Which graph shows the function y=(13)3x

Geoffrey is evaluating the expression StartFraction (negative 3) cubed (2 Superscript 6 Baseline) Over (Negative 3) Superscript

makkiz [27]

The mathematical expression does not seem clear but I have made an attempt to make sense of what is implied.

Answer:

a = 4, b = 2, c = 16, d = 9

Step-by-step explanation:

$\dfrac{(-3)^3(2^6)}{(-3)^5(2^2)} = \dfrac{(2)^a}{(-3)^b} = \dfrac{c}{d}$

Solving the first part of the question by indices,

$\dfrac{(-3)^3(2^6)}{(-3)^5(2^2)} = (-3)^{3-5}(2)^{6-2} = (-3)^{-2}(2)^{4} = \dfrac{(2)^4}{(-3)^2}$

Comparing the rightmost term with the second term in the question,

a = 4, b = 2

Solving on,

$\dfrac{(2)^4}{(-3)^2} = \dfrac{(2)\times(2)\times(2)\times(2)}{(-3)\times(-3)} = \dfrac{16}{9}$

Comparing with the final term in the question,

c = 16 and d = 9

Therefore,

a = 4, b = 2, c = 16, d = 9

3 0

2 years ago

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Three trigonometric functions for a given angle are shown below. cosecant theta = thirteen-twelfths; secant theta = Negative thi

Kay [80]

Answer:

(–5, 12) is the correct answer.

Step-by-step explanation:

We are given the following values:

$cosec\theta = \dfrac{13}{12}\\sec\theta=-\dfrac{13}{5}\\cot\theta =-\dfrac{5}{12}$

Now, we know the following identities:

$sin \theta = \dfrac{1}{cosec\theta}\\cos \theta = \dfrac{1}{sec\theta}\\tan \theta = \dfrac{1}{cot\theta}$

Now, the values are:

$sin\theta = \dfrac{12}{13}\\cos\theta=-\dfrac{5}{13}\\tan\theta =-\dfrac{12}{5}$

Sine value is positive and cos, tan values are negative.

It can be clearly observed that $\theta$ is in 2nd quadrant.

2nd quadrant means, the value of $x$ will be negative and $y$ will be positive.

Let us have a look at the value of $tan\theta$ :

$tan\theta = \dfrac{Perpendicular}{Base}\\OR\\tan\theta = \dfrac{y-coordinate}{x-coordinate} = -\dfrac{12}{5}\\\therefore y = 12,\\x = -5$

Please refer to the attached image for clear understanding and detailed explanation.

Hence, the correct answer is coordinate (x,y) is (–5, 12)

8 0

2 years ago

What is the length of segment BD? Round your answer to the nearest hundredth. triangles ABC and ABD in which the triangles share

hichkok12 [17]

Answer:

BD = 4.99 units

Step-by-step explanation:

Consider the triangle ABD only.

The angle formed is 31 degrees which occurs between two sides that are AD and BC.

We know that for a right angled triangle, the angle can always be taken as an angle between hypotenuse and base.

Thus, The perpendicular sides is then 3 units, where base is BD and Hypotenuse is AD

Using formula for tanθ

tanθ = Perpendicular/Base

tan31 = 3/BD

0.601 = 3/BD

BD = 3/0.601

BD = 4.99 units

6 0

2 years ago

Polygons ABCD and EFGH are similar. Find the length of EH?

3241004551 [841]

Most likely, polygon ABCD has sides of known lengths.
It is also likely that one of the sides of polygon EFGH (not EH) is also known. For instance, its side EF.

If the above is true, we can find the scaling factor as a ratio between lengths of corresponding sides:
r=EFAB

Since this ratio is constant for any two corresponding lengths,
r=EHAD

From the last two equations we can derive:
EH=AD⋅EFAB

Hope That Helped : ) (Took a minute)

5 0

2 years ago

Choose Yes or No to tell if the digit in the ones place is 1/10 the value of the digit in the tens place.

Radda [10]

Answer:

4099 yes
4110 no
5909 no
5011 yes

Step-by-step explanation:

The digits will be related by a factor of 10 if they are the same digit. 4099 and 5011 have the same digit in the tens and ones places. 4110 and 5909 do not.

5 0

2 years ago

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