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3 years ago

Write the equation of a line that is perpendicular to the given line and that passes through the given point. -x+5y=14; (-5,-2)

1 answer:

3 0

$Let\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\ k:-x+5y=14\qquad|+x\\\\5y=x+14\qquad|:5\\\\y=\dfrac{1}{5}x+\dfrac{14}{5}\to m_1=\dfrac{1}{5}\\\\l:y=mx+b\to\dfrac{1}{5}m=-1\qquad|\cdot5\\\\m=-5\\\\l:y=-5x+b\\\\\text{Put the coordinates of the point (-5, -2) to the equation of the line}\ l:\\\\-2=-5(-5)+b\\-2=25+b\qquad|-25\\b=-27\\\\Answer:\ y=-5x-27\to5x+y=-27$

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Which of these needs the denominator rationalized? -PLEASE HELP

valentinak56 [21]

Answer:

option b

Step-by-step explanation:

$\sqrt{ \frac{5}{3} }$

$\frac{ \sqrt{5} }{ \sqrt{3} }$

the denominator is in the surd form, so it must be rationalized

4 0

3 years ago

PLEASE ANSWER FOR BRAINLIEST!!

e-lub [12.9K]

Answer:

mFG = 67r ( Where r is the radius of the circle)

∠ECF = 67°

Step-by-step explanation:

i) m FG

Join CG

∠GCF=67°

(As FG=ED and equal chords subtend equal angle at center)

Now The length of the minor arc is given by the formula

m arc FG =

$\frac {C}{2 \pi} \times 2 \pi r$

∠C=67

m arc FG = $\frac {67}{2 \pi} \times 2 \pi r$

m arc FG = 67r

Where r is the radius of the circle.

2. ∠ECF = 67°

It is because of the rule which says that equal chords subtend equal angle at center

DE = EF

Hence ∠DCE = ∠ECF

7 0

3 years ago

How does the graph of y=-3√2x-4 compare to the graph of y=-3√x-4?

kifflom [539]

Assuming the graph is y=-3(√2x)-4 and y=-3√(x-4) the transformation would be:

The graph is compressed horizontally by a factor of 2
x=1/2x'
y=-3(√2x)-4
y=-3(√x')-4 

moved left 4
x=x'-4
y=-3(√x)-4
y=-3(√x'-4)-4

moved down 4
y=y'-4
y=-3(√x-4)-4
y'-4=-3(√x'-4)-4
y'=-3(√x'-4)-4 +4
y'=-3(√x'-4)

Answer: C. The graph is compressed horizontally by a factor of 2, moved left 4, and moved down 4.

6 0

4 years ago

Read 2 more answers

HELP AGAIN!!! Plzzzzz thank you!!!

never [62]

Absolute value of -1/3 is 1/3

6 0

3 years ago

If you answer God will bless you:

VashaNatasha [74]

Answer:

600 m³

Step-by-step explanation:

Given:

length of swimming pool = 30 m
width of swimming pool = 10 m
depth at deep end = 3 m
depth at shallow end = 1 m

To find the volume of the water in the pool, find the area of a cross section (see attached image) and multiply it by the width of the pool.

Area of cross section

= area of rectangle - area of triangle

= (3 × 30) - [1/2 × 30 × (3 - 1)]

= 90 - 30

= 60 m²

Volume of pool

= area of cross section × width

= 60 × 10

= 600 m³

6 0

2 years ago