Simplify 9 exponent 2

Which triangles are right triangles? Select all that apply.

Setler79 [48]

Answer:

triangle 1, triangle 3,

Step-by-step explanation:

Triangle 1= $14^{2} + 24^{2} = 772\\196+ 576 = 772$

Triangle 2= is wrong

Triangle 3= $11^{2} + 22^{2} = 605\\121+ 484= 605$

Triangle 4= is wrong.

7 0

3 years ago

Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec

julia-pushkina [17]

Answer:

$(2,6,6) \not \in \text{Span}(u,v)$

$(-9,-2,5)\in \text{Span}(u,v)$

Step-by-step explanation:

Let $b=(b_1,b_2,b_3) \in \mathbb{R}^3$ . We have that $b\in \text{Span}\{u,v\}$ if and only if we can find scalars $\alpha,\beta \in \mathbb{R}$ such that $\alpha u + \beta v = b$ . This can be translated to the following equations:

1. $-\alpha + 3 \beta = b_1$

2. $2\alpha+4 \beta = b_2$

3. $3 \alpha +2 \beta = b_3$

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for $\alpha,\beta$ and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

$-\alpha + 3 \beta = 2$

$2\alpha+4 \beta = 6$

whose unique solutions are $\alpha =1 = \beta$ , but note that for this values, the third equation doesn't hold (3+2 = 5 $\neq$ 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

$-\alpha + 3 \beta = -9$

$2\alpha+4 \beta = -2$

whose unique solutions are $\alpha=3, \beta=-2$ . Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

4 0

3 years ago

What is the answer to 36÷9 using a number line?

Katarina [22]

To divide 36/9 using the number line you have to jump from zero with length of 9 until reach 36, and the result will be the number of jumps.

I do the jumps by steps, but you can draw in the number line:

0. First jump from 0 to 9.

,

1. Second jump from 9 to 9+9=18.

,

2. Third jump from 18 to 18+9=27.

,

3. Fourth jump from 27 to 27+9=36.

,

4. Great!! We already reach 36.

So, we need four jumps of 9 to reach 36 from 0.

So, the result is 36/9=4

4 0

1 year ago

Marie currently has a collection of 58 stamps if she buys s stamps each week for w Weeks which expression represents the total n

laila [671]

58 stamps is the number she gets each week. So if she went for one week, 58*1=58. 58*2=116 and so on. Because we don't know the exact number of weeks, we say 58w or 58*w because you multiply however many number of weeks she collects.

8 0

3 years ago

Suppose the probability of an irs audit is 2.8 percent for U.S. taxpayers who file form 1040 and who earn 100,000 or more. What

stiks02 [169]

Answer:

So, the odds that a taxpayer would be audited 28 to 972 or 2.88%

Step-by-step explanation:

Given

Let P(A) = Probability of irs auditing

P(A) = 2.8%

Let n = number of those who earn above 100,000

To get the odds that taxpayer would be audited, we need to first calculated the proportion of those that will be audited and those that won't.

If the probability is 2.8% then 2.8 out of 100 will be audited. That doesn't make a lot of sense since you can't have 2.8 people; we multiply the by 10/10

i.e.

Proportion, P = 2.8/100 * 10/10

P = 28/1000

The proportion of those that would not be audited is calculated as follows;

Q = 1000 - P

By substituton

Q = 1000 - 28

Q = 972

So, the odds that a taxpayer would be audited 28 to 972 or P/Q

P/Q = 28/972

= 0.0288065844

= 2.88% --- Approximately

3 0

3 years ago