Solve the inequality −6b + 3 ≤ −57

In one month, Mikhail’s Furnishings can make 160 carpets or 160 quilts, while Dominique’s Parlor can make 120 carpets or 200 qui

marysya [2.9K]

Answer:

Step-by-step explanation:

Mikhail’s Furnishings: 160 carpets or 160 quilts

Dominique’s Parlor: 120 carpets or 200 quilts

Current production per month

Mikhail’s: 80 carpets and 80 quilts

Dominique’s: 60 carpets and 100 quilts

Post-trade

Mikhail’s: produces 160 carpets

Dominique’s: produces 200 quilts

They trade 90 quilts for 70 carpets so at the end of trade they will have items as follows

Mikhail’s carpets will reduce from 160-70=90 carpets but have additional 70 quilts

Dominique’s quilts will reduce from 200-90=110 but have additional carpets of 70

Gains from trade

Comparing outcome of post-trade with current production

Mikhail’s Furnishings: 90 carpets-80 carpets=10 carpets

90 quilts-80 quilts=10 quilts

Dominique’s Parlor: 70 carpets -60 carpets=10 carpets

110 quilts-100 quilts=10 quilts

8 0

3 years ago

Consider the diagram below. Which of the following statements is correct?

Nutka1998 [239]

Answer:

A

Step-by-step explanation:

The diagram shows two parallel lines XY and WV.

1. Parallel lines XY and WV are cut by transversal XW, then angles YXZ and VWZ are congruent as alternate interior angles.

2. Parallel lines XY and WV are cut by transversal YV, then angles XYZ and WVZ are congruent as alternate interior angles.

AA similarity theorem states if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

So, $\triangle XYZ\sim \triangle WVZ$ by AA similarity

7 0

4 years ago

Read 2 more answers

Let V be the volume of a right circular cone of height h=14 whose base is a circle of radius R=2. An illustration a right circul

Alla [95]

Answer:

The area of a horizontal cross section at a height is $\pi\times(2-\dfrac{y}{7})^2$

Step-by-step explanation:

Given that,

Height = 14 m

Radius = 2 m

Let V be the volume of a right circular cone

We need to calculate the value of R

Using given data

$\dfrac{h}{r}=\dfrac{h-y}{R}$

Put the value into the formula

$\dfrac{14}{2}=\dfrac{14-y}{R}$

$7R=14-y$

$R=2-\dfrac{y}{7}$

We need to calculate the area of a horizontal cross section at a height y

Using formula of area

$A=\pi R^2$

Put the value into the formula

$A=\pi\times(2-\dfrac{y}{7})^2$

Hence, The area of a horizontal cross section at a height is $\pi\times(2-\dfrac{y}{7})^2$

3 0

3 years ago

Caleb and luke are playing a video game. Luke has scored fifteen less than twice the number of points caleb has. If they have sc

olga nikolaevna [1]

Answer:

129 points

Step-by-step explanation:

Let L and C represent the scores of Luke and Caleb, respectively.

L = 2C -15 . . . . . Luke scored 15 less than twice the number Caleb did

L +C = 201 . . . . . they scored 201 points altogether

Add twice the second equation to the first:

2(L +C) + (L) = 2(201) + (2C -15)

3L +2C = 387 +2C . . . . simplify

3L = 387 . . . . . . . . . . . . .subtract 2C

L = 387/3 = 129 . . . . . . .divide by 3

Luke scored 129 points.

_____

Comment on the solution

Normally, you might solve this set of equations by substitution, since you have an expression for L in terms of C. Doing that would give a value for C, and an extra step would be required to find L. We wanted to avoid the step of finding C, since that was not a value we needed to know.

You could also substitute 201-L for C, which is effectively what we did. After substitution, that equation looks like ...

L = 2(201-L) -15

L = -2L +387 . . . . simplify

Adding 2L and dividing by 3 gets the same result as above.

6 0

4 years ago

Solve this equation for n. -5(4n - 2.4) + 2(1.3 + 6n) = -5.4

DIA [1.3K]

Answer:

n = 2.5

Step-by-step explanation:

distribute

-20n + 12 + 2.6 + 12n = -5.4

combine terms

-8n + 14.6 = -5.4

subtract 14.6 from both sides

-8n = -20

divide by -8

n = 2.5

6 0

3 years ago

Read 2 more answers