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4 years ago

What is the value of x to the nearest tenth?

Mathematics

1 answer:

Alex_Xolod [135]4 years ago

7 0

Hi there!

In order to solve for x, we'll need to use a trigonometry ratio. In this case, we'll use tangent, which is opposite over adjacent.

Here is our equation:
tan(37)/1 = x/2.1

Cross-Multiply:
x = tan(37) * 2.1

Solve:
x = 1.8 (rounded to the nearest tenth)

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

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the axis of symmetry for the graph of the function is f(x) = 1/4x2 bx 10 is x = 6. what is the value of b?

Lady bird [3.3K]

we have

$f(x)=\frac{1}{4} x^{2} +bx+10$

This is a vertical parabola open upward

The axis of symmetry is equal to the x-coordinate of the vertex

The vertex is the point (h,k)

the equation of the axis of symmetry is $x=h$

In this problem

$x=6$

so the x-coordinate of the vertex is $h=6$

Convert the quadratic equation in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-10=\frac{1}{4} x^{2} +bx$

Factor the leading coefficient

$f(x)-10=\frac{1}{4}(x^{2} +4bx)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-10+b^{2}=\frac{1}{4}(x^{2} +4bx+4b^{2})$

Rewrite as perfect squares

$f(x)+(b^{2}-10)=\frac{1}{4}(x+2b)^{2}$

$f(x)=\frac{1}{4}(x+2b)^{2}-(b^{2}-10)$

remember that

$h=6$

$(x+2b)=(x-6)$

$2b=-6$

$b=-3$

substitute in the equation

$f(x)=\frac{1}{4}(x-6)^{2}-((-3)^{2}-10)$

$f(x)=\frac{1}{4}(x-6)^{2}+1$

therefore

the answer is

$b=-3$

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4 years ago

Read 2 more answers

Evaluate the expression for b = 5 4b^2

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Answer: 100

Step-by-step explanation:

Sub in 5 for b in the expression

$4b^2\\4(5)^2$

You must do the exponent first as it comes before multiplication in the order of operations

$4(5)^2\\4(25)$

Now multiply

$4(25)\\100$

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