Subtract 8 + 7 i from 4 - 167.<br> O A. -4- 231<br> OB. 4- 23;<br> C. 4+91<br> OD. 4-111

Given that α and β are the roots of the quadratic equation <img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B6x-7%3Dp" id="Tex

siniylev [52]

Answer:

$\large \boxed{\sf \ \ \ p=-11 \ \ \ }$

Step-by-step explanation:

Hello,

$\alpha \text{ and } \beta \text{ are the roots of the following equation}$

$2x^2+6x-7=p$

It means that

$2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\$

And we know that

$\alpha= 2\cdot \beta$

So we got two equations

$2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\6\beta^2+6\beta =0\\\\\beta(\beta+1)=0\\\\ \beta =0 \ or \ \beta=-1$

For $\beta =0, \ \ \alpha =0, \ \ p = -7$

For $\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11$

I assume that we are after two different roots so the solution for p is p=-11

b) $\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1$

So a quadratic equation with the expected roots is

$x(x-1)=x^2-x$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

3 0

3 years ago

A tile installer charges $12 per square foot to install floor tile. What is the cost to install tile in a room of the size shown

babunello [35]

Answer: $480.00

Step-by-step explanation:

6 0

3 years ago

See attached photo below

Daniel [21]

Answer:

Library 2 charges more for each book loaned.
Library 1 has a cheaper subscription fee.

Step-by-step explanation:

Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...

y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values

y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit

y = 1.75x -3.50 +15.50 . . . . . . simplify more

In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...

C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1

_____

Now, we can answer the questions.

Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)

Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)

_____

The numbers in the cost equations are ...

C = (subscription fee) + (cost per book loaned)·n

8 0

3 years ago

If Jaime is riding at 14 miles per hour and Cori is riding at 0.40 km per minute, how far will each of them bike in two hours? 1

sladkih [1.3K]

Answer:

<h2> Jaime will bike 28 miles and Cori will bike 29.82</h2>

Step-by-step explanation:

In this exercise we are dealing with unit conversion, that is we are expected to convert from one unit to another.

Jaime's speed= 14mph

Cori's speed= 0.4km/min

now since the options for the answer is in miles, we have to convert Coris's speed for Km per min to mile per hour

we have

0.4km/min = 14.9129 mph

Applying the equation

d = ut

for Jaime

d= 14*2= 28 mph

for Cori

d= 14.9129 *2= 29.8258 mph

4 0

3 years ago

an equation for loudness L, in decibels, is L= 10 log R, where R is the relative intensity of the sound. solve 120= 10 log R to

Romashka [77]

Answer:

sorry I don't know the answer

3 0

2 years ago

Subtract 8 + 7 i from 4 - 167. O A. -4- 231 OB. 4- 23; C. 4+91 OD. 4-111