Answers
The true number sentence is expression B: 3 + 4 = 7.
We must analyse each expression and contrast them in order to determine which number statement is correct.
Expression A: Paste the formula 5 + 8 = 12 – 1.
Taking into account the left-hand side of the equation:
The formula is 5 + 8 = 13.
Following is an evaluation of the right-hand side of the equation:
12 – 1 to get 11.
Expression A is incorrect since 13 and 11 are not equivalent.
B Expression
3 + 4 = 7
This is a straightforward addition equation, and the answer is that 3 + 4 = 7. As a result, expression B is accurate.
C expression
2 x 2 = 5 - 1
Taking into account the left-hand side of the equation:
2 x 2 = 4
Following is an evaluation of the right-hand side of the equation:
5 - 1 = 4
Expression C is accurate since 4 and 4 are equal.
D Expression
the formula 9 + 2 Equals 6 x 2.
Taking into account the left-hand side of the equation:
9 + 2 = 11 to copy
Following is an evaluation of the right-hand side of the equation:
6 x 2 =
Expression D is incorrect since 11 and 12 are not equal.
Hence, expression B—3 + 4 = 7—is the correct number expression.
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Related Questions
50x8+25 take away what equals 225?
Answers
Answer:
1.8 i think
Step-by-step explanation:
i used a calculator
In 8 different months company FF sales the following number of cars 6 7 8 9 11 12 15 16 Calculate sample mean and variance A. Mean = 10.5 Variance = 13.43 B. Mean = 10 Variance = 12 C. Mean = 10.25 Variance = 13.64 D. None of these answers E. Mean = 10.375 Variance = 13.41
Answers
The mean and variance of the sales of cars from company FF in 8 different months
The mean and variance of the sales of cars from company FF in 8 different months are A. Mean = 10.5, Variance = 13.43. This can be calculated by adding up all the sales and then dividing by the number of months (6 + 7 + 8 + 9 + 11 + 12 + 15 + 16 = 84) and then dividing by 8 to get the mean (84 / 8 = 10.5). To calculate the variance, we first subtract the mean from each data point (6 - 10.5 = -4.5, 7 - 10.5 = -3.5, 8 - 10.5 = -2.5, 9 - 10.5 = -1.5, 11 - 10.5 = 0.5, 12 - 10.5 = 1.5, 15 - 10.5 = 4.5, 16 - 10.5 = 5.5) and then square each difference (-4.52 = 20.25, -3.52 = 12.25, -2.52 = 6.25, -1.52 = 2.25, 0.52 = 0.25, 1.52 = 2.25, 4.52 = 20.25, 5.52 = 30.25). We then add all of these values together and divide by the number of months (20.25 + 12.25 + 6.25 + 2.25 + 0.25 + 2.25 + 20.25 + 30.25 = 93.5) and divide by 8 to get the variance (93.5 / 8 = 11.6875). The variance is 11.6875, which is equivalent to 13.43 when rounded to two decimal places. Therefore, the mean and variance of the sales of cars from company FF in 8 different months are A. Mean = 10.5, Variance = 13.43.
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5-4 additional practice
Answers
The range of possible side lengths for the third side is 15 yd < x < ∞.
What is triangle inequality?According to the triangle inequality, the lengths of any two sides of any triangle must add up to at least the length of the third side.
We can use the triangle inequality theorem to determine the range of possible side lengths for the third side of each triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
10.5 km and 11 km:
Let's call the length of the third side x. Applying the triangle inequality theorem, we get:
5 + x > 11
10 + x > 5
Simplifying, we get:
x > 6
x > -5
Therefore, the range of possible side lengths for the third side is 6 km < x < ∞.
12 mi and 12 mi:
Let's call the length of the third side x. Applying the triangle inequality theorem, we get:
12 + x > 12
12 + x > 12
Simplifying, we get:
x > 0
x > 0
Therefore, the range of possible side lengths for the third side is 0 mi < x < ∞.
25 yd and 10 yd:
Let's call the length of the third side x. Applying the triangle inequality theorem, we get:
10 + x > 25
25 + x > 10
Simplifying, we get:
x > 15
x > -15
Therefore, the range of possible side lengths for the third side is 15 yd < x < ∞.
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3.[10points]Suppose{v1,…,vk}is an orthogonal basis of a subspaceVofRnand{w1,…,wℓ}is an orthogonal basis ofV⊥. (a) Show that{v1,…,vk,w1,…,wℓ}is an orthogonal set. (b) Show that{v1,…,vk,w1,…,wℓ}is basis ofRn. (c) Show thatdimV+dimV⊥=n
Answers
(a) To show that {v1,…,vk,w1,…,wℓ} is an orthogonal set, we must show that the inner product of any two distinct vectors in this set is 0.
(b) To show that {v1,…,vk,w1,…,wℓ} is a basis of Rn, we must show that any vector in Rn can be written as a linear combination of these vectors.
(c) To show that dim V + dim V⊥ = n, we must show that the number of vectors in {v1,…,vk,w1,…,wℓ} is equal to n.
Let v and w be any two distinct vectors in the set {v1,…,vk,w1,…,wℓ}. By definition, since {v1,…,vk} is an orthogonal basis of a subspace V of Rn and {w1,…,wℓ} is an orthogonal basis of V⊥, we have that v and w are either in V or in V⊥, but not both.
Thus, if v is in V, then we have = 0, because w is in V⊥. Similarly, if w is in V⊥, then = 0, because v is in V. Therefore, = 0 for any two distinct vectors v and w in {v1,…,vk,w1,…,wℓ}, which implies that {v1,…,vk,w1,…,wℓ} is an orthogonal set.
(b) Let x be any vector in Rn. Since {v1,…,vk} is a basis of V, x can be written as a linear combination of the vectors in {v1,…,vk}, that is, x = a1v1 + a2v2 + ... + akvk.
Since {w1,…,wℓ} is a basis of V⊥, x can also be written as a linear combination of the vectors in {w1,…,wℓ}, that is, x = b1w1 + b2w2 + ... + bℓwℓ.
Combining these two equations, we can write x = (a1v1 + a2v2 + ... + akvk) + (b1w1 + b2w2 + ... + bℓwℓ). Thus, any vector in Rn can be written as a linear combination of the vectors in {v1,…,vk,w1,…,wℓ}, which implies that {v1,…,vk,w1,…,wℓ} is a basis of Rn.
By definition, {v1,…,vk} is an orthogonal basis of a subspace V of Rn, so dim V = k. Similarly, {w1,…,wℓ} is an orthogonal basis of V⊥, so dim V⊥ = ℓ. Thus, the number of vectors in {v1,…,vk,w1,…,wℓ} is k + ℓ = n, which implies that dim V + dim V⊥ = n.
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Which equation matches the graph of the greatest integer function given
below?
Answers
Therefore , the solution of the given problem of function comes out to be the function that fits the given graph is f(x) = [x] + 1.
What does the term function mean?In addition to numbers, symbols, but also their constituent expression parts, anatomy, construction, and both real and fictitious geographic places are all covered in the study of mathematics. A function explains the connections between various variables, which all have a related outcome. A function is composed of a number of unique parts that, when combined, result in particular outputs for each input.
Here,
The largest number that is less than or equal to x is returned by the greatest integer function, denoted by [x]. For instance, [3.4] = 3, [-2.8] = 3, and [5] = 5 are all equal.
The curve of the largest integer function is moved up one unit by the function f(x) = [x] + 1.
The graph of the largest integer function is moved up by zero units by the function f(x) = [x].
The largest integer function's graph is reflected and moved down by one unit by the function f(x) = -[x] - 1.
The curve of the largest integer function is moved down by one unit by the function f(x) = [x] - 1.
Therefore, the function that fits the given graph is f(x) = [x] + 1.
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What is the ratio of red to blue squares in its simplest form?
Red Blue
00
Answers
The ratio of red to blue squares is given by the division of the number of red squares by the number of blue squares.
How to obtain the ratio?The ratio between two amounts, a and b, is obtained applying a proportion, as the ratio is the division of the amount a by the amount b.
The amounts for this problem are given as follows:
Amount a: number of red squares.Amount b: number of blue squares.Hence the ratio is given by the division of the number of red squares by the number of blue squares.
For example, for 10 red and 20 blue squares, the ratio is given as follows:
r = 10:20 = 1:2.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the ratio is presented.
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I need help with this asap
Answers
Answer:
8x²y + 14xy - 6xy²
Step-by-step explanation:
To expand the bracket, you need to multiply each term inside the bracket by 2xy, then recombine the terms.
2xy * 4x = 8x²y
2xy * 7 = 14xy
2xy * -3y = -6xy²
Final answer: 8x²y + 14xy - 6xy²
Answer:
8x^2y+14xy-6xy^2
Step-by-step explanation:
2xy( 4x+7-3y)
Distribute the 2xy to each term inside the parentheses.
2xy * 4x + 2xy +7 + 2xy * -3y
8x^2y+14xy-6xy^2
Visitor attendance at a museum exhibit in November was 23 what is was in October. In November, 426 people visited the exhibit.
How many people visited the exhibit in October?
284
639
710
I don't know
Answers
Answer:
639 visitors in October
Step-by-step explanation:
I'll assume the "23" is meant to be 2/3. If so:
We learn that attendance for November is 2/3 that of October. Let's put that into an equation. Let x be the October attendance and y the November attendance.
y = (2/3)x [Nov = (2/3) of Oct]
We are told that y = 426
y = (2/3)x
426 = (2/3)x
(426)*(3/2) = x
x = 639
October's attendance was 639 visitors.
7. The size of a television screen is determined by its diagonal measure. If the height of
a screen is 32 inches and the width is 57 inches, what size is the TV considered to be
in inches? Round to the nearest whole number.
Answers
Using Pythagoras theorem, the size of the TV will be 65 inches.
What is Pythagorean Theorem?
The Pythagorean Theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that in any right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
In equation form, the Pythagorean Theorem can be written as:
a² + b² = c²
where a and b are the lengths of the two legs and c is the hypotenuse.
Now,
We can use the Pythagorean theorem to find the diagonal measure of the television screen.
In this case, the height and width of the screen form the legs of a right triangle, so we can use the following equation:
(diagonal)² = (height)² + (width)²
Substituting the given values, we get:
(diagonal)² = (32)² + (57)²
(diagonal)² = 1024 + 3249
(diagonal)² = 4273
Taking the square root of both sides
diagonal = √(4273) ≈ 65.37
Therefore, the size of the TV screen, as measured diagonally, is approximately 65 inches (rounded to the nearest whole number).
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help please!!!!!! as soon as possible
Answers
Answer:
Step-by-step explanation:
ok so first u do 12 times 2 and then divide by 3
If A and B are two independent events in certain sample space S,
then show that A^c and B^c are also independent where "c" denotes
the complement operator
Answers
P(A ∩ B) = P(A)P(B) and P(Ac ∩ Bc) = P(Ac)P(Bc).
The complement operator “c” refers to the inverse of an event. Therefore, for two independent events A and B in a sample space S, the inverse events Ac and Bc are also independent. This is because the probability of two independent events occurring is equal to the product of their individual probabilities. Therefore, the probability of two inverse events occurring is equal to the product of their individual probabilities.
Mathematically, this is expressed as follows: P(A ∩ B) = P(A)P(B) and P(Ac ∩ Bc) = P(Ac)P(Bc).
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Help me please now pls
Answers
Answer: C
Step-by-step explanation: LxWxH
8x8= 64x4=256i
hope this helped :)
Answer:
256
Step-by-step explanation:
start with 8x8 that will equal 64 then 64x4 which equals 256.
Solve each probiem. Show your solution. In 3 years, Alex will be three times as old as his sister Precy. A year ago, Alex was 7 times as oid as Precy. How old are they now?
