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bezimeni [28]
4 years ago
8

Solve each equation -(4x+2)-(-3x-5)=3

Mathematics
1 answer:
blondinia [14]4 years ago
8 0

-4x-2+3x+5=3

-x+3=3

x=0

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Which value of x makes the equation 2/3x-3=11 true?
harkovskaia [24]

Answer:

x = 21

Step-by-step explanation:

To see for what value of x is the equation true, we have to solve x.

\displaystyle \frac{2}{3} x - 3 = 11\\\\Adding \ 3 \ to \ both \ sides\\\\\frac{2x}{3} = 11 + 3\\\\\frac{2x}{3} = 14\\\\Multiply \ 3 \ to \ both \ sides\\\\2x = 14 \times 3\\\\2x = 42 \\\\Divide\ both\ sides\ by\ 2\\\\x = 42/2\\\\x = 21\\\\For \ x = 21\ the \ given \ equation \ is \ true.\\\\\rule[225]{225}{2}

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3 years ago
Hillary needs a few new items for the start of softball season. She found some great sales! Help her find out the price she will
kolezko [41]

Answer:Hillary will pay $35.00 for softball glove, $20.00 for  soft ball bat and $40.00 for cleats

Step-by-step explanation:

Step 1

A percentage off of a price of an item  is the amount that can be saved from purchasing that item, it can also be referred as a discount given on an item purchase.

Step 2 --- Calculation

Actual  Price of Softball glove= $50

Discount= 50 x 30/100 = $15.00

 Price to pay= $50 - $15.00 = $35.00

Actual Price of soft ball bat= $50

Discount= 50 x 60/100 = $30.00

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Actual Price of cleats= $50

Discount= 50 x 20/100 = $10.00

Price to pay= $50 - $10.00 = $40.00

Therefore, Hillary will pay $35.00 for softball glove, $20.00 for  soft ball bat and $40.00 for cleats

4 0
3 years ago
Given that tan θ ≈ −0.087, where 3 2 π &lt; θ &lt; 2 , π find the values of sin θ and cos θ.
elena-s [515]

Answer:

  • sin θ ≈ -0.08667
  • cos θ ≈ 0.99624

Step-by-step explanation:

Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

  sin(-0.08678 radians) ≈ -0.08667

  cos(-0.08678 radians) ≈ 0.99624

_____

<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

We have shown radians in the above answer because the restriction on the angle is written in terms of radians.

_____

<em>Alternate solution</em>

The relationship between tan and sin and cos in the 4th quadrant is ...

  \cos{\theta}=\dfrac{1}{\sqrt{1+\tan^2{\theta}}}\\\\\sin{\theta}=\dfrac{\tan{\theta}}{\sqrt{1+\tan^2{\theta}}}

That is, the cosine is positive, and the sign of the sine matches that of the tangent.

This more complicated computation gives the same result as above.

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Answer:

10,500

Step-by-step explanation:

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