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3 years ago

9

ella opend a coffe shop in her neighborhood. the graph below shows the number of cups of coffe sold each hour ,x, on the opening

day of the shop

2 answers:

faltersainse [42]3 years ago

8 0

Answer:

The x-intercept represents the number of hours after opening when there were zero cups of coffee sold.

Step-by-step explanation:

Katen [24]3 years ago

5 0

Time is 4 hrs., coffee is 0 cups. Point (4,0)
So A

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The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

MA_775_DIABLO [31]

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let <em>x</em> be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

$a^2 + b^2 = c^2$

Where <em>c</em> is the hypotenuse and <em>a</em> and <em>b</em> are the two legs.

The hypotenuse is given to be 6 cm and the two legs are <em>x</em> and (<em>x</em> + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for <em>x</em>. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}$

In this case, <em>a</em> = 1, <em>b</em> = 2, and <em>c</em> = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$

Hence, our two solutions are:

$\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1$

Lengths cannot be negative, so we can ignore the second solution.

Hence, the value of <em>x</em> or the first side length is about 3.1 centimeters.

Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.

In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

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3 years ago

Find q.<br> Write your answer as an integer or as a decimal rounded to the nearest tenth.

neonofarm [45]

Answer:

13.9

Step-by-step explanation:

To get the length, or the hypotenuse, you do the equation a^2 + b^2 = c^2

Meaning you multiply those known lengths by themselves, then add them.

169 + 25 = 194

Then you find the square root of 194.

The square root would be 13.9283882772, or when rounded to the nearest tenth, 13.9

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2 years ago

Write two hundred and thirteen to the nearest ten

Naya [18.7K]

Two hundred and thirteen = 213
To the nearest ten = 210.

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3 years ago

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If four of the exterior angles of a convex pentagon measure

MakcuM [25]

Answer:

120 degrees.

Step-by-step explanation:

The 5 exterior angles sum to 360 degrees.

So the 5th exterior angle = 360 - 4(60)

= 360 - 240

= 120 degrees.

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6/16 OR 30/80 WHICH ONE is bigger?

spin [16.1K]

There's two possible ways to find the answer to this. First you can find a common denominator to reduce both to. In this case, they can both reduce to a common denominator of 8. So 6/16 reduces to 3/8 and 30/80 also reduces to 3/8, so they are equal. The other way is to use a calculator and turn them into decimals by dividing the numerator by the denominator. They both come out to be .375. Once again they are equal. You can use whichever method is easier for you.

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4 years ago

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