Jared has a wooden board 11 ft long. He wants to cut it into two pieces so that the longer piece (y) is 4 ft less than 4 times the length of the shorter piece (x).
Choose the two equations that will create our system of equations for this story problem.


y = 4x - 4

x + y = 11

x - y = 11

y = 4 - 4x

Answer:

3

Step-by-step explanation:

Determine the coefficient of y+ 6 - 3 in the binomial expansion y+ 3(2-1)  

3(2+-1) + y = + 3(2) - (3)^-1   = 3

= y + 6 - 3   = y+3

remember to add a minus sign before every second term then a plus.

Now we see that in the term where y is in factor 3 as asked in the question (this is the term  2(3), the coefficient is therefore 3.

Answer: the two trains will meet in 2.8 hours

Step-by-step explanation:

Step 1

Speed of train A  = 90mph

Speed of train B = 110 mph

Since both trains  are travelling towards each other , their effective speed will be= 90 mph + 110mph= 200mph

Step 2

we know that Speed = distance / time

therefore Time = Distance / speed

Distance = 560 miles

Speed = 200 mph

Time = 560miles / 200mph

2.8 hours

Answer:

In 1 year ( 12months ) ...............

Answer:

It is 1 YEAR OR 12 MONTHSSSSS

Step-by-step explanation:

Given:

Score in first round = 5 points

Score in second, third and fourth rounds was identical.

A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round.

To find:

The inequality for the given problem.

Solution:

Let p be the number of points, p, that Steward scored in each of the second, third, and fourth rounds.

Score in first 4 rounds = Score of 1st round + Score of 2nd round + Score of  1s 3rd round + Score of 4th round

Score in first 4 rounds [tex]=5 + p + p + p[/tex]

                                     [tex]=5 +3p[/tex]

A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. It means the total score in first 4 rounds must be greater than or equal to 30.

[tex]5+3p\geq 30[/tex]

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

4y+1=17

Subtract the 1 from the 17, giving you...

4y =16

Divide 16 by 4y, giving you...

Y= 4

I hope this helps you out!

Answer:

669 dollars and 70 cents

Step-by-step explanation:

just minus all the money spent and add the money added

Answer:

how bout 4 bracelets?

Step-by-step explanation:

Answer:

a sum is a result of adding two or more numbers

Step-by-step explanation:

example : 9 is the sum of 2. 4 and 3 because ( 2 plus 4 us 3 = 9

Answer:

common difference

d=8-(-1)=8+1=9

or d=17-8=9

or 26-17=9

and so on

Answer:

12) y=25x

13) 14 gallons

Step-by-step explanation:

m= (y2-y1)/(x2-x1)

m= (75-50)/(3-2)

m=25/1=25

y-y1=m(x-x1)

y-75=25(x-3)

y-75=25x-75

y=25x

------------------------------------

350=25x

x=350/25

x=14

Answer:

49

Step-by-step explanation:

it is 49 because i worked it out and if you look closely it says 4 mour that

Answer:

-9.45238095238

Step-by-step explanation:

Just use the fraction to add to the whole number

Answer:

=−14.73809524

Step-by-step explanation:

Answer:

B and C

Step-by-step explanation:

Step-by-step explanation:

The right trangular prism has 5 surface areas. 2 of them are triangles and 3 of them are rectangles.

Area of triangle

= 0.5(3/2)(2) = 3/2 square units.

Area of 1st rectangle

= (5/2)(5) = 25/2 square units.

Area of 2nd rectangle

= (3/2)(5) = 15/2 square units.

Area of 3rd rectangle

= (2)(5) = 10 square units.

Total Surface Area

= 2 * (3/2) + (25/2) + (15/2) + 10

= 33 square units. (A)

Answer: Length  = 11 cm

Width = 14 cm

Step-by-step explanation:

Let x = Length of the rectangle.

then, width = x+ 3

Perimeter of rectangle =  2 (length +width)

Then, Perimeter = 2 (x+x+3)

= 2 (2x+3)

Since perimeter = 50 cm

[tex]\Rightarrow\ 2(2x+3)=50[/tex]

[tex]\Rightarrow\ 2x+3=25[/tex]                              [Divide both sides by 2]

[tex]\Rightarrow\ 2x=22\\\\\Rightarrow\ x=11[/tex]

