Find the slope of the line.

Answer:

4a. 8.7

4b. 11

Step-by-step explanation:

use formulas

#a

[tex]\\ \sf\longmapsto H=\dfrac{√3}{2}a[/tex]

[tex]\\ \sf\longmapsto H=dfrac{√3}{2}10[/tex]

[tex]\\ \sf\longmapsto H=5√3in[/tex]

#b

[tex]\\ \sf\longmapsto a=\dfrac{Diagonal}{√2}[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{√242}{√2}[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{11√2}{√2}[/tex]

[tex]\\ \sf\longmapsto a=11in[/tex]

Answer:

x = 8.8 or x = 44/5

Step-by-step explanation:

1) Multiply both sides of the equation by 4, and cancel out the 4 on the bottom of 3/4, this turns the equation into: 8x - 4 = 3x + 40

2) Move the x to the lefthand side and change the side, do the same for the constant (4), this turns the equation into: 8x - 3x = 40 + 4

3) Combine like terms, subtract 8x from 3x and add 40 to 4: 5x = 44

4) Divide both sides by 5, and your answer is 44/5 (or 8.8 when converted to a decimal)

The cut-out from each corner that maximizes the volume is 3 inches.

The dimensions are given as:

[tex]\mathbf{Length = 15}[/tex]

[tex]\mathbf{Width = 24}[/tex]

Assume the cut-out is x.

So, the dimension of the board is:

[tex]\mathbf{Length = 15 - 2x}[/tex]

[tex]\mathbf{Width = 24 - 2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

The volume (V) is calculated as:

[tex]\mathbf{V = Length \times Width \times Height}[/tex]

So, we have:

[tex]\mathbf{V = (15 - 2x) \times (24 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{V = 360x - 78x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V' = 360 - 156x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{ 360 - 156x + 12x^2 = 0}[/tex]

Divide through by 12

[tex]\mathbf{ 30 - 13x + x^2 = 0}[/tex]

Rewrite as:

[tex]\mathbf{ x^2 - 13x + 30 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = \{3, 10\}}[/tex]

The value of x = 10 is greater than the dimensions of the box.

So, we have:

[tex]\mathbf{x = 3}[/tex]

Hence, the cut-out from each corner that maximizes the volume is 3 inches.

Read more about maximum volumes at:

https://brainly.com/question/7063268

32/5

本题已由中国数学会官方解答（现有会员：3人）  

Answer:

Step-by-step explanation:

b

Hola!!

[tex]\frac { 63 } { 5 } - \frac { 21 } { 5 } - \frac { 73 } { 5 }[/tex]

[tex]\frac{63-21}{5}-\frac{73}{5} [/tex]

[tex] \frac{42}{5}-\frac{73}{5} [/tex]

[tex] \frac{42-73}{5} [/tex]

[tex]\boxed{-\frac{31}{5}=-6.2}[/tex]

_____

¡Espero eso ayude!

Comenta si tienes dudas.

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Answer:

The line representing the number of miles Nick drives while performing x oil changes is steeper than the line representing the number of miles Natalie drives while performing x oil changes because he drives farther between oil changes than Natalie does.

Answer:

-360 degrees celcius

Step-by-step explanation:

Answer:

Integer

-NULL

Brainliest will be appreciated thank you!

Answer:

-8 ÷ 2 = -4

Step-by-step explanation:

just divide y by x

Answer:

the answer would be A

Step-by-step explanation:

Answer: Single, under the age of 65 and not older or blind, you must file your taxes if: Unearned income was more than $1,050. Earned income was more than $12,000. Gross income was more than the larger of $1,050 or on earned income up to $11,650 plus $350.

i dont get the second part .. sorry

Step-by-step explanation:

I don't get the question

Answer:

y = -1/6x + 1/3

Step-by-step explanation:

y2 - y1 / x2 - x1

-5 - 0 / 32 - 2

-5 / 30

= -1/6

y = -1/6x + b

0 = -1/6(2) + b

0 = -1/3 + b

1/3 = b

Answer:

inconsistent; none

Step-by-step explanation:

Because 29 ≠ 94, the system is inconsistent. There are no solutions.

