Question 5(Multiple Choice Worth 1 points)

(01.07 MC)

Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. They are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees.

Given: line BC is parallel to line ED
m∠ABC = 70°
m∠CED = 30°

Prove:m∠BEC = 40°

Statement Justification
line BC is parallel to line ED Given
m∠ABC = 70° Given
m∠CED = 30° Given
m∠ABC = m∠BED Corresponding Angles Theorem

m∠BEC + 30° = 70° Substitution Property of Equality
m∠BEC = 40° Subtraction Property of Equality


Which of the following accurately completes the missing statement and justification of the two-column proof?

m∠BEC + m∠CED = m∠BED; Definition of a Linear Pair
m∠ABC + m∠BEC = m∠BED; Angle Addition Postulate
m∠ABC + m∠BEC = m∠BED; Definition of a Linear Pair
m∠BEC + m∠CED = m∠BED; Angle Addition Postulate

Answer:

You already have the equations ready so I will just explain

Step-by-step explanation:

The first equation: place a point on the y-axis on -5. then proceed to place points by going down 2 and right 1 or by going up 2 and left 1. that will make your first line.

second equation: on the y-axis place a point on -1 then proceed to go up 1 right 1 or down 1 left 1. that makes your second line

Answer:

Step-by-step explanation:

(-4*5 - 1) + (-4)

(-20 - 1) - 4

-21 - 4

-25

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53\)

9514 1404 393

Answer:

Step-by-step explanation:

If there are 3 times as many dimes as nickels, the coins can be grouped as 3 dimes and 1 nickel, worth $0.35 per group. Then the total number of groups is ...

   $46.55/$0.35 = 133

That means there are 133 nickels and 3×133 = 399 dimes.

The number of students who belong to neither club is 6 students.

The number of students who are not in either club is 6.

Let's say that there are x students in the classroom.

We know that 1/2 of the students belong to the Chess Club, so 1/2 * x = 6 students belong to the Chess Club.

We also know that 1/3 of the students belong to the Drama Club, so 1/3 * x = 4 students belong to the Drama Club.

Since 1/4 of the students belong to both clubs, then 1/4 * x = 3 students belong to both clubs.

Therefore, the number of students who belong to only one club is 6 - 3 = 3 students.

The number of students who belong to neither club is 6 + 3 - 3 = 6 students.

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Answer:

1 cubic centimeter

Step-by-step explanation:

volume = 1 × 1 × 1 = 1 cm²

Answer:

b. -3

Step-by-step explanation:

9(2x+1) < 9x-18

(distribute the 9)

18x+9 <9x-18

(subtract 9 from both sides)

18x<9x-27

(subtract 9x from both sides)

9x<-27

(divide both sides by 9)

x<-3

Answer:

82°

Step-by-step explanation:

total wine of quadrilateral=360°

130+ 46+ 102 +x =360

x=360- 278

x=82°

The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.

During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.

So,

\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)

\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)

\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)

Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

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Answer:

I think it's 2

Step-by-step explanation:

Answer:

1/11 is correct.

Step-by-step explanation:

You can see that the 3 is spun 2 times, but we need to know how many times he spun in total.

2 + 3 + 2 + 4 + 5 + 2 + 1 + 3 = 22

2/22 = 1/11

Have a nice day!

Answer:

\( \sqrt[2]{?5} x25 \geqslant 6 - 9 + 88 = 2\)

Answer:

f^-1(x)=(3/4)x

1. The average daily balance for this credit card account is $187.74.

2. The finance charge for the month of April is $249.22.

The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.

A billing cycle for a credit card account is usually one month.

Interest rate = 16.15% compounded monthly

Date       Activity            Amount     Balance  

April 1    Beginning Balance          $1,000.00

April 5   Purchase           29.10         1,029.10

April 12  Payment      −225.00           804.10

April 15  Purchase         97.25            901.35

April 23 Purchase         19.00           920.35

April 26 Purchase        28.40           948.75

April 30 Ending Balance                  948.75

Total                                            $5,632.05

Average daily balance = $187.735 ($5,632.05/30 days)

Daily interest rate = 0.04425 (16.15%/365)

Finance charge = $249.22 ($187.74 x 0.04425 30 days)

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The digits from 0-9 should Jimmy use to represent him winning is 4-9.

We are given that;

Hockey games won= 609

Now,

To use a random number table to determine the probability of him winning the next two games, Jimmy needs to assign digits from 0 to 9 to represent him winning or losing.

