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Shkiper50 [21]
3 years ago
12

Suppose the equation of the axis of symmetry for a quadratic function is x = 3 and one of the x-intercepts is 8. What is the oth

er x-intercept?
Mathematics
1 answer:
soldi70 [24.7K]3 years ago
8 0

Answer:

-2

Step-by-step explanation:

The axis of symmetry divides the quadratic exactly in half. If one x-intercept is 8, then the other will be the same distance on the other side of it. 8 is 5 from 3 where the axis of symmetry is. So 3-5 = -2. -2 will be the other intercept.

You might be interested in
In one day, Ricardo hiked 2_ 2 3 times as far as Bernie and Chloe hiked before they ate lunch. How far did he hike?
umka21 [38]

Complete question :

Bernie and Chloe hiked the Tremont Trail to the end and back. Then they hiked the Wildflower trail to the end before stopping to eat lunch. Before Ricardo ate his lunch, he hiked 2 2/3 times as far as Bernie and Chloe. How far did he hike?

Required diagram is attached below

Answer:

25 miles

Step-by-step explanation:

Tremont Trail = 3 1/2 miles

Wildflower trail = 2 3/8 miles

Distance covered ; Tremont Trail and back : (3 1/2 * 2). = 7/2 * 2 = 14 /2 = 7 miles

Total distance covered by Bernie and Chloe before stopping for lunch /

(7 miles + 2 3/8 Miles) = 9 3/8 miles = 75/8 miles

Ricardo's distance = 2 2/3 * Bernie and Chloe's total distance

Ricardo's distance = 8/3 * 75/8 = 600 /24 = 25 miles

6 0
3 years ago
1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she fi
AleksAgata [21]

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x

The table is:

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table above we can see that Anna makes more stuffing than Jason.

c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100

We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)

For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100

D) The line pass through (10, 10) and (100, 40), hence:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}

3 0
3 years ago
The area of a triangular sign is 81ft2 if the base of the sign measures 18 what is the height of the sign
bagirrra123 [75]
The answer would be 9. Hope that helped!
4 0
3 years ago
What is the area of the circle if DF=20 in.
crimeas [40]
We know that

DF is the diameter of the circle
so
radius r=DF/2----->20/2-----> r=10 in

area of the circle=pi*r²------> pi*10²-----> 100*pi in²-----> 314 in²

the answer is

100*pi in² or 314 in²
4 0
3 years ago
Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.
Aleks [24]

Answer:

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

Step-by-step explanation:

The actual Series is::

\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}

The method we are going to use is comparison method:

According to comparison method, we have:

\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}

Now:

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty}  \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

\sum_{n=1}^{inf}\frac{1}{n^p}

if p>1 then series converges. In oue case we have:

\sum_{n=1}^{inf}b_n=\frac{1}{n^4}

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

5 0
3 years ago
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