Given: /\ABC, KM || AC

a) AB=10, KB=2, KM=1

AC-?

b) KM=3, AC=6,BC=9

BM-?

c)BC=25, MC=10, AC=5

KM-?

d)AK=10,KB=4,BC=21

BM-?,MC-?

The ratio of red to blue squares is given by the division of the number of red squares by the number of blue squares.

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:

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.

The problem is incomplete, hence the general procedure to obtain the ratio is presented.

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tan 49° = x/55

tan Θ = opposite/adjacent

x - opposite

55 cm - adjacent

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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The requried rate of change of the function f[x] on the interval -5 ≤ x ≤ 0 is F(x)' = -11/5.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
From the graph we have,
F(-5) = 1 and F(0) = -10

So the rate of change is given as,
F(x)' = F(0) - F(-5) / 0 + 5
F(x)' = -10 - 1 / 5
F(x)' = -11/5

Thus, the requried rate of change of the function f[x] on the interval -5 ≤ x ≤ 0 is F(x)' = -11/5.

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The augmented matrix of a system of linear equations is given: , determine value(s) of k if 2 k - 2 if  the system has no solution there are no values of k that will make the system inconsistent.  The system has one solution for all values of k except k = 4.The system has infinitely many solutions if k = 0, a unique solution if k ≠ 0 and k ≠ 4, and no solutions if k = 4

To determine the value(s) of k for each case, we will perform row reduction on the augmented matrix and analyze the resulting echelon form.

1 3 1 | 0

2 k - 2 | 0

R2 - 2R1 -> R2

1 3 1 | 0

0 k - 4 | 0

Case (a): If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions. If k ≠ 4, then we can use back-substitution to find the solution(s):

k - 4 = 0 => k = 4

Since this contradicts our assumption, there are no values of k that will make the system inconsistent.

Case (b): If k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions.

Case (c): If k = 0, then the second row reduces to 0 = 0, which means we have a free variable and infinitely many solutions. If k ≠ 0 and k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the system is inconsistent with no solutions.

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Answer:

Step-by-step explanation:

ok so first u do 12 times 2 and then divide by 3

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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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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Answer: 6 and 12

Step-by-step explanation:

The equation for the line that passes through the point (4, -4) and is parallel to the line with the equation -6x - 2y = 14 is y = -3x + 8.

To find the equation for the line that passes through the point (4, -4) and is parallel to the line with the equation -6x - 2y = 14, we first need to find the slope of the given line. We can do this by rearranging the equation to solve for y and putting it in slope-intercept form, y = mx + b.

-6x - 2y = 14

-2y = 6x + 14

y = -3x - 7

The slope of the given line is -3. Since the line we are trying to find is parallel to the given line, it will have the same slope. Therefore, the slope of the line we are trying to find is also -3.

Now, we can use the point-slope form of a linear equation, y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line, to find the equation of the line. Plugging in the slope and the point (4, -4), we get:

y - (-4) = -3(x - 4)

y + 4 = -3x + 12

y = -3x + 8

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gf(x) = (x-5)(7x)

Part 1
a) The domain of f is all real numbers, since 7x is defined for all real numbers x. The domain of g is all real numbers, since x-5 is defined for all real numbers x. The domain of f+g is all real numbers, since the sum of two real numbers is a real number. The domain of f-g is all real numbers, since the difference of two real numbers is a real number. The domain of fg is all real numbers for which the product 7x(x-5) is defined, which is all real numbers except for x=5. The domain of ff is all real numbers, since the product of two real numbers is a real number. The domain of fg is all real numbers, since the product of two real numbers is a real number. The domain of gf is all real numbers, since the product of two real numbers is a real number.

b) (f+g)(x) = 7x + x - 5 = 8x - 5
(f-g)(x) = 7x - x + 5 = 6x + 5
(fg)(x) = 7x(x-5)
(ff)(x) = (7x)^2
fg(x) = (7x)(x-5)
gf(x) = (x-5)(7x)

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The polynomial P(x) must have a degree of 4.

This is because a polynomial with real coefficients must have complex zeros in conjugate pairs. This means that if 1+i is a zero of the polynomial, then its conjugate, 1-i, must also be a zero. Similarly, if 2-i is a zero, then its conjugate, 2+i, must also be a zero. Therefore, the polynomial P(x) must have zeros at 1, 1+i, 1-i, 2-i, and 2+i. Since a polynomial's degree is equal to the number of its zeros, the polynomial must have a degree of 4.

In summary, a polynomial with real coefficients and zeros at 1, 1+i, and 2-i must have a degree of 4.

