Answer:
\(v = {15}^{o} \\ \)
Step-by-step explanation:
\(9v = {31}^{o} + (4v + {44}^{o}) \\ \)
An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
\(9v = {31}^{o} + (4v + {44}^{o} ) \\ 9v = {31}^{o} + 4v + {44}^{o} \\ 9v = {75}^{o} + 4v \\ 9v - 4v = {75}^{o} \\ 5v = {75}^{o} \\ v = \frac{ {75}^{o} }{5} \\ v = {15}^{o} \\ \)
the equation of a curve is xy^3-2x^2y^2=0. find the gradient of the tangent to the curve at (1,2)
Differentiate both sides of
xy ³ - 2x ²y ² = 0
with respect to x :
d(xy ³ - 2x ²y ²)/dx = d(0)/dx
d(xy ³)/dx - 2 d(x ²y ²)/dx = 0
By the product rule,
d(x)/dx y ³ + x d(y ³)/dx - 2 (d(x ²)/dx y ² + x ² d(y ²)/dx) = 0
By the chain rule,
y ³ + 3xy ² dy/dx - 2 (2xy ² + 2x ²y dy/dx) = 0
y ³ + 3xy ² dy/dx - 4xy ² - 4x ²y dy/dx = 0
y ³ - 4xy ² + (3xy ² - 4x ²y) dy/dx = 0
(3xy ² - 4x ²y) dy/dx = 4xy ² - y ³
dy/dx = (4xy ² - y ³) / (3xy ² - 4x ²y)
dy/dx = (4xy - y ²) / (3xy - 4x ²)
At the point (1, 2), the gradient is
dy/dx (1, 2) = (4×1×2 - 2²) / (3×1×2 - 4×1²) = 4/2 = 2
graph g(x)= 2^x mark 5 plots
Answer:
(0,1),(1,2),(-10, .001),( 3.804,13.997), (5,32)
what is the factor of -2x^3-6x+56x
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
how long is each side of the box
Based on the information in the image, it can be inferred that the sides of the box measure 5 cm each.
How to find the measure of the sides of the box?To find the measure of the sides of the box we must carry out the following mathematical procedure:
As we know the volume of a cube is the equivalent to the length of its sides raised to the cube (raised to the 3). In this case, to identify the value of the sides we must find the cube root of the volume and the result is the length of the sides.
So this cube has a volume of 125cm³, so its sides would be the cube root of 125.
\(\sqrt[3]{125} = 5\)
According to the above, the length of the sides is 5 taking into account that all the sides are equal.
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16.
a. How many Egyptian numerals are needed to represent the following problema?
i. 59 +88
Answer: 12
Step-by-step explanation:
59 +88 = 147
1 numeral in 100s place
4 numerals in 10s place
7 numeral in 1s place
1+4+7 = 12
Answer:
12
Step-by-step explanation:
Write an expression to represent: 9 more than the quotient of 2 and x
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is \(\frac{2}{x}\).
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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solve this. plss urgent
Answer:
[2] It shows the commutative property over addition
[3] -5/6
[4] A. 6/7 and B. -101/213
[5] Refer to picture below
[6] True, 1/2 *(-2/3*1/4) = (1/2*-2/3)*1/4.
Step-by-step explanation:
[3] 5/8 × 8/-6
Simplify
\(\frac{5}{8}\left(-\frac{4}{3}\right)\)
\(=-\frac{5}{6}\)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[4] -6/7
Opposite
6/7
x + ( - 6/7 ) = 0
⇒ x = 6/7
Hence additive inverse of - 6/7 is 6/7
101/213
Opposite
-101/213
x + (101/213)=0
⇒ x = -101/213
Hence additive inverse of 101/213 is -101/213
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[6] Since x = 1/2 , y = -2/3 and z = 1/4
x * (y*z)=(x*y)*z
Substitute:
1/2 *(-2/3*1/4) = (1/2*-2/3)*1/4
-1/12 = - 1/12
TRUE
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~Lenvy~
Samuel rides his bike 14 blocks from his house to get to the bus stop. Then he takes the bus another 34 blocks to get to work. At the end of the day, he travels back home the same way. How many blocks does he travel each day? *
Answer:
96?
Step-by-step explanation:
The total number of blocks the first time in the day:
14 +34 = 48
Mutiply that by 2 to see how many blocks he does twice a day
48(2)= 96
a garden store is making seed package . Each package contains 35 seeds. There are 1960 seeds available. How many seed package can be made ?
Divide total seeds by seeds per package:
1960 / 35 = 56
56 packages can be made.
Can't figure this out some assistance with this math problem please?
Becky would be borrowing money for a quarter of a century.
A century is 100 years.
Therefore, the value of time (t) would be 1/4 times 100, and that is 25.
The correct answer is 25 years
50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!
