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baherus [9]
2 years ago
13

Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartF

raction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 3) = StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 4). Her work is correct and is shown below. StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 3) = StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 4) 4x – 2 = 3x – 2 When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation?
Mathematics
2 answers:
mixas84 [53]2 years ago
8 0

Answer:

<h3>The best interpretation of this equation 4x=3x is that the equation has no solution</h3>

Step-by-step explanation:

Given that Kate begins solving the equation

\frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)

<h3>To find the best interpretation of the given equation :</h3><h3>Katie's steps are</h3>
  • \frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)
  • \frac{2}{3}(3(2x-1))=\frac{1}{2}((2(3x-4))
  • 2(2x-1)=1(3x-2)
  • 2(2x)+2(-1)=1(3x)+1(-2)
  • 4x-2=3x-2

When she adds 2 to both sides, the equation becomes

  • 4x-2+2=3x-2+2
  • 4x=3x

Therefore 4\neq 3

<h3>Therefore the given equation has no solution </h3><h3>The best interpretation of this equation 4x=3x is that the equation has no solution.</h3><h3>Therefore the option no solution is correct</h3>
Zinaida [17]2 years ago
5 0

Answer:

The equation has one solution: x = 0

Step-by-step explanation:

took the quiz

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A man has a 10m X 10m square garden. In the center is a 2m X 2m square patch which he cannot use. He divides his usable space in
ra1l [238]

Answer:

4m X 6m

Step-by-step explanation:

This is because if there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.

Because the 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.

Becuase 4m is the width, there is 10 - 4 = 6m along each rectangle's length.

8 0
2 years ago
Using the midpoint method, find the cross-price elasticity of demand for FedEx and UPS overnight shipping if the price of FedEx
IrinaK [193]

Answer:

Cross price elasticity using midpoint method = 0.56

Step-by-step explanation:

Using the mid-point method

Cross-price Elasticity of Demand = <u>% change in Quantity demanded of UPS</u>

                                                          % change of price of FedEx

%change in Quantity demanded of UPS

using Mid-point method                          = <u> Q2-Q1           </u>  × 100

                                                                     (Q1+Q2)÷ 2

                                      = <u>1.3-1.2           </u>   × 100

                                        (1.2+1.3)÷2

                                     = <u>0.1      </u> × 100

                                       1.25

                                     = 8%

% change in price of FedEx

using midpoint method    =<u> P2-P1            </u>× 100

                                             (P1+P2)÷ 2

                                          =<u> 75-65           </u>× 100

                                            (65+75)÷2

                                          =<u> 10  </u>   × 100

                                             70

                                          = 14.28%

Cross-price Elasticity of Demand =  8% ÷ 14.28%

using midpoint method                = 0.56

             

6 0
2 years ago
After 8 years a loan grows to $75 210. If the interest was compounded annually at a rate of 8.5%, find the size of the initial l
stealth61 [152]
Given:
Future Value = $75,210
term = 8 years
rate = 8.5%
Initial loan = ?

In this case, we need to find the present value of the loan. Compounded means that even the interest has an interest.

PV = FV / (1 + i)^n

PV = 75,210 / (1 + 0.085)⁸

PV = 75,210 / (1.085)⁸

PV = 75,210 / 1.9206

PV = 39,159.64

Initial loan is $39,159.64
total interest is $75,210 - 39,159.64 = $36,050.36

3 0
2 years ago
A rectangle is 9 ft long and 40 in. wide. What is its area in square feet? (Note: 1 ft = 12 in.)
ivolga24 [154]

Answer: first option

Step-by-step explanation:

Let's make the following conversion:

40 inches to feet (Knowing that 1 feet=12 inches):

(40in)(\frac{1ft}{12in})=3.333ft

The formula for calculate the are of  a rectangle is:

A=l*w

Where l is the lenght and w is the width.

Therefore, when you substitute values, you obtain the following result:

l=9ft\\w=3.33ft\\\\A=(9ft)(3.333ft)\\A=30ft

4 0
2 years ago
Read 2 more answers
Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: S(p) = 400 - 4
BlackZzzverrR [31]
S(p) = 400 - 4p + 0.00002p^4
D(p) = 2800 - 0.0012p^3

S(p) = D(p)
400 - 4p + 0.00002p^4 = 2800 - 0.0012p^3
0.00002p^4 + 0.0012p^3 - 4p - 2400 = 0
p = $96.24
6 0
2 years ago
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