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3 years ago

Given: 3x+7+2(4x+1) = 3(x-1) -4 prove: x=-2

Mathematics

1 answer:

denis23 [38]3 years ago

7 0

Answer:

x = -2, proven below.

Step-by-step explanation:

3x + 7 + 2(4x+1) = 3(x-1) - 4

3x + 7 + 8x + 2 = 3x - 3 - 4

9 + 11x = 3x - 7

16 + 11x = 3x

16 = - 8x

-2 = x

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If a/b = 4/3 and b/c = 2/3, what is a,b, and c?

kaheart [24]

Answer:

Step-by-step explanation:

$\frac{a}{b} = \frac{4}{3}$

$\frac{b}{c} = \frac{2}{3}$

to give b from both equation the same value

$\frac{a}{b} = \frac{4}{3} \times \frac{2}{2} = \frac{8}{6}$

$\frac{b}{c} = \frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$

a:b:c = 8:6:9

a = 8

b = 6

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3 years ago

1.<br> Explain why the diagram shows that 6 (3 + 4) = 6*3 + 6*4

anygoal [31]

Answer:

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3 years ago

A fence must be built to enclose a rectangular area of 45 comma 000 ftsquared. Fencing material costs $ 3 per foot for the two s

Tatiana [17]

Answer:

150 feet by 300 feet.

Step-by-step explanation:

The fence is to enclose a rectangular area of 45,000 ft squared.

If the dimensions of the rectangle are x and y

Area of a rectangle = xy

xy=45000
$x=\frac{45000}{y}$

Perimeter of the Rectangle =2x+2y

Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides.

Cost of Fencing, C=$(6*2x+3*2y)=$(12x+6y)

Substitute $x=\frac{45000}{y}$ into the Cost to get C(y)

C=12x+6y

$C(y)=12(\frac{45000}{y})+6y\\C(y)=\frac{540000+6y^2}{y}$

The value at which the cost is least expensive is at the minimum point of C(y), when the derivative is zero.

$C^{'}(y)=\dfrac{6y^2-540000}{y^2}$

$\dfrac{6y^2-540000}{y^2}=0\\6y^2-540000=0\\6y^2=540000\\y^2=\frac{540000}{6} =90000\\y=\sqrt{90000}=300$

Recall,

$x=\frac{45000}{y}=\frac{45000}{300}=150$

Since x=150, y=300

The dimensions that will be least expensive to build is 150 feet by 300 feet.

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2 years ago

B 5 3 a 4 What is the length of the hypotenuse of this triangle? 3 units 5 units 4 units

Lunna [17]

Answer:

5 units

Step-by-step explanation:

The hypotenuse is always the longest segment on a triangle. If the lengths of the sides of this triangle are 3 units, 4 units, and 5 units, the hypotenuse will be 5 units. You can use the pythagorean theorem to check.

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If you substitute the variable with the lengths of the legs in ascending order, you will get 3^2+4^2=5^2. Simplifying the equation, you will get 9+16=25, or 25=25. Thus, proving the equation.

Hope this helped! :)

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3 years ago

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Lesechka [4]

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3 years ago

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