I NEED HELP ASAP!! WILL MAKE YOU BRAINLIEST IF RIGHT +40 points!

Mathematics

2 answers:

Simora [160]3 years ago

8 0

The standard form of a quadratic equation is ,

ax² + bx + c = 0.

And the formula to find the discriminant is b² - 4ac.

Here the first step is to change the given equation into standard form. So, add 1 to each sides of the equation. Therefore,

2x² – 9x + 2+1 = –1 + 1

2x² – 9x + 3 = 0

Next step is to compare the given equation with this equation to get the value of a, b and c.

After comparing the equations we will get a = 2, b = -9 and c = 3.

So, discriminant = b²- 4ac

=( -9)²-4 (2)(3)

= 81 - 24

= 57

So, discriminant of the given equation is 57.

57 is greater than 0 and square root of 57 will result real number.

So, the correct choice is C: The discriminant is greater than 0, so there are two real roots.

Nata [24]3 years ago

7 0

C. The discriminant is greater than 0, so there are two real roots.

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A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.