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Natalija [7]
3 years ago
9

Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x < 2 a

nd y ≤ 4x + 1
(5, 6)


(5, –2)

(–3, –15)


(1, 11)

Mathematics
1 answer:
marysya [2.9K]3 years ago
4 0
We want to solve the inequalities
x < 2
y ≤ 4x + 1

<span>Graph </span>the lines:
x = 2
y = 4x +1

The solution to the system of inequalities is the shaded region shown in the graph below.

Test the given points to see whether they fall within the solution region.

Point   Pass/Fail
--------  --------------
(5,6)     Fail
(5,-2)    Fail
(-3,-15)  Pass
(1,11)       Fail

Answer: (=3, -15)

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A single card is drawn from a deck. Find the probability of selecting
shepuryov [24]

Answer:

A. 1/2.

B. 15/26.

Step-by-step explanation:

Note when you have an 'OR' in the statement we <u>add </u>the probabilities.

A .  Club or a diamond . There are 13 clubs and 13 diamonds so

The Required Probability =  13/52 + 13/52

= 1/4 + 1/4 = 1/2.

B. There are 4 jacks and 26 black cards.

The Required Probability =   4/52 + 26/52

= 1/13 + 1/2

= 2/26 + 13/26

= 15/26.

5 0
4 years ago
What is this answer???
max2010maxim [7]

I think the answer is c) 4,1 .

3 0
3 years ago
Length of a rectangle is 4 inches less than twice it’s width of the perimeter is 70 inches what’s the dimensions?
Vedmedyk [2.9K]
W= width
L= length= 2W-4
Perimeter= 70

FIND WIDTH:
P= 2(L + W)
P= 2L + 2W
substitute 2W-4 for L
70= 2(2W-4) + 2W
multiply 2 by all in parentheses
70= (2*2W) + (2*-4) + 2W
70= 4W - 8 + 2W
combine like terms
70= 6W - 8
add 8 to both sides
78= 6W
divide both sides by 6
13= W

FIND LENGTH:
substitute w=13 to find width
L= 2W-4
L= 2(13)-4
L= 26-4
L= 22

CHECK:
P= 2(L + W)
70= 2(22 + 13)
70= (2*22) + 2(13)
70= 44 + 26
70= 70

ANSWER:
length= 22 inches
width= 13 inches

Hope this helps! :)
3 0
3 years ago
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 2 sin(xy), (0, 5)
andrew-mc [135]

Answer:

<h2>10</h2>

Step-by-step explanation:

Given the function f(x, y) = 2 sin(xy) at (0,5), the maximum rate of change of the function at that point will occur in the direction \nabla f(0,5)

\nabla f(x, y) = \frac{\delta(2sin(xy)) }{\delta x} i + \frac{\delta(2sin(xy)) }{\delta y} j\\\\\nabla f(x, y) = 2ycos(xy)i + 2xcos(xy)j\\\\\nabla f(0, 5) =  2(5)cos(0*5)i + 2(0)cos(0*5)j\\\\\nabla f(0, 5) = 10cos0i+ 0j\\\\\nabla f(0, 5) = 10i+0j\\\\||\nabla f(0, 5)|| = \sqrt{10^2+0^2} \\\\||\nabla f(0, 5)||  = \sqrt{100} = 10

Hence, the magnitude of the maximum rate of the function at the point (0, 5) is 10

6 0
3 years ago
Which equation represents the line that passes through points (1, -5) and (3,-17)?
pochemuha

Answer:y=-6x+1

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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