Ask question

Ask question

All categories

2 years ago

6

Simplify: 7(-2x - 3) * -14x - 21 -14x - 3 14x - 21 14x - 3

1 answer:

seraphim [82]2 years ago

4 0

The correct answer is A

You might be interested in

Show that the sets of upper-triangular and lower-triangular matrices are subspaces of F n,n . Call them U and L respectively. Wh

soldi70 [24.7K]

Answer:

dim L = dim U = $\frac{n(n+1)}{2}$

Step-by-step explanation:

We can do it only for the lower-triangular matrices, the case of the upper-triangular matrices is similar. We might caracterice nxn the lower-triangular matrices, as the nxn matrices $A=(a_{ij})$ such that the entry $a_{ij}=0$ if i<j.

Now let $A=(a_{ij})$ and $B=(b_{ij})$ be two lower triangular matrices, now if

$C=A+\lambda B$ for some $\lambda \in \mathbb{F}$

then the entry $c_{ij}$ of C is equal to

$c_{ij}=a_{ij}+\lambda b_{ij}$

Now, if i<j, it must hold that $a_{ij}=0 \quad \text{and} \quad b_{ij}=0$ . Therefore, if this is the case we must have that $c_{ij}=0$ and so we get that C is also a lower triangular matrix. This showa that L is closed under sum and scalar multiplcation, hence it is a linear subspace.

To find the dimension, note that all the entries of a lower-triangular matrix over the diagonal must be equal to zero. However, each entry of the matrix under the diagonal and in the diagonal might be any element of $\mathbb{F}$ , any entry that can be choosen add up to the dimension of L, we n such elemnts for the first column, (n-1) for the second column, (n-2) for the third column etc.... Therefore,

$\dimL=n+(n-1)+(n-2)+...+2+1=\dfrac{n(n+1)}{2}$

5 0

2 years ago

Which expression is equivalent to 24 Superscript one-third

Tems11 [23]

Answer:

The expression that is equivalent is 2 RootIndex 3 StartRoot 3 EndRoot :

$2\sqrt[3]{3}$

Step-by-step explanation:

Hi

As we have 24 Superscript one-third, this is $(24)^{\frac{1}{3}} =\sqrt[3]{24}$ .

$\sqrt[3]{24}=\sqrt[3]{8*3}=\sqrt[3]{8} \sqrt[3]{3}$ , therefore

$\sqrt[3]{8} =2$ , so $\sqrt[3]{8} \sqrt[3]{3}=2\sqrt[3]{3}$ .

3 0

3 years ago

Sam takes out a $167,000 mortgage for 20 years. He makes monthly payments and at the end calculates

cupoosta [38]

Answer:

The Annual rate of interest for the mortgage is 1.8%

Step-by-step explanation:

Given as :

The mortgage principal = p = $167,000

The time period of mortgage = t = 20 years

The Amount paid towards mortgage in 20 years = A = $240,141

Let the Annual percentage rate on interest = r % compounded annually

Now, <u>From Compound Interest method</u>

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $240,141 = $167,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

or, $\dfrac{240,141}{167,000}$ = $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or , 1.437 = $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or, $(1.437)^{\frac{1}{20}}$ = $(1+\dfrac{r}{100})$

or, 1.018 = $(1+\dfrac{r}{100})$

Or, $\dfrac{r}{100}$ = 1.018 - 1

Or, $\dfrac{r}{100}$ = 0.018

∴ r = 0.018 × 100

i.e r = 1.8

So, The rate of interest applied = r = 1.8 %

Hence, The Annual rate of interest for the mortgage is 1.8% Answer

8 0

2 years ago

-1/4a- 4 = 4 <br><img src="https://tex.z-dn.net/?f=%20-%20.25a%20-%204%20%3D%204" id="TexFormula1" title=" - .25a - 4 = 4" alt="

Ganezh [65]

-.25a-4=4
Add for on both sides
-.25a=8
Divide by -.25
A=

5 0

2 years ago

A square has a area of 81 square feet.

Setler [38]

Answer:

the side is 9 ft.

Step-by-step explanation:

7 0

2 years ago