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3 years ago

Find the missing terms in each arithmetic sequence

Mathematics

1 answer:

katrin [286]3 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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3 years ago

X squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?

cluponka [151]

Answer:

$x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}$ and $y=-1,\frac{1}{2}$

The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

Step-by-step explanation:

I'm assuming the system is $\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.$ :

$x^2+y^2=2$

$x^2+(2x^2-3)^2=2$

$x^2+(4x^4-12x^2+9)=2$

$x^2+4x^4-12x^2+9=2$

$4x^4-11x^2+9=2$

$4x^4-11x^2+7=0$

$x^4-11x^2+28=0$

$(x^2-7)(x^2-4)=0$

$(4x^2-7)(x^2-1)=0$

$4x^2-7=0$

$4x^2=7$

$x^2=\frac{7}{4}$

$x=\pm\sqrt{\frac{7}{4}}$

$x^2-1=0$

$x^2=1$

$x=\pm1$

$y=2x^2-3$

$y=2(\pm\sqrt{\frac{7}{4}})^2-3$

$y=2({\frac{7}{4}})-3$

$y=\frac{7}{2}-3$

$y=\frac{1}{2}$

$y=2x^2-3$

$y=2(\pm1)^2-3$

$y=2(1)-3$

$y=2-3$

$y=-1$

Therefore, $x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}$ and $y=-1,\frac{1}{2}$

The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

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2 years ago

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Nataly [62]

Answer:

What is this ?

Step-by-step explanation:

Sorry i can't answer it because i can't see it.

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2 years ago

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Seven different names were put into a hat. A name chosen 100 times. And the name Michael is chosen 9 times. What is experimental

iris [78.8K]

Answer:

Experimental probability = 9 / 100

Theoretical probability = 1/7

Step-by-step explanation:

The experimental probability of an event is written as :

P = number of times event occur / total number of trials

Experimental probability is based on the outcome of an experiment that has taken place.

Theoretical probability is based on expected outcome of an event.

P = number of expected or required outcomes / total possible outcomes

Experimental probability of choosing the name Michael is :

Number of times Michael is chosen / number of trials

Experimental probability = 9 / 100 = 0.09

Theoretical probability of choosing michael:

Number of names in hat = 7

Number of names called Michael in hat = required outcome = 1

P = 1 / 7

If the number of names in hat was different from 7, then the theoretical probability will change.

Also, if the number of times a name was chosen was different from 100, then number of trials will also change and hence, the experimental probability.

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3 years ago

Find the missing terms in each arithmetic sequence​

Find the missing terms in each arithmetic sequence