Evaluate all numerical expressions with exponents

Enter an expression for the perimeter of the given figure. Simplify the expression.

marishachu [46]

Step-by-step explanation:

2(19.2) + 4(x + 7)

= 66.4 + 4x

= 4(16.6 + x)in

3 0

3 years ago

Find all real solutions of the polynomial equation. (enter your answers as a comma-separated list.) z^4 + z^3 + z^2 + 3z − 6 = 0

viva [34]

I can't figure out a factor for this but graphing it shows x = -2 and +1 as real roots.

3 0

3 years ago

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.

Serjik [45]

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

$M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]$

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U = {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

$\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]$

The change of coordinate matrix is therefore,

$M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]$

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

3 0

2 years ago

This is a 30-60-90 triangle. a What is the measure of x? Х 43 X= = [ ?

kherson [118]

Answer:

See below:

Step-by-step explanation:

Hello! I hope you are having a nice day!

We can solve this problem in two steps; solving and theory.

I'll go and start off with the theory part!

Theory

We know that in geometry there are many types of triangles that have various different angles. With that, there are a few special triangles that people have made formulas for, one being a 30, 60, and 90 degree triangle.

The theorem states that the hypotenuse is $2x$ , the side opposite to 60 degrees is $x\sqrt{3}$ , and the bottom is $x$ .

Solving

We can solve this problem in a step, we just need to know what the theorem said and implement it here, since we know the values of the sides of the triangle, we can solve it by finding out the opposite side and applying the theorem rules.

If we look at the graph, we can see that the $x$ part of the side opp. of 60 degrees is 4, that means that $x$ would be double of 4, which is 8.

Therefore your answer would be: $x=8$

Cheers!

8 0

2 years ago

Distrubutive property (m-3)(-10)?

mrs_skeptik [129]

Answer: -10m + 30

Step-by-step explanation:

Given expression

(m - 3) (-10)

Expand parentheses and apply the distributive property

=m · (-10) - 3 · (-10)

Simplify by multiplication

= $\boxed{-10m+30}$

Hope this helps!! :)

Please let me know if you have any questions

4 0

3 years ago