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3 years ago

(a) Draw in radii OA, OB, OC and OD. Then, explain why OAB must

Mathematics

1 answer:

lions [1.4K]3 years ago

7 0

Answer:

In the given circle, segments OA, OB, OC and OD are radius of the circle.

In other words, all those segments are congruent.

From that we can deduct that triangles OAB and OCD are isosceles triangles, because all segments are equal. That makes those triangles congruent, because they have the same sides.

From the congruence we can deduct that all corresponding internal angles inside those triangles are actually congruent, that's why angle OAB and ODC must be congruent.

Also, angles DOC and BOA are also congruent, which means their subtended arcs are also congruent, because they have the same radius, so mAB = mCD.

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Tom put 18 gallons of mid grade gas in his truck and filled up his empty five gallon gas tank with regular gas for his lawn mowe

LuckyWell [14K]

Answer:

Mid grade gas per gallon = $2.67

Regular gas per gallon = $2.37

Step-by-step explanation:

Let, x= mid grade gas, y=regular gas.

So, for 18 gallons of mid grade gas and 5 gallon of regular gas at $59.91, it can be expressed as,

$18x+5y=59.91$ ------------------(equation 1)

for 14 gallon of mid grade gas and 1 gallon of regular gas at 39.75, it can be expressed as,

$14x+y=39.75$ -------------------(equation 2)

$y=39.75-14x$ -------------------(equation 3)

Now substituting the value of y from (equation 3) in (equation 1) we get,

$18x+5y=59.91$

$18x+5(39.75-14x)=59.91$

$18x+198.75-70x=59.91$

$52x=198.75-59.91$

$52x=138.84$

$x=\frac{138.84}{52}$

$x=2.67$ -------------------------(equation 4)

Now substituting value of x from (equation 4) in (equation 3) we get,

$y=39.75-14x$

$y=39.75-(14\times2.67)$

$y=39.75-37.38$

$y=2.37$

Therefore price per gallon of mid grade gas is x = $2.67, and price per gallon of regular gas y = $2.37.

4 0

3 years ago

Write the equation of the line that passes through (3, 4) and ( 2, -1) in slope-intercept form

rjkz [21]

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{3}}}\implies \cfrac{-5}{-1}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{5}(x-\stackrel{x_1}{3}) \\\\\\ y-4=5x-15\implies y=5x-11$

3 0

3 years ago

How do you simplify (2xy2)3

pantera1 [17]

$(2xy^{2})^{3} = (2xy^{2})(2xy^{2})(2xy^{2})$
Now, we can just multiply it and obtain the result
$(2xy^{2})(2xy^{2})(2xy^{2})=(4x^{2}y^{4})(2xy^{2})=8x^{3}y^{6}$

I used law presented on this example
$2^{3}*2=2^{3}*2^{1}=2^{3+1}=2^{4}$

4 0

3 years ago

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Yanka [14]

Answer:

The answer is A. k = 4.25.

Step-by-step explanation:

To find proportionality, solve for 8.5 divided by 2 and 17 divided by 4.

Both of those answers are 4.25, so that would be the final answer.

<h2><u><em>PLEASE MARK AS BRAINLIEST!!!!!</em></u></h2>

3 0

2 years ago

Read 2 more answers

How do you factor 14xy + 21x

jek_recluse [69]

Answer:

7x(2y+3)

Step-by-step explanation:

5 0

3 years ago