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3 years ago

If 2(x + 3) = x + 10, then x equals what

Mathematics

1 answer:

Rama09 [41]3 years ago

8 0

Answer:

$x=4$

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You need to apply the Distributive property on the left member of the equation:

$2(x + 3) = x + 10\\ 2x+6=x+10$

2. Now, you must solve for $x$ , as following:

$2x-x=10-6\\ x=4$

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How to differentiate ?

Bas_tet [7]

Use the power, product, and chain rules:

$y = x^2 (3x-1)^3$

• product rule

$\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}$

• power rule for the first term, and power/chain rules for the second term:

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}$

• power rule

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3$

Now simplify.

$\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}$

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

$\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) = \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)$

Differentiate both sides and you end up with the same derivative:

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2$

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2 years ago

During a sale, a store offered a 20% discount on a TV that originally sold for $710. After the sale, the discounted price of the

Mademuasel [1]

Answer:

$681.60

Step-by-step explanation:

Given:

During a sale, a store offered a 20% discount on a TV that originally sold for $710. After the sale, the discounted price of the TV was marked up by 20%

To Find:

What was the price of the TV after the markup? Round to the nearest cent.

Solution:

$710 × (1 + 20%) × (1 - 20%)

$710 × 1.2 × (1-0.2)

$710 × 1.2 × 0.8

($710 × 1.2) × 0.8

852 × 0.8

= $681.60

Kavinsky

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1 year ago

If 28% of a sum is 100.80 what is the sum

Sveta_85 [38]

$360.00*.28= 100.80

Or do a portion 

28%/100%=100.8/x 

Then cross multiply 

10080=28x 

x=360

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3 years ago

Find the surface area of the figure below.

Eduardwww [97]

The answer is b: 95.03 ft^2

Divide 5.5 by 2 to get the radius of 2.75.

Use 4(pi)(r)^2 to get the surface area of the sphere.

8 0

3 years ago

Read 2 more answers

PLEASE HELP WILL MARK BRAINILIEST!!!

muminat

Answer:

y=-50x-20

Step-by-step explanation:

6 0

2 years ago