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3 years ago

The graphs of four quadratic equations are shown. Identify the number of real solutions of each equation by

Mathematics

1 answer:

labwork [276]3 years ago

3 0

Answer:

1. 2 real solutions

2. no real solutions

3. 2 real solutions

4. 1 real solution

Step-by-step explanation:

The 'solution' to a quadratic equation means the x - intercepts of a graph, so how many times the parabola crosses the x-axis.

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A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h i

astra-53 [7]

Given:

The given equation is:

$-3t^2+24t=h$

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

$-3t^2+24t=h$

The height of the ball is at least 36 feet above the ground. It means $h\geq 36$ .

$-3t^2+24t\geq 36$

$-3t^2+24t-36\geq 0$

$-3(t^2-8t+12)\geq 0$

Splitting the middle term, we get

$-3(t^2-6t-2t+12)\geq 0$

$-3(t(t-6)-2(t-6))\geq 0$

$-3(t-2)(t-6)\geq 0$

The critical points are:

$-3(t-2)(t-6)=0$

$t=2,6$

These two points divide the number line in 3 intervals $(-\infty,2),(2,6),(6,\infty)$ .

Intervals Check point $-3(t-2)(t-6)\geq 0$ Result

$(-\infty,2)$ 0 $(-)(-)(-)=(-)$ False

$(2,6)$ 4 $(-)(+)(-)=+>0$ True

$(6,\infty)$ 8 $(-)(+)(+)=(-)$ False

The inequality is true for (2,6) and the sign of inequality is $\geq$ . So, the ball is above 36 feet between 2 to 6 seconds.

$6-2=4$

Therefore, the required inequality is $-3t^2+24t\geq 36$ and the ball is 36 feet above for 4 seconds.

3 0

3 years ago

Paolo is using his grandmother's breakfast bar recipe. He always doubles

Papessa [141]

Answer:

$6\frac{1}{3}$ = $2\frac{1}{2}$ * 2 + $\frac{x}{2}$

Step-by-step explanation:

lets start with what we know.

the recipe calls for 2 $\frac{1}{2}$ cups of yogurt. and Paolo doubles the recipe. so multiply the recipe for yogurt by 2

2 $\frac{1}{2}$ * 2 = 5 cups of yogurt.

the total of yogurt and oats is $6\frac{1}{3}$ and we know how much yogurt we have so we subtract that from the total of both.

$6\frac{1}{3}$ - 5 = $1\frac{1}{3}$

the oats after doubling were $1\frac{1}{3}$ cups so u divide it by 2

$1\frac{1}{3}$ / 2 = $\frac{2}{3}$ before doubling

7 0

3 years ago

Please help math !!!!!!

Andrews [41]

I think it’s the second choice

3 0

4 years ago

Read 2 more answers

Let f(x)=3x+5 and g(x)=x^2 find f(x).g(x)

Alina [70]

Assuming you want them multiplied

f(x)*g(x)=(3x+5)(x^2)=3x³+6x²

6 0

3 years ago

Evaluate 3 – 5 · 2 + 8 ÷ 4 – 2 using the correct order of operations.

soldi70 [24.7K]

The answer is
C) -7

Multiply -5 by 2
Divide 8 by 4 :
3-10+2-2
Subtract 10 from 3 :
-7+2-2
Add -7 and 2 :
-5 - 2
Subtract 2 from -5:
-7

3 0

3 years ago