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Serhud [2]
3 years ago
5

1. Storing milk at temperatures colder than 35°F can affect its quality of taste. However, storing milk at temperatures warmer t

han 40°F is an unsafe food practice. Which of the inequalities below represent the union of these improper storage temperatures, t, in degrees Fahrenheit? A. T > 35 or t <40 B. T < 35 or t >40 C. T > 35 AND t < 40 D. T < 35 AND t > 40 2. What are the solution(s) to the absolute value equation below? 15| x-7|+4=10|x-7|+4 A. X= - 5\7 or x = 5\7 B. X=5 or x= -5 C. Only x=7 D. X= 7/5 or x= -7\5 3. Match the absolute value equation with the statement that describes the solutions to that equation. A. Two solutions B. Solution C. No solution |x+1|+5=2 |4x+12|=0 |3x|=9
Mathematics
1 answer:
Mazyrski [523]3 years ago
3 0

Answer:

Part (A): The required inequality is T < 35 or t >40.

Part (B): The correct option is C) Only x=7.

Part (C) |x+1|+5=2 has no solution; |4x+12|=0 has one solution; |3x|=9 has two solution.

Step-by-step explanation:

Consider the provided information.

Part (A)

Storing milk at temperatures colder than 35°F can affect its quality of taste. However, storing milk at temperatures warmer than 40°F is an unsafe food practice.

The union is written as A∪B or “A or B”.

The intersection of two sets is written as A∩B or “A and B”

We need to determine the inequalities represent the union of these improper storage.

That means we will use A∪B or “A or B”.

The improper storage temperatures is when temperature is less than 35°F or greater than 40°F.

Hence, the required inequality is T < 35 or t >40.

Part (B) 15| x-7|+4=10|x-7|+4

Solve the inequality as shown below:

Subtract 4 from both sides.

15| x-7|+4-4=10|x-7|+4-4

Subtract 10|x-7| from both sides

15\left|x-7\right|-10\left|x-7\right|=10\left|x-7\right|-10\left|x-7\right|

5\left|x-7\right|=0\\\left|x-7\right|=0\\x=7

Hence, the correct option is C) Only x=7.

Part (C) Match the solution,

\left|x+1\right|+5=2

Subtract 2 from both sides.

\left|x+1\right|=-3

Absolute value cannot be less than 0.

Hence, |x+1|+5=2 has no solution.

|4x+12|=0

4x+12=0

x=-3

Hence, |4x+12|=0 has one solution.

|3x|=9

\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a

3x=-9\quad \mathrm{or}\quad \:3x=9\\x=-3\quad \mathrm{or}\quad \:x=3

Hence, |3x|=9 has two solution.

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7 0
2 years ago
Justin Verlander of the Astros threw a pitch 100 miles per hour. How many seconds did it take to get to home plate. The plate is
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It will take 0.4 seconds to get to the home plate.

Given:

The speed of the pitch thrown by Justin is 100 miles per hour

The distance of home plate from the pitching rubber is 60.5 feet

To find:

The time taken by a pitch to reach the home plate

Solution:

The distance home plate from the pitching rubber = d = 60.5 feet

1 mile = 5280 feet\\1 foot=\frac{1}{5280} mile\\60.5 feet=60.5 \times \frac{1}{5280} mile=\frac{60.5}{5280}miles

The speed of pitch thrown by Justin = s = 100 miles/hr

The time taken by a pitch to reach the home plate = t =?

The speed of the moving object is given by dividing the distance covered from the time taken to cover that distance.

Speed=\frac{Distance}{Time}\\s=\frac{d}{t}\\100 miles/hr=\frac{\frac{60.5}{5280}miles}{t}\\t=\frac{60.5}{5280}miles\times \frac{1}{100 miles/hr}\\= 0.000114583 hr

In an hour there are 3600 seconds, then in 0.000114583 hours will be:

1 hour=3600 seconds\\=0.000114583 \times 3600=0.4124988 s\approx 0.4 s

It will take 0.4 seconds to get to the home plate.

Learn more about conversions here:

brainly.com/question/24530464

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5 0
2 years ago
Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is pai
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Answer:

35x = 155-15

It will take 4 months.

Step-by-step explanation:

7 0
3 years ago
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A hot air balloon can hold up to 300 pounds of weight. The balloon's pilot weighs 140 pounds. How many 20-pound bags or sand can
VARVARA [1.3K]

Answer:

8 sand bags can be carried along.

Step-by-step explanation:

First you want to subtract 300-140. That subtracts the pilots weight giving you the maximum weight capacity left. (160) Then you want to divide 160 (the weight that can be carried) by 20 (the weight of the sand bags) after doing that you will get 8. And that is how i got 8 sand bags as my answer.

7 0
3 years ago
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For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).
Ivanshal [37]

Answer:

\displaystyle F(b + 3) = b^2 + 4b + 7

Step-by-step explanation:

We are given the function:

\displaystlye F(x) = x^2 - 2x + 4

And we want to find F(<em>b</em> + 3).

We can substitute:

\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4

Expand:

\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4

Rearrange:

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Combine like terms. Hence:

\displaystyle = b^2 +4b + 7

In conclusion:

\displaystyle F(b + 3) = b^2 + 4b + 7

6 0
3 years ago
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