Simplify: f (x)

A The length of a rectangle is 4 m more

Lady bird [3.3K]

Given :

The length of a rectangle is 4m more than the width.
The area of the rectangle is 45m²

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To Find :

The length and width of the rectangle.

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Solution :

We know that,

$\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:$

So,

Let's assume the length of the rectangle as x and the width will be (x – 4).

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Now, Substituting the given values in the formula :

$\qquad \sf \: { \dashrightarrow x \times (x - 4) = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 9x+ 5 x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow x(x - 9) + 5(x - 9) = 0 }$

$\qquad \sf \: { \dashrightarrow (x - 9) (x + 5) = 0 }$

$\qquad \sf \: { \dashrightarrow x = 9, \: \: x = - 5}$

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Since, The length can't be negative, so the length will be 9 which is positive.

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$\qquad { \pmb{ \bf{ Length _{(rectangle)} = 9\:m}}}\:$

$\qquad { \pmb{ \bf{ Width _{(rectangle)} = 9 - 4=5\: m}}}\:$

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8 0

2 years ago

A driveway has an area of 96 square feet. The width of the driveway is 8 feet.

Mrrafil [7]

Answer:

12 feet

Step-by-step explanation:

A driveway is rectangular in shape.

Therefore we can calculate the area using the formula;

$A = L \times W$

From the question;

The area,A=96 feet square

The width, W=8 feet

We substitute this values into the formula to find the length, L.

This implies that

$96 =L \times 8$

Dividing through by 8.

$\implies \frac{96}{8}= \frac{L \times 8}{8}$

$\implies L = 12$

Hence,the length of the driveway is 12 feet.

4 0

3 years ago

A man wants to beautify his front yard by planting four 20−foot-tall palm trees alongside his house. Each tree will need a cylin

GREYUIT [131]

He have to buy 4 bags to put all the dirt at once.

Step-by-step explanation:

Radius = 17 inches

Height = 28 inches

Volume of dirt from the cylindrical hole = π(r x r) h

= π(17 x 17) 28

= (3.14) (289) 28

= 25408.88 cubic inches

1 foot = 12 inches

Volume of dirt the bag can hold= 24 x 18 x 48

= 20736 cubic inches of dirt

The man fills only one third of the bag.

The volume of dirt the man fills = (1/3)20736

= 6912 cubic inches

Total bags = 25408.88/6912

= 3.69

= appx. 4 bags

He have to buy 4 bags to put all the dirt at once.

5 0

3 years ago

Triangle PQR and triangle XYZ are similar. The length of PQ= 4 inches, PR = 9 inches and QR = 12 inches. The length of the short

defon

Simplified Recap:

PQR and XYR are similar.

PQ: 4 inches (shortest side)

PR: 9 inches

QR: 12 inches (longest side)

Solving:

Because they are similar triangles, we know that the sides of one triangle are proportional to the ones on the other. Therefore, the smallest side of PQR is proportional to the smallest side of XYZ. Now, we just need to figure out the constant of proportionality , and we can do that by dividing the smallest side of XYZ triangle by the smallest side of PQR.

$16 \div 4 = 4$

Now we know that the constant of proportionality is 4. All we have to do now is solve the problem. The question is asking what the longest side of XYZ is, and to find that we just need to multiply the longest side of PQR by our constant of proportionality.

$12 \times 4 = 48$

Therefore, our answer is 48.

8 0

2 years ago

Solve For A -40+10a = -70

nordsb [41]

-40 + 10a = -70

Add 40 to both sides:

10a = -30

Divide both sides by 10:

A = -3

7 0

3 years ago

Read 2 more answers

Simplify: f (x) – 4g (x)