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GenaCL600 [577]
1 year ago
9

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.Which statements about the function are true? Select thre

e options. Select three options.The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.
Mathematics
1 answer:
sertanlavr [38]1 year ago
7 0

The statements about the function that are true are

  • The vertex of the function is at (–3,–16).
  • The graph is increasing on the interval x > –3.
  • The graph is positive only on the intervals where x < –7 and where x > 1.

<h3>How to interpret the graph?</h3>

The equation of the graph is given as

f(x) = (x - 1)(x + 7)

The graph of the function is added as an attachment

On the graph, we have

Vertex = (-3, -16)

This is so because the graph has a minimum point of (-3, -16)

Also, the graph crosses the x-axis at x = 1 and x = -7

This means that the graph is positive at x >1 and x >-7

Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3

Read more about quadratic functions at

brainly.com/question/14933288

#SPJ1

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Each set of numbers below represents the lengths of three line segments. Which set represent line segments that could be connect
LenKa [72]

Answer:

B is the triangle

A and E can be thought of as triangles as well with angles 0°, 0° and 180°, but it will be just a line with 3 points. So it depends whether this is a question with multiple answers or not.

Step-by-step explanation:

  • Thinking Process:

We need to find a formula for a triangle that uses all the sides

Cosine rule uses all sides:

c^2 = a^2 + b^2 -2ab(cosA)

we can rearrage this formula and make the angle A the subject:

A = cos^{-1}(\frac{a^2+b^2-c^2}{2ab})

  • now you can just put the values from each option in the question into this formula and see if it gives an answer or not.

<u>Try A. (1,2,3)</u>

put a = 1, b = 2, c = 3 (keep in mind that you can take 'a' 'b' and 'c' as 3,2 and 1 or any other arrangement within the option A(1,2,3). All we are doing here is checking whether the answer exists or not)

A = cos^{-1}(\frac{1^2+2^2-3^2}{2(1)(2)})

A = 180, now graphically it seems that this is just a line with 3 points, or technically you can think of as the sides of the triangle are overlapping each other, and the angle between the sides is 0 0 and 180. It depends on whether the question is asking you to be technical or not. Since the question already stated there are 3 line segments, so we can think of it as a triangle.

<u>Try B.(3,4,5)</u>

A = cos^{-1}(\frac{3^2+4^2-5^2}{2(3)(4)})

A = 90, this is a triangle (specifically, this is a right angled triangle)

<u>Try C.(1,10,100)</u>

A = cos^{-1}(\frac{1^2+10^2-100^2}{2(1)(10)})

from the calculator you'll see a 'math error', this shows that there is no answer, because cos^{-1} can only accept values within -1 and 1 inclusive. Hence no such triangle exists with lengths (1,10,100).

Similarly you can try the formula with all other options, and find whose answers exists or not.

Finally, to complete the answer, let's

Try E.(1,3,4)

A = cos^{-1}(\frac{1^2+3^2-4^2}{2(1)(3)})

A = 180, hence this is also one of those "3 points on a straight line  triangles" similar to A(1,2,3)

so the answer is either A,B and E OR just B

Hope this helps :)

5 0
3 years ago
I WILL BRAINLIEST !!!
olya-2409 [2.1K]

Answer:  11/18

=======================================================

Explanation:

We need to add the fractions, but first we need to get each fraction to have the LCD (lowest common denominator) of 18

18 is the LCM of the denominators 6 and 9

The fraction 1/6 turns into 3/18 when multiplying top and bottom by 3

The fraction 4/9 turns into 8/18 after multiplying top and bottom by 2

Therefore,

(1/6) + (4/9) = (3/18) + (8/18) = (3+8)/18 = 11/18

So Mike has a total of 11/18 of a gallon of paint when combining the two given amounts 1/6 a gallon of blue paint and 4/9 of a gallon of green paint.

6 0
2 years ago
Need help with this problem
Gnom [1K]

Answer:

x=180-31-40

Step-by-step explanation:

It doesn’t show all the possible answers, but it should be:

x=180-31-40

6 0
3 years ago
A music store sold 10 to the third power CDs and 10 to the second power cd players if each CD cost $12 in each CD player cost 35
Mamont248 [21]

Answer:

$15500

Step-by-step explanation:

10^3 x 12 = 12,000

10^2 x 35 = 3,500

12,000 + 3,500 = 15,500

6 0
2 years ago
3 to the 3rd power plus 20 divided by 2 to the second power
otez555 [7]

Answer:

32

Step-by-step explanation:

3 to the 3rd power is 27 and 2 to the 2nd power is 4 so,

27+20 divided by 4

and PEMDAS so exponents, divided then add. 20 divided by 4 is 5. So 27+5 is 32. Hope this helps!

3 0
3 years ago
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