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3 years ago

14

Staci has seven more cats then Taylor. Write an expression that Illustrates how many cats staci has use x to represent the numbe

r of cats that Taylor has

1 answer:

Fofino [41]3 years ago

8 0

X + 7 x represents taylor but we don't know how many cats we have so we put x. If staci has 7 more, that mean that Staci has 7 more than x.

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If x+a is a factor of 2x²+2ax+5x+10,find a.

vazorg [7]

If $x+a$ is a factor of the polynomial, it means that $-a$ is a root of the polynomial.

In fact, if a polynomial $p(x)$ has a root $x_0$ (i.e. $p(x_0)=0$ ), then the polynomial is divisible by $(x-x_0)$

In your case, you know that the polynomial is divisible by $(x+a)=(x-(-a))$ , so $-a$ is a solution.

Let's evaluate $p(-a)$ and set it to zero:

$2(-a)^2+2a(-a)+5(-a)+10 = 0 \iff 2a^2-2a^2-5a+10=0 \iff -5a+10 = 0 \iff a = 2$

We can check the answer: if $a=2$ the polynomial becomes

$2x^2+2(2)x+5x+10 = 2x^2+9x+10$

And we're claiming that $-a=-2$ is a root of this polynomial:

$2(-2)^2+9(-2)+10 = 2\cdot 4 - 18 + 10 = 0$

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3 years ago

I need to give an equation for an absolute value function that has a minimum. How do I determine that it has a minimum?.

tatyana61 [14]

To determine the minimum of an equation, we derive the <span>equation using differential calculus twice (or simply </span><span>take the second derivative of the function). If the </span><span>second derivative is greater than 0, then it is minimum; </span><span>else, if it is less than 1, the function contains the </span><span>maximum. If the second derivative is zero, then the </span><span>inflection point </span><span>is</span><span> identified.</span>

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3 years ago

Type 8,580 words in 2 hours 45 minutes

Inessa05 [86]

You would average 52 words a minute.

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2 years ago

Alysha’s average speed when walking home from the market was 5 mph, and it takes her 21 minutes longer than when she drives to t

Delicious77 [7]

9514 1404 393

Answer:

3 minutes

Step-by-step explanation:

Let x represent Alysha's time to drive home from the market.

Speed and time are inversely proportional to each other (for the same distance), so we have ...

(walking speed)(walking time) = (driving speed)(driving time)

5(x +21) = (8·5)(x)

x +21 = 8x . . . . . . . . . divide by 5

21 = 7x . . . . . . . . subtract x

3 = x . . . . . . .divide by 7

It takes Alysha 3 minutes to drive home from the market.

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3 years ago

Simplify the rational expression. State any restrictions on the variable.

AveGali [126]

Answer:

The last choice.

Step-by-step explanation:

$\dfrac{k^2-k-2}{k^2-4k-5}=\dfrac{(k+1)(k-2)}{(k+1)(k-5)}=\dfrac{k-2}{k-5}$

The value of k must be restricted from being one that makes the original denominator zero. Hence k ≠ -1 or 5.

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2 years ago