Write an algebraic equation for the following. The product of three and a squared number is twice the sum of the number and four.

Answers

Answer 1

Answer: 3*x^2 = 2*(x+4)

x is the unknown number

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if the length of certain rectangle is decreased by 4 cm and breadth is increased by 2 cm, it would result in a square of the same area. what is the perimeter of the original rectangle?

Answers

Answer:

To find the perimeter of the original rectangle, we first need to find the dimensions of the rectangle.

Let's assume the length of the original rectangle is L cm and the breadth is B cm.

According to the given information, if the length is decreased by 4 cm, the new length becomes (L - 4) cm. Similarly, if the breadth is increased by 2 cm, the new breadth becomes (B + 2) cm.

We are told that this new rectangle with dimensions (L - 4) cm and (B + 2) cm is actually a square with the same area as the original rectangle.

The area of a rectangle is given by length multiplied by breadth. So, the area of the original rectangle is L * B square cm.

The area of the new square is equal to the area of the original rectangle. Therefore, we can set up the equation:

(L - 4) * (B + 2) = L * B

Expanding the equation:

LB - 4B + 2L - 8 = LB

Simplifying the equation:

2L - 4B - 8 = 0

2L = 4B + 8

L = 2B + 4

Now that we have an equation relating the length and breadth of the original rectangle, we can find the perimeter.

The perimeter of a rectangle is given by the formula: 2 * (length + breadth).

Substituting the value of L from the equation above, we get:

Perimeter = 2 * [(2B + 4) + B]

Perimeter = 2 * (3B + 4)

Perimeter = 6B + 8

Therefore, the perimeter of the original rectangle is 6B + 8 cm.

Step-by-step explanation:

a washer and a dryer cost 659$ combined. The washer costs 91$ less than the dryer, how much was the dryer?

Answers

W+D=659

W=D-91

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

(D-91)+D=659

D-91+D=659

2D=750

D=750/2=375

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

W+375=659

W=284

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So the dryer had cost $375 and the washer had cost $284.

a washer and a dryer cost 659$ combined. The washer costs 91$ less than the dryer, how much was the dryer?
washer --> x
dryer --> y

x + y = 659$
y = x + 91$

x + x + 91$ = 659$

2x = 659$ - 91$

2x = 568$ |:2

x = 284$
y = x + 91$ = 284$ + 91$ = 375$

The dryer costs 375$ and washer costs 284$

Write in pence the value of The 9 in £8.90

Answers

For the full it's 890p but for the 9 it's 90p

Angle P is 3 more than twice angle M. If the two angles are complementary, find the measure of the two angles.

Answers

Answer:

29° and 61°

Step-by-step explanation:

Complementary angles sum up to 90°

Given

P + M = 90°
P = 2M + 3°

Substituting P in the first equation

2M + 3° + M = 90°
3M = 87°
M = 29°

Then

P = 90° - 29° = 61°

GiveN:

Angle P is 3 more than twice angle M.
The two angles are complementary.

ToFinD:

Measure of the two angles.

Step-wise-StepExplanation:

Complementary angles are angles that add upto 90°. They need not to be adjacent Always $.$

According to question, Angle P = 2(Angle M) + 3°. And they add upto 90°.

⇒ Angle P + Angle M = 90°

⇒ 2(Angle M) + 3° + Angle M = 90°

⇒ 3 Angle M + 3° = 90°

⇒ 3 Angle M = 87°

⇒ Angle M = 29°

Then, Angle P = 2(29°) + 3° = 61°. Hence, the two complementary angles are 29° and 61°.

Find all solutions of the equation. Check your solutions in the original equation. 8 x^3 − 343=0

Answers

$8x^3-343=0\ \ \ \ \ |add\ 343\ to\ both\ sides\n\n8x^3=343\ \ \ \ \ \ |divide\ both\ sides\ by\ 8\n\nx^3=(343)/(8)\n\nx=\sqrt[3]{(343)/(8)}\n\nx=\frac{\sqrt[3]{343}}{\sqrt[3]8}\n\nx=(7)/(2)$

$solution:x=(7)/(2)\n\ncheck:\n\n8\cdot\left((7)/(2)\right)^3-343=0\n\n8\cdot(343)/(8)-343=0\n\n343-343=0\n\n0=0$

$8 x^3-343=0\n\n(2x)^3-7^3=0\ \ \ \ \ \ and\ \ \ \ \ \ a^3-b^3=(a-b)(a^2+ab+b^2)\n\n(2x-7)(4x^2+14x+49)=0\n\n2x-7=0\ \ \ or\ \ \ 4x^2+14x+49=0\n2x=7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \Delta=14^2-4\cdot4\cdot49=196-784=-588\n x= (7)/(2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ no\ solution\n.\ \ \ \ \ \ \ \ Ans.\ x= (7)/(2) \n\ncheck:\nL=8x^3-343=\n=8\cdot( (7)/(2) )^3-343=8\cdot (7^3)/(2^3) -343=8\cdot (343)/(8) -343=343-343=0$

Steve is turning half of his backyard into a chicken pen. His backyard is a 24-meter by 45-meter rectangle. He wants to put a chicken wire fence along the west side of the yard, the south side of the yard, and along the diagonal connecting the northwest to the southeast corner of the yard. How many meters of fencing will Steve need to fully enclose this area?

Answers

The diagonal line is equal to $\sqrt{24^(2) + 45^(2) }$ using pythagoras' theorem of $a^(2) + b^(2) = c^(2)$ . This gives us a value of 51m for the diagonal line.

TOTAL; 51+24+45=120m of fencing

Answer:

51 meters

Step-by-step explanation:

We can use the Pythagorean Theorem to find the length of the diagonal line.

The equation for the Pythagorean Theorem is

a^2 + b^2 = c^2a

a, squared, plus, b, squared, equals, c, squared

where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.

In this case a=24,b=45,a=24,b=45,a, equals, 24, comma, b, equals, 45, comma and c=xc=xc, equals, x.

Hint #33 / 4

\begin{aligned} 24^2+45^2 & = x^2\\ 576+2025 & = x^2\\ 2601 & = x^2\\ \sqrt{2601} & = x\\ 51 & = x \end{aligned}

+45