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emmainna [20.7K]

3 years ago

7

Diego solved an equation by multiplying both sides of the equation by 6. Then he checked that 6 is the correct solution by subst

ituting it back into the original equation. Which of the following gives the properties of equality that he used and their correct order?

1 answer:

Studentka2010 [4]3 years ago

6 0

C. on e2020 . Good luck!

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Eric has 1 5/9 cups of yogurt to make smoothies.Each smoothie uses 1/3 of a cup of yogurt.What is the maximum number of smoothie

Vedmedyk [2.9K]

Maximum number of smoothies that Erica can make with the yogurt is 5

<h3><u>Solution:</u></h3>

Given that Eric has $1\frac{5}{9}$ cups of yogurt to make smoothie

Each smoothie uses $\frac{1}{3}$ of a cup of yogurt

To find: maximum number of smoothies that Erica can make with the yogurt

Let 'n' be the number of smoothies that Erica can make with the available yogurt

number of smoothies that Erica can make with the yogurt is calculated by divinding the total available cups of yogurt by cups of yogurt needed for one smoothie

<em><u>Therefore we get:</u></em>

$n=\frac{\text { total available cups of yogurt }}{\text { cups of yogurt needed for one smoothie }}$

total available cups of yogurt = $1\frac{5}{9} = \frac{9 \times 1 +5}{9} = \frac{14}{9}$

cups of yogurt needed for one smoothie = $\frac{1}{3}$

Substituting the values in above formula we get,

$\begin{aligned}&n=\frac{\frac{14}{9}}{\frac{1}{3}}\\\\&n=\frac{14}{9} \times \frac{3}{1}=\frac{14}{3}=4.66 \approx 5\end{aligned}$

Thus maximum number of smoothies that Erica can make with the yogurt is 5

4 0

3 years ago

SinA/sinB=2/√3 and cosA/cosB=1/√2 ,tan^2B=?

Talja [164]

Answer:

3/8 tan²A

Step-by-step explanation:

sinB = √3/2 sinA and cos B= √2 cosA (from given)

6 0

2 years ago

If something starts out costing $500, and then is marked down by 25% on each of three separate occasions,what is the final price

astra-53 [7]

First markdown: 0.75($500) = $375
Second markdown: 0.75($375) = $281.25
Third markdown: 0.75($281.25) = $210.94

3 0

3 years ago

What is the percent change of 36;63

STatiana [176]

First, find the difference.
63-36=27
Then, divide by the original number.
27/36=0.75
Then, put it in percentage form.
75%

7 0

3 years ago

Pls help with 29..tank you

trapecia [35]

Answer:

See below

Step-by-step explanation:

Let the 2 roots be A and A^2.

Then A^3 = c/a and A + A^2 = -b/a.

Using the identity a^3 b^3 = (a + b)^3 - 3ab^2 - 3a^2b:-

A^3 + (A^2)^3 = ( A + A^2)^3 - 3 A.A^4 - 3 A^2. A^2

= (A + A^2)^3 - 3A*3( A + A^2)

Substituting:-

c/a + c^2/a^2 = (-b/a)^3 - 3 (c/a)(-b/a)

Multiply through by a^3:-

a^2c + ac^2 = -b^3 + 3abc

Factoring:-

ac(a + c) = 3abc - b^3

This is not the formula required in the question but let's see if the formula in the question reduces to this. If it does we have completed the proof.

a(c - b)^3 = a(c^3 - 3c^2b + 3cb^2 - b^3) = ac^3 - 3ac^2b + 3acb^2 - ab^3

c(a - b)^3 = c(a^3 - 3a^2b + 3ab^2 - b^3) = ca^3 - 3a^2bc + 3acb^2 - cb^3.

These are equal so we have

ca^3 - 3a^2bc + 3acb^2 - cb^3 = ac^3 - 3abc^2 + 3acb^2 - ab^3

The 3acb^2 cancel out so we have:-

a^3c - ac^3 = 3a^2bc - 3abc^2 + b^3c - ab^3

ac(a^2 - c^2) = 3abc( a - c) + b^3(c - a)

ac(a + c)(a -c) = 3abc(a - c) - b^3 (a - c)

Divide through by (a - c):-

ac(a + c) = 3abc - b^3 , which is the result we got earlier.

This completes the proof.

3 0

3 years ago

Read 2 more answers