If lines I and m are parallel, which pair of angles are congruent?
o 2 and 3
o 1 and 8
o 4 and 5
o 1 and 7

Answer:

(7, 4)

Step-by-step explanation:

[tex]\text{Let the coordinates of B } = x_{B} , y_{B} \\\text{Let the coordinates of A} = x_{A} , y_{A} \\\text{Let the coordinates of midpoint M} = x_{M} , y_{M}[/tex]

By the midpoint formula,
[tex](x_{M},y_{M}) = (\frac{x_{A} + x_{B}}{2} , \frac{y_{A} + y_{B}}{2} )[/tex]

[tex]x_{M} = \frac{x_{A} + x_{B}}{2} \\y_{M} = \frac{y_{A} + y_{B}}{2} \\[/tex]

We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So
[tex]5 = \frac{3 + x_{B}}{2} \\\\\\textrm{Cross-multiplying } 10 = 3 + x_{B}} \textrm{ or } x_{B} = 10-3 = 7\\[/tex]

[tex]6 = \frac{8 + y_{B}}{2} \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_{B}} \textrm{ or } y_{B} = 12-8 = 4\\[/tex]

So coordinates of B are (7,4)

Answer:

[tex]\textsf{a)} \quad \textsf{Recursive Rule}: \quad a_n=5n-2[/tex]

     [tex]\textsf{Explicit Rule}: \quad \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]

b)  4998

c)  explicit rule (see below for explanation)

d)  see below

Step-by-step explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Explicit Formula

[tex]a_n=a+(n-1)d[/tex]

where:

Given sequence:  3, 8, 13, 18, 23, ...

To find the common difference, subtract one term from the next term.

Therefore:

Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:

[tex]\implies a_n=3+(n-1)5[/tex]

[tex]\implies a_n=3+5n-5[/tex]

[tex]\implies a_n=5n-2[/tex]

Recursive Formula

[tex]a_n=a_{n-1}+d \quad \textsf{for }n\geq 2[/tex]

where:

We already know the common difference our previous calculations.

Therefore:

[tex]\implies a_n=a_{n-1}+5[/tex]

When giving a recursive rule we also have to define the first term of the sequence, as it is not part of the formula.  Therefore, the full recursive rule for the given sequence is:

  [tex]\begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]

To find the 1000th term of the sequence, use the explicit rule and substitute n = 1000:

[tex]\implies a_{1000}=5(1000)-2[/tex]

[tex]\implies a_{1000}=5000-2[/tex]

[tex]\implies a_{1000}=4998[/tex]

Therefore, the 1000th term of the sequence is 4998.

We used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence without having to know any previous terms.

The disadvantage of a recursive rule when compared to an explicit rule is that we need to know the previous term to find the nth term, whereas the explicit rule doesn't need this information.

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Answer:

y = (x - 2)² - 5

Step-by-step explanation:

y = x² - 4x - 1

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 - 1

y = (x - 2)² - 5 ← in vertex form

The likelihood that it contains a letter just after an odd number is 1/2 . D's likelihood of being in the code but not at the first position is 1/4.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

A three-digit code is needed to unlock the lock on a locker. One letter and two numbers are required for the code, and neither a letter nor a number may be repeated.

Four letters, A, B, C, and D, as well as two numerals, 5 and 6, are available for selection.

The sample space has a size of (8, 16, 20, and 24)

If a random code is chosen,

The likelihood that it contains a letter after an odd number (1/8, 1/6, 1/3, 2/5, or 2/3)

= 1/2

If a random code is chosen,

Probability (1/8, 1/6, 1/3, 2/5, 2/3) that D is in the code but not at the first position.

= 1/4

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Answer:

1:2

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

Concluimos que hay 8 libros de aritmética.

Sabemos que la relacion entre el número de libros de aritmetica y el total de libros es de 4 a 9.

Es decir, sí el número total de libros es N, entonces (4/9)*N de esos libros son de aritmética.

Sea X el número de libros de aritmética. Sabemos que hay 10 libros de algebra, entonces el número total N es:

N = 10 + X

Y usando la relación de arriba, podemos escribir:

X = (4/9)*N = (4/9)*(10 + X)

Ahora podemos resolver esto para X.

X*(9/4) = 10 + X

X*(9/4) - X = 10

X*(5/4) = 10

X = (4/5)*10 = 8

Concluimos que hay 8 libros de aritmética.

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Answer:

The given lines are parallel.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (0,6) and (3,-24). Whereas, line 2 passes through (-1,19) and (8,-71).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{-24-6}{3-0} \\&m_{1}=\frac{-30}{3} \\&m_{1}=-10\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{-71-19}{8-(-1)} \\&m_{2}=\frac{-90}{9} \\&m_{2}=-10\end{aligned}$$[/tex]

Since, both slopes are equal.

Therefore, the lines are parallel.

