Find the slope of the line on the graph. Write your answer as a fraction or whole number, but a mixed number or decimal.

Answer:

x = 134°

Step-by-step explanation:

Let

\(\angle A=64^{\circ}\\\\\angle B =70^{\circ}\)

We need to find the value of x.

We can see from the figure that x is exterior angle. To find x we can use exterior angle theorem. According to this theorem,

\(x=\angle A+\angle B\\\\x=64+70\\\\x=134^{\circ}\)

Hence, the value of x is 134°

The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.

According to the question,

We have to divide 430 by 8 by following the long division method.

Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.

Now, we will solve it step by step.

In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.

So, we have a = 5, b = 4 and c = 0.

Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.

So, we have d = 3.

Now, when we will subtract 24 from 30, we will get 6.

So, we have e = 6.

And e is also the remainder, R. So, we have R = 6.

Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.

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Using the arrangements formula, it is found that the number of different arrangements that can be made using all of the letters of TOPIC is given by:

c. 120

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

In this problem, the word TOPIC has 5 non-repeating letters, hence the number of arrangements is given by:

\(A_5 = 5! = 120\).

Which means that option C is correct.

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Answer:

Blank 1 = 53 + 90 = 143

Blank 2 = 143 - 229 = -86

Blank 3 = 0 - 86 = 86

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.

Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty.

Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that exactly two of the students are guilty.

Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty. Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that only one of the three is not guilty and it is not A or B. Therefore, exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.

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Hey there!

DISTRIBUTE

3(–2x – 3) + 4x – 3 = 8

3(–2x) + 3(–3) + 4x – 3 = 8

COMBINE LIKE TERMS

–6x – 9 + 4x – 3 = 8

–2x – 12 = 8

ADD by 12 on BOTH SIDES

–2x – 12 + 12 = 8 + 12

CANCEL out: –12 + 12 because that gives 0

KEEP: 8 + 12 because it helps us solve for x

“8+ 12 = 20”

–2x = 20

DIVIDE by –2 on BOTH SIDES

–2x/–2 = 20/–2

CANCEL out: –2/–2 because that gives 1

KEEP: 20/–2 because that gives you x

“x = 20/–2”

Answer: x = –10 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

To find the conditional probability of event A given event B, we can use the formula:

P(A|B) = P(A ∩ B) / P(B)

where P(A ∩ B) is the probability that events A and B both occur, and P(B) is the probability of event B.

Assuming that a power hand consists of 5 cards, the probability that a randomly selected power hand contains exactly 2 aces (event B) can be calculated as follows:

P(B) = (4C2 * 48C3) / 52C5

= (6 * 17296) / 2598960

= 0.0404

where 4C2 is the number of ways to choose 2 aces from 4, 48C3 is the number of ways to choose 3 non-ace cards from the remaining 48 cards, and 52C5 is the total number of possible 5-card hands.

The probability that a randomly selected power hand contains exactly 3 aces (event A) and also contains 2 aces (event B) can be calculated as follows:

P(A ∩ B) = (4C3 * 48C2) / 52C5

= (4 * 1128) / 2598960

= 0.00173

where 4C3 is the number of ways to choose 3 aces from 4 (there is only one), and 48C2 is the number of ways to choose 2 non-ace cards from the remaining 48 cards.

Therefore, the conditional probability of event A given event B is:

P(A|B) = P(A ∩ B) / P(B)

= 0.00173 / 0.0404

= 0.0428

So the probability that a randomly selected power hand contains exactly 3 aces, given that it contains exactly 2 aces, is approximately 0.0428 or 4.28%.

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

From the question, we have the following parameters that can be used in our computation:

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

\(\sf{x+9 < 4x}\)

Flip it

\(\sf{4x > x+9}\)

Solve

\(\sf{4x-x > 9}\)

Combine like terms

\(\sf{3x > 9}\)

Divide each side by 3

\(\sf{x > 3}\)

Answer:

1

Step-by-step explanation:

easy

9514 1404 393

Answer:

  1.4.1  35.34 mm²

  1.4.2  113.10 mm

Step-by-step explanation:

1.4.1 There are 5 circles in the first two patterns. The area of one circle in terms of its diameter is ...

  A = (π/4)d²

Then the area of the 5 circles is ...

  A = 5(π/4)(3 mm)² = 45π/4 mm² ≈ 35.34 mm²

__

1.4.2 There are 12 circles in the first 3 patterns. The perimeter of one circle is given by the formula ...

  P = πd

Then the total perimeter of the 12 circles is ...

  P = 12π(3 mm) = 36π mm ≈ 113.10 mm

Based on the amount that the first and second washing machines are marked down by, the sale price of each washing machine is:

Joanne should buy the first washing machine because there as a higher discount on it.

The selling price of the first machine can be found by the formula:
= Selling price - ( 1 - discount rate)

= 520 x (1 - 40%)

= 520 x 60%

= $312

The selling price of the second machine will be calculated in two steps to cater for the two discounts:

= 520 x (1 - 10%)

= 520 x 90%

= $468

It was then reduced by 30%:

= 468 x (1 - 30%)

= $327.60

Joanne should therefore buy the first machine which was discounted by a greater amount.

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Answer:

By moving the decimal at the end of the number to the correct amount of places for x 10 you move it once to the right for x 100 you move it right twice.

Step-by-step explanation:

The possible line of best fit is given by y = -0.5x + 10

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the y intercept.

Let y represent the students still participating in the final round while x represent the number of spelling words attempted.

Since the line of best fit has a negative, linear association, this means that the slope is negative. A possible linear function is:

y = -0.5x + 10

The possible line of best fit is given by y = -0.5x + 10

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Answer:

Distance = 110.5 cm

Step-by-step explanation:

It is given that,

The basement floor is at  an elevation of −10.5 feet

The second story floor has an  elevation of 121 feet.

We need to find the distance between the basement floor and the second story floor.

Distance = -10.5 + 121

= 110.5 feet

So, the distance between the basement floor and the second story floor is 110.5 cm.

Answer:

0.42 dollar per pint

2.36 pints per dollar

The ranking based on average speed is 1 > 2 > 4 > 3

(a) Based on the given information, we have:

V1 = V2: The objects on paths 1 and 2 have the same average velocity.

V3 < V4: The object on path 4 has a greater average velocity than the object on path 3.

(b) Average speed is simply the distance traveled divided by the time interval. If the objects move at a constant speed along each path, then the paths with the greatest distances will have the greatest average speeds. Therefore, the ranking based on average speed is:

1 > 2 > 4 > 3

Note that this ranking is based only on the distances traveled along each path, and does not take into account the directions of motion or any changes in direction.

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Answer:

8x+14

Step-by-step explanation:

Answer:

621.72

Step-by-step explanation:

The explanation is that the formula is V=2HπR

Multiply all of that and you get your answer of 621.72

The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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Answer:

f(-1) = 0.75

Step-by-step explanation:

\(f(x)=1.5(2)^x\\f(-1)=1.5(2)^{-1}\\f(-1)=1.5(\frac{1}{2})\\f(-1)=0.75\)

Remember to write \(2^{-1}\) as \(\frac{1}{2}\), that was probably where you were stuck!

Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Answer:

-8

Step-by-step explanation:

If x = -2, then plug -2 into the equation where the x is:

y = 3(-2) - 2

Then solve:

3 * -2 = -6

-6 - 2 = -8

So, y = -8

Answer:15/16 > 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(x,y)=(0,4)

Step-by-step explanation:

write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)

Answer:

I think it's 300

Step-by-step explanation:

Answer:

the answer is D) 55 cubic centimetres

Step-by-step explanation:

5×2×2.5= 25 cm³

3×4×2.5=30 cm³

25+30= 55 cm³

Answer:

Negative

Step-by-step explanation:

Goes down from left to right

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

d. none

Step-by-step explanation: