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2 years ago

Item 2 Simplify the linear expression. −53a+18−16a−12 Enter your answer as simplified fractions in the boxes.

Mathematics

2 answers:

marissa [1.9K]2 years ago

8 0

Answer:

- 11/6a - 3/8

Step-by-step explanation: trust

iogann1982 [59]2 years ago

3 0

Answer:

a=2/23

Step-by-step explanation:

-53a-16a+18-12=0

-69a+6=0

-69a=-6

-69a/-69=-6/-69

a=2/23

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The coordinates of the endpoints of AB and CD are A(2,

Ratling [72]

Answer:

Option 1: CD is a perpendicular bisector of AB

Step-by-step explanation:

Let us find out the slopes of various line segments and the Distances and then we will draw the conclusions accordingly.

Formula to find slope

$m= \frac{y_2-y_1}{x_2-x_1}$

Formula to Find Distance between two points

$D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

mAB ( represents , Slope of AB )

1. $mAC= \frac{3-2}{2-5}=\frac{1}{-3}=-\frac{1}{3}$

2. $mBC=\frac{2-1}{5-8}=\frac{1}{-3}=-\frac{1}{3}$

3. $mCD=\frac{5-2}{6-5}=\frac{3}{1}=3$

4. $AC=\sqrt{(3-2)^2+(2-5)^2} =\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}$

5. $BC=\sqrt{(2-1)^2+(5-8)^2} =\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}$

mAC = mBC , and C is common point , hence these three are collinear points making a straight line whole slope is $-\frac{1}{3}$

$mAB=-\frac{1}{3}$

$mCD=3$

$mAB \times mCD = -\frac{1}{3} \times 3 = -1$

Hence CD ⊥ AB

Also

From Point 4 and point 5 above , we see that

AC = CB

Hence CD bisect AB at C, also CD ⊥ AB

There fore

CD is a perpendicular bisector of AB

Therefor option 1 is true

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3 years ago

<img src="https://tex.z-dn.net/?f=%20-%2020x%20-%205" id="TexFormula1" title=" - 20x - 5" alt=" - 20x - 5" align="absmiddle" cla

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3 years ago

An aluminum can is a right cylinder. Find the amount of paper needed for the can's label and the total

Rina8888 [55]

Answer:

Label: About 527.9 square centimeters

Aluminum: About 835.7 square centimeters

Step-by-step explanation:

Amount of paper needed for the label:

You can imagine taking off the label and unrolling it, forming a rectangle. The height of this rectangle will be the height of the cylinder, while the length of the rectangle will be the circumference of the cylinder. Therefore, the area of that rectangle will be $2\pi r h= 2 \cdot \pi \cdot 7 \cdot 12\approx 527.9$ .

Amount of aluminum needed for the can:

This time, you need to add in the top and bottom of the can as well, which each have area $\pi r^2$ . Together, they have area $2\pi r^2=2\cdot \pi \cdot 7^2\approx 307.9$ . Adding this to the area of the sides, you get a total of about 835.7 square centimeters.