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bulgar [2K]
3 years ago
13

Zach's phone plan costs $0.10 for each text message he sends. He has a $10 limit. Write and solve an inequality to determine how

many texts Zach can send.
Mathematics
1 answer:
sergejj [24]3 years ago
6 0

Answer:

Zach can send at most 100 messages, or if x is how many messages, x≤100

Step-by-step explanation:

We will start by putting the amount of money Zach's limit has into cents. This will be 1000 cents. We will also put how much money Zach uses per message as cents, which will be 10. Now here is the first inequality you can make with this information

10x≤1000

From here you divide both sides of the inequality by 10 and get

x≤100

This is the final inequality, and it means Zach can send less than or equal to 100 messages

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Solve this equation for x: 2x^2 + 12x - 7 = 0
zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: 2x^2 + 12x - 7 = 0

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7

Step 2: Divide the equation all through by the coefficient of x^2 which is 2.

x^2 + 6x=\frac{7}{2}

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3=3^2

Therefore, we have:

x^2 + 6x+3^2=\frac{7}{2}+3^2

Step 4: Write the Left Hand side in the form (x+k)^2

(x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\

Step 5: Take the square root of both sides and solve for x

x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355

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3 years ago
a homeowner has just installed a swimming pool with a capacity of 3.5 x 10⁴ gallons.of the pool is initially empty, how many hou
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2 years ago
8. Mr. Gardner is contemplating which shullle service to take lo the airport. Fost
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Step-by-step explanation:

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3 years ago
What is the volume of a sphere with a radius of 9.2 cm, rounded to the nearest tenth of a cubic centimeter?
chubhunter [2.5K]

Answer:

3262.9 cm^3

Step-by-step explanation:

Formula =

\frac{4}{3}  \times \pi r ^{3}

Pi = 3.145

So,

\frac{4}{3}  \times 3.145 \times 9.2 ^{3}  \\   =  3262.183595 \\  = 3262.9 cm^{3}

Here you go

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2 years ago
Pentagon PQRST is drawn on a coordinate plane below. what rule best represents a dilation to create pentagon PQRST with a scale
otez555 [7]

Answer: (x,y) \to (\dfrac12 x, \dfrac12 y)

Step-by-step explanation:

  • Dilation is a transformation, in which the size of the image gets changed but not shape.

The rule of dilation with scale factor k and wither origin as center of dilation :

(x,y) → (kx, ky)

Here , k= \dfrac12 , center of dilation = Origin

Then, the rule best represents a dilation to create pentagon PQRST will be :

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