What is the measure of

The two column proof of the given angles are;

Statement 1; m∠AOB = 180°

Reason 1; Sum of angles on a straight line sums up to 180°

Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB

Reason 2; Opposite angles

Statement 3; x + 3x + x + 12 = 152

Statement 3; Substitution

Statement 4; x = 28°

Reason 4; Algebra

From the attached image, we can complete the two column proof as follows;

Statement 1; m∠AOB = 180°

Reason 1; Sum of angles on a straight line sums up to 180°

Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB

Reason 2; Opposite angles

Statement 3; x + 3x + x + 12 = 152

Statement 3; Substitution

From statement 3, we can use algebra to find x as;

x + 3x + x + 12 = 152

5x + 12 = 152

5x = 152 - 12

5x = 140

x = 28°

Thus;

Statement 4; x = 28°

Reason 4; Algebra

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The difference between of the cost of the phones in the USA and the UK is $51. 2

Exchange rate can be defined as the price of the unit of foreign currency in terms of the home currency.

It is also known as the rate at which a currency is exchanged to another currency

From the information given, we have that;

We also have that;

The exchange rate is expressed as;

£1 = $1.36

Now, let's convert the cost from dollars to euros, we have;

If £1 = $1.36

Then, £920 = $x

cross multiply, we have;

x = 920 × 1. 36

x = $1251. 36

Now, let's find the difference between the cost in the USA and UK, we have;

=  $1251. 36 - $1200

= $51. 2

Hence, the difference is $51. 2

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The money in the account at the end of 5 years is 2208.16

The formula for calculating the compound interest is expressed according to the formula:

Compound interest = P(1+r)^t

Given the following parameters

Principal = 2000

rate = 2 % = 0.02

time = 5 years

Substitute

A = 2000(1+0.02)^5

A = 2000(1.02)^5

A = 2208.16

Hence the amount of money that will be in that account at the end of 5 years is 2208.16

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Answer:

97 miles

Step-by-step explanation:

pls mark brainlest

Answer:

97 miles

Step-by-step explanation:

65 mph * 1.5 hours = 97 miles

The inequality which correctly represents the fact that the spending limit cannot be exceeded as described in the task content is; 100x ≤ 200.

It follows from the task content that the inequality which correctly represents the spending limit as described be determined.

Since the given spending limit is; $200.

Let, x = the number of figures made.

Therefore, the cost of making x number of figures can be written algebraically as; 100x.

Hence, since it costs $100 to make each figure, it follows that the required inequality is;

100x ≤ 200.

This follows from the fact that each figure costs $100 to make.

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Answer: 960

Step-by-step explanation:

Let the number of pennies Keiko's bank hold be x

Now, According to the question,

[tex]\frac{1}{6} \times x+320=\frac{1}{2} \times x[/tex]

⇒ [tex]\frac{1}{6} \times x+320=\frac{x}{2}[/tex]

⇒ [tex]\frac{(x+1960)}{6}=\frac{x}{2}[/tex]

⇒ 2(x + 1920) = 6x

⇒ 2x + 3840 = 6x

⇒ 6x - 2x = 3840

⇒ 4x = 3840

⇒ [tex]x = \frac{3840}{4}[/tex]

⇒ x = 960

Hence, the total number of pennies Keiko's bank hold = 960.

Answer:

See below

Step-by-step explanation:

99.87-71 = 28.81     this is   28.81/12 = z-score = +2.4

   corresponding to .9918  ( from z-score table)  =  a score of 99.18%

Answer: 12.8x2

Step-by-step explanation:

Based on the given task content; the solution to the Multiplication of 3.2x and 4x is 12.8x².

The correct answer option is option a.

This is a process of computing the sum of a number with itself in a specified number of times. Multiplication is also called product and it is represented by the sigh ×. The product of a and b means ab.

For instance, from the task which is given above;

3.2x and 4x

= 3.2x × 4x

= 12.8x²

In this answer above,

12.8 is the coefficient and

x² is the variable.

