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2 years ago

PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!!

Mathematics

2 answers:

jok3333 [9.3K]2 years ago

6 0

Answer:

x=9

Step-by-step explanation:

Given information: KM bisects ∠JKL, m∠JKL = 92, and m∠MKL = (5x+1).

It is given that KM bisects ∠JKL. It means line KM divides the angle in two equal parts.

$m\angle JKM=m\angle MKL$ .... (1)

The ∠JKL is the sum of ∠JKM and ∠MKL.

$m\angle JKM=m\angle JKM+m\angle MKL$

Using equation (1) we get

$m\angle JKM=m\angle MKL+m\angle MKL$ $m\angle JKM=m\angle MKL$

$m\angle JKM=2(m\angle MKL)$

Substitute m∠JKL = 92 and m∠MKL = (5x+1) in the above equation.

$92=2(5x+1)$

$92=2(5x)+2(1)$

$92=10x+2$

Subtract 2 from both sides.

$92-2=10x$

$90=10x$

Divide both sides by 10.

$\frac{90}{10}=x$

$9=x$

Therefore, the value of x is 9.

lorasvet [3.4K]2 years ago

5 0

Answer:

x = 9

Step-by-step explanation:

The trick here is knowing that JKM and MKL are equal, which means MKL is equal to JKL/2. From that knowledge, we can solve.

MKL = JKL/2

5x + 1 = 46

5x = 45

x = 9

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What integer is equivalent to 25 3/2

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Answer
26 1/2 is not equivalent to and integer but it can be approximated to 27 which is an integer.

Explanation
An integer is a whole number. It is a number that is not a fraction.
253/2=25+3/2=25+1 1/2=26 1/2
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1 year ago

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Genrish500 [490]

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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1 year ago

What is the ratio of the area of sector ABC to the area of sector DBE?

shusha [124]

We have to find the" ratio of the area of sector ABC to the area of sector DBE".

Now,

the general formula for the area of sector is

Area of sector= 1/2 r²θ

where r is the radius and θ is the central angle in radian.

180°= π rad

1° = π/180 rad

For sector ABC, area= 1/2 (2r)²(β°)

= 1/2 *4r²*(π/180 β)

= 2r²(π/180 β)

For sector DBE, area= 1/2 (r)²(3β°)

= 1/2 *r²*3(π/180 β)

= 3/2 r²(π/180 β)

Now ratio,

Area of sector ABC/Area of sector DBE = $\frac{2r^{2}*\ \frac{\pi}{180} beta}{3/2 r^{2}*\ \frac{\pi}{180}beta}$

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nika2105 [10]

Given:

Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).

Vertices of A'B'C'D' are A'(3,-4), B'(5,-2), C'(5,1) and D'(3,-1).

To find:

The sequence of transformations that changes figure ABCD to figure A'B'C'D'.

Solution:

Part A:

The figure ABCD reflected across the x-axis, then

$(x,y)\to (x,-y)$

Using this rule, we get

$A(-4,4)\to A_1(-4,-4)$

Similarly, the other points are $B_1(-2,-2),C_1(-2,1),D_1(-4,-1)$ .

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$(x,y)\to (x+7,y)$

$A_1(-4,-4)\to A'(-4+7,-4)=A'(3,-4)$

Similarly, the other points are $B'(5,-2), C'(5,1),D'(3,-1)$ .

Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.

Therefore, the two figures congruent.

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2 years ago

To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married

Xelga [282]

Answer:

a. See the table below

b. See the table below

c. 0.548

d. 0.576

e. 0.534

f) i) 0.201, ii) 0.208

Explanation:

First, order the information provided:

Table: "Who is better at getting deals?"

Who Is Better?

Respondent I Am My Spouse We Are Equal

Husband 278 127 102

Wife 290 111 102

a. Develop a joint probability table and use it to answer the following questions. 

The joint probability table shows the same information but as proportions. Hence, you must divide each number of the table by the total number of people in the set of responses.

1. Number of responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Calculate each proportion:

278/1,010 = 0.275
127/1,010 = 0.126
102/1,010 = 0.101
290/1,010 = 0.287
111/1,010 = 0.110
102/1,010 = 0.101

3. Construct the table with those numbers:

Joint probability table:

Respondent I Am My Spouse We Are Equal

Husband 0.275 0.126 0.101

Wife 0.287 0.110 0.101

Look what that table means: it tells that the joint probability of being a husband and responding "I am" is 0.275. And so for every cell: every cell shows the joint probability of a particular gender with a particular response.

Hence, that is why that is the joint probability table.

b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.

The marginal probabilities are calculated for each for each row and each column of the table. They are shown at the margins, that is why they are called marginal probabilities.

For the colum "I am" it is: 0.275 + 0.287 = 0.562

Do the same for the other two colums.

For the row "Husband" it is 0.275 + 0.126 + 0.101 = 0.502. Do the same for the row "Wife".

Table Marginal probabilities:

Respondent I Am My Spouse We Are Equal Total

Husband 0.275 0.126 0.101 0.502

Wife 0.287 0.110 0.101 0.498

Total 0.562 0.236 0.202 1.000

Note that when you add the marginal probabilities of the each total, either for the colums or for the rows, you get 1. Which is always true for the marginal probabilities.

c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? 

For this you use conditional probability.

You want to determine the probability of the response be " I am" given that the respondent is a "Husband".

Using conditional probability:

P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

P ("I am" ∩ "Husband) = 0.275 (from the intersection of the column "I am" and the row "Husband)

P("Husband") = 0.502 (from the total of the row "Husband")

P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?

You want to determine the probability of the response being "I am" given that the respondent is a "Wife", for which you use again the formula for conditional probability:

P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

P ("I am" / "Wife") = 0.287 / 0.498

P ("I am" / "Wife") = 0.576

e. Given a response "My spouse," is better at getting deals, what is the probability that the response came from a husband?

You want to determine: P ("Husband" / "My spouse")

Using the formula of conditional probability:

P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

P("Husband" / "My spouse") = 0.126/0.236

P("Husband" / "My spouse") = 0.534

f. Given a response "We are equal" what is the probability that the response came from a husband? What is the probability that the response came from a wife?

What is the probability that the response came from a husband?

P("Husband" / "We are equal") = P("Husband" ∩ "We are equal" / P ("We are equal")

P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

What is the probability that the response came from a wife:

P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208

6 0

2 years ago