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1 year ago

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Anton will be constructing a segment bisector with a compass and straightedge, while Maxim will be constructing an angle bisecto

r with a compass and straightedge. Describe the similarities and differences between their construction steps. please help quick

1 answer:

Genrish500 [490]1 year ago

7 0

The similarities are;

Compass and a straight edge required for both construction

Both construction includes a line drawn from the intersection of arcs to bisect a segment or an angle

The bases for the construction of both bisector are the ends of segment and the angle to be bisected

The width of the compass when drawing intersecting arcs, is more than half the width of the segment or angle being bisected

The differences are;

Two points of intersection of arcs are used in the segment bisector while only one is requited in an angle bisector
The bisecting line crosses the segment in a segment bisector, while it stops at the vertex of the angle being bisected in an angle bisector

The sources of the above equations are as follows;

The steps to construct a segment bisector are;

Place the needle of the compass at one of the ends of the line segment to be bisected

Widen the compass so as to extend more than half of the length of the segment to be bisected

Draw two arcs, one above, and the other below the line

Place the compass needle at the other end and with the same compass width draw arcs that intersects with the arcs drawn in the above step

Draw a line segment by placing the ruler on the points of intersection of the arcs above and below the line

The steps to construct an angle bisector are;

With the compass needle at the vertex, open the pencil end such that arcs can be drawn on the rays (lines) forming the angle

Draw an arc on both lines forming the angle

Place the compass needle at one of the intersection points and draw an arc in between the lines forming the angle

Repeat the above step with the same compass width from the other intersection point with the rays forming the angle

Join the point of intersection of the two arcs to the vertex of the angle to bisect the angle

Therefore, we have;

The similarities are;

A compass and a straight edge can be used for both construction

A straight line is drawn from the point of intersection of arcs to bisect the segment or the angle

The arcs are drawn from the ends of the segment or angle to be bisected

The width of the compass is more than half the width of the line or angle when drawing the arcs

The differences are;

In a segment bisector, the intersection point is above and below the line, while in an angle bisector only one pair of arcs are drawn to intersect above the line

The bisecting line passes through the segment being bisected, while the line stops at the vertex in an angle bisector

Learn more about the construction of segment and angle bisectors here;

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A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFract

KengaRu [80]

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Step-by-step explanation:

Question 1)

Two lines, with their corresponding equations are given and we have to find the solution to the system of equations.

The given lines are:

Equation of Line 1:

$y=\frac{-7}{4}x+\frac{5}{2}$

This line passes through the points: (0, 2.5) , (2.2, -1.4)

Equation of Line 2:

$y=\frac{3}{4}x-3$

This line passes through the points (0, -3) , (2.2, -1.4)

By looking at the graph/given data we have to find the solution of these linear equations.

Remember that the solution of linear equations is an ordered pair, through which both the lines pass i.e. the point at which both the given lines intersect is the solution of the linear equations.

From the given data we can see that both the lines pass through one common point, (2.2, -1.4). Since, both lines pass through this point, this means this is the point of intersection of the lines and hence there solution.

So, the answer to this questions is (2.2, -1.4)

Question 2)

The given equations are:

y = 1.5x - 1 Equation 1

y = 1 Equation 2

We can solve these equations by method of substitution.

Substituting the value of y from Equation 2, in Equation 1, we get:

1 = 1.5x - 1

1 + 1 = 1.5x

2 = 1.5x

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the given linear equations is (1.33, 1)

5 0

1 year ago

Read 2 more answers

what do i write for this " Write a problem that requires adding 1 to the quotient when interpreting the remainder."

Mariana [72]

You should write a ( real world situation ) question that can only have whole numbers as a solution because you would divide and then you can not have a fraction left over so instead you add one. For instance there are 132 students going on a field trip. 20 students can fit on each bus. how many buses are needed? 7 because when you divide 132 by 20 you get 6 remainder 12. You can not just make 12 students walk to the location so you would add an extra bus.

6 0

2 years ago

Each airline passenger and his or her luggage must be checked to determine whether he or she is carrying weapons on to the airpl

Dafna1 [17]

Answer:

a

$P_k = 0.83$

b

$N_{\mu} \approx 4 \ passengers$

c

$T_{\lambda} = 0.5 \ minutes$

Step-by-step explanation:

From the question we are told that

The average number of passengers that arrive per minute is $\lambda = 10$

The average number of check that can be carried out in one minute is $\mu= 12$

Generally the probability that a passenger will have to wait before being checked for weapons is mathematically represented as

$P_k = \frac{\lambda }{ \mu }$

=> $P_k = \frac{10 }{ 12}$

=> $P_k = 0.83$

Generally the number of passengers are waiting in line to enter the checkpoint is mathematically represented as

$N_{\mu} = \frac{\lambda^2}{\mu (\mu -\lambda) }$

=> $N_{\mu} = \frac{10^2}{12 (12 -10) }$

=> $N_{\mu} \approx 4 \ passengers$

Generally the average time a passenger spend at the checkpoint is mathematically represented as

$T_{\lambda} = \frac{ \frac{\lambda}{(\mu - \lambda)} }{ \lambda}$

=> $T_{\lambda} = \frac{ \frac{ 10}{(12 - 10)} }{10}$

=> $T_{\lambda} = 0.5 \ minutes$

5 0

1 year ago

If tan B = 1.6732, what is the measure of B to the nearest tenth of a degree

Lilit [14]

Answer:

59.1 °

Step-by-step explanation:

-Given that Tan B=1.6732

-Angle B is equivalent to the tan inverse of the tan B value:

$\angle B=Tan^{-1}B\\\\\angle B=Tan^{-1}(1.6732)\\\\=59.1350\approx59.1\textdegree$

Hence, angle B is 59.1 °

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2 years ago

Mike runs for the president of the student government and is interested to know whether the proportion of the student body in fa

Alik [6]

Answer:

We conclude that the proportion of student body in favor of him is significantly less than or equal to 50%.

Step-by-step explanation:

We are given that Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.

A random sample of 100 students was taken. Fifty-five of them favored Mike.

<em>Let p = </em><u><em>proportion of the students who are in favor of Mike.</em></u>

So, Null Hypothesis, $H_0$ : p $\leq$ 50% {means that the proportion of student body in favor of him is significantly less than or equal to 50%}

Alternate Hypothesis, $H_A$ : p > 50% {means that the proportion of student body in favor of him is significantly more than 50%}

The test statistics that would be used here <u>One-sample z proportion</u> <u>statistics</u>;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students body in favor of Mike = $\frac{55}{100}$ = 0.55

n = sample of students taken = 100

So, <em><u>test statistics</u></em> = $\frac{0.55-0.50}{\sqrt{\frac{0.55(1-0.55)}{100} } }$

= 1.01

The value of z test statistics is 1.01.

<em>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</em>

<em>Since our test statistic is less than the critical value of z as 1.01 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><u><em>we fail to reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the proportion of student body in favor of him is significantly less than or equal to 50% or proportion of the students in favor of Mike is not significantly greater than 50 percent.

4 0

2 years ago