Answer:
D
Step-by-step explanation:
Answer:
D. \(8a^{9} -4a^{3} +1\)
Step-by-step explanation:
Given \(r(x)=x^{3} -2x+1\) and find \(r(2a^{3} )\) :
\(r(2a^{3} )\) is the same as saying \(x=2a^{3}\)So, we have \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1\)Solve for \(r(2a^{3} )\) :
1. \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1\)
Start with simplifying \((2a^{3})^{3}\)\((2a^{3})^{3}=2^{3}*(a^{3})^{3}=8*a^{3*3}=8a^{9}\)When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.When you multiply two terms that are raised to a power, you add the powers.When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.When you have a power raised to a power, you multiply the powers.2. \(r(2a^{3} )=8a^{9} -2(2a^{3})+1\)
Simplify \(2(2a^{3})\)Multiply two times the quantity\(2(2a^{3})=4a^{3}\)3. \(r(2a^{3} )=8a^{9} -4a^{3}+1\)
Answer:
So, if \(r(x)=x^{3} -2x+1\), then \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1\).
Then the answer is D. \(r(2a^{3} )=8a^{9} -4a^{3}+1\)
A garden is to designed with a rectangular part in the middle with two semi-circles on the ends.
The dimensions of the rectangular portion are 18.4 feet long and 8.6 feet wide.
a) What is the area of one semi-circle at one end?
b) What is the area of the garden?
c) Find the area in square metres.
Given statement solution is :- a) The area of one semi-circle at one end is 58.09 square feet.
b) The area of the garden is 274.42 square feet.
c) The area in square metres is approximately 58.09 square feet.
The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.
a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.
Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.
Now we can calculate the area of the semi-circle:
A = (π * 4.3²) / 2
A ≈ 58.09 square feet
b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.
Area of the rectangular portion = length * width
Area of the rectangular portion = 18.4 feet * 8.6 feet
Area of the rectangular portion ≈ 158.24 square feet
Area of the two semi-circles = 2 * (area of one semi-circle)
Area of the two semi-circles ≈ 2 * 58.09 square feet
Area of the two semi-circles ≈ 116.18 square feet
Total area of the garden = area of the rectangular portion + area of the two semi-circles
Total area of the garden ≈ 158.24 square feet + 116.18 square feet
Total area of the garden ≈ 274.42 square feet
c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.
Area in square meters = Total area of the garden * (0.3048)²
Area in square meters ≈ 274.42 square feet * 0.3048²
Area in square meters ≈ 25.49 square meters
Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.
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Point P is (1,2)
Point Q is (7,6)
Which of the following best represents the length of segment PQ?
Four family members compared their ages. Terell is 3 years younger than Danny. Danny is 1 year younger than Pablo. Pablo's age is 1/3 Shaniqua's age. How old is Terell if Shaniqua is 36 years old?
The picture below is wrong so don't say this you little l=UCK.
Answer:
8 years
Step-by-step explanation:
Shaniquas age is given as 36. This age is going to help us to find the rest.
Pablo is said to 1/3 of Shaniquas age
= 1/3 of 36 = 36/3 = 12
Pablo is 12
Danny is younger than pablo by 1
12 - 1 = 11
Danny is 11
Terrell is younger than danny by 3
11-3 = 8
Terrell is 8 years old
Answer:
I think ur profile pic is cute
Step-by-step explanation:
A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Joe made $42 in 6 hours. How many hours would he have to work to make $56? (Do not solve)
Answer:
42 dollars for 6 hrs means that each hour, he gets 7 dollars, assuming that this is a proportional relationship.
56-42=14, he needs 14 more dollars
14/7=2
2 more hrs
Step-by-step explanation:
Given:LM/PQ=MN/QR=LN/PR Prove:
LM/PQ = MN/QR = LN/PR because triangle LMN and PQR are similar.
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The conditions for two triangles to be similar are;
1. The corresponding angles of the similar triangles must be congruent i.e they must be equal.
2. The ratio of the corresponding sides are equal. The corresponding sides are :
LM and PQ, MN and QR , LN and PR
since LM/PQ = MN/QR = LN/PR , then we can say triangle LMN and PQR are similar.
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What is the value of x? Round the answer to the nearest tenth.
DONT RESPOND WITH A LINK!!!!!!!
Answer:
i believe x is 16.1
Step-by-step explanation:
hope this helps
Jack wants to buy a pair of trousers for $60. When he went to the store he found that the price was marked down by 20%. How much do they cost now?
Sean bought 3/7 of a pound of cherries and then he ate 1/4 of a pound of them. When he got home, he saw that he still had 2/3 of a pound of cherries in his cupboard. How many total pounds of cherries does he have? Give your answer as an exact simplified improper fraction, not as a mixed number. Do not include units.
Answer:
71 /84
answer is not in imporper fraction.
Step-by-step explanation:
fractions need to be changed or converted to equivalent fractions inorder to solve them.
1.Total amount of cherries he bought and he already had in cupboard= 3/7 + 2/3
convert them to equivalent fractions inorder to add them by using LCM of the denominators.Which in this case is 21 (LCM of 7 and 3 is 21)
2. Now the common denominator is 21
change 3/7 to a fraction with 21 as denominator by multiplying the numerator to 3 and denominator also by 3 which will give you 3×3=9/ 7×3=21 or 9/21
note: you have to multiply both numerator and denominator by the same number which is used to convert the denominator to the number given by LCM.
