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2 years ago

9

Write an expression for 327 fewer than the product of 120 and p.

1 answer:

ValentinkaMS [17]2 years ago

3 0

good morning,

Answer

327 ≤ 120×p

:)

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Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “nor

Olenka [21]

Answer:

He have <u>47</u> ducks and <u>7</u> cows.

Step-by-step explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.

Let the number of ducks be $x.$

And the number of cows be $y.$

So, total number of animals are:

$x+y=54$

$x=54-y$ ....( 1 )

As, the feet of cows are 4 and ducks are 2.

Now, the total number of feet are:

$2(x)+4(y)=122$

$2x+4y=122$

Substituting the value of $x$ from equation (1) we get:

$2(54-y)+4y=122$

$108-2y+4y=122$

$108+2y=122$

<em>Subtracting both sides by 108 we get:</em>

$2y=14$

<em>Dividing both sides by 2 we get:</em>

$y=7.$

<em>The number of cows = 7.</em>

Now, to get the number of ducks we substitute the value of $y$ in equation (1):

$x=54-y\\x=54-7\\x=47.$

<em>The number of ducks = 47.</em>

Therefore, he have 47 ducks and 7 cows.

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3 years ago

Which is the graph of f(x) = ∛-x

scZoUnD [109]

Answer:

F

Step-by-step explanation:

FFF

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3 years ago

Write the equation for a 3rd degree polynomial function that has roots at x = 1–3i and x = 2. The y‑intercept is (0,10). Write a

HACTEHA [7]

Answer:

$\displaystyle P(x)=-\frac{1}{2}(x^2+2x+10)(x-2)$

Step-by-step explanation:

<u>Factored Form Of Polynomials </u>

If we know the roots of a polynomial as

$\alpha _1,\alpha _2,\alpha _3$

the polynomial can be expressed in factored form as

$a(x-\alpha _1)(x-\alpha _2)(x-\alpha _3)$

We are given two of the three roots of the polynomial:

$\alpha _1=1-3i$

$\alpha _2=2$

The other root must be the conjugate of the complex root:

$\alpha _3=1+3i$

Recall the product of two complex conjugate numbers is

$(1-3i)(1+3i)=1^2-(3i)^2=1+9=10$

The required polynomial is

$P(x)=a\left[ x-(1-3i)\right ]\left[ x-(1+3i)\right ](x-2)$

$P(x)=a(x^2+2x+10)(x-2)$

This is the factored form of the polynomial where only real numbers appear

We need to find the value of a, such as

$P(0)=10$

$P(0)=a(0^2+2(0)+10)(0-2)=10$

$-20a=10$

Thus the value of a is

$\displaystyle a=-\frac{1}{2}$

The expression of the required polynomial is

$\boxed{P(x)=-\frac{1}{2}(x^2+2x+10)(x-2)}$

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2 years ago

At a parade, 1/4 of the participants have red hair, 1/6 of them have brown hair, and the rest of the participants have black hai

Orlov [11]

Add 1/4 by 1/6 and get 5/12 so then you have 7/12 with black hair.

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3 years ago

Triangle ABC is reflected across the x-axis, and then across the y-axis. Which rotation is equivalent to this composition of tra

Gennadij [26K]

Answer:

C) 180 degree rotation

Step-by-step explanation:

I hope this helps you :)

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3 years ago