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cestrela7 [59]
4 years ago
9

Evaluate the arithmetic series described : 2+(-2)+(-6)+(-10)...,510

Mathematics
1 answer:
Alex_Xolod [135]4 years ago
4 0
It goes -4 each time.
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Find the y intercepts of 3x^2+24x-51. quadratic formula
julia-pushkina [17]
  • Quadratic Formula: x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} , with a = x^2 coefficient, b = x coefficient, and c = constant.

Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

y=3*0^2+24*0-51\\y=0+0-51\\y=-51

<u>Your y-intercept is (0,-51).</u>

Next, using our equation plug the appropriate values into the quadratic formula:

x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}

Next, solve the multiplications and exponent:

x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}

Next, solve the addition:

x=\frac{-24\pm \sqrt{1224}}{6}

Now, simplify the radical using the product rule of radicals as such:

  • Product Rule of Radicals: √ab = √a × √b

√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

x=\frac{-24\pm 6\sqrt{34}}{6}

Next, divide:

x=-4\pm \sqrt{34}

<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>

Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83

<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>

5 0
4 years ago
Janet can plant nine feet of carrots in 15 minutes while her daughter Amy can plant 17 feet of carrots in half an hour.
Lena [83]

Answer:

Step-by-step explanation:

In order to find who is more efficient at planting carrots, we want to put both ratios in terms of the same amount of time.

For simplicity, lets see how many carrots each can make in 1 hour.

Janet:\\9ft \: in \: 15 \:minutes

\frac{9ft}{15min} = \frac{xft}{60min}\\x = \frac{60*9}{15} = 36

Janet can plant 36 feet of carrots in one hour

Amy:\\\frac{17ft}{30min} = \frac{xft}{60min}\\x = \frac{17*60}{30} = 34

Amy can plant 34 feet of carrots in one hour

So, Janet can plant carrots more quickly

6 0
3 years ago
Please answer this correctly
MrMuchimi

Answer:

11 pt

Step-by-step explanation:

There are 2 pints in one quart. This means that there are 10 pints in 5 quarts, plus 1 would be 11.

3 0
3 years ago
Find the answer what is X?
Sati [7]
The answer to the question is C
6 0
3 years ago
Read 2 more answers
If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (–6, 8) must also be a
ch4aika [34]

Definition: A function is "even" when f(x) = f(−x) for all x.

Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis.

If point (6, 8) is one the points on the graph of f(x), then f(6)=8 and since function is even, you can state that f(-6)=f(6)=8. This means that point (-6,8) must also be a point on the graph. Geometrically it means that the output of a negative x-value and its opposite is the same.

Answer: correct choice is A.

5 0
3 years ago
Read 2 more answers
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