To obtain an orthogonal basis of Col(K) using the Gram-Schmidt process, we start with the given vectors in K:
v₁ = [1, -1, 3, 1],
v₂ = [0, -1, -2, 1],
v₃ = [-3, 0, -1, -1],
v₄ = [2, 6, 3, 2],
v₅ = [-1, 2, -1, 0],
v₆ = [1, 0, 1, 0].
We will perform the Gram-Schmidt process step by step:
Step 1: Set the first vector as the first basis vector:
u₁ = v₁ = [1, -1, 3, 1].
Step 2: Compute the projection of v₂ onto u₁ and subtract it from v₂ to obtain the second orthogonal vector:
u₂ = v₂ - projₙ(v₂, u₁),
where projₙ(v, u) is the projection of vector v onto vector u.
Calculating the projection:
projₙ(v₂, u₁) = (v₂ · u₁) / (u₁ · u₁) * u₁,
where · denotes the dot product.
projₙ(v₂, u₁) = ((0*1) + (-1*(-1)) + (-2*3) + (1*1)) / ((1*1) + (-1*(-1)) + (3*3) + (1*1)) * [1, -1, 3, 1],
projₙ(v₂, u₁) = 2/12 * [1, -1, 3, 1],
projₙ(v₂, u₁) = [1/6, -1/6, 1/2, 1/6].
Subtracting the projection from v₂:
u₂ = v₂ - projₙ(v₂, u₁),
u₂ = [0, -1, -2, 1] - [1/6, -1/6, 1/2, 1/6],
u₂ = [5/6, -5/6, -11/6, 5/6].
Step 3: Repeat the process for the remaining vectors v₃, v₄, v₅, and v₆.
u₃ = v₃ - projₙ(v₃, u₁) - projₙ(v₃, u₂),
u₄ = v₄ - projₙ(v₄, u₁) - projₙ(v₄, u₂) - projₙ(v₄, u₃),
u₅ = v₅ - projₙ(v₅, u₁) - projₙ(v₅, u₂) - projₙ(v₅, u₃) - projₙ(v₅, u₄),
u₆ = v₆ - projₙ(v₆, u₁) - projₙ(v₆, u₂) - projₙ(v₆, u₃) - projₙ(v₆, u₄) - projₙ(v₆, u₅).
Calculating each projection and subtraction, we get:
u₃ = [13/3, 1/3, 5/3, 1/3],
u₄ = [4/15, 26/15, -1/15, -2/15],
u₅ = [2/5, -4/5, -1/5
, 0],
u₆ = [5/13, 0, 5/13, 0].
Therefore, an orthogonal basis for Col(K) is given by:
{u₁, u₂, u₃, u₄, u₅, u₆} = {[1, -1, 3, 1], [5/6, -5/6, -11/6, 5/6], [13/3, 1/3, 5/3, 1/3], [4/15, 26/15, -1/15, -2/15], [2/5, -4/5, -1/5, 0], [5/13, 0, 5/13, 0]}.
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WHAT DOES THE WORD MILD MEAN
A HUMID
B MOSTLY COULD
C NO TOO HOT OR TOO COLD
D NEVER THE SAME
Answer:
C NO TOO HOT OR TOO COLD
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
Brainliest plz
Karen has $33 to buy pencils for her art school. She buys boxes of pencils that each cost $1.50 and is left with $9 after her purchase. How many boxes of pencils did she buy? Enter your answer in the box below.
Answer:16
Step-by-step explanation:
33-9=24
24/1.50=16
i dont actually have a question to put here so look at the photo
Answer:
it's the third option
Step-by-step explanation:
I think I'm pretty sure
hope this helped ;)
(PLEASE PLEASE HELP)
Find the area of the triangle.
Answer:
40.2 in²
Step-by-step explanation:
h*b/2
h= 6.7
b= 12
37.7in
aments
endar
7. A cylindrical test tube holds 6n cm3 of liquid when filled to the 6 cm mark. What is the
diameter of the
test tube to the nearest hundredth of a centimeter?
Answer:
Rewrite the question correctly! it's totally absurd
- A computer modem can transmit
1.5 X 10 bytes per second. How many
bytes can it transmit in 300 seconds?
Write your answer in scientific notation.
b. A child appears to be running into the street ahead. It takes 2.3 seconds for the driver to react and begin to brake, but this time at a rate of -7.5 m/s2. What is the stopping distance for the car in this situation?
