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4 years ago

Determine the value of a if one solution to the quadratic equation is x equals 5 + 3/2 I

Mathematics

1 answer:

Sindrei [870]4 years ago

8 0

The value of a is $\frac{-9}{4}$

Step-by-step explanation:

1. Determine the other solution of x

If one value is 5 + $\frac{3}{2}$ then the other value is 5 - $\frac{3}{2}$

2. Use reverse technique to find the equation

(5 + $\frac{3}{2}$ ) (5 - $\frac{3}{2}$ ) = 0

25 - $\frac{-15}{2}$ + $\frac{15}{2}$ - $\frac{9x^{2} }{4}$ = 0

- $\frac{9x^{2} }{4}$ + 25 = 0

3. The equation is - $\frac{9x^{2} }{4}$ + 25 = 0

4. Find the value of a

a is the number with the variable $x^{2}$ therefore it is - $\frac{9}{4}$

Keyword: quadratic equation, solution

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To manage a rental property, a property manager charges $65 per month plus 6% of the rent.

Igoryamba

Given parameters:

Charge per month = $65

Percentage on rent= 6%

Amount paid by Jack per month = $164

Unknown:

Monthly rent on his property = ?

Solution:

Monthly rent on his property can be found by;

Amount paid by Jack per month = Charge per month + 6% of monthly rent

Let the monthly rent = x ;

So;

164 = 65 + $\frac{6}{100} x$ x

164 - 65 = $\frac{6x}{100}$

99 = $\frac{6x}{100}$

6x = 9900

x = 1650

Monthly rent on his property is $1650

3 0

4 years ago

Explain answer GIVING BRAINIEST

AveGali [126]

Answer:

The slope of the line is 2. To find the slope I marked two points on the line, which were (-3, 0) and (-2, 2). Then I used the $\frac{Rise}{Run}$ technique. Moving up 2 units and to the right 1 unit, which would be represented by $\frac{2}{1}$ .

5 0

3 years ago

Read 2 more answers

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown. f(x) = 4(x2 + 12x) + 10 (twelve-halves) squared = 36

brilliants [131]

Answer:

$f(x)=4(x+6)^2-134$

Step-by-step explanation:

We are required to write the function $f(x) = 4x^2 + 48x + 10$ in vertex form.

First, bring the constant to the left-hand side.

$f(x) -10= 4x^2 + 48x$

Factorize the right hand side.

$f(x) -10= 4(x^2 + 12x)$

Take note of the factored term(4) and write it in the form below.

$f(x) -10+4\Box= 4(x^2 + 12x+\Box)$

$\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36$

Substitute 36 for the boxes.

$f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})$

$f(x) -10+144= 4(x^2 + 12x+6^2)$

$f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134$

The function written in vertex form is $f(x)=4(x+6)^2-134$

4 0

4 years ago

Select the correct answer. Which is the minimum or maximum value of the given function?

Korvikt [17]

Answer:

The answer is D I believe

Step-by-step explanation:

If you look at the lowest point it lands on -4

8 0

3 years ago

Please help me with the below question.

marta [7]

Let y = f(x). By the fundamental theorem of calculus, differentiating f(x) twice yields

$f'(x) = \dfrac1{4 + x + 3x^2}$

$f''(x) = -\dfrac{1 + 6x}{(4 + x + 3x^2)^2}$

y is concave upward wherever f''(x) > 0. The denominator is positive for all real x, so the numerator determines the sign of f''(x). We have 6x + 1 = 0 when x = -1/6, and

• for x ∈ (-∞, -1/6), we have e.g. with x = -1, 6x + 1 = -5 < 0

• for x ∈ (-1/6, ∞), we have e.g. with x = 0, 6x + 1 = 1 > 0

Then y is concave upward on the interval (-1/6, ∞).

4 0

2 years ago