Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.

Answer:

[tex]y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}[/tex]

Step-by-step explanation:

Given equation:

[tex]y = 3x^2 - 9x + 17[/tex]

Factor out 3 from the first 2 terms:

[tex]y = 3(x^2 - 3x) + 17[/tex]

Divide the coefficient of x by 2 and square it:  (-3 ÷ 2)² = 9/4

Add this inside the parentheses and subtract the distributed value of it outside the parentheses:

[tex]y = 3\left(x^2 - 3x+\dfrac{9}{4}\right) + 17-\dfrac{27}{4}[/tex]

Factor the parentheses and combine the constants:

[tex]y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}[/tex]

Answer:

x = 2

Step-by-step explanation:

This is a 45-45-90 special right triangle. The legs in this triangle are equal and the hypotenuse is leg multiplied with √2. Refer to the picture at the bottom.

One leg is x, the second leg is x and hypotenuse x√2.

[tex]x \sqrt{2} = 2 \sqrt{2} \\\\\text{Divide both sides with } \sqrt{2} \text{ to isolate } x.\\\frac{x \sqrt{2}}{\sqrt{2}} = \frac{2 \sqrt{2}}{\sqrt{2}}\\\\x = 2[/tex]

Answer:

Appearantly, you forgot to mention the question

Answer:

Step-by-step explanation:

3(1) + 4(3) + 9 = 0

3 + 12 + 9 = 0

24 ≈ 0                                                                                                                                                                                                                                                                                                                                                                              

Answer:

Step-by-step explanation:

The number of bottles of water and cheese sticks will be the same when both numbers are equal to the least common multiple (LCM) of 6 and 10, the numbers in each kind of package.

__

The LCM can be found by factoring out the greatest common divisor of each of the numbers:

  6 = 2 × 3

  10 = 2 × 5

The LCM is the product of the unique numbers here: 2 × 3 × 5 = 30.

The number of packages of bottles of water will be 30/6 = 5 packages.

The number of packages of cheese sticks will be 30/10 = 3 packages.

_____

Additional comment

You may notice that the number of packages of each kind is the unique factor in the other number.

Answer:

  A

Step-by-step explanation:

The rate of change for the table is found using the slope formula. The rate of change for the linear function is the coefficient of x.

__

The slope formula tells us the rate of change is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-9 -(-10))/(-1 -(-4)) = 1/3

The coefficient of x in the equations of the offered answer choices are 1/4 and 6.

The relations between the various slopes are ...

  1/4 < 1/3 < 6

That is, the equation with a slope of 1/4 has a rate of change less than that of the function represented by the table:

  y = 1/4x +4 because ... table of values is 1/3

Answer: A

Step-by-step explanation:

Given:

Budget = $25

Shoes rental = $5.00

Price per game = $4.00

To find the greatest number of games he played...

↓

First, subtract the rent for the shoes from the budget.

25 - 5 = 20

Second, divide the remaining money or budget by the price per game.

20 ÷ 4 = 5 (greatest number of games played)

Lastly, check if the expense is the same as the original amount of money.

5 (shoes) + 4(5) (number of games played)

5 + 20 = 25 (original amount of money)

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4618 mega liters of water, in 7 years, will be used annually.

Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.

here, we have,

I=PRT/100

=6740×10/100×7

=674×1×7

=4618

the nearest hundredth is a 4618 this is the answer.

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Answer:

13,134.35 megaliters

Step-by-step explanation:

Plug in 6,740 megaliters for the initial amount, 0.1 for the rate of increase, and 7 years for the time elapsed.

y

= a(1+r)t

y

= 6,740(1+0.1)7 Plug in values

y

= 6,740(1.1)7 Add

y

= 6,740(1.94871…) Simplify

y

= 13,134.35325… Multiply

Round to the nearest hundredth.

13,134.35325… → 13,134.35

To the nearest hundredth, Rockport will use 13,134.35 megaliters of water annually.

Answer:

If you plot points accordingly to the points on the table, Option A. is correct.

Answer:

50

Step-by-step explanation:

Add all of the values together, which will equal 600, and then divide this number by how many numbers are here, which is 12.

600 / 12 = 50.

Answer:

10*(n-6)

Step-by-step explanation:

Break up the equation above and use words. ex.

10 (times) n (minus) 6

                         ^

               this is the difference  

Answer:

Step-by-step explanation:

(

81

m

6

)

1

2

Simplify the expression.

9

2

(

1

2

)

(

m

6

)

1

2

Cancel the common factor of

2

.

9

1

(

m

6

)

1

2

Simplify the expression.

