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3 years ago

The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1, 7) and

Mathematics

1 answer:

Galina-37 [17]3 years ago

6 0

Answer:

y = 1/2x -1

Step-by-step explanation:

The slope of AB is ...

(y2 -y1)/(x2 -x1) = (1 -7)/(4 -1) = -6/3 = -2

Segment BC will be perpendicular to AB, so will have a slope that is the negative reciprocal of this:

slope of BC = -1/(-2) = 1/2

The line containing BC must go through point B, so we can use a point-slope form of the equation for a line:

y = m(x -h) +k . . . . for a line with slope m through point (h, k)

Point B is (4, 1) and our slope is 1/2, so the line's equation can be written ...

y = (1/2)(x -4) +1

y = 1/2x -2 +1 . . . . eliminate parentheses

y = 1/2x -1 . . . . . . . collect terms. This is the equation.

_____

The attachment shows segment AB and a perpendicular line through B. You will note that it has y-intercept -1 and slope 1/2, as above.

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Which pair of expressions represents inverse functions

Natali5045456 [20]

Answer: C. $\dfrac{x+3}{4x-2}$ and $\dfrac{2x+3}{4x-1}$

Step-by-step explanation: if a function f(x) has g(x) as its inverse then it satisfies fog(x)=x and gof(x)=x

C. f(x)= $\dfrac{x+3}{4x-2}$ and g(x)= $\dfrac{2x+3}{4x-1}$

fog(x)=f( $\dfrac{2x+3}{4x-1}$ )

= $\dfrac{\dfrac{2x+3}{4x-1}+3 }{\dfrac{4(2x+3)}{4x-1}-2 }$

gof(x)=g( $\dfrac{x+3}{4x-2}$ )

= $\dfrac{\dfrac{2(x+3)}{4x-2} +3}{\dfrac{4(x+3)}{4x-2}-1 }$

hence C. is the pair of inverse functions

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3 years ago

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Michelle has 21 ⅙ cups of flour in a container. She uses 6 ⅚ cups of flour to make 5 loaves of bread. How much flour does Michel

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It should be about -13 cups

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3 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

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3 years ago

Mrs teed bought 22 packs of hot dog rolls at the store for the 4th-grade picnic there were 12 rolls in each pack how many hot do

creativ13 [48]

Answer:

Step-by-step explanation:

To find out

22 x 12 = 264 rolls

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3 years ago