Answer:

[tex]\{3\}[/tex]

Step-by-step explanation:

Strictly speaking, we need to know the point of [tex]f(x) = 3x[/tex] intersecting [tex]f(x) = 9[/tex]. In other words, we need to solve the equality:

[tex]3x = 9; \\ x = \frac{9}{3}; \\ x = 3[/tex]

Here it is.

Based on the translated image and the original triangle ABC, the true statements are:

The pre-image of triangle ABC and the image are shown to have sides that are congruent because they are exactly the same. This is why triangle A¹B¹C¹ is a slide of triangle ABC.

In order to form the image, the translation must have been such that each point of the preimage moved the same number of units.

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Answer:

a, d, g

Step-by-step explanation:

i took da test

Answer:

The expression for the statement using absolute value notation is [tex]|x|\geq 100[/tex]

Step-by-step explanation:

It is given in the question that the distance from city A to city B is at least  100 miles.

It is required to express the statement using absolute value notation.

To express the statement using absolute value notation, deduce the statement in the form of an equation.

x represents the distance from city B to A city .

Deduce the statement in the form of an equation
[tex]|x|\geq 100[/tex]

The degree the tree was leaning is 70 degrees.

Using cosine law,

c² = a² + b² - 2ab cos C

Therefore,

6² = 2² + 5² - 2 × 2 × 5 cos C

36  = 4 + 25  - 20 cos C

36  = 29 - 20 cos C

36  - 29 = - 20 cos C

7 = - 20 cos C

cos C = 7 / - 20

cos C = -0.35

C = cos⁻¹ 0.35

C = 69.5126848853

C = 70 degrees.

Therefore, the degree the tree was leaning is 70 degrees.

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According to graph, GMT time when the plane flew over the beacon was 9:24.

While looking closely at the graph on x axis , one will notice that each hour is divided into 5 parts and hence each part has 12 minutes. looking at y axis, one may find that each part on y axis resembles 20miles. Hence at 280 miles away from Bristol, The GMT time is 9:24.

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The measure of ab and df are 3cm and 7.5cm respectively

In order to determine the missing sides, we need to take the ratio of the similar sides as shown:

1) ab/de = ac/df

ab/de = ab+bc/df

Substitute the given values

ab/2 = ab+4.5/2+3

ab/2 = ab+4.5/5

2(ab+4.5) = 5ab
2ab+9=5ab

3ab = 9

ab = 3cm

Hence the measure of ab is 3cm

2) ae/ce = bf/df

24/9 = 20/df

24df =. 9(20)

24df = 180

df = 7.5cm

Hence the measure of ab and df are 3cm and 7.5cm respectively

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Answer:

If they worked together it would take 4 hours for the machines to produce 100 widgets

Step-by-step explanation:

w = widgets     hr = hour     ph = per hour

Old machine - 50w = 5hr = 10ph

New machine - 30w = 2hr = 15ph

Old machine - 20w = 2hr

New machine - 30w = 2hr

     I hope this helped!

Answer:

The decimal number 8,500,000 has been converted to its corresponding scientific notation, which is [tex]$8.5 \times 10^{6}$[/tex].

Step-by-step explanation:

Step 1 of 1

Remember that the decimal lies at the end of 8,500,000. Move the decimal next to 8 such that the result is greater than 1 and less than 10 . So the decimal point will move 6 places to the left.

As 8,500,000 is greater than 1 so the power of 10 will have an exponent of 6 .

So,

[tex]$$8,500,000=8.5 \times 10^{6}$$[/tex]

Verifying the result we can see that

[tex]$$10^{6}=1,000,000$$[/tex]

when multiplied by 8.5 will result in 8,500,000.

Answer:12

Step-by-step explanation:(1307.50-812.50)/41.25 = 12

The lacrosse team can bring 12 players to the tournament.

Let's assume the number of players on the lacrosse team is "n."

The total amount raised by the team is $1307.50, and they rented a bus for $812.50. The remaining amount after renting the bus is available for meals.

Amount available for meals = Total amount raised - Bus rental cost

Amount available for meals = $1307.50 - $812.50

Amount available for meals = $495

Now, the budgeted amount per player for meals is $41.25. To find the number of players the team can bring to the tournament, we need to divide the total amount available for meals by the budgeted amount per player:

Number of players = Amount available for meals / Budgeted amount per player

Number of players = $495 / $41.25

Number of players = 12

So, the lacrosse team can bring 12 players to the tournament.

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Answer:

900 liters of water is pumped in 1 hour

Step-by-step explanation:

Time taken to pump 15 liters of water =  1 minute.

Time taken to  pump 1 liters of water  = 1/15 minute

[tex]\sf \text{Time taken to pump 900 liters of water=$\dfrac{1}{15}*900$}[/tex]

                                                             = 60 minutes

                                                             = 1 hour

19 : 125 = 0.152, and because there is a finite amount of digits after the decimal, this is a terminating decimal. (if anything's wrong just message)

hi hermes

Answer:

120 different ways

Step-by-step explanation:

The formula to count the permutation since the order the matters: nPr = n! / (n - r)!, where n is the total number and r is the total number of chosen.

1) Substitute values into the formula. SMILE has 5 letters, and we choose 5.

5P5 = 5! / (5 - 5)!

5P5 = 5! / 0!

Zero factorial (0!) is always 1.

So, 5P5 = 5! / 1

5! = 5 × 4 × 3 × 2 × 1

5! = 120

Therefore, 5P5 = 120 / 1, which is 120. We can arrange the word SMILE in 120 different ways.

The internet service provider charges 40 cents for each extra hour used.

Also, he provides 40 hours of free service for every account.

Solved using linear equations.

Let the number of free hours provided by the internet service provider be x, and the charge for each extra hour be p cents.

Let the time consumed by Wells, Ted, and Vino be t1, t2, and t3 respectively.

Chargeable time used by Wells = t1 - x.

Cost for Wells = p(t1 - x).

Chargeable time used by Ted = t2 - x.

Cost for Ted = p(t2 - x).

Chargeable time used by Vino = t3 - x.

Cost for Vino = p(t3 - x).

Now, we are given that Wells and Ted, in total used 105 hours, that is, t1 + t2 = 105.

The cost for them together is $10 or 1000 cents.

This can be shown as the linear equation:

p(t1 - x) + p(t2 - x) = 1000.

or, p{(t1 - x) + (t2 - x)} = 1000,

or, p{(t1 + t2) - 2x} = 1000,

or, p(105 - 2x) = 1000,

or, p = 1000/(105 - 2x) ... (i).

Time consumed by Vino is given as 105 hours, thus, t3 = 105.

The total cost to Vino is given as $26 or 2600 cents.

This now can be shown as the linear equation:

p(t3 - x) = 2600,

or, {1000/(105 - 2x)}(105 - x) = 2600 {Substituting t3 = 105, and p = 1000/(105 - 2x)}.

This is the required linear equation in one variable.

It can be solved as follows:

{1000/(105 - 2x)}(105 - x) = 2600,

or, 105000 - 1000x = 273000 - 5200x,

or, 5200x - 1000x = 273000 - 105000,

or, 4200x = 168000,

or, x = 168000/4200 = 40.

Substituting x = 40 in (i), we get:

p = 1000/(105 - 2x),

or, p = 1000/(105 - 2(40)),

or, p = 1000/(105 - 80),

or, p = 1000/25,

or, p = 40.

Thus, the internet service provider charges 40 cents for each extra hour, and he provides 40 hours of free internet on every account.

The provided question is incomplete. The complete question is:

"An Internet service provider allows a certain number of free hours each month and then charges for each additional hour used. Wells, Ted, and Vino each have separate accounts. This month the total hours used by Wells and Ted was 105, and each used all of their free hours. Their total cost was $10. Vino used 105 hours by himself and had to pay $26. What is the number of cents charged for each extra hour?"

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Answer:

Step-by-step explanation:

A woman buys 3 dezen eggs. Later she discovers that x of them are broken. How many mang eggs are not broken

3 = 3

Dozen = 12

x = broken eggs

3 * 12 - x =

36 - x

The absolute value expression for the given statement is  |10|

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign

Marcus was going up stairs in his office. Therefore, he was ascending .

This means the 10 staircase will be added since there is an increase.

Hence, the absolute value expression for the given statement is as follows:

absolute value = |10|

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Answer:

36 miles and 10 miles

Step-by-step explanation:

area = length × width

A = LW

W = unknown = x

L = 26 ft more than width = x + 26

A = LW

360 = (x + 26)x

360 = x² + 26x

x² + 26x - 360 = 0

(x + 36)(x - 10) = 0

x + 36 = 0  or  x - 10 = 0

x = -36 or x = 10

We discard the solution x = -36 since the width of a rectangle cannot be a negative number.

W = x = 10

L = x + 26 = 10 + 26 = 36

Answer: 36 miles and 10 miles

Work Shown:

f(x) = x + 10

f(x+1) = x+1 + 10 .... replace every x with x+1

f(x+1) = x + 11

The value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. This a can be obtained by solving the linear inequality by taking terms with x to one side of the inequality similar to solving of linear equation.

Given that  

         3x + 3 - x + (-7) > 6

         3x - x > 6 + 7 - 3

         2x > 10

          x > 5

Hence the value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. The correct option is c.

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Answer:

7

Step-by-step explanation:

Whenever you shifting an exponential function to the left/right, you're going to generally have the equation: [tex]y=2^{x-k}[/tex] where k is the shift. So in this case we can think of x+3 as x and k as 10, since the shift is 10. This gives you the equation: (x+3) - 10, which simplifies to x-7, meaning the k value in this case is going go be 7. You can also think of it as already being shifted 3 units to the left, and you shift it 10 units to the right, that means this new function will be shifted 7 units to the right relative to the origin. This means the k=7.