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Anni [7]
3 years ago
5

Changing Bases to Evaluate Logarithms In Exercise, use the change-of-base formula and a calculator to evaluate the logarithm.

Mathematics
1 answer:
Ymorist [56]3 years ago
3 0

Answer:

\frac{3}{2}

Step-by-step explanation:

Changing Bases to Evaluate Logarithms

log_{16}(64)

Apply change of base formula'

log_b(a)= \frac{log a}{log b}

log term should be the numerator and denominator is the log base

log_{16}(64)

log_{16}(a)= \frac{log 64}{log 16}

64 is 4^3  and 16 is 4^2

log_{16}(a)= \frac{log 4^3}{log 4^2}

Move the exponent before log

\frac{3log 4}{2log 4}

top and bottom has same log so cancel it out

\frac{3}{2}

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Show that the triangle below is not a right-angled triangle.
Paha777 [63]

Step-by-step explanation:

A right triangle is a triangle in which one of the angles is a 90∘ angle.

(5x - 8)  + (2x - 5)  + (2x  + 3) = 180 \\ 9x - 10 = 180 \\ 9x = 190 \\ x =  \frac{190}{9}  \\ x = 21.11

(5x - 8) =97.56  \\ (2x - 5)  =37.22  \\ (2x + 3) =45.22  \\

Since None of the angels is 90° , so the triangle is not a right triangle.

7 0
3 years ago
A triangle has one angle that measures 39 degrees, one angle that measures 104 degrees, and one angle that measures 37 degrees.
Nikitich [7]

Answer: Scalene triangle

Step-by-step explanation:

All triangles have three sides with specific lengths and angles, but a scalene triangle is a kind of triangle that has each of its three sides to be of different lengths and angles.

Hence, a triangle that measures 39°, 104°, and 37° definitely has three sides with different lengths and angles.

Thus, it is a scalene triangle.

8 0
3 years ago
Select from the following choices those graphs that represent only a dilation applied to this polygon with a scale factor great
romanna [79]

Answer:

B and C

Step-by-step explanation:

Required

Select graphs that are dilated by a scale factor greater than 1

For graph A:

Graph A is smaller than the original graph. This indicates dilation with a scale factor less than 1

For graph B:

Graph B is bigger than the original graph and is dilated over (0,0). This indicates dilation with a scale factor greater than 1

For graph C:

Graph C is bigger than the original graph; however, it is not dilated over (0,0). This indicates dilation with a scale factor greater than 1

For graph D:

Graph D is bigger than the original graph; however, it is not only dilated but also flipped over (i.e. rotated).

<em>Hence, b and c is true</em>

5 0
3 years ago
If cot theta= 4/3, find csc theta
Marrrta [24]

Answer: Option d.

Step-by-step explanation:

The trigonometric identity needed is:

csc^2\theta=cot^2\theta+1

Knowing that cot\theta=\frac{4}{3}:

Substitute it into csc^2\theta=cot^2\theta+1:

csc^2\theta=(\frac{4}{3})^2+1

Simplify the expression:

csc^2\theta=(\frac{4}{3})^2+1\\\\csc^2\theta=\frac{16}{9}+1\\\\csc^2\theta=\frac{25}{9}

Solve for csc\theta. Apply square root at both sides of the expression:

\sqrt{csc^2\theta}=\±\sqrt{\frac{25}{9}}

csc\theta=\frac{5}{3}

8 0
2 years ago
-1/2x - 3 =4 <br> which is the value of x?
garik1379 [7]

Answer:

x = -14

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5 0
3 years ago
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