Answer:
I got about 28.01 ft you might want to round or something
hope this helped
The required stopping distance of the car is 17.24 metes.
A child appears to be running into the street ahead. It takes 2.3 seconds for the driver to react and begin to brake, but this time at a rate of -7.5 m/s2. What is the stopping distance for the car in this situation is to be determined.
What is speed?Speed is ratio of distance to the time. speed = distance / time.
The intial speed of the driver is 11m/s
Now total stopping distance = thinking distance + break applying distance
= v*t + u²/2a
= 11 * 2.3 - 11²/2*7.5
= 17.24 meters,
Thus, the required stopping distance of the car is 17.24 metes.
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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 x < 0 x2 16 0 ? x ? 4 1 4 ? x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ? 1). (b) Calculate P(0.5 ? X ? 1). (c) Calculate P(X > 1.5). (d) What is the median checkout duration mu tilde? [solve 0.5 = F(mu tilde)]. (e) Obtain the density function f(x). f(x) = F?'(x) = (f) Calculate E(X). (g) Calculate V(X) and ?x. V(X) = ?x = (h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].
X denote the amount of time a book on two-hour reserve is actually checked out, and for the given cdf the following are the answers for the questions asked
(a) P(X ≤ 1) ≈ 0.0625
(b) P(0.5 ≤ X ≤ 1) ≈ 0.0469
(c) P(X > 1.5) ≈ 0.8594
(d) Median checkout duration ≈ 2.828
(e) Density function f(x) is defined as:
f(x) = 0 for x < 0
f(x) = x/8 for 0 ≤ x ≤ 4
f(x) = 0 for x > 4
(f) Expected value E(X) ≈ 2.667
(g) Variance V(X) ≈ 0.889, Standard Deviation σ(X) ≈ 0.943
(h) Expected charge E[h(X)] = 8
In probability theory, a cumulative distribution function (CDF) provides information about the probabilities of certain events occurring in a random variable. In this scenario, let's consider a book that is on a two-hour reserve and denote the amount of time it is checked out as X. We are given the CDF of X and we will use it to calculate various probabilities and statistics related to the checkout duration of the book.
The given CDF is as follows:
F(x) = 0 for x < 0
F(x) = x²/16 for 0 ≤ x ≤ 4
F(x) = 1 for x > 4
(a) P(X ≤ 1):
To calculate this probability, we need to find F(1) since F(x) represents the cumulative probability up to x. From the given CDF, we see that F(x) = x²/16 for 0 ≤ x ≤ 4. Substituting x = 1 into the equation, we get:
F(1) = (1²)/16 = 1/16.
(b) P(0.5 ≤ X ≤ 1):
To calculate this probability, we need to find F(1) - F(0.5) since F(x) represents the cumulative probability up to x. From the given CDF, we have F(0.5) = (0.5²)/16 = 1/64 and F(1) = (1²)/16 = 1/16. Therefore,
P(0.5 ≤ X ≤ 1) = F(1) - F(0.5) = (1/16) - (1/64) = 3/64.
(c) P(X > 1.5):
To calculate this probability, we need to find 1 - F(1.5) since F(x) represents the cumulative probability up to x. From the given CDF, we have F(1.5) = (1.5²)/16 = 9/64. Therefore,
P(X > 1.5) = 1 - F(1.5) = 1 - (9/64) = 55/64.
(d) Median checkout duration:
The median is the value that divides the distribution into two equal parts, meaning that half of the checkouts are below this value and half are above it. We need to solve the equation F(median) = 0.5. From the given CDF, we have:
F(median) = 0.5
0.5 = (median²)/16
Solving for the median, we get median = √(8) ≈ 2.828.
(e) Density function f(x):
The density function f(x) represents the derivative of the cumulative distribution function F(x). To obtain f(x), we differentiate the given CDF:
f(x) = F'(x)
For x < 0, f(x) = 0 since F(x) is constant in that range.
For 0 ≤ x ≤ 4, we have F(x) = x²/16.
Differentiating with respect to x, we get:
f(x) = d/dx (x²/16) = (2x)/16 = x/8.
For x > 4, f(x) = 0 since F(x) is constant in that range.
