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3 years ago

Anyone knows this I'm stuck

Mathematics

1 answer:

Reptile [31]3 years ago

5 0

Answer:

A. Dividing both sides by 4 isolates the variable.

Step-by-step explanation:

In order to solve for x, you need to get it all by itself. Dividing both sides of the equation by 4 gives you 8 on the right side and only x on the left side , therefore the variable is isolated. (This uses the Division Property of Equality.)

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Need help with trig problem in pic

Sidana [21]

Answer:

a) $cos(\alpha)=-\frac{3}{5}\\$

b) $\sin(\beta)= \frac{\sqrt{3} }{2}$

c) $\frac{4+3\sqrt{3} }{10}\\$

d) $\alpha\approx 53.1^o$

Step-by-step explanation:

a) The problem tells us that angle $\alpha$ is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

$tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}$

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

$cos(\alpha)=-\frac{3}{5}$

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

$cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}$

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find $sin(\alpha -\beta)$ by using the identity:

$sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\$

Notice that we need to find $sin(\alpha)$ , which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

$sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}$

Then:

$sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}$

Since $sin(\alpha)=\frac{4}{5}$

then $\alpha=arcsin(\frac{4}{5} )\approx 53.1^o$

4 0

3 years ago

Plz help I’ll give a crown

Molodets [167]

Jake is the answer :)

5 0

3 years ago

Jayden’s new puppy weighed 11 1/4 pounds at 4 weeks old. At 16 weeks old, the puppy weighed 1 2/3 times more.

musickatia [10]

Answer:

18.75 or 18 3/4 lbs

Step-by-step explanation:

We just have to multiply 11 1/4 and 1 2/3 to get the product, 18.75 or 18 3/4.

First we have to translate our fractions into decimals:

11.25 (11 1/4) and 1.166667 (1 2/3)

multiply:

11.25 x 1.166667 = 18.75

convert back to fraction:

18 3/4

Hope This helps! Good Luck! If you have any questions please ask me, I would me more than happy to help you understand this method. If you are doing it a different way, I can help with that too.

5 0

3 years ago

-a(a² + 2a-1) for a = 2 pls help me solve this

Paraphin [41]

Answer:

I got you covered

Its -2(2^2 + 2 * 2 -) = -14 ^ = exponent

Step-by-step explanation:

!!HOpe ThIs HeLps!!

Calculate with parentheses (2^2 + 2 * 2 -1) :7

= -2 * 7

The multiply and divide (left to right)

= -14

GL on the test

5 0

2 years ago

Read 2 more answers

Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation. What is the scale factor of the dilat

Fynjy0 [20]

Answer:

The scale factor is 4

Step-by-step explanation:

This question requires an attachment; I'll answer this question using the attached figure

From the attachment

Length OA = 3 units

Length OA' = 3 units + 9 units

Length OA' = 12 units

Scale Factor is calculated as follows;

$Scale\ Factor = \frac{New\ Side}{Original\ Side}$

Given that the original shape is ABC, the original side will be OA

Hence, Original Side = 3 units

New Side = OA' = 12 units

The formula becomes

$Scale\ Factor = \frac{12\ units}{3\ units}$

$Scale\ Factor = 4$

Hence, the scale factor is 4

4 0

3 years ago

Anyone knows this I'm stuck​

Anyone knows this I'm stuck