find the unit vector in the direction of v= 2i+ j + k

Answer:

Answer In this Picture.

Answer:

X=1, Y=0

Step-by-step explanation:

Solve for X and Y using a2 +b2 = c2

Answers:

[tex](f \circ g)(x) = 2x^2-5x\\\\(g \circ f)(x) = 2x^2+7x\\\\[/tex]

The domain is "all real numbers" which you could type in (-infinity, infinity) or [tex](-\infty, \infty)[/tex] when doing interval notation. This applies to both.

=========================================================

Explanation:

See the attached image for the steps of each.

The domain is the set of all real numbers because each result is a polynomial. We don't have to worry about dividing by zero, taking a square root of a negative number etc. There are no restrictions on x. Any real number can replace x to get some real number result for y. This applies to both composite functions.

Answer:

[tex]x=-72[/tex]

Step-by-step explanation:

[tex]-\frac{x}{8}-11=-2\\ -\frac{x}{8}=9\\ -x=72\\x=-72[/tex]

Answer:308

Step-by-step explanation:Multiply 4*7*11

Answer:

[tex]KL=45.6[/tex]

Step-by-step explanation:

Property of a Rectangle: Opposite sides are equal.

This means:

[tex]KL = JM \text{ where JM = 45.6}[/tex]

[tex]KL = 45.6[/tex]

Day 6/11 = $6,920

Day 6/15 = $6,505

Day 6/20 = $6,305

She withdrew $279 to buy clothes

Therefore her final balance= $6,920

Therefore, her balance is

= $6,920 - $415

= $6,505

Therefore her balance is

= $6,505 - $200

= $6,305

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Answer:

  90°; 55°; 35°; 110°; 70°

Step-by-step explanation:

A rectangle has corner angles that are 90°. When the corner angle is divided into two parts, the total of the parts is 90°.

Each of the triangles is isosceles. The figure is symmetrical about its center.

An exterior angle to a triangle is equal to the sum of the remote interior angles.

__

∠SRT = 90° . . . . a corner angle

∠STR = 55° . . . . symmetrical to the given angle

∠QRS = 180° -55° -90° = 35° . . . . sum of angles in ΔQRS is 180°

∠QPT = 2×55° = 110° . . . . exterior angle to ΔQPS; ∠QSP =∠SQP

∠TPR = 180° -110° = 70° . . . . forms a linear pair with ∠QPT

_____

There are numerous ways to figure any or all of these angles. They come down to the fundamentals: angles in a triangle total 180°; angles that form a line total 180°; corner angles of a rectangle are 90°. Base angles of an isosceles triangle are congruent.

The exterior angle rule derives from the sum of angles in a triangle and on a line both being 180°.

Answer:

1) 1/2or 50%
2) 38/50 or 76%
3) 38/60 or 63%
4) not sure tbh

Step-by-step explanation:

The equation that has exactly one solution will be 2x + 31 = - 2x - 31. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equations are given.

Check whether the equation is linear or not.

1.   2x + 31 = 2x - 31, this is not a linear equation.

2.  2x + 31 = - 2x - 31, this is a linear equation.

Then the solution of the linear equation will be

4x = - 62

 x = - 15.5

3.  2x + 31 = 2x - 31, this is not a linear equation.

4.    2x - 2 = 2x - 31, this is not a linear equation.

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Answer: 20 sq ft

Step-by-step explanation: The base is AB = 5 ft because AB = CD. Recall that opposite sides in a parallelogram are congruent and parallel.

area of parallelogram = base * height = 5*4 = 20

note: the base is always perpendicular to the height

The coordinates of the new triangle's vertices are (0, -1), (-4, -3), and

(-2, -1). Hence option A is true.

Used the rule of a point (x, y) when rotated over the y-axis of 90° clockwise rotation from point (0, 0),

(x, y) → (y, - x)

Given that the triangle BCD is shown in the image.

Here, the coordinates of the vertices of BCD are,

B = (1, 0)

C = (3, - 4)

D = (1, - 2)

Now apply the rotation rule, the coordinates of the new triangle's vertices are;

B' = (0, - 1)

C' = (- 4, - 3)

D' = (- 2, - 1)

Therefore, the option A is true.

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The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

From the graph, we have the following observations:

This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5

So, we have:

f(x) = a(x + 5)³(x - 2)²

The curve is inverted,

This means that a < 0

Assume a = -1.

Then, we have:

f(x) = -(x + 5)³(x - 2)²

Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

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Answer:

260 cm^2

Step-by-step explanation:

Area of rectangle = 20 x 10 = 200 cm^2

Area of triangle = 6 x 20 /2 = 60 cm ^2

Area of figure = 200 + 60 = 260 cm^2

Answer:

Graph B

Step-by-step explanation:

Point-line graphs are usually used to compare data over a course of time, and bar graphs are more commonly used to compare statistics between different data sets (in this case it is between different countries)

Answer:

64

Step-by-step explanation:

Answer:

Volume of a cone = (1/3) πr³

r = radius = d/2 = 2/2 = 1 ft

Volume = (1/3) * π * 1³

volume = 1.04 cubic ft

Answer/Step-by-step explanation:

Given:

A gas station offers a lucky draw to customers. Each time you spend more than $20 on gas, you can make a draw to win a prize. The probability of winning a prize is 1/12 suppose you buy gas 4 times.

To Find:

what is the probability of you winning a prize each time?

Solve:

Since, it given that you buy gas 4 times. Thus that means:

1/12 × 1/12 × 1/12 × 1/12 or  1/12⁴

Now solving it:

1/12 × 1/12 × 1/12 × 1/12 = 1/20736

Which also means (0.0048%) in decimal form since, 1 divide by 2076 equal to 0.0048%

Kavinsky

Answer:

a. Solve the System of Equations. Show your work

Answer:

[tex]\huge\boxed{\sf x = \pm \sqrt{7} }[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-7[/tex]

We can also write it as:

[tex]y =x^2-7[/tex]

x-intercept is the point where y = 0

Put y = 0 in the above equation

[tex]0=x^2-7\\\\Add \ 7 \ to \ both\ sides\\\\7 = x^2\\\\Take \ sqrt \ on \ both \ sides\\\\\pm \sqrt{7} =x\\\\x = \pm \sqrt{7} \\\\\rule[225]{225}{2}[/tex]

The number of green watches that were sold is 78

The given parameters are:

The number of watches can be represented as

Gold + Green + Blue + Red = 234

Substitute Blue = Green

Gold + Green + Green + Red = 234

Gold + 2 * Green + Red = 234

Substitute Red = 2 * Gold

Gold + 2 * Green + 2 * Gold = 234

Evaluate the like terms

2 * Green + 3 * Gold = 234

Make Gold the subject in Green = 3* Gold

Gold = Green/3

Substitute Gold = Green/3 in 2 * Green + 3 * Gold = 234

2 * Green + 3 * Green/3 = 234

Evaluate the product

2 * Green + Green = 234

Evaluate the sum

3 * Green = 234

Divide both sides by 3

Green = 78

Hence, The number of green watches that were sold is 78

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The length of the windshield wiper to the nearest inch is 24 inches

The formula for calculating the area of a sector is given as:

A = r²β/2

r is the length of the wiper

β is the subtended angle

Given the following

A = 500.3 square in

β = 98 degrees = 98pi/180 = 49pi/90

Substitute

500.3 =  r²49pi/180
500.3 = 153.86r²/180

153.86r² = 90054
r² = 585.298

r = 24.19

Hence the length of the windshield wiper to the nearest inch is 24 inches

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Answer:

The answer 7|3+6 is irrational because the sum of a rational number and irrational number is an irrational number.

Addition:

Increased by, greater than, more than, sum

Subtraction:

Decreased by, decrease, less than, difference

Multiplication:

Times, equal groups, __ times as many, product

Division:

Quotient, divided by, goes into, split equally

By applying algebra properties for simplifying rational numbers, we conclude that the rational number 14/16 is equivalent to the rational number 7/8.

Rational numbers are real numbers of the form n/m, where n, m ∈ [tex]\mathbb{Z}[/tex] and n ≠ 0. Rational numbers are in lowest terms whether they cannot be reduced. A rational number is simplified by applying the following property:

[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex]     (1)

Where c is the common multiplier.

Now we proceed to simplify the given rational number, whose common multiplier is 2:

[tex]\frac{14}{16} = \frac{7}{8}[/tex]

By applying algebra properties for simplifying rational numbers, we conclude that the rational number 14/16 is equivalent to the rational number 7/8.

The statement is poorly formatted: Write 14/16 in lowest terms.

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The difference between the two polynomials is 11x²3y³ - 4xy².

The difference between two polynomials is the result you get by subtracting one from the other.

Thus:

= (4x²2y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)

= 4x²2y³ + 2xy² – 2y + 7x²y³ - 6xy² + 2y

= 11x²3y³ - 4xy²

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Answer:

d) 190,172,154

Step-by-step explanation:

208-18=190

190-18=172

172-18=154

Answer:

908

Step-by-step explanation:

879+29=908

Let's solve this problem step by step:

 ⇒ on one side, I solve the equaiton

    ⇒ on the other side, I give you the property that I use to solve the

        equation

         ⇒ you don't need to write down those properties if your teachers

             didn't ask you for it

  [tex]4(5x-2)=2(9x+3)\\[/tex]      |   Given equation

  [tex]20x-8=19x+6[/tex]           |    Distributive Multiplication over subtract/add

  [tex]x=14[/tex]                             |    Subtraction Property of Equality

Answer: x = 14

Definition of Properties: