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3 years ago

The solution to an inequality is 5≤x<9. What is the smallest value of x that will make the original inequality true?

Mathematics

1 answer:

Strike441 [17]3 years ago

7 0

Answer:

Step-by-step explanation:

It is given that the solution to an inequality is

$5\leq x$

It means the original inequality is true for any values of x which is greater than or equal to 5 and less than 9.

We need to find the smallest value of x that will make the original inequality true.

$5\leq x\text{ and }x$

Therefore, smallest value of x is 5 that will make the original inequality true.

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Beth buys 5 gallons of tea for a party. If each serving is 1 cup how kany servings will there be at the party

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Step-by-step explanation:

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3 years ago

Write an equivalent expression using distributive property and simplify for each question

Lana71 [14]

Answer:

Check explanations

Step-by-step explanation:

For all real numbers a,b, and c, the distributive property states that:

$a(b + c) = ab + ac$

For Part A, we have

$2x + 10x = x(2 + 10) = x(12) = 12x$

$2x + 10x = 2x(1 + 5) = 2x(6) = 12x$

For Part B, we have

-4(3x-10)+5(2-6x)=-4*3x--4*10+5*2-5*6x

This simplifies to:

-4(3x-10)+5(2-6x)=-12x+40+10-30x

-4(3x-10)+5(2-6x)=-12x-30x+40+10

-4(3x-10)+5(2-6x)=-42x+50

For the C part, we have:

$2(x - 4) + x = 2 \times x - 2 \times 4 + x$

$2(x - 4) + x = 2x - 8+ x$

$2(x - 4) + x = 3x - 8$

For Part D, we have:

$-3-7(3-4x)+8x = - 3 - 7 \times 3 - 7 \times - 4x + 8x$

We simplify to get:

$-3-7(3-4x)+8x = - 24+28x + 8x$

Simplify further to get:

$-3-7(3-4x)+8x =-24+36x$

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3 years ago

What is the first step in determining if 6 is a solution to 3 x = 18?

andreev551 [17]

Answer:

Step-by-step explanation:I think it's C :)

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3 years ago

Read 2 more answers

Adam started to run at a rate of 6 mph from city A towards city B, which is 18 miles away. Ten minutes later, Benjamin started t

amm1812

Answer:

<u>Benjamin's rate in mph was 6.44</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Rate or speed of Adam = 6 mph
Ten minutes later, Benjamin started to run from city B towards city A
Simultaneously, Caroline started to bicycle at a rate of 11 mph from city A towards city B

2. If Caroline caught up to Benjamin 50 minutes after passing Adam, what was Benjamin's rate in mph?

A. Let's calculate when Caroline caught up Adam:

Adam's rate = 6 mph

Caroline's rate = 11 mph

10 minutes = 1/6 of an hour

Distance covered by Adam when Caroline started to bike = 6 * 1/6 = 1 mile

t = Time it took Caroline to catch up to Adam

Therefore, we can solve for t, this way:

11t = 6t + 1

11t - 6t = 1

5t = 1

t = 1/5 of an hour

t = 12 minutes

Caroline passed Adam after biking 12 minutes, therefore she caught up to Benjamin 50 minutes later, or after 62 minutes.

B. Let's calculate the distance she covered after 62 minutes, this way:

62 minutes = 1 hour and 2 minutes or 1 2/60 or 1.03

Distance covered by Caroline = Time * rate

Replacing with the values we have:

Distance covered by Caroline = 1 2/60 * 11

Distance covered by Caroline = 11 11/30 or 11.37 miles

Let's recall the distance from city A to city B is 18 miles, therefore Benjamin covered 6.63 miles (18 - 11.37) when Caroline caught up to him

C. Finally let's calculate Benjamin's rate, this way:

Rate = Distance/Time

Replacing with the values we know:

Rate = 6.63/1.03

<u>Rate = 6.44 mph (rounding to the next hundredth)</u>

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3 years ago