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3 years ago

12

Beth is four years older than two thirds the

1 answer:

Goshia [24]3 years ago

7 0

Answer:

15

Steps:

B = 2/3M + 4

14 = 2/3M + 4

10 = 2/3M

M = 15

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What is 2.5x0.012= <br><br> (20 POINTS)

mr Goodwill [35]

Answer: 0.03

Step-by-step explanation:

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3 years ago

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What is the equation of the line shown in this graph? Enter your answer in the box.

Mariana [72]

The given line (in blue) is a vertical line, so it is in the form
Ax=C (i.e. with the y-term missing).

Since we know that the line passes through (-2,2), and (-2,-3), this means that all points on the line has the x-coordinate equal to -2 (characteristic of vertical lines).

The equation is therefore
x=-2, or alternatively
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L :V --> W is a linear transformation. Prove each of the following (a) ker L is a subspace of V. (b) range L is a subspace of

iragen [17]

Answer:

a) Assume that $x,y\in\ker L$ , and $\alpha$ is a scalar (a real or complex number).

<em>First. </em>Let us prove that $\ker L$ is not empty. This is easy because $L(0_V)=0_W$ , by linearity. Here, $0_V$ stands for the zero vector of V, and $0_W$ stands for the zero vector of W.

<em>Second.</em> Let us prove that $\alpha x\in\ker L$ . By linearity

$L(\alpha x) = \alpha L(x)=\alpha 0_W=0_W$ .

Then, $\alpha x\in\ker L$ .

<em>Third. </em> Let us prove that $y+ x\in\ker L$ . Again, by linearity

$L(x+y)=L(x)+L(y) = 0_W + 0_W=0_W$ .

And the statement readily follows.

b) Assume that $u$ and $v$ are in range of $L$ . Then, there exist $x,y\in V$ such that $L(x)=u$ and $L(y)=v$ .

<em>First.</em> Let us prove that range of $L$ is not empty. This is easy because $L(0_V)=0_W$ , by linearity.

<em>Second.</em> Let us prove that $\alpha u$ is on the range of $L$ .

$\alpha u = \alpha L(x) = L(\alpha x) = L(z)$ .

Then, there exist an element $z\in V$ such that $L(z)=\alpha u$ . Thus $\alpha u$ is in the range of $L$ .

<em>Third.</em> Let us prove that $u+v$ is in the range of $L$ .

$u+v = L(x)+L(y) = L(x+y)=L(z)$ .

Then, there exist an element $z\in V$ such that $L(z)= u +v$ . Thus $u +v$ is in the range of $L$ .

Notice that in this second part of the problem we used the linearity in the reverse order, compared with the first part of the exercise.

Step-by-step explanation:

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3 years ago

Translate the sum of a number and 10 is 30

Alexandra [31]

Number is n

And is +

Is means equals

therefore

n +10=30

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Find the perimeter in feet and in yards

Goryan [66]

<h3>Given</h3>

a circle with diameter 8 yd

<h3>Find</h3>

the circumference in feet and yards

<h3>Solution</h3>

The circumference of a circle is given by ...

C = πd

where C is the circumference and d is the diameter. For your circle, the circumference is

... C = π(8 yd) = 8π yd ≈ 25.13 yd

There are 3 feet in a yard, so 3 times as many feet.

... C = 24π ft ≈ 75.40 ft

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4 years ago