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2 years ago

The expression 2x² + ax is equivalent to x (2x + 7) for some constant a. What is the value of a ?

Mathematics

1 answer:

NNADVOKAT [17]2 years ago

7 0

2x^2 + ax = x(2x+ 7)
2x^2 + ax = 2x^2 + 7x
Subtract 2x^2 from both sides
ax = 7x
a = 7

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Tju [1.3M]

Answer:

Step-by-step explanation:

Rationalize the denominator of b. So, multiply the numerator and denominator by $\sqrt{x}$

$b = \frac{(1-2\sqrt{x}) *\sqrt{x}}{\sqrt{x}*\sqrt{x} }=\frac{1*\sqrt{x} -2\sqrt{x} *\sqrt{x} }{\sqrt{x} *\sqrt{x} }\\\\=\frac{\sqrt{x} -2x}{x}\\$

Now, find a +b

$a +b = \frac{2x+\sqrt{x} }{x}+\frac{\sqrt{x} -2x}{x}\\\\=\frac{2x+\sqrt{x} +\sqrt{x} -2x}{x}$

Combine like terms

$= \frac{2x-2x+\sqrt{x} +\sqrt{x} }{x}\\\\=\frac{2\sqrt{x} }{x}$

Now find (a + b)²

(a +b)² = $(\frac{2\sqrt{x} }{x})^{2}$

$= \frac{2^{2}*(\sqrt{x} )^{2}}{x^{2}}\\\\= \frac{4* x}{x^{2}}\\\\= \frac{4}{x}$

Hint: $\sqrt{x} *\sqrt{x} =\sqrt{x*x}=x$

5 0

2 years ago

Ivan rented a truck for the day. There is a base fee of $17.95, and there was an additional charge of 91 cents for each mile dri

lozanna [386]

Answer:

293 miles

Step-by-step explanation:

284.58-17.95=266.63

266.63/0.91=293

293 miles

7 0

2 years ago

Solve the equation and check your answer. 0.95 t plus 0.05 left parenthesis 100 minus t right parenthesis equals 0.49 left paren

Triss [41]

<h2>Answer:</h2>

The value of t is:

t=48.8889

<h2>Step-by-step explanation:</h2>

We are asked to solve the linear equation in terms of variable t.

The equation is given by:

$0.95t+0.05(100-t)=0.49(100)$

Firstly we will solve the parentheses term in the left and right hand side of the equality as follows:

$0.95t+0.05\times 100-0.05t=49$

Now we combine the like terms on the left side of equality by:

$0.95t-0.05t+5=49\\\\i.e.\\\\0.90t+5=49$

Now we subtract both side of the equation by 5 to get:

$0.90t=44$

Now on dividing both side of the equation by 0.90 we get:

$t=\dfrac{44}{0.90}\\\\i.e.\\\\t=48.8889$

Hence, the value of t is: 48.8889

7 0

3 years ago

Please help me solve this

Rashid [163]

Answer:

??????????????

Step-by-step explanation:

,nooooooo

8 0

2 years ago

5. Which is a better buy, 4 bouncy

tatyana61 [14]

Answer:

5 bouncy balls for 9$

Step-by-step explanation:

Unite rate for 7.60= 1.90

unit rate for 9=1.8

5 0

3 years ago

Read 2 more answers