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2 years ago

Simplify the given equation.

Mathematics

1 answer:

levacccp [35]2 years ago

3 0

Answer:

Step-by-step explanation:

5x + 2(x-3) = -2(x - 1)

1. Distribute 2 through the parentheses:

5x + 2x - 6 = -2 (x - 1)

2. Distribute -2 through the parentheses:

5x + 2x - 6 = -2x + 2

3. Collect like terms:

7x - 6 = -2x + 2

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Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!

FromTheMoon [43]

Answer: $t\in [\dfrac{1}{4},2]$

Step-by-step explanation:

Given

Inequality is $4t^2\leq9t-2$

Taking variables one side

$\Rightarrow 4t^2-9t+2\leq0\\\Rightarrow 4t^2-8t-t+2\leq0\\\Rightarrow 4t(t-2)-1(t-2)\leq0\\\Rightarrow (4t-1)(t-2)\leq0$

Using wavy curve method

$t\in [\dfrac{1}{4},2]$

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2 years ago

the length of a rectangle is 8cm more than the width and its area is 172cm2 .find the width of the rectabgle

nikdorinn [45]

$l-the\ length\\l+8-the\ width\\A=172\ cm^2\\\\A=lengtf\cdot width\\\\subtitute\\\\l(l+8)=172\\\\l^2+8l=172\ \ \ |subtract\ 172\ from\ both\ sides\\\\l^2+8l-172=0\\a=1;\ b=8;\ c=-172\\\\\Delta=b^2-4ac\\\\\Delta=8^2-4\cdot1\cdot(-172)=64+688=752 > 0\\\\l_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ l_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{752}=\sqrt{16\cdot47}=4\sqrt{47}\\\\l_1=\dfrac{-8-4\sqrt{47}}{2\cdot1}=-4-2\sqrt{47} < 0\\\\l_2=\dfrac{-8+4\sqrt{47}}{2\cdot1}=-4+2\sqrt{47} > 0\\\\The\ width:l+8=-4+2\sqrt{47}+8=4+2\sqrt{47}\\\\Answer:\boxed{length=(2\sqrt{47}-4)cm;\ width=(4+2\sqrt{47})cm}$
$length\approx9.71cm;\ width\approx17.71cm$

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3 years ago

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3 years ago

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jonny [76]

Answer:

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3 years ago

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Amanda has at most $40 to spend on flowers. She wants to buy a pair of red rose flowers for $18 dollars and spend the rest on li

Mkey [24]

Answer:

x ≤ 2

Step-by-step explanation:

2 red rose cost $ 18

x flowers cost $ 11x

"At most " means ≤.

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11x ≤ 40 - 18

11x ≤ 22

x ≤ 2

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3 years ago