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3 years ago

Evaluate each expression (image provided). A.) 5 B.) 7 C.) 4 D.) 6

Mathematics

1 answer:

Mkey [24]3 years ago

3 0

<h3>The answer is option A.</h3>

Step-by-step explanation:

$log_{3}(243)$

Can be written as

$log_{3}( {3}^{5} )$

Which is the same as

$5 log_{3}(3)$

But

$log_{3}(3) = 1$

So we have

5(1) = 5

Hope this helps you

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Solve triangle ABC if A = 65°, B = 65°, and c = 6. If no triangle exists, explain why.

WINSTONCH [101]

Answer:

Part 1) $m\angle C=50^o$

Part 2) $a=7.1\ units$

Part 3) $b=7.1\ units$

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

$m\angle A+m\angle B+m\angle C=180^o$

substitute the given values

$65^o+65^o+m\angle C=180^o$

$130^o+m\angle C=180^o$

$m\angle C=180^o-130^o$

$m\angle C=50^o$

step 2

Find the measure of side a

Applying the law of sines

$\frac{a}{sin(A)}=\frac{c}{sin(C)}$

substitute the given values

$\frac{a}{sin(65^o)}=\frac{6}{sin(50^o)}$

solve for a

$a=\frac{6}{sin(50^o)}sin(65^o)$

$a=7.1\ units$

step 3

Find the measure of side b

Applying the law of sines

$\frac{b}{sin(B)}=\frac{c}{sin(C)}$

substitute the given values

$\frac{b}{sin(65^o)}=\frac{6}{sin(50^o)}$

solve for b

$b=\frac{6}{sin(50^o)}sin(65^o)$

$b=7.1\ units$

The triangle ABC is an isosceles triangle

7 0

4 years ago

Evaluate Vb2 - 4ac when a = -2, b = 8 and c = 1/2 Write your answer in simplest form and in decimal form rounded to the

lubasha [3.4K]

Nauru jejejeje r rhrhhr ejejejr rjrjrjr th

5 0

3 years ago

A line and a circle intersect at the points A and B. Use the equations below to find the coordinates of the points of intersecti

Margaret [11]

Answer:

Step-by-step explanation:

Given the equation of a line y = x + 4 and equation of a circle as

( x − 3 )² + ( y − 5 )² = 34, if the line and the circle intersect at points A and B, to get this points, we will substitute the equation of the line into that of the circle as shown;

We will have to expand the equation of the circle first before making the substitute.

( x − 3 )² + ( y − 5 )² = 34

x²-6x+9+y²-10y+25 = 34

x²+y²-6x+-10y+34-34 = 0

x²+y²-6x+-10y = 0

Substituting y = x+ 4 into the resulting expression;

x²+(x+4)²-6x+-10y = 0

x²+x²+8x+16-6x+-10(x+4) = 0

x²+x²+8x+16-6x+-10x-40 = 0

2x²-8x-24 = 0

x²-4x-12 = 0

(x²-6x)+(2x-12) = 0

x(x-6)+2(x-6) = 0

x+2 = 0 and x-6 = 0

x = -2 and 6

when x = -2;

y = -2+4

y = 2

when x = 6

y = 6+4

y = 10

The coordinates of the point of intersection are A(-2, 2) and B(6, 10).

4 0

4 years ago

Solve the following system of equation express answer as a order pair 2x+5y=16 -5x-2y=2

Alex17521 [72]

Answer:

7y=11x-2y=2

7y-2y=2-12x

5y=9x

y=9x÷5

y=45ans

Step-by-step explanation:

have a nice day!

4 0

3 years ago

Question 10 of 11 Step 1 of 1

MrRa [10]

Answer:

Good luck

Step-by-step explanation:

4 0

4 years ago