The Pythagorean theorem is a formula used in solving for missing side lengths of a(n)______________

0 find the smallest values of n which will guarantee a theoretical error less than if the integral is estimated by: (a) the trap

goldenfox [79]

Answer:

Step-by-step explanation:

Check attachment for answers.

3 0

3 years ago

Read 2 more answers

Use the discriminant to determine the number of solutions to the quadratic equation 3x^2+5x=-1

kari74 [83]

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

<u>Background of the Discriminant</u>

The discriminant $b^2-4ac$ applies to quadratic equations when they are organised in standard form: $ax^2+bx+c=0$ .

All quadratic equations can be solved with the quadratic formula: $x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}$ .

When $b^2-4ac$ is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

<u>Solving the Problem</u>

We're given the above equation. It hasn't been organised completely in $ax^2+bx+c=0$ , but we can change that by adding 1 to both sides to make the right side equal to 0:

$3x^2+5x+1=0$ <u />

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

$D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13$

Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

4 0

3 years ago

Pls help brainlist pls help

Len [333]

Answer:

1. V = 157in³, so the volume of the sugar container is 157in³

2. h = 12in, so the height of the rice container is 12in

3. The rice container's height is 12in and the height of the sugar container is 8in, which means the rice container is taller by 4in. The rice container's volume is 235.5in and the sugar container's volume is 157in, so the rice container's volume is greater than the volume of the sugar container's volume by 78.5in.

4. V = 50.24in³, so the volume of the flour container is 50.24in³

5. The rice container's volume is 235.5in, the sugar container's volume is 157in, and the flour container's volume is 50.24in. This means the container that contains the greatest volume is the rice container and the container that contains the smallest volume is the flour container.

Step-by-step explanation:

1. to find the volume of a cylinder, we use the formula:

V = πr²h

V = 3.14(2.5² × 8)

V = 3.14(6.25 × 8)

V = 3.14(50)

V = 157in³

2. To find the height of a cylinder when given the volume and radius, you use the formula:

h = V / πr²

h = 235.5/3.14(2.5²)

h = 235.5/3.14(6.25)

h = 235.5/19.625

h = 12in

h = height

3. The rice container's height is 12in and the height of the sugar container is 8in, which means the rice container is taller by 4in. The rice container's volume is 235.5in and the sugar container's volume is 157in, so the rice container's volume is greater than the volume of the sugar container's volume by 78.5in.

4.

V = bh

V = 12.56 × 4

V = 50.24in³

5. The rice container's volume is 235.5in, the sugar container's volume is 157in, and the flour container's volume is 50.24in. This means the container that contains the greatest volume is the rice container and the container that contains the smallest volume is the flour container.

5 0

2 years ago

Bacteria colonies increase by 37% every 2 days. If you start with 55 microorganisms, how large would the colony be after 10 days

ahrayia [7]

The number of microorganisms that I will have after 10 days would be: 245.41 microoganisms.

<h3>How to calculate the number of microorganisms that I will have after 10 days?</h3>

To calculate the number of microorganisms that I will have after 10 days, I must perform the following operations:

We need to find 37% of 55 as shown below:

55 ÷ 100 = 0.55
0.55 x 37% = 20.35
55 + 20.35 = 75.35

So after 2 days I will have 75.35 microorganisms.

75.35 ÷ 100 = 0.75
0.7535 x 37% = 27.87
75.35 + 27.87 = 103.22

On the fourth day I will have: 103.22 microorganisms.

103.22 ÷ 100 = 1.0322
1.0322 x 37% = 38.19
103.22 + 38.19 = 141.41

On the sixth day I will have 141.41 microorganisms.

141.41 ÷ 100 = 1.4141
1.4141 x 37% = 52.32
141.41 + 52.32 = 193,73

On the eighth day I will have 193.73 microorganisms.

193.73 ÷ 100 = 1.9373
1.9373 x 37% = 71.68
193.73 + 71.68 = 265.41

On the tenth day I will have 245.41 microoganisms.

Learn more about percentages in: brainly.com/question/13450942

#SPJ1

3 0

1 year ago

If f(x) = 2x + 3, what is f(-2)?<br>evaluate a linear function

jok3333 [9.3K]

Answer:

The answer is bellow

Step-by-step explanation:

The -2 is the x so you would put it in like so

2(-2) + 3

So you would get

-4+3

Which would give you

-1 as the final answer

7 0

3 years ago

The Pythagorean theorem is a formula used in solving for missing side lengths of a(n)_______________ triangle.