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Luden [163]
3 years ago
10

The ration of girls to boys in a marching band is 10to8 if there are 32 boys in the marching band how many of the students in th

e marching band are girls
Mathematics
1 answer:
daser333 [38]3 years ago
5 0

Answer:

40 girls

Step-by-step explanation:

if there r 32 than u know 8 times 4 equals 32. Then u have to multiply 4 on the other side as well. So 10 times 4 equals 40 girls

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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
Charles will babysit for up to 4 hours and charges $7 per hour. Write a function in function notation for this situation.
I am Lyosha [343]
Assume Charles charges $7*3=$21 if he babysits for 2,5 hours (that is 2 and a half hours).

That is we are not considering Charles babysitting exactly 1, 2, 3 or 4 hours, but also in between times.


then we can write the following piecewise function to describe the situation:


f is a function from (0, 4] to {$7, $14, $21, $28}

f(x)=\begin{cases} 
      \$7 & if \enspace \enspace x\leq 1 \\
      \$14 & if \enspace \enspace 1\ \textless \  x\leq 2 \\
      \$21 & if \enspace\enspace 2\ \textless \ x\leq 3 \\
      \$28 & if \enspace\enspace 3\ \textless \ x\leq 4 \
   \end{cases}
6 0
3 years ago
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stiks02 [169]

Answer:

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3 0
3 years ago
Can someone help me please?
Mars2501 [29]

Answer:

Answer below

Step-by-step explanation:

Point D: (-6,-1)

Point C: (-3,0)

Point B: (-3,6)

Point A: (0,0)

8 0
2 years ago
The instructions on the bag of concrete mix say to add 2 gallons of water to each 8 pound bag of concrete mix.
SVETLANKA909090 [29]

Answer:

B

Step-by-step explanation:

The ratio of water to mix is 1:4.

3 0
3 years ago
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