Mrs. Thompson was asked to provide at least 180

Mathematics

1 answer:

zhuklara [117]3 years ago

3 0

Answer: c

Step-by-step explanation:

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Write a polynomial function in factored form with double roots at -2 and 5 and the constant term of the polynomial in standard f

Amanda [17]

Answer:

$f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40$

Step-by-step explanation:

If -2 and 5 are double roots of the polynomial function, then the function expression is

$f(x)=a(x-(-2))^2(x-5)^2\\ \\f(x)=a(x+2)^2(x-5)^2$

Rewrite this function in standard form:

$f(x)=a(x^2+4x+4)(x^2-10x+25)\\ \\f(x)=a(x^4-10x^3+15x^2+4x^3-40x^2+100x+4x^2-40x+100)\\ \\f(x)=a(x^4-6x^3-21x^2+60x+100)\\ \\f(x)=ax^4-6ax^3-21ax^2+60ax+100a$

The constant term of the polynomial in standard form is -40, so

$100a=-40\\ \\a=-\dfrac{40}{100}=-0.4$

Therefore, the function expression is

$f(x)=-0.4x^4-6\cdot (-0.4)x^3-21\cdot (-0.4)x^2+60\cdot (-0.4)x+100\cdot (-0.4)\\ \\f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40$

7 0

4 years ago

Convert the rate 30 cm/s to m/h

MrRissso [65]

$1m=100cm\to1cm=\dfrac{1}{100}m\\\\1h=3600s\to1s=\dfrac{1}{3600}h\\\\\\30\dfrac{cm}{s}=30\cdot\dfrac{\frac{1}{100}}{\frac{1}{3600}}\ \dfrac{m}{h}=30\cdot\dfrac{1}{100}\cdot3600\ \dfrac{m}{h}=30\cdot36\ \dfrac{m}{h}=\boxed{1,080\ \frac{m}{h}}\\\\\\Answer:\boxed{30\frac{cm}{s}=1,80\frac{m}{h}}$