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Archy [21]
3 years ago
9

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the g

raph of the following inequality: y < two thirds x + 2
Answers:
A.The origin is not included in the shaded region and the shaded area is above the line.

B.The origin is not included in the shaded region and the shaded area is below the line.

C.The origin is included in the shaded region and the shaded area is above the line.

D.The origin is included in the shaded region and the shaded area is below the line.

Mathematics
1 answer:
kati45 [8]3 years ago
6 0

Answer:

Option: D is correct.

Step-by-step explanation:

since we are given a inequality as:

y

Clearly from the graph of the following inequality we could see that the origin is included in the shaded region and the shaded area is below the line.

Also it could be seen that if we put the origin points i.e. (0,0) in the inequality than 0<2 and the condition is true and hence origin is included in the shaded area.

Hence, option D is true.

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10
sveta [45]

This question was not written properly

Complete Question

Steve has 54 stamps in his collection of 13 cent, 29 cent, and 45 cent stamps, totaling a value of $15.98. If the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80. Find the number of each type of stamp in his collection.

Answer:

a) The number of 13 cent = 14

b) The number of 29 cent = 24

c) The number of 45 cent = 16

Step-by-step explanation:

We are told he has 54 stamps in total.

These stamps are;13 cent, 29 cent, and 45 cent stamps.

Let's

Number of 13 cent = a

Number of 29 cent = b

Number of 45 cent = c

Hence,

a + b + c = 54........... Equation 1

The total value of the 3 stamps are $15.98.

1 cent = $0.01

We have

0.13a + 0.29b + 0.45c= $15.98 ......... Equation 2

We know from the question that:

13 cent stamps is doubled, the new total value of his stamp collection would be $17.80.

Therefore

2(0.13a) + 0.29b + 0.45c = 17.8

0.26a + 0.29b + 0.45c = 17.8 ......... Equation 3

Combining Equation 2 and 3 together

0.13a + 0.29b + 0.45c= 15.98 ......... Equation 2

0.26a + 0.29b + 0.45c = 17.8 ......... Equation 3

We eliminate b and c by Subtracting Equation 3 from 3

0.13a = 1.82

a = 1.82/0.13

a = 14

a + b + c = 54........... Equation 1

Since a = 14

14 + b + c = 54

b + c = 54 - 14

b + c = 40

c = 40 - b

Substitute 40 - b for c and 14 for a is Equation 2

0.13a + 0.29b + 0.45c= 15.98 ......... Equation 2

0.13(14 ) + 0.29b + 0.45(40 - b) = 15.98

= 1.82 + 0.29b + 18 - 0.45b = 15.98

Collect like terms

1.82 + 18 - 15.98 = 0.45b - 0.29b

3.84 = 0.16b

b = 3.84/0.16

b = 24

Hence: Solving for c

a + b + c = 54........... Equation 1

14 + 24 + c = 54

38 + c = 54

c = 54 - 38

c = 16

Therefore,

The number of 13 cent = 14

The number of 29 cent = 24

The number of 45 cent = 16

8 0
3 years ago
An Athlete wants to increase muscle mass through weight training. The athlete has P pounds of muscle before weight training and
Vladimir [108]

Answer:

B. 0.88p

Step-by-step explanation:

3 0
3 years ago
The force in Newtons acting on a particle located x meters from the origin is given by the function F(x)=12x2+7. What is the wor
Shkiper50 [21]

W = \displaystyle \int^{5}_{2}   F(x) ~ dx\\\\\\= \displaystyle \int^{5}_{2} \left(12x^2 +7\right) ~dx\\\\\\= 12\displaystyle \int^{5}_{2} x^2 ~dx + \displaystyle \int^{5}_{2} 7~ dx\\\\\\=12 \left[\dfrac{x^3}3 \right]^{5}_{2}  + 7\left[x\right]^{5}_{2}\\\\\\=4(5^3-2^3) + 7(5-2) = 468 + 21 = 489~ J

5 0
2 years ago
The segment with endpoints (0,8) and (−6,0) is dilated to a segment with endpoints (0, 6) and (−4.5,0). What is the scale factor
sergiy2304 [10]
I think it would be 4/3 because when you multiply 8 by 4/3 you get 6 and when you multiply-6 by 4/3 you get -4.5 so

4/3
5 0
3 years ago
Mary borrowed 400.00 from a bank for 2 years. The total interest she paid was 24.00 Mary bro 400 from a bank for 2 years and was
iogann1982 [59]

Answer:

3%

Step-by-step explanation:

24÷400=.06

.06=6%

6%÷2=3%

5 0
3 years ago
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