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Mashcka [7]
2 years ago
6

What is the value of x in this proportion?

Mathematics
1 answer:
astra-53 [7]2 years ago
6 0

Answer:

  (a)  x=−20 1/2

Step-by-step explanation:

Multiply by the product of the denominators and solve the resulting linear equation in the usual way.

  \dfrac{2}{7}=\dfrac{-5}{x+3}\\\\2(x+3)=-5(7)\qquad\text{multiply by $7(x+3)$}\\\\2x+6=-35\qquad\text{simplify}\\\\2x=-41\qquad\text{subtract 6}\\\\\boxed{x=-20\dfrac{1}{2}}\qquad\text{divide by 2}

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Please apply the properties of rational exponents to simplify expressions with radical or rational exponents. Explain the steps
schepotkina [342]

Step-by-step explanation:

<u>Product property</u>

  • If the bases are the same, you don't multiple them. However, if they are the same, you do multiple for example : (2³ * 2¹ = 2⁴.when the bases are the same) (2³ * 3¹ =6⁴. When the bases are not the same
  • We add the index.

<u>Quotient</u><u> </u><u>property</u>

  • Same here, if the bases are the same, they stay the way they were
  • We subtract the index

<u>Power</u><u> </u><u>property</u>

  • Here we multiple the index because of the bracket for example : (9²)²= 9⁴

<u>Negetive</u><u> </u><u>exponent</u><u> </u><u>property</u>

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6 0
3 years ago
A surfboard costs $240. The sales tax on a surfboard is $12. What is the percent in sales tax?
Pie
The tax rate is 5%

Hope this helps!
6 0
3 years ago
Read 2 more answers
The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th
Fantom [35]

Answer:

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C

Step-by-step explanation:

To find:

∫6x^5(x^6-2)\,dx

Solution:

Method of substitution:

Let x^6-2=t

Differentiate both sides with respect to t

6x^5\,dx=dt

[use (x^n)'=nx^{n-1}]

So,

∫6x^5(x^6-2)\,dx = ∫ t\,dt = \frac{t^2}{2}+C_1 where C_1 is a variable.

(Use ∫t^n\,dt=\frac{t^{n+1} }{n+1} )

Put t=x^6-2

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1

Use (a-b)^2=a^2+b^2-2ab

So,

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C

where C=2+C_1

Without using substitution:

∫6x^5(x^6-2)\,dx = ∫6x^{11}-12x^5\,dx = \frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C

So, same answer is obtained in both the cases.

7 0
2 years ago
Find the value of x<br> (x +40)<br> x
gayaneshka [121]

Answer: x^2 + 40x

Nothing can further be done with the topic.....

8 0
3 years ago
if you go out to eat with 3 friends and your meal was $72.50, there is 6.75% sales tax. how much should each person pay
pickupchik [31]

Answer:

$25.80

Step-by-step explanation:

First find the price of the meal with sales tax. Multiply 6.75% by $72.50.

72.50 * 0.0675 = 4.89

Add this value onto 72.50.

72.50 + 4.89 = 77.39

Divide this amount by 3.

77.39 / 3 = 25.7966...

Round this to the nearest hundredth because we're dealing with money.

$25.80 is how much each person should pay.

5 0
3 years ago
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