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Whitepunk [10]
1 year ago
5

Hear is a diagram showing a mixture of red paint and green paint needed for 1 batch of a particular shade of brown

Mathematics
1 answer:
Lelechka [254]1 year ago
4 0

From the diagram above

mixtures of 3 cups of red paints and 2 cups of green paints for 1 batch

this means for every one batch of brown paint

you have 3 cups of red paints and 2 cups of green paints

for three batches

3 red cups + 3 red cups + 3 red cups = 9 reds cup

2 green cups + 2 green cups + 2 green cups = 6 greens cup

to produce three batches you will need the mixture of 9 red cups of paints and 6 green cups of paint

adding to the diagram you will have 6 more red cups and 4 more green cups

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Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.
laila [671]

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
  • if |a|< b then a<b or a>-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

6 0
3 years ago
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
Verdich [7]

Answer:

6x ≥ 3 + 4(2x - 1)

⇔ 6x ≥ 3 + 8x - 4        => remove the parentheses

⇔ 6x - 8x ≥ 3 - 4

⇔ -2x ≥ -1

⇔ 2x ≤ 1 (or 1 ≥ 2x)

⇔ x ≤ 1/2

⇔ x ≤ 0.5

The answer for the question should be:

1 ≥ 2x

6x ≥ 3 + 8x – 4

and the first graph.

6 0
3 years ago
Read 2 more answers
Somebody help me with this question!
dimulka [17.4K]

\frac{z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z}{z\cdot z}=\frac{z^7}{z^2}=z^{7-2}=\boxed{z^5}

7 0
3 years ago
Read 2 more answers
Urgentttt please❤️ Urgent
prisoha [69]

Answer: a = 110ᴼ

Step-by-step explanation:

The angles on each line of the figure add to equal 180ᴼ

180 - 70 = 110

a = 110ᴼ

b and 70ᴼ are vertical angles, so their measures are congruent.

b = 70ᴼ

180 - 70 = 110

c = 110ᴼ

3 0
3 years ago
Drag each number to the correct location on the equation. Not all numbers will be used.
sveticcg [70]

Answer:

The equation of the hypotenuse line is y = -3·x + 9

Therefore, the correct options are -3 and 9

Step-by-step explanation:

The question asks to fill the boxes

y = _ x + _

We note that the equation is that of a straight line of the form;

y = m·x + c

Where:

m = Slope of the straight line graph and

c = Y intercept, that is the y-coordinate of the point on the line where x = 0

From the graph, we find the slope as follows;

Slope = \frac{y_2 - y_1}{x_2 -x_1} = \frac{(-9) -0}{6-3} = -3

Therefore, m = -3

The y intercept is found by extending the hypotenuse line to the point where it touches the y axes that is at x = 0;

From the graph, it is observed that the line, when extended, touches the y axes at the point y = 9, therefore, c = 9

Hence we have, the equation of the hypotenuse line is y = -3·x + 9.

8 0
3 years ago
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