Complete the proof by choosing the correct "Reason".

Answer:

1

2

[

x

2

2

−

x

3

3

]

2

0

=

1

2

[

(

4

2

−

8

3

)

−

(

0

)

]

=

1

2

(

−

2

3

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=

−

1

3

Step-by-step explanation:

The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;

x = 4°, y = 10°

11. x = 9°, y = 12°

12. x = 14°, y = 5°

13. x = 8°, y = 11°

14. x = 16°, y = 23°

15. x = 9°, y = 13°

Parallel lines are lines that maintain the same distance from each other along their lengths.

From the figure, we get;

(29·x - 3) and (15·x + 7) are linear pair angles, therefore;

(29·x - 3) + (15·x + 7) = 180°

44·x + 4 = 180

x = (180 - 4)/44 = 4

x = 4°

(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;

(15·x + 7) + (13·y - 17) = 180°

(15×4 + 7) + (13·y - 17) = 180°

67 + 13·y - 17 = 180°

50 + 13·y = 180

13·y = 180 - 50 = 130

y = 130 ÷ 13 = 10

y = 10°

11. (18·x - 44)° and  (8·x - 10)° are same side exterior angles, therefore;

(18·x - 44)° +  (8·x - 10)° = 180°

26·x - 54 = 180

x = (180 + 54)/26 = 9

x = 9°

(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;

(8·x - 10)° + (13·y - 38)° = 180°

(8 × 9 - 10)° + (13·y - 38)° = 180°

62 - 38 + 13·y = 180

13·y = 180 - (62 - 38) = 156

y = 156 ÷ 13 = 12

y = 12°

12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;

(9·x - 2)° = (5·x + 54)°

(9·x - 2)° = (5·x + 54)°

9·x - 5·x = 54 + 2 = 56°

4·x = 56°

x = 56° ÷ 4 = 14°

x = 14°

(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;

(9·x - 2)° + (10·y + 6)° = 180°

(9 × 14 - 2)° + (10·y + 6)° = 180°

124 + 6 + 10·y = 180

10·y = 180 - 130 = 50

y = 50 ÷ 10 = 5

y = 5°

13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;

(8·x - 1)° is congruent to angle (11·x - 25)°

(8·x - 1)° = (11·x - 25)°

11·x - 8·x = 25 - 1 = 24

3·x = 24

x = 24 ÷ 4 = 8

x = 8°

Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;

(15·y - 48)° + (8·x - 1)° = 180°

(15·y - 48)° + (8 × 8 - 1)° = 180°

(15·y - 48)° + 63° = 180°

15·y + 15° = 180°

15·y = 180° - 15° = 165°

y = 165° ÷ 15 = 11°

y = 11°

14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;

(4·x + 4)° = (7·x - 44)°

7·x - 4·x = 44° + 4° = 48°

3·x = 48°

x = 48° ÷ 3 = 16°

x = 16°

The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°

Therefore;

39 + 8·y - 43 = 180°

8·y  = 180 + 43 - 39 = 184

y = 184 ÷ 8 = 23

y = 23°

15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;

(15·x - 26) = (12·x + 1)

(15·x - 12·x) = (26 + 1)

3·x = 27

x = 27 ÷ 3 = 9

x = 9°

The vertical angle to (2·x + 1) is therefore;

12·x + 1 = 12 × 9 + 1 = 109

The angle sum property indicates that we have;

28° + 109° + (4·y - 9)° = 180°

(4·y - 9)° = 180° - (28° + 109°) = 43°

(4·y - 9)° = 43°

(4·y)° = 43° + 9° = 52°

y = 52°/4 = 13°

y = 13°

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Answer:

C: 108 cubic inches

Step-by-step explanation:

This problem is simply asking us to calculate volume, and in a rectangular shape can be calculate as: length * width * height

Since we know that the base is 4 inches by 9 inches, we already have the length and width.

We're also given that the depth, which in this case is our height, as 3 inches.

So we multiply these three numbers: [tex]4 \text{ in} * 9 \text{ in} * 3\text{ in} = 108\text{ in}^3[/tex]

So our answer is 108 cubic inches

The solution for the given inequality has been graphed in detail.

A linear inequality can be gives the values for a variable in an interval of numbers.

Given inequalities are as below,

2x - 7 > 3 and 4 - x < -4

They can be simplified as,

2x - 7 > 3    

=> 2x > 10    

=> x > 5

And,  

4 - x < -4

=> x - 4 > 4

=> x > 8

The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.

This is graphed as follows,

Hence, the given inequality has solution x > 8 which has been graphed.

