Answer:3.008
Step-by-step explanation:
She can type 4,800 words in one hour.
Answer:
b. a unique real solution
Step-by-step explanation:
A quadratic equation ax² + bx + c = 0 ,
Has two distinct real roots,
If discriminant, ![D=b^2 - 4ac > 1](https://tex.z-dn.net/?f=D%3Db%5E2%20-%204ac%20%3E%201)
Has two equal real roots,
If D = 0,
Has two imaginary roots or no real roots,
if D < 1,
Here. the given qudratic equation,
![4x^2 + 32x + 64=0](https://tex.z-dn.net/?f=4x%5E2%20%2B%2032x%20%2B%2064%3D0)
By comparing,
a = 4, b = 32, c = 64,
![\implies D = 32^2 - 4\times 4\times 64 = 1024 - 1024 = 0](https://tex.z-dn.net/?f=%5Cimplies%20D%20%3D%2032%5E2%20-%204%5Ctimes%204%5Ctimes%2064%20%3D%201024%20-%201024%20%3D%200)
Hence, the equation has two equal real roots or a unique real solution.
i.e. OPTION 'b' is correct.
The sum of the given sequence is -6384.
<u>Step-by-step explanation:</u>
The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).
- The first term of the sequence = 14
- The last term of the sequence = -280
- The common difference ⇒ 14 - 8 = 6
<u>To find the number of terms in the sequence :</u>
The formula used is ![n = (\frac{a_{n}-a_{1}} {d})+1](https://tex.z-dn.net/?f=n%20%3D%20%28%5Cfrac%7Ba_%7Bn%7D-a_%7B1%7D%7D%20%7Bd%7D%29%2B1)
where,
- n is the number of terms.
is the late term which is -280.
is the first term which is 14.- d is the common difference which is 6.
Therefore, ![n =(\frac{-280-14}{6}) +1](https://tex.z-dn.net/?f=n%20%3D%28%5Cfrac%7B-280-14%7D%7B6%7D%29%20%2B1)
⇒ ![n =( \frac{-294}{6}) + 1](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cfrac%7B-294%7D%7B6%7D%29%20%2B%201)
⇒ ![n = -49 + 1](https://tex.z-dn.net/?f=n%20%3D%20-49%20%2B%201)
⇒ ![n = -48](https://tex.z-dn.net/?f=n%20%3D%20-48)
⇒ n = 48, since n cannot be negative.
∴ The number of terms, n = 48.
<u>To find the sum of the arithmetic progression :</u>
The formula used is ![S = \frac{n}{2}(a_{1} + a_{n} )](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28a_%7B1%7D%20%2B%20a_%7Bn%7D%20%29)
where,
- S is the sum of the sequence.
is the first term which is 14.
is the late term which is -280.
Therefore, ![S = \frac{48}{2}(14+ (-280))](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B48%7D%7B2%7D%2814%2B%20%28-280%29%29)
⇒ ![S = \frac{48}{2}(-266)](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B48%7D%7B2%7D%28-266%29)
⇒ ![S = 48 \times -133](https://tex.z-dn.net/?f=S%20%3D%2048%20%5Ctimes%20-133)
⇒ ![S = -6384](https://tex.z-dn.net/?f=S%20%3D%20-6384)
∴ The sum of the given sequence is -6384.
Answer:
24/6048 = 252
Step-by-step explanation:
brainlest plz
and why does she have so many beads