Lyle creates a peach dye by mixing 8 ounces of white dye with 5 ounces of orange dye. He wants to know how much orange dye he needs to use if he needs a total of 195 ounces of peach dye.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Rewrite and add each vector:

[tex]p=\langle40cos70^\circ,40sin70^\circ\rangle\\q=\langle50cos270^\circ,50sin270^\circ\rangle\\r=\langle60cos235^\circ,60sin235^\circ\rangle\\p+q+r=\langle40cos70^\circ+50cos270^\circ+60cos235^\circ,40sin70^\circ+50sin270^\circ+60sin235^\circ\rangle\\p+q+r\approx\langle-20.73,-61.56\rangle[/tex]

Find the magnitude of the resulting vector:

[tex]||p+q+r||=\sqrt{x^2+y^2}\\||p+q+r||=\sqrt{(-20.73)^2+(-61.56)^2}\\||p+q+r||\approx64.96[/tex]

Therefore, the best answer is D) 64.959

Problem 2

Think of the vectors like this:

[tex]t=\langle7cos240^\circ,7sin240^\circ\rangle\\u=\langle10cos30^\circ,10sin30^\circ\rangle\\v=\langle15cos310^\circ,15sin310^\circ\rangle[/tex]

By adding the vectors, we have:

[tex]t+u+v=\langle7cos240^\circ+10cos30^\circ+15cos310^\circ,7sin240^\circ+10sin30^\circ+15sin310^\circ\rangle\\t+u+v\approx\langle14.8,-12.55\rangle[/tex]

Since the direction of a vector is [tex]\theta=tan^{-1}(\frac{y}{x})[/tex], we have:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{-12.55}{14.8})\\\theta\approx-40.3^\circ[/tex]

Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:

[tex]\theta=360^\circ+(-40.3)^\circ\\\theta=319.7^\circ[/tex]

Therefore, the best answer is D) 320°

Problem 3

Again, rewrite the vectors and add them:

[tex]u=\langle30cos70^\circ,30sin70^\circ\rangle\\v=\langle40cos220^\circ,40sin220^\circ\rangle\\u+v=\langle30cos70^\circ+40cos220^\circ,30sin70^\circ+40sin220^\circ\rangle\\u+v\approx\langle-20.38,2.48\rangle[/tex]

Using the direction formula:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{2.48}{-20.38})\\\theta\approx-6.94^\circ[/tex]

As the vector is located in Quadrant II, we need to add 180° to our angle:

[tex]\theta=180^\circ+(-6.94)^\circ\\\theta=173.06^\circ[/tex]

Therefore, the best answer is D) 173°

Problem 4

Using scalar multiplication:

[tex]-3u=-3\langle35,-12\rangle=\langle-105,36\rangle[/tex]

Find the magnitude of the resulting vector:

[tex]||-3u||=\sqrt{x^2+y^2}\\||-3u||=\sqrt{(-105)^2+(36)^2}\\||-3u||=111[/tex]

Find the direction of the resulting vector:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{36}{-105})\\\theta\approx-18.92^\circ[/tex]

As the vector is located in Quadrant II, we need to add 180° to our angle:

[tex]\theta=180^\circ+(-18.92)^\circ\\\theta=161.08^\circ[/tex]

Therefore, the best answer is C) 111; 161°

Problem 5

Using scalar multiplication:

[tex]5v=5\langle25cos40^\circ,25sin40^\circ\rangle=\langle125cos40^\circ,125sin40^\circ\rangle[/tex]

Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be [tex]||5v||=125[/tex], making the correct answer C) 125; 200°

Answer:

(- infinitysymbol,-5]

see image.

Step-by-step explanation:

Interval notation uses parenthesis or square brackets in the format:

( or [ begin , end )or]

Always use parenthesis around the infinity or negative infinity symbol. Square brackets are for when the number is included. Like in this case where it says "or equal to -5"

see image.

Answer:

Step-by-step explanation:

aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:

tanθ = opp/adj = y/x

y = xtanθ

What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):

dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)

We need to find out values for all of the variables:

The observer is not moving, therefore dx/dt = 0.

The observer is standing 4 miles away from the lift-off point, so x = 4.

The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.

The rate of change for the angle, dθ/dt, is 0.1.