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Answer:

Never

Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45

Answer:

Step-by-step explanation:

never

Answer:

-8

Step-by-step explanation:

i think

Answer:

Your answer is -8

Step-by-step explanation:

For given equation, the constant of proportionality is 4

In this question, we have been given an equation m = 4b that represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).

We need to determine the constant of proportionality.

We know that the the constant of proportionality is nothing but the ratio of two proportional values.

In this case the time a chef needs to cook depend on the number of bacon cheeseburgers (b).

So, m is directly proportional to the b

Therefore, the constant of proportionality is 4

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Answer:

The answer is 4

Step-by-step explanation:

I hope this helps!!

Juan's winnings has an expected value of $360

The given parameters in the question are:

$100 with probability 0.2,

$300 with probability 0.3,

$500 with probability 0.5.

The expected value is then calculated as

E(x) = Sum of (amount * probability)

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

E(x) = 100 * 0.2 + 300 * 0.3 + 500 * 0.5

Evaluate

E(x) = 360

Hence, the expected value  is $360

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Answer:5) gcf=6 lcm=42 | 6) gcf=2 lcm=270 | 7) gcf=2 lcm=224

Step-by-step explanation:

Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

f(x) = x³ - 4x² - 5x + 14

-2    |    1    -4     -5     14

                -2      12   -14

           1    -6       7     0

x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)

x²-6x+7=0

x²-6x+9-2=0

(x²-6x+9)-2=0

x²-6x+9=2

x²-3x-3x+9=2

x(x-3)-3(x-3)=2

(x-3)²=2

x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]

x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

our first "suspicion" for a factoring is an integer factor of the constant term : 14.

14 = 2 × 7 or -2 × -7

I started to try 2 or -2 and found that -2 is indeed a zero solution.

so, the first factors are

f(x) = (x + 2)(x² + ...)

let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.

x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7

- x³ + 2x²

--------------

0 -6x² - 5x

- -6x² - 12x

----------------

0 7x + 14

- 7x + 14

------------

0 0

f(x) = (x + 2)(x² - 6x + 7)

the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation

ax² + bx + c = 0

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =

= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =

= 3 ± sqrt(8/4) = 3 ± sqrt(2)

x1 = 3 + sqrt(2)

x2 = 3 - sqrt(2)

so, the zeros are

-2, 3 - sqrt(2), 3 + sqrt(2)

The momentum of the automobile is 7200 kgm/s

Momentum can be described as the product of the velocity and mass of an object.

It is a vector quantity which is defined as a quantity having both magnitude and  direction.

The formula for calculating momentum is expressed as;

p = mv

Where;

Now, let's substitute the values

p = 1200(6)

expand the bracket

p = 1200 × 6

Multiply the values

p = 7200 kgm/s

Hence, the value is 7200 kgm/s

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Answer: 35

Step-by-step explanation:

If 85 students signed up for mathematics but 50 of those students also signed up for both then you need to subtract 85 from 50 to get 35.

Using the percentage, Rapunzel participated in 9581/100 matches.

In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.

Rapunzel's team participated in a total of 143 wrestling matches.

Rapunzel participated in 67 percent of the wrestling matches.

Total matches = 143

Participated in = 67%

Total number of matches in which Rapunzel participated is

= 143*67%

= 143* 67/100

= 9581/100

Rapunzel participated in 9581/100 matches.

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Answer:

10, 17

Step-by-step explanation:

let the number be n then the other number is n + 7 and

n + n + 7 = 27

2n + 7 = 27 ( subtract 7 from both sides )

2n = 20 ( divide both sides by 2 )

n = 10

n + 7 = 10 + 7 = 17

the numbers are 10, 17

The statement that correctly describes the graph of the relationship is (d) A line that goes through (0, 0) and (4.3, 17.2).​

The table of values is given as

x 4.3 9.2 3.4

y 17.2 36.8 13.6

The table shows a proportional relationship

This means that the line of the graph must pass through the origin i.e. (0, 0)

From the table of values, we have the following point

(4.3, 17.2)

This means that the line of the graph goes through (0, 0) and (4.3, 17.2).​

Hence, the true statement is (d)

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Answer:

No, it is not proportional because 9.2 over 18.4 does not equal 17.6 over 52.8.

Step-by-step explanation:

Answer:

60, 80, 100

Step-by-step explanation:

All 3 of these numbers are between 55 and 101, and can be divided by all 3 numbers provided.

Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8

Mike has some t-shirts

The fraction of pink t-shirts = 1/4

The remaining t-shirts = 1 - (1/4)

= 3/4

1/2  of the remaining t-shirts are white

Then the fraction of white t-shirt = 3/4 × 1/2

= 3/8

The fraction of purple t-shirt = 1 - (1/4 + 3/8)

= 3/8

Hence, Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8

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The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.

