Explain how to estimate the quotient using compatible numbers. 27 and two-thirds divided by 3 and StartFraction 9 over 10 EndFra

Answer:

x=2c/3+1

Step-by-step explanation:

First, subtract 2c from both sides.

−3x=−3−2c

The equation has been transformed into standard form.

−3x=−2c−3

Next, divide both sides by −3.

-3x/-3=-2c-3/-3

Dividing by −3 negates the multiplication by −3.

x=-2c-3/-3

Finally, divide −3−2c by −3.

x=2c/3+1

The correct illustration is provided.

Explanation:

Utilizing a tool like Geogebra, commence by creating a line segment. Label the endpoints as C and D.

Next, draw the perpendicular bisector of the segment and denote the intersection with CD as B, then introduce a point A above this line.

Measure the distance from C to B and from B to D. Both distances will be equal.

Measure the length from A to B. If this distance is not equal to that from C to B, adjust A along line AB until the distances match.

With a compass and straightedge:

First, create segment CD and ensure the endpoints are labeled.

Adjust your compass to slightly more than half the distance between C and D. With it set at C, draw an arc above CD.

Using the same compass setting at D, draw another arc to intersect your first arc above CD. Mark the intersection as E.

Connect E to CD with a straightedge and label the intersection as B.

Set your compass to the distance from C to B. Position it on B and mark an arc on EB. Designate this intersection point as A.

Thus, AB will equal both CB and BD.

This issue involves a basic dimensional analysis. We are required to express the rate of 0.992 atm/m in the unit of atm/km.

In straightforward terms, dimensional analysis means converting a measurement into a different unit using conversion factors.

For this case, the necessary steps are:



We observe that 1000 meters = 1 kilometer was used as the conversion factor to change atm/m into atm/km. Consequently, we conclude with the answer 992 atm/km.

Answer:

The price per kilogram of salami amounts to = $9.1

Step-by-step explanation:

Given:

Hailey spent $13 on kg of sliced salami.

We need to determine the cost per kg of the salami.

Solution:

We will use the unitary method to find the cost for one kilogram of salami.

If kg of salami costs $13

Then the cost for 1 kg of salami in dollars =

When dividing mixed numbers, we convert them to fractions.

⇒

⇒

To divide fractions, we take the reciprocal of the divisor and multiply.

⇒

⇒

⇒

⇒

Hence, the cost per kilogram of salami is = $9.1

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

Multiply both sides by 10:

Next, factor the quadratic:

Solving for x gives:

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.