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Sindrei [870]
3 years ago
10

Analyze the graph of the function f(x) to complete the statement.

Mathematics
1 answer:
ozzi3 years ago
5 0

f(x) is the same as y, so we can say y = f(x)

Writing f(x) < 0 means we want to find when y < 0.

Visually, we are looking at the graph when the curve is below the horizontal x axis.

This is the portion in red that I have marked in the diagram (see attached image below). I apologize for the numbers being blurry.

The left red portion is from negative infinity to -3. In terms of a compound inequality we write -\infty < x < -3 which in interval notation is (-\infty, -3). The curved parenthesis tells the reader to exclude both endpoints.

The right red portion is from x = -1.1 to x = 0.9, excluding both endpoints. So we say -1.1 < x < 0.9 which becomes the interval notation (-1.1, 0.9). This is not ordered pair notation even though it looks identical to it.

-------------

<h3>Answer in interval notation:  (-\infty, -3) \cup (-1.1, 0.9)</h3>

The "U" means "set union" which glues together the two separate intervals. Basically it's saying "x is either in the interval (-infinity, -3) or it is in the interval (-1.1, 0.9)"

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Use natural logarithms to solve the equation 9e 4x = 54 forx. Give the exact solution and an approximate
GuDViN [60]

Answer:

.448

Step-by-step explanation:

9e^{4x} = 54 \\e^{4x} = 54/9\\e^{4x} = 6\\ln{6} = 4x\\ln{6}/4 = x\\.448 =x\\(approx)

8 0
3 years ago
Determine by checking the group axiom (Associativity) whether this set is a group:
slavikrds [6]

Let x, y, z ∈ C, the set of complex numbers.

By definition of ○,

(x ○ y) ○ z = (x + y - 2i) ○ z

… = (x + y - 2i) + z - 2i

… = x + y + z - 4i

and

x ○ (y ○ z) = x ○ (y + z - 2i)

… = x + (y + z - 2i) - 2i

… = x + y + z - 4i

so (x ○ y) ○ z = x ○ (y ○ z), which means ○ is indeed associative under C.

7 0
3 years ago
Could I please get help with this, I’m very confused and don’t know how to do this. Please and thank you
Step2247 [10]

Answer:

(See bolded numbers)

<u>Factoring</u><u> -1 out of negative numbers</u><u>:</u>

11) (-6) • (3)= (-1 • 6) • 3= -1 • 6 • 3= -18

-6 is the negative number here and factoring out -1 from -6 will give us -1(6). In the second last step, multiply 6 and 3 together then multiply the product by -1.

-1(6 ×3)= -1(18)= -18

12) (-4) • (-8)= (-1 • 4) • (-1 • 8)= 1 • 4 • 8= 32

Multiplying 2 negative numbers will give us a positive number. The 3rd step is 1 as (-1)(-1)= 1.

13) (-9) • (-5)= (-1 • 9) • (-1 • 5)= 1 • 9 • 5= 45

14) (2) • (-8)= 2 • (-1 • 8)= -1 • 2 • 8= -16

Negative numbers are numbers with a negative sign and are numbers less than zero. Factoring -1 out of negative numbers will leave us with the positive number.

8 0
3 years ago
Find BD<br> 2x - 9<br> 11<br> - D<br> B<br> С<br> X + 9
Gnesinka [82]

Answer:

10

Step-by-step explanation:

AB + BC = AC and AC = 14

x + 15 + 2x + 32 = 14 add like terms

3x + 47 = 14 subtract 47 from both sides

3x = -33 divide both sides by 3

x = -11 now the length of BC

2x + 32 replace x with -11

2*(-11) + 32 = 10

8 0
3 years ago
What are the terms in the expression 7x + 4y + 1?
antoniya [11.8K]
7x, 4y, 1are the terms, and 7x is the leading term.
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