2 years ago

Calculate the distance between the points (-6, 4) and (5, -1). Round to the nearest tenth.

Mathematics

1 answer:

ludmilkaskok [199]2 years ago

4 0

It will be 42 because of the with times the 2nd highest

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3 years ago

Find the smallest zero of f(x+5)

podryga [215]

ANSWER

1. k=13

2. x=-10

EXPLANATION

The given function is

$f(x) = {x}^{2} + 3x - 10$

To find f(x+5), plug in (x+5) wherever you see x.

This implies that:

$f(x) = {(x + 5)}^{2} + 3(x + 5) - 10$

Expand:

$f(x) = {x}^{2} + 10x + 25+ 3x + 15- 10$

Simplify to obtain

$f(x) = {x}^{2} + 13x + 30$

We now compare with,

$f(x) = {x}^{2} + kx + 30$

This implies that:

$k = 13$

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

${x}^{2} + 13x + 30 = 0$

${x}^{2} + 10x + 3x + 30 = 0$

$x(x + 10) + 3(x + 10) = 0$

$(x + 3)(x + 10) = 0$

$x = - 10 \: or \: x = - 3$

The smallest zero is -10.

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