A rectangle has a width of 3 cam and a length of 9cm. the rectangle is to be enlarged by a scale factor of 8 what is the length of the enlargement. (include units)

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:

x = 16

Step-by-step explanation:

The sum of the exterior angles of a triangle = 360°

Sum the exterior angles and equate to 360

5x + 12 + 10x - 37 + 9x + 1 = 360 , that is

24x - 24 = 360 ( add 24 to both sides )

24x = 384 ( divide both sides by 24 )

x = 16

Answer:

x = 15

Step-by-step explanation:

The sum of angles in a triangle is 180deg.

Let's mark the measures of the internal angles as A, B and C.

We know that

A + B + C = 180deg

180deg - A + 180deg - B + 180deg - C = (9x + 1)deg + (5x + 12)deg + (10x - 37)deg

3*180deg - (A + B + C) = (24x - 24)deg

540deg - 180deg = (24x - 24)deg

360deg = (24x - 24)deg

360 = 24x - 24

384 = 24x

15 = x

Answer:

$241,910.31

Step-by-step explanation:

Compound interest

125,000(1.045)^15

Also, Gal Gadot is the best!

Given:

The length of the football field = 360 feet

The length of the titanic = 883 feet

To find:

About how many football fields long was the titanic?

Solution:

We have,

Length of the football field = 360 feet

Length of the titanic = 883 feet

Now we need to divide the length of the titanic by length of the football field to find the number of football fields whose length is equal to the titanic.

[tex]\text{Number of required football fields}=\dfrac{\text{Length of the titanic}}{\text{Length of the football field}}[/tex]

[tex]\text{Number of required football fields}=\dfrac{883}{360}[/tex]

[tex]\text{Number of required football fields}=2.452777...[/tex]

[tex]\text{Number of required football fields}=2.452\overline{7}[/tex]

[tex]\text{Number of required football fields}\approx 2[/tex]

Therefore, the answer in whole number is 2 and the answer in decimal is [tex]2.452\overline{7}[/tex].

Step-by-step explanation:

anyway.. for your answer i only know that number of fifths in 1 is correct I dont know about the rest.

Answer:

A

Step-by-step explanation:

1/2f

Answer:

A

the first option

Step-by-step explanation:

Answer:

A measure of exposure-disease association one could use is the odds ratio (OR)

Step-by-step explanation:

An Odds ratio (OR) is a statistical measure quantifying the level of association between two events such as an exposure and an outcome

The odds ratio gives the probability of outcome where there is a given amount of exposure

We have the table;

[tex]\begin{array}{ccc}&Developed \ lung \ cancer& Did \ not \ develop \ lung \ cancer\\Smokers&50&350\\Non-smokers&10&590\end{array}[/tex]

The odds ratio = (The number of smokers with the lung-cancer)/(The number of non-smokers with lung-cancer) ÷ (The number of smokers smokers without long cancer).(The number of non-smokers without long cancer)

∴ OR = (50/10) ÷ (350/590) = 59/7 = 8.[tex]\overline{428571}[/tex] ≈ 8.4

Therefore, a smoker is approximately 8.4 times more likely to develop lung cancer than a non-smoker.

Answer:

No.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

If you graph the equations, then you see that (3,8) is not the solution.

Answer:

States sent representatives to Congress and provided soldiers and some officers to protect the country.

Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

6×3−3

Multiply 6 and 3 to get 18.

18−3

Subtract 3 from 18 to get 15.

15

Answer:

Incomplete problem, read the step-by-step.

Step-by-step explanation:

$1200-$300=$900

5% of $900 is $45

You didn't say if the 5% is per month or per year, if you want more help, comment on this answer the per year/whatever/month and then I'll help you further into this word problem.

Hope this helped! :)

[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]

[tex] \frac{ {x}^{12} - {6x}^{10} + {15x}^{8} - {20x}^{6} + {15x}^{4} - {6x}^{2} + 1 }{ {x}^{6} } [/tex]

[tex]\huge\red{\boxed{\tt{\colorbox{pink}{Solution:}}}}[/tex]

[tex](x - 1 \div x) {}^{6} [/tex]

Arrange the powers

[tex] \frac{x {}^{12} - {6x}^{10} + {15x}^{8} - {20x}^{6} + {15x}^{4} - {6x}^{2} + 1 }{ {x}^{6} } [/tex]

Answer:

1) 6447,55 unități pătrate

2) 25192,43 unități cubice

Step-by-step explanation:

1) Suprafața totală a unui cilindru

Formula = 2πr (r + h)

r = 27 de unități

h = 11 unități

Suprafața totală = 2 × π × 27 × (27 + 11)

= 6446.54813 unități pătrate

Aproximativ = 6447,55 unități pătrate

2) Volumul cilindrului

Formula = πr²h

= π × 27² × 11

= 25192,43 unități cubice

Answer:

x = 4

Step-by-step explanation:

Eliminate y by setting the first equation equal to the second:

2x - 7 = -x + 5

Combining like terms, we get:

3x = 12, so that x must be 4.

Answer:

You need to buy 3 quarts of paint.

Step-by-step explanation:

Given

[tex]Coats =2[/tex]

[tex]Paint = 90ft^2/qt[/tex]

See attachment for stage

Required

Determine the number of quarts needed

First, we calculate the surface area of the stage (without the base).

This is calculated as:

Area = Area of Rectangle1 + Area of Rectangle 2 + 2 * Area of each triangle on both sides.

For the first rectangle, we have:

[tex]A_1 =Length * Width[/tex]

[tex]A_1 = 15.2 * 19.5 =296.4[/tex]

For the second rectangle, we have:

[tex]A_2 =Length * Width[/tex]

[tex]A_2 = 6* 19.5 = 117[/tex]

For each triangle on both sides

[tex]A_3 = 0.5 * Base * Height[/tex]

[tex]A_3 = 0.5 * 14 * 6 = 42[/tex]

So, the total area is:

[tex]Area = A_1 + A_2 + 2 *A_3[/tex]

[tex]Area = 296.4 + 117+ 2 *42[/tex]

[tex]Area = 497.4ft^2[/tex]

The amount of paint need is:

[tex]Amount = \frac{Area}{2\ coats}[/tex]

From the question, we understand that:

[tex]1\ coat =90ft^2/quart[/tex]

Multiply both sides by 2

[tex]2 * 1\ coat =90ft^2/quart * 2[/tex]

[tex]2 \ coats =180ft^2/quart[/tex]

So, we have:

[tex]Amount = \frac{Area}{2\ coats}[/tex]

[tex]Amount = \frac{497.4ft^2}{180ft^2/quart}[/tex]

[tex]Amount = \frac{497.4ft^2}{180ft^2}quart[/tex]

[tex]Amount = \frac{497.4}{180}quart[/tex]

[tex]Amount = 2.763\ quarts[/tex]

[tex]Amount \approx 3\ quarts[/tex] --- approximated

Answer:(x-0)^2 + (y-0)^2=30^2

Step-by-step explanation:

The equation of the circle is x^2 +y^2 = 7656.25

The given parameters are:

Center = (0,0)

Diameter = 175

The equation of a circle is represented as:

(x - a)^2 +(y - b)^2 = r^2

Where

Center = (a,b) = (0,0)

r = radius = 175/2

So, we have:

(x - 0)^2 +(y - 0)^2 = (175/2)^2

Evaluate

x^2 +y^2 = 7656.25

Hence, the equation of the circle is x^2 +y^2 = 7656.25

Read more about circle equations at:

https://brainly.com/question/1506955

Answer:

33lbs

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

Answer:

The answer is 256

Step-by-step explanation:

You just have to get the divisor  

(

40

)

and multiply by the quotient  

(

6

)

, then add the remainder  

(

16

)

.

So we have:  

(

40.6

)

+

16

=

256

The number is 276.

Let us assume that the number is N.

So according to the question we can say that

N= 15(18) +1

because dividend= divisor x (quotient) + remainder and quotient is odd.

 So now, N (on expanding) =15 × 18 + 5

                                              = 275

So if N is divided by 15 the remainder would be  275+1=276.

Learn more about Parts of a Division Problem brainly.com/question/15305334 here.

#SPJ2

Answer:

C

Step-by-step explanation:

volumes are width x height x length

4 x 2 x 2 = 16

8 x 2 x 1 = 16

Answer:

area of semi circle πr=π×2=44/7 feet²