Answers
Answer:M1=50 M2=130
Step-by-step explanation:
M2=130 because corresponding angles and M1=50 because 180-130=50
Related Questions
3. Given:f(x)=x2+2x−8A: What is the vertex? B: What is the line (or axis) of symmetry (in equation form)? C: What are thex-intercepts and they-intercept? D: What is the Domain: E: What is the Range: F: Increasing interval: G: Decreasing interval:H: End Behavior: asx→+[infinity],y⇒AND asx→−[infinity],y→1: Graph the function. Make sure you graph the vertex and 4 additional key points.
Answers
A: The vertex of the equation f(x)=x^2+2x−8 can be found by using the formula (-b/2a, f(-b/2a)) where a=1, b=2, and c=-8. Plugging in the values gives us the vertex (-1, -9).
B: The line of symmetry can be found by using the formula x=-b/2a. Plugging in the values gives us the equation x=-1.
C: The x-intercepts can be found by setting f(x)=0 and solving for x. This gives us the equation x^2+2x-8=0. Using the quadratic formula, we get x=(-2±√(2^2-4(1)(-8)))/(2(1)). Simplifying gives us x=(-2±√36)/2, which gives us the x-intercepts (-5.24, 1.24). The y-intercept can be found by setting x=0 and solving for y. This gives us the equation y=-8.
D: The domain of the function is all real numbers, or (-∞,∞).
E: The range of the function is all real numbers greater than or equal to -9, or [-9,∞).
F: The increasing interval of the function is (-1,∞).
G: The decreasing interval of the function is (-∞,-1).
H: The end behavior of the function is as x→+∞,y→∞ and as x→-∞,y→∞.
I: To graph the function, first plot the vertex (-1, -9) and the x-intercepts (-5.24, 0) and (1.24, 0). Then, plot two additional points on either side of the vertex, such as (-2, -6) and (0, -8). Connect the points with a smooth curve to complete the graph.
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T-1.3 Let W be the subspace with dimension of n-1 within vector space V. Prove that there exists a basis in vector space V (denote as S), will satisfy the condition of SO W = 0.
Answers
The proof is complete.
To prove that there exists a basis in vector space V that satisfies the condition of $W = \{0\}$, we will use the dimension theorem. The dimension theorem states that if $V$ is an $n$-dimensional vector space, then any subspace of $V$ has a dimension that is less than or equal to $n$. In this case, the given subspace $W$ has a dimension of $n-1$ and so it must be a subspace of $V$. Since the dimension of $W$ is less than the dimension of $V$, the dimension theorem states that there exists a basis in $V$ that satisfies the condition of $W = \{0\}$. Therefore, the proof is complete.
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What is the slope of a line, in the standard (x,y) coordinate plane, that is parallel to x+5y=9 ?
Answers
Answer:-15
Step-by-step explanation:
For the following polynomial one zero is given. f(x)=x^(4)+16x^(2)-225,-5i is a zero.
Answers
The zeros of the polynomial are -5i, √5i, -√5i.
The given polynomial is: f(x)=x⁴+16x²-225.
What is Zeros of a polynomial?Zeros of a polynomial are the values of x that make the polynomial equal to zero. These will be the x-intercepts of the polynomial's graph. To find the zeros of a polynomial, use the factored form of the polynomial and set each factor equal to zero. The solutions of this equation are the zeros of the polynomial.
The given zero is: -5i
To find the remaining zeros of the polynomial, we need to factor the polynomial.
We can factorize the polynomial as:
f(x) = (x² + 5i)(x² - 5i)
Finding Zeros:
Therefore, the remaining zeros of the polynomial are:
x = ±√5i
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Enter the zero element (zero vector) for each vector space. Use the following syntax to enter your answers. Enter the vector⟨1,2,3⟩using⟨1,2,3⟩. Enter the matrix[1324]using[[1,2],[3,4]]. Enter the functionf(x)=x2−sin(x)usingf(x)=x−2−sin(x), including the partf(x)=. 1. The zero vector of the vector spaceR2is 2. The zero vector of the vector space of2×2matrices is 3. The zero vector for the vector space of all functionsf:R→Ris
Answers
1) The zero vector of the vector space R2 is ⟨0,0⟩.
2) The zero vector of the vector space of 2×2 matrices is [[0,0],[0,0]].
3) The zero vector for the vector space of all functions f:R→R is f(x) = 0.
What is vector space?
A vector space is a mathematical structure consisting of a set of vectors that can be added together and scaled (multiplied) by scalars, such as real numbers, satisfying certain axioms.
The zero vector of the vector space R2 is ⟨0, 0⟩. This is because the zero vector of a vector space is the unique vector which when added to any vector in the space results in that same vector. In R2, the vector ⟨0, 0⟩ has this property, because for any vector ⟨a, b⟩ in R2, ⟨0, 0⟩ + ⟨a, b⟩ = ⟨a, b⟩.
The zero vector of the vector space of 2×2 matrices is [[0,0],[0,0]]. This is because the zero vector of a vector space is the unique matrix which when added to any matrix in the space results in that same matrix. In the space of 2×2 matrices, the matrix [[0,0],[0,0]] has this property, because for any matrix [[a,b],[c,d]] in the space, [[0,0],[0,0]] + [[a,b],[c,d]] = [[a,b],[c,d]].
The zero vector for the vector space of all functions f:R→R is f(x) = 0. This is because the zero vector of a vector space is the unique function which when added to any function in the space results in that same function. In the space of all functions f:R→R, the function f(x) = 0 has this property, because for any function f(x), f(x) + 0 = f(x).
Hence,
1) The zero vector of the vector space R2 is ⟨0,0⟩.
2) The zero vector of the vector space of 2×2 matrices is [[0,0],[0,0]].
3) The zero vector for the vector space of all functions f:R→R is f(x) = 0.
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Math Recommendations If h(v)=2v^(3)-25v+4, use synthetic division to find h(-4). Submit
Answers
Using synthetic division, the value of h(-4) is - 24.
To find h(-4) using synthetic division, we will use the following steps:
1. Set up the synthetic division grid with the divisor (-4) in the top left corner and the coefficients of the polynomial in the top row.
-4 | 2 0 -25 4
2. Bring down the first coefficient to the bottom row.
-4 | 2 0 -25 4
|
2
3. Multiply the divisor (-4) by the first number in the bottom row (2) and put the result (-8) in the second column of the top row.
-4 | 2 0 -25 4
| -8
2
4. Add the numbers in the second column (0 and -8) and put the result (-8) in the second column of the bottom row.
-4 | 2 0 -25 4
| -8
2 -8
5. Repeat steps 3 and 4 for the remaining columns.
-4 | 2 0 -25 4
| -8 32 -28
2 -8 7 -24
6. The last number in the bottom row (-24) is the remainder and the value of h(-4). The other numbers in the bottom row (2, -8, 7) are the coefficients of the quotient polynomial.
Therefore, h(-4) = 24.
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er -5x^(6)-7x^(3)+7x^(2)+4 is a monomial, binomial, trinomial, or other polynomial.
Answers
The given expression -5x⁶-7x³+7x²+4 is a polynomial.
A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable. The terms in a polynomial are called monomials, and they can be either constants or variables with a coefficient.
In the given expression, there are four terms: -5x⁶, -7x³, 7x², and 4. Each of these terms is a monomial. Since there are four terms in the expression, it is classified as a polynomial with four terms, also known as a quadrinomial.
Therefore, the given expression -5x⁶-7x³+7x²+4 is a quadrinomial, which is a type of polynomial.
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Which ordinal numbers match the cardinal numbers below? Check all that
apply.
183, 201, 82
A. 183rd
B. 183st
C. 87th
☐ D. 82nd
E. 201th
OF. 201 st
Answers
The correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.
What is cardinal number ?
A cardinal number is a type of number used to represent the size or quantity of a set or collection of objects. It is a number that expresses how many objects are in a particular set or group, and is used to answer questions like "how many?"
For example, the cardinal number of the set {1, 2, 3} is 3, because there are three objects in the set. The cardinal number of a set can be finite or infinite, depending on whether the set has a definite number of elements or not.
The ordinal numbers corresponding to the cardinal numbers are:
183: 183rd
201: 201st
82: 82nd
Therefore, the correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.
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Caleb needs to place a ground cover
under a tent. The floor of the tent measures 82 feet by 92 feet.
He purchases a ground cover that states that it covers 90 square
feet. Will the ground cover be able to be used under the tent?
Explain your reasoning.
Answers
One cover is not enough to cover tent, Caleb will need at least 84 ground covers to cover the entire floor of the tent.
How to find the Cover area of the tent?To determine if the ground cover will be sufficient, we need to calculate the area of the tent floor and compare it with the area covered by the ground cover.
The area of the tent floor is:
82 feet x 92 feet = 7544 square feet
The area covered by one ground cover is:
90 square feet
To determine the number of ground covers needed to cover the tent floor, we can divide the area of the tent floor by the area covered by each ground cover:
7544 square feet ÷ 90 square feet ≈ 84
Therefore, Caleb will need at least 84 ground covers to cover the entire floor of the tent. As the number of ground covers required is greater than one, we can conclude that the ground cover will be able to be used under the tent.
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For each relationship described, type an equation using the variables y and z to create an identity. a. addition and subtraction: b. multiplication and division: (when y 0 or when z = 0)
Answers
Step-by-step explanation:
addition and subtraction:
y + z - z = y
b. multiplication and division:
When y ≠ 0:
yz / y = z
When z ≠ 0:
y / z * z = y
Due to an unforeseen case of asthma, Big Wolf Demolition has to buy a wrecking ball. The ball, along with its equipment, will cost $10,000. The cash flows resulting from the investment are as follows: Year 1: $6,000; Year 2: $7,500; Year 3: $7,000; Year 4: $2,000. Calculate the IRR of the project
Answers
The project is expected to generate a return of 16.1% per year, which is higher than the company's cost of capital.
To calculate the IRR of the project, we need to find the discount rate at which the present value of the cash inflows equals the initial cost of the investment. We can use the following formula to find the IRR:
NPV = 0 = CF0 + CF1/(1+IRR)¹ + CF2/(1+IRR)² + CF3/(1+IRR)³ + CF4/(1+IRR)⁴
Where:
CF0 = initial investment = -$10,000
CF1, CF2, CF3, CF4 = cash flows in years 1, 2, 3, and 4, respectively
IRR = the discount rate we want to find
Using the given values, we can plug them into the formula and solve for IRR using a financial calculator or Excel. Alternatively, we can use a trial-and-error method to find the discount rate that makes NPV equal to zero.
Here is one way to solve for IRR using Excel:
In Excel, create a new spreadsheet.
In cells A1 to A5, enter the cash flows: -10000, 6000, 7500, 7000, and 2000.
In cell B1, enter the formula: =IRR(A1:A5)
Press Enter. The IRR of the project is displayed in cell B1 as a percentage.
Using this method, we find that the IRR of the project is approximately 16.1%.
Therefore, the Internal Rate of Return (IRR) of the project is calculated to be 16.1%, which indicates that the project is expected to generate a return that is greater than the cost of capital for the company. Hence, investing in this project is considered financially viable for Big Wolf Demolition.
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evaluate the expression using scientific notation. Express the result in scientific notation.
5.4 X 10^-8/1.5 X 10^4
Answers
Answer:
We can simplify this expression as follows:
5.4 x 10^-8 / 1.5 x 10^4 = (5.4/1.5) x (10^-8 / 10^4) = 3.6 x 10^-12
Therefore, the result in scientific notation is 3.6 x 10^-12.
Which of the following lists the sides of the triangle in order of length, from longest to shortest?
Answers
Answer: EF, DF, DE
Step-by-step explanation:
The smaller the opposite angle, the smaller the side, and vice versa.
∠EDF = 85°
∠DEF = 60° (Because the total degrees in a triangle must be 180°)
∠DFE = 35°
EF, DF, DE
Hope this helps!
A= [ 1 1 1]
[ 1 2 3]
[ 4 5 6]
v = [ 2 ]
[ 3 ] [ -1]. (a) Find the image ofvunderTA. (b) Can you find vectorswthat are different fromvbut that get mapped to the same image? (c) Find all vectorszthat get mapped to zero. (Hint: No new row reduction is needed.) (d) Write down a nontrivial linear dependence relation between the columns ofA.
Answers
One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.
A= [ 1 1 1] [ 1 2 3] [ 4 5 6] and v = [ 2 ] [ 3 ] [ -1]. To find the image of v under TA, we simply multiply A and v to get:
TA = [ 1 1 1] [ 2 ] = [ 4 ]
[ 1 2 3] [ 3 ] [ 7 ]
[ 4 5 6] [ -1] [ 17 ]
So the image of v under TA is [ 4 7 17 ].
