what is vertically opposite Angle??​

The correct equation representing the synthetic division problem is given by:

(3x³ + 5x² - 14x - 18) ÷ (x - 2) = 3x² + 11x + 8 - 2/(x - 2)

From the top coefficients, we have that the dividend is given by:

3x³ + 5x² - 14x - 18

From the left coefficient, we have that the divisor is:

x - 2.

From the bottom coefficients, the quotient and the remainder are given, respectively, by:

3x² + 11x + 8, and -2.

Hence the correct option is given by:

(3x³ + 5x² - 14x - 18) ÷ (x - 2) = 3x² + 11x + 8 - 2/(x - 2)

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The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.

The variables for this problem are given as follows:

To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.

Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.

The table is given by the image shown at the end of the answer.

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Answer:

B. (-7,-3)

Step-by-step explanation:

Given the circle: \((x + 7)^2 + (y - 10)^2 = 13^2\)

The point (x,y) which lie on the circle are the coordinate which satisfies the given equation of the circle.

We now consider the given options.

Option A (5,12)

When x=5, y=12

\((5 + 7)^2 + (12 - 10)^2 =12^2+2^2=148\neq 169= 13^2\)

Option B (-7,-3)

When x=-7, y=-3

\((-7 + 7)^2 + (-3 - 10)^2 =0^2+(-13)^2= 169=13^2\)

Option C (-6,-10)

When x=-6, y=-10

\((-6 + 7)^2 + (-10 - 10)^2 =1^2+(-20)^2=401\neq 169= 13^2\)

Option D (6,23)

When x=6, y=23

\((6 + 7)^2 + (23 - 10)^2 =13^2+13^2=338\neq 169= 13^2\)

We can see that only (-7,-3) satisfies the equation of the circle. Thus it is the point which lies on the circle.

The correct option is B.

The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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Answer:

C

Step-by-step explanation:

As the legs and hypotenuse are same, these triangles are congruent by HL congruency

The maximum weight that the balloon can lift is 5020.31 Newtons.

We have to give that,

A 3.2 kg balloon is filled with helium with a density of 0.179 kg/m³.

And, the balloon is a sphere with a radius of 4.9 m.

Since The formula for the volume of a sphere is,

\(V = \dfrac{4}{3} \pi r^3\)

Here, \(g = 9.8 \text{m/s}\)

\(\rho_{air} = 1.225\) kg/m³

So, Buoyant force on the ballons is,

\(F_B = V \times \rho_{air} \times g\)

Substitute all the given values,

\(F_{B} = \dfrac{4}{3} \times\pi \times (4.9)^3 \times 1.225 \times 9.8\)

\(F_B = 5916.15 \text{N}\)

So, the maximum weight that the balloon can lift is calculated as,

\(W +M_b +V \times \rho_{He} \times g = F_B = V \times \rho_{air} \times g\)

\(W = F_B - (M_bg +V \times \rho_{He} \times g)\)

Where, \(M_b\) is the mass of balloons.

Substitute all the values,

\(W = 5916.15 - [(3.2 \times 9.8) + \dfrac{4}{3} \pi (4.9)^3 \times (0.179) \times(9.8)]\)

\(W = 5916.15 - 31.36 - 864.48\\\)

So, the maximum weight that the balloon can lift is,

\(W = 5020.31\)

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Answer:

More than two factors

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

more than 2 answers

Stay safe,wear a mask,stay at home <3

The probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

To calculate the probability of rolling all six numbers at least once when rolling a six-sided die 12 times, we can use the concept of permutations.

The total number of possible outcomes when rolling a six-sided die 12 times is 6^12 since each roll has six possible outcomes. This represents the denominator of our probability calculation.

Now, let's calculate the numerator, which represents the number of favorable outcomes where we get all six numbers at least once. We can use the concept of derangements (or the principle of inclusion-exclusion) to determine this.

A derangement is a permutation in which none of the elements appear in their original position. In our case, we want to find the number of derangements for a set of six elements (the six numbers on the die).

The formula to calculate the number of derangements for a set of n elements is given by n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).

Using this formula, we can calculate the number of derangements for six elements:

Number of derangements = 6! * (1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!) = 265

Therefore, the numerator of our probability calculation is 265.

