Operations on Wh b) 6 X (5 + 4) ​

Answer:

a. 25.98i - 15j mi/h

b. 1.71i + 4.7j mi/h

c. 27.69i -10.3j mi/h

Step-by-step explanation:

a. Identify the ship's vector

Since the ship moves through water at 30 miles per hour at an angle of 30° south of east, which is in the fourth quadrant. So, the x-component of the ship's velocity is v₁ = 30cos30° = 25.98 mi/h and the y-component of the ship's velocity is v₂ = -30sin30° = -15 mi/h

Thus the ship's velocity vector as ship moves through the water v = v₁i + v₂j = 25.98i + (-15)j = 25.98i - 15j mi/h

b. Identify the water current's vector

Also, since the water is moving at 5 miles per hour at an angle of 20° south of east, this implies that it is moving at an angle 90° - 20° = 70° east of north, which is in the first quadrant. So, the x-component of the water's velocity is v₃ = 5cos70° = 1.71 mi/h and the y-component of the water's velocity is v₄ = 5sin70° = 4.7 mi/h

Thus the ship's velocity vector v' = v₃i + v₄j = 1.71i + 4.7j mi/h

c. Identify the vector representing the ship's actual motion.

The velocity vector representing the ship's actual motion is V = velocity vector of ship as ship moves through water + velocity vector of water current.

V = v + v'

= 25.98i - 15j mi/h + 1.71i + 4.7j mi/h

= (25.98i + 1.71i + 4.7j - 15j )mi/h

= 27.68i -10.3j mi/h

Answer:

The answer is below

Step-by-step explanation:

The equation for a linear function is given as:

y = mx + b

where m is the slope of the function (that is the rate of change), b is the initial value of y when x is 0.

Given that the function where x represent the number of years since 1960 and y is the cost in dollar as:

[tex]f(x)=\frac{2.14}{55}x+0.31[/tex]

a) In the year 1960, that is x = 0, the cost of a gallon of gas is given as:

[tex]f(0)=\frac{2.14}{55}(0)+0.31\\\\f(0)=\$0.31[/tex]

b) From the function [tex]f(x)=\frac{2.14}{55}x+0.31[/tex], we can see that the rate of change is 2.14/55. Therefore, the cost increase each year by 4 cents per year.

Answer:

Step-by-step explanation:

One solution if they intersect (which is the case), and zero if they are parallel and apart, and infinite if they are parallel and coincident, two lines piled on top of each other.

Answer:

452 m

Step-by-step explanation:

Answer:

y = 1/2x - 3/2

Step-by-step explanation:

y = 1/2x + b

1 = 1/2(5) + b

1 = 5/2 + b

-3/2 = b

Answer:

y=1/2x-3/2

Step-by-step explanation:

y-y1=m(x-x1)

y-1=1/2(x-5)

y-1=1/2x-5/2

y=1/2x-5/2+1

y=1/2x-5/2+2/2

y=1/2x-3/2

Answer:

x = 8

Step-by-step explanation:

According to trigonometry identity

sin x = Cos (90-x)

Hence if we have;

Sin (4x + 10) º = Cos (6x)

Sin (4x + 10) º = Sin(90- 6x)

4x + 10 = 90 - 6x

4x+6x = 90 - 10

10x = 80

x = 80/10

x = 8

Hence the value of x is 8

Answer:

Step-by-step explanation:

According to problem description, we have two triangles

The first one:   the fish pond and feet and eyes of Kendra

The second one the fish  pond and the side wall of the apartment

These two triangles have angle  α  as common angle and its tan

tan α  =  1.5/ 2   =  x/ 40     then         note  :  150 cm  =  1.5 m

1.5/ 2   =  x/ 40

x  =  40 * 1.5 / 2

x  =  30 m

9514 1404 393

Answer:

  63°

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(G) = HF/HG

  G = arctan(HF/HG) = arctan(2.9/1.5) ≈ 63°

Answer:

C. 49

Step-by-step explanation:

Start by filling in your values.

[tex]7^{2} + 99 / 11 - 9[/tex]

Solve using PEMDAS.

49 + 99 / 11 - 9

49 + 9 - 9

58 - 9

49

Answer:

[tex]c .\: \: 49[/tex]

Step-by-step explanation:

[tex] {y}^{2} + 99 \div x - 9[/tex]

[tex] {7}^{2} + 99 \div 11 - 9[/tex]

[tex] 49 +99÷11-9[/tex]

[tex]49+9-9[/tex]

[tex]58-9[/tex]

[tex]49[/tex]

Answer: keith

Step-by-step explanation:

The system of equations to represent the number of pages read per day by Keith and Tameka, using d for days and p for pages are,

p = 6d

p = 5d + 15

Since we know that,

A system of equations is the set of equations in which the finite set of equations is present for which the common solution is sought.

Two students are reading a book.  Keith reads 6 pages a day.

