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3 years ago

Write an expression for the model. Find the sum. options: a) 2 + (–3); 1 b) –3 + 2; 5 c) 2 + 3; 5 d) 2 + (–3); –1

Mathematics

1 answer:

Dima020 [189]3 years ago

5 0

Answer:

c) 2 + 3 = 5 TRUE

d) 2 + (–3) = -1 True

Step-by-step explanation:

When adding integers (positive and negative whole numbers), there are three cases:

Positive and positive increases and sum is positive. Ex. 4 + 6 = 10
Positive and negative where you subtract and take the sign of the larger number. Ex. 3 + -8 = -5 or -3 + 8 = 5
Negative and negative decrease and the sum if negative. Ex. -4 + -6 = -10.

Use these rules to simplify each expression.

a) 2 + (–3) = -1 not 1 FALSE

b) –3 + 2 = -1 not 5 FALSE

c) 2 + 3 = 5 TRUE

d) 2 + (–3) = -1 True

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1. ) Consider the function f(x)=5−7x2,−5≤x≤1

Marat540 [252]

1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.

Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170

Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2

2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:

$f'(c)= \frac{f(b)-f(a)}{b-a}$

The differentiated form would be f'(x) = -2x. Then,

$-2c = \frac{(4- 0^{2} )-(4- (-1)^{2}) }{0--1}=1$

$c=- \frac{1}{2}$

Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.

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Once each day, Erika tracks the depth of the water in her local creek. Her first nine measurements, in inches, are: 16, 15, 13,

solniwko [45]

Answer:

Median = 13

Step-by-step explanation:

We are given the following data:

16, 15, 13, 12, 17, 14, 11, 9, 11

Formula:

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 9, 11, 11, 12, 13, 14, 15, 16, 17

Median =

$=\dfrac{9+1}{2}^{th} = 5^{th}\text{ term} = 13$

Thus, the median of the given data is 13.

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Answer:

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Step-by-step explanation:

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Answer:

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