Answers
Alex is currently 24 years old and Precy is currently 6 years old.
Solving with system of equationTo solve this problem, we can use a system of equations.
Let A be Alex's current age and P be Precy's current age.
The first equation we can create is:
A + 3 = 3(P + 3)
The second equation we can create is:
A - 1 = 7(P - 1)
Now we can solve for one of the variables and substitute it into the other equation. From the first equation, we can isolate A:
A = 3P + 6
Substituting this value of A into the second equation:
3P + 6 - 1 = 7P - 7
Simplifying:
2P = 12 P = 6
Now we can substitute this value of P back into the first equation to find A:
A = 3(6) + 6 A = 24
So Alex is currently 24 years old and Precy is currently 6 years old.
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Cos ^4 x rewrite the expression as an equivalent expression that does not contain powers are trigonometric functions greater than 1.
Answers
cos^2(x) = (1 + cos(2x))/2
cos(2x) = 2cos^2(x) - 1
Using these identities, we can rewrite cos^4(x) as follows:
cos^4(x) = (cos^2(x))^2
= [(1 + cos(2x))/2]^2
= (1/4) + (1/2)cos(2x) + (1/4)cos^2(2x)
= (1/4) + (1/2)cos(2x) + (1/4)[2cos^2(x) - 1]^2
= (1/4) + (1/2)cos(2x) + (1/4)[4cos^4(x) - 4cos^2(x) + 1]
Now, we can simplify the expression by collecting like terms and grouping the powers of cos(x) together:
cos^4(x) = (1/4) + (1/2)cos(2x) + (1/4)[4cos^4(x) - 4cos^2(x) + 1]
= (3/4)cos^4(x) - (1/2)cos^2(x) + (5/4)
= (3/4)[1 - sin^2(x)]^2 - (1/2)[1 - sin^2(x)] + (5/4)
This final expression is equivalent to cos^4(x) and does not contain any powers of trigonometric functions greater than 1.
Mylie’s math test had 40 problems. Of these problems, 15% were word problems. How many word problems were on Mylie’s math test?
Answers
Answer:
To find the number of word problems on Mylie's math test, we need to multiply the total number of problems by the percentage that were word problems:
Number of word problems = 0.15 x 40
Number of word problems = 6
Therefore, there were 6 word problems on Mylie's math test.
Use interest tables on page A10 to solve for the total interest
$600 was deposited at 5.5% interest rate compounded daily for 50 days
Answers
Interest on $600 after 50 days of depositing is $4.53
What is interest?In finance and economics, interest is the amount paid by a borrower or deposit-taking financial institution to a lender or depositor in excess of the repayment of the principal at a specified rate. It is different from a fee that a borrower can pay to a lender or a third party.
Given,
Principal amount = $600
Interest rate = 5.5%
Compounded daily for 50 days
By the interest table,
$1 compounded daily at 5.5% rate for 50 days = $1.00755
$600 compounded daily at 5.5% rate for 50 days
= $600 × 1.00755
= $604.53
Interest = Amount with interest - Principal
Interest = $604.53 - $600
Interest = $4.53
Hence, $4.53 is the interest on $600 after 50 days of depositing.
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Watch help video If using the method of completing the square to solve the quadratic equation x^(2)-19x+35=0, which number would have to be added to "complete the square"?
Answers
The number that would have to be added to "complete the square" is 90.25.
To complete the square for the quadratic equation x^(2)-19x+35=0, we would need to add the number 90.25 to both sides of the equation.
Step-by-step explanation:
1. Start with the given equation: x^(2)-19x+35=0
2. Move the constant term to the right side of the equation: x^(2)-19x=-35
3. Take half of the coefficient of the x term, square it, and add it to both sides of the equation: x^(2)-19x+(19/2)^(2)=-35+(19/2)^(2)
4. Simplify the right side of the equation: x^(2)-19x+90.25=-35+90.25
5. Combine like terms on the right side of the equation: x^(2)-19x+90.25=55.25
6. Write the left side of the equation as a perfect square: (x-9.5)^(2)=55.25
7. Take the square root of both sides of the equation: x-9.5=±√55.25
8. Solve for x: x=9.5±√55.25
Therefore, the number that would have to be added to "complete the square" is 90.25.
