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il63 [147K]
3 years ago
9

Yolanda and yoko ran in a 100-yd dash. when yolanda crossed the finish line, yoko was 10 yd behind her. the girls then repeaed t

he race, with yolanda starting 10 yd behind the starting line. if each girl ran the same rate as before, who won the race? by how many yards?
Mathematics
1 answer:
aksik [14]3 years ago
3 0
Yolanda won, she won by 1 yard
I hope this helps.
YOU'RE WELCOME :D
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According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
HACTEHA [7]

Answer:

Option (1)

Step-by-step explanation:

Fundamental theorem of Algebra states degree of the polynomial defines the number of roots of the polynomial.

8 roots means degree of the polynomial = 8

Option (1)

f(x) = (3x² - 4x - 5)(2x⁶- 5)

When we multiply (3x²) and (2x⁶),

(3x²)(2x⁶) = 6x⁸

Therefore, degree of the polynomial = 8

And number of roots = 8

Option (2)

f(x) = (3x⁴ + 2x)⁴

By solving the expression,

Leading term of the polynomial = (3x⁴)⁴

                                                     = 81x¹⁶

Therefore, degree of the polynomial = 16

And number of roots = 16

Option (3)

f(x) = (4x² - 7)³

Leading term of the polynomial = (4x²)³

                                                    = 64x⁶

Degree of the polynomial = 6

Number of roots = 6

Option (4)

f(x) = (6x⁸ - 4x⁵ - 1)(3x² - 4)

By simplifying the expression,

Leading term of the polynomial = (6x⁸)(3x²)

                                                     = 18x¹⁰

Degree of the polynomial = 10

Therefore, number of roots = 10

3 0
3 years ago
Pls help xDDDDD thx!
prohojiy [21]

Answer:

-25

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
DUE IN THE NEXT 10 MINUTES, PLEASE HELP! Describe the strategy used to find an equation of a line, given its slope and a point o
Llana [10]
Y=mx+b helps to find slope of a line.
B is where it starts on the y axis.
m is the slope.
3 0
3 years ago
PLZ HELP PLZ PLZ PLZ
Temka [501]

Answer:

The top option is false.

Step-by-step explanation:

Both segments have a <em>rate</em><em> </em><em>of</em><em> </em><em>change</em><em> </em>[<em>slope</em>] of ⅔. It just that their ratios have unique qualities:

\frac{2}{3} = \frac{4}{6}

Greatest Common Factor: 2

___ ___

<em>BC</em><em> </em>is at a 4⁄6 slope, and <em>AB</em><em> </em>is at a ⅔ slope. Although their quantities are unique, they have the exact same value.

I am joyous to assist you anytime.

3 0
3 years ago
The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

4 0
3 years ago
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