To find vectors w that are different from v but that get mapped to the same image, we can use the equation TA*w = TA*v. Since TA*v = [ 4 7 17 ], we can set up the following system of equations:
1w1 + 1w2 + 1w3 = 4
1w1 + 2w2 + 3w3 = 7
4w1 + 5w2 + 6w3 = 17
Solving this system of equations will give us all the possible vectors w that get mapped to the same image as v. One possible solution is w = [ 1 2 0 ], which is different from v but gets mapped to the same image.
To find all vectors z that get mapped to zero, we can use the equation TA*z = 0. This gives us the following system of equations:
1z1 + 1z2 + 1z3 = 0
1z1 + 2z2 + 3z3 = 0
4z1 + 5z2 + 6z3 = 0
Solving this system of equations will give us all the possible vectors z that get mapped to zero. One possible solution is z = [ -3 2 1 ], which gets mapped to zero under TA.
Finally, to write down a nontrivial linear dependence relation between the columns of A, we can use the equation c1*A1 + c2*A2 + c3*A3 = 0, where A1, A2, and A3 are the columns of A and c1, c2, and c3 are constants. One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.
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100 POINTS PLEASEEE SOMEBODY I NEED TO TURN THIS IN
Answers
The diagonals are 17.4 inches
The length does not meet the regulationThe measurement of KR is 8 unitsHow to determine the lengths of the diagonalsFrom the question, we have the following parameters that can be used in our computation:
DH = 10, HK = 8.2, KB = 6, HR = 8 and KY = 6.8
Given that DHB is a right triangle, we have
DB² = HB² + DH²
So, we have
DB² = (8.2 + 6)² + 10²
DB² = 301.64
Take the square root
DB = 17.4
Does the length meet the regulationThe triangles DBY and RYB are congruent triangles
So, we have
RY = 17.4
The figure is an isosceles triangle, and the length does not meet the regulation
This is so because the length is less than the required 20 inches
The measurement of KRThe two non-parallel sides of an isosceles triangle are of equal length
So, we have
1/2x + 5 = 2x - 4
Evaluate the like terms
3/2x = 9
This gives
x = 9 * 2/3
x = 6
So, we have
KR = 1/2x + 5
This gives
KR = 1/2 * 6 + 5
KR = 8
So, the value of KR is 8 units
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Use a graphing Utility to approximate the local macmum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6
1. the local maximum is y=__and it occurs at x=__
2. the local minimun is y=___ and it occurs at x=__
please explain process
if its possible please ans thank you
Answers
The local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.
Using a graphing Utility, we can approximate the local maximum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6.
1. The local maximum value occurs at the highest point on the graph within the given interval of -6. By observing the graph, we can see that the local maximum value is y=2.2 and it occurs at x=-1.2.
2. The local minimum value occurs at the lowest point on the graph within the given interval of -6. By observing the graph, we can see that the local minimum value is y=-4.6 and it occurs at x=-4.8.
It is important to note that these values are approximations and may not be exact. The graphing Utility is a useful tool for visualizing the function and finding approximate values, but it is not always precise.
the local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.
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a) Find the definite integral L (x + 1)(x - 1)dx Answer: I= b) Find the indefinite integral (x– 1)dx Answer: I =
c) Calculate the integral \2cos(t)dt Answer: I= =
Answers
a) To find the definite integral of L (x + 1)(x - 1)dx, we first need to expand the expression and then integrate it.
L (x + 1)(x - 1)dx = L (x^2 - 1)dx
Now we can integrate this expression:
I = ∫(x^2 - 1)dx = (x^3/3) - x + C
Since we are looking for the definite integral, we need to evaluate this expression at the limits of integration.
I = [(b^3/3) - b] - [(a^3/3) - a]
b) To find the indefinite integral of (x - 1)dx, we simply need to integrate the expression and add a constant of integration.
I = ∫(x - 1)dx = (x^2/2) - x + C
c) To calculate the integral of 2cos(t)dt, we simply need to integrate the expression and add a constant of integration.
I = ∫2cos(t)dt = 2sin(t) + C
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Use polynomial fitting to find the formula for the nth term of the sequence (an)nzo which starts,
4, 15, 44, 109, 228, 419,...
an=
Answers
The formula for the nth term of the sequence is:
an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3
To find the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting, we need to follow the following steps:
1. Identify the degree of the polynomial: Since the sequence has 6 terms, the degree of the polynomial is 5.
2. Create a system of equations: Use the given terms of the sequence to create a system of equations with the polynomial coefficients as unknowns.
3. Solve the system of equations: Use any method to solve the system of equations to find the values of the polynomial coefficients.
4. Write the formula for the nth term: Use the values of the polynomial coefficients to write the formula for the nth term of the sequence.
The system of equations is:
a5n^5 + a4n^4 + a3n^3 + a2n^2 + a1n + a0 = an
Plugging in the values of the terms of the sequence, we get:
a5(1)^5 + a4(1)^4 + a3(1)^3 + a2(1)^2 + a1(1) + a0 = 4
a5(2)^5 + a4(2)^4 + a3(2)^3 + a2(2)^2 + a1(2) + a0 = 15
a5(3)^5 + a4(3)^4 + a3(3)^3 + a2(3)^2 + a1(3) + a0 = 44
a5(4)^5 + a4(4)^4 + a3(4)^3 + a2(4)^2 + a1(4) + a0 = 109
a5(5)^5 + a4(5)^4 + a3(5)^3 + a2(5)^2 + a1(5) + a0 = 228
a5(6)^5 + a4(6)^4 + a3(6)^3 + a2(6)^2 + a1(6) + a0 = 419
Solving this system of equations, we get:
a5 = 1
a4 = -5
a3 = 9
a2 = -7
a1 = 3
a0 = 3
Therefore, the formula for the nth term of the sequence is:
an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3
So, the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting is an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3.
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2 Three different forces act on an object. They are: -- F1 = F2 = F3 = < -2, -3 > Find the net force Fnet on the object (the sum of the forces) Fnet = Find what fourth force, FA would need to be add
Answers
So the fourth force FA that would need to be added to make the net force zero is < 6, 9 >.
The net force on an object is the sum of all the forces acting on it. In this case, there are three different forces acting on the object: F1, F2, and F3. Each of these forces has a magnitude of < -2, -3 >. To find the net force Fnet, we simply add up all the forces:
Fnet = F1 + F2 + F3
Fnet = < -2, -3 > + < -2, -3 > + < -2, -3 >
Fnet = < -6, -9 >
To find the fourth force FA that would need to be added to make the net force zero, we simply need to find a force that is equal and opposite to Fnet. That is:
FA = -Fnet
FA = -< -6, -9 >
FA = < 6, 9 >
So the fourth force FA that would need to be added to make the net force zero is < 6, 9 >.
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when f(x)=4 what is the of x
Answers
When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).
How did we determine the value of x?According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.
When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.
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Find the diviative of the following
[tex] y = ( \sqrt{1 + 2x)} 5[/tex]
Answers
Answer:
Step-by-step explanation:
1+2x)5
First you minus the 1 with the 5
Which you'll get a four then divide it by 2
Which you'll get x=2
But then times it by 5
Then you get y=10
Answer:
[tex]\dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5 = \boxed{\dfrac{5}{\sqrt{1+2x}}}[/tex]
Step-by-step explanation:
Given [tex]y = \left(\sqrt{1\:+\:2x}\right)5[/tex]
we are asked to find [tex]\dfrac{dy}{dx}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5\\\\= 5\dfrac{d}{dx}\left(\sqrt{1+2x}\right)\\\\[/tex]
Find [tex]\dfrac{d}{dx}\left(\sqrt{1+2x}\right)[/tex]:
[tex]Let \;u = 1 + 2x\\\\f(u) = \sqrt(u)\\\\[/tex]
[tex]\mathrm{Apply\:the\:chain\:rule}:\quad \dfrac{df\left(u\right)}{dx}=\dfrac{df}{du}\cdot \dfrac{du}{dx}[/tex]
[tex]= \dfrac{d}{du}\left(\sqrt{u}\right)\dfrac{d}{dx}\left(1+2x\right)[/tex]
[tex]\dfrac{d}{du}\left(\sqrt{u}\right) = \dfrac{d}{du}\left(u^{\dfrac{1}{2}}\right)\\\\= \dfrac{1}{2}u^{\dfrac{1}{2}-1}\\\\= \dfrac{1}{2\sqrt{u}}\\\\\\[/tex]
Substitute back u = 1 + 2x
[tex]= \dfrac{1}{2\sqrt{1+2x}}[/tex]
[tex]\dfrac{d}{dx}(1 + 2x) =\dfrac{d}{dx}(1)} + \dfrac{d}{dx}{2x}\\\\= 0 + 2 \\\\= 2\\[/tex]
Therefore
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5\\\\= 5\dfrac{d}{dx}\left(\sqrt{1+2x}\right)\\\\[/tex]
[tex]= 5\cdot \dfrac{1}{2\sqrt{1+2x}}\cdot \:2\\\\= 5\cdot \dfrac{1}{\sqrt{1 + 2x}}\\\\=\dfrac{5}{\sqrt{1+2x}}[/tex]
ative. Check your work by evaluating the ve rules given in this chapter. 3. g(x)=(1)/(x^(2)+5) 27. 29.
