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marshall27 [118]
3 years ago
5

Write the number and the nature of the roots of the quadratic

Mathematics
1 answer:
schepotkina [342]3 years ago
3 0

Answer:

two unequal real roots

Step-by-step explanation:

35 - 5(4)(-3) simplifies to 35 + 60, or 95.

Because the discriminant is positive, the quadratic has two unequal real roots.

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\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{ope ns~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \stackrel{\textit{vertex}}{(3,-2)}~~ \begin{cases} h = 3\\ k = -2 \end{cases}\implies y=a(x-3)^2-2 \\\\\\ \stackrel{\textit{passes through}}{(5,-1)}~~ \begin{cases} x=5\\ y= -1 \end{cases}\implies -1=a(5-3)^2-2\implies 1=a(2)^2 \\\\\\ 1=4a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}(x-3)^2-2}

5 0
3 years ago
Read 2 more answers
The sum of two numbers is 14. The first number is 2/5 of the second number. What are the numbers?​
zlopas [31]

Answer:

4 and 10

Step-by-step explanation:

To solve this problem, we need to find all the numbers between 1 and 13 that have a sum of 14. The list is shown below:

1 + 13,   2 + 12,   3 + 11,   4 + 10,   5 + 9,   6 + 8,   7 + 7

Now we must figure out which set of numbers include one number that is 2/5 of the value of the other. We can do that by turning the sets of numbers into fractions as shown below:

\frac{1}{13}\neq \frac{2}{5}

\frac{2}{12}\neq \frac{2}{5}

\frac{3}{11}\neq \frac{2}{5}

\frac{4}{10}= \frac{2}{5}    (answer)

\frac{5}{9}\neq \frac{2}{5}

\frac{6}{8}\neq \frac{2}{5}

\frac{7}{7}\neq \frac{2}{5}

8 0
3 years ago
The angles in this diagram are complementary. (4x)° (2x + 6°) What is the value of x?​
Alexeev081 [22]
Answer 1 I think I’m not sure
7 0
3 years ago
Can i get some help on this question?
Yakvenalex [24]
Divide both sides by 8.5 to get b on its own

68/8.5 = 8
So b = 8
7 0
2 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%2864%20%7Ba%7D%5E%7B6%7D%29%20%7B%7D%5E%7B2%7D%20%20%7D%20" id="TexFormul
Natalija [7]

Answer:

8a³ and the explaination in the photo

5 0
3 years ago
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