Just plug all the numbers in:

dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)

dy/dt = 0 + 1.6

dy/dt = 1.6 mi/min

Answer:

2/4 * 40 4/5 * 5/7 = 102/

7

= 14 4/

7

≅ 14.5714286

Step-by-step explanation:

To find a new numerator:

a) Multiply the whole number 40 by the denominator 5. Whole number 40 equally 40 * 5/

5

= 200/

5

b) Add the answer from previous step 200 to the numerator 4. New numerator is 200 + 4 = 204

c) Write a previous answer (new numerator 204) over the denominator 5.

Forty and four fifths is two hundred four fifths

Multiple: 2/

4

* 204/

5

= 2 · 204/

4 · 5

= 408/

20

= 102 · 4/

5 · 4

= 102/

5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(408, 20) = 4. In the following intermediate step, cancel by a common factor of 4 gives 102/

5

.

In other words - two quarters multiplied by two hundred four fifths = one hundred two fifths.

Multiple: the result of step No. 2 * 5/

7

= 102/

5

* 5/

7

= 102 · 5/

5 · 7

= 510/

35

= 102 · 5/

7 · 5

= 102/

7

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(510, 35) = 5. In the following intermediate step, cancel by a common factor of 5 gives 102/

7

.

In other words - one hundred two fifths multiplied by five sevenths = one hundred two sevenths.

Answer: Any number smaller than 6

3k - 6 < 12

(Add six to both sides)

= 3k < 18

(Divide by 3 on both sides)

= k < 6

Also a side note that may be helpful in other similar problems: If you are dividing or multiplying by a negative number you have to flip the inequality sign.

Answer: 13

Step-by-step explanation:

Answer:

Hey Dude....

Step-by-step explanation:

This is ur answer.....

Hope it helps!

Brainliest pls!

Follow me! :)

Answer:

11 5/4

Step-by-step explanation:

make the denominator the same then add.the common factor of 2 and 7 is 14 so make all the denominator to 14 then u can add.thus having the answer

Answer:

Bob swam 70 meters on Monday

Step-by-step explanation:

Let x = Meters swam on Monday

and y = Meters swam on Tuesday

x + y = 250

y = 250 - x

y = 3x - 30

250 - x = 3x - 30

4x = 280

x = 70

y = 180

Answer:

Depends on whether you're looking for area or perimeter. Follow the equations below

Step-by-step explanation:

This depends on whether you're being asked to find perimeter of area

Perimeter is equal to 2(length) + 2(width)

In which case perimeter would be 2(4 + w) + 2(w)

Which can be simplified to 8 + 2w + 2w = 4w + 8

However, Area is equal to length times width

Which would be (4 + w) * w = 4w + w^2

Answer:

Step-by-step explanation:

✔ w(4 +w) = 60

Answer:

y = 5.5 ·x

Step-by-step explanation:

x= pounds purchased

y = cost in $

Given:

4 pounds for $22

x pounds for $ y

Find unit price so will know how much will pay for 1 pound

22/4 = 11/2 = $ 5.5 for 1 pound

Make a general formula :

y = 5.5 ·x

Answer:

10 inches by 8 inches

The length and with would be half the perimeter: 36/2 = 18

find 2 numbers when added together equal 18 and when multiplied together equal 80.

8 + 10 = 18

8 x 10 = 80

Answer:

x=20

y and z=160

Step-by-step explanation:

the arc of the circle is congruent to the central angle therfore x is also 20

next for y and z we can tell they are congruent now to find the measure. we can tell A is 180 so we do 360-180-20=160

Answer:

Step-by-step explanation:

7) m + 6 > 17

   m > 17- 6

8. 500 + p > 1500

9. Let cost of pencil be 'x' and it is 5 less than y

x < y -5

Cost of pencil and ruler is less than $ 30.

x + y < 30

10. r + 5 > 17

         r > 17 - 5

         r > 12

12.She is spending $ x. So, we have to subtract from $10.

10 -x < 5

Using linear function concepts, it is found that consumption would increase by $800.

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

In this problem, the function is given by:

C = 200 + 0.8Y.

Which means that the slope is of m = 0.8 per unit of Y.

For 1000 units:

0.8 x 1000 = 800.

Consumption would increase by $800.

More can be learned about linear function concepts at https://brainly.com/question/24808124

Answer:x.

Step-by-step explanation:

Answer:

40+20 = 72-12 is the simplified version.

Step-by-step explanation:

Your equations

4(10+5) = 6(12-2)

Multiply 4 by 10 and 5 for the "4(10+5)"
Multiply 6 by 12 and -2 for the "6(12-2)"

40+20 = 72-12 is the simplified version.

If you want to solve/verify:

40+20 = 72-12

60 = 60

The nanswer is correct.

Answer:

40 + 20 = 72 - 12

Step-by-step explanation:

The number outside the parenthesis will be multiplied to both numbers inside the parenthesis, making the equation

(4 * 10) + (4 * 5) = (6 * 12) + (6 * (-2))

simplifying the equation...

40 + 20 = 72 - 12

there will be your 1000 caterpillars

Answer:

12

Step-by-step explanation:

4a = b and A-41=b-5

a-41+5=b

a-36 =b

which means a+36 =4a

so 3a=36 and a=12

Answer:

65.2 cm

Step-by-step explanation:

P = a + b + c + d

P = 16.7 cm + 12.9 cm + 16.7 cm + 18.9 cm

P = 65.2 cm

The perimeter of the trapezoid is 65.2 cm.

Answer:

To find the perimeter of this trapezoid, simply add all four sides (since there are only four sides to a trapezoid):-

16.7 + 12.9 + 16.7 + 18.9

= 65.2 centimetres is the perimeter.

You can picture it like this;

Answer:

unit price= $23.75

Step-by-step explanation:

$71.25/ 3

unit price means the price of 1

Answer:

concave up

Step-by-step explanation:

there is no negatives in the equation (in front of x-value)

Answer:

I think 9 units is the correct answer

Answer:

its 15 units

Step-by-step explanation:

momma told me it was right

4 * x = 12.44

4/4 * x = 12.44 / 4

x = 3.11

Answer:

x = 3.11

Step-by-step explanation:

To find the value of 'x', divide both sides of the equation by 4

12.44 = 4x

[tex]\dfrac{12.44}{4}=\dfrac{4x}{4}\\\\\\3.11=x[/tex]

Answer:

3x>18

Step-by-step explanation:

Three times the number x will be called 3x. If an expression is more or greater than a number, we use the greater symbol: >

So, we can write,

3x>18

C = 2 x pi x r

if r = 5 cm

C = 2 x pi x 5 = 10 x pi

≈ 10 x 3,14 ≈ 31,4 cm

C = 2 x pi x r = pi x d

if d = 2 m

C = pi x 2

≈ 3,14 x 2 ≈ 6,28 m

Hello!

a)

C  = 2πr                     C= 2*π     *5                     31,4cm    

                                   =  2*3,14* 5

d)

r =2/2 => 1m

C=  2πr                   C= 2*π*1                             6,28m

                               =  2 *3,14*1                      

[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]

Answer:

2,3,4

Step-by-step explanation:

Given data:

2,0,2,4,4,4,3,2,3,4,1,3,3,2

Solution:

Mode = Most often number

There are

4 = two's

1 = zero's

4 = four's

4 = Three's

1 = ones's

Hence the mode is:

2,3,4

~lenvy~

Answer: Is Square feet/minute if there is two of them the second one is Cubic feet/minute

Step-by-step explanation: feet/minute would cover anything linear {forward, backward, left, right}

square feet/minute would cover two-dimensional areas  {walls, floors, sides of buildings, etc.}

cubic feet/minute would cover three dimensional situations  {swimming pools, buckets, containers, etc.}

Answer:

35

area of traingle b xh/2 5x4/2 - 10

area of square lxl - 5x5 -25

add- 35

Answer:

The answer would be 35.

Step-by-step explanation:

The area of the shape would be 35 square centimeters because if we divide the shape into 3 different shapes, a square on the bottom and 2 triangles at the top, we can multiply the square's length and width to get an area of 25. Next, we'll multiply the 2 triangles length of 4 with the width of 5 to get a total area of 20 from both of them, we'll then divide the area of 20 by 2 to get 10. Now add 20 and 10 to get 35.