Answers
The five rules given in this chapter are important for algebraic manipulation. Firstly, the Commutative Rule states that when two numbers are added or multiplied, the order of the numbers does not matter.
Secondly, the Associative Rule states that when three or more numbers are added or multiplied, the order in which the operations are performed does not affect the result.
Thirdly, the Distributive Rule states that when a number is multiplied by a sum of two numbers, the number can be distributed to each of the two numbers.
Fourthly, the Additive Identity Rule states that when any number is added to zero, the result is the same number. Finally, the Multiplicative Inverse Rule states that if a number is multiplied by its reciprocal, the result is one.
Together, these five rules form the basis for many algebraic operations. They are important for understanding and manipulating equations, solving for unknowns, and more. By understanding and applying these five rules, students will be able to work more efficiently and accurately with algebraic expressions.
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The diameter of a circle is 38 centimeters. What is the circle's circumference?
Use 3.14 for л.
Answers
Answer: 119.32 centimeters
Step-by-step explanation:
Circumference = diameter x π
C = 38 (3.14)
C = 119.32
The circumference is 119.32 centimeters
Hope this helps!
f/3+22=17
What is f?
Answers
Answer:
To solve for f in the equation:
f/3 + 22 = 17
We need to isolate f on one side of the equation. We can start by subtracting 22 from both sides:
f/3 = 17 - 22
Simplifying the right-hand side:
f/3 = -5
To isolate f, we can multiply both sides by 3:
f = -5 * 3
Simplifying:
f = -15
Therefore, the solution to the equation f/3 + 22 = 17 is f = -15.
Math is not my thing help
Answers
Answer:
mine either hahahahahaha
Problem 7(a). Find the inverse of \( A=\left[\begin{array}{rr}-3 & 0 \\ 0 & 5\end{array}\right] \) 7 (b). Find the inverse of \( A=\left[\begin{array}{rrr}4 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 3\end{arra
Answers
The solution is \boxed{A^{-1} = \left[\begin{array}{rr}-\frac{1}{3} & 0 \\ 0 & -\frac{1}{5}\end{array}\right]} and \boxed{A^{-1} = \left[\begin{array}{rrr}-\frac{1}{6} & 0 & 0 \\ 0 & \frac{1}{12} & 0 \\ 0 & 0 & -\frac{1}{8}\end{array}\right]}.
(a) To find the inverse of \( A=\left[\begin{array}{rr}-3 & 0 \\ 0 & 5\end{array}\right] \), we need to use the formula:
\( A^{-1} = \frac{1}{ad-bc} \left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right] \)
where \( a=-3, b=0, c=0, d=5 \).
Plugging in the values, we get:
\( A^{-1} = \frac{1}{(-3)(5)-(0)(0)} \left[\begin{array}{rr}5 & 0 \\ 0 & -3\end{array}\right] \)
\( A^{-1} = \frac{1}{-15} \left[\begin{array}{rr}5 & 0 \\ 0 & -3\end{array}\right] \)
\( A^{-1} = \left[\begin{array}{rr}-\frac{1}{3} & 0 \\ 0 & -\frac{1}{5}\end{array}\right] \)
So, the inverse of \( A=\left[\begin{array}{rr}-3 & 0 \\ 0 & 5\end{array}\right] \) is \( A^{-1} = \left[\begin{array}{rr}-\frac{1}{3} & 0 \\ 0 & -\frac{1}{5}\end{array}\right] \).
