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3 years ago

How many and what type of solutions does a quadratic have with a discriminant = -9?

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

7 0

Answer:

The value of the discriminant tells you whether the quadratic has 2 solutions, 1 solution, or no real solutions. If b2 – 4ac simplifies into a positive number, then the quadratic has 2 solutions. If b2 – 4ac simplifies into a 0, then the quadratic has 1 solution.

Step-by-step explanation:

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Which system or equation is represented in the graph?

melamori03 [73]

Answer:

$(A)\displaystyle \begin{array} {ccc} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{array}$

Step-by-step explanation:

<h3>Equation of the blue line:</h3>

since the line is horizontal and passes <u>-</u><u>2</u> the equation of the blue line should be

$\displaystyle \large y = - 2$

<h3>Equation of the red line:</h3>

remember The form of equation of a line

$\displaystyle \boxed{ \displaystyle y = mx + b}$

where m is slope of the line and b is the y-intercept we can clearly see that the red line crosses y-axis at (0,-3) therefore b=-3

to figure out m we can consider the following formula:

$\displaystyle m = \frac{ \Delta y}{ \Delta x}$

from the graph we acquire ∆y=1 and ∆x=2

thus substitute:

$\displaystyle m = \frac{ 1}{ 2}$

so we have figured out m and b

therefore our equation of blue line is

$\displaystyle y = \frac{1}{2} x - 3$

our given options are in standard form so

move -3 to left hand side and change its sign:

$\displaystyle y + 3= \frac{1}{2} x$

cross multiplication:

$\displaystyle 2y + 6= x$

move 6 to right hand side and x to left hand side and change its sign

$\displaystyle - x + 2y = - 6$

multiply both sides by -1:

$\displaystyle x - 2y = 6$

hence, our system of linear equation is

$\displaystyle \begin{cases} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{cases}$

3 0

3 years ago

Find the first six terms of the sequence.<br><br> a1 = -1, an = 2 • an-1

allochka39001 [22]

The prompt says that the value at n is equal to 2 times the previous value.
-1, -2, -4, -8, -16, -32

3 0

3 years ago

Read 2 more answers

Which unit of measurement would Guatemalans typically use to measure the weight of flour?

Angelina_Jolie [31]

Grams
At least that is what we use in Mexico and in most Latin-American countries

5 0

3 years ago

Read 2 more answers

Russell, Sarah, and Terry share money in the ratio 2:5:8. In total they have £120. Work out how much each gets.

Sholpan [36]

Answer:

£16, £40, £64

Step-by-step explanation:

sum the parts of the ratio, 2 + 5 + 8 = 15 parts

Divide the amount by 15 to find the value of one part of the ratio.

£120 ÷ 15 = £8 ← value of i part of ratio , then

2 parts = 2 × £8 = £16 ← amount Russell gets

5 parts = 5 × £8 = £40 ← amount Sarah gets

8 parts = 8 × £8 = £64 ← amount Terry gets

5 0

3 years ago

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What is the quotient of 1.888\times 10^91.888×10 9 and 5.9 \times 10^65.9×10 6 expressed in scientific notation?

Jlenok [28]

Given:

The expressions are $1.888\times 10^9$ and $5.9\times 10^6$ .

To find:

The quotient of $1.888\times 10^9$ and $5.9\times 10^6$ expressed in scientific notation.

Solution:

Quotient of $1.888\times 10^9$ and $5.9\times 10^6$ is:

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=\dfrac{1.888}{5.9}\times \dfrac{10^9}{10^6}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=0.32\times 10^{9-6}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=0.32\times 10^{3}$

In the scientific notation, the first number is between 1 to 10. So, 0.32 can be written as $\dfrac{3.2}{10}$ .

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=\dfrac{3.2}{10}\times 10^{3}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=3.2\times 10^{3-1}$

$\dfrac{1.888\times 10^9}{5.9\times 10^6}=3.2\times 10^{2}$

Therefore, the value of the quotient is $3.2\times 10^{2}$ .

8 0

3 years ago