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3 years ago

What two things have to be true in order to use the Zero Product Property?

Mathematics

1 answer:

11111nata11111 [884]3 years ago

8 0

Answer:

D - One side is a factored polynomial and the other side is 0.

A - Incorrect; If each side is 0, the equation would be equal since 0 = 0.

B - Incorrect; It cannot be -1 because the property states Zero product which means 0 should be the product.

C - Incorrect; It cannot be 1 because the property states Zero product which means 0 should be the product.

D - Correct; One side is 0, and the other is a factored polynomial, which correctly displays the correct definition of Zero Product Property.

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B. Lauren bought a new package of notebook

Anvisha [2.4K]

Answer:

Step-by-step explanation:

300 × x/100 = 27
=> 3 × x = 27
=> x = 27/3
=> x = 9

This means that 9% of the notebook is used in science.

100% - 9% = Percentage of paper left in notebook.
=> 91% = Percentage of paper left in notebook.

This means that 91% of the notebook pages is remaining.

4 0

3 years ago

Which is an equivalent fraction for

Andru [333]

Answer:

I believe the answer is C

Step-by-step explanation:

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3 years ago

Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter

babunello [35]

Answer:

The curve is given by r(s)= $3\frac{s}{\sqrt{29}} i + (7 - 4\frac{s}{\sqrt{29}} ) j + (3 + 2\frac{s}{\sqrt{29}} ) k$

Step-by-step explanation:

The aec length of the curve is given by:

L= $\int\limits^t_0 {|r'(t)|} \, dt$

r(t) = 3t i + (7 − 4t) j + (3 + 2t) k

r'(t)= 3 i -4 j + 2 k

|r'(t)|= $\sqrt{3^2+(-4)^2+2^2} =\sqrt{9+16+4} =\sqrt{29}$

L= $\int\limits^t_0 {\sqrt{29}} \, dt=\sqrt{29}\int\limits^t_0 \, dt$

L= $\sqrt{29}t|^t_0=\sqrt{29}t-\sqrt{29}0=\sqrt{29}t$

s(t)= $\sqrt{29}t$

We have to obtain t in terms of s, hence:

t= $\frac{s}{\sqrt{29}}$

Finally,

r(s)= $3\frac{s}{\sqrt{29}} i + (7 - 4\frac{s}{\sqrt{29}} ) j + (3 + 2\frac{s}{\sqrt{29}} ) k$

8 0

3 years ago

Change each standard form equation to slope-intercept form!

goldenfox [79]

Hello!

Slope-intercept form is this one: $y=a*x+b$ where a is the slope and b the intercept.

So, for transforming these equations to Slope-Intercept you'll need to rearrange the equations by adding or subtracting the same amounts on both sides of the equation (as a rule of thumb, sums are transformed into subtractions and multiplications into divisions).

1) 3x + y = 12

You should notice that Y and X are on the same side of the equation, so by subtracting 3x on both sides of the equation you'll cancel X on the left side:

 $3x+y-3x=12-3x \\ y=12-3x$

To finish, we rearrange this equation to the form y=a*x+b

 $y=-3x+12$

So, the slope is -3 and the intercept is 12

2) 8=y+5x

You should notice that Y and X are on the same side of the equation, so by subtracting 5x on both sides of the equation you'll cancel X on the right side:

$8-5x=y+5x-5x \\ 8-5x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=-5x+8$

So, the slope is -5 and the intercept is 8

3) 6x + 3y = -9

You should notice that Y and X are on the same side of the equation, so by subtracting 6x on both sides of the equation you'll cancel X on the left side:

$6x+3y-6x=-9-6x \\ 3y=-9-6x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 3 to cancel this number on the left side.

$\frac{3}{3}y= \frac{9}{3}- \frac{6}{3}x \\ y=3-2x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-2x+3$

So, the slope is -2 and the intercept is 3

4) x - 5y = 55

You should notice that Y and X are on the same side of the equation, so by subtracting x on both sides of the equation you'll cancel X on the left side:

$x-5y-x=-55-x \\ -5y=-55-x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -5 to cancel this number on the left side.

$\frac{-5}{-5}y= \frac{55}{-5}- \frac{1}{-5}x \\ y=-11+ \frac{1}{5}x$

To finish, we rearrange this equation to the form y=a*x+b

$y=\frac{1}{5}x-11$

So, the slope is 1/5 and the intercept is -11

5) -4x-y=-2
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the left side:

$-4x-y+4x=-2+4x \\ -y=2+4x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -1 to cancel this number on the left side.

$\frac{-1}{-1} y= \frac{-2}{-1}+ \frac{4}{-1}x \\ y=2-4x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-4x+2$

So, the slope is -4 and the intercept is 2

6) -16 = -4x + 2y

You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the right side:

$-16+4x=-4x+2y+4x \\ -16+4x=2y$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 2 to cancel this number on the right side.

$\frac{-16}{2}+ \frac{4}{2} x= \frac{2}{2}y \\ -8+2x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=2x-8$

So, the slope is 2 and the intercept is -8

I hope that this helps. Have a nice day!

8 0

4 years ago

Which is the best estimate for 19% of 205? • A. 40 • B. 50 • C. 100 • D. 400

adelina 88 [10]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers