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zimovet [89]
3 years ago
8

Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 42

inches. Find the length and width of the rectangle.

Mathematics
1 answer:
liubo4ka [24]3 years ago
5 0
Length is 16.4 inches and width is 5.1 inches

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The length of a rectangle is 4 less than twice the width. If the perimeter of the rectangle is 130, find the length of the recta
Alchen [17]

Answer:

Let L be the length of the rectangle and w be the width of the rectangle.

"The lenght of a rectangle is one less than twice the width" means L=2W-1

Using perimeter formula of a rectangle which is P=2(L+W) you have:

P=2(L+W)

130=2(2W-1+W)

Solve equation above to find W

130=2(3W-1)

130=6W-2

130+2=6W

132=6W

W=22

From here you find L=2W-1=2x22-1=43

Only thing left is to find area A=LxW

4 0
3 years ago
The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of
Jet001 [13]

Answer:

The coordinates of the endpoints of the side congruent to side EF is:

E'(-8,-4) and F'(-5,-7).

Step-by-step explanation:

<em>" when point M (h, k) is rotated about the origin O through 90° in anticlockwise direction or we can say counter clockwise. The new position of point </em><em>M (h, k) will become M' (-k, h) "</em>

We are given a trapezoid such that the vertices of trapezoid are:

E(-4,8) , F(-7,5) , G(-4,3) , H(-2,5)

Then the new coordinates after the given transformation is:

E(-4,8) → E'(-8,-4)

F(-7,5) → F'(-5,-7)

G(-4,3) → G'(-3,-4)

H(-2,5) → H'(-5,-2)

Hence the coordinates of the endpoints of the side congruent to side EF is:

E'(-8,-4) and F'(-5,-7).


4 0
3 years ago
How do you solve this URGENT (50pts)
Aliun [14]

Explanation:

x + 3y = 2

<u>Converting it to slope intercept form</u>:

y = mx + b  [where m is slope, b is y-intercept]

<u>Make y the subject</u>:

\sf \rightarrow  3y = 2 - x

\sf \rightarrow 3y = -x + 2

\sf \rightarrow y = -\dfrac{x}{3} + \dfrac{2}{3}

\sf \rightarrow y = -\dfrac{1}{3} x+ \dfrac{2}{3}

<u>which reveals slope</u>:

\star \   slope: \sf  - \dfrac{1}{3}

7 0
1 year ago
Read 2 more answers
{x^2+6x-27/x^2-9x+18<br> how to solve step by step
Alika [10]

Answer:

Step-by-step explanation:

Step by Step Solution:

More Icon

STEP

1

:

5

Simplify ———————

x2 - 81

Trying to factor as a Difference of Squares:

1.1 Factoring: x2 - 81

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 81 is the square of 9

Check : x2 is the square of x1

Factorization is : (x + 9) • (x - 9)

Equation at the end of step

1

:

(((x2)-18x)+81) 5

———————————————•———————————

(((x2)-6x)-27) (x+9)•(x-9)

STEP

2

:

x2 - 18x + 81

Simplify —————————————

x2 - 6x - 27

Trying to factor by splitting the middle term

2.1 Factoring x2 - 18x + 81

The first term is, x2 its coefficient is 1 .

The middle term is, -18x its coefficient is -18 .

The last term, "the constant", is +81

Step-1 : Multiply the coefficient of the first term by the constant 1 • 81 = 81

Step-2 : Find two factors of 81 whose sum equals the coefficient of the middle term, which is -18 .

-81 + -1 = -82

-27 + -3 = -30

-9 + -9 = -18 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -9

x2 - 9x - 9x - 81

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

9 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x-9) • (x-9)

Which is the desired factorization

Trying to factor by splitting the middle term

2.2 Factoring x2-6x-27

The first term is, x2 its coefficient is 1 .

The middle term is, -6x its coefficient is -6 .

The last term, "the constant", is -27

Step-1 : Multiply the coefficient of the first term by the constant 1 • -27 = -27

Step-2 : Find two factors of -27 whose sum equals the coefficient of the middle term, which is -6 .

-27 + 1 = -26

-9 + 3 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 3

x2 - 9x + 3x - 27

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

3 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x+3) • (x-9)

Which is the desired factorization

Canceling Out :

2.3 Cancel out (x-9) which appears on both sides of the fraction line.

Equation at the end of step

2

:

(x - 9) 5

——————— • —————————————————

x + 3 (x + 9) • (x - 9)

STEP

3

:

Canceling Out

3.1 Cancel out (x-9) which appears on both sides of the fraction line.

Final result :

5

—————————————————

(x + 3) • (x + 9)

5 0
2 years ago
A discounted amusement park ticket costs $12.95 less than the original price (p). Write and solve an equation to find the origin
Elena-2011 [213]
P = the original price of the ticket.

Let x =  the discounted price.
The discounted price IS $12.95 less than the original price. Therefore
x = p - 12.95

Add 12.95 to each side.
p = x + 12.95

Answer:
The equation is
p = x + 12.95
where
p = original price
x = discounted price
3 0
3 years ago
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