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2 years ago

Helppp

Mathematics

1 answer:

adoni [48]2 years ago

7 0

Answer:

- Early in the race,_Alberto_ runs faster.

- Alberto maintains a speed of _20_ km/h during the first hour of the race.

- meanwhile, Bianca’s running speed _Is exponential_

-The first person to cross the finish line is_Bianca_

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Suppose that a family wants to increase the size of the garden which is currently 16 feet long and 8 feet wide without changing

Cloud [144]

Answer:

See below

Step-by-step explanation:

Sides of the garden

16 feet and 8 feet

New dimensions of the garden

16 + 2x and 8 + x

1. The area of the new garden

(16 + 2x)(8 + x) =
2x^2 + 32x + 128

2. The difference in area

2x^2 + 32x + 128 - 16*8 =
2x^2 + 32x

3. x= 2 effect on the area

2*2^2 + 32*2 =
8 + 64 =
72 ft²

4. Area difference = 160

2x^2 + 32x = 160
x^2 + 16x - 80 = 0
Solving we get positive root of 4 ft

5. Area difference = 4 times

2x^2 + 32x = 128*3
2x^2 + 32x - 384 = 0
x^2 + 16x - 192= 0
Solving we get positive root of 8 ft

3 0

3 years ago

For an outdoor concert by the city orchestra, concert organizers estimate that 10,000 people will attend if it's not raining. If

Vlada [557]

Answer:

The number of expected people at the concert is 8,500 people

Step-by-step explanation:

In this question, we are asked to determine the expected number of people that will attend a concert if we are given the probabilities that it will rain and it will not rain.

We proceed as follows;

The probability that it will rain is 30% or 0:3

The probability that it will not rain would be 1 -0.3 = 0.7

Now, we proceed to calculate the number of people that will attend by multiplying the probabilities by the expected number of people when it rains and when it does not rain.

Mathematically this is;

Number of expected guests = (probability of not raining * number of expected guests when it does not rain) + (probability of raining * number of expected guests when it rains)

Let’s plug values;

Number of expected guests = (0.3 * 5,000) + (0.7 * 10,000) = 1,500 + 7,000 = 8,500 people

4 0

3 years ago

(x+16)²=12 plz help me and show work

Readme [11.4K]

Answer:

The answer is $x=-16$ ± $2\sqrt{3}$ in exact form or $x=-12.535898$ , $x=-19.464102$ in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring $x+16$ , which will look like $x^{2} +32x+256-12=0$ . Next, simplify the equation again, which will look like $x^{2} +32x+244=0$ .

Then, use the quadratic formula to find the solutions. The quadratic formula looks like $\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}$ .

For this problem, the quadratic variables are as follows:

$a=1$

$b=32$

$c=244$

The next step is to substitute the values $a=1$ , $b=32$ , and $c=244$ into the quadratic formula and solve. The quadratic formula will look like $\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}$ . To simplify the equation, start by simplifying the numerator, which will look like $x=\frac{-32(+-)4\sqrt{3} }{2*1}$ . Then, multiply 2 by 1 and simplify the equation, which will look like $x=-16(+-)2\sqrt{3}$ . The final answer is $x=-16$ ± $2\sqrt{3}$ in exact form. In decimal form, the final answer is $x=-12.535898$ , $x=-19.464102$ .