Therefore, the density function f(x) is:
f(x) = 0 for x < 0
f(x) = x/8 for 0 ≤ x ≤ 4
f(x) = 0 for x > 4
(f) Expected value E(X):
The expected value of a random variable X is a measure of its average value. To calculate E(X), we integrate the product of x and the density function f(x) over the entire range of X:
E(X) = ∫[x * f(x)] dx
For x < 0 and x > 4, f(x) = 0, so we only need to consider the interval 0 ≤ x ≤ 4:
E(X) = ∫[x * (x/8)] dx
= (1/8) ∫[x²] dx (integrating x²)
= (1/8) * (x³/3) + C (integrating x²)
= (1/24) * (x³) + C
Evaluating this expression from x = 0 to x = 4, we get:
E(X) = (1/24) * (4³) - (1/24) * (0³)
= 64/24
= 8/3
≈ 2.667
(g) Variance V(X) and Standard Deviation σ(X):
Variance is a measure of the spread or dispersion of a random variable. To calculate V(X), we need to calculate the second moment E(X²) and subtract the square of the expected value [E(X)]². The standard deviation σ(X) is the square root of the variance.
E(X²):
E(X²) = ∫[x² * f(x)] dx
For x < 0 and x > 4, f(x) = 0, so we only need to consider the interval 0 ≤ x ≤ 4:
E(X²) = ∫[x² * (x/8)] dx
= (1/8) ∫[x³] dx (integrating x³)
= (1/8) * (x⁴/4) + C (integrating x³)
= (1/32) * (x^4) + C
Evaluating this expression from x = 0 to x = 4, we get:
E(X²) = (1/32) * (4⁴) - (1/32) * (0⁴)
= 256/32
= 8
V(X):
V(X) = E(X²) - [E(X)]²
= 8 - (8/3)²
= 8 - 64/9
= 8 - 7.111
≈ 0.889
Standard deviation:
σ(X) = √(V(X))
= √(0.889)
≈ 0.943
(h) Expected charge E[h(X)]:
Given the function h(X) = X², we want to calculate the expected value of h(X). This can be done by finding E[h(X)] = E(X²).
From the previous calculations, we know that E(X²) = 8. Therefore, the expected charge is E[h(X)] = 8.
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What is an appropriate horizontal scale and vertical scale for the viewing window?
a. Horizontal scale: 1 unit = 10, Vertical scale: 1 unit = 5
b. Horizontal scale: 1 unit = 5, Vertical scale: 1 unit = 10
c. Horizontal scale: 1 unit = 1, Vertical scale: 1 unit = 1
d. Horizontal scale: 1 unit = 10, Vertical scale: 1 unit = 10
option D: Horizontal scale: 1 unit = 10, Vertical scale: 1 unit = 10 is the correct answer.
To determine an appropriate horizontal scale and vertical scale for the viewing window, one must analyze the problem, the graph, and the data presented in the problem. The appropriate horizontal scale and vertical scale for the viewing window is given by option D, that is Horizontal scale: 1 unit = 10, Vertical scale: 1 unit = 10. The horizontal scale and vertical scale refer to the scale of the x-axis and y-axis of the graph. These scales are used to represent data in a graphic format that can be easily understood by readers. The horizontal scale is used to determine the value of the x-axis in the graph. The vertical scale is used to determine the value of the y-axis in the graph. The scale should be chosen based on the range of values in the graph. When the values in the graph are too small or too large, the scale must be adjusted accordingly. In this case, since the values of horizontal and vertical scale are large, the scale must be adjusted accordingly. Therefore, option D is the correct answer.
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The size of the horizontal and vertical scales should be chosen so that the graph fits in the viewing window. So, that is why the answer is "b. Horizontal scale: 1 unit = 5, Vertical scale: 1 unit = 10."
When graphing a function, it is important to choose an appropriate horizontal scale and vertical scale for the viewing window. The answer is "b. Horizontal scale: 1 unit = 5, Vertical scale: 1 unit = 10."Why is the answer (b) Horizontal scale: 1 unit = 5, Vertical scale: 1 unit = 10?The answer to this question is based on the graph. It is more appropriate to use (b) horizontal scale: 1 unit = 5, vertical scale: 1 unit = 10. In this situation, the x-axis should have a horizontal scale of 1 unit = 5 so that the x-axis can fit within the viewing window. Meanwhile, the y-axis should have a vertical scale of 1 unit = 10 so that the entire graph can fit in the viewing window.
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Please help soon!!!!!
i need help with this question -10 + 3√2.
Answer:
-5.75736 or [tex]\frac{1}{-10+3√2}[/tex]
Step-by-step explanation
HURRY I NEED HELP PLS
Find the volume of each solid. Round to the nearest tenth if necessary.
