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3 years ago

13

if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplemantary are the lines pa

rallel?

1 answer:

Mnenie [13.5K]3 years ago

3 0

Yes, and you can look at the interior angle theorem for extra evidence. hope this helps, xx

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I need help w/ this!! thank you

Fittoniya [83]

<h3><u>Answer:</u></h3>

$\boxed{\pink{\sf \leadsto Yes \ there \ is \ a \ solution \ of \ the \ given \ inequality .}}$

<h3><u>Step-by-step explanation:</u></h3>

A inequality is given to us and we need to convert it into standard form and see whether if it has a solution . So let's solve the inequality.

The inequality given to us is :-

$\bf\implies |2y + 3 | - 1 \leq 0 \\\\\bf\implies |2y+3|\leq 1 \\\\\bf\implies (|2y+3|)^2 \leq 1^2 \\\\\bf\implies (2y+3)^2 \leq 1 \\\\\bf\implies (2y)^2+3^2+2(2y)(3) \leq 1 \\\\\bf\implies 4y^2+9+12y - 1 \leq 0 \\\\\bf\implies 4y^2+12y+8 \leq 0 \\\\\bf\implies 4( y^2 + 3y + 2 ) \leq 0 \\\\\bf\implies y^2+3y +2 \leq 0 \:\:\bigg\lgroup \purple{\bf Standard \ form \ of \ inequality }\bigg\rgroup \\\\\bf\implies y^2y+2y+y+2 \leq 0 \\\\\bf\implies y(y+2)+1(y+2)\leq 0 \\\\\bf\implies ( y+2)(y+1)\leq 0 \\\\\bf\implies \boxed{\red{\bf y \leq (-2) , (-1) }}$

Let's plot a graph to see its interval . Graph attached in attachment .

Now we can see that the Interval notation of would be ,

$\boxed{\boxed{\orange \tt \purple{\leadsto}y \in [-2,-1] }}$

<h3><u>Hence</u><u> the</u><u> </u><u>standa</u><u>rd</u><u> </u><u>form</u><u> </u><u>of</u><u> </u><u>inequa</u><u>lity</u><u> </u><u>is</u><u> </u><u>y²</u><u>+</u><u>3y</u><u> </u><u>+</u><u>2</u><u> </u><u>≤</u><u> </u><u>0</u><u> </u><u>and</u><u> </u><u>the </u><u>Solution</u><u> </u><u>set</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>ineq</u><u>uality</u><u> </u><u>is</u><u> </u><u>[</u><u> </u><u>-</u><u>2</u><u> </u><u>,</u><u> </u><u>-</u><u>1</u><u> </u><u>]</u><u> </u><u>.</u></h3>

4 0

2 years ago

A test is worth 140 points. Ten percent of those points are from one short-answer question. How many points is the short-answer

Vlada [557]

If the total amount of points in a test is 140, and we want to find 10% of those points, we can do the following to figure out how much points the question is worth...

140 points x 10% = 140 x 0.1 = 14 points for the short-answer quesion.

3 0

3 years ago

Read 2 more answers

Ardi and lei are both travelling by train. Ardi’s train travels 70km in 35 minutes. Lei’s train travels 585km. It leaves at 9:05

LuckyWell [14K]

Answer:47.14km/h

Step-by-step explanation:

585÷3 and 1/2=167.14km/h

70÷35/60=120km/h

167.14-120=47.14km/h

8 0

2 years ago

Evaluate 5+(-3) — 6.

WARRIOR [948]

Answer:

-4

Step-by-step explanation:

5+(-3)-6

2-6

-4

4 0

2 years ago

Read 2 more answers

2. In the ratio of 3:2:2, three brothers invested a total of 249,000 to open a store. Find each

GaryK [48]

Answer:

$106,714.29

$71,142.86

$71,142.86

Step-by-step explanation:

There's a total of 7 pieces that they invested (3 + 2 + 2 = 7) so you can do 249,000 / 7 to find what each piece was worth.

249000/7 = about 35571.43

(you always have to round money to 2 decimal places)

Then the amount each brother spent would be:

3 * 35571.43 = 106714.29

2 * 35571.43 = 71142.86

2 * 35571.43 = 71142.86

8 0

2 years ago