(b) To find the inverse of \( A=\left[\begin{array}{rrr}4 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 3\end{arra \), we need to use the formula:
\( A^{-1} = \frac{1}{\det(A)} \left[\begin{array}{rrr}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]^{T} \)
where \( a_{11}=4, a_{12}=0, a_{13}=0, a_{21}=0, a_{22}=-2, a_{23}=0, a_{31}=0, a_{32}=0, a_{33}=3 \) and \( \det(A) = (4)(-2)(3) - (0)(0)(0) - (0)(0)(0) = -24 \).
Plugging in the values, we get:
\( A^{-1} = \frac{1}{-24} \left[\begin{array}{rrr}4 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 3\end{array}\right]^{T} \)
\( A^{-1} = \frac{1}{-24} \left[\begin{array}{rrr}4 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 3\end{array}\right] \)
\( A^{-1} = \left[\begin{array}{rrr}-\frac{1}{6} & 0 & 0 \\ 0 & \frac{1}{12} & 0 \\ 0 & 0 & -\frac{1}{8}\end{array}\right] \)
So, the inverse of \( A=\left[\begin{array}{rrr}4 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 3\end{arra \) is \( A^{-1} = \left[\begin{array}{rrr}-\frac{1}{6} & 0 & 0 \\ 0 & \frac{1}{12} & 0 \\ 0 & 0 & -\frac{1}{8}\end{array}\right] \).
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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.
21. A path 1 m wide is built along the border and inside a square garden of side 30 m. Find:
(i) the area of the path
(ii) the cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m2
Answers
(i) The area of the path is 120x - 4x² square meters.
(ii) The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² is (900 - 120x + 4x²) × 40
To find the area of the path and the remaining portion of the garden, we need to first find the dimensions of the inner square after the path has been constructed.
Let the width of the path be "x" meters. Then the dimensions of the inner square garden will be (30-2x) meters on each side.
(i) The area of the path can be found by subtracting the area of the inner square from the area of the outer square.
Area of outer square = 30 × 30 = 900 sq.m.
Area of inner square = (30-2x) × (30-2x) = 900 - 120x + 4x² sq.m.
Area of path = Area of outer square - Area of inner square
= 120x - 4x² sq.m.
(ii) The remaining portion of the garden is the area of the inner square.
Area of remaining portion = (30-2x) × (30-2x) sq.m.
= 900 - 120x + 4x² sq.m.
The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² can be found by multiplying the area of the remaining portion by the rate.
Cost of planting grass = Area of remaining portion × Rate
= (900 - 120x + 4x²) × 40
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Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 0.82. If they have four children, what is the probability that exactly two of their four children will have that trait? Round your answer to the nearest thousandth.
Answers
Using binomial distribution, the probability of exactly two of their four children having the trait is 0.13 (rounded to the nearest thousandth).
What is the probability that a child born to them with a certain trait is 0.82This is a binomial distribution problem with n = 4 trials (number of children) and p = 0.82 probability of success (having the trait) for each trial.
The probability of exactly two children having the trait can be calculated using the binomial distribution formula:
P(X = 2) = (4C2) * 0.82^2 * (1 - 0.82)^(4-2)
where (4C 2) is the number of ways to choose 2 children out of 4.
Using a calculator or statistical software, we get:
P(X = 2) = (4 C 2) * 0.82^2 * (1 - 0.82)^(4-2)
= 6 * 0.82^2 * 0.18^2
= 0.13
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I’ll give brainlyyyyy
Answers
Answer:
CD = 22
Step-by-step explanation:
You would double the side lengths given since this is a rectangle and set them equal to 80 cause that is the perimeter. So the equation would be 6z + 6 + 8z + 4 = 80. You would use the PEDMAS rule and subtract 6 from both sides which gives you:
6z + 8z +4 = 74
Subtract 4 from both sides
6z + 8z = 70
Add 6z + 8z
14z = 70
Divide 70 and 14z
z = 5.
AB and CD is equal in length so all you have to do is plug in 5 to z in the AB equation.
4(5) + 2
= 22