Finally, we can calculate the probability by dividing the numerator by the denominator:

Probability = Number of favorable outcomes / Total number of possible outcomes = 265 / 6^12

Calculating this value:

Probability ≈ 0.0263

So, the probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

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Answer:

x=30

Step-by-step explanation:

i just wrote it down and here the photo of the steps

Answer: C -  square root of 74

Step-by-step explanation: took the test and got it right. hope this helps.

have a good day :)

Answer:

\(\sqrt{74}\)

Step-by-step explanation:

The perimeter is defined as the total length measurement of the curcumference of a polygon.

But generally we are given the measurements of sides of the polygon.

So the perimeter is found by summing up all these sides that act as a circumference or boundary of the polygon,

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x denotes the rectangle's length and y its width.

The beam is made of four planks with widths of d = 125 mm and h = 270 mm. The load on the beam is w = 6 kN/m and P = 12 kN, with a = 5 m and b = 3 m.The distance x from the left end of the beam to the point of maximum bending can be determined using the formula below.

Let the bending moment at the point of maximum bending be Mmax.

Mmax = P(a-b) + w((a^2)/2 - ab).

First, calculate the maximum bending moment:

Mmax = 12(5-3) + 6((5^2)/2 - 5*3) = 3 kN.m.

Now we can calculate the distance x from the left end of the beam to the point of maximum bending.

x = (Mmax * (h/2)) / (w * d^2) = (3 * 0.135) / (6 * (0.125^2)) = 3.24 m

In this case, the beam is made of four planks with widths of d = 125 mm and h = 270 mm. The load on the beam is w = 6 kN/m and P = 12 kN, with a = 5 m and b = 3 m. The maximum bending moment can be found using the formula

Mmax = P(a-b) + w((a^2)/2 - ab).

When we plug in the values for P, w, a, and b,

we get

Mmax = 12(5-3) + 6((5^2)/2 - 5*3) = 3 kN.m.

The distance x from the left end of the beam to the point of maximum bending can be determined using the formula

x = (Mmax * (h/2)) / (w * d^2).

Plugging in the values for Mmax, h, w, and d, we get x = (3 * 0.135) / (6 * (0.125^2)) = 3.24 m.

Therefore, the distance from the left end of the beam to the point of maximum bending is 3.24 m.

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Answer:

76

Step-by-step explanation:

180-(56+48)

put in calculator

76

The solution to the system of equations is x = 8/3 and y = 41/43.

To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Given equations:

3x + 2y = 22 ---(1)

-x + 15y = 21 ---(2)

To eliminate one variable, we can multiply equation (2) by 3 and equation (1) by -1, then add the resulting equations:

-3x + 45y = 63 ---(3) (multiplying equation (2) by 3)

-3x - 2y = -22 ---(4) (multiplying equation (1) by -1)

Adding equations (3) and (4) eliminates the x variable:

43y = 41

Dividing both sides by 43 gives us:

y = 41/43

Now we can substitute this value of y into either equation (1) or (2). Let's use equation (1):

3x + 2(41/43) = 22

Multiplying both sides by 43 to eliminate the fraction:

129x + 82 = 946

Subtracting 82 from both sides:

129x = 864

Dividing both sides by 129:

x = 864/129

Simplifying:

x = 8/3

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Answer:

A

Step-by-step explanation:

Answer:

pir^2 = Area of Circle

Step-by-step explanation:

A circle is formed by all points in a plane that are at a particular distance from the center and the area of a circle is equal to pi squared times the radius (A = π r²).

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The radius of a circle is the separation between any point on the circle and its center.

The radius must typically be a positive integer.

A degenerate situation is a circle with a radius equal to zero (one point).

Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.

A circle's area is equal to pi times the radius squared (A = π r²).

Therefore, a circle is formed by all points in a plane that are at a particular distance from the center and the area of a circle is equal to pi squared times the radius (A = π r²).

