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strojnjashka [21]

3 years ago

5

6(2x-8)+3=15help me its multi-step equation

2 answers:

lubasha [3.4K]3 years ago

4 0

6(2x-8)+3=15
12x-48+3=15 Distribute the 6
12x-45=15 Add (-48) and (3)
12x=60 Add 45 to both sides
x=5 Divide both sides by 12

Vanyuwa [196]3 years ago

3 0

Distribute.
6 times 2x= 12x
6 times 8= 48
12x+48+3=15
12x+51=15
subtract 51 from both sides.
12x=-36
divide by 12 on each side
-3=x

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Paraphin [41]

The area of a shape is the amount of space a shape can occupy, while the perimeter is the sum of its lengths.

<em>The perimeter is </em> $18 + 3\sqrt 5 + 3\sqrt 2$ <em>units</em>
<em>The area of the sanctuary is 27 square units</em>

We have:

$A = (5,7)\\B=(8, 7)\\C=(8, 1)\\D=( 1, 1)\\E=( 1, 4)\\F= ( 5,4)$

<u>Perimeter</u>

See attachment for the layout of the sanctuary

$BC = \sqrt{(8 - 8)^2 + (7 - 1)^2} = 6$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

$FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3$

From the attachment, the sides are

<em>AB, BF, FC, CD, DE and EA</em>

Start by calculating the length of each side using the following distance formula:

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

So, we have:

$AB = \sqrt{(5 - 8)^2 + (7 - 7)^2} = 3$

$BF = \sqrt{(8 - 5)^2 + (7 -1)^2} = \sqrt{45} = 3\sqrt 5$

$FC = \sqrt{(8 - 5)^2 + (1 -4)^2} = \sqrt{18} = 3\sqrt 2$

$CD = \sqrt{(8 - 1)^2 + (1 - 1)^2} = 7$

$DE = \sqrt{(1 - 1)^2 + (1 - 4)^2} = 3$

$EA = \sqrt{(1 - 5)^2 + (4 -7)^2} = 5$

So, the perimeter (P) is:

$P = AB + BF + FC + CD + DE + EA$

$P = 3 + 3\sqrt 5 + 3\sqrt 2 + 7 + 3 + 5$

$P = 18 + 3\sqrt 5 + 3\sqrt 2$

<em>Hence, the perimeter is </em> $18 + 3\sqrt 5 + 3\sqrt 2$ <em>units</em>

<u />

<u>Area</u>

To calculate the area, we need to divide the sanctuary into three.

<em>Triangle ABF</em>
<em>Triangle EFA</em>
<em>Trapezium CDEF</em>

The area of ABF is:

$Area = \frac 12 \times AB \times FA$

Where:

$AB = 3$

$FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3$

$Area = \frac 12 \times 3 \times 3$

$Area = \frac 92$

The area of EFA is:

$Area = \frac 12 \times EF \times FA$

Where:

$FA = 3$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

So:

$Area = \frac 12 \times 4 \times 3$

$Area = 6$

The area of CDEF is:

$Area = \frac 12(CD + EF) \times DE$

Where

$CD = 7$

$EF = 4$

$DE = 3$

So, we have:

$Area = \frac 12 (7 + 4) \times 3$

$Area = \frac 12 \times 11 \times 3$

$Area = \frac {33}2$

So, the area of the sanctuary is:

$Area = \frac 92 + 6 + \frac {33}2$

$Area = \frac {9 +12 + 33}2$

$Area = \frac {54}2$

$Area = 27$

<em>Hence, the area of the sanctuary is 27 square units</em>

Read more about areas and perimeters at:

brainly.com/question/11957651

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3 years ago

Write an exponential expression: choose an odd number between

Ronch [10]

Chicken nuggets and fries please

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3 years ago

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A living room has a circular rug with a radius of 1 yard. What is the rug's circumference?

dedylja [7]

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3 0

2 years ago

please HELP MEEEEEE .A store owner wants to make a candy that sells for $1 per pound.he has 50 lb of sugar candies that cost $1.

serious [3.7K]

Answer:

50 pounds

Step-by-step explanation:

we can use the equation 60+80/100x=1(x+50)

we get 80/100 x because the gummy candies are 80 cents or 80/100x

we get 60 from multiplying 1.20$ x 50 = 60

solve:

60+80/100x = x+50

60 = x-80/100x+50

60-50 = 20/100x

10 = 20/100x

x= 10 x 100/20 = 10x5= 50 pounds

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2 years ago

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What is the standard form of the following equation?<br> y+3=1/4x

dimaraw [331]

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So it would be y = 1/4x - 3

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2 years ago