Ask question

Ask question

All categories

GarryVolchara [31]

2 years ago

13

Jack collected 31.1 pounds of cans to recycle and plans to collect 5.9 more pounds each week. Write an equation in slope-interce

pt form where x represents the number of weeks Jack has been recycling cans, and y represents the total amount recycled.

1 answer:

butalik [34]2 years ago

8 0

Answer:36.10

Step-by-step explanation: add 31+5= 36 the other one 1 +9 = 10 that's the answer please mark me as brainlest

You might be interested in

Solve the absolute value equation. 4|4x - 3| - 8 = -4

soldier1979 [14.2K]

Answer:

x = $1,\frac{1}{2}$

Step-by-step explanation:

$4|4x-3|-8=-4\\$

Add 8 to both sides;

4|4x - 3| = 4 4|4x - 3| = -4

Divide both sides by 4;

4x - 3 = 1 4x - 3 = -1

Add 3 to both sides;

4x = 4 4x = 2

Divide both sides by 4;

x = 1 x = $\frac{1}{2}$

8 0

2 years ago

Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).

aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0

3 years ago

Ryan bought 6 apples and 9 peaches for a total of $7.86. Madi bought 4 apples and 5 peaches for $4.82.

sergey [27]

Let's call:
a = price of 1 apple
p = price of 1 peach

The total cost is the price of 1 apple times the number of apples plus the price of 1 peach times the number of peaches, therefore the system can be:
$\left \{ {{6a + 9p = 7.86} \atop {4a + 5p = 4.82}} \right.$

Solve for a in the second equation (you can choose to solve for any of the variables in any of the equations, try to understand what is the best):
a = (4.82 - 5p) / 4

Now, substitute in the first equation:
6 · (4.82 - 5p) / 4 + 9p = 7.86
7.23 - (15/2)p + 9p = 7.86
(3/2)p = 0.63
p = 0.42

Now, substitute this value in the formula found for a:
<span>a = (4.82 - 5·0.42) / 4</span>
= 0.68

Therefore, one apple costs 0.68$ and one peach costs 0.42$.

6 0

2 years ago

Need help please help me

ANTONII [103]

Megan:
x to the one third power = $x ^{1/3}$
<span>x to the one twelfth power = </span> $x ^{1/12}$

<span>The quantity of x to the one third power, over x to the one twelfth power is:
</span> $\frac{x ^{1/3}}{x ^{1/12}}$
<span>
Since </span> $\frac{ x^{a} }{ x^{b} } = x ^{a-b}$
then $\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12}$

Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4

$\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12} = x^{1/4}$

Julie:
x times x to the second times x to the fifth = x * x² * x⁵

<span>The thirty second root of the quantity of x times x to the second times x to the fifth is
</span> $\sqrt[32]{x* x^{2} * x^{5} }$
<span>
Since </span> $x^{a}* x^{b}= x^{a+b}$
Then $\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }$

Since $\sqrt[n]{x^{m}} = x^{m/n} }$
Then $\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}$

Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.

3 0

3 years ago

Plz help 10 mins left!!!!!!

mr_godi [17]

I think the ans is 5

3 0

3 years ago