Translate the given phrase into an algebraic expression and simplify if possible: the sum of -4 and the difference of 3 and 1

An apple farmer is deciding how to use each day’s harvest. She can use the harvest to produce apple cider or apple juice for the

vitfil [10]

Answer:

A)

There are 18 bushels of apples.

1 bushel of apples will make 20 quarts of apple cider.

1 bushel of apples will make 15 quarts of apple juice.

x = number of bushels to make cider out of.

y = number of bushels to make juice out of.

B)

As there are 18 bushels

x + y = 18

The apple farmer needs to produce a total of 330 quarts.

1 bushel of apples will make 20 quarts of apple cider.

1 bushel of apples will make 15 quarts of apple juice.

20x + 15y = 330

C)

x + y = 18. Thus we can express y in terms of x:

y = 18 - x

We can substitute the y in 20x + 15y = 330 and solve for x:

20x + 15 (18 - x) = 330

20x + 270 - 15x = 330

5x = 60

x = 12

And as y = 18 - x

y = 18 - 12

y = 6

[ C_1 ]: We could have done the same with x, expressing x in terms of y:

x = 18 - y, substitute the x in 20x + 15y = 330 and solve for y:

20 (18 - y) + 15y = 330

360 - 20y + 15y = 330

-5y = -30

y = 6

And as x = 18 - y

x = 18 - 6

x = 12

D)

As we had defined in A)

x = number of bushels to make cider out of

y = number of bushels to make juice out of,

there will 12 bushels of apples be processed into cider and

there will 6 bushels of apples be processed into juice

in order to produce

20 quarts of cider per bushel * 12 bushels = 240 quarts of cider, and

15 quarts of juice per bushel * 6 bushels = 90 quarts of juice,

which sum up to a total of

240 + 90 = 330 quarts of apple beverages, as required.

5 0

3 years ago

Define the function

miss Akunina [59]

Given that

$g(x) = x^3 + x$

the inverse $g^{-1}(x)$ is such that

$g\left(g^{-1}(x)\right) = g^{-1}(x)^3 + g^{-1}(x) = x$

or

$g\left(f(x)\right) = f(x)^3 + f(x) = x$

Differentiating both sides using the chain rule gives

$3f(x)^2f'(x) + f'(x) = 1 \\\\ f'(x) \left(3f(x)^2+1\right) = 1 \\\\ f'(x) = \dfrac1{3f(x)^2+1}$

Then the derivative of f at 2 is

$f'(2) = \dfrac1{3f(2)^2+1} = \boxed{\dfrac14}$

7 0

2 years ago

Please help me please

olga55 [171]

Answer:

the ham is the least expensive, the roast beef is most expensive

Step-by-step explanation:

hope this helps.

4 0

3 years ago

Linda calculated that the saucer for her teacup has an area of 50.24 square centimeters. What is the saucer's circumference?

Brilliant_brown [7]

Answer:

The saucer's circumference is 25.12 centimeter.

Step-by-step explanation:

Given:

Linda calculated that the saucer for her tea cup has an area of 50.24 square centimeters.

Use 3.14 for π.

Now, to find the saucer's circumference.

So, we get the radius first by putting the formula of area:

Area = 50.24 square centimeters.

Let radius be $r.$

$Area = \pi r^2.$

$Area = \pi\times r^2.$

As given we use 3.14 for π.

$50.24 = 3.14\times r^2.$

Dividing both sides by 3.14 we get:

$16=r^2.$

Using square root on both sides we get:

$4=r$

$r=4$

Thus, the radius = 4 centimeters.

Now, to get the circumference we put formula:

$Circumference=2\pi r$

$Circumference=2\times \pi \times r$

$Circumference=2\times 3.14\times 4$

$Circumference=25.12$

Circumference = 25.12 centimeter.

Therefore, the saucer's circumference is 25.12 centimeter.

3 0

3 years ago

ik to use the pythagoream theorem, but idk how to set it up and therefore solve the problem? could someone pls help :))

mihalych1998 [28]

Answer:

52.2

Step-by-step explanation:

Light reflects off a mirror at the same angle it hits it at (as shown in the image). Since both triangles are right triangles, we can say they are similar by AA similarity.

Since they're similar, we can write a proportion.

HT / TV = JS / SV

Plugging in values:

5.8 / 4 = JS / 36

JS = 52.2

The wall is 52.2 feet tall.

5 0

3 years ago