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3 years ago

Slope is 1/2 and (4,6) is on the line

Mathematics

2 answers:

AleksandrR [38]3 years ago

6 0

Answer:

y-6=1/2(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-6=1/2(x-4)

bearhunter [10]3 years ago

5 0

Answer: y=1/2x+4

To solve this, we will use point-slope form.
Let’s write out the equation for
this: y-y1=m(x-x1)

The y1 and x1 are for the point, and the m is for the slope. Let’s substitute this into the equation and solve

y-6=1/2(x-4)

*distribute*

y-6=1/2x-2

*add 6 on both sides*

y=1/2x+4

Hope this helps comment below for more questions :)

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Step-by-step explanation:

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Marta_Voda [28]

Answer:

$3x+5 < n < x-1$

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the Triangle Inequality Theorem

1) $(2x+2)+(x+3) > n$

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3 years ago

Find the volume of the shaded figure by subtracting the smaller volume from the larger

alekssr [168]

Answer:

a. $9a^3 - 9ab^2$

b. $9a(a^2 - b^2)$

Step-by-step explanation:

$Volume = l*w*h$

$Volume_{smaller} = l*w*h$

Where, $l = 9a, w = b, h = b$

$Volume_{smaller} = 9a*b*b = 9ab^2$

$Volume_{larger} = l*w*h$

Where, $l = 9a, w = a, h = a$

$Volume_{smaller} = 9a*a*a = 9a^3$

Volume of the shaded figure = $9a^3 - 9ab^2$

b. $9a^3 - 9ab^2$ expressed in factored form:

Look for the term that is common to 9a³ and 9ab², then take outside the parenthesis.

$9a^3 - 9ab^2 = 9a(a^2 - b^2)$

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3 years ago

Please Help Write a system of linear Inequalities to represent each graph.

docker41 [41]

Answer:

$\left\{\begin{array}{l}5x-y-7\le 0\\2x+3y-9\ge 0\end{array}\right.$

Step-by-step explanation:

1. Blue region. The boundary blue line passes through the points (0,-7) and (3,8), then its equation is

$\dfrac{x-0}{3-0}=\dfrac{y+7}{8+7},\\ \\15x=3(y+7),\\ \\5x=y+7,\\ \\5x-y-7=0.$

This line is solid, so the sign for the inequality should be with the notion "or equal to".

From the diagram you can see that the origin belongs to the blue region, then its coordinates satisfy the inequality. Thus,

$5x-y-7\le 0.$

2. Green region. The boundary green line passes through the points (6,-1) and (0,3), then its equation is

$\dfrac{x-0}{6-0}=\dfrac{y-3}{-1-3},\\ \\-4x=6(y-3),\\ \\-2x=3y-9,\\ \\2x+3y-9=0.$

This line is solid, so the sign for the inequality also should be with the notion "or equal to".

From the diagram you can see that the origin doesn't belong to the blue region, then its coordinates satisfy the inequality. Thus,

$2x+3y-9\ge 0.$

3. The system of linear inequalities that represents these graphs is

$\left\{\begin{array}{l}5x-y-7\le 0\\2x+3y-9\ge 0\end{array}\right.$

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