The dimensions are :

Length  = 11 cm

Width = 11+3= 14 cm

Answer:

A: 24°

B: 22°

C: 134°

Step-by-step explanation:

A triangle will always add up to 180°

A + B + C = 180°

(2x + 4) + (2x + 2) + (13x + 4) = 180

2x + 2x + 13x + 4 + 2 + 4 = 180

17x + 10 = 180

17x = 180 - 10

17x = 170

17x/17 = 170/17

x = 10

A: 2x + 4

B: 2x + 2

C: 13x + 4

A: 24°

2x + 4

2(10) + 4

20 + 4

24°

B: 22°

2x + 2

2(10) + 2

20 + 2

22°

C: 134°

13x + 4

13(10) + 4

130 + 4

134°

Answer:

m=19h

Step-by-step explanation:

19 dollars per number of hours worked(h) equals the amount of money you would receive.

Answer:

She bought 3 bottles of oil, and that would be a total of 21$ of oil so she should have recieved 29.00$ back so no change

Step-by-step explanation:

Answer:

[tex]x = 12[/tex]

Step-by-step explanation:

Perimeter of a square:

The perimeter of a square of side x is given by:

[tex]P_s = 4x[/tex]

Perimeter of a rectangle:

The perimeter of a rectangle of length l and width w is given by:

[tex]P_r = 2(l + w)[/tex]

The length of the sides of a square measure 2x-5.

This means that the perimeter of the square is:

[tex]P_s = 4(2x - 5) = 8x - 20[/tex]

The length of a rectangle measures 2x, and the width measures x + 2.

This means that the perimeter of the rectangle is:

[tex]P_r = 2(2x + x + 2) = 2(3x + 2) = 6x + 4[/tex]

For what value of x is the perimeter of the square the same as the perimeter of the rectangle?

This is x for which:

[tex]P_s = P_r[/tex]

So

[tex]8x - 20 = 6x + 4[/tex]

[tex]8x - 6x = 20 + 4[/tex]

[tex]2x = 24[/tex]

[tex]x = \frac{24}{2}[/tex]

[tex]x = 12[/tex]

Answer:

volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Step-by-step explanation:

Given the data in the question and as illustrated in the image below;

R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)

from the image;

the equation of AB will be;

y-b / b-0 = x-0 / 0-a

(y-b)(0-a) = (b-0)(x-0)

0 - ay -0 + ba = bx - 0 - 0 + 0

-ay + ba = bx  

ay = -bx + ba

divide through by a

y = [tex]\frac{-b}{a}[/tex]x + ba/a

y = [tex]\frac{-b}{a}[/tex]x + b

so R is bounded by  y = [tex]\frac{-b}{a}[/tex]x + b and y =0, 0 ≤ x ≤ a

The volume of the solid revolving R about x axis is;

dv = Area × thickness

= π( Radius)² dx

= π ( [tex]\frac{-b}{a}[/tex]x + b )² dx

V = π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Therefore,  volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

The volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

Equation of the line AB

[tex]y-0 = \frac{b-0}{0-a} (x-a)[/tex]

[tex]y = \frac{-b}{a} (x-a)[/tex]

The volume generated when a curve f(x) is rotated about the x-axis in x∈(c,d) is given by:

[tex]V=\int\limits^d_c {y^2} \, dx[/tex]

So, the volume generated when line AB is rotated about the x-axis will be [tex]V=\int\limits^b_0 ({\frac{-b}{a} (x-a))^2} \, dx[/tex]

[tex]V=\frac{b^{5} }{3a^{2} }[/tex]

Therefore, the volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

To get more about volume generation visit:

https://brainly.com/question/20784784

Answer:

$500

Step-by-step explanation:

0.16x=80

x=80/0.16

x=500

Hope I helped!

Answer:

3 3/4

Step-by-step explanation:

8 1/4 - 4 2/4 = 4 1/4 - 2/4 = 3 3/4

Answer:

An expression is a combination of numbers, variables, and symbols to be solved. An equation has expressions that are separated by an equals sign.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sample Response: An expression is written as a phrase and an equation is written as a statement. Equations are written as sentences with capitalization and punctuation. Expressions are written as phrases with no capitalization or punctuation. An equation has an equals sign and an expression does not.

Answer:

66

Step-by-step explanation: