Solving Systems of Equations by Elimination
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10x + 9y= -17
7x + 10y= 14

An easy way to do this is to parameterize the directed line segment from B to A by the function

\(\ell_{B\to A}(t) = (1-t) B + t A = (1 - t) (11, 17) + t (-9, 4)\)

with 0 ≤ t ≤ 1.

The point P₂ splits up AB so that BP₂ = 3/8 AB and AP₂ = 5/8 AB. Then we reach the point P₂ when t = 3/8, so its coordinates are

\(P_2 = \ell_{B\to A}}\left(\dfrac38\right) = \dfrac58 (11,17) + \dfrac38 (-9,4) = \boxed{\left(\dfrac72, \dfrac{97}8\right)}\)

-4v5i

Step-by-step explanation:

Answer:

Step-by-step explanation:

If ∠A=8x+14 and ∠B=2x+50 are supplementary, then the sum of both angles is 180.

∠A + ∠B = 180

8x+14 + 2x+50 = 180

10x + 64 = 180

10x = 180-64

10x = 116

x = 11.6

To get m∠B, substitute x = 11.6 into m∠B = 2x+50

m∠B = 2(11.6)+50

m∠B = 23.2+50

m∠B = 73.2°

Answer:

x=23.2

Step-by-step explanation:

because 3 is the opposite and 7 is the adjacent, we can use tangent (opposite over adgacent) so 3/7 = tan(x) then you take the inverse tangent of both sides to get inversetangent(3/7)=x and then you plug that in the calculator and get that x is 23.2

The equation of the parabola is y = 2(x - 1)² + 3

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

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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Answer:

Problem 8:
Option C)       DE = √21

Problem 9:
Option C)     Perimeter = 30 cm

Step-by-step explanation:

1. Problem 8

Draw a line segment connecting the center of the circle, X, to A. This is the radius of the circle

The points ABX form a right triangle with AX as the hypotenuse and AB, BX as the legs of the right triangle

By the Pythagorean theorem
hypotenuse² = sum of the squares of the two legs

Plugging in line segment references

AX² = AB² + BX²

We are given AC = 8, BX = 3

Since the segment BX intersects AC at right angles, AB = BC = AC/2

So AB = 8/2= 4

Plugging these values into the Pythagorean formula
AX² = AB² + BX²

AX² = 4² +3²

AX² = 16 + 9

AX² = 25

Draw a line connecting X and D
The points DEX form a right triangle with DX as the hypotenuse and EX and DE as the legs

Again, by the Pythagorean theorem

DX² = DE² + EX²

But DX is the radius of the circle so it must be the same as AX

Substitute for DX in terms of AX
DX² = DE² + EX²

=> AX² = DE² + EX²

But AX² = 25 and EX = 2 giving EX² = 4

Therefore

AX² = DE² + EX² becomes
25 = DE² + 4

DE² = 25 - 4

DE² = 21

DE = √21

This is choice C

Problem 9

To find the perimeter, just add up the individual side lengths:

Perimeter = 10 + 8 + 7 + 5 = 30 cm

Option C

The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.

A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.

Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

The answer is that point  is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.

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Answer:

4 1/9, 0.94, -9/4, -4.9

Step-by-step explanation:

Putting them in decimals results in:
4 1/9: 4.11111(repeated)

0.94

-9/4 = -2.25

-4.9

Using the rules of negative numbers, we have the answer above.

The asymptotic relationship between x and x^2(2+sin(x)) is x=Θ(x^2(2+sin(x))) and x=o(x^2(2+sin(x))).

To determine the asymptotic relationship between x and x^2(2+sin(x)), we need to examine the growth rates of these functions as x approaches infinity.

x^2(2+sin(x)) grows faster than x because the x^2 term dominates over x. Additionally, the sinusoidal term sin(x) does not affect the overall growth rate significantly as x becomes large.

