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Anuta_ua [19.1K]

3 years ago

11

What is the rate of change of y=7x+9

1 answer:

Leona [35]3 years ago

3 0

The rate of change is 7

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Isaiah already has 16 dollars. Every hour (x) that he works at the bakery, he earns another 4 dollars (y). How many total dollar

Lena [83]

$68
4x13=52 + 16 = 68

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3 years ago

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11/12 - 3/4 in simplest form

VladimirAG [237]

Answer:

1/6

Step-by-step explanation:

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3 years ago

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

Victor needs to box 61 laptop computers for a shipment. If he can fit 9 laptops in each box, how many boxes does he need?

just olya [345]

Answer:

he would need 7 boxes

Step-by-step explanation:

61/9= 6 with a remainder of 7 therefore instead of 6 boxes you would need 7 to put the rest of the laptops in

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3 years ago

Which is A Prime Number?<br> A)7<br> B)33<br> C)27<br> D)63

Paraphin [41]

7 is a prime number because it is only divisible by 1 and itself which is 7.

6 0

3 years ago

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