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poizon [28]
3 years ago
9

If you have a $54.40 balance in your checking account, and you make a deposit of $150.00, what will the new balance be?A. $194.4

0
B. $209.90
C. $204.40
D. $209.40
Mathematics
1 answer:
yarga [219]3 years ago
7 0
Simply add the two numbers;

Beginning Balance:  $   54.40
Add: cash deposit   <u> $ 150.00</u>
Ending Balance        $ 204.40

ANSWER IS C. $204.40


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Factor 25a2−30a+9

25a2−30a+9

=(5a−3)(5a−3)

Answer:

(5a−3)(5a−3)


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3 years ago
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DochEvi [55]
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3 years ago
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along
sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}

Then, the time (speed divided by distance) is:

t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1

To optimize this function we have to derive and equal to zero:

\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\  \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\

x

As d_b=x, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0
3 years ago
Bank A is offering a loan with a simple interest rate of 8% for 2 years. Bank B is offering a loan with a simple interest rate o
Brut [27]

Answer:

what is difficult about this problem?   do you not have a calculator?  what part is tough?

Step-by-step explanation:

5 0
2 years ago
Pearl's Biking Company manufactures and sells bikes. Each bike costs £40 to make, and the company's fixed costs are £5000. In ad
____ [38]

Answer:

R(x) =300·x - 2·x²

C(x) = £5000 + £40 × x

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Step-by-step explanation:

Given that the price function P(x) = 300 -2·x

Cost per bike = £40

The revenue function R(x) is given by  bike price × total number of bikes manufactured and sold

∴ R(x)  = P(x)×x = (300 - 2·x)×x = 300·x - 2·x²

The company's cost function, C(x) is Fixed cost + cost to produce each bike × total number of bikes produced

∴ C(x) = £5000 + £40 × x

The break even point is given by the relation;

Total revenue - total cost = 0

That is, break even point is R(x) - C(x) = 0

300·x - 2·x² - (5000 + 40·x) = 0

-2·x²+260·x-5000 = 0 or 2·x²- 260·x + 5000 = 0

Factorizing, we have;

(x - (65 -5√69))(x - (65 +5√69))

Solving gives x = 23.47 or 106.53

Therefore, the break even points are 23.47 and 106.53.

That is the company is profitable when they produce less than 23 bikes or more than 107 bikes.

3 0
3 years ago
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