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Vedmedyk [2.9K]
3 years ago
11

flvs hope If $x^2+bx+16$ has at least one real root, find all possible values of $b$. Express your answer in interval notation.

Enter your answer Focus Quadratic Inequalities 18 Week 5 Quests © 2018 Art of Problem Solving Terms Privacy Contact Us About Us ap
Mathematics
1 answer:
Galina-37 [17]3 years ago
5 0
If x^2+bx+16 has at least one real root, then the equation x^2+bx+16=0 has at least one solution. The discriminant of a quadratic equation is b^2-4ac and it determines the nature of the roots. If the discriminant is zero, there is exactly one distinct real root. If the discriminant is positive, there are exactly two roots. The discriminant of <span>x^2+bx+16=0 is b^2-4(1)(16). The inequality here gives the values of b where the discriminant will be positive or zero:
                                           b^2-4(1)(16) ≥ 0
                                                  </span><span>b^2-64 ≥ 0
                                             (b+8)(b-8) </span><span>≥ 0
The answer is that all possible values of b are in the interval (-inf, -8]∪[8,inf) because those are the intervals where </span>(b+8)(b-8) is positive.
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Show work please thank you
kaheart [24]
The easiest way to solve this is to divide the shape into 2 rectangles.

The first rectangle being the big one on the left with the 12 and 6
and the second one being the little one on the right, next to it with the 5

So 12 x 6 = 72 (dont pay attention to the 7, 5, or 10, because all we need is 1 length and 1 width)

And for the smaller one it is a little bit trickier.

So on the bottom we see that is says 10ft, but we cant use that because what we really need is the measurement between the 5 and 7 on the top of the little rectangle

At the top we see that it says 6ft

We can do 10-6 to find the missing measurement.

Because the length of the whole like is 10, and the length of one of the little lines is 6, so the length of 6 + some number =10

So 10-6 = 4

Which means the number we need is 4

So now we have 5 x 4 = 20

72 + 20 = 92

Answer: 92

I also attatched an image, I hope this helps! Ask me if you have any other questions about this problem!

7 0
3 years ago
The circular mirror below has a frame with a circumference of 28.26 inches.
Karo-lina-s [1.5K]

Answer: it is 3

Step-by-step explanation:

6 0
3 years ago
Complete the steps to find the area of the trapezoid.
Yuki888 [10]

Answer:

Area of rectangle: 256

Area of triangle 1: 24

Area of triangle 2: 16

Area of triangle 3: 96

Area of trapezoid: 120

Step-by-step explanation:

I just did the question on the thing so Ik I'm right.

-The graph measures by twos. To get the area of the rectangle get the base times height of it. That would be 16x16=256.

-Get base (8) times height (6) of triangle 1 then divide by 2, remember to count the squares by 2 for finding all areas. The formula would be 1/2(b)(h) because dividing by 2 is the same as multiplying times 1/2. Plug it in and     (8)(6)=48 then divide by 2 which equals 24.

-Same formula for triangle 2. Plug it in and (8)(4)=32 and divide by 2 and it equals 16.

-Same formula for triangle 3. Plugged in is (12)(16)=192 divide by 2 and it equals 96.

-To find the area of the trapezoid get your rectangle area (256) and subtract all the triangle areas. So 256 - 6 - 16 - 96 = 120.

4 0
3 years ago
Read 2 more answers
How much higher is Checkpoint 5 than Checkpoint 2?
Akimi4 [234]
You have to find the difference in height between both checkpoints. To do this just calculate 196 - 52. Checkpoint 5 is 144 (meters?) higher than Checkpoint 2.
5 0
3 years ago
Read 2 more answers
What is the area of this trapezoid?<br><br> 175 in²<br> 140 in²<br> 129 in²<br> 85 in²
aksik [14]
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B1 = 15 in. + 4 in. + 6 in. = 25 in.
B2 = 15 in.
h = 7 in.

Area = (25 in. + 15 in.)(7 in.)/2 = 140 in.^2
3 0
3 years ago
Read 2 more answers
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