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3 years ago

Find the x and y intercepts of the quadratic equation f(x)=-x^2+4x-4

1 answer:

8 0

X - Intercept
f(x) = -x² + 4x - 4
 0 = -x² + 4x - 4
 x = -(4) +/- √((4)² - 4(-1)(-4))
 2(-1)
 x = -4 +/- √(16 - 16)
 -2
 x = -4 +/- √(0)
 -2
 x = -4 +/- 0
 -2
 x = -4 + 0 x = -4 - 0
 -2 -2
 x = -4 x = -4
 -2 -2
 x = 2 x = 2

The solution to the problem is {2, 2}, or {2}. The x - intercept of the problem is (2, 0).

Y - Intercept
f(x) = -x² + 4x - 4
f(x) = -(0)² + 4(0) - 4
f(x) = -(0) + 0 - 4
f(x) = -0 + 0 - 4
f(x) = 0 - 4
f(x) = -4

The y - intercept of the problem is (0, -4).

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3 years ago

If there are 6 serving in a 2/3 pound lb package of pound is in each serving

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Answer:

$\boxed{\math{\frac{1}{9}\text{ lb}}}$

Step-by-step explanation:

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3 years ago

Determine which of these sequences is an arithmetic sequence. Then determine the explicit formula that would be used to define t

vagabundo [1.1K]

34, 43, 52, 61, ...

43-34 = 9; 52-43 = 9; 61-52 = 9

The difference between one term and the next is a constant so it is arithmetic sequence

first term: a = 34

difference: d = 9

so the formula:

$a_n=a+d(n-1)\\\\a_n=34+9(n-1)\\\\a_n = 34+9n-9\\\\\underline{a_n=9n+25}$

10, 6, 2, -2, ...

6-10 = -4; 2-6 = -4; -2-2 = -4

The difference between one term and the next is a constant so it is arithmetic sequence

first term: a = 10

difference: d = -4

so the formula:

$a_n=a+d(n-1)\\\\a_n=10+(-4)(n-1)\\\\a_n = 10-4n+4\\\\\underline{a_n=-4n+14}$

-3, -10, -17, -24, ...

-10-(-3) = -7; -17-(-10) = -7; -24-(-17) = -7

The difference between one term and the next is a constant so it is arithmetic sequence

first term: a = -3

difference: d = -7

so the formula:

$a_n=a+d(n-1)\\\\a_n=-3+(-7)(n-1)\\\\a_n =-3-4n+7\\\\\underline{a_n=-7n+4}$

7, 8.5, 10, 11.5, ...

8.5-7 = 1.5; 10-8.5 = 1.5; 11.5-10 = 1.5

The difference between one term and the next is a constant so it is arithmetic sequence

first term: a = 7

difference: d = 1.5

so the formula:

$a_n=a+d(n-1)\\\\a_n=7+1.5(n-1)\\\\a_n =7+1.5n-1.5\\\\\underline{a_n=1.5n+5.5}$

10)

30, 22¹/₂, 15, 7¹/₂, ...

22¹/₂-30 = -7¹/₂; 15-22¹/₂ = -7¹/₂; 7¹/₂-15 = -7¹/₂

The difference between one term and the next is a constant so it is arithmetic sequence

first term: a = 30

difference: d = -7¹/₂

so the formula:

$a_n=a+d(n-1)\\\\a_n=30+(-7\frac12)(n-1)\\\\a_n =30-7\frac12n+7\frac12\\\\ \underline{a_n=-7\frac12n+37\frac12}$

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3 years ago

Write an expression to represent:One more than the quotient of a number X and 4

astra-53 [7]

Answer:

X/4 +1

Step-by-step explanation:

The word "quotient" tells us that we'll be dividing X and 4.

This can be modeled as X/4

To this quantity, we will be adding 1.

We now get X/4 +1

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3 years ago