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Oksanka [162]
3 years ago
14

Which is true regarding the sequence below?

Mathematics
1 answer:
strojnjashka [21]3 years ago
7 0
What? Add more detail please
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Help please
rusak2 [61]

Answer:

  • See below

Step-by-step explanation:

f(x) is quadratic function and g(x) is linear (since AP in the right column).

<u>Find the equation of the function f(x), use the points on the graph:</u>

  • f(x) = ax² + bx + c
  • c = 5 as the y-intercept is (0, 5)
  • a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
  • a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4

<u>The function is:</u>

  • f(x) = -x² + 4x + 5

Find the equation of g(x)

<u>Find the slope of g(x):</u>

  • m = (1 - 7)/(-1 + 4) = -2

<u>Use (-4, 7) to find its equation:</u>

  • y - 7 = -2(x + 4)
  • y = -2x + 7 - 8
  • y = -2x - 1
<h3>See the required comparison below</h3>

<u>The y-intercepts:</u>

  • f(x) ⇒ 5,
  • g(x) ⇒ -1
  • -5 < - 1

<u>Values at x = 3:</u>

  • f(3) = -3² + 4(3) + 5 = 8
  • g(3) = -2(3) - 1 = - 7
  • 8 > 7

<u>Average rate of change in the interval [2,5]:</u>

  • f(x) ⇒ (0 - 9)/(5 - 2) = -3
  • g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
  • -3 < -2

<u>Max of function in the interval [-5, 5];</u>

  • f(x) ⇒ 9, vertex of the function
  • g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
  • 9 = 9
4 0
3 years ago
Read 2 more answers
Cheese sticks that were previously priced at "10 for $1" are now "4 for $1". Find each percent change.
statuscvo [17]

original quantity : 10 for $1

new quantity: 4 for $1

now we have to find each percent change

10-4=6

6÷100=0.06

0.06=6%

the quantity went down 6%

6 0
3 years ago
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. T
VARVARA [1.3K]

Answer:

(D)56.4

Step-by-step explanation:

According to the question, Let AB=10, AC=12 and m∠B=90°.

Thus, from ΔABC, using trigonometry, we have

\frac{AB}{AC}=sinx

\frac{10}{12}=sinx

\frac{5}{6}=sinx

sinx=0.83

x=sin^{-1}(0.83)

x=56.4

Therefore, at x=56.4 the wire meet the ground.

8 0
3 years ago
PLZ HELP MEEEEEEEEEEEEE
ivolga24 [154]

Answer:

Ill do this quick...

Its B.

Step-by-step explanation:

5 0
3 years ago
Which is the equation of the line? Mid-Unit Test A. 3x + y = 9 B. x – y = 9 C. 3x – y = 9 D. x + 3y = 9
nirvana33 [79]
I think the answer would be D
3 0
3 years ago
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