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disa [49]
3 years ago
10

Solve the equation 3(x+4.5x ) = 36. Explain your reasoning THOROUGHLY.

Mathematics
1 answer:
Vesna [10]3 years ago
3 0

Answer:

x \approx 2.18

Step-by-step explanation:

3(x+4.5x)=36

we can use the distributive property and get

3(x)+3(4.5x)=36\\\\3x+13.5x=36\\\\

and we can add like terms

(3+13.5)x=36\\\\16.5x=36

and know we divide both sides by 16.5

16.5x*(\frac{1}{16.5})=36*(\frac{1}{16.5})\\\\x=\frac{36}{16.5}

and doing the dvision we get that

x\approx 2.18

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A dog pen in the shape of a rectangle is to be built using one wall of a house as a side. If 132 feet
diamong [38]
This is a very poorly written question. im assuming the house wall is at least 130 ft since there is no information given about it.

each set of side lengths has three elements, the long side and the two short sides. we're asked to list all whole number possibilities so start anywhere, the two short sides being 1ft
(1 1 130). the long side has to be the difference of 132 and the length of both short sides.

the area is one of the short sides times the ling side, in the first case 1*130=130 sqft

continuing the list

(2 2 128) area=256
(3 3 126) area=378
(4 4 124) area=496
(5 5 122) area=610

the short sides increase by 1, the long side decreases by 2, the area gets bigger, but the difference between the areas are 4 less each time. dividing the first difference, 122, by 4 will give us a number to make a better guess from.

122÷4=30.5

so lets try

(30 30 72) area=2160

lets try 31 and see if that gives a smaller area

(31 31 70) area = 2170

(32 32 68) area =2176

(33 33 66) area = 2178

(34 34 64) area = 2176

so the area is decreasing now which means the maximum area is found when thw long side is 66 feet and the short sides are 33 feet.

as far as listing all possibilities, you see the pattern i started, i leave the rest to you
6 0
3 years ago
Which of the following number is a rational number?<br> a) 1/4<br> b) 4π<br> c) √3<br> d) √45
lawyer [7]

Answer:

1/4

Step-by-step explanation:

All fractions, both positive and negative, are rational numbers.

5 0
3 years ago
What is the end behavior of the function f(x) = 3x4−x3 + 2x2 + 4x + 5? (1 point)
ELEN [110]

Answer: both the left and right sides go to +∞

<u>Step-by-step explanation:</u>

End behavior can be determined by two things:

  • Sign of the leading coefficient
  • Degree of the function

<u>Sign of leading coefficient</u>:

positive: right side goes to +∞

negative: right side goes to -∞

⇒ Leading coefficient of this function is 3 so the right side goes to +∞

<u>Degree (exponent of leading coefficient)</u>:

even: both the left and right sides point in the SAME direction

odd: the left and right sides point in OPPOSITE directions

⇒ Degree of this function is 4 so the left side will point in the same direction as the right side.

8 0
3 years ago
Change the repeating decimal to a fraction:<br> 0.376376376...
taurus [48]

Answer:

Answer is 3/4

Step-by-step explanation:

3 0
3 years ago
The sides of a triangle are in the ratio 3:4:5. What is the length of each side if the perimeter of the
Brut [27]

Answer:

A. 22.5 cm, 30 cm, and 37.5 cm

Step-by-step explanation:

If three sides of a triangle are in the ratio 3:4:5, then the lengths of the sides are 3x cm, 4x cm and 5x cm.

The preimeter of the triangle is the sum of the lengths of all sides, thus

3x+4x+5x=90\\ \\12x=90\\ \\x=\dfrac{90}{12}=\dfrac{30}{4}=7.5\ cm

So, the lengths of the triangle's sides are

3x=3\cdot 7.5=22.5\ cm\\ \\4x=4\cdot 7.5=30\ cm\\ \\5x=5\cdot 7.5=37.5\ cm

6 0
3 years ago
Read 2 more answers
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