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sdas [7]
3 years ago
5

. If y varies directly with x when y = -4 and x = 10, determine y when x = 2. Write and equation for the direct variation and de

termine the value.
Mathematics
1 answer:
taurus [48]3 years ago
7 0

Answer:

y = - 0.8

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition when y = - 4, x = 10, then

- 4 = 10k ( divide both sides by 10 )

- 0.4 = k

y = - 0.4x ← equation of variation

When x = 2 , then

y = - 0.4 × 2 = - 0.8

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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
In ΔABC, if m ∠A = m∠C, m∠B = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposi
chubhunter [2.5K]

Answer:

The length of b is \sqrt{2x^2(1-cos\beta)}.

Step by step explanation:

Given information: In ΔABC, ∠A =∠C, ∠B = ß (where ß is an acute angle), and BC = x.

Since two angles are same therefore triangle ABC is an isosceles triangle and side AB and BC are congruent.

AB=BC=x

According to Law of cosine

b^2=a^2+c^2-2ac\cos B

b^2=x^2+x^2-2(x)(x)\cos \beta

b^2=2x^2-2x^2\cos \beta

b^2=2x^2(1-\cos \beta)

\sqrt{2x^2(1-cos\beta)}

Therefore the length of b is \sqrt{2x^2(1-cos\beta)}.

6 0
3 years ago
describe how to find the price of a blender 3 years from now the inflation is constant at 4% and the the blender costs 38$ today
Ludmilka [50]
FV =  PV / (1 +r)^n

Where FV = Future Value,  PV = Present Value, r = inflation rate in %,
n = number of years.

PV = $38, r = 4%, n = 3 years.

FV =    38 / (1 + 4%)^3

      =   38 / (1 + 0.04)^3

      =     38 / (1.04)^3 =    33.782

Hence the value 3 years from now = $33.78    
5 0
3 years ago
Write the expression that is equivalent to 2z + 2z + 2z
Dennis_Churaev [7]

Answer: 4z + 2z

Step-by-step explanation:

Add 2 + 2 get 4. Then bring z down and have 4z. Now you only have 2z so it'll be 4z + 2z

3 0
3 years ago
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PLEASE HELP AND GIVE EXPLANATION I GIVE BRAINLY
spayn [35]

Answer: 21 273 divided by 13 =21

Step-by-step explanation:

3 0
3 years ago
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