme the points
cuz
scientific
Which correctly renames
7
8
and
5
6
using a common denominator?
A.
42
48
and
40
48
B.
42
48
and
30
48
C.
14
16
and
15
18
D.
28
24
and
20
24
Answer:
woahhh thats confusing ash
Step-by-step explanation:
Answer:
b)
Step-by-step explanation:
7/42 8/