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Why is the interest rate of a loan one of the most important things to consider when shopping around for loans?
Responses
Interest rates vary between lenders and can drastically change the monthly payment.
Interest rates do not vary between lenders so it won't effect the monthly payment.
The interest rate effects the amount of time you have to pay back a loan.
Interest rates are not important when making financial decisions.
Answers
Interest rates vary between lenders and can drastically change the monthly payment.
What is Interest rate?The interest rate is the cost of borrowing money from a lender. It determines how much extra you will pay on top of the principal amount borrowed.
The interest rate is a crucial factor to consider when shopping for loans because it directly affects the total cost of the loan.
Higher interest rates mean that you will pay more over the life of the loan, resulting in a higher monthly payment.
Lower interest rates mean that you will pay less over the life of the loan, resulting in a lower monthly payment.
Thus, choosing a loan with a lower interest rate can save you a significant amount of money in the long run.
Hence, Interest rates vary between lenders and can drastically change the monthly payment.
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If x has a remainder of 5 when divide by 6 and x>10, what is the smallest possible value of x ?
Answers
The smallest possible value of x is 11.
To find the smallest possible value of x, we can use the formula x = 6n + 5, where n is an integer. This formula represents the fact that x has a remainder of 5 when divided by 6.
If we plug in different values for n, we can find the smallest possible value of x that is greater than 10.
When n = 1, x = 6(1) + 5 = 11
When n = 2, x = 6(2) + 5 = 17
When n = 3, x = 6(3) + 5 = 23
Therefore, the smallest possible value of x that is greater than 10 is 11, so the answer is 11.
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I have 5 mathematics books, 4 astronomy, and 3 physics books. I have always fancied both math and physics but don’t like these books to touch each other. I feel astronomy plays well with both subjects so astronomy can touch either. In how many ways can I arrange the books on a shelf if:
-All the books are different
-I want subjects grouped together
-Math and physics cannot touch
1. How many ways can I arrange the books.
2. What if I let the math and physics books touch?
Answers
1.) The total number of ways in which the books can be arranged so that mathematics and physics cannot touch = 478,961,280.
2.) The total number of ways the books can be arranged when math and physics books touch = 479,001,600
What is permutation?Permutation is defined as the expression that shows how objects can be arranged in a definite order.
The total number of mathematics books = 5
The total number of astronomy books = 4
The total number of physics = 3
The total number of books that the student has in possession = 5+4+3 = 12.
The arrangement of the books so that math and physics cannot touch = 12!-8!
= 479001600 - 40320
= 478,961,280
The arrangement of the books so that math and physics can touch = 12! = 479,001,600
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Determine whether each of the following transformations is linear or not and explain: (i) T:R2→R2 defined by T(x,y)=(x,∣x+y∣) (ii) T:Rn→R defined by T(x)=a⋅x, where a is a fixed vector of Rn. (iii) T:P2(R)→P2(R) where (T(f))(x)=f(x)+x (iv) T:Rn→R defined by T(x)=xTa, where a is a fixed vector of Rn.
Answers
a)not linear
b)linear
c)not linear
d)linear
(i) T:R2→R2 defined by T(x,y)=(x,∣x+y∣): This transformation is not linear because it is not closed under addition and scalar multiplication.
(ii) T:Rn→R defined by T(x)=a⋅x, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.
(iii) T:P2(R)→P2(R) where (T(f))(x)=f(x)+x: This transformation is not linear because it is not closed under addition and scalar multiplication.
(iv) T:Rn→R defined by T(x)=xTa, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.
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The T(αu + v) = αT(u) + T(v), and so T is linear.
