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Genrish500 [490]
1 year ago
6

5. Enter the answer as a decimal

Mathematics
1 answer:
Hitman42 [59]1 year ago
5 0

Answer:

6.5%

Step-by-step explanation:

I = prt

5616 = 7200 × r × 12

r = 5616/(7200 × 12)

r = 0.065

r = 6.5%

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Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

7 0
3 years ago
A flea weighs 8 decigrams, and an ant weighs 3 milligrams. How much more does a flea weigh than an ant?
dusya [7]
In this question weight of a flea and an ant is given, but their units are different. So comparing and finding out the weight of flea and ant would be difficult. First thing that needs to be done is to bring the units of both the flea and the ant under same unit.
Weight of flea = 8 decigrams
Weight of ant = 3 milligrams.
Now let us convert the weight of the flea from decigrams to milligrams.
We already know that
1 decigram = 100 milligram
Then
8 decigrams = 100 * 8 milligrams
                     = 800 milligrams
Then
The weight by which the flea is greater than the ant = (800 - 3) milligrams
                                                                                   = 797 milligrams.
So the flea weighs 797 milligrams more than the ant.

5 0
3 years ago
Read 2 more answers
QUESTION 1 What is the value of 12C3? 1320 495 220 792 1 points QUESTION 2 What is the value of 12C5? 95,040 60 792 120
Anettt [7]
200 hope i helped you a little 200 come after 120 in your question
4 0
3 years ago
Read 2 more answers
Solve for x in the given triangle. A) -9 B) -7 C) 7 D) 6
Gelneren [198K]
Wheres the triangle??
6 0
2 years ago
Graph ƒ(x) = 2x - 3. Click on the graph until the graph of ƒ(x) = 2x - 3 appears.
bonufazy [111]

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : Function f(x)=2x-3

To find : Graph the given function?

Solution :

We have given the function f(x)=2x-3 is a linear function which passes through origin the points

x    f(x)

0      -3

1.5     0

1        -1

Joining these points will create a graph of a line with slope 2.

Refer the attached figure below.

7 0
2 years ago
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