Since he wins 60% of his games, he should assign 6 digits to represent him winning and 4 digits to represent him losing.

One possible way to do this is to use 0-5 to represent him winning and 6-9 to represent him losing.

Another possible way is to use 4-9 to represent him winning and 0-3 to represent him losing.

Therefore, by probability the answer will be 4-9.

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Answer:

.22

Step-by-step explanation:

The number of times a 3 was rolled is 44 out of 200

The experimental probability is  44/200 = .22

The frequency of rolling a 3 was 44.

So... 44/200

After dividing we get 0.22

Therefore, the answer is A

Best of Luck!

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

y = 1/2x + 10  

Step-by-step explanation:

I'm not sure if this is right but:

First you work out the gradient of the line which is the difference in y divided by the difference in x:  

Gradient = (14 - 11) ÷ (8 - 2) = 3 ÷ 6 = 1/2    

the gradient is 1/2 so you'd write that as: y= 1/2x + c

Then you need to work out the y-intercept ( c )  

You do this by substitution:

14 = 1/2(8) + c

14 = 4 + c

c = 10

So the y-intercept is 10 so you'd write that as:

y = 1/2x + 10

Answer:

3

Step-by-step explanation:

Answer:

What do we have to do in this? Find x? Let me know I'll explain it in the comment section

Answer:

The answer is D. Selections of objects in which the order of the objects matters.

Step-by-step explanation:

Permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

The formula for permutation: A permutation is the choice of (r) things from a set of (n) things without replacement and where the order matters. Formula-  

\(nPr= \frac{n!}{(n-r)!}\)

Permutation can be classified in three different categories:

Answer:

2.35714285714

Step-by-step explanation:

Thank you!

Answer:

2 times

Step-by-step explanation:

You can subtract to find it. 33 - 14 = 19. 19 - 14 = 4. That is 2 times. If you subtract again, it won't work.

Answer:

20.25 pi

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

9 pi = 2 * pi *r

Divide each side by 2pi

9pi / 2 pi = 2 pi r / 2 pi

4.5 = r

Now we can find area

A = pi r^2

= pi ( 4.5)^2

20.25 pi

The relationship between the number of balls Lucia lost at the golf

courses can be expressed as an equation.

Reasons:

The given parameters are;

The number of balls Lucia loses at the Rolling Hills, r = 12 balls

The number of balls Lucia loses at the Meandering Meadows, m = 8 balls

The total number of balls Lucia lost after playin at Rolling Hills and Meandering Meadows = 100 balls

The relationship between r and m is therefore;

Number of balls lost at Rolling Hills + Number of balls lost at Meandering Meadows = 100

12 × r + 8 × m = 100

12·r + 8·m = 100

The equation that best represents the relationship between r and m is therefore; 12·r + 8·m = 100

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Answer:

All parallelograms are rectangles.

Answer:

52.63% probability that thids intial repair was made by the first technican

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Incomplete repair

Event B: Made by the first technican.

The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.

This means that \(P(B) = 0.4, P(A|B) = 0.05\).

Probability of an incomplete repair:

5% of 40%(first technican) or 3% of 60%(second technican). So

\(P(A) = 0.05*0.4 + 0.03*0.6 = 0.038\)

Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican

\(P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263\)

52.63% probability that thids intial repair was made by the first technican

Answer:

its A and D dont listen to the other person lol

W

A straight line segment can be drawn between any two points.

Answer:

B. xy(y - x) (y + x)

Step-by-step explanation:

Answer:

Step-by-step explanation:

the degree of a polynomial determines 1:1 the number of solutions.

a quadratic equation (degree 2) has 2 solutions.

the general solution is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = -4

b = -4

c = -1

so,

x = (4 ± sqrt((-4)² - 4×-4×-1))/(2×-4)

when we look at the square root

16 - 16

we see that it is 0.

the square root of 0 is 0, and there is no difference between -0 and +0.

so, we get only one (real) solution : 4/-8 = -1/2

but : formally, there are still 2 solutions (as this is a quadratic equation). they are just identical.

so, I am not sure what your teacher wants to see in this case as answer.

my answer would be 2 real identical solutions. did this help?

Answer:

-59

Step-by-step explanation:

f(x) = -2x - 7 and g(x) = -4x + 6.

f(g(x)) =

Replace x in the function f(x) with g(x)

     = -2(-4x+6) -7

    = 8x -12 -7

    = 8x - 19

Let x = -5

f(g(-5) = 8(-5) -19

    = -40 -19

   = -59