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mel-nik [20]
3 years ago
9

Find the value of x in the triangle shown below. a.164 b.2 c.6 d.80

Mathematics
2 answers:
Alexxandr [17]3 years ago
4 0

THEOREM:

  • <u>Pythagorean theorem</u>:— In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

ANSWER:

By pythagorean property,

  • x² = 10² - 8²
  • x² = 100 - 64
  • x² = 36
  • x = √36
  • x = 6 units.

So, <u>Correct choice</u> - [C] 6 units.

finlep [7]3 years ago
3 0

Answer:

\huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\

by using Pythagoras law:

h²=p²+b²

10²=z²+8²

z²=100-64

z=√36=6

<u>z</u><u>=</u><u>6</u><u> </u><u>u</u><u>n</u><u>i</u><u>t</u><u>s</u><u>.</u>

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torisob [31]

The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

h and k represent the coordinates at the center.

r is the radius of a circle.

The midpoint of the given points represents the center of this circle:

h = (4 + 4)/2 = 4

k = (5.5 + 10.5)/2 = 8

Next, we would determine the radius by using the distance formula for coordinates:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

r = √[(4 - 4)² + (10.5 - 5.5)²]

r = √[0² + 5²]

r = √25

r = 5 units.

Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Learn more about circle here: brainly.com/question/12823137

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2 years ago
Find the following integral
ololo11 [35]

There's nothing preventing us from computing one integral at a time:

\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2

\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2

\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx

Expand the integrand completely:

x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x

Then

\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}

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3 years ago
Donna is a computer repair person. She charges a flat fee of $20 for each computer plus an hourly charge of $9 per hour. Yesterd
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Answer:

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When sales of a particular hybrid automobile reach 60,000 units, federal income tax credits begin to phase out. One year after r
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Answer:

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direct and fast answer :

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now, a little bit longer to explain % calculations in general.

let's say, we are talking 27%. now we have a problem to find a fast fraction as factor.

it always starts with the identification of 100%.

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to get said 27% we have to multiply this by 27

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or in general

x% = 100% × x / 100

that also works for more complex questions. e.g. calculate 1.5%

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and that is all there is to % calculations. all the questions are just some variations, where your are missing one of the 3 "ingredients" : 100% amount, x% amount and x itself.

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