In the xy-plane, triangular region R is bounded by the lines x=0, y=0, and 4x+3y=60. Which of the following points lie inside region R?a. (2, 18)
b. (5, 12)
c. (10, 7)
d. (12, 3)
e. (15, 2)

Answers

Answer 1

Answer: Convert the equation of the line to the slope-intercept form:
$4x+3y=60 \n3y=-4x+60 \ny=-(4)/(3)x+20$

All points which lie inside region R satisfy the system of inequalities:
$x\ \textgreater \ 0 \ny\ \textgreater \ 0 \ny\ \textless \ -(4)/(3)x+20$

You can see all coordinates in your choices are positive, so the first two inequalities are satisfied. We must check which points satisfy the third inequality.
Plug the values (x,y) into the inequality and check:
$(2,18) \n18 \ \textless \ -(4)/(3) * 2+20 \n18 \ \textless \ -(8)/(3)+20 \n18\ \textless \ -2(2)/(3)+20 \n18\ \textless \ 17 (1)/(3) \nfalse \n \n(5,12) \n12\ \textless \ -(4)/(3) * 5+20 \n12\ \textless \ -(20)/(3)+20 \n12\ \textless \ -6(2)/(3)+20 \n12\ \textless \ 13 (1)/(3) \ntrue$

$(10,7) \n7 \ \textless \ -(4)/(3) * 10+20 \n7\ \textless \ -(40)/(3)+20 \n7\ \textless \ -13 (1)/(3)+20 \n7\ \textless \ 6 (2)/(3) \nfalse \n \n(12,3) \n3\ \textless \ -(4)/(3) * 12+20 \n3\ \textless \ -(48)/(3)+20 \n3\ \textless \ -16+20 \n3\ \textless \ 4 \ntrue$

$(15,2) \n2 \ \textless \ -(4)/(3) * 15+20 \n2\ \textless \ -(60)/(3)+20 \n2\ \textless \ -20+20 \n2\ \textless \ 0 \nfalse$

The answer is B and D.

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Convert 6.42 kilograms to grams.

0.00642 g
64.2 g
642 g
6,420 g

Answers

1 kilogram (kg) equals to 1000 grams (g). Since you have 6.42 kilograms, divide 6.42 kilograms to 1000 grams. Your final answer is 6420 grams in total.

Answer: 6420 grams

Step-by-step explanation:

Solve the following systems of equations:
- 7x + y = 4
8x - 3y = 1
X=
y =

Answers

Answer:

x=-1 y=-3

............

Answer:

(−1,−3) or x=−1,y=−3

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Give the digits in the ones place and the hundredths place.
53.19

Answers

The ones place is 3 and the hundredths place is 9. Always remember, on the left side of the point starts with ones followed be tens, but in the right side of the point it starts with tenths followed by hundredth.

Megan has 25 phone numbers stored in her cell phone. Abby has some phone numbers stored in her cell phone. Together they have a total of 61 phone numbers stored. If n = the number of phone numbers Abby has stored in her cell phone, write a mathematical sentence to express the information above.

Answers

Answer:

$25+n =61$

Step-by-step explanation:

Given that Megan has 25 phone numbers stored in her cell phone. Abby has some phone numbers stored in her cell phone. Together they have a total of 61 phone numbers stored.

If n= the number of phone numbers Abby has stored in her cell phone

then we have sum of phone numbers both have

$25+n =61$

$n=61-25=36$