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3 years ago

Express the solution graphically of – }(2x + 1) < 3.

Mathematics

1 answer:

Anit [1.1K]3 years ago

7 0

Answer:

The third one counting from the top.

Step-by-step explanation:

We have the inequality:

(-1/3)*(2x + 1) < 3

The first thing we need to do is isolate x on one side of the inequality.

First we can by -3 in both sides of the inequality, and remember, because we are multiplying by a negative number, the inequality sign changes its direction:

(-3)*(-1/3)*(2x + 1) > 3*(-3)

(2x + 1) > -9

Now we can subtract 1 in both sides:

2*x + 1 - 1 > -9 - 1

2*x > -10

Now we can divide by 2 in both sides:

2*x/2 > -10/2

x > -5

Then we should see a number line such that all the points at the right of -5 are colored.

The correct option is the third one, counting from the top.

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Andy has 31 coins made up of quarters and half dollars, and their total value is $11.00. How many quarters does he have?

charle [14.2K]

Answer:

Step-by-step explanation:

This situation has two unknowns - the total number of half dollars and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

h+q=31 is an equation representing the total number of coins
0.50h+0.25q=11 is an equation representing the total value in money based on the number of coin. 0.50 and 0.25 come from the value of a half dollar and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get h=31-q. We now substitute this for h in the second equation.

0.50(31-q)+0.25q=11

15.5-0.50q+0.25q=11

15.5-0.25q=11

After simplifying, we subtract 15.5 across and divide by the coefficient of q.

-0.25q=-4.5

q=4

We now know of the 31 coins that 4 are quarters.

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4 years ago

Given right triangle ABC what is the value of tan(A)

Katarina [22]

Answer:

Step-by-step explanation:

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2 years ago

Can someone help me with # 5

Flauer [41]

Being in love/caring for someone clouds your judgement causing you to overlook their faults. however, once the "rose colored glasses" come off you start to recognise where they were wrong.

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3 years ago

Trevor and Marissa sell T-shirts at the craft fair Marisa has six fewer T-shirts then Trevor and together they have a total of 2

avanturin [10]

M + t = 26
m = t - 6

t - 6 + t = 26
2t - 6 = 26
2t = 26 + 6
2t = 32
t = 32/2
t = 16 <== Trevor has 16

m = t - 6
m = 16 - 6
m = 10...and Marissa has 10

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3 years ago

Will give brainliest! 20 Points! Hi! Some help with these problems would be great thank you!

erica [24]

Answer:

Question 1:

Draw a line that crosses the largest number of dots. Then use the line to check the best prediction of the number of baseballs that will be used if 275 pitches are thrown.

Question 2:

A). y = 1.2x - 6

Question 3:

J). y = $\frac{9}{4}x - 81$

Question 4:

F). f(n) = -3n + 24 *Although it doesn't work when f(n) = 6 and n = 6*

Step-by-step explanation:

Question 2:

The line passes throught point (5, 0) and is parallel to the line whose equation is y = 1.2x + 3.8

For parallel lines, their values of slope is the same.

So our line, that passes through point (5, 0), also has a slope of 1.2

Taking another point (x, y) on our line;

Slope = change in y ÷ change in x

1.2 = $\frac{y - 0}{x - 5}$

y = 1.2x - 1.2(5)

y = 1.2x - 6

Question 3:

The line passes x-axis at point (36, 0)

The line is perpendicular to another line whose equation is y = - $\frac{4}{9}x$ + 5

For perpendicular lines, the product of their slopes = -1

Let's say the slope of our unknown line is a ;

Given: The slope of our second line is -4/9

So,

a × -4/9 = -1

a = -1 × -9/4 = 9/4

Taking another point (x, y) on our unknown line;

Slope = change in y ÷ change in x

9/4 = $\frac{y - 0}{x - 36}$

Cross-multiplying that you get;

y = $\frac{9}{4}x - 81$

Question 4:

The function that model that situation is f(n) = -3n + 24 though it doesn't work when f(n) = 6 and n = 6

3 0

4 years ago

Read 2 more answers