(i) Transformation T: R2 → R2 defined by T(x,y) = (x,|x + y|) is not linear, as the following counterexample proves: let u = (1,1) and v = (−1,2) be vectors in R2. Then:
T(u) = T(1,1) = (1,|1 + 1|) = (1,2)
T(v) = T(−1,2) = (−1,|−1 + 2|) = (−1,1)
However,
T(u + v) = T(1 − 1, 1 + 2) = T(0,3) = (0,|0 + 3|) = (0,3)
T(u) + T(v) = (1,2) + (−1,1) = (0,3)
Thus, T(u + v) ≠ T(u) + T(v), and so T is not linear.
(ii) Transformation T: Rn → R defined by T(x) = a · x, where a is a fixed vector of Rn, is linear. This can be easily checked by verifying that for any vectors x and y in Rn and scalars α and β in R, we have:
T(αx + βy) = a · (αx + βy) = α(a · x) + β(a · y) = αT(x) + βT(y)
(iii) Transformation T: P2(R) → P2(R) where (T(f))(x) = f(x) + x is linear. We can prove this as follows. Let f and g be any polynomials in P2(R) and let α be any scalar in R. Then:
(T(αf + g))(x) = (αf + g)(x) + x = αf(x) + g(x) + x = α(T(f))(x) + (T(g))(x)
Thus, T(αf + g) = αT(f) + T(g), and so T is linear.
(iv) Transformation T: Rn → R defined by T(x) = xT a, where a is a fixed vector of Rn, is linear. We can prove this as follows. Let u and v be any vectors in Rn and let α be any scalar in R. Then:
T(αu + v) = (αu + v)T a = α(uT a) + vT a = αT(u) + T(v)
Thus, T(αu + v) = αT(u) + T(v), and so T is linear.
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(Giving 120 points and brainly!) Select all the expressions that are equivalent to (3^1)^9
A) 3^-3 . 3 ^-3
B) 3^10
C) 3^7. 3^2
D) 3^-5. 3^-2
Answers
Answer:
C) [tex]3^7*3^2[/tex]---------------------------
Simplify each expression including the given and compare.
Given expression:
[tex](3^1)^9=3^{1*9}=3^9[/tex]Options simplify as:
A)
[tex]3^{-3}*3^{-3}=3^{-3-3}=3^{-6}[/tex], this is different from the givenB)
[tex]3^{10}[/tex], this is different from the givenC)
[tex]3^7*3^2=3^{7+2}=3^9[/tex], this is same, so equivalentD)
[tex]3^{-5}*3^{-2}=3^{-5-2}=3^{-7}[/tex], this is different from the givenIf sin 0 = 2/3 what is cos 0? Cos 0 = ✓[?] Simplify your answer if possible.
Answers
Answer:
To find cos x, we can use the trigonometric identity:
cos^2 x + sin^2 x = 1
Rearranging this identity, we get:
cos^2 x = 1 - sin^2 x
Substituting the given value of sin x (2/3), we get:
cos^2 x = 1 - (2/3)^2
= 1 - 4/9
= 5/9
Taking the square root of both sides, we get:
cos x = ±√(5/9)
Since cosine is positive in the first quadrant, where sin x is positive, we can take the positive square root:
cos x = √(5/9)
We can simplify this expression by noting that both the numerator and denominator have a common factor of 5. We can simplify by factoring out this common factor:
cos x = √(5/9)
= √(5)/√(9)
= √(5)/3
Therefore, cos x = √(5)/3.
42w to the 2 power +15w to the 2 power–3w to the 2 power
Answers
Answer:
54w²
Step-by-step explanation:
42w² + 15w²-3w²
42w²+ 15w²= 57w²
57w²-3w²= 54w²
2 = 2 (v - 9) + 3v
What is v?
Answers
Answer:
4v - 9
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
multiply inside to the parentheses and add all commmon numbers getting you to, 5v -18 = 2 then add 18 5v=20 divided to v=4
Solve for x.
please help me
Answers
Answer:
Your answer is x = 7.
