A ​108-inch is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.

Answer:

x=5

Step-by-step explanation:

-5(-x - 1) + 4x – 1= 49

Distribute

5x +5 +4x -1 = 49

Combine like terms

9x +4 = 49

Subtract 4 from each side

9x+4-4 = 49-4

9x = 45

Divide by 9

9x/9 =45/9

x = 5

Answer:

[tex]\huge \boxed{x=5}[/tex]

Step-by-step explanation:

[tex]{\Large -5(-x - 1) + 4x -1= 49}[/tex]

Expand brackets.

[tex]5x+5+ 4x -1= 49[/tex]

Combine like terms.

[tex]9x+4=49[/tex]

Subtract 4 from both sides.

[tex]9x+4-4=49-4[/tex]

[tex]9x=45[/tex]

Divide both sides by 9.

[tex]\displaystyle \frac{9x}{9} =\frac{45}{9}[/tex]

[tex]x=5[/tex]

Answer:

Step-by-step explanation:

[tex]5\frac{1}{6}=\frac{(5*6)+1}{6}=\frac{31}{6}[/tex]

Answer:

31/6 (improper fraction).

Step-by-step explanation:

5 1/6 = (6 × 5) + 1/6 = 31/6

31/6 is the improper fraction.

Answer:

Answer:  In number theory, two integers a and b are said to be relativley prime or co prime, if the only positive integer (factor) that divides both of them is 1.Consequently, any prime numbers that divides one does not divide the other.

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope of the line m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (1, - 2)

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

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Answer:

17

Step-by-step explanation:

b(1) = 16

b(2) = b(2-1) +1

      = b(1) +1

     = 16+1

    = 17

Answer:

[tex] \boxed{\sf Perimeter \ of \ semicircle = 3 \pi \ cm} [/tex]

Given:

Radius of semicircle (r) = 3 cm

Step-by-step explanation:

[tex]\sf Perimeter \ of \ semicircle = \pi r [/tex]

[tex] \sf = 3 \pi \: cm[/tex]

Work Shown:

A = P*(1+r/n)^(nt)

A = 500*(1+0.04/1)^(1*3)

A = 562.432

A = 562.43

Answer: $562.43

Step-by-step explanation:

The initial start up amount is 500  and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.

So 100%  + 4 % = 104% = 1.04  

The common difference is 1.04.

so  500 * 1.04^n= A where n is the number of years and A is the total amount.

A = 500 * [tex]1.04^{3}[/tex]  

A= 562.43

Answer:

The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.

Answer:

Quadrant IV

Step-by-step explanation:

If x is greater than 0, then it will remain on the right side, on quadrants I and IV. If y is less than 0, then it will be on the bottom, so we are left with quadrant IV:

x is greater than 0, so all possible values are positive

y is less than 0, so all possible values are negative

(x,-y)

Following are the description of the wrong choice:

That's why the "Quadrant IV" is the correct answer.

Learn more:

Answer:

Alice will have to pay $13.33

Ben will have to pay $23.33

Kelvin will have to pay $43.33

Step-by-step explanation:

Given that

Alice destination is 20 miles away

Ben destination is 30 miles away

Calvin destination is 40 miles away.

For a mile, taxi costs 2 dollars.

To find:

How much each person has to pay if they share the same taxi to their respective destinations?

Solution:

For the first 20 miles, the taxi will be shared by all 3 of them.

Charges for 20 miles = 20 [tex]\times[/tex] 2 = $40

This $40 will be shared among all 3.

Each will pay = [tex]\frac{40}{3} = \$13.33[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33

Charges for Calvin = $13.33

For the next 10 miles, the taxi will be shared by Ben and Calvin.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be shared between Ben and Calvin.

Each will pay = [tex]\frac{20}{2} = \$10[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33 + 10 = $23.33

Charges for Calvin = $13.33 + 10 = $23.33

For the next 10 miles, Calvin travels alone.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be paid by Calvin alone.

Charges for Alice = $13.33

Charges for Ben = $23.33

Charges for Calvin = $23.33 + 20 = $43.33

Answer:

z=-3

Step-by-step explanation:

z=(-3)^2 - 3(4)

z=9 - 12

z=-3

The correct answer is D. ​No because the permutations rule would be used to determine the total number of combinations.

Explanation:

The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.

[tex]\dfrac{x}{y}=\dfrac{5}{8}\Big|\cdot\dfrac{y}{5}\\\\\dfrac{x}{5}=\dfrac{y}{8}[/tex]

Answer:

x/5 = y/8

Step-by-step explanation:

x          5

----- = -------

y          8

Using cross products

8x = 5y

Divide each side by 8

x = 5/8 y

Divide each side by 5

x/5 = y/8

Answer:

1. 2/5,-3 2. [tex]x=\frac{-5+-\sqrt{13} }{6}[/tex]

Step-by-step explanation:

i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13  

Step-by-step explanation:

5x² + 13x - 6 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a = 5 , b = 13 c = - 6

We have

[tex]x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} [/tex]

[tex]x = \frac{ - 13± \sqrt{169 + 120} }{10} [/tex]

[tex]x = \frac{ - 13± \sqrt{289} }{10} [/tex]

[tex]x = \frac{ - 13±17}{10} [/tex]

[tex]x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} [/tex]

3x² + 5x + 1 = 0

a = 3 , b = 5 , c = 1

[tex]x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} [/tex]

[tex]x = \frac{ - 5± \sqrt{25 - 12} }{6} [/tex]

[tex]x = \frac{ - 5± \sqrt{13} }{6} [/tex]

[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]

Hope this helps you

Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

Answer:

11 shots

Step-by-step explanation:

Why we did this:

So therefore, Owen made 11 of 18 shots he attempted.

