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3 years ago

Find the graph of the inequality y<-1/5x+1

Mathematics

2 answers:

mina [271]3 years ago

6 0

<h2>Answer with explanation:</h2>

We are given a inequality as:

$y$

We know that the graph will be a dotted straight line( since the inequality is strict) and it passes through (0,1) and (5,0)

(

since , we could write it as

$y=\dfrac{-1}{5}x+1$

when y=0 we have:

$\dfrac{-1}{5}x+1=0\\\\i.e.\\\\x=5$

and when x=0 we have:

$y=1$

)

and the shaded region is towards the origin since it passes the zero-point test

( i.e. when x=y=0 then,

0<1 which is a true inequality )

The graph of the inequality is attached to the answer.

Artemon [7]3 years ago

4 0

Your answer should be y< -x/5 +1

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Carter draws one side of equilateral △PQR on the coordinate plane at points P(-3,2) and Q(5,2). Which ordered pair is a possible

Law Incorporation [45]

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

$pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

$or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} }$

By simplifying it we get,

$8$

Now,

again finding the distance between PR,

$pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} }$

or,

$\sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} }$

By simplifying it we get,

$= \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 }$

now, finding the distance of QR,

$qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} }$

or, by simplification we get,

$\sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

now, equating PR and QR,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

we cancelled the root ,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29$

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8}$

cancel the roots,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = 8$

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

<em>Hope it helps</em><em>.</em><em>.</em><em>.</em>

3 0

4 years ago

Given that A, O & B lie on a straight line segment, evaluate COD.

GrogVix [38]

(3x + 94) I’m not sure

8 0

3 years ago

Read 2 more answers

A conservative estimate of the number of stars in the universe is 6 x 10^22. The average human can see about 3,000 stars at nigh

Ilia_Sergeevich [38]

$2 \times 10^{19}$ times more stars are there in universe compared to human eye can see

<h3><u>Solution:</u></h3>

Given that, conservative estimate of the number of stars in the universe is $6 \times 10^{22}$

The average human can see about 3,000 stars at night with only their eyes

To find: Number of times more stars are there in the universe, compared to the stars a human can see

Let "x" be the number of times more stars are there in the universe, compared to the stars a human can see

Then from given statement,

$\text{Stars in universe} = x \times \text{ number of stars human can see}$

<em><u>Substituting given values we get,</u></em>

$6 \times 10^{22} = x \times 3000\\\\x = \frac{6 \times 10^{22}}{3000}\\\\x = \frac{6 \times 10^{22}}{3 \times 10^3}\\\\x = 2 \times 10^{22-3}\\\\x = 2 \times 10^{19}$

Thus $2 \times 10^{19}$ times more stars are there in universe compared to human eye can see

5 0

4 years ago

X−6>−2 solve the inequality

hjlf

Answer:

x>4

Step-by-step explanation:

3 0

3 years ago

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Could someone help me understand how to solve this?

monitta

Answer:

Amount in 4% account: $550

Step-by-step explanation:

Use simple interest formula $I=P\cdot r\cdot t,$ where

I = interest

P = principal

r = rate (as decimal)

t = time.

<u>4% account:</u>

$P_1=x\\ \\r_1=0.04\\ \\t_1=1,$

then

$I_1=x\cdot 0.04\cdot 1=0.04x$

<u>5% account:</u>

$P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,$

then

$I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)$

You have earned $69.50 in total, so

$I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950$

Amount in 4% account: $550

Amount in 5% account: $950

8 0

3 years ago