Given that,

In the picture there is a triangle with angles 53°, 8p+10°, 2p+17°.

We have to find the p value and each of the angles also.

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.

Take the angles ,

180 degrees is the sum of the angles in an triangle.

53°+ 8p+10°+ 2p+17°=180°

10p+80°=180°

10p=180°-80°

10p=100°

p=100/10

p=10°

The value of p=10.

The angles of the triangles are:

53°

8p+10=8(10)+10=80+10=90°

2p+17=2(10)+17=20+17=37°

Therefore, The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.

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The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .

In the question ,

it is given that

the cost of 1 ticket for the theater is = $8.00

let the number of ticket be = t

so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )

Substituting the values of number of tickets and cost of 1 ticket ,

we get ,

cost for t tickets = 8 × t

= 8t

Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .

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Answer:

No, the point is on the x-axis, it is not a y-intercept.

Answer:

Luis had to make a $420 down payment

Step-by-step explanation:

10%: $2,100 / 10 = $210

20%: $210 x 2 = $420

Regarding the velocity and acceleration functions, it is found that:

b) The particle is moving to right on these following intervals: (0,1) U (3,10).

c) The velocity when the acceleration is of zero is: -1 m/s.

A particle is moving to right when it's velocity is positive.

In this problem, the velocity function is presented as follows:

v(t) = 3t² - 12t + 9.

The velocity function is a concave up quadratic function, which is positive to left of the smaller root and to the right of the larger root.

The roots of the function are given as follows:

v(t) = 3(t² - 4t + 3)

Then:

3(t² - 4t + 3) = 0

t² - 4t + 3 = 0

(t - 1)(t - 3) = 0.

Considering the domain of the function, the intervals in which the car is moving right are:

(0,1) U (3,10).

The acceleration is given by the following equation:

a(t) = 6t - 12.

It is of zero when:

6t - 12 = 0

6t = 12

t = 12/6

t = 2.

The velocity at this instant is of:

v(2) = 2² - 4(2) + 3 = -1 m/s.

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Answer:

v = 4

Step-by-step explanation:

[tex]collect \: like \: terms \: \\ 7v - 4v - v + 4v = 7 + 7 + 10\\ 3v - v + 4v = 14 + 10\\ \\ 2v + 4v = 24 \\ 6v = 24 \\ v = 4[/tex]

The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million

We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;

A(h) = -0.06h² + 2h + 4

where h is the time in number of hours after which the concentration is recorded.

Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;

A(4) = -0.06(4²) + 2(4) + 4

A(4) = -0.96 + 12

A(4) = 11.04 parts per million

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Answer: Yes

Step-by-step explanation:,

The factors of 10 are 2 and 5 any number divisible by 10 will also be divisible by both 2 and 5.

Hope this helps! ^-^  Have a good day! :)

Answer:

Yes, Because factors of 10 are 1,2,5,10.

So all numbers divisible by 10 must be divisible by 2 and 5.

Step-by-step explanation:

The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c

Information given in the question include

a linear function graph

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m = -2/3

negative slopes slants from top left to bottom right as in a and c

from the graph, option c has points (-1, 0) and (0, -2/3)

m = (-2/3 - 0) / (0 - -1)

m = (-2/3) / (0 + 1)

m = -2/3

This matches with option C

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Considering the five number summary of the data-set, we have that:

a. None of the prices were outliers, as all the prices are within 1.5 IQR of the quartiles.

b. That is not a very low price, as it is above the first quartile, while very low prices have to be 1.5 IQR below the first quartile.

The outliers, considering the five number summary of a data-set, are the values that are more than 1.5 Interquartile Ranges from the quartiles, that is, either:

The interquartile range of a data-set is the difference between the third quartile and the first quartile, hence, for the given data-set:

IQR = Q3 - Q1 = 110 - 30 = 80.

Hence the bounds for outliers are given as follows:

Since the maximum value of 200 is less than 230, there are no outliers in the data-set.

The five number summary is given by the image at the end of the answer.

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The circumference of the circle is 25.1 inches.

The length of the arc ACB is 4.2 inches.

The circumference of a circle is the perimeter of the circle.

Therefore,

circumference of a circle = 2πr

where

Hence,

circumference of a circle = 2 × 3.14 × 4

circumference of a circle = 8 × 3.14

circumference of a circle = 25.1 inches

The length of the arc ACB can be found as follows:

length of arc = ∅/ 360 × 2πr

length of the arc = 60 / 360 ×  2 × 3.14 × 4

length of the arc = 60 / 360 ×  25.12

length of the arc = 1507.2 / 360

length of the arc = 4.18666666667

length of the arc = 4.2 inches

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