9m3

Answer:

Step-by-step explanation:

Given

(81 m^6) ^ (1/2)

Solution

change 81 to 9^2

(9^2 m^6)^(1/2)

Now multiply the 1/2 by each of the powers

9^2*(1/2)  m^6^1/2

Answer 9 m^3

Comment

It's hard to show this, but the 1/2 only multiplies by power. It doesn't influence the base. That's because 1/2 is a power itself.

Answer:

remainder = 4

Step-by-step explanation:

using the remainder theorem

when f(x) is divided by (x - a) then the remainder is f(a)

so when f(x) is divided by (x - 7) the remainder is f(7) , that is

f(7) = 7³ - 13(7)² + 40(7) + 18

      = 343 - 13(49) + 280 + 18

      = 343 - 637 + 298

      = 4

Hence, the remainder is [tex]4[/tex].

What is the remainder value?

The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.

Applying the remainder theorem

In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].

So, here when [tex]f(x)[/tex]  is divided by [tex](x - 7)[/tex]  the remainder is [tex]f(7)[/tex], that is

[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]

Hence, the remainder is [tex]4[/tex].

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The answers to the options are:

This inequality is known tp imply that the normal body temperature is taken (subtracted) from the minimum and maximum body temperature.

Note that in case A, the The inequality that represent the temperatures  is less than sign.

In case b, it is an open interval because it means that in -40°F to -140°F , it is not equal to as that is the reason that  the gas cannot stay liquid.

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Answer:

C. 103,748

Step-by-step explanation:

The one in the first number is worth 10,000

The one in the Second number is worth 100,000

Answer:

140

Step-by-step explanation:

b/7-12=8

b/7=8+12  add

b/7=20

b=7*20    multiply

b=140

answer is 140 it is right answer

Answer: 8

Step-by-step explanation:

The discriminant is [tex]b^2-4ac[/tex]

in the equation:

[tex]-x^2+4x-2[/tex]

A = -1, B = 4, C = -2

plug into equation

[tex]4^2-4(-1)(-2)[/tex]

[tex]16-8[/tex]

⇒ [tex]8[/tex]

Answer:

1,728

Step-by-step explanation:

v = a³

v = 12³

v = 1,728 in³

The probability can be calculated as given because there are a total of 52 cards.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of card = 52

Number of king of heart = 1

P(getting a king of hearts) = 1/52

P(getting a spade) = 13/52 = 1/4

P (getting a 5 or a club) = (16/52) = 4/13

P(getting a 5 or a 7) = 4/52 + 4/52 = 8/52 = 2/13

P(getting a card which is not a spade) = 1 - 1/4 = 3/4

P(getting 11 of clubs) = 1/52

Thus, the probability can be calculated as given because there are a total of 52 cards.

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Answer:

1. 1

2. 51

3. 7

4. 9

Step-by-step explanation:

hope i helped

BE and CD are parallel, so the triangles ABE and ACD are similar. Then the following relation holds:

AE/AD = AB/AC

10/(10 + 8) = x/(x + 6)

Solve for x :

10 (x + 6) = x (10 + 8)

10x + 60 = 18x

8x = 60

x = 60/8 = 7/5

Answer:

3,600 x (1.0375) ^ 1

Step-by-step explanation:

Compund interest formula.

IA * (r + 1) ^t

IA = Initial amount; r = rate (as decimal); t = time (in years)

IA = 3600

r = .0375

t = 1 (2008-2009)

3,600 x (1.0375)^1

-- Gage Millar, Algebra 1/2 Tutor, (Pending Pre-Calc Tutor)

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

From above, we can write that

cosθ = sinθ/tanθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

tanθ = sinθ/cosθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

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Answer:

43.8

When you round look at the number after the one your rounding up to. If its greater than 5 round up. If its lower than 5 keep it the same number

Answer:

She is wrong.

Step-by-step explanation:

The mean score is

7 + 8 + 3 + 0 + 2= 20

We then divide it by the number which is 5

20/5= 4.

Therefore, Maria is wrong.

This is because she divided by 4 instead of 5, as she didn't include the rational number 0.

The probability that the spinner lands on an even number or on the unshaded section is; 3/5

From the spinner attached, we see that the number of sections on the spinner is 5 sections.

Now, we can also see that;

Number of even numbers section = 2

Number of shaded sections = 1

Thus, probability that the spinner lands on an even number or on the unshaded section is;

P(even number or unshaded section) = (2 + 1)/5 = 3/5

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The type of data that contains results from other people that are of similar age and gender is known as normative data.

Normative data is a type of data that is observed that contains information about the characteristics of a population of interest. For example, normative data about students in a class would contain information such as age, gender, height.

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