The designers of drink cartons must consider the length of the straw required so that it will reach the bottom
of the carton. We will make the following assumptions:
-the straw must stick out of the carton by an additional 1.5 cm
-the hole is at one vertex of the carton
-the straw must be able to reach into the diagonally opposite corner of the base of the carton
use the formula a^2+b^2+c^2=d^2
CHECK IMAGE FOR VISUAL REPRESENTATION OF THE CARTON

Answer:cab

Step-by-step explanation:

Answer: c. GBF

Step-by-step explanation:

Answer:

Question 3)

[tex]\stackrel{\frown}{AC}=36\text{ inches}[/tex]

[tex]\angle BCA\approx103^\circ[/tex]

Question 1)

[tex]\stackrel{\frown}{AB}\approx 8.9\text{ cm}\\[/tex]

[tex]A\approx44.5\text{ cm}^2[/tex]

Step-by-step explanation:

Question 3)

We are given that the central angle is 1.8 radians and has a radius of 20 inches.  

Part A)

The formula for arc length in terms of radians is given by:

[tex]s=r\theta[/tex]

Where s is the arc length, r is the radius, and θ is the angle in radians.

In this case, r is 20 and θ is 1.8. Hence, the arc length is:

[tex]\stackrel{\frown}{AC}=(20)(1.8)=36\text{ inches}[/tex]

Part B)

∠BCA is the central angle that measures 1.8 radians.

We can convert radians to degrees using the following formula:

[tex]\displaystyle d=\theta\cdot\frac{180^\circ}{\pi}[/tex]

Where d is the measure in degrees, and θ is the measure in radians.

Therefore:

[tex]\displaystyle d=1.8\cdot\frac{180^\circ}{\pi}\approx103.1324\approx103^\circ[/tex]

Question 1)*

Part A)

We will use the arc length formula in degrees given by:

[tex]\displaystyle s=2\pi r\cdot \frac{\theta^\circ}{360}[/tex]

Where r is the radius and θ is the angle measured in degrees.

We have a radius of 10 centimeters and a central angle of 51°. Therefore, our arc length is:

[tex]\displaystyle \stackrel{\frown}{AB}=2\pi(10)\cdot\frac{51}{360}=20\pi\cdot\frac{51}{360}\approx8.9\text{ cm}[/tex]

Part B)

We will use the formula for the area of a sector in degrees given by:

[tex]\displaystyle A=\pi r^2\cdot\frac{\theta^\circ}{360}[/tex]

So, we will substitute 10 for r and 51 for θ. Hence, the area of the sector is:

[tex]\displaystyle A=\pi (10)^2\cdot \frac{51}{360}=100\pi\cdot\frac{51}{360}\approx44.5\text{ cm}^2[/tex]

*Notes:

For this question, it is possible and completely fine for us to convert 51° to radians and then use the formulas in terms of radians.

Answer:

(1). 36 inch. , 103° ; (2). 8.9 cm , 44.5 cm² ;

Step-by-step explanation:

1).

(b). m∠BCA = 1.8 rad. × [tex]\frac{180}{\pi }[/tex] ≈ 103° ( π ≈ [tex]\frac{22}{7}[/tex] )

(a). C = 2 π r , the length of arc AB = ( 2 × [tex]\frac{22}{7}[/tex] × 20 ) ÷ 360° × 103.132° ≈ 36 inches

3).

(a).  The length of arc AB = ( 2 × [tex]\frac{22}{7}[/tex] × 10 ) ÷ 360° × 51° ≈ 8.9 cm

(b). A = π r² , the area of the sector = ( [tex]\frac{22}{7}[/tex] × 10² ) ÷ 360° × 51° ≈ 44.5 cm²

Answer: 24.8 and 155.2

Step-by-step explanation:

x+x+130.4=180

2x=49.6

x=24.8

Answer:

155.2

Step-by-step explanation:

let x be the supplimentary angle

then the angle is

130.4+x

we have

130.4+x+x=180

2x=49.6

multiply both sides with 2

x=24.8

then the angle is

130.4+24.8

155.2

Answer:

she paid 68 so it is d i think

Answer:

2

Step-by-step explanation:

it may not be right because i guessed

Answer:

D. Jacob rode a 45-kilometer race in 3 hours.

Step-by-step explanation:

1h = 15km

A. : 30m = [tex]\frac{30}{60}[/tex] × 15km

              = 7.5km (not 2km)

B. : 15m = [tex]\frac{15}{60}[/tex] × 15km

             = 3.75km (not 4km)

C. : 5h = 5 × 15km

             = 75km (not 20km)

