What number does these numbers share -21,22,65?

Which expression can be simplified by applying the additive inverse property

harina [27]

D, because 9 3/4 and -9 3/4 cancel out to 0, which is the additive inverse property.

4 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

2 years ago

Jada solved the equation Negative StartFraction 4 over 9 EndFraction = StartFraction x over 108 EndFraction for x using the step

Lilit [14]

Answer: First option.

Step-by-step explanation:

The complete exercise is attached.

In order to solve this exercise, it is necessary to remember the following property:

The Multiplication property of Equality states that:

$If\ a=b\ then\ a*c=b*c$

In this case, the equation that Jada had is the folllowing:

$-\frac{4}{9}=\frac{x}{108}$

Jada needed to solve for the variable "x" in order to find its value.

The correct procedure to solve for for "x" is to multiply both sides of the equation by 108. Then, you get:

$(108)(-\frac{4}{9})=(\frac{x}{108})(108)\\\\-48=x$

As you can notice in the picture, Jada did not multiply both sides of the equation by 108, but multiplied the left side by $-\frac{4}{9}$ <em> </em>and the right side by $-\frac{9}{4}$ .

Therefore,you can conclude that Jada should have multiplied both sides of the equation by 108.

3 0

2 years ago

Read 2 more answers

Solve for x.<br> X + 142<br> 135°

Lyrx [107]

Answer:

X=-7

Step-by-step explanation:

X + 142=135°

X=135-142

X=-7

So the value of X is -7

4 0

2 years ago

What is the volume of the prism?

mezya [45]

Answer:

40 $\frac{5}{8}$ $cm^{3}$

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length = 6 $\frac{1}{2}$ cm

width = 2 $\frac{1}{2}$ cm

height = 2 $\frac{1}{2}$ cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

6 $\frac{1}{2}$ = $\frac{13}{2}$

2 $\frac{1}{2}$ = $\frac{5}{2}$

Volume = $\frac{13}{2}$ x $\frac{5}{2}$ x $\frac{5}{2}$

When you multiply everything together you should get $\frac{325}{8}$ .

As a mixed number, that would be 40 $\frac{5}{8}$ $cm^{3}$ .

7 0

2 years ago