Answer:
3,454 cm³
Step-by-step explanation:
This is a cylinder so the volume formula is [tex]V=\pi r^{2} h[/tex]
The problem gives us the diameter (20 cm) and the height (11 cm). Since the formula uses the radius instead of the diameter, we have to divide the diameter by 2.
20 ÷ 2 = 10
The radius is 10 cm
Now, we plug our height and radius into the formula to find the volume.
[tex]V=\pi r^{2} h\\V=(\frac{22}{7})(10)^{2}(11)\\V=(\frac{22}{7})(100)(11)\\[/tex]
V≈3,454
Which angle is congruent to <4 <1<2<5<8
Answer:
The angle that will be congruent to angle 4 is :
Angle 1
Step-by-step explanation:
It is given that:
angle 4 and angle 5 are complements.
Also, angle 1 and angle 5 are complements.
Congruent complementary Theorem--
It states that if two angles are complementary to the same angle, then the two angles are congruent to each other.
Here both angle 1 and angle 4 are complementary to the same angle i.e. angle 5.
WILL NAME BRAINLIST! The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. 1 in 1 in. 3 in. What is ine area of one trapezoidal face of the figure? ___ in. 2
Area= 1/2 (a+b)h
1/2(1in. +3in.)1in.
1/2(4in.)1in.
2in.× 1in.
2in. Therefore the area is 2in.
Need help with this question thank you!
Answer:
(5,-1)
Step-by-step explanation:
The researchers are in short of budget so they would like to minimize the respondents needed for their research. They decided to use σ = 0.4 with CL = 92.5% but they are undecided on 1% and 2% margin of error. Help the researchers on choosing between the two margin of errors if their best of interest is the least possible number of respondents. [6 points]
(a) Find Z.
(b) Determine the 2 sample sizes.
(c) Write your conclusion.
(a) The Z-Score is 1.78,
(b) The two sample-sizes are 5070 and 1268,
(c) The researchers should choose the 2% margin-of-error.
Part (a) : To find Z, we use the confidence-level (CL) to find the corresponding Z-score.
The confidence-level (CL) is given as 92.5%, which corresponds to an area of 0.925 under the standard normal-distribution curve. Since the remaining area on both tails is (1 - 0.925) = 0.075, we divide this value by 2 to get the area for one tail: 0.075/2 = 0.0375,
The "Z-score" that corresponds to area of 0.0375 in one tail. The Z-score is approximately 1.78,
Part (b) : To determine the two sample sizes for the 1% and 2% margin of error, we use the formula,
Sample size (n) = (Z² × σ²)/(E²),
For a 1% margin-of-error (E = 0.01),
We have,
n₁ = (1.78² × 0.4²)/(0.01²),
n₁ ≈ 5070
For a 2% margin of error (E = 0.02),
We have,
n₂ = (1.78² × 0.4²)/(0.02²),
n₂ ≈ 1268
Part (c) : The researchers should choose the margin-of-error that results in the least possible number of respondents since they have a limited budget.
Comparing the two sample-sizes, we find that sample-size for 2% margin of error (n₂ ≈ 1268) is smaller than the sample-size for the 1% margin of error (n₁ ≈ 5070).
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Each side of a square has a length of 5x. Use your area expression to find the area of the square when x = 2.2 centimeters. Show your work.
*edit (please it's 3:54 AM and I want to go to bed)
Answer:
121 centimeters ²
Step-by-step explanation:
Area of a square = length ²
Each side of a square = 5x
find the area of the square when x = 2.2 centimeters
Area of a square = length ²
= (5x)²
= 5x * 5x
= 5(2.2) * 5(2.2)
= 11 * 11
= 121 centimeters ²
Area of a square = 121 centimeters ²
If the two equations in a system of linear equations are added and the results is 9x=0 the system has no solution
Answer:
0
Step-by-step explanation:
HOPE I HELPED!
What are the next three terms of this pattern?
- 4, - 7, - 2, -5, 0, __, __, __
Answer:
-4, -7, -2, -5, 0, -3, 2, -1
Step-by-step explanation:
the pattern is -3, +5.
i hope this helps :)
Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. = = = F = (-2x + 10y) i +(6x -8y)}; C is the region bounded above by y=-3x 2 + 7 and below by y = 4x2 in the first quadrant O -3 64 4ဝ O 56 3 24
The counterclockwise circulation of the vector field F around the closed curve C is 112/3 (or approximately 37.33).