3)Now change the second fractions denominator to 21 by multiplying the denominator 3 by 7 and numerator 2 to 7 :
2×7/3×7 = 14/21
4) Now the fractions have same denominator which means they can be added or subtracted.
5) Total amount of cherries he had= 9/21+14/21 = 23/21
6) The amount of cherries he ate = 1/4
7) Amount of cherries he has now with him after he ate 1/4 from 23/21 = 23/21 - 1/4
8) Again the fractions need to be changed to equivalent fractions inorder to subtract them.So,Take the LCM of the denominators (LCM 21 and 4 is 84).Now change the denominator of each fraction to 84.
9) 23/21 becomes 23× 4/21×4 = 92/84
1/4 becomes 1×21/4×21 = 21/84
now subtract them
92/84 - 21/84 = 71/84
71/84 cannot be properly divided so, 71/84 is the answer.
He has 71/84 pounds of cherries with him.
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel.
The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that
changes a 1 to a 0 with probability 0.1 and changes a 0 to a 1 with probability 0.2. Show your work below.
a. What is the probability a 1 is received?
b. If a 1 is received, what is the probability a 0 was sent?
Answer:
A: the probability that a 1 is received is 0.56.
B: the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
Step-by-step explanation:
To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.
a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.
Let's denote:
P(1 sent) = 0.6 (probability a 1 is sent)
P(0→1) = 0.2 (probability a 0 is flipped to 1)
P(1 received) = ?
P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)
= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)
= 0.6 * (1 - 0.2) + 0.4 * 0.2
= 0.6 * 0.8 + 0.4 * 0.2
= 0.48 + 0.08
= 0.56
Therefore, the probability that a 1 is received is 0.56.
b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.
Let's denote:
P(0 sent) = ?
P(1 received) = 0.56
We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).
Using Bayes' theorem:
P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)
P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08
P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56
Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):
P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56
Simplifying:
P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56
= 0.08 * (1 - P(0 sent)) * (1 / 0.56)
= 0.08 * (1 - P(0 sent)) * (25/14)
= (2/25) * (1 - P(0 sent))
Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?
What is the area of the trapezoid?
5 km
4 km
13 km
9 km
Answer:
21 km²
Step-by-step explanation:
A = ᵃ ⁺ ᵇ/2 (h)
A = 5 + 9/2 (3)
A = 14/2 (3)
A = 7 x 3
A = 21 km²
What is the difference (2 x minus 3) minus (x minus 1)?
Answer:
2x - 3 - (x-1)
2x - 3 -x +1
x-2
Answer:
x-2 or B. if you're on edgMatch to the correct one
Answer:
1. b_ 2. a_ 3. c_ 4. d
Step-by-step explanation:
1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.
Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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A is twice as good a workman as B and together
they finish a piece of work in 18 days. In how
many days will A alone finish the work?
Answer:
vbnmnbv nbbnmbnmvbr
Step-by-step explanation:
Tom saved x silver coins, y gold coins and z bills. How much has Tom saved?
A) xyz
B) x+y+z
C) 3(xyz)
D) z-(y+x)
Answer:
B) x+y+z
Step-by-step explanation:
CARRY ON LEARNING
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Find the slope
(3,5) and (6,9)
Answer:
4/3 or 1 1/3
Step-by-step explanation:
To find slope, we subtract the y-values (9 - 5), then divide the difference we find from that by the difference of the x-values (6 - 3). So, let's go ahead and do that now. First, what's 9 - 5? Well, the answer is 4. Next, we have to divide this value by 6 - 3, which is equivalent to 3. Then, we divide the two numbers - what is 4 ÷ 3? Well, we can represent this as 4/3, or 1 1/3. Hopefully that's helpful - if you have any questions on that, let me know! :)
Answer:
Slope is 4/3
Step-by-step explanation:
Slope or gradient can be found by using several formulas. For this situation, we can use rate of changes between two points also known as rise over run or changes in y over change so in x.
The formula of slope between two points can be expressed as several equations, expressions, etc such as:
\(\displaystyle \large{m=\frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} =\frac{\Delta y}{\Delta x}\) where m is a variable representing the slope.
Since we are given two points, we are going to use the y2-y1 over x2-x1 formula.
Let (3,5) be (x1,y1,) and (6,9) be (x2,y2) thus the slope is \(\displaystyle \large{m=\frac{y_2-y_1}{x_2-x_1} =\frac{9-5}{6-3} =\frac{4}{3}\)
Therefore the slope of two points is 4/3.
__________________
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Solve 2-3 cos x=5+3 cosx for 0° ≤ 180°
The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.
1. Start with the given equation: 2-3cos(x) = 5+3cos(x).
2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.
3. Combine like terms: 2-6cos(x) = 5.
4. Subtract 2 from both sides: -6cos(x) = 3.
5. Divide both sides by -6: cos(x) = -1/2.
6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.
7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.
8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.
9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.
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