solve the system of linear equations. separate the x- and y- with a coma.
6x=-14-8y
-12x=20+8y

40 miles x 5280 = 211200 feet per hour

1 hour = 3600 seconds

211200 / 3600 = 58.67 feet per second

Answer:

The answer is 59 feet per second (B)

Step-by-step explanation:

edge hope ya do well

The seventh term in the sequence is 1093.5.

A sequence in mathematics is a ordered set od objects or numbers which are related with something.

For example, 1, 3, 5, ..... is a sequence of odd numbers.

Given sequence is,

1.5, 4.5, 13.5, 40.5....

There must be a predictable relation between the numbers in order for them to form in a sequence.

It is clear that,

First term = 1.5

Second term = 3 × 1.5

Third term = 3 × 3 × 1.5 = 1.5 (3)²

............

nth term = 1.5 (3)ⁿ⁻¹

seventh term = 1.5 (3)⁷⁻¹ = 1.5 (3)⁶ = 1093.5

Hence the seventh term is 1093.5.

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Since 3 members want to sit together, we'll calculate total ways for it and then for remaining seats in each of its case, we'll see in how many ways can those rest of 5 people wants to sit.

The total number of ways those 8 people can sit is 3,991,680 ways.

In how many ways can those people sit?

Since 3 people wants to sit together, then suppose seats are numbered 1,2,3,...,14.

Then those 3 people can choose seats as:

1,2,3

2,3,4

...

...

12,13,14

Total 12 ways.

In each way, those three can sit on those 3 chairs in any order. The number of ways 3 people will arrange themselves is 3! = 6 ways.

Thus:

Total ways those 3 people can sit in = 12 times 6 = 72 ways.

( i did multiplication since for each of 3 seat chosen they were sitting in 6 ways, and this repeated 12 times would end up on 12 times 6 = 72 ways).

On remaining seats (14-3 = 11), we have 5 people to sit.

Those people can choose any seat they want to sit on.

Total ways(combinations) they together choose 5 seats is given by: [tex]^11C_5 = 462 [/tex]

For each of those choice of seats, they can arrange themselves in 5! = 120 ways.

Thus, those 5 people can sit in 120 times 464 = 55440 ways.

Since on each choice of those 3 family members , we have 55440 ways of 5 people sitting on remaining 11 seats, thus in total we have:

55440 times 72 = 3,991,680 ways.

Thus, in total, those 8 people can sit in 3,991,680 number of ways in that row of the doctor's waiting room.

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Answer:

$5.5

Step-by-step explanation:

16.5 ÷ 3= 5.5

Answer:7,13

Step-by-step explanation:

Answer:

Option 3 - (8,4)

Step-by-step explanation:

Given : Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0).

To find : The fourth vertex is point ?

Solution :

We have given that points are forming a parallelogram.

Let the fourth coordinate is (x,y)

Now, we draw a rough image of the given situation.

Refer the attached figure below.

Draw a parallelogram ABCD with mid point O.

Applying the mid point between two points (2,4) and (6,0).

[tex]O=\frac{2+6}{2}, \frac{4+0}{2}\\\\ O=4,2[/tex]

Now, Applying mid point between points (0,0) and (x,y)

[tex](4,2)=\frac{x+0}{2}, \frac{y+0}{2}[/tex]

[tex]\frac{x+0}{2}=4, \frac{y+0}{2}=2[/tex]

[tex]x=8 ,y=4[/tex]

Therefore, The fourth vertex point is (8,4).

Hence, Option 3 is correct.

To find dw/dt for w = xy + yzw, we use the chain rule, yielding dw/dt = y(dx/dt) + x(dy/dt) + z(dz/dt) + y(dy/dt) + z(dy/dt). The derivatives dx/dt, dy/dt, dz/dt are calculated using derivative rules. The question-specific parameters are then substituted back into these functions.

Let's denote w as a function of x, y, and z, where x, y, and z are functions of t. We will use the chain rule to find dw/dt as a function of x, y, z, and t.

Given the function: w = xy + yzw, using the chain rule, we get the derivative dw/dt as:

dw/dt = x * dy/dt + y * dx/dt + y * dz/dt + z*dy/dt + z * dy/dt = y(dx/dt) + x(dy/dt) + z(dz/dt) + y(dy/dt) + z(dy/dt)

To particularize this expression for our given parameter values, we need to find dx/dt, dy/dt, and dz/dt. Each derivative can be calculated using the derivative rules. In this case we are to leave the equations x=e^2t, y=2+sin(4t), z=2+cos(5t) as they are, not rewriting them in terms of t, and also not rewriting e^2t as x. This results in dw/dt as a function of x, y, z, and t.

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1   is   a

2   is   b

3   is  b

hope   it   helped

Answer:

Ava's heart will beat for 341640000 beats in 10 years.

Step-by-step explanation:

Heart rate of Ava is = 65 beats per minute

We have to calculate the heart beat in 10 years.

