Choose the algebraic expression that best represents the situation.

F (a)=2a^2-16a+32<br> For which 'a' is this equation 0?

sergiy2304 [10]

If xy=0 assume that at leas 1 is zero
set it to zero

0=2a^2-16a+32
undistribute 2
0=2(a^2-8a+16)
2*0=0 so assume
a^2-8a+16=0
factor
(a-4)(a-4)=0
set to zero
a-4=0
a=4

when a=4, equation equals zero

7 0

3 years ago

Rob is saving to buy a new MP3 player. For every $15 he earns babysitting, he saves $10.On Saturday, Rob earned $45 babysitting.

Dmitrij [34]

Answer:

$30

Step-by-step explanation:

Okay, so we can solve this problem using fractions; $10 saved for every $15 made..

10/15=x/45

Using cross multiplication we can conclude 10*45=15x

450=15x

x=30

Hope this helps :)

7 0

2 years ago

Are the two parabolas defined below similar or congruent or both? Justify your reasoning. Parabola 1: The parabola with a focus

Dominik [7]

Answer:

They are similar by a factor of 14

Step-by-step explanation:

From the general equation of a parabola opening up (since the directrix is on the y axis and the focus is upwards this line) the focus coordinates are:

$Focus = (h,k+p) = (0,2)$

So h=0 and k+p=2, for the directrix:

$y = k-p=-4$

solving k and p from the two equations above:

$k=-1 and p=3$

So for Parabola 1 the equation would be:

$x^{2} =4*3(y+1)$

For Parabola 2 the general equation is:

$x^{2} =4*(3/2)(y)$

here h=0, k=0, p=3/2 so focus is (0,3/2), directix is y=-3/2, they have the same orientation.

they are not congruent. For them to be similar it must comply:

$x_{1}=k x_{2}\\y_{1}=ky_{2} => (1/12)x_{1} ^{2} -1 = k(1/6)x_{2} ^{2}$

replacing $x_{1}$ and solving for k:

$(1/12)(kx_{2}) ^{2} -1 = k(1/6)x_{2} ^{2}\\ (1/12)k^{2} x_{2}^{2}-1 = k(1/6)x_{2} ^{2}\\k-12 = (12/6)=2\\k = 2+12=14\\$

They are similar by a factor of 14

8 0

3 years ago

Please help meeeeeeeee

Allushta [10]

Answer:

B

Step-by-step explanation:

The screenshot given explains the formula of standard deviation, which measures the variation of numbers in a set.

It basically says we have to find the sum of all the numbers subtracted by the mean squared, and divide that by the number of data sets, and then square root.

The only way we can get this problem is by B.

5 0

3 years ago

Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf

Mamont248 [21]

Answer:

a) 5<x<25

b) x≤5 or x≥25

c) x≥5 and x≤25

Step-by-step explanation:

Given the expression the

(x - 5) (50 - 2x) to represent sofie profit based on the price per scarf, x.

a) If Sofie's profit is increasing, them the expression for her profit must be greater than zero as shown.

(x - 5) (50 - 2x)> 0

Solving the inequality:

x-5>0 and 50-2x>0

If x-5>0

x > 5 or 5<x... (1)

Similarly when 50-2x>0

50-2x>0

50>2x

Dividing both sides by 2:

50/2>2x/2

25>x or x<25 ...(2)

Combining 1 and 2

5<x<25

b) if Sofie's profit is decreasing, the profit function must be less than or equal to zero as shown;

(x - 5) (50 - 2x)≤0

Solving the inequality

x-5≤0 and 50-2x≤0

x≤5 and 50≤2x

x≤5 or 25≤x

x≤5 or x≥25

c) If Sofia is not making profit then, the function (x - 5) (50 - 2x) is equal to zero i.e

(x - 5) (50 - 2x) = 0

x - 5 = 0 or 50-2x =0

x = 5 and 50 = 2x

x = 5 and x = 25

x≥5 and x≤25

5 0

3 years ago