Please help!!<br> Simplify the expression.<br> csc^2x-1/ 1 +sinx

Given the trinomial 2x2 + 4x + 4, predict the type of solutions.

rodikova [14]

Trinomial 2x² + 4x + 4.

It's of the form ax²+bx+c and it's discriminant is Δ=b² - 4.a.c

(in our case Δ = 4² - (4)(2)(4) → Δ = - 32

We know that: x' = -1 + i and x" = -1 - i

If Δ > 0 we have 2 rational solutions x' and x"

If Δ = 0 we have1 rational solution x' = x"

If Δ < 0 we have 2 complex solutions x' and x", that are conjugate

In our example we have Δ = - 16 then <0 so we have 2 complex solutions

That are x'= [-b+√Δ]/2.a and x" = [-b-√Δ]/2.a

x' =

4 0

2 years ago

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A first number plus twice a second number is 11. Twice the first number plus the second totals 16. Find the numbers.

satela [25.4K]

<h3><u>The first number, x, is equal to 7.</u></h3><h3><u>The second number, y, is equal to 2.</u></h3>

x + 2y = 11

2x + y = 16

We can subtract 2y from both sides of the first equation to get a value for x.

x = 11 - 2y

Because we have a value for x, we can plug it into the second equation.

2(11 - 2y) + y = 16

Distributive property.

22 - 4y + y = 16

Combine like terms.

22 - 3y = 16

Subtract 22 from both sides.

-3y = -6

Divide both sides by -3.

y = 2

Now that we have a value for y, we can plug it into either equation to solve for x.

x + 2(2) = 11

x + 4 = 11

Subtract 4 from both sides.

x = 7

4 0

2 years ago

A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 9

valkas [14]

Answer:

Perimeter of NCAA court=288 feet

Perimeter of new court=259.2 feet

Step-by-step explanation:

We are given that

Length of NCAA court, l=94 feet

Width of NCAA court, b=50 feet

Width of new court, b'=45 feet

We have to find the perimeter of an NCAA court and new court in the school.

Perimeter of NCAA court= $2(l+b)$

Perimeter of NCAA court= $2(94+50)$ feet

Perimeter of NCAA court=288 feet

When two rectangles are similar then the ration of their corresponding sides are equal.

Using the property

$\frac{Perimeter\;of\;NCAA\;court}{Perimeter\;of\;new\;court}=\frac{Width\;of\;NCAA\;court}{Width\;of\;new\;court}$

$\frac{288}{Perimeter\;of\;new\;court}=\frac{50}{45}$

Perimeter of new court= $\frac{288\times 45}{50}$ feet

Perimeter of new court=259.2 feet

6 0

2 years ago

Hellppppp........ pleasee

Bumek [7]

Answer:

Step-by-step explanation:

The set of points in the 2nd row does not represent a function, because the x-coordinate 2 is associated with more than one y-coordinate.

Functions are one-to-one: For each x value there is one y value associated.

4 0

2 years ago

You stand at point C and look at an aquarium tank. Calculate the radius of the aquarium tank.

leonid [27]

Answer:

The radius of the aquarium tank is $8.25\ ft$

Step-by-step explanation:

we know that

Applying the Tangent Secant Theorem

$DC^{2}=AC*8$

we have that

$AC=(D+8)\ ft$

$DC=14\ ft$

substitute

$14^{2}=(D+8)*8$

$196=8D+64$

Solve for D

$8D=196-64$

$8D=132$

$D=16.5\ ft$

Find the radius

The radius is half the diameter

$r=16.5/2=8.25\ ft$

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2 years ago

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Please help!! Simplify the expression. csc^2x-1/ 1 +sinx