Since Ava's heart beats in 1 minute = 65 times

Heart beat in 1 hour = 65 × 60

                                 = 3900 beats

Heart beats in 24 hours or one day = 3900 × 24

                                                         = 93600 beats

Heart beats in 365 days or 1 year = 93600 × 365

                                                        = 34164000 beats

Heart beats in 10 years = 34164000×10

                                       = 341640000 beats

Therefore, Ava's heart will beat for 341640000 beats in 10 years.

There were 30 families that had a parakeet.

By using the concept of Sets :

- Total number of families surveyed (denoted as N) = 240.

- Number of families with dogs (denoted as D) = 91.

- Number of families with cats (denoted as C) = 70.

- Number of families with both dogs and cats (denoted as D ∩ C) = 31.

- Number of families with neither cats nor dogs nor parakeets (denoted as neither) = 91.

- Number of families with cats, dogs, and parakeets

(denoted as D ∩ C ∩ P) = 7.

We want to find the number of families that had parakeets

(denoted as P).

To find the number of families with parakeets, we can use the principle of inclusion-exclusion. It states that:

N(D ∪ C ∪ P) :

= N(D) + N(C) + N(P) - N(D ∩ C) - N(C ∩ P) - N(D ∩ P) + N(D ∩ C ∩ P).

Substitute the given values:

240 = 91 + 70 + P - 31 - N(C ∩ P) - N(D ∩ P) + 7.

Now, we can calculate the number of families with both cats and parakeets (C ∩ P) and the number of families with both dogs and parakeets (D ∩ P):

C ∩ P + D ∩ P = (C + D + P) - (N(D) + N(C) + N(P)) = 240 - 91 - 70 - P = 79 - P.

From the given information, we also know that the number of families with neither cats nor dogs nor parakeets is 91. Therefore, we can write:

neither + N(D ∩ P) + N(C ∩ P) + N(D ∩ C ∩ P) = 91.

Substitute the values:

91 + N(D ∩ P) + C ∩ P + 7 = 91.

Now, we can solve for C ∩ P:

C ∩ P = 91 - N(D ∩ P) - 7.

Substitute the value of C ∩ P we found earlier:

79 - P = 91 - N(D ∩ P) - 7.

Now, we can find N(D ∩ P):

N(D ∩ P) = 79 - P - 91 + 7 = -P - 5.

However, we know that the number of families cannot be negative. So, we ignore this solution. Instead, we use the previously calculated value of C ∩ P:

C ∩ P = 91 - N(D ∩ P) - 7.

91 - (79 - P) - 7 = 91 - 79 + P - 7 = P - 7.

P - 7 = 30.

Finally, we get the value of P:

P = 30.

Therefore, there were 30 families that had a parakeet.

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Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.

A percentage is a number or ratio that can be expressed as a fraction of 100.

here, we have,

Imagine what x is tea grocer selling for 80 cents per pound

y is tea grocer selling for 60 cents per pound

{80x+60y

=50*74

=3700

{x+y=50  //*60

{80x+60y=3700

-{60x+60y=3000

20x=700

x=35

y=50-35=15

hence, Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.

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Answer:

399.21 newtons or 40.73 kg

Step-by-step explanation:

In order to solve this you first have to do a rule of threes to calculate how much would the fish will weight compared with the stretching of the spring:

[tex]\frac{21}{162} =\frac{62.1}{weight} \\weight=\frac{62.1*162}{21}=399.21 Newtons[/tex]

So the weight would be 399.21 newtons and it would have 40.73 kilograms in mass.

Answer:

the rate is equal to [tex]3.2\frac{inches}{week}[/tex]

Step-by-step explanation:

we have

[tex]h-15=3.2t[/tex]

where

h is the height of a plant

t is the number of weeks after planting

so

Find the rate at which the plant's height is increasing

we know that

The given formula is a linear equation

The rate is equal to the slope of the linear equation

Isolate the variable h

[tex]h=3.2t+15[/tex]

the slope is equal to [tex]m=3.2\frac{inches}{week}[/tex]

therefore

the rate is equal to [tex]3.2\frac{inches}{week}[/tex]

The height was 31 inches in (D) Some time between 3 and 7 weeks.

To find out when the height of the plant was 31 inches using the formula given, we start with the equation:

h - 15 = 3.2t

We want to find the value of ( t ) when the height ( h ) is 31 inches. First, substitute ( h ) with 31 in the equation:

31 - 15 = 3.2t

Now, simplify the left side:

16 = 3.2t

Next, divide both sides by 3.2 to isolate ( t ):

t = [tex]\frac{16}{3.2}[/tex]

Calculating this gives:

t = 5

Therefore, the height of 31 inches was reached at 5 weeks.

So, the answer is: D. Some time between 3 and 7 weeks.

The full question is:

The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting

When was the height 31 inches?

A. Some time between 11 and 18 weeks

B. Some time between 7 and 12 weeks

C. Some time between 6 and 10 weeks

D. Some time between 3 and 7 weeks