In conclusion, 3.2x × 4x will give the result 12.8x².

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The value of x is 14 °

The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.

In ΔOPQ,

∠O = (2x- 5)°

∠P = (3x-8)°

∠Q= (10x- 17)°

Thus by angle sum property of triangle we know:

∠O+ ∠P + ∠Q = 180

thus 2x - 5 + 3x - 8 + 10x - 17 = 180

15x - 30 = 180

= 15 x = 180 + 30

= 15 x = 210

= x= 210 / 15

= x = 14 .

Thus ∠O = (2x- 5)° = 2X 14 - 5 = 23 °

∠P = (3x-8)° = 3× 14 - 8 = 44°

∠Q= (10x- 17)° = 10 × 14 - 17 = 123°

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The circumference of the circle will be given by 62.84 cm.

A circle is a closed figure having a fixed point known as center of the circle and the distance from the center to any point on the boundary of circle is known as the radius of the circle. Circumference is the total length of the boundary of the circle. The circumference of the circle is given by the formula

C = 2πr where r is the radius of the circle and the value of π is given as 3.142.

Now, according to question r = 10cm

C = 2×3.142×10

C = 20×3.142

=> C = 62.84 cm

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In the picture there are 4 graphs.

1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).

2nd graph we get domain as [-4,4] and range as [3,-1].

3rd graph we get domain as [-4,1] and range as [1,-4].

4th graph we get domain as (-∞,4] and range as (-∞,-2].

Given that,

In the picture there are 4 graphs.

We have to find the domain and range of the each function using inequality or set-builder notation.

A function's domain is the set of values that we are allowed to enter into our function.

This set consists of the values of the x-axis for a function like f. (x).

The range of values that can be used as input for a function is called this. The values in this set hence, once we input an x value, the function returns. The y values are those.

1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).

2nd graph we get domain as [-4,4] and range as [3,-1].

3rd graph we get domain as [-4,1] and range as [1,-4].

4th graph we get domain as (-∞,4] and range as (-∞,-2].

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Answer:

answer is B

Step-by-step explanation:

Sorry if this is incorrect

Answer:  38.46

Step-by-step explanation:

             ↓

   38.456 It means round by 0.05, so when you round you look at the place value after the specified digit.

After using translation the image of the given points will be at Q( 6 , 6 ) and  M( -2 , -11 ).

What is translation ?

The linear movement of a point relative to its initial position is known as translation. The horizontal position is labeled first and the vertical position is labeled second when describing a point's coordinates with respect to the origin of an x-y coordinate plane.

The translation is given to be (x,y) → (x + 1, y - 3)

The tow points are Q(5,9), M(-3,-8)

using translation  we get,

Q( 5 , 9 ) → (5 + 1, 9 - 3) = Q( 6 , 6 )

M( -3 , -8 ) → (-3+ 1, -8- 3) = M( -2 , -11 )

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Answer:

C

Step-by-step explanation:

Since the y-coordinates of both points are -3, the equation is [tex]y=-3[/tex].

The only option with a y-coordinate of -3 is option C.

Answer:

A. -11x + 7y

Step-by-step explanation:

4y - 9x + 3y - 2x

4y + 3y = 7y

-9x - 2x = -11x

-11x + 7y

I hope this helps!

The solution set of the given inequality is:

9.52  ≤  x  ≤ 22.22

Or [9.52, 22.22] if we write this as an interval.

Here we have the inequality:

200 ≤ 15.75x + 50 ≤ 400

Which represents Kali's earning potential.

To solve the inequality we need to isolate the variable in the middle, if we subtract 50 in the 3 sides we get:

200 - 50 ≤ 15.75x + 50  - 50 ≤ 400 - 50

150 ≤ 15.75x ≤ 350

Now we need to divide both all by 15.75, so we get:

150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75

9.52  ≤  x  ≤ 22.22

This is the solution of the inequality, the solution set written as an interval will be [9.52, 22.22]

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Answer:

9

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]

Answer:

Circumference 87.92 ft

Step-by-step explanation:

You have a radius of 14 so u multiply by 2 to get the diameter, then u mulptiply by pie (3.14) thats how u get the circumference.

14×2=28

28×3.14=87.92

For given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'

Part A:

We need to write the converse to the conditional statement.

The converse of given conditional statement would be:

'If it is a television, then the object has a remote.'

Part B:

We need to write a biconditional statement from the conditional statement.

A biconditional statement of the given conditional statement would be:

'The object has a remote if and only if it is a television.'

Part C:

We need to validate the above biconditional statement.

The biconditional statement is true because the conditional statement and the converse are true.

Therefore, for given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

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Following the descriptions of the relationship existing  between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d

Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.

Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.

Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.

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The rate of change of the level of the swimming pool is -0.019 inches per hour.

The rate of change will be given by the quotient between the change in the level of the water (-3/16 inches) and the time in which that change happens.

We know that the change happens between 10 pm and 7:45pm, so the number of hours is:

2 hours + 7 hours + 45 min

Where:

1 hour  = 60 min

45 min = 45/60 hours = 0.75 hour

Then the total time is:

2h + 7h + 0.75h = 9.75h

Then the rate of change is:

R = (-3/16 inches)/(9.75 h) = -0.019 inches per hour.

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The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.

Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.

Where P exists at the origin and line segment is a horizontal one.

The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).

The segment exists not a horizontal or vertical line:

The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].

Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).

where neither P nor Q exists at the origin.

Use the end points of the segment PQ to estimate the components of the directed segment.

[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle[/tex]

= (6,-4)

The components of the segment PX where X exists a point on the segment 1 / 3 of the way from P to Q are

[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle=(2,-1.25)$$[/tex]

To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.

Therefore, the coordinates of the point X exists (1+2,6-1.25) = (3, 4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

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Answer:

c. Yes, she is correct because 0.45 and 0.333 are rational numbers. The sum of two rational numbers is a rational number.

The mean of the number of hours spent watching television is 15.75

The mean absolute deviation of the number of hours spent watching television is 6.625.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10 +  11 + 22 + 7 + 17 + 17 + 20 + 31 + 0 + 12 + 19 + 23) / 12 = 189/12 = 15.75

Mean absolute deviation is the average of the sum of the absolute difference between the numbers and the mean.

MAD =  1/n ∑ l x - m(x) l

(|10 - 15.75) + |11 - 15.75| + |22 - 15.75| + |7 - 15.75| + |17 - 15.75|+ |17 - 15.75| + |20 - 15.75| + |31 - 15.75| + |0 - 15.75| + |12 - 15.75| + |19 - 15.75| + |23 - 15.75|

= (5.75 + 6.75 + 6.25 + 8.75 + 1.25 + 1.25 + 4.25 + 15.25 + 15.75 + 3.75 + 3.25 + 7.25) / 12 = 6.625

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Answer:

Cost Function is:

c = 4n

Or, using n as a function variable, we write:

c(n) = 4n

Step-by-step explanation:

c represents total cost
n represents notebook

4 represents cost per notebook

Answer:

151, 29, 151

Step-by-step explanation:

[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)

[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)

Answer:

[tex]m \angle 1= \boxed{159}\;^{\circ}\\\\m \angle 2= \boxed{21}\;^{\circ}\\\\m \angle 4= \boxed{21}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠3 + m∠4 = 180°

⇒ 159° + m∠4 = 180°

⇒ m∠4 = 21°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

Answer:

MP = 19

Step-by-step explanation:

MP = MN + NO + OP

we require to find OP and MN before we can evaluate MP

NO + OP = NP , that is

8 + OP = 15 ( subtract 8 from both sides )

OP = 7

and

MN + NO = M0 , that is

MN + 8 = 12 ( subtract 8 from both sides )

MN = 4

Then

MP = MN + NO + OP = 4 + 8 + 7 = 19