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3 years ago

Two perpendicular lines intersect at the origin if the slope of the first line is 3,what is the equation of the second line

Mathematics

1 answer:

ddd [48]3 years ago

3 0

· Perpendicular lines have slopes that are opposite reciprocals of each other

· Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

If the slope of the first line is 3, the slope of the second line is -1/3. Since the lines intersect at the origin, neither of them have a y-intercept.

Answer:

C) y = -1/3x

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Spencer made a quilt for his cousin's doll. The quilt had a 7x7 array of different color square patches. If each patch is 1 3/4

Damm [24]

Answer:

$\frac{2401}{16}$ square inches

Step-by-step explanation:

Given:

The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is $1\frac{3}{4}$ in long.

To find: the area of the whole quilt

Solution:

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3 years ago

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Find the exact value of the given expression.<br> sin(2cos^-1(5/13))

xeze [42]

Answer:

+120/169 or -120/169

Step-by-step explanation:

let $cos^{-1}[\frac{5}{13} ] = \alpha$

where, alpha is some angle that satisfies the assumed condition.

so, $cos\alpha= 5/13$

[ taking cos to the other side or applying cos on both sides]

now, substitute this in the given expression

$sin(2cos^-1(5/13)) = sin(2\alpha )$

as sin $\beta$ = $+ or -\sqrt{1-(cos\beta) ^{2}$

[by general trigonometry formula: $cos^{2}[\beta] +sin^{2}[\beta]=1$ ]

so if $cos\alpha= 5/13$ , we can get sin $\alpha$ from the above formula as + or - 12/13

(because, after taking square root on both sides we keep + or -]

as, sin $2\beta = 2*sin[\beta ]*cos[\beta ]$

[by general trigonometry formula]

here, now $sin[2\alpha ]=2*(+or- 12/13)*5/13\\$

so, the final value can be 120/169 or -120/169.

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3 years ago

What number must i add to complete the square x^2+8x=-3

Sonja [21]

Answer:

Step-by-step explanation:

(b/2)^2

(8/2)^2 = (4)^2 = 16

(x^2+8x+16) = -3+16

(x+4)^2 = 13

so on so forth, but basically you add 16 which completes the square

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2 years ago

John is six years older than his sister Ella. Three times Ella’s age less two times John’s age is 13?

Vladimir [108]

Answer:

John is 31

Ella is 25

Step-by-step explanation:

Let sister's age be x, then John's age is (x + 6). So from sentence 2,

(3x) - 2(x + 6) = 13

3x - 2x - 12 = 13

x = 13 + 12 = 25

and x + 6 = 31

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2 years ago