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3 years ago

5x/8 ≥ 30, solve the inequality

2 answers:

7 0

$\frac{5x}{8} \geq 30 \\ \\ 5x \geq 30 \times 8 \\ \\ 5x \geq 240 \\ \\ x \geq \frac{240}{5} \\ \\ x \geq 48 \\ \\$

The answer is: x ≥ 48

I am Lyosha [343]3 years ago

3 0

Ok. the first thing we have to do is isolate the variable.

to undo the division we can multiply the 8 on both sides

5x/8 ≥30
×8 ×8
5x≥240

then divide to undo the multiplication

5x≥30
--- ---
5 5
x≥48

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Write an equivalent expression -3 + 2/3y - 4 - 1/3y

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Answer:

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ie -7+1/3y

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Step-by-step explanation:

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2 years ago

5000 is 1/10 of what

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2 years ago

Explain proportionality to me 7th grade math

kari74 [83]

If two quantities a and b are directly proportional to one another, then both a and b change in the same direction.

For example, if the amount/volume of coffee I have in a cup is directly proportional to the total volume of the cup, then the larger the cup gets, the more coffee I can fill it with. On the other hand, if the cup gets smaller, the amount of coffee it can hold also gets smaller.

Both a and b don't necessarily change at the same rate, though, which means one of these needs to get appropriately scaled by some factor k, so that

a = kb

Continuing the coffee example: Suppose I only fill my cup halfway. If the total volume of the cup is a, then the amount of coffee I pour in is b = 1/2 a. So the relationship of these two quantities is governed by the equation,

a = 2b

and in this case, k = 2.

If instead a and b are inversely proportional, this means as one quantity changes, the other changes in the opposite direction.

Suppose I have two cups that I use for coffee that can both hold the same amount k if they are filled completely, but one cup is taller than the other. In order for both cups to be able to hold the same volume of coffee, the taller cup must have a thinner profile.

The cups are cylindrical, so that their volumes are equal to the products of the area of their base a and their height b. If one cup is twice as tall as the other, then for the smaller cup we could have

ab = k

and for the taller one,

a (2b) = k

But in order to get the same volume, the quantity a for the shorter cup must be cut in half to preserve equality:

(1/2 a) (2b) = ab = k

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3 years ago

Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also

Anna35 [415]

The linear equation B. y = -x +7.5 best describes the given model. The mood rating for a student that spent 5.5 hours online would be 2.

Step-by-step explanation:

Step 1; We plot the points that fall on the line and that lie on an exact x or y coordinate. The following 4 points are plotted (0.5, 7), (2, 5.5), (2.5, 5) and (3.5, 4). We substitute the values of x in the given equations to see which best describes the model.

Step 2; When y = x + 7.5, we get the coordinates as (0.5, 8), (2, 9.5), (2.5, 10) and (3.5, 11).

When y = -x + 7.5, the coordinates are (0.5, 7), (2, 5.5), (2.5, 5) and (3.5, 4).

When y = $\frac{-1x}{2}$ + 7.5, the coordinates are (0.5, 7.25), (2, 6.5), (2.5, 6.25) and (3.5, 5.75).

So equation 2 has the closest values to the actaul graph.

Step 3; By substituting x = 5.5, y = -(5.5) + 7.5 = 7.5 - 5.5 = 2.

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3 years ago

Bob thought of an even and odd number, multiplies the numbers together, added 6, divided by 5, and subtracted 3 to give an answe

Marina CMI [18]

Answer:

Step-by-step explanation:

Working backward, we can find Bob's initial product.

We subtracted 3 to get 1, so we had 4.

We divided by 5 to get 4, so we had 20.

We added 6 to get 20, so we had 14

After Bob multiplied the two numbers together, he had 14. We know that 14 is the product of 2 and 7. The odd number is 7.

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3 years ago