To compute the counterclockwise circulation of the vector field F = (-2x + 10y)i + (6x - 8y)j around the closed curve C, we can apply Green's Theorem.
Green's Theorem states that the counterclockwise circulation of a vector field around a closed curve C is equal to the double integral of the curl of the vector field over the region R enclosed by the curve.
First, let's obtain the curl of the vector field F:
curl(F) = (∂F₂/∂x - ∂F₁/∂y)k
= (6 - (-2))k
= 8k
Now, let's obtain the region R enclosed by the curve C. The curve is described by two functions:
Upper curve: y = -3x^2 + 7
Lower curve: y = 4x^2
To get the limits of integration, we need to determine the x-values where the curves intersect. Setting the upper and lower curves equal to each other:
-3x^2 + 7 = 4x^2
7 = 7x^2
x^2 = 1
x = ±1
Since we are only considering the first quadrant, we take the positive value, x = 1.
The limits of integration for x will be from 0 to 1.
For y, the limits are determined by the upper and lower curves:
y = -3x^2 + 7
y = 4x^2
The limits of integration for y will be from 4x^2 to -3x^2 + 7.
Now, we can set up the double integral to calculate the counterclockwise circulation using Green's Theorem:
Circulation = ∬R curl(F) · dA
= ∬R 8k · dA
= 8 ∬R dA
Integrating with respect to x and y over the region R:
Circulation = 8 ∫[0,1] ∫[4x^2, -3x^2 + 7] dy dx
Evaluating the double integral will give us the counterclockwise circulation of F around the closed curve C.
Circulation = 8 ∫[0,1] ∫[4x^2, -3x^2 + 7] dy dx
First, we integrate with respect to y:
Circulation = 8 ∫[0,1] [y] |[4x^2, -3x^2 + 7] dx
= 8 ∫[0,1] ((-3x^2 + 7) - 4x^2) dx
= 8 ∫[0,1] (-7x^2 + 7) dx
= 8 [-7/3 * x^3 + 7x] |[0,1]
= 8 [(-7/3 * 1^3 + 7 * 1) - (-7/3 * 0^3 + 7 * 0)]
= 8 [-7/3 + 7]
= 8 [-7/3 + 21/3]
= 8 [14/3]
= 112/3
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Which of the following numbers is not a
rational number?
A. -3
B. 2.7
C. 14
D. 15
Trick question! All are rational numbers.
..................................................................................
The total cost of a catered meal for the Armstrong family reunion was to be split equally by the 20 people who came. Before the meal started, five more Armstrong's unexpectedly appeared. The total cost was shared equally among the 25 people, and so each person in the original group owed $4 less. What was the total cost of the catered meal?
Answer:
$400
Step-by-step explanation:
Let the initial total cost be represented = $X.
Hence, for 20 family members
= $ x/20 each .......1
Now that they are 25 members
= $x/25 each.......2
Each in the original group which is equation 1 owed $4 less.
That is,
x/20 - 4 ........ 3
Now equate 2 and 3
X/20 - 4/1 = X/25
Taking the LCM of both sides
X-80/20 = X/25
Cross multiply both sides
25( x-80 ) = 20x
25x-2000 = 20x
Collecting like terms
25x-20x = 2000
5x = 2000
Divide through by 5
X = 2000/5
X = 400
The total cost for the catered meal is $400.
To check if it was correct
Put 400 into equation 1 and 2 and then minus whatever you get from each other, you will get $4
From equation 1
400/20 = $20
From equation 2
400/25 =$16
$20-$16 = $4
Thanks
Calculate the third-order Taylor Polynomial P3 (x), about xo for f(x) (2) Use the polynomial in part (1) to approximate f(0.1) 0.1 1dx (3) Use the polynomial in part (1) to approximate 0.¹ 1+x 1+x
a. The third-order Taylor polynomial, P3(x) = f(xo) + f'(xo)(x - xo) + (f''(xo)(x - xo)^2)/2 + (f'''(xo)(x - xo)^3)/6.
b. The polynomial P3(x) obtained in part a can be used to approximate f(0.1).
c. The polynomial P3(x) obtained in part a can be used to approximate the integral of (1+x)/(1+x^2) from 0 to 0.1.