Based on this analysis, we can conclude the following relationships:

x=Θ(x^2(2+sin(x))): This notation indicates that x and x^2(2+sin(x)) have the same growth rate. As x approaches infinity, the difference between the two functions becomes negligible.

x=o(x^2(2+sin(x))): This notation indicates that x grows at a slower rate than x^2(2+sin(x)). In other words, the growth of x is "smaller" compared to x^2(2+sin(x)) as x becomes large.

Other notations such as x=O(x^2(2+sin(x))), x=Ω(x^2(2+sin(x))), and x=ω(x^2(2+sin(x))) do not accurately represent the relationship between x and x^2(2+sin(x)). These notations imply upper or lower bounds on the growth rates, but they do not capture the precise relationship between the two functions.

In summary, the correct asymptotic relationships are x=Θ(x^2(2+sin(x))) and x=o(x^2(2+sin(x))).

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Wireshark is the tool used to capture data packets over time, either continuously or overnight.

Wireshark is a powerful network protocol analyzer that allows you to capture and examine data packets flowing through a network. It provides a comprehensive set of features for capturing, analyzing, and interpreting network traffic.

With Wireshark, you can capture packets from various network interfaces and save them to a capture file for later analysis. It supports capturing packets in real-time, allowing you to monitor network activity as it happens.

Wireshark offers detailed packet-level inspection, allowing you to examine packet headers, payloads, protocols, and other relevant information.

Furthermore, Wireshark supports numerous protocols and provides protocol-specific decoders to interpret and analyze different network protocols. It also offers advanced features like packet coloring, statistical analysis, packet comparison, and the ability to export captured data for further analysis or sharing with others.

Overall, Wireshark is widely used by network administrators, security professionals, and developers to diagnose network issues, troubleshoot problems, analyze network performance, and investigate security incidents by capturing and analyzing data packets over time.

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Answer:

c

Step-by-step explanation:

The line segment OD is congruent to line segment OB. Therefore, option C is the correct answer.

Equal chords of a circle are equidistant from the center of the circle.

From the given figure, AC=EF=9.07.

So, AC and EF are equal chords.

Since, the chords are equal, they are equidistance from center.

Then, OD=OB

Therefore, option C is the correct answer.

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Answer:

-15

Step-by-step explanation:

-3(2)2-4(2)+5

-12-8+5

-20+5

5-20= -15

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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Answer:Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles. Thus the vertex angle is 38 and the base angle is 71 and their sum is 109. :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

I believe it's (4, -1/4)

Step-by-step explanation:

Hope this helps! ^^

Answer:

B) x = 3

Step-by-step explanation:

This is the axis of symmetry because the graph is symmetric in this line

Answer:

1: 9

2: 25.75

Step-by-step explanation:

Question 1:

1. Set up the equation to find the mean.

2. (Solving)

Therefore, the answer to question #1 is 9.

Question 2:

1. Set up the equation to find the mean.

2. (Solving)

Therefore, the answer to question #2 is 25.75.

Answer:

Miranda made 9 visits to the store and Savannah made 7 visits to the store

Step-by-step explanation:

To find how many times Miranda and Savannah went to the store we would need to find the Greatest Common Multiple of the amount that each of them spends per visit. We do this by simply going through each of these numbers' times tables until we find a common one.

7 * 1 =  7                     9 * 1 = 9

7 * 2 =  14                   9 * 2 = 18

7 * 3 =  21                   9 * 3 = 27

7 * 4 =  28                  9 * 4 = 36

7 * 5 =  35                  9 * 5 = 45

7 * 6 =  42                  9 * 6 = 54

7 * 7 =  49                  9 * 7 = 63

7 * 8 =  56                  

7 * 9 =  63      

Finally, we can see that the first time that both Miranda and Savannah have spent the exact same amount would be when Miranda made 9 visits to the store and Savannah made 7 visits to the store. Each of which wasted $63          

The possible range of the measurement is 211.43 to 216.57

The range in statistics for a given data set is the difference between the highest and lowest values.

