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3 years ago

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Ociel has designed a square mural that measures 10 feet on each side. Bill has also designed a square mural, but his measures y

feet shorter on each side. How much smaller than Ociel's mural is Bill's mural? Explain

1 answer:

WINSTONCH [101]3 years ago

6 0

Ocel’s 10x10=100
Bill’s (10 - y) (10 - y)

I don’t know which answer your teacher wants
100 - [(10-y)(10-y)]
100 - (100 -20y + y^2}
20y - y^2

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How to figure out pythagoras theorem?

Paladinen [302]

Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

<h3>What is the Pythagoras Theorem?</h3>

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ABD and △ACB,

∠A = ∠A (common)

∠ADB = ∠ABC (both are right angles)

Thus, △ABD ∼ △ACB (by AA similarity criterion)

Similarly, we can prove △BCD ∼ △ACB.

Thus △ABD ∼ △ACB,

Therefore, AD/AB = AB/AC.

We can say that AD × AC = AB².

Similarly, △BCD ∼ △ACB.

Therefore,

CD/BC = BC/AC.

We can also say that

CD × AC = BC².

Adding these 2 equations, we get

AB² + BC² = (AD × AC) + (CD × AC)

AB² + BC² =AC(AD +DC)

AB² + BC² = AC²

Hence proved

Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Learn more about Pythagoras theorem from:

brainly.com/question/343682

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6 0

2 years ago

Which equation is the inverse of y = x2 + 16?<br> 0 y=x²-16<br> y=i -16<br> y=+-16<br> y = x2 - 4

denpristay [2]

Answer:

y = ±√(x-16)

Step-by-step explanation:

To find the inverse of an equation, swap the x- and y-variables:

y = x² + 16

x = y² + 16

Then, solve for the y-variable:

x = y² + 16

y² = x - 16

y = ±√(x-16)

8 0

3 years ago

Ten friends went out to dinner. two friends each paid $12 for dinner, three friends each paid $13 for dinner, and five friends e

NeX [460]

$12 + $12 + $13 + $13 + $13 + $17 + $17 + $17 + $17 + $17 = 148

148 ÷ 10 = 14.8

$14.80 is the median amount the ten friends had to pay.

7 0

3 years ago

Sarah Wiggum would like to make a single investment and have $1.7 million at the time of her retirement in 34 years. She has

vovangra [49]

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$

In this question:

$t = 35, I = 0.07, T = 1700000$

She has to invest P today.

$T = E + P$

$1700000 = E + P$

$E = 1700000 - P$

So

$E = P*I*t$

$1700000 - P = P*0.07*34$

$3.38P = 1700000$

$P = \frac{1700000}{3.38}$

$P = 502958.58$

Sarah has to invest $502,958.58 today.

8 0

3 years ago

Suppose a random variable x is best described by a uniform probability distribution with range 22 to 55. Find the value of a tha

const2013 [10]

Answer:

(a) The value of <em>a</em> is 53.35.

(b) The value of <em>a</em> is 38.17.

(c) The value of <em>a</em> is 26.95.

(d) The value of <em>a</em> is 25.63.

(e) The value of <em>a</em> is 12.06.

Step-by-step explanation:

The probability density function of <em>X</em> is:

$f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}$

Here, 22 < X < 55.

(a)

Compute the value of <em>a</em> as follows:

$P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35$

Thus, the value of <em>a</em> is 53.35.

(b)

Compute the value of <em>a</em> as follows:

$P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17$

Thus, the value of <em>a</em> is 38.17.

(c)

Compute the value of <em>a</em> as follows:

$P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95$

Thus, the value of <em>a</em> is 26.95.

(d)

Compute the value of <em>a</em> as follows:

$P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63$

Thus, the value of <em>a</em> is 25.63.

(e)

Compute the value of <em>a</em> as follows:

$P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06$

Thus, the value of <em>a</em> is 12.06.

7 0

3 years ago