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liberstina [14]
3 years ago
12

5(2x+7) - 3x = 7(x + 5) how many solutions does it have??

Mathematics
1 answer:
Ivan3 years ago
6 0

Answer:

Infinite real solutions

Step-by-step explanation:

5(2x+7) - 3x = 7(x+5)

lets expand

10x+35 - 3x = 7x + 35

combine like terms

7x = 7x -- i subtracted 35 on each side and combined 10x - 3x

we see that

7x = 7x

Therefore, there is infinite real solutions.

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Step-by-step explanation:

tan 0 = 1/ cot 0

so, tan 0=11/60,

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Identify all rational numbers from the list below. -17,0,81,4.31,√11,√49,2 1/9,-9/43,1.3939399939993
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saveliy_v [14]

5. Answer: see explanation

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

If the roots are m and 3m, then x = m and x = 3m

⇒ x - m = 0    and      x - 3m = 0

⇒ (x - m)(x - 3m) = 0

⇒ x² - 4mx + 3m² = 0

Since x² + px + q = 0   then  p = -4m   and q = 3m²

3p² = 3(-4m)²               16q = 16(3m²)

      = 3(16m²)                      = 48m²

      = 48m²

3p² = 48m² = 16q     ⇒           3p² = 16q

**********************************************************************************************

6. Answer: 8 or 18

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

The Area of the entire rectangle (A = L × w) is 12 × 10 = 120

The Area of the shaded region is 72, so the Area of the non-shaded region is 120 - 72 = 48.

There are two non-shaded triangles.

  • Bigger non-shaded Δ: L = 12-x, w = 10  ⇒ A = \dfrac{10(12-x)}{2}
  • Smaller non-shaded Δ: L = x, w = x ⇒ A=\dfrac{x(x)}{2}

Combine the Areas of both triangles and set it equal to the Area of the non-shaded region:

\dfrac{x(x)}{2}+\dfrac{10(12-x)}{2}=48\\\\\\\dfrac{x^2}{2}+\dfrac{120-10x}{2}=48\\\\\\\dfrac{x^2-10x+120}{2}=48\\\\\\x^2-10x+120=96\\\\x^2-10x+24=0\\\\(x-4)(x-6)=0\\\\x - 4 = 0\quad or\quad x-6=0\\x=4\qquad or\qquad x=6\\\\\text{Based on the image provided, it appears that the x-value will be the}\\\text{smallest of the two possible solutions (4), but both solutions are valid.}

Area of ΔBEF:

\text{when x = 4, A =}\ \dfrac{4(4)}{2}=\dfrac{16}{2}=8\\\\\\\text{when x = 6, A =}\ \dfrac{6(6)}{2}=\dfrac{36}{2}=18

5 0
3 years ago
Lina is packing to move to a new house. She has 561 items to transfer to the new house. 36 of the items are large items that wil
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Answer: See explanation

Step-by-step explanation:

Your question isn't complete but let me give different scenarios to help you solve.

Firstly, assuming we want to calculate the amount of items left after the large items are carried alone, this will be:

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Secondly, if we want to know the percentage of the large items that will be carried alone. This will be:

= 36/561 × 100.

= 6.42%

Thirdly, if you want to know the percentage of the items that will be left after the large ones have been carried alone. This will be:

= 100% - 6.42%

= 93.58%

5 0
3 years ago
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