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vfiekz [6]
4 years ago
13

1.6.AP-9

Mathematics
1 answer:
Lyrx [107]4 years ago
5 0

Answer:

a. i. x ≤ 25 ii. 16 < x < 35 iii. 25 < x ≤ 95  

b. The second and third car seats are appropriate for a 35 lb child.

Step-by-step explanation:

a. Model those ranges with compound inequalities

Let x represent the car seat.

i. A car seat designed for a child weighing up to  and including 25 lb is described by the inequality.

x ≤ 25

ii. A car seat designed for a child weighing between 16 lb  and 35 lb is described by the inequality.

16 < x < 35

iii. A car seat designed for a child weighing between 25 lb  and 95 lb inclusive is described by the inequality.

25 < x ≤ 95

b. Which car seats are appropriate for a  33-lb child?

Since 35 lb is included in the range of the inequalities for the second and third card seats, the second and third car seats are appropriate for a 35 lb child.

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Answer:

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Which of the following expressions represents a function? (5 points) a {(1, 2), (4, −2), (8, 3), (9, −3)} b y2 = 16 − x2 c 2x2 +
34kurt

Answer: Option "a" is the only expression that represents a function.

Step-by-step explanation:

A function f(x) = y is a "operator" that takes an input element, x, and assigns it to only one output element, y.

So, if we have that for a given value of x.

f(x) = y and f(x) = h

where y and h are different values, then this is not a function, because is assigning the input value x to two different output values.

Let's see the different options:

a) {(1, 2), (4, −2), (8, 3), (9, −3)}

This points are of the form (x, y)

We can see that each value of x is assigned to only one value of y, so this can represent a function.

b)  y^2 = 16 − x^2

Ok, suppose that x = 0, then:

y^2 = 16 - 0 = 16

then we have that y*y = 16.

So y can take two different values:

y = 4 ---> 4*4 = 16

y = -4 ---> -4*-4 = 16.

So this is not a function.

c) 2x^2 + y^2 = 5

First, we want to isolate y in one side:

y^2 = 5 - 2*x^2

Here we have a similar case to the option b, and we can use a similar argument to prove that this is not a function, so we can discard this.

d) x = 7.

Ok, this is not a relation between two variables, so this is not a function, as if x is the input value, we have only one value of x that solves the equation.

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How can I find the volume of a prism
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The formula is V=wlh. So, take all of the numbers on the example and multiply them.
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3 years ago
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
OLga [1]

Answer:

The coordinates of the vertex are (-5, 41)

Step-by-step explanation:

For a quadratic function of the form

f(x) = ax ^ 2 + bx + c

Where a, b and c are constants and represent the coefficients of the function, then the symmetry of the parabola always passes through its vertex.

In this case we have the following parabola

f (x) = -x2 - 10x + 16

And we know that its axis of symmetry is the line x = -5

Then we know that this axis of symmetry passes through the vertex of the parabola.

Therefore, the x coordinate of the vertex is -5.

To find the coordinate in y of the vertex, we substitute x = -5 in the function.

f (-5) = -(- 5) ^ 2 -10 (-5) +16\\\\f (-5) = 41

Finally, the vertices are in the point (-5, 41).

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4 years ago
Function notation
skelet666 [1.2K]

Answer:

250.110864745

Step-by-step explanation:

31.02-22

2,256÷9.02

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