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Answer:

Step-by-step explanation:

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Answer:

Slope Intercept form: y = mx + b

Step-by-step explanation:

mx: the slope

b: y- intercept

To find the slope, use this formula:

y₂ - y₁ / x₂ - x₁

Add in the numbers

1 - (-5) / 0 - 2

-6/2 (or -3) = slope

Use point-slope form to find the Y- intercept

y - y₁ = m (x - x₁)

y - (-5) = -3 (x - 2)

y + 5 = -3x + 6

Subtract 5 from both sides

y = -3x + 1 ← Slope intercept form

Graph the y- intercept at 1, and go down 3 and to the right 1. Your two coordinates will be (0 , 1) and (1, -2) .

The probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

To find the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur, we need to determine the individual probabilities of each event and then multiply them together since the events are independent.

Event A: The coin lands on heads

A fair coin has two equally likely outcomes, heads or tails. Since we are interested in the probability of heads, there is only one favorable outcome out of two possible outcomes.

P(A) = 1/2

Event B: The die is 5 or greater

A fair six-sided die has six equally likely outcomes, numbers 1 through 6. Out of these six outcomes, there are two favorable outcomes (5 and 6) for Event B.

P(B) = 2/6 = 1/3

To find the probability of both events occurring (A and B), we multiply the individual probabilities:

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6

Therefore, the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

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Answer:

(20-5)/(-4-1)

15/-5= -3

Answer:

y = 5/4x - 6

Step-by-step explanation:

First, put 4x + 5y= -45​ in y = mx + b form

4x + 5y= -45​

5y = -4x - 45

y = -4/5x - 9

So, the slope is -4/5. Perpendicular lines have a opposite reciprocal slope, so the line's slope will be 5/4 right so to find the equation of the perpendicular line in this question, plug in the slope and given point into y = mx + b, and solve for b

y = mx + b

-11 = 5/4(-4) + b

-11 = -5 + b

-6 = b

so you should Plug in b and the slope into y = mx + b

y = 5/4x - 6

So, the equation is y = 5/4x - 6

if this doesn't make sense i don't know what will

Answer:

The answer is 36

How to get there:

11*11=121

10*10=100

9*9=81

8*8=64

7*7=49

6*6=36

Ans 36

The pattern is basically multiplying by the same factor. As the number decreases, the factors decrease by one. So we go from 7*7 which equals 49, to 6*6 which equals 36. Just notice the patterns :)

Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

The function increases in the interval where the value of the function increases as x increases. Then, based in the previous description and based on the given graph, you can conclude that the intervals of increase are:

(-oo , -1.8), (0 , 0.3)

Answer:

1.05 a minute is the answer

Answer:

C. 1.05 mi/min

Step-by-step explanation:

Use this formula to find your answer Y2-Y1/ X2-X1

=(4.2-2.1) over (4-2)

=21 over 2

=1.05 mi/min

To calculate the amount of each installment, we can use the formula for the present value of an annuity.

PV = (PMT / r) x [1 - (1 + r)^(-n)]

Where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate (which is 18% divided by 12 months), and n is the total number of payments (which is 36).

Substituting the given values into the formula, we get:

PV = 300,000

r = 0.18/12 = 0.015

n = 36

300,000 = (PMT / 0.015) x [1 - (1 + 0.015)^(-36)]

Solving for PMT, we get:

PMT = PV x r / [1 - (1 + r)^(-n)]

PMT = 300,000 x 0.015 / [1 - (1 + 0.015)^(-36)]

PMT = $11,877.64

Therefore, each installment will be $11,877.64.

Answer:

bottom right i did that 1 yesterday

Step-by-step explanation:

In a metes-and-bounds description, directions are typically given as a bearing, which is the angle measured clockwise from north.

So, if a direction is given as "north 10 degrees east," it means that the direction is 10 degrees to the east of due north.

To determine the opposite direction, we need to find the bearing that is 180 degrees opposite to "north 10 degrees east." To do this, we subtract 10 from 180, giving us a bearing of "south 170 degrees east."

In other words, the opposite direction of "north 10 degrees east" is "south 170 degrees east."

Metes-and-bounds descriptions are commonly used in real estate to describe the boundaries of a property. These descriptions rely on a series of directions and distances to outline the boundaries. Accurately understanding the directions in these descriptions is important in order to avoid boundary disputes or errors in land surveys.

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