D. : 3h = 3 × 15km

             = 45km (Yep, 45km)

Answer:

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. ... When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

Step-by-step explanation:

Answer:

The equation of the line is y =  [tex]-\frac{4}{5}[/tex] x + [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where

∵ A line passes through points (2, -1) and (-3, 3)

∴ x1 = 2 ad y1 = -1

∴ x2 = -3 and y2 = 3

→ Use the rule of the slope above to find the slope of the line

∵ m = [tex]\frac{3--1}{-3-2}[/tex] = [tex]\frac{3+1}{-5}[/tex] = [tex]\frac{4}{-5}[/tex]

∴ m = [tex]-\frac{4}{5}[/tex]

→ Substitute the value of m in the form of the equation above

∴ y =  [tex]-\frac{4}{5}[/tex] x + b

→ To find b substitute x and y in the equation by the coordinates of one  

   point of the given points

∵ x = 2 and y = -1

∴ -1 = [tex]-\frac{4}{5}[/tex] (2) + b

∴ -1 = [tex]-\frac{8}{5}[/tex] + b

→ Add [tex]\frac{8}{5}[/tex] t both sides

∵ -1 + [tex]\frac{8}{5}[/tex] = b

∴ [tex]\frac{3}{5}[/tex] = b

→ Substitute the value of b in the equation

∴ y = [tex]-\frac{4}{5}[/tex] x + [tex]\frac{3}{5}[/tex]

∴ The equation of the line is y =  [tex]-\frac{4}{5}[/tex] x + [tex]\frac{3}{5}[/tex]

Answer:

7y + 4

Step-by-step explanation:

2y + 5y+4

add 2y and 5y

7y+ 4

Answer:

7y +4

Step-by-step explanation:

Open up the brackets ans collect your like terms and simplify the expression.

Answer:

(8-5) + (16-1)=18

Answer:

12 weeks

Step-by-step explanation:

Make an inequality equation with x being the number of weeks:

200 > 500 - 25x

*subtract 500 from both sides*

-300 > -25x

*divide both sides by -25*

12 > x

Answer: Ok so what i'v got for this one is that i averaged up all three numbers and i got an average of about 85%. Now you have to put in a fourth number which will actually be another 80% i believe

Step-by-step explanation: add up all 3 divide them all by the numbers then once your done with that plug in the 80% and see what your answer will be.

Answer:

P would be substituted with 15, so the equation would be accurate

Step-by-step explanation:

Answer:

x - intercept: -1.2

y - intercept: -0.7

Answer:

Step-by-step explanation:

(Sin27) / 11 = (sin x) / 15

cross multiply

15 sin27 = 11 sin x

keep in calculator as you divide 15sin27 by 11.

sin x = .6190779542

do sin ^ -1 (.6190779542) (It’s a key on the calculator.)

x = 38.25*

9514 1404 393

Answer:

  38.2°

Step-by-step explanation:

According to the equation you are give, ...

  sin(x)/15 = sin(27°)/11

Multiplying by 15 gives you ...

  sin(x) = 15·sin(27°)/11 ≈ 0.619078

The inverse sine function is used to find the angle x. It may show as sin⁻¹ on your calculator.

  x = arcsin(0.619078)

  x ≈ 38.2°

_____

Additional comment

x is shown in the figure as an acute angle, so that is the value we have chosen. The other angle that has sin(x) = 0.619078 is the supplement of this, or 141.8°. The two solutions are shown in the 2nd and 3rd attachments.

Answer:

-3<x</2

Step-by-step explanation: the slash is the line.

Answer  

1,863.5

Step-by-step explanation: add 165.85 +20.50 =186.35 the do 186.35 x 10 =1,863.5

Answer:

r u going to be a little late to the party but I

Expand log (10^x).

x = 21

Answer:

10x=21

divide both sides by 10

WIll equal x=2.1

Answer:

It is 50 mph

Step-by-step explanation:

Answer:

that's standard form for slope

Step-by-step explanation:

have a nice day :)

Answer:

What she said

Step-by-step explanation:

Answer:

a=4b/u-4g/u

Step-by-step explanation:

You got this!

Answer:

x =2 nd y= -4

Step-by-step explanation:

That is your answer for the question I hope you get a good grades in school!!!

Answer:

C or D definitely not A or B bc it is too close of a number to 24.75 for 15

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You want to find out how much it would be for 15 boxes

(5 , 11.25)

this is the first pair on the table multiply both by 3 because 5 x 3 = 15(boxes)

so we need to find how much it costs so now you multiply 11.25 by 3 which will be 33.75.

I have done this problem in my class and it is a believe me!