Answer:

x = 9

Step-by-step explanation:

A midpoint is found by adding up two numbers and then dividing by 2 (Also known as an average). Therefore, a midpoint marks half of a line. That means that DP is 1/2 of DE. We can now form an equation. 6x + 4 = 1/2 * (14x - 10), making 6x + 4 = 7x - 5 by using the distributive property. Next, isolate x by subtracting by 6x on both sides and adding by 5 on both sides. You would get x = 5 + 4, which means that x = 9.

Answer:

(1)+(2) Substitute Y from (2) in (1):

X2+(1−X)2=1X2+(1−X)2=1

...

2X(X−1)=02X(X−1)=0

Hense X= 0 or X = 1.

by-step explanation:

Answer: I think 10ft apart

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Okay so we plug in the values for x and y to make the equation:

1 - 2 x -6 = 4

And then we just solve the left side:

2 x -6 = -12

1 - -12 = 1 + 12 = 13

So this is false

Answer: D

Step-by-step explanation: Cause there's not year for how long alma saved so its D not here

Answer:

C. 7980.00

Step-by-step explanation:

by using the formula of interest =ie. 4200*4.75*4 and the answer will come 7980.00

Answer:

<B = 3(14) + 6 = 48 degrees

Step-by-step explanation:

4x+6+3x+6+5x = 180 degrees

12x + 12 = 180

12x = 180 - 12

x = 168/12

x = 14

Answer:

Step-by-step explanation:

r = 50

Circumference = 2πr

                          [tex]= 2 * 3.14 * 50\\\\= 314 \ ft[/tex]

Answer: y= -4x -24

Step-by-step explanation:

Answer: c

Step-by-step explanation: doesnt show a number so example lets say its 0

Answer:

the anwser is actually b

Answer:

The answer is 4

Step-by-step explanation:

2/4 = 1/2

Answer:

4

Because 2/4 is basically 1/2

Answer:

314 cm^2

Step-by-step explanation:

A = pi(r^2)

A = (3.14)(10)^2

A = (3.14)(100)

A = 314 cm^2

Answer:

314.16

Step-by-step explanation:

a = πr²

a = π 10²

a = 314.16

I hope that this helps!!!!!

Answer:

0.0302782

Step-by-step explanation:

Answer:

0.05124653739

Step-by-step explanation:

Answer: It should be D

Answer:The Indianapolis Motor Speedway is an automobile racing circuit located in Speedway, Indiana (an enclave suburb of Indianapolis) in the United States. It is the home of the Indianapolis 500 and the Verizon 200,[4] and formerly the home of the United States Grand Prix. It is the largest sports venue in the world. It is located on the corner of 16th Street and Georgetown Road, approximately six miles (10 km) west of Downtown Indianapolis.

Constructed in 1909, it is the second purpose-built, banked oval racing circuit after Brooklands and the first to be called a 'speedway'. It is the third-oldest permanent automobile race track in the world, behind Brooklands and the Milwaukee Mile. With a permanent seating capacity of 257,325,[1] it is the highest-capacity sports venue in the world.[5]

Considered relatively flat by American standards, the track is a 2.5-mile-long (4.0 km) rectangular oval with dimensions that have remained essentially unchanged since its construction. It has two 5⁄8-mile-long (1,000 m) straightaways, four geometrically identical 1⁄4-mile (400 m) turns, connected by two 1⁄8-mile (200 m) short straightaways, termed "short chutes", between turns 1 and 2, and between turns 3 and 4.

Step-by-step explanation:

The average displacement of the car would be 33.33 Km

Displacement [x] of an object is the length of the straight line joining the initial and final position of the object. Mathematically, if the velocity of the body is  'v' m/s at an instant of time, then displacement can be written as-

v = dx /dt

x = vdt

∫dx = ∫vdt

Given is the following problem -

A race car completes race in 10 minutes. Its average speed is 200km/hr.

The average displacement of the racetrack would be -

[x] = v x t = 200 x 1/6 = 33.33 Km

Therefore, the average displacement of the car would be 33.33 Km

To solve more questions on Kinematics, visit the link below

brainly.com/question/17465675

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[The question given is not completely written. Race track example is - A race car completes race in 10 minutes. Its average speed is 200km/hr. ]