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Answer:

x = 23 degress

Step-by-step explanation:

(x + 2) + 65 = 90

x + 2 = 25

x = 23 degress

Given:

The given vector is:

[tex]v=9i-6j[/tex]

To find:

The unit vector in the direction of the given vector.

Solution:

If a vector is [tex]v=ai+bj[/tex], then the unit vector in the direction of the this vector is

[tex]\hat v=\dfrac{v}{|v|}[/tex]

Where, [tex]|v|=\sqrt{a^2+b^2[/tex]

We have,

[tex]v=9i-6j[/tex]

Here, [tex]a=9[/tex] and [tex]b=-6[/tex]. So,

[tex]|v|=\sqrt{9^2+(-6)^2}[/tex]

[tex]|v|=\sqrt{81+36}[/tex]

[tex]|v|=\sqrt{117}[/tex]

[tex]|v|=3\sqrt{13}[/tex]

Now, the unit vector in the direction of the given vector is:

[tex]\hat v=\dfrac{9i-6j}{3\sqrt{13}}[/tex]

[tex]\hat v=\dfrac{9i}{3\sqrt{13}}-\dfrac{6j}{3\sqrt{13}}[/tex]

[tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex]

Therefore, the required unit vector is [tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex].

Answer:

Perimeter = (16z - 2)

Step-by-step explanation:

Perimeter of a polygon = sum of the lengths of all sides of the polygon

Sum of all sides of the trapezoid = (z + 5) + (8z - 10) + (4z + 9) + (3z - 6)

By adding like terms,

Perimeter of the trapezoid = ( z + 8z + 4z + 3z) + (5 - 10 + 9 - 6)

                                            = 16z - 2

Therefore, expression representing the perimeter of the trapezoid will be,

(16z - 2)

The cost of bill is,

⇒ $24

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

A 15% tip on a restaurant bill is $3.60.

Now,

Let the cost of bill is, $x

Hence, We can formulate;

⇒ 15% of x = 3.60

⇒ 15x/100 = 3.60

⇒ 15x = 360

⇒ x = 360 / 15

⇒ x = 24

Thus, The cost of bill is, $24

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Answer:

Area = 2x^4  + x^3 - 15x^2 + 8x + 24

Step-by-step explanation:

A = (x + 3)(2x^3 - 5x^2 + 8)

A = 2x^4 - 5x^3 + 8x + 6x^3 - 15x^2 +24

combine like terms:

Area = 2x^4  + x^3 - 15x^2 + 8x + 24

Answer:

$2961.41

Step-by-step explanation:

Base rate for a state workers compensation insurance = $5,12 per $100 paid in wages

Scott park payroll for march = $5784 ( inclusive of insurance payment )

Determine the monthly premium for insurance

$5.12 = $100

First; calculate how many $100 are in $5784

 = 5784 / 100 = 578.4

Hence the monthly premium for workers compensation insurance

= $5.12 * 578.4

= $2961.41

Answer:

Step-by-step explanation:

Let line to be found be Line 2

Given:

Line 1

x - 5y = 15

x - 15 = 5y

Therefore slope = 1/5

Line 2

Point = (-5,7)

Slope = 1/5

Therefore: 7 = (1*-5)/5 + c

=> 7 = -1 + c

=> c = 8

Answer:

19.5°

Step-by-step explanation:

IN EFG the measure of G=90 DG=21 feet and EF=63 feet find the measure of E to the nearest degree.​

We solve the question using Sine rule

= a/sin A = b/sin B

= 21/sin E = 63/sin 90

Cross Multiply

Sin E × 63 = 21 × sin 90

sin E = 21 × sin 90/63

E = arc sin( 21 × sin 90/63)

E = 19.47122°

Approximately = 19.5°

Answer:

51.0feet

Step-by-step explanation:

To get the length of the given diagonal, we will use pythagoras theorem as shown;

First we need to get the diagonal of the  base;

d² = 40²+30²

d² = 1600+900

d² = 2500

d = √2500

d = 50ft

The diagonal of the base is 50ft

Get the required diagonal

Let the required diagonal be x

x² = 10²+50²

x² = 100+2500

x² = 2600

x = √2600

x = 50.99feet

Hence the distance of the red line is 51.0feet to the nearest tenth

Answer:

18 People bought hot dogs

Step-by-step explanation:

The question is not complete, but I’m assuming you need the number of people who bought hot dogs.

25 customers bought gas.

72% of them also bought a hot dog.

So thE number of customers who bought hot dogs are 72% of 25

=> 72/100 * 25

=> 0.72 * 25

= 18 people

Answer:

M=t/x

Step-by-step explanation:

I love these math problems! Do u have more? I really need something 2 do

Answer: Annalise says that Philip will earn $320 more at First Bank than at GrandBank.

Step-by-step explanation:

Formula for Simple interest = Principal × Rate × Time

At GrandBank, the simple Interest will be:

= $2000 × 6% × 8

= $2000 × 0.06 × 8

= $960

At First Bank, the Simple interest will be:

= $2000 × 8% × 8

= $2000 × 0.08 × 8

= $1280

Based on the above, Philip will earn ($1280 - $960) = $320 more at First Bank.

Answer:

x=12.124

y=14

Step-by-step explanation:

tan(30)= 7/x

x= 7/tan(30)

sin(30)= 7/y

y= 7/sin(30)

Answer:

so far i think 9 but that's all I know for how

Step-by-step explanation:

image them turning into triangles

Answer:

A.

Step-by-step explanation:

The slope increases from left to right.

Answer: Positive Slope

Step-by-step explanation:

If it’s from left to right in an upwards direction, it’s positive, if it’s left to right in a downwards directio, it’s negative

Answer:

x = 25°

Step-by-step explanation:

The secant- secant angle is half the difference of the intercepted arcs, that is

x = [tex]\frac{1}{2}[/tex] (80 - 30)° = 0.5 × 50° = 25°

Answer:

x = 25°

Step-by-step explanation:

Hope this helps

Answer:

D) [tex]6+2\sqrt{6}[/tex]

Step-by-step explanation:

[tex]2\sqrt{3} *(\sqrt{2} +\sqrt{3} )\\\\6+2\sqrt{6}[/tex]

Answer:

2.26

Step-by-step explanation:

To round our answer to nearest hundredth, we will round our answer to 2 digits after decimal. We can see that thousandth value is less than 5 that is 3, so will keep last digit 6 as: Therefore, the decimal value of our given fraction is approximately 2.26 to the nearest hundredth.

Answer:

x=0,-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

see you have to add something that equalles 0 so any questions like this you put a negitive infront of the 7.

Answer:

18.044

Step-by-step explanation:

hope it helps you good day if I'm wrong tell me right away I'll try it out again.

The measure of  ∠B   is 31.6 .

Trigonometric ratios are the ratios of the length of sides of a triangle.

These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below,

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

According to the question

In right angle triangle ACB

Base BC= 22.9

Perpendicular AC = 14.1

now , using trigonometric ratio

tan ∠B  = [tex]\frac{AC}{BC}[/tex]

tan ∠B  = [tex]\frac{14.1}{22.9}[/tex]

∠B  = [tex]tan^{-1} 0.615[/tex]

∠B  = 31.6

Hence, The measure of  ∠B   is 31.6 .

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We can find the slope using any two points on the line. Readily identifiable are the points (2, 0) and (0, 3), from which we can find the slope:

[tex]\text{slope} = m=\frac{y_2-y_1}{x_2-x_1} \\ m = \frac{3-0}{0-2} = -\frac{3}{2}.[/tex]

The y-intercept is the y value when x = 0, which we already know is 3. So, the slope-intercept equation of this line is:

[tex]y=-\frac{3}{2}x+3.[/tex]

Answer:

b. c. d

Step-by-step explanation:

Answer:

Some teens are at greater risk than others.

For example, youth who are victims of teen dating violence are more likely to experience symptoms of depression and anxiety. Engage in unhealthy behaviors, like using tobacco, drugs, and alcohol. Exhibit antisocial behaviors, like lying, theft, bullying, or hitting.

Step-by-step explanation:

Yes  all 3 you choose are correct

Answer:

A≈24.65in²

Step-by-step explanation:

A=πr2

C=2πr

Solving forA

A=C2

4π=17.62

4·π≈24.64992in²

Happy Friday!

Answer:

(x-2)*(x-9)

Step-by-step explanation:

hope this helps!!

Answer:

0..99

Step-by-step explanation:

613 Step-by-step explanation: