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3 years ago

Determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases.

Mathematics

1 answer:

Orlov [11]3 years ago

8 0

Answer:

it is invertible

Step-by-step explanation:

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2x-y=5solve the equation for y

Taya2010 [7]

2x-y=5 Subtract 2x from both sides -y=-2x+5 Multiply everything by -1 y=2x-5 would be your answer

7 0

4 years ago

An investment of $900 earns 6% annual interest and is compounded semi-annually. Write an equation

nalin [4]

Answer:

$A=900(1+\frac{0.06}{2})^{2(t)}$

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

$A=P(1+\frac{r}{n} )^{nt}$

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 6% into a decimal:

6% -> $\frac{6}{100}$ -> 0.06

Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:

$A=900(1+\frac{0.06}{2})^{2(t)}$

4 0

2 years ago

He solution is n = –2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?

Nimfa-mama [501]

Answer:

$-0.8=-0.8$

Step-by-step explanation:

We have been given that n=-2 verified as a solution to the equation $1.4n+2=2n+3.2$ .

As n=-2 is the solution for our given equation, so it will satisfy our equation.

Let us substitute n=-2 is our given equation.

$1.4*-2+2=2*-2+3.2$

$-2.8+2=-4+3.2$

$-0.8=-0.8$

Since the value of n satisfies our equation, therefore, last line of the justification will be $-0.8=-0.8$ .

5 0

3 years ago

What does this equal to? 8ft 12 in. = ____yd

MissTica

First:
3 feet=1 yard
36 inches=1 yard

8 feet=2 $\frac{2}{3}$ of a yard
12 inches=1/3 of a yard.

2 $\frac{2}{3}$ + $\frac{1}{3}$ =2 $\frac{3}{3}$ or 3.

Hope this helps!

8 0

3 years ago

Read 2 more answers

The figure is made up of a hemisphere and a cylinder.

Goryan [66]

Data: (Cylinder)
h (height) = 8 cm
r (radius) = 5 cm
Adopting: $\pi \approx 3.14$
V (volume) = ?

Solving:(Cylinder volume)
 $V = h* \pi *r^2$
$V = 8*3.14*5^2$
$V = 8*3.14*25$
$\boxed{ V_{cylinder} = 628\:cm^3}$

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)
V (volume) = ?
r (radius) = 5 cm
Adopting: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4 * \pi * \frac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3} 
$

Formula: (Volume of the hemisphere)
 $V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}$

Solving:
$V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}$
$V = \frac{1}{2} * 4 * 3.14 * \frac{5^3}{3}$
$V = \frac{1}{2} * 4 * 3.14 * \frac{125}{3}$
$V = \frac{1570}{6}$
$\boxed{V_{hemisphere}\approx 261.6\:cm^3}$

Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)

Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 628 cm³ + 261.6 cm³
$\boxed{\boxed{Volume\:of\:the\:figure = 1517.6\:cm^3}}\end{array}}\qquad\quad\checkmark$

3 0

3 years ago

Read 2 more answers