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Temka [501]
2 years ago
11

Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly

with the number of calories they consumed.
The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.
Mathematics
1 answer:
borishaifa [10]2 years ago
7 0

Answer: C= 1,090 and the W= 5.

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What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.
faltersainse [42]
Factoring x2-6x+5

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5

Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization

Equation at the end of step
1
:

(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-1 = 0

Add 1 to both sides of the equation :
x = 1

Solving a Single Variable Equation:

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :
x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-6x+5

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000

Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}
4 0
2 years ago
The FDA recommends that women who are pregnant avoid eating more than three 6.00 oz servings of bluefish per month because of th
kirza4 [7]

Answer:

5,562 x 10^{-6}

Step-by-step explanation:

  • Firts, we need to find the maximum recommended amount of bluefish per month. Since the FDA recommends <em>3 servings of 6.00 oz each</em>, the maximum amount would be:

the maximum amount of bluefish per month = 3 * 6.00 oz = 18.00 oz

  • Since bluefish contains <em>0.309 ppm of mercury per 1x10^{6} oz of fis</em>h, then:

0.309 oz mercury --------> 1x10^{6} oz of fish

How many  (y)      --------> 18.00 oz of fish

y = \frac{18.00 oz of fish * 0.309 oz of mercury}{1 x 10^{6} oz of fish }  = 0.000005562 = 5.562 x 10^{-6} oz mercury

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3 years ago
Help fast please
Lady_Fox [76]

Answer:

Acute and Obtuse..I cant see any right

Step-by-step explanation:

3 0
3 years ago
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please help I am really stuck on this one!! I would like an explanation with the answer please so I can learn how to do it from
dexar [7]

ANSWER:

x° = 24°

y° = 72°

Analysis on picture hope it helps

4 0
2 years ago
Rusty's hair grows at the rate of 1 over 4 inch per month.
Nadya [2.5K]
1/4 = 2/8. Remember that. This means that 1/8 is equal to half of a month. It there is 5/8, you can add a half month for every eights. In this case, it will take 2 and a half months
Easy Way:<span>If your hair were to grow 1/4 inches a month, it would also grow 2/8 inches a month, since 1/4 = 2/8. How long with it take 1/8 (0.5/4)inches to grow? It would take a half of a month for your hair to grow 1/8 inches.
</span><span>Now that we know 1/8 inches grows in a half of a month, we add a half of a month for every eigths. Since we are trying to figure out how long it would take for it to grow 5/8 inches, we add 5 half months to get the answer of 2 and a half months. Kind of confusing, but that is the best way I can describe it.</span>
8 0
3 years ago
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