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fredd [130]
3 years ago
11

If -5 is a root of the quadratic equation 2x^2+px+15=0 and the equation p(x^2+x) +k=0 has equal rootsv then find p and k

Mathematics
1 answer:
grigory [225]3 years ago
4 0

Answer:

p=13, k = 3.25

Step-by-step explanation:

First, determine p:

2x^2+px+15=0\\x=-5:\\2(-5)^2+p(-5)+15=0\\-5p+65=0\\\implies p=13

Use this value in the second equation

13(x^2+x)+k=0

and write the condition for that equation having equal roots, i.e., its determinant must equal 0:

13x^2+13x+k=0\\D=b^2-4ac=13^2-4\cdot13\cdot k=0\\52k=169\implies k = 3.25


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After a storm, two street lights with the same length are leaning against each
Ray Of Light [21]

Answer:

c = 4.79 feet

Step-by-step explanation:

Given question is incomplete without a picture; find the question with the attachment.

Two poles AD and DB of same length are leaning against each other.

Distance between the poles (AB) = 45 feet

m(∠ADB) = 180°- (60 + 50)°

               = 70°

By sine rule,

\frac{sin50}{AD}=\frac{sin70}{45}=\frac{sin60}{DB}

AD=\frac{45\times (sin50)}{sin70}

      = 36.68 ft

Similarly,

DB = \frac{45\times sin60}{sin70}

     = 41.47 ft

Now c = DB - AD

           = 41.47 - 36.68

           = 4.79 feet

4 0
3 years ago
Solve for X. Show your work<br><br> 2x + 6 = x - 5
irina1246 [14]

2x + 6 = x - 5

2x - x = -5 - 6

x = -11 ← the end

8 0
2 years ago
Expand and simplify 2(2x+3)+(5x+4)
LekaFEV [45]
2(2x+3)+(5x+4) simplified would be 4x+6+5x+4 and if you add those together you get 9x+10. Hope I helped! if you have any questions just leave a comment
4 0
3 years ago
Read 2 more answers
the sum of the first nine terms of an arithmetic series is 162, and the sum of the first 12 terms is 288. Determine the first fi
Natali5045456 [20]

Answer:

\boxed{\pink{\tt \leadsto Sum \ of \ first \ five \ terms \ is \ 50 . }}

Step-by-step explanation:

Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.

\boxed{\red{\bf \bigg\lgroup For \ answer \ refer \ to \ attachment \bigg\rgroup  }}

<h3><u>Related</u><u> </u><u>Infor</u><u>mation</u><u> </u><u>:</u><u>-</u><u> </u></h3>

• The sum of n terms of an AP is

\boxed{\orange{\sf S_n = \dfrac{n}{2}[2a+(n-1)d] }}

• nth term of an AP is given by ,

\boxed{\blue{\sf T_n = a+(n-1)d }}

8 0
2 years ago
Use the formula to evaluate the series 1+2+4+8+...a10
valina [46]

Answer:

The sum of the given series is 1023

Step-by-step explanation:

Geometric series states that a series in which a constant ratio is obtained by multiplying the previous term.

Sum of the geometric series is given by:

S_n = \frac{a(1-r^n)}{1-r}

where a is the first term and n is the number of term.

Given the series: 1+2+4+8+.................+a_{10}

This is a geometric series with common ratio(r) = 2

We have to find the sum of the series for 10th term.

⇒ n = 10 and a = 1

then;

S_n = \frac{1(1-2^{10})}{1-2} =\frac{1-1024}{-1} =\frac{-1023}{-1}=1023

Therefore, the sum of the given series is 1023



8 0
3 years ago
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