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2 years ago

A rectangle is 4 cm longer than it is wide, and its area is 117 cm2 . find its dimensions.

Mathematics

2 answers:

Orlov [11]2 years ago

7 0

Answer:

Step-by-step explanation:

its 13 cm

Brilliant_brown [7]2 years ago

3 0

The area of a rectangle is equal L x W

4 cm longer than it is wide L = 4 + W

L x W = 117 we replace L here

(4 + W ) x W = 117

4W + W ^2 = 117

4W + W ^2 -117 = 0
W ^2 +4 W -117 = 0

W² + 4W - 117 = 0


THEN u want to use the use the quadratic formula

OR Factoring gives us

(W + 13)(W - 9) = 0

W = -13 or 9

But it can't be negative, so

W = 9 and L= 9+4 = 13

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A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

2 years ago

Bella has joined a new gym in town. The cost of membership is $25 per month. The after-hours policy at the gym allows her to wor

hjlf

The total monthly bill of the gym = $53

The cost of membership of a month = $25

Let 'n' be extra the number of hours Bella worked on.

The cost for working on extra hours = $4

So, we have to determine the equation, Bella worked out after hours.

We will determine the equation by:

(Monthly cost of membership) + ( cost for extra hours $\times$ number of hours extra worked on ) = Total monthly bill received

So, we get

$\$25+(4 \times n) = \$53$

$25+4n = $53 is the required equation.

Therefore, $25+4n = $53 equation can be used to determine how many times Bella worked out after hours.

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2 years ago

The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5.

castortr0y [4]

Let's say x is J because it's Lemon Juice.

It's said that the pH of J is less than 4 so: pH(J) < 4 and pH(J) is greater than 1.5 so: pH(J) > 1.5

Now we can construct:

$1.5 < pH(J) \wedge pH(J) < 4$

Or simply:

$1.5 < pH(J) < 4$

We can also write this with an interval:

$pH(J)\in(1.5, 4)$

Hope this helps.

r3t40

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2 years ago

Amala listed her assets and liabilities. Credit Card Balance Car (Paid in full) Jewelry Student Loan Savings Account Stocks $850

MakcuM [25]

Answer:

Total of Amala’s liabilities is $5500 .

Step-by-step explanation:

Liabilities is defined as the sums of money which it owes .

As given

Amala listed her assets and liabilities. Credit Card Balance Car (Paid in full) Jewelry Student Loan Savings Account Stocks $850 $2,200 $125 $2,500 $1,200 $1,500 .

As Credit card balance , car (Paid in full) and student loan are Amala liabilities .

Thus

Total amount of Amala’s liabilities = Credit card balance + car + student loan .

Putting all the values in the above

Total amount of Amala’s liabilities = 850 + 2200 + 2500

= $5500

Therefore the total of Amala’s liabilities is $5500 .

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2 years ago

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The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the

zhannawk [14.2K]

V=p+prt

now we solve for P

V=P (1+rt)

Divide both sides by (1+rt)

P=V÷(1+rt)...answer

P=V÷(1+rt)

P=3,000÷(1+0.06×5)

P=2,307.69

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2 years ago