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Korolek [52]
2 years ago
9

Which expression is equivalent to 2(3x+4)(x-3)

Mathematics
1 answer:
natali 33 [55]2 years ago
7 0

Answer:

6x^2  − 10x − 24

Step-by-step explanation:

2(3x + 4)(x - 3)

(6x + 8)( x − 3)

6x^2  − 18x + 8x − 24

6x^2  − 10x − 24

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At an end- of-season sale, a kid's pool was on sale for $168 . A sign advertised that this was 20% off the original price. What
Bogdan [553]

Answer: $134.40

Step-by-step explanation: Just find 80% of 168. That is because 100 - 20 is 80. The question says 20% OFF.

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cody's Bikes rents bikes for $18 plus $5 per hour. Mark paid $48 to rent a bike. For how many hours did he rent the bike.
kkurt [141]
He rented the bike for 6 hours. If Cody charges an 18 dollar fee up front you subtract that from the total 48 to get 30. Then once you get down to the what he payed for the time used you divide it by 5 because that’s the hourly fee and get 6 hours
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Suppose that X1 and X2 are independent random variables each with a mean μ and a variance σ^2. Compute the mean and variance of
Deffense [45]

Mean:

E[Y] = E[3X₁ + X₂]

E[Y] = 3 E[X₁] + E[X₂]

E[Y] = 3µ + µ

E[Y] = 4µ

Variance:

Var[Y] = Var[3X₁ + X₂]

Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]

(the covariance is 0 since X₁ and X₂ are independent)

Var[Y] = 9 Var[X₁] + Var[X₂]

Var[Y] = 9σ² + σ²

Var[Y] = 10σ²

5 0
3 years ago
A recipe calls for 1 cup of ground almonds. How many ounces of ground almonds should you use for this recipe if 1 pint of ground
aleksley [76]

Answer: There are 3.36 ounces of ground almonds in 1 cup.

Step-by-step explanation:

Since we have given that

1 pint = 0.42 pounds

As we know that

1 cup = 0.5 pints

1 pound = 16 ounces

So, We need to find the number of ounces.

As 1 pint = 0.42 pounds = 0.42 × 16 = 6.72 ounces

0.5 pints is given by

6.72\times 0.5\\\\=3.36\ ounces

Hence, there are 3.36 ounces of ground almonds in 1 cup.

3 0
3 years ago
What is the equation of a parabola with a directrix of y=2 and a focus point of 0,-2
KiRa [710]
Hope this helped. :)

Any point, <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> on the parabola satisfies the definition of parabola, so there are two distances to calculate:

<span>Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix</span>

To find the equation of the parabola, equate these two expressions and solve for <span><span>y0</span><span>y0</span></span> .

Find the equation of the parabola in the example above.

Distance between the point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> :

<span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span></span>

Distance between point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and the line <span><span>y=c</span><span>y=c</span></span> :

<span><span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span><span>| <span><span>y0</span>−c</span> |</span></span>

(Here, the distance between the point and horizontal line is difference of their <span>yy</span> -coordinates.)

Equate the two expressions.

<span><span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span>=<span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span></span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span>=<span>| <span><span>y0</span>−c</span> |</span></span></span>

Square both sides.

<span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span>=<span><span>(<span><span>y0</span>−c</span>)</span>2</span></span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span>=<span><span>(<span><span>y0</span>−c</span>)</span>2</span></span></span>

Expand the expression in <span><span>y0</span><span>y0</span></span> on both sides and simplify.

<span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span><span>y0</span></span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span><span>y0</span></span></span>

This equation in <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> is true for all other values on the parabola and hence we can rewrite with <span><span>(<span>x,y</span>)</span><span>(<span>x,y</span>)</span></span> .

Therefore, the equation of the parabola with focus <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> and directrix <span><span>y=c</span><span>y=c</span></span> is

<span><span><span><span>(<span>x−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span>y</span></span>

3 0
3 years ago
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