Find the missing terms in each arithmetic sequence

Mathematics

1 answer:

katrin [286]2 years ago

3 0

Answer:

9) 7, 18, 29, 40, 51, 62

10) 35, 29, 23, 17, 11, 5, -1

Step-by-step explanation:

9) The terms that are 5 apart differ by 55, so each term differs from the next by 55/5 = 11. Add 11 to each term to get the next one.

7, 18, 29, 40, 51, 62

10) The terms that are 6 apart differ by -36, so each term differs from the next by -36/6 = -6. Subtract 6 from each term to get the next one.

35, 29, 23, 17, 11, 5, -1

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Factorise 10x²+19x+6 Show working out please.

stepladder [879]

Answer:

(2x+3)(5x+2)

Step-by-step explanation:

10x²+19x+6

multiply to get 60

add to get 19

10x²+19x+6

(10x²+15x)(+4x+6)

factorise:

10x²+15x

5x(2x+3)

4x+6

2(2x+3)

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8 0

3 years ago

After the addition of an acid, a solution has a volume of 90 milliliters. The volume of the solution is 3 milliliters greater th

11111nata11111 [884]

Answer: $21.75\ milliliters$

Step-by-step explanation:

Let be "x" the original volume of the solution (in milliliters) before the acid was added and "y" the volume of the solution (in milliliters) after the addition of the acid.

Set up a system of equations:

$\left \{ {{x+y=90} \atop {y=3x+3}} \right.$

Applying the Substitution Method, you can substitute the second equation into the first equation and then solve for "x":

$x+y=90\\\\x+(3x+3)=90\\\\4x+3=90\\\\x=21.75$

6 0

3 years ago

Help me guys! 50 points!

timama [110]

Answer:

The volume of the irregular figure would be 144 $cm^3$ .

Step-by-step explanation:

If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is $l*w*h$ , where $l$ , $w$ , and $h$ , represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be 12 * 3 * 3 = 12 * 9 = 108 $cm^3$ , and the volume of the smaller rectangular prism would be 4 * 3 * 3 = 12 * 3 = 36 $cm^3$ . So the volume of the entire irregular figure would be 108 + 36 = 144 $cm^3$ .