Explain why f(x) = x^2+4/x^2-2 is continuous at x = 2. a. f is defined at x = 2 b. f is not defined at x = 1 c. f is defined at x = -2 d. f is defined at x = 0

Answer: [tex]x=3.0206[/tex]

Step-by-step explanation:

Given

[tex]3(2^{2x}+3)-5(2^x+2)-156=0[/tex]

Replace [tex]2^x[/tex] by [tex]y[/tex]

We can write

[tex]\Rightarrow 3(y^2+3)-5(y+2)-156=0\\\Rightarrow 3y^2+9-5y-10-156=0\\\Rightarrow 3y^2-5y-157=0\\\\\Rightarrow y=\dfrac{5\pm \sqrt{25-4(3)(-157)}}{2\times 3}\\\\\Rightarrow y=\dfrac{5+43.69}{6}\\\\\Rightarrow y=8.115\\\Rightarrow 2^x=8.115\\\therefore \quad x=3.0206[/tex]

~Refer to the attachment for the solution.

[tex] \to \bf { Sum = 3500 } [/tex]

Answer:

Total Number of students taking Math and History and not music are 68.

Number of students who took both math and history at the same time is 6.

Step-by-step explanation:

History = 30

Math = 32

Music= 33

Math and Music= 9

History and Music= 13

History and Music and Math = 2

History but not math = 14

We have to find students taking history and math but not music.

Total number of students = 125

From the figure  number of students taking Math and History and not music are

=30+6+32= 68

Number of students who took both math and history at the same time is 6.

Answer:

5 x 4 = 20, 20 divided by 2 ( x 1/2 ) = 10

Step-by-step explanation:

Formula area of a Triangle:

B(base) x H(height) x 1/2(basically just dividing by 2)

Answer:

Minor Arc AC = 360 - 235 = 125°

[tex]mABC = \frac{Major \ arc - Minor \ arc}{2} = \frac{235 - 125}{2} = \frac{110}{2} = 55[/tex]

Answer:

First, when we have a function f(x), an horizontal dilation of scale factor k, is written as:

g(x) = f(x/k)

Then f((2/3)*x) is an horizontal dilation of scale factor 3/2 of the function f(x).

(The graph will be a little bit wider than the graph of f(x))

Also, knowing that f(x) = x^3 + 3

Then:

f((2/3)*x) = ( (2/3)*x)^3 + 3

              = (8/27)*x^3 + 3

And the graph of this function is shown below:

answer: the answer is c

Answer:

6/5t + 4/15s - 3

Step-by-step explanation:

(-4/5t + 5/3s) + (-3 -7/5s + 2t)

You can only add like terms together so convert like terms to have the same denominator:

(-4/5t + 25/15s) + (-3 - 21/15s + 10/5t)

Get rid of the parentheses:

-4/5t + 25/15s - 3 - 21/15s + 10/5t

Combine like terms:

6/5t + 4/15s - 3

Answer:

35 is the 'is' and 40 is the 'of'

Step-by-step explanation:

is/of = %/100

35/40 = x/100

cross-multiply to get:

40x = 3500

x = 3500/40

x = 87.5

Answer:

2

Step-by-step explanation:

Answer:

2t

Step-by-step explanation:

3t-t is the same as 3-1, so it equals 2t

Answer:

50 cups

Step-by-step explanation:

ratio of water to juice = 10 : 6 = 5 : 3

amount of cup = (5 x 30) / 3 = 50

Answer:

-7

Step-by-step explanation:

Area of this trapezoid is 264 unit²

Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides.

Given perpendicular distance as 12 and parallel sides as 20,24 units respectively.

Thus Area is (20+24 /2) ×12=264 units²

Hence, the Area of trapezoid is 264 unit²

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Answer:

52 degrees

Step-by-step explanation:

a line is 180 degrees so just subtract 128 from 180 which is 52

Answer:

Simplify.

Rewrite the expression in the form z”. Z5 • Z6Simplify.

Rewrite the expression in the form z”. Z5 • Z6

Answer:

Simplify.

Rewrite the expression in the form z”. Z5 • Z6Simplify.

Rewrite the expression in the form z”. Z5 • Z6

Answer:

20

Step-by-step explanation:

Answer:

ajnasnnanananandbabbabbansbansbz svabsvsb

Answer: The function described in this scenario above is a “Growth Function”

Have a nice day!

