Let f (x) = log2(x) + 2 and g(x) = log2(x3) – 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)

1 T-Shirt for every 5 people

First of all, B & C are wrong, because they say 5 T-shirts for one person.

Next, we will look at A & D. A is more grammatically correct, and so you should use A.

OR

Answer:

The last one

When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.

By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.

Total area = A₁ + A₂ + A₃ + A₄

However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.

Area of a semicircle = πr²/4

Thus, the total area of both the semicircle (half circle) and the larger square is given by:

Area = πr²/4 - d²

Note: d = 2r

Area = πr²/4 - (2r)²

Area = πr²/4 - 4r²

Area = (π - r²)/4 sq. units.

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Answer:

The required probability = 0.9345

Step-by-step explanation:

Given that:

p = 0.17

n = 6

The required probability that two or less light bulbs are defective = (P<2)

(P<2) = P(X=0) +P(X=1) +P(X=2)

\((P<2) =\bigg [ ({^6C_0}\times 0.17^0 \times (1-0.17)^{6-0})+ ({^6C_1}\times 0.17^1 \times (1-0.17)^{6-1}) +( {^6C_2}\times 0.17^2 \times (1-0.17)^{6-2}) \bigg ]\)

\((P<2) =\bigg [ \dfrac{6!}{0!(6-0)!}\times 0.17^0 \times (1-0.17)^{6})+ (\dfrac{6!}{1!(6-1)!} \times 0.17^1 \times (1-0.17)^{5}) +( \dfrac{6!}{2!(6-2)! }\times 0.17^2 \times (1-0.17)^{4}) \bigg ]\)

\(\mathbf{(P<2) = 0.9345}\)

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

A. 21

I just took my exam and got it right.

Answer: a²+2b+2ab

Step-by-step explanation:

(2a²+62+2b+1)-(a²+62-2ab+1)

2a²+62+2b+1 - a²-62+2ab-1

a²+2b+2ab

Answer: 5

Step-by-step explanation:

8/10 = 4/N

0.8 = 4/N

0.8N  = 4

N = 4/0.8 = 5

Answer:

x - 9 = -1

Step-by-step explanation:

When you see less than you switch the numbers. So, for instance, it says 9 less than x means x-9

Entry ticket = $7

Gift shop money = $g

Maximum to spend = $30

Inequality => 7+g ≤ 30

Hope it helps!

Answer:

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

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

17) c

18) a) 19

19) i dont know sorry

Step-by-step explanation:

the first two i can solve, the first one i simply put in a calculator and observed that it did not pass the vertical line test, so it is now a function. the second one all you have to do is sub in -3 for x so the equation reads |-(-3)^3-8| which equal 19, sorry i couldnt help on 19

Answer:

174

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Using it's concept, the average rate of change of the function over the interval 10 < x < 22 is given by:

\(r = \frac{f(22) - f(10)}{12}\)

It is given by the change in the output divided by the change in input.

Over the interval 10 < x < 22, the outputs are f(10) and f(22), hence the rate of change is given by:

\(r = \frac{f(22) - f(10)}{12}\)

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Just put -2 in,where X is and get your answer that way

A percentage is a number or ratio expressed as a fraction of \(100\). It is often denoted using the percent sign, "%".

Hence,

the amount desired at end of a period is $\(9400\).

The length of time is \(4 years\).

The rate is \(2\)%.

Compounded is monthly.

The period used is \(48\).

The rate used is \(1\)%.

The PV factor used is \(0.62026\).

The PV of the amount desired at the end of the period is $\(5830.45\)

What is the percentage?

A percentage is a number or ratio expressed as a fraction of \(100\). It is often denoted using the percent sign, "%".

Here from the question,

PV factor \(=(1+i)^{-n} ........(1)\)

where, \(i=\frac{12}{12}\)%

\(i=1\)

and

\(n=4(12)\\n=48\)

Substituting the values in the equation \((1)\), we get

PV factor \(=(1+0.01)^{-48}\\\)

PV factor \(=0.62026\)

Hence,

the amount desired at end of a period is $\(9400\).

The length of time is \(4 years\).

The rate is \(2\)%.

Compounded is monthly.

The period used is \(48\).

The rate used is \(1\)%.

The PV factor used is \(0.62026\).

The PV of the amount desired at the end of the period is $\(5830.45\)

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Answer:

can u plz make a good picture to solve I can't see good

Step-by-step explanation:

and thanks

Answer:

C

Step-by-step explanation:

The angle is almost a full circle. A full circle would be 360,but since it is just hardly missing a piece ,that means it is 350. Simplistic explanation without the extra math,

a. It represents the spread of the middle 50% of the data.

b. At least 50% of the students scored between 80 and 86.

c. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

How evenly distributed the middle 50% of the data is is determined by the interquartile range. In order to calculate it, the first quartile is subtracted from the third quartile.

A. The interquartile range (IQR) in a box-and-whisker plot is the distance between the first quartile (Q1) and the third quartile (Q3) of the data. It represents the spread of the middle 50% of the data.

B. To determine what percent of the students got 80% or higher, we need to find the upper fence, which is defined as 1.5 times the IQR above Q3. From the box-and-whisker plot, we can see that Q3 is approximately 86 and Q1 is approximately 71. Therefore, the IQR is 86 - 71 = 15. The upper fence is 1.5 * 15 + 86 = 108.5.

Looking at the plot, we can see that there are no data points above 100, so we can safely assume that no students scored above 100%. The highest score is 94, which is within the whiskers of the box-and-whisker plot. Therefore, we know that the percent of students who scored 80% or higher is between the percent of students who scored 80% or higher and the percent of students who scored 94% or higher.

From the plot, we can see that the median is approximately 80 and the third quartile (Q3) is approximately 86. This means that at least 50% of the students scored between 80 and 86. Additionally, we know that the maximum score is 94, so we can say that at least some students scored higher than 86. However, we don't know how many students scored between 86 and 94.

C. Based on the interquartile range, we can say that the middle 50% of the students scored between approximately 71 and 86. This suggests that there is a significant amount of variability in the test scores, as the range is quite wide. Additionally, we know that at least some students scored above 86, but we don't have enough information to determine how many or how high their scores were. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

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Answer: (D) x=20

I know this because i took the test and got the answer right....amen

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

Between 50 and 60

Step-by-step explanation:

4,346/82 is 53 which is between 50 and 60.

Hope this helps!

\( \: \: \: \: \: \)

Answer:

x=5 and y=2

Step-by-step explanation:

I hope this helps

By using the substitution method, we will see that the value of y is 23.

Here we have a system of linear equations, the system is:

y - x = 11

x = 12

The second equation is trivial, it just gives the value of x. Then we can use the substitution method and replace it in the first equation, then we will get:

y - 12 = 11

Now we can solve this for y, we will get:

y = 11 + 12

y = 23

That is the value of y.

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Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

Answer:

A is the answer

Step-by-step explanation:

if its wrong than its C

she saved $162

hope it helps