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According to the given information, the probabilites are a) 0.159, b)0.107, d) 0.893 e) 0.662 c) expected value is 12.192 f) standard deviation is 3.0121.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a) Using the binomial probability formula, we have:

P(X = 13) = (48)^13 * (0.254)^13 * (0.746)^35

= 0.159

So the probability that 13 out of 48 flowers will bloom early is 0.159.

b) To find the probability that fewer than 13 flowers will bloom early, we can find the cumulative probability up to 12:

P(X < 13) = P(X = 0) + P(X = 1) + ... + P(X = 12)

= ∑(48 choose k) * (0.254)^k * (0.746)^(48-k) from k=0 to 12

= 0.107

So the probability that fewer than 13 flowers will bloom early is 0.107.

c) The expected value of a binomial distribution is given by n*p, where n is the number of trials and p is the probability of success. In this case, we have:

E(X) = 48 * 0.254

= 12.192

So on average, we expect to observe about 12.192 early blooming flowers.

d) To find the probability that at least 13 flowers will bloom early, we can use the complement rule and find the probability that 12 or fewer flowers will bloom early, and subtract that from 1:

P(X ≥ 13) = 1 - P(X < 13)

= 1 - 0.107

= 0.893

So the probability that at least 13 flowers will bloom early is 0.893.

e) To find the probability that between 9 and 14 flowers (inclusive) will bloom early, we can find the cumulative probability from 9 to 14:

P(9 ≤ X ≤ 14) = P(X = 9) + P(X = 10) + ... + P(X = 14)

= ∑(48 choose k) * (0.254)^k * (0.746)^(48-k) from k=9 to 14

= 0.662

So the probability that between 9 and 14 flowers (inclusive) will bloom early is 0.662.

f) The variance of a binomial distribution is given by np(1-p), and the standard deviation is the square root of the variance. In this case, we have:

Var(X) = 48 * 0.254 * (1-0.254)

= 9.078

SD(X) = sqrt(Var(X))

= sqrt(9.078)

= 3.0121 (rounded to 4 decimal places)

So the standard deviation of the number of flowers that bloom early in a row of 48 flowers is approximately 3.0121.

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Answer:

54w²

Step-by-step explanation:

42w² + 15w²-3w²

42w²+ 15w²= 57w²

57w²-3w²= 54w²

a) maximum profit 20.5.

b) maximum profit 20,025.

c)  price 10.35

The given function, f(p)=-50p+2050p-20,700, is not a degree 3 polynomial. It is a degree 1 polynomial or a linear function. Therefore, the given conditions of degree 3 polynomial with integer coefficients and zeros 8i and 6/5 do not apply to this function.

Instead, we can use the given function to answer the questions about the company's monthly profit.

(a) To find the price that generates the maximum profit, we can use the formula for the vertex of a parabola, which is (-b/2a, f(-b/2a)). In this case, a = -50 and b = 2050.
The price that generates the maximum profit is -b/2a = -2050/(2*-50) = 20.5.

(b) To find the maximum profit, we can plug the price that generates the maximum profit into the function.
f(20.5) = -50(20.5) + 2050(20.5) - 20,700 = 20,025.

(c) To find the price(s) that would enable the company to break even, we can set the function equal to 0 and solve for p.
0 = -50p + 2050p - 20,700
20,700 = 2000p
p = 10.35

Therefore, the price that would enable the company to break even is 10.35. There is only one price that would enable the company to break even.

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The value of −tanx is 1−secx, which is option c) in the given choices.

The correct answer is option c) 1−secx.

To find the value of −tanx, we can use the identity tanx = sinx/cosx. Multiplying both sides of the equation by −1 gives us −tanx = −sinx/cosx.

We can then substitute the value of cosx from the given equation into the equation for −tanx:

−tanx = −sinx/(1−sinx)

Multiplying both sides of the equation by (1−sinx) gives us:

−tanx(1−sinx) = −sinx

Distributing the −tanx on the left side of the equation gives us:

−tanx + tanx*sinx = −sinx

Rearranging the equation and factoring out sinx gives us:

tanx*sinx + sinx = tanx

sinx(tanx + 1) = tanx

Dividing both sides of the equation by (tanx + 1) gives us:

sinx = tanx/(tanx + 1)

Using the identity 1/cosx = secx, we can substitute secx for 1/cosx in the equation:

sinx = (sinx/cosx)/(sinx/cosx + 1/cosx)

Simplifying the equation gives us:

sinx = sinx/(sinx + secx)

Cross multiplying and rearranging the equation gives us:

sinx*(sinx + secx) = sinx

sinx^2 + sinx*secx = sinx

Subtracting sinx from both sides of the equation gives us:

sinx^2 + sinx*secx - sinx = 0

Factoring out sinx gives us:

sinx(sinx + secx - 1) = 0

Setting each factor equal to 0 gives us:

sinx = 0 or sinx + secx - 1 = 0

Solving for secx in the second equation gives us:

secx = 1 - sinx

Therefore, the value of −tanx is 1−secx, which is option c) in the given choices.

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Answer:

1.8 i think

Step-by-step explanation:

i used a calculator

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.

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

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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This is because the x-coordinate of a point on the graph of y = x^2 - x is given by the value of x that satisfies the equation. Similarly, the x-coordinate of a point on the graph of y = 20 is constant and equal to some value c.

To find the x-coordinates of the points where the graphs of the equations y = x^2 - x and y = 20 intersect, we need to solve the system of equations:

y = x^2 - x

y = 20

Since both equations are equal to y, we can set them equal to each other:

x^2 - x = 20

Now, if we solve for x, we will get the x-coordinates of the points where the two graphs intersect.

Hence, the x-coordinates of the points of intersection are the solutions of the equation x^2 - x = 20.

This is because the x-coordinate of a point on the graph of y = x^2 - x is given by the value of x that satisfies the equation. Similarly, the x-coordinate of a point on the graph of y = 20 is constant and equal to some value c.

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Answer:

the ans is f(x)=1.7x+21,472

The equation of the function is exponential and the function is f(x) = 21472(1.017)ˣ.

The population of a small town in Connecticut is 21,472 and the expected population growth is 1.7% each year.

Let's use a function to represent the town's population x years from now.

Hence,

1.7% = 1.7  / 100 = 0.017

Therefore,

f(x) = 21472(1 + 0.017)ˣ

Hence,

f(x) = 21472(1.017)ˣ

Therefore, the function is exponential.

The equation of the function is f(x) = 21472(1.017)ˣ

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(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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The value of x in the function 4x+6=8x-22 is 7.

The slope is equal to -10.

The slope-intercept form of the function 4x+5y=24 is y = -4x/5 + 24/5.

The value of f(-5) is equal to -36.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m = (-12 - 8)/(-4 + 6)

Slope, m = -20/2

Slope, m = -10.

4x+6=8x-22

8x - 4x = 22 + 6

4x = 28

x = 7.

4x + 5y = 24

5y = -4x + 24

y = -4x/5 + 24/5

For f(-5), we have:

f(x)=7x-1

f(-5)=7(-5)-1

f(-5) = -36.

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To find a general solution to the equation ax^(2) + bx + 1 = 0 using the completion of the square, we need to follow these steps:

1. Divide the entire equation by a to get x^(2) + (b/a)x + 1/a = 0.

2. Move the constant term to the right side of the equation: x^(2) + (b/a)x = -1/a.

3. Complete the square by adding (b/2a)^(2) to both sides of the equation: x^(2) + (b/a)x + (b/2a)^(2) = -1/a + (b/2a)^(2).

4. Factor the left side of the equation: (x + b/2a)^(2) = -1/a + (b/2a)^(2).

5. Take the square root of both sides of the equation: x + b/2a = ±√(-1/a + (b/2a)^(2)).

6. Solve for x: x = -b/2a ± √(-1/a + (b/2a)^(2)).

This is the general solution to the equation.

The conditions for both solutions to be real are that the discriminant, -1/a + (b/2a)^(2), is greater than or equal to 0. This means that b^(2) - 4a >= 0.

The conditions for both solutions to be complex numbers are that the discriminant, -1/a + (b/2a)^(2), is less than 0. This means that b^(2) - 4a < 0.

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Answer:

13400

Step-by-step explanation:

Answer: [tex]\frac{2}{35}[/tex] hour

Step-by-step explanation:

      We will divide the time it takes it to do 7 tasks (⅖ hour) by the number of tasks it does in that time frame (7 tasks) to find the time per task.

[tex]\frac{2}{5}[/tex] hour / 7 tasks = [tex]\frac{2}{5} *\frac{1}{7}[/tex] = [tex]\frac{2}{35}[/tex] hour or about 3.43 minutes

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Answer:

c

Step-by-step explanation:

1 2/3 = 5/3 = 20/12

3 1/4 = 13/4 =39/12

Answer: 11.6

Step-by-step explanation: plug in x for 4. 3.2(4)-1.2 = 11.6

The solution to the all six equations is that they have infinite many real solutions

Expression (a)

We have:

√(x^2-14x+49)=x-7

Squaring both sides we get:

x^2 - 14x + 49 = x^2 - 14x + 49

Evaluate the like terms

0 = 0

This means that the equation has infinite many solutions

Expression (b)

Here, we have:

√(4x^2-20x+25)=5-2x

Squaring both sides we get:

4x^2-20x+25 = 25 - 20x + 4x^2

Evaluate the like terms

0 = 0

This means that the equation has infinite many solutions

For the remaining expressions, we have the following (using the above steps)

Expression (c)

√(y^4+2y^2+1) = y^2 + 1

y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1

0 = 0

Expression (d)

√(x^2+2x+1)=x+1

x^2 + 2x + 1 = x^2 + 2x + 1

0 = 0

Expression (e)

√(y^2-20y+100)=y-10

y^2 - 20y + 100 = y^2 - 20y + 100

0 = 0

Expression (f)

√(y^6-2y^3+1)=y^3-1

y^6-2y^3+1 = y^6-2y^3+1

0 = 0

Hence, the equations have infinite solutions

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