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3 years ago

If x is an acute angle and tan x = 5,

1 answer:

4 0

We have that
tan x=5

we know that
tan x =sin x/ cos x
sin x/ cos x=5------> squaring-----> sin² x/cos² x=25
remember that
sin² x+cos² x=1-----> cos² x=1-sin² x
substitute
sin² x/[1-sin² x]=25
sin² x=25-25*sin² x
26*sin² x=25
sin² x=25/26
sin x=5/√26

cos² x=1-(5/√26)²----> 1-(25/26)----> 1/26
cos x=1/√26

the answers are
sin x=5/√26
cos x=1/√26

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Which of the following is a solution of 4x2 = − 9x − 4?

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The solution is -0.609611 and -1.64, I do not think you can simply find this by factoring but the only way is graphing it

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What is -3(2 - x) = 9x

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Answer:

-1=x

Step-by-step explanation:

You multiply the -3 into the (2-x). which gives you -6+3x=9x. Know you wanna get ride of the 3x so you subtract from both sides, which then gives you. -6=6x. From here were gonna need to get x by itself so you divide both sides by 6.

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On a family vacation, Aaron took 1,276 digital photos. His twin sister Ashley took 4 times as many as Aaron. Write and solve an

aleksandr82 [10.1K]

Answer:

Equation : 4(1,276) = p

That means that Ashely took 5104 pics.

Step-by-step explanation:

Before we come up with an equation we can solve the problem and see how we solved it. If Aaron had 1,276 pics and his sister took 4 times that, we would multiply 1,276 by 4 to get how many his sister took. We don't need to do the math, but that's how we would solve it. So to find p, or Ashely's amount of pics, it's just 1,276 times 4 = p

Equation : 4(1,276) = p

That means that Ashely took 5104 pics.

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3 years ago

Which number is divisible by 2, 3, and 6

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Any multiple of 6 is divisible by 2, 3, and 6.

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4 years ago

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Use the graph of f at the right to complete each of the parts (a) through (h)

Maru [420]

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

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4 years ago

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