Answer:

33464.25

Step-by-step explanation:

Using BODMAS : brackets, division, multiplication, addition

[tex]177\times ((177+(9-4+7)) +\frac{90}{8}\\\\177\times (177+12) +\frac{90}{8}\\\\177\times 189 +\frac{90}{8}\\\\\\177 \times 189 + 11.25\\\\33453 + 11.25\\\\33464.25[/tex]

Answer:

35444.25

Step-by-step explanation:

OFC by computing them

Answer:

[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.

Step-by-step explanation:

Uniform distribution:

An uniform distribution has two bounds, a and b.

The probability of getting a value lower than x is:

[tex]P(X < x) = \frac{x - a}{x - b}[/tex]

The express bus arrives at your neighborhood at a random time between 7:30 and 7:36 a.m.

6 minutes, so [tex]a = 0, b = 6[/tex]

You arrive at 7:33, so if x < 3, you lose the express bus:

[tex]P_E = P(X < 3) = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2}[/tex]

The local bus arrives at your neighborhood at a random time between 7:30 and 7:40 a.m.

10 minutes, so [tex]a = 0, b = 10[/tex]

[tex]P_B = P(X < 3) = \frac{3 - 0}{10 - 0} = \frac{3}{10}[/tex]

Find the probability that you missed both the express bus and the local bus.

[tex]p = P_E*P_B = \frac{1}{2}*\frac{3}{10} = \frac{3}{20}[/tex]

[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.

The probability that you missed both the express bus and the local bus is 3/20

The individual probability of a uniform distribution is calculated as:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

For the express bus

At 7:30 am, a = 0

At 7:36 am, b = 6

You arrived at 7:33 am; this means that:

x = 3

For you to miss the express bus, it means that the express bus left before 7:33 am.

i.e. x < 3

So, the probability that you miss the express bus is:

[tex]P(X < 3) = \frac{3 - 0}{6 - 0}[/tex]

[tex]P(X < 3) = \frac{3}{6}[/tex]

[tex]P(X_E < 3) = \frac{1}{2}[/tex]

For the local bus

At 7:30 am, a = 0

At 7:40 am, b = 10

You arrived at 7:33 am; this means that:

x = 3

For you to miss the local bus, it means that the local bus left before 7:33 am.

i.e. x < 3

So, the probability that you miss the local bus is:

[tex]P(X < 3) = \frac{3 - 0}{10 - 0}[/tex]

[tex]P(X_L < 3) = \frac{3}{10}[/tex]

So, the probability that you miss both bus is:

[tex]P(Both) = P(X_E < 3) * P(X_L < 3)[/tex]

This gives

[tex]P(Both) = \frac 12 * \frac 3{10}[/tex]

[tex]P(Both) = \frac 3{20}[/tex]

Hence, the probability that you missed both the express bus and the local bus is 3/20

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Answer:

x=18

Step-by-step explanation:

Both angles are supplementary angles and form 180

Set your formula up as following

(x-6) + (8x+24) = 180

x+8x-6+24=180

9x=180+6-24

9x=162

x=162/9

x=18

Now substitute 18 for x to get your angles and check your work .

Answer:

8.

[tex]8. - 1. - 44 [/tex]

9

Answer:

[tex]16m^{10} -25m^{12}[/tex]

Step-by-step explanation:

hope this helps :)

The expand and combination like terms (4m^5) – 5m^6) (4m^5 + 5m^6) is -9m^12 + (16)m^10.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

The equation=(4m^5) – 5m^6) (4m^5 + 5m^6)

Now,

To expand the expression, we need to multiply each term inside the first parentheses by each term inside the second parentheses. This gives us:

(4m^5 - 5m^6) (4m^5 + 5m^6) = 4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6

To simplify the expression, we need to use the exponent rule that a^b * a^c = a^(b + c) and combine the terms that have the same base and exponent. This gives us:

4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6 = 16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6)

To further simplify the expression, we need to add the exponents and simplify the coefficients. This gives us:

16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6) = 16m^10 + 20m^11 - 20m^11 - 25m^12

To combine like terms, we need to add or subtract the coefficients of the terms that have the same base and exponent. This gives us:

16m^10 + 20m^11 - 20m^11 - 25m^12 = (16 - 25)m^12 + (20 - 20)m^11 + (16)m^10

= -9m^12 + (0)m^11 + (16)m^10

= -9m^12 + (16)m^10

Therefore, the equation will be equal to -9m^12 + (16)m^10.

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Answer:

See below

Step-by-step explanation:

This is a piece-wise function.

         4, -4≤ x ≤ -2

f(x) =  2,  -2 ≤ x < 2

        -3,  2 ≤ x ≤ 4