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1 year ago

Write the expression |x − 9| + |x − 6| without the absolute value symbols if x is in the given interval.

Mathematics

1 answer:

tangare [24]1 year ago

6 0

Recall the definition of absolute value.

$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$

Now,

$x$

and

$x$

so that

$|x-9| + |x-6| = (9-x) + (6 - x) = \boxed{15 - 2x}$

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3 years ago

Mr. Wang needs a total of 410 spoons for his son's birthday party. He currently has 278 spoonsIf has 12 spoons, what is the mini

Marina86 [1]

Answer:

Minimum amount of sets needed = 11 sets

Step-by-step explanation:

Total number of needed spoons = 410

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Amount needed to be bought = 132 spoons

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Therefore minimum amount of sets needed = 132/12 = 11 sets

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4 years ago

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sleet_krkn [62]

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3 years ago

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What clockwise rotation would result in the same figure

Mekhanik [1.2K]

Answer:

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Step-by-step explanation:

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3 years ago

Graph the line with a slope of 2/5 that goes through (3,1)

Triss [41]

Answer:

$y = \dfrac{2x}{5} - \dfrac{1}{5}$

Step-by-step explanation:

Given:

$\bullet \ \ \text{Slope of line:}\ \dfrac{2}{5} \\\\ \bullet \ \text{Passes through:} \ (3, 1)$

To determine the equation of the line, we will use point slope form.

<u>Formula of point slope form:</u>

→ y - y₁ = m(x - x₁)

Where "x₁" and "y₁" are the coordinates of the point and "m" is the slope.

Substitute the coordinates and the slope:

$:\implies y - 1 = \dfrac{2}{5} (x - 3)$

Simplify the R.H.S:

$:\implies y - 1 = \dfrac{2x}{5} - \dfrac{6}{5}$

Add 1 both sides:

$:\implies y - 1 + 1 = \dfrac{2x}{5} - \dfrac{6}{5} + 1$

Simplify the equation:

$:\implies y = \dfrac{2x}{5} - \dfrac{6}{5} + \dfrac{5}{5}$

$:\implies \boxed{y = \dfrac{2x}{5} - \dfrac{1}{5}}$

<u>Graphing the line on a coordinate plane:</u>

In this case, we are already given a point (3, 1). We can simply plot the y-intercept $[\bold{\frac{-1}{5} }]$ on the coordinate plane. Then, we can draw a straight line through both points. It is suggested that you use a ruler to do so.

Graph attached**

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3 years ago

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