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Use the quadratic formula to solve x² + 9x + 10 = 0.<br><br> What are the solutions to the equation?

jok3333 [9.3K]

Answer:

$-1.30\ and\ -7.70$ (2 decimal places)

Step-by-step explanation:

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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$x^2+9x+10=0$

Plug in values:

$x=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \:10}}{2\cdot \:1}$

First value of x:

$x=\frac{-9+\sqrt{41}}{2}=-1.30$ (2 decimal places)

Second value of x:

$x=\frac{-9-\sqrt{41}}{2}=-7.70$ (2 decimal places)

6 0

3 years ago

An employee is marking up new merchandise by 35%. the price they paid for an item is $120. what price will the employee place on

kolezko [41]

The answer would be D: $162 because $120 x 35% or (0.35) = $42 so $120 + $42 gives you $162

4 0

4 years ago

Read 2 more answers

Sam can prepare 30 wall paintings in four weeks.How much time will he need to do 90 wall painting s

telo118 [61]

Sam needs 12 weeks.

explanation: if he can do 30 paintings in 4 weeks then find out if 30 can go into 90. since it can when you multiply it by 3, then also multiply 4 by 3 since he needs 3 times more than the original amount. in total, he will need 12 weeks

8 0

3 years ago

A long-jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above th

Alexeev081 [22]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2} +12$ × $x-27$

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a$ × $x^{2} +b$ × $+ C$

Where:

x - Horizontal distance from the start line, measured in meters.

y - Height of the long jumper, measured in meters.

a,b,c - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m), (x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m),$ this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0 (Eq. 1)81\cdot a + 9\cdot b + c = 0 (Eq. 2)64\cdot a + 8\cdot b + c = 0.05 (Eq. 3)$

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}, b = \frac{3}{25}, c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}.$