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erastova [34]
2 years ago
12

QUESTIONS IN Picture TYSM Guys

Mathematics
1 answer:
babymother [125]2 years ago
5 0

Option E:

The value of m that makes the inequality true is 5.

Solution:

Given inequality is 3m + 10 < 30.

Let us first simplify the expression.

3m + 10 < 30

Subtract 10 from both side of the equation.

3m < 20 – – – – (1)

<u>To find the value of m that makes the inequality true:</u>

Option A: 20

Substitute m = 20 in (1),

⇒ 3(20) < 20

⇒ 60 < 20

It is not true because 60 is greater than 20.

Option B: 30

Substitute m = 30 in (1),

⇒ 3(30) < 20

⇒ 90 < 20

It is not true because 90 is greater than 20.

Option C: 8

Substitute m = 8 in (1),

⇒ 3(8) < 20

⇒ 24 < 20

It is not true because 24 is greater than 20.

Option D: 10

Substitute m = 10 in (1),

⇒ 3(30) < 20

⇒ 90 < 20

It is not true because 90 is greater than 20.

Option E: 5

Substitute m = 5 in (1),

⇒ 3(5) < 20

⇒ 15 < 20

It is true because 15 is less than 20.

Hence the value of m that makes the inequality true is 5.

Option E is the correct answer.

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Solution:

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Solve it using mid-point formula:

$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right  )

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Using this midpoint find the missing coordinate.

$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right  )

Let the missing coordinates by x and y.

Here x_1=0, y_1=0, x_2=x,  y_2=y

$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right  )

$\left( \frac{m+h}{2}, \frac{n}{2}\right  )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right  )

$\left( \frac{m+h}{2}, \frac{n}{2}\right  )=\left( \frac{x}{2}, \frac{y}{2}\right  )

Now equate the x-coordinates and y-coordinates.

$ \frac{m+h}{2}=\frac{x}{2}, \  \  \  \frac{n}{2} =  \frac{y}{2}

Multiply by 2 on both sides of the equation, we get

m + h = x, n = y

x = m + h and y = n

Hence the missing coordinates of the parallelogram is (m + h, n).

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