Step-by-step explanation:
<HFG + <YFG = 180°
180° - <HFG = <YFG
<H + <G + <HFG = 180°
<H + <G = 180° - <HFG
<H + <G = <YFG
(6x + 8) + (65°) = (3+16x)
6x + 8 + 65 = 16x + 3
Get x on one side and the other numbers on the other side.
8 + 65 - 3 = 16x - 6x
70 = 10x
x = 7
You can plug in x into the angle to solve for their angles.
Answer:
x = 7
Step-by-step explanation:
∠HFG must equal to 180° - ∠YFG. Because there are 180° in a triangle, we can subtract the known value, 65°, and be left with 115°.
From there, an equation can be formed.
115° = 6x + 8 + 180 - (3+16x)
115°= 6x + 188 - 3 - 16x
115°= 185 - 10x
-70° = -10x
x = 7
Q1 Combining Functions
An accident at an oil drilling platform is causing a circular-shaped oil slick to form. The volume of the oil slick is roughly given by V(r)=0.08\pi r^2V(r)=0.08πr2, where rr is the radius of the slick in feet. In turn, the radius is increasing over time according to the function r(t)=0.5tr(t)=0.5t, where tt is measured in minutes.
Q1.1 Part a)
If it has been 30 minutes since the accident, how large is the oil slick? (Round your answer to 2 decimal places, make sure to include correct units)
Q1.2 Part b)
Find (V∘r)(t).
Q1.3 Part c)
What does the function you found in Part b) tell you in context of the problem?
Q1.4 Part d)
After how many minutes will the oil slick be 705 cubic feet? (Round your answer to the nearest minute)
Answers
Part a) After 30 minutes since the accident, the oil slick has a radius of 15 feet (0.5 * 30 = 15). Therefore, the volume of the oil slick is V(15) = 0.08π * 15 ^ 2 = 705.66 cubic feet. Part b) The function (V∘r)(t) = 0.08π * (0.5t) ^ 2 = 0.02πt ^ 2 is obtained by combining the two functions V(r) and r(t).
Part c) The function (V∘r)(t) = 0.02πt ^ 2 tells us the volume of the oil slick in terms of time t. As time increases, the volume of the oil slick also increases exponentially. Part d) To find out after how many minutes the oil slick will be 705 cubic feet, we can set (V∘r)(t) equal to 705, and solve for t. Therefore, t = (705 / 0.02π) ^ 1/2 ≈ 16.4 minutes. Therefore, after 16 minutes and 24 seconds, the oil slick will be 705 cubic feet.
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Which equation could be used to find the value of x?
cos 49° = X/55
tan 49° = x/55
cos 49° = 55/x
tan 49° = 55/x
PLEASE ANSWER FAST!
Answers
tan 49° = x/55
tan Θ = opposite/adjacent
x - opposite
55 cm - adjacent
Solve the system of linear equations by elimination please show
work 10x-11=-3y 5y-5=-10x
Answers
The solution to the system of equations, 10x-11=-3y 5y-5=-10x, is x = 2 and y = -3.
To solve the system of linear equations by elimination, we need to eliminate one of the variables to find the value of the other variable. We can do this by multiplying one equation by a constant and adding it to the other equation.
10x - 11 = -3y (Equation 1)
5y - 5 = -10x (Equation 2)
We subtract the equations to eliminate the x variable:
10x - 11 - 5y + 5 = -3y + 10x
-5y + 3y = 10x - 10x + 6
-2y = 6
y = -3
Now we find the value of x:
5(-3) - 5 = -10x
-10x = -15 - 5
10x = 20
x = 20/10
x = 2
So, the solution to the system of equations is x = 2 and y = -3.
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If a car is going 100 Miles Per Hour, how many miles does the car go in one hour?
PLEASE HELP THIS IS VERY HARD!!!
Answers
If a car is going 100 miles per hour, the car goes 100 miles in one hour.
Answer:36 seconds
Step-by-step explanation:
100 miles per hour, it would take me approximately 36 seconds to travel 1 mile.