The final step of completing a “solve by substitution” problem is to

What slope would make the lines

nignag [31]

Answer:

4

Step-by-step explanation:

Parallel lines have the same slope and since the slope of the first line is 4 the second lines slope is also 4

3 0

3 years ago

Read 2 more answers

Lana makes $8 an hour plus $12 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week.

11111nata11111 [884]

44 hours because...

Part A: W=8x where x equals amount of hours, and W equals wages.
<span>Part B: S=8x+12(y) where y equals overtime hours and S equals wages </span>
<span>Part C: 368=8(40)+12(y) </span>
<span>-320=12(y) </span>
<span>48=12y </span>
<span>48/12=y </span>
<span>4=y </span>
<span>x=40, y=4. </span>
<span>X+Y=44 hours</span>

5 0

3 years ago

A piece of cardboard measures 10 in. by 15 in. Two equal squares are removed from the corners of a 10-in. side as shown in the f

ella [17]

Answer:

$V(x) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6$

Step-by-step explanation:

The volume of a rectangular prism is found using the formula: V = lwh.

In order to write a formula in terms of the variable x, we need to write expressions for the length, width, and height of the rectangle.

We can say the length is the bottom of the base of the prism. To find this value, we can subtract x and x from 15 and divide this by 2, since there are two equal rectangles (base and lid).

Length: $\frac{15-2x}{2} =7.5-x$

We can say the width is the side of the base of the prism. To find this value, we can subtract 2x from 10.

Width: $10-2x$

The height of the prism can be x, which is the labeled length of the rectangle next to the base and lid.

Height: $x$

Now we are able to write a formula for volume in terms of x.

$V(x)=(7.5-x)(10-2x)(x)$
$V(x)=x(75-25x+2x^2)$
$V(x)=75x-25x^2+2x^3$

The domain of the volume is where x > 0, 2x < 10, and 2x < 15.

This is because our expressions for length ( $\frac{15-2x}{2}$ ), width (10-2x), and height (x) cannot go below 0, because you cannot have a negative value for measurement - realistically.

Therefore, if we take into account all of these restrictions on x, the domain is where 0 < x < 5.

x cannot be > 5 since that would not satisfy 2x < 10.

The domain of V for this problem situation is D: (0, 5).

In order to find the maximum volume of the rectangular prism using our formula we derived, we can use the idea of optimization in calculus.

Start by taking the derivative of V(x).

$V'(x)=75-50x+6x^2$

Set the derivative equal to 0. This gives us the critical point(s) in order to determine the extreme values of the function, aka where the max and min occur.

$0=75-50x+6x^2$
$0=6x^2-50x+75$

Solve for x by using the quadratic formula.

$x=\frac{-(-50)\pm\sqrt{(-50)^2-4(6)(75)} }{2(6)}$
$x=\frac{50\pm\sqrt{2500-1800}}{12}$
$x=\frac{50\pm\sqrt{700} }{12}$

Input this into your calculator and you should get:

$x=6.37, \ 1.96$

We are going to use x = 1.96 since 6.37 is NOT in the domain of V(x).

$\boxed{x=1.96}$

Now, since this value of x is going to give the maximum volume of this rectangular prism, or cardboard box, we can plug it back into the V(x) equation for volume to determine the maximum volume of the box.

$V(1.96)=75(1.96)-25(1.96)^2+2(1.96)^3$
$V(1.96) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6$

The maximum volume of the cardboard box is 66.02 in³ and the value of x that gives this is 1.96.

3 0

3 years ago

Katy’s little sister has 2 stuffed bears for every 3 dolls. If she has 8 stuffed bears, how many dolls does she have

Finger [1]

Answer:

She has 12 dolls

There are four 2's in the number eight, so 3 x 4 = 12.

7 0

3 years ago

Compare 8 ⋅ 107 to 2 ⋅ 104. Convert 0.00049 to scientific notation.

elena-s [515]

ANSWER 1: 8•107=856 and 2•104=208 so 856-208=648, meaning that the difference between 8•107 and 2•104 is 648.
ANSWER 2: If 49 in scientific notation is 8•10^0 then we divide by 100,000 and get 0.00008•0.00010^0

5 0

3 years ago