Please help ASAP, thank you!

Working alone and at a constant rate, Machine A takes 3 hours to create a widget. Machine B, working alone and at a constant rat

PilotLPTM [1.2K]

Answer:

Time required by Machine B to create a widget = 4 hours

Step-by-step explanation:

Time taken by Machine A ( $T_{A}$ ) = 3 hours

Time taken by Machine B ( $T_{B}$ )= x hours

Time taken by both machines by working together = 12 hours

The time required to both machines by working together to finish a task is given by the formula = $\frac{T_{A} {T_{B} } }{T_{A} + T_{B} }$

Put the values in above formula we get

⇒ T = $\frac{3 x}{3 + x}$

⇒ 12 = $\frac{3 x}{3 + x}$

⇒ 36 + 12 x = 3 x

⇒ x = - 4 hours

This is the time required by Machine B to create a widget.

8 0

3 years ago

If f(x) =1/x and g(x) = x - 2 what is f(g(x)) when X = 1

Fed [463]

Answer:

f(g(x)) = -1

Step-by-step explanation:

$f(x) = \frac{1}{x} \\ \\ g(x) = x - 2 \\ \\ \implies \: f(g(x)) = \frac{1}{x - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{1 - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{ - 1} \\ \\ \implies \: f(g(1)) = - 1$

8 0

2 years ago

Rectangle STUV has square PQRS removed, leaving an area of 92 m^2. Side PT is 4 m in length and side RV is 8m in length

Andrei [34K]

Answer:

117 $m^{2}$

Step-by-step explanation:

First think of the square that was removed. All 4 sides are equal but you don't know the length so lets gives them the variable X.

So to find the area of the rectangle, insert those variables into the area equation for a rectangle.

(RV + (X) ) (PT +(X)) = rectangle area

Now you are given what the area is if you remove the square. So subtract the the square's area from the equation above and set it equal to the size they told you.

(RV + (X)) (PT + (X)) - [(X)(X)] = 92 $m^{2}$

rectangle - square = remaining area

Now plug in the numbers you know and solve for X.

(8 + X) (4 + X) - ((X)(X)) = 92

Use FOIL to multiply the first part of the equation (first, outer, inner, last)

32 + 8x + 4x + $x^{2}$ - $x^{2}$ = 92

32 + 12x = 92

12x = 60

x = 5

So now you know the size of the square. Each side is 5m. So add 5m onto the top of the rectangle and onto the side. The top is 13m and the side is 9m. The area of the rectangle is the length times the height to 13 x 9 which is 117 $m^{2}$

6 0

2 years ago

Sam's father bought a cat for $26,304. He expects to pay for it in 24 equal monthly payments. How much will Sam's father have to

podryga [215]

Price of the car= $26304
Monthly payments= 24
Just divide
26304/24 which equals $1096

3 0

3 years ago

Help my grade depends on it

Veseljchak [2.6K]

Lily made $75.36 more than Layla did. If Layla raised her price to $1.00, she would still not make more money than Lily.

Use a proportion to find the number of cupcakes Lily makes in 8 hours. She bakes 7 cupcakes in 10 minutes; we want to know how many she makes in 8(60)=480 (since there are 8 hours and each hour is 60 minutes):

7/10 = x/480

Cross multiply:
7*480 = 10*x
3360 = 10x

Divide both sides by 10:
3360/10 = 10x/10
336 = x

Lily bakes 336 cupcakes.

She sells 2/3 of these; 2/3(336) = 2/3(336/1) = 672/3 = 224 cupcakes sold.

Each cupcake is sold for $1.29; 224(1.29) = 288.96

To find the number of cupcakes Layla makes in 8 hours, we set up a different proportion. We know she bakes 8 cupcakes in 12 minutes; we want to know how many she bakes in 8(60) = 480 minutes:

8/12 = x/480
8*480 = 12*x
3840 = 12x

Divide both sides by 12:
3840/12 = 12x/12
320 = x

She bakes 320 cupcakes. She sells 75% of those; 75% = 75/100 = 0.75:
0.75(320) = 240

Each of those 240 cupcakes sells for $0.89:
0.89(240) = 213.60

This means Lily makes 288.96-213.60 = 75.36 more than Layla.

If Layla raised her price to $1.00, she would make 1(240) = $240; this is still less than Lily.

6 0

3 years ago