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Sonja [21]
3 years ago
9

Ratio And Rates. Each ratio or rate needs to be a fraction in simples terms 1. 30 ft. To 60.Ft 2. 51 males to 21 females 3. 1,50

0 meters in 6 seconds 4. $36 for 4 rounds of shrimp
Mathematics
1 answer:
otez555 [7]3 years ago
4 0

Given:

The ratio and rates:

1. 30 ft. To 60.Ft

2. 51 males to 21 females

3. 1,500 meters in 6 seconds

4. $36 for 4 rounds of shrimp

To find:

The fraction in simple terms for the given ratio and rates.

Solution:

1. 30 ft. To 60.Ft

\dfrac{30\text{ ft}}{60\text{ ft}}=\dfrac{1}{2}

2. 51 males to 21 females

\dfrac{51}{21}=\dfrac{17}{7}

3. 1,500 meters in 6 seconds

\dfrac{1500\text{ meters}}{6\text{ seconds}}=250\text{ meter/second}

4. $36 for 4 rounds of shrimp

\dfrac{\$ 36}{4}=\$ 9\text{ per round of shrimp}

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Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
hram777 [196]

Answer:

\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }

Step-by-step explanation:

Hello,

I assume that we are working in \mathbb{C}, otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

   p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }

Now, we need to find the zeroes of the second factor, meaning finding x so that:

x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4}  \\ \\  x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\  x = 2+5i \ \text{ or } \ x = 2-5i

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0
3 years ago
3. The masses of two gorillas are given below. A female gorila has a mass of
loris [4]
Answer: 135,000g

Hope this helped :)
6 0
2 years ago
Determine the slope of the line segment<br> A.) 2<br> B.) 5<br> C.) 1/2<br> D.) 5/3
ohaa [14]

up 5

over to the right 3

rise/run

5/3

Choice D

6 0
3 years ago
Can anyone please help with these 2 questions. If you can, please show step-by-step.
valentinak56 [21]

Answer:

1. x = 21

2. m∡ABC =  51°

Step-by-step explanation:

First problem, solve for x

the sum of inside angles of a triangle is 180

also the supplementary angle for L = 180 - 100 is 80°

now you can add all angles

80 + 2x - 11 + 2x + 27 = 180

4x + 96 = 180

4x = 84

x = 21

Second problem, solve for m∡ABC

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also the supplementary angle for C = 180 - 148 is 32°

now you can add all angles

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3x + 12 = 180

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now solve for  m∡ABC = (x - 5)° = (56 - 5)° = 51°

8 0
3 years ago
Read 2 more answers
What is the volume of the prism
Scilla [17]
Hey there :)

We know the volume formula of triangular prism
Volume = base x height of prism
             = \frac{1}{2} (base)(height)(height of prism)

We are given:
The base = 8 in
The height = 15 in
You do not need the 17 in ( it is there to trick you )
The height of the prism = 10 in

Apply the formula,
V = \frac{1}{2} (8)(15)(10)
   = 600 in³

Your final answer will be the last option

6 0
3 years ago
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