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2 years ago

10

the area of a rectangle is given by the equation y=x^2-9x+14 and the length of the rectangle is x-2. which of the following expr

essions represents the width of the rectangle?

1 answer:

Rudik [331]2 years ago

3 0

Divide x2 - 9x +14 by x-2
You get x - 7

Check your work by multiplying x-2 and x-7
Since you get x2 - 9x +14,

x-7 is the answer.

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Which number line shows the solution set for |y-9| <12

RUDIKE [14]

Answer:

Option c

$y\geq-3$ or $y \leq 21$

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function $f(x) = |x|$ x> 0 for all real numbers.

Then the inequation:

$|y-9| \leq 12$ has two cases

$(y-9)$ if $y \geq 9$ (i)

$-(y-9)$ if $y < 9$ (ii)

We solve the case (i)

$y \leq 9 + 12\\y\leq21$

We solve the case (ii)

$-y +9 \leq 12\\-y \leq 12-9\\y \geq -3$

Then the solution is:

$y\geq-3$ or $y \leq 21$

8 0

3 years ago

Can you help me please

svetoff [14.1K]

Answer:

don't write sloppy and I'll be able to answer it

6 0

3 years ago

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Solve the system of equations and choose the correct answer from the list of options. (4 points)

Viefleur [7K]

Answer:

Negative 8 over 5 comma negative 6 over 5

8 0

2 years ago

. Evaluate tan(α + β) = sin(????+????) / cos(????+????) to show tan(???? + ????) = tan(????)+tan(????????) / 1−tan(????) tan(???

grandymaker [24]

Answer with Step-by-step explanation:

We are given that

$tan(\alpha+\beta)$

$\frac{sin(\alpha+\beta}{cos(\alpha+\beta)}$

By using formula $tan x=\frac{sin x}{cos x}$

$\frac{sin\alpha cos\beta+sin\beta cos\alpha}{cos\alpha cos\beta-sin\alpha sin\beta}$

By using property: $sin(x+y)=sin x cosy+cos x sin y$

$cos(x+y)=cos x cosy-sin x siny$

Divide numerator and denominator by $cos\alpha cos\beta$

Then, we get

$\frac{\frac{sin\alpha}{cos\alpha}+\frac{sin\beta}{cos\beta}}{1-\frac{sin\alpha sin\beta}{cos\alpha cos\beta}}$

$tan(\alpha+\beta)=\frac{tan\alpha+tan\beta}{1-tan\alpha tan\beta}$

Hence, proved

Substitute $\alpha=\beta$

Then we get

$tan 2\alpha=\frac{tan\alpha+tan\alpha}{1-tan^2\alpha}$

$tan(2\alpha)=\frac{2tan\alpha}{1-tan^2\alpha}$

Hence, proved.

3 0

3 years ago

HELP!!! I will rate brainliest to fastest and correctly: Paula invests 10,000 for 5 years at an interest rate of 10% per year. I

Tomtit [17]

15,000

Since her interest is simple, it adds the 10% to the original amount.

So, we multiply her amount (10,000) by the interest rate (.1) and by the amount of years (5).

10,000 * .1 * 5= 5,000

This is how much she has gained from said interest. Adding this to 10,000 gives us 15,000, which is the amount she will have.

Another way to do this would be to make a chart/table:

Start: 10,000
1. 11,000
2. 12,000
3. 13,000
4. 14,000
5. 15,000

And thus, we get the same answer.

7 0

3 years ago