Owen attempted 11 shots during the hockey practice.

Number of shots attempted by Owen = 18

Percentage of shots made = 60%

Then, the number of shots made will be calculated as:

= Percentage of shots made × Number of shots attempted

= 60% × 18

= 60/100 × 18

= 0.6 × 18

= 10.8 shots

= 11 shots approximately

In conclusion, Owen made 11 shots

Read related link on:

https://brainly.com/question/18298965

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▹ Answer

3² * a² - b²

▹ Step-by-Step Explanation

9a² - b²

Break down each coefficient and variable:

9 = 3²

a² = a²

b² = b²

Combine everything together:

3² * a² - b²

Hope this helps!

CloutAnswers ❁

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Answer:

Since both terms are perfect squares, factor using the difference of squares formula,  a^2-b^2=[a+b][a-b] where a=3a and b=b

Answer:

  x = 11/9

Step-by-step explanation:

Eliminate parentheses, add 16x, subtract 21.

  7(3 -x) = 8(4 -2x) . . . . given

  21 -7x = 32 -16x . . . . . eliminate parentheses using the distributive property

  9x +21 = 32 . . . . . . . . add 16x

  9x = 11 . . . . . . . . . . . . subtract 21

  x = 11/9 . . . . . . . . . . . .divide by the coefficient of x

Answer:

50%

Step-by-step explanation:

Answer:

x > 16/5 or x < -3/4

Step-by-step explanation:

Equation 1: 5x - 4 > 12

Equation 2: 12x + 5 < -4

Equation 1: 5x - 4 > 12

add 4 to both sides

5x > 16

divide by 5 on both sides

x > 16/5

Equation 2: 12x + 5 < -4

subtract 5 on both sides

12x < -9

divide by 12 on both sides

x < -9/12

simplify

x < -3/4

Answer:

4 quarts

Hope it helps!

Step-by-step explanation:

Answer: 5 gallons= 20 quarts

              1 gallon = 4 quarts

Answer:

[see below]

Step-by-step explanation:

Finding the slope of the two points:

[tex]m=\frac{-17+5}{3-1}=\frac{-12}{2}=\boxed{-6}[/tex]

The slope is -6.

Using an incomplete slope-intercept form equation to find the y-intercept:

[tex]y=6x+b\\\\-5=6(1)+b\\\\-5=6+b\\\\-5-6=6-6+b\\\\\boxed{1=b}[/tex]

The equation for the line passing the points is [tex]y=-6x+1[/tex].

The equation in standard from would be [tex]6x+y=1[/tex].

Answer:

4775.9 [tex]cm^3[/tex]

Step-by-step explanation:

To find the volume of a cone use the expression [tex]\pi r^2\frac{h}{3}[/tex]

r = radius

h = height

Now substitute h for 27 and r for 13, [tex]\pi 13^2\frac{27}{3}[/tex]

First do 13 x 13 (because of the exponent), then divide 27 and 3, which is 9

169 x 9 = 1521

Lastly multiply by pi or use 3.14

1521 x 3.14 = 4775.94

Since it asks to round to the tenth it is just 4775.9

Answer:

4778.4 cm^3

Step-by-step explanation:

The formula for the volume of a cone is [tex]V=\pi r^2\frac{h}{3} \\[/tex].

In this case, the height is 27 and the radius is 13, so we plug in the values and get [tex]V = \pi (13)^2 \frac{27}{3}\\[/tex].

We solve and get the volume of the cone as [tex]1521\pi[/tex] or 4778.4 cm^3.

Answer:

well just do area, and since it's the same in each side 12×4= 144

Answer:

the terms of any of the 2 terms should have been given

Answer:

1176in^2

Step-by-step explanation:

find the surface area of the cube

(14*14)6=1176 inches cubed

14*14 is finding the area of one side and then we multiply it by six because that's how many congruent sides there are

Answer:

[tex]\large\boxed{1,176 in^{2} }[/tex]

Step-by-step explanation:

The cube is 14 inches tall

All of the sides in a cube are the same, which means:

Length = 14 inches

Width = 14 inches

Height = 14 inches

There are 6 sides in a cube. Each side has a length and a width.

We can use the following formula to find the surface area (SA) of the cube, or how much wrapping paper Jayde will use.

SA = # of Sides(Length(Width))

Plug in known values

SA = 6((14)(14))

The 14s represent the length and width while the 6 represents the number of sides in the cube.

Solve/Simplify

SA = 6(196)

SA = 1,176 inches²

Jayde will need to use 1,176 in² of wrapping paper to wrap the whole present.

Hope this helps :)

Answer:

C. <3, E. <1

Step-by-step explanation:

A triangle has 3 vertices, so it has exactly 3 interior angles, one at each vertex.

A triangle has 2 exterior angles at each vertex, so a triangle has 6 exterior angles. Each exterior angle is adjacent to an interior angle. The interior angles that are not adjacent to an exterior angle are that exterior angle's remote interior angles.

<6 is an exterior angle of the triangle. <5 is the other exterior angle at that vertex. <2 is an interior angle of the triangle and is adjacent to <6, so <2 is not a remote interior angle to <6.

The other two interior angles of the triangle are <1 and <3.

<1 and <3 are interior angles that are not adjacent to <6, so they are the remote interior angles to <6.

Answer: <1, <3