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3 years ago

Which expression is equivalent to 4^5 x 4^-3?

Mathematics

1 answer:

dybincka [34]3 years ago

5 0

Answer and Step-by-step explanation:

$4^{5}$ × $4^{-3}$

This is the same as:

$4^{5 - 3}$

When you are multiplying, and they have the same base, the exponents gets added to each other.

The answer is:

$4^2$ , or B.

#teamtrees #PAW (Plant And Water)

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I can't figure out how to do (i + j) x (i x j)for vector calc

Vinil7 [7]

In three dimensions, the cross product of two vectors is defined as shown below

$\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}$

Then, solving the determinant

$\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}$

In our case,

$\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}$

Where we used the formula for AxB to calculate ixj.

Finally,

$\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}$

Thus, (i+j)x(ixj)=i-j

8 0

1 year ago

Factor complete −2x2 + 10x.

mezya [45]

The factors of the quadratic equation is (x + 1) and (x - 6)

Given,

The quadratic equation; -2x² + 10x + 12

We have to find the factors of this equation using quadratic formula;-

Quadratic formula;- $\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}$

Here,

a = -2, b = 10 and c = 12

Now,

$\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}$ = $\frac{-10(+-)\sqrt{10^{2} -4 . -2. 12} }{2.-2}$ = $\frac{-10(+-)\sqrt{100 +96} }{-4}$ = (-10±14) ÷ -4

Solve for,

- 10 + 14 / -4 = -4/4 = -1

That is, (x + 1)

Solve for,

- 10 - 14 / -4 = -24/-4 = 6

That is, (x - 6)

Therefore, the factors for the given quadratic equation is (x + 1) and (x - 6)

Learn more about quadratic formula here;

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#SPJ1

6 0

1 year ago

2. Suppose the temperature that most foods can stay bacteria free in restaurants varies approximately according to a normal dist

vagabundo [1.1K]

Answer:

28.4

Step-by-step explanation:

Given that:

Mean, m = 31.3

Standard deviation, s = 2.8

Since, data is normally distributed :

P(x < 0.15) gives a Z value of - 1.036

Using the Zscore formula :

Z = (x - mean) / standard deviation

-1.036 = (x - 31.3) / 2.8

-1.036 * 2.8 = x - 31.3

-2.9008 = x - 31.3

-2.9008 + 31.3 = x

28.3992 = x

The temperature which correlates to the bottom 15% of the distribution is 28.4

7 0

2 years ago

Find the value of y in the formula y=5a-3b c, if a=12,b=4,c=8

liberstina [14]

Y=5a-3b
Y=5(12)-3(4)
Y=60-12
Y=48

You don't have a sign between b and c in the equation, so I cannot help you with the last operation

8 0

3 years ago

Read 2 more answers

What kind of expression is: Answer quickly, correct answer will get brainlist

Sphinxa [80]

Answer:

The answer is A. ( x-3/x-6 x X^3 + 5/x+1 ) is rational because it is a product of rational expressions since rational expressions are closed under multiplication.

Step-by-step explanation:

4 0

2 years ago