Mathematics : asked on Averyruss9245

28.09.2021

Which equation is equivalent to 10+2(x−1)+7x=3x+1?

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09.07.2023, solved by verified expert

Mathematics, DAV Post Graduate College

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Answer is x = -7/6

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Which equation is equivalent to 10+2(x−1)+7x=3x+1?, №18009844, 28.09.2021 21:23

Which equation is equivalent to 10+2(x−1)+7x=3x+1?, №18009844, 28.09.2021 21:23

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Mathematics

Which equation is equivalent to 10+2(x−1)+7x=3x+1?

Step-by-step answer

P Answered by Specialist

Answer is x = -7/6

Step-by-step explanation:

please look at the image

Which equation is equivalent to 10+2(x−1)+7x=3x+1?

Which equation is equivalent to 10+2(x−1)+7x=3x+1?

Mathematics

1. which of the following is the factored form of the expression: 3x2 – 4x? a. x(3x - 4) b. x(3 – 4x) c. (3x -1) (x -1) d. (3x +1)(x -1) 2. which is a completely factored form of the expression: x2 + 21x +20 ? a. (x + 5)(x + 4) b. (x + 10)(x + 2) c. (x + 20)(x + 1) d. (x + 21)(x - 1) 3. which expression is factored form of 4x2 -9? a. 2(x - 3)2 b. (x - 3)2 c. 2(x + 3)(x - 3) d. (2x + 3)(2x - 3) 4. below are factored forms of the expression: 12x3 – 36x2 . which expression has the greatest common factor as the first term? a. 3x (4x2 – 12x) b. 4x2(3x

Step-by-step answer

P Answered by PhD

34

1. 3x^2-4x=x(3x-4) - A.

2. x^2 + 21x +20=(x-x_1)(x-x_2)

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ \sqrt{D}=19,\\ \\x_1=\dfrac{-21-19}{2}=-20, \ x_2=\dfrac{-21+19}{2}=-1$ ,

then

x^2 + 21x +20=(x+20)(x+1) - C.

3. 4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3) - D.

4. 12x^3-36x^2=12x^2(x-3) - C.

5. x^2 -5x -6=(x-x_1)(x-x_2)

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ \sqrt{D}=7,\\ \\x_1=\dfrac{5-7}{2}=-1, \ x_2=\dfrac{5+7}{2}=6$ ,

then

x^2 -5x -6=(x-6)(x+1) and the width of the lawn is x-6 - A.

6. Since x^2 + 5x -24=(x+8)(x-3) the length and width are x+8 and x-3 - A.

7. 32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z) - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \\24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \\ 46xy=2\cdot 23\cdot x\cdot y$ .

So the greatest common divisor is $2\cdot x=2x$ - D.

9. 2x^2 -3x -35=2(x-x_1)(x-x_2)

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ \sqrt{D}=17,\\ \\x_1=\dfrac{3-17}{2\cdot 2}=-\dfrac{7}{2}, \ x_2=\dfrac{3+17}{2\cdot 2}=5$ ,

then

$2x^2 -3x -35=2(x+\dfrac{7}{2})(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+\dfrac{5}{2})(x+\dfrac{4}{3})=(6x+15)(3x+4)$ , the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. 30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2) .

14. x^2 -16=(x-4)(x+4) - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$ , the length of one side is 9p+5.

Mathematics

1. which of the following is the factored form of the expression: 3x2 – 4x? a. x(3x - 4) b. x(3 – 4x) c. (3x -1) (x -1) d. (3x +1)(x -1) 2. which is a completely factored form of the expression: x2 + 21x +20 ? a. (x + 5)(x + 4) b. (x + 10)(x + 2) c. (x + 20)(x + 1) d. (x + 21)(x - 1) 3. which expression is factored form of 4x2 -9? a. 2(x - 3)2 b. (x - 3)2 c. 2(x + 3)(x - 3) d. (2x + 3)(2x - 3) 4. below are factored forms of the expression: 12x3 – 36x2 . which expression has the greatest common factor as the first term? a. 3x (4x2 – 12x) b. 4x2(3x

Step-by-step answer

P Answered by PhD

34

1. 3x^2-4x=x(3x-4) - A.

2. x^2 + 21x +20=(x-x_1)(x-x_2)

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ \sqrt{D}=19,\\ \\x_1=\dfrac{-21-19}{2}=-20, \ x_2=\dfrac{-21+19}{2}=-1$ ,

then

x^2 + 21x +20=(x+20)(x+1) - C.

3. 4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3) - D.

4. 12x^3-36x^2=12x^2(x-3) - C.

5. x^2 -5x -6=(x-x_1)(x-x_2)

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ \sqrt{D}=7,\\ \\x_1=\dfrac{5-7}{2}=-1, \ x_2=\dfrac{5+7}{2}=6$ ,

then

x^2 -5x -6=(x-6)(x+1) and the width of the lawn is x-6 - A.

6. Since x^2 + 5x -24=(x+8)(x-3) the length and width are x+8 and x-3 - A.

7. 32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z) - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \\24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \\ 46xy=2\cdot 23\cdot x\cdot y$ .

So the greatest common divisor is $2\cdot x=2x$ - D.

9. 2x^2 -3x -35=2(x-x_1)(x-x_2)

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ \sqrt{D}=17,\\ \\x_1=\dfrac{3-17}{2\cdot 2}=-\dfrac{7}{2}, \ x_2=\dfrac{3+17}{2\cdot 2}=5$ ,

then

$2x^2 -3x -35=2(x+\dfrac{7}{2})(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+\dfrac{5}{2})(x+\dfrac{4}{3})=(6x+15)(3x+4)$ , the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. 30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2) .

14. x^2 -16=(x-4)(x+4) - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$ , the length of one side is 9p+5.

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics

In a parking lot, for every 8 cars there are 7 trucks. What is the ratio of cars to trucks? A)7 : 8 B)8 : 7 C)8 : 15 D)15 : 8

Step-by-step answer

P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics

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P Answered by PhD

The answer is in the image

The answer is in the image

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The answer is in the image

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The answer is in the image

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