The range could also be defined as the difference between the highest observation and lowest observation.

The obtained result is called the range of observation.

In the given question it is given measurement 214oz ± 1.2%

To find the range first we need to find its minimum and maximum value.

So,

1.2% of 214 = 0.012×214

=2.568

Rounding off to nearest hundredths

=2.57

Then the minimum possible value is

214-2.57=211.43

And the maximum possible value is

214+2.57=216.57

So the range would be between 211.43 to 216.57

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Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

\(x+146=546\)

Subtract 146 from both sides:

\(x+146-146=546-146\\\)

\(x=400\)

Answer:

x = 400

Step-by-step explanation:

x + 146 = 546

We need to subtract 146 on both sides.

146 - 146 is equal to 0 so we cancel out. 546 - 146 is equal to 400.

So now x is alone and we have our answer.

x = 400

Answer:

c = 180

Step-by-step explanation:

Varies joint with d and the square of g

c = k d g^2  where k is a constant

30 = k * 15 * 2^2

30 = 60k

30/60 = k

1/2 = k

c = 1/2 d g^2

Let d = 40 and g=3

c = 1/2 ( 40) (30^2

c = 20 (9)

c = 180

Answer:

It depends on what your trying to solve and what the question is asking you to do. If you give me a problem, ill be more than happy to show how I solved it step-by-step.

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is about understanding real and complex numbers.

Complex Numbers; 7 - 5i, √-6, 0 + 9i, , -i² + i³

Real Numbers; i⁶, 2 - 7i², -12, √(-5)²

Let's first define real and complex numbers.

The. expressions we are given are;

i⁶, 2 - 7i², 7 - 5i, √-6, 0 + 9i, -12, √(-5)², -i² + i³

       2 - 7i² = 2 - 7(-1) = 9 which is a real number.

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Answer:

6x=24

Step-by-step explanation:

Because if Cindy has 6 friends and they all ride 4 miles it should equal 24.

Answer:

True. The statement is also equivalent to: If m<B + m<C does not equal m<D, then m<A does not equal m<B and m<A + m<C is not equal to m<D.

Answer:  100000

Step-by-step explanation: If you take 80 percent of a number and get 80000, then what is that number? In other words, you know that 80 percent of a number is 80000 and you want to know what that initial number is.

To solve this problem, you multiply 80000 by 100 and then divide the total by 80 as follows: (80000 x 100) / 80.

AND I LOOKED IT UP ON GOGLE

The margin of error is 3.083 min

Margin of Error: The margin of error is the range of error permitted around the sample statistic in order to estimate the population parameter. The margin of error indicates the size of the confidence interval. The breadth of the confidence interval increases with the margin of error.

Sample size, n=24

Sample mean, ¯x=31.5 min

Sample standard deviation, s=7.3 min

Confidence level, c=95%

=0.95

From the given information we can calculate the below-required quantities,

Significance level, α=1−c=1−0.95=0.05

Degrees of freedom, DOF=n−1

=24−1

=23

Now from the t-distribution table,

The value of t (α2, DOF) is,

t (0.025,23) = 2.069  

Hence the margin of error will be,

MOE= t (α2, DOF) × s/√ n

=2.069×7.3/√24

=3.083 min

i. The upper limit of the confidence interval will be,

UL=¯x + MOE=31.5+3.083=34.583

The lower limit of the confidence interval will be,

LL=¯x−MOE

=31.5−3.083

=28.417

Hence, the 95% confidence interval is (28.417,34.583)

(28.417,34.583)

The answer is 28.417,34.583

ii. The required answer is MOE=3.083 min

ii. We have found the 95% confidence interval for the population mean to be (28.417,34.583). This means with 95 % confidence; it can be said that the population mean commute time is between the bounds of the confidence interval.

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