Suppose y varies directly with x, and y=24 when x=8. what is the value of y when x=10?

Answers

Answer 1

Answer: varies directly
y vaires diretly with x means
y=kx where k is constant
y=24
x=8
find k
24=k8
divide 8
3=k

y=3x
when x=10
y=3*10
y=30

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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

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.

What is the solution to the system of equations gaphed below
y=-x+3
y=x-3

Answers

The answer is (x,y)= (3,0)

The answer will be (0,3)

Groucho, Harpo, Chico, Zeppo, and Gummo have won 2 tickets to the opera. They will randomly choose which two of them have to attend. How many different 2-person groups are possible?

Answers

There are 10, 2 person groups that are possible.

Find the product.(7x - 6)2
A. 49x2 + 36
B. 49x2 - 84x + 36
C. 7x2 - 84x + 36
D. 7x2 + 36

Answers

When we square brackets, it is always advised to write out the brackets fully.
(7x - 6)² becomes
(7x - 6)(7x - 6)

Next, we follow FOIL
First (The first term in the set 1 multiplied by the first term in set 2)
Outer (The first term in set 1 multiplied by the second term in set 2)
Inner (The second term in set 1 multiplied by the first term in set 2)
Last (The second term in set 1 multiplied by the second term in set 2)

F   7x x 7x = 49x²
O  7x x -6 = -42x
I    -6 x 7x = -42x
L -6 x -6 = 36

Now, we add together all the terms

49x² + -42x + -42x +36

Adding a negative is the same as subtracting

49x² - 42x - 42x + 36

Finally, simplify (add together the like terms)

49x² -84x + 36

Answer:

Option B: 49x² -84x + 36

Step-by-step explanation:

What is the value of |−44|?