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12345 [234]
3 years ago
14

The temperature was recorded for four straight days.The temperatures was recorded for the first three days were -2°,10°,and 7°.W

hat must be the temperature recorded on the fourth day if the total temperature change was -4°?
Mathematics
1 answer:
lubasha [3.4K]3 years ago
7 0

Answer:

-19^{\circ}

Step-by-step explanation:

Let x represent temperature on 4th day.

We have been given that the temperatures was recorded for the first three days were -2°,10°,and 7°.

The total temperature on f days would be -2^{\circ}+10^{\circ}+7^{\circ}+x.

We have been given that total temperature change was -4°. We can represent this information in an equation as:

-2^{\circ}+10^{\circ}+7^{\circ}+x=-4^{\circ}

15^{\circ}+x=-4^{\circ}

x=-4^{\circ}-15^{\circ}

x=-19^{\circ}

Therefore, the temperature on 4th day must be equal to -19^{\circ}.

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A rectangular prism has a base area 56 ft.² and a volume of 840 ft.³ the length of the base is longer than the width if the sum
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Answer:

The length of the base in feet is 8 ft.

Step-by-step explanation:

The volume V of the rectangular prism is given by

V = l × w × h

But Area, A = l × w

∴ V = A × h

Where A is the base area and h is the height

From the question

A = 56 ft.²  and V = 840 ft.³

∴ 840 ft.³ = 56 ft.² × h

840 ft.³ / 56 ft.² = h

15 ft. = h

∴ h = 15 ft.

Hence, the height of the rectangular prism is 15 ft.

Also, from the question

the sum of the length and the width of the base is equal to the height

i.e l + w = h

where l is the length of the base and w is the width of the base

Then, l + w = 15 ------ (1)

Also, A = l × w

Then, 56 = l × w ------- (2)

From equation (1)

l + w = 15

Then, w = 15 - l ------- (3)

Substitute this into equation (2)

56 = l × w

56 = l × (15-l)

56 = 15l - l²

Then,

l²- 15l + 56 = 0

l² -8l -7l + 56 = 0

l(l - 8) -7(l - 8) = 0

(l - 7)(l - 8) = 0

l - 7 = 0 OR l - 8 = 0

∴ l = 7 OR l = 8

Substitute the values of l into equation (3)

w = 15 - l

when l = 7

w = 15 - 7

w = 8

and when l = 8

w = 15 - 8

w = 7

From the question, the length of the base is longer than the width

∴ l = 8 and w = 7

Hence, the length of the base in feet is 8 ft.

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