Someone please help me

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

2 years ago

Paul is saving for a video game. It costs $70, including tax. He has already saved $35. How much more does he need to save?

MrMuchimi

Answer:

35

Step-by-step explanation:

70 takeaway 35 is 35 which is what is left over.

7 0

3 years ago

Read 2 more answers

Kay is a student in Mrs. Hudson’s class. Assuming you know nothing else about Kay, what is the probability that Kay’s birthday w

Drupady [299]

Answer:

262/365

Step-by-step explanation:

So as you can see there is no more information aout Kay on her birthday, so the chances of her birthday being on a week day is given by the total number of the weekdays of the year between the total number of days in a year, so in 2019 there are 262 weekdays, divided by 365 you get the probability that Kay´s birthday falls on a weekday.

262/365=,7178=71,78%

So the probability of Kay´s brithday falling on a week day will be 71,72%

5 0

3 years ago

11. If you want to enlarge a square with area 36 square inches

larisa86 [58]

Answer:

e. 72 inches

Step-by-step explanation:

Well, firstly to find the lengths of the sides, we would have to find the square root of 36 (which is 6, as 6x6=36).

Now, if we enlarge the square by SF 3, the new side lengths would be 6x3=18 inches. That is only one side.

Now we know the length of one side, we can do 18x4 (because as we all know, squares have 4 sides) to find the perimeter.

18x4=72 inches. This means the answer is option e.

7 0

2 years ago

A rescue helicopter flew from its home base for 35 kilometers on a course of 330 degrees to pick up an accident victim. It then

artcher [175]

I've drawn a triangle to represent the journey (see attached.

The angle from Home to Victim to Hospital is:

a = $90 - (360 - 330) = 90- 30 = 60^o$

Using the cos rule, we can solve for the length x:

$a^2 = b^2 +c^2 - 2bccosA
\\x^2 = 35^2+25^2-2(35)(25)cos60
\\x^2 = 1850 - 875
\\x^2 = 975
\\x = \sqrt{975}
\\x = 31.2249...$

Using the cos rule, we can solve for angle b:

$a^2 = b^2 +c^2 - 2bccosA
\\35^2 = 31.22...^2+25^2-2(31.22...)(25)cosb
\\1225 = 975 + 625 - 1561.249...cosb
\\-375 = -1561.249...cosb
\\b = cos^{-1}( \frac{-375}{-1561.249...}) 
\\b = 76.1...$

So the bearing the helicopter has to travel is:

270 - 76.1 = <u>193.9 degrees (1 dp)</u>

And the distance it travels is <u>31.2 km (1 dp)</u>

5 0

3 years ago