a. To calculate the third-order Taylor polynomial P3(x) about xo for f(x), we need to find the values of f(x), f'(x), f''(x), and f'''(x) at x = xo. Once we have these values, we can use the formula: P3(x) = f(xo) + f'(xo)(x - xo) + (f''(xo)(x - xo)^2)/2 + (f'''(xo)(x - xo)^3)/6. Plugging in the values of f(xo), f'(xo), f''(xo), and f'''(xo) will give us the third-order Taylor polynomial.
b. The polynomial P3(x) obtained in part a can be used to approximate the value of f(0.1). We can substitute x = 0.1 into P3(x) to obtain the approximation.
c. Similarly, the polynomial P3(x) obtained in part a can be used to approximate the integral of (1+x)/(1+x^2) from 0 to 0.1. We can evaluate the polynomial P3(x) at x = 0.1 and substitute the result into the integral expression.
In summary, the third-order Taylor polynomial P3(x), about xo, for f(x) is calculated using the formula involving the values of f(xo), f'(xo), f''(xo), and f'''(xo). This polynomial can then be used to approximate the value of f(0.1) and the integral of a given function.
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Is it just me or do you guys get annoyed when people give us a whole explanation like, I only need the letter of the answer.
Answer:
Yes lol
Step-by-step explanation:
Well the app says it helps people learn the answers but when I'm in a test i just look at letters:)
Answer:
I mean i'm the type to give a long winded answer. But i guess it depends on the context. Sometimes people ask for an explanation yk? Like most of those ppl who ask questions for History and English need a written response.
need help asap hurry
Answer:
4(x+5)
Step-by-step explanation:
according to your question
y=A + cx is the general solution of the exact DEQ: Y- xy' = 75. 75. Determine A.
The exact value of A in the general solution y = A + cx is 75
How to determine the value of A in the general solutionFrom the question, we have the following parameters that can be used in our computation:
y = A + cx
The differential equation is given as
y - xy' = 75
When y = A + cx is differentiated, we have
y' = c
So, we have
y - xc = 75
Recall that
y = A + cx
So, we have
A + cx - xc = 75
Evaluate the like terms
A = 75
Hence, the value of A in the general solution is 75
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Determine the number of triangles ABC possible with the given parts.
A=43.7° a 8.7 b = 10.3
How many possible solutions does this triangle have?
Given: A = 43.7°, a = 8.7, and b = 10.3We can find the number of possible triangles by using the Law of Sines, which states that a / sin A = b / sin B = c / sin C, where a, b, and c are the side lengths and A, B, and C are the opposite angles. Let's first use the Law of Sines to find the value of sin B: a / sin A = b / sin B => sin B = b sin A / a.
Substituting the given values, we get: sin B = 10.3 sin 43.7° / 8.7≈ 0.641Now we know the value of sin B. We can use the inverse sine function (sin⁻¹) to find the possible values of angle B: B = sin⁻¹ (0.641)≈ 40.4° or B ≈ 139.6°Note that there are two possible angles for B because sine is a periodic function that repeats every 360°.Now that we know the possible values of angle B, we can use the fact that the sum of the angles of a triangle is 180° to find the possible values of angle C: C = 180° - A - B. For B = 40.4°, we get: C = 180° - 43.7° - 40.4° = 95.9°For B = 139.6°, we get: C = 180° - 43.7° - 139.6° = -2.3°Note that we get a negative value for angle C in the second case, which is not possible because all angles of a triangle must be positive. Therefore, the second case is not valid and we only have one possible triangle. Answer: There is only one possible triangle.
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What is the value of a ?
The value of a in the given function is 4
What is the value of a?To find the value of a in the equation f(g(x)) = (1 - x²)³, we need to substitute the function g(x) = a + x² into the function f(x) = (5 - x)³.
Replacing x in f(x) with g(x), we have:
f(g(x)) = (5 - g(x))³.
Substituting g(x) = a + x², we get:
f(g(x)) = (5 - (a + x²))³.
f(g(x)) = (5 - a - x²)³.
Comparing this expression with (1 - x²)³, we can equate the corresponding terms:
5 - a - x² = 1 - x².
5 - a = 1.
a = 5 - 1
a = 4
Therefore, the value of a is 4.
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Which of the following is not a solution for finding the perimeter of the square?
Answer:
y
Step-by-step explanation:
y needs to provide a number
6v=-9 v= what does v =
Answer:
v = -3/2
Step-by-step explanation:
6v = -9
v = -9/6
v = -3/2