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2 years ago

PLEASE HURRY Quadrilateral ABCD is inscribed in OZ such that AB | DC and Find m

Mathematics

1 answer:

salantis [7]2 years ago

5 0

Answer:

41°

Step-by-step explanation:

First note that m arc BC = m∠BZC

The reason is because a central angle of a circle is always congruent to its

intercepted arc.

Also m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its intercepted arc.

Hence, the calculation is given below:

m∠BZC = 82°

m arc BC = m∠BZC

m arc BC = 82°

m∠BAC = 1/2 × 82°

m∠BAC = 41°

It is important to note that

∠DCA ≅ ∠BAC because alternate interior angles are congruent.

So m∠DCA = m∠BAC.

Therefore, m∠DCA = 41°.

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What is an equation of a the line through (-1, -4) and parallel to the line 3x+y=5

Greeley [361]

Answer: y + 4 = -3(x+1)

Step-by-step explanation:

We need to rewrite in form of y=mx+b.

3x+y=5

y = -3x + 5

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In addition, the slope of two parallel line would be equal, the slope of the line would be -3.

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2 years ago

Henry ran five races, each of which was a different positive integer number of

dolphi86 [110]

Answer:

10 miles.

Step-by-step explanation:

Let x be the number of miles on Henry's longest race.

We have been given that Henry ran five races, each of which was a different positive integer number of miles.

We can set an equation for the average of races as:

$\frac{\text{The sum distances of 5 races}}{5}=4$

As distance covered in each race is a different positive integer, so let his first four races be 1, 2, 3, 4.

Now let us substitute the distances of 5 races as:

$\frac{1+2+3+4+x}{5}=4$

$\frac{10+x}{5}=4$

Let us multiply both sides of our equation by 5.

$\frac{10+x}{5}*5=4*5$

$10+x=20$

Let us subtract 10 from both sides of our equation.

$10-10+x=20-10$

$x=10$

Therefore, the maximum possible distance of Henry's longest race is 10 miles.

7 0

2 years ago

The population of deer in a state park can be predicted by the expression 106(1.087)t, where t is the number of years since 2010

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Answer:

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Step-by-step explanation:

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

Find the average value of f over region

SVETLANKA909090 [29]

$D$ is a right triangle with base length 1 and height 8, so the area of $D$ is $\dfrac12(1)(8)=4$ .

The average value of $f(x,y)$ over $D$ is given by the ratio

$\dfrac{\displaystyle\iint_Df(x,y)\,\mathrm dA}{\displaystyle\iint_D\mathrm dA}$

The denominator is just the area of $D$ , which we already know. The average value is then simplified to

$\displaystyle\frac74\iint_Dxy\,\mathrm dA$

In the $x,y$ -plane, we can describe the region $D$ as all points $(x,y)$ that lie between the lines $y=0$ and $y=8x$ (the lines which coincide with the triangle's base and hypotenuse, respectively), taking $0\le x\le1$ . So, the integral is given by, and evaluates to,

$\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx$
$=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx$
$=14x^4\bigg|_{x=0}^{x=1}$
$=14$

3 0

2 years ago