The equation for Keith, where d for days and p for pages can be given as,

p = 6xd

p = 6d

Tameka reads 5 pages a day, but he starts sooner and has already read 15 pages. The equation for Tameka, where d for days and p for pages, can be given as,

p = 5xd + 15

p = 5d + 15

Hence, the system of equations to represent the number of pages read per day by Keith and Tameka, using d for days and p for pages are,

p = 6d

p = 5d + 15

Learn more about the system of equations here;

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Answer:

If it's AL to A'L' then its 1/2

If it's A'L' to AL then its 2

Answer:

Step-by-step explanation:

Jose is trying to calibrate his new fitness watch. The app that come with the watch asks the user to input their average stride. Jose measures this to be approximately 2.5 feet. Using 2.5 feet as his stride how many feet will Jose walk if he takes 6000 steps in a day?

Answer:

The answer is 136 .

Answer:

Hello! answer: 1/6

Step-by-step explanation:

The probability of landing on D is 1/6 because there are 6 spots on the spinner you can land on A, B, C, D, E, and F and there is only 1 section labelled "D" therefore the probability of landing on D is 1/6 hope that helps!

Step-by-step explanation:

b= 140 ( alternate angle)

k = 130 ( veetically opposite angles)

may it help ub

Answer:

Step-by-step explanation:

Distribute the Negative Sign:

=−9x+32+−1(15x+41)

=−9x+32+−1(15x)+(−1)(41)

=−9x+32+−15x+−41

Combine Like Terms:

=−9x+32+−15x+−41

=(−9x+−15x)+(32+−41)

=−24x+−9

Answer:

-24x - 9

Step-by-step explanation:

Combine like terms.

Answer:

A

Step-by-step explanation:

first, you turn 3 1/2 into 3 2/4'ths and change 3 two fourth's into 14/4 fraction.

next, you change 2 one fourth into 9/4th's fraction

your equation would be 14/4 divided by 9/4th's = a times b/c

when you used divide, you get get flip one of the fractions being divided, and it could turn into 14/4 TIMES 4 over 9 = a times b/c.

wait this area down here could be wrong:

when you get your equation, multiply them together and you get 56 over 36 equals a times b/c.

A times B /C is equal to 56/36 which can simple out to 28/18 which AGAIN simpled out to 14/9

C IS 9 BECAUSE IT IS THE DENOMINATOR

and because of that, A would be the answer.

Measure of x :

[tex]\longrightarrow4 \sqrt{5} \: \: units[/tex]

Measure of y :

[tex]\longrightarrow8 \sqrt{5} \: \: units[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: \: it \: \: helps }}{\orange{....}}}}}[/tex]

Given:

The scale factor of the actual sports utility vehicle to the toy model is 50:1.

Actual length = 7 feet

Actual width = 5 feet

To find:

The length and width of the toy model.

Solution:

a. Let l be the length of the toy model, then

[tex]\dfrac{\text{Actual length}}{\text{Length of the toy model}}=\dfrac{50}{1}[/tex]

[tex]\dfrac{7}{l}=\dfrac{50}{1}[/tex]

[tex]7=50l[/tex]

[tex]\dfrac{7}{50}=l[/tex]

[tex]0.14=l[/tex]

Therefore, the length of the toy model is 0.14 feet.

b. Let w be the width of the toy model, then

[tex]\dfrac{\text{Actual width}}{\text{Width of the toy model}}=\dfrac{50}{1}[/tex]

[tex]\dfrac{5}{w}=\dfrac{50}{1}[/tex]

[tex]5=50w[/tex]

[tex]\dfrac{5}{50}=w[/tex]

[tex]0.10=w[/tex]

Therefore, the width of the toy model is 0.10 feet.

Answer:

Option 1

Step-by-step explanation:

Take

[tex]10 {}^{11} [/tex]

common out.

[tex](5.29 - 3.86) \times 10 {}^{11 } \\ 1.43 \times 10 {}^{11} [/tex]

Answer: a

Step-by-step explanation: edge 2023

Answer:

V=942.5

Step-by-step explanation:

V=(π)(r)^2(h)

V= (π)(10/2)^2(12)

V=942.5

The equation for the given circle is:

[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]

Remember that for a circle whose center is (a, b) and has a radius r, the equation is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this case, the center is (-2, -3) and the diameter is 8 units, so the radius is r = 4.

Then the equation is:

[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]

Expanding the squares we get:

[tex](x^2 + 2*2*x + 4) + (y^2 + 2*3*y + 3^2) = 16\\\\x^2 + y^2 + 4x + 6y + 4 + 9 - 16 = 0\\\\x^2 + y^2 + 4x + 6y - 3 = 0[/tex]

So the correct option is the third one.

If you want to learn more about circles:

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Answer:

here u go

Step-by-step explanation:

8.98 x 10^6

Answer:

There isnt a diagram

Step-by-step explanation:

Answer:  I believe it's (x-1) 2+(y-1) 2=13

Answer:

20.5 mpg

Step-by-step explanation:

Here we're looking to calculate the car's fuel economy, expressed in miles per gallon, or mpg:

 164 miles

------------------ = 20.5 mpg

  8 gallons

Answer:

Step-by-step explanation:

x = 55

x + 55 = 110

x + 20 = 75

x + 65 = 120

Answer:

x°=130°

The sum of two opposite angles in a quadrilateral is 180

⇒x+55°+x+65°=180°

⇒2x+120°=180°

⇒2x=60°

⇒x=30°

Có x+20 °+x°=180°

⇒30°+20°+x°=180°

⇒x°=130°