What is the sum of the fractions below? 1/2x + 6/2x

Answer:

-4 < x < 1/2

Step-by-step explanation:

Given the inequality:

[tex]\displaystyle{\dfrac{x+4}{2x-1} < 0}[/tex]

Where x can not equal 1/2 since it will result the undefined expression. Furthermore, by solving a rational inequality (fractional inequality) is different from solving a linear inequality.

If we assume that for the expression on the left side is always positive, we can say that:

[tex]\displaystyle{\dfrac{x+4}{2x-1} < 0}[/tex]

However, the expression can remain negative. If a denominator remains somewhat negative and you multiply both sides by the denominator, you'll end up from < to >, basically swap in inequality sign.

Thus. If we let x > 1/2, the interval where the expression is always positive, we can solve the inequality as:

[tex]\displaystyle{\dfrac{x+4}{2x-1} \cdot \left(2x-1\right) < 0 \cdot \left(2x-1\right)}\\\\\displaystyle{x+4 < 0}\\\\\displaystyle{x < -4}[/tex]

However, this inequality is false so we can say that there's no region where this expression is less than 0 at x > 1/2.

Now let's say that at x < 1/2, the expression will start to remain in negative (although there is an interval that the expression is positive at x < 1/2 but majority negative.) Therefore, let's say:

[tex]\displaystyle{-\dfrac{x+4}{2x-1} < 0}\\\\\displaystyle{\dfrac{x+4}{2x-1} > 0}[/tex]

When we solve for the inequality, we should have x + 4 > 0 which results in x > -4. When union x > -4 with x < 1/2, it fits perfectly. Thus, the solution is:

[tex]\displaystyle{-4 < x < \dfrac{1}{2}}[/tex]

To identify the correct weight to the nearest 1/8 pound, you need to have a weight measurement that is divisible by 1/8 pound. If you have a weight that is not divisible by 1/8 pound, then you need to round it to the nearest 1/8 pound.

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By following this rounding method, you can determine the correct weight to the nearest 1/8 pound based on the specific weight measurement provided.

To identify the correct weight to the nearest 1/8 pound, we need a specific weight or measurement to work with.

Once we have that information, we can apply the rounding method.

When rounding to the nearest 1/8 pound, we look at the digit immediately after the 1/8 pound mark, which is 0.125 pounds.

If this digit is 4 or less, we round down, and if it is 5 or greater, we round up.

For example, let's say we have a weight of 15.6 pounds. The digit after the 1/8 pound mark is 6, which is greater than 4.

Therefore, we round up, and the weight to the nearest 1/8 pound is 15.75 pounds.

On the other hand, if we have a weight of 12.3 pounds, the digit after the 1/8 pound mark is 3, which is less than 4.

Thus, we round down, and the weight to the nearest 1/8 pound is 12.25 pounds.

Similarly, if the weight is 22.7 pounds, the digit in the thousandth place is 7. Since 7 is greater than 4, we round up.

The 1/8 pound measurement is 0.125 pounds, so rounding up gives us 22.875 pounds.

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Answer:

f(10) = 3(10) - 5 = 30 - 5 = 25

f(-10) = 3(-10) - 5 = -30 - 5 = -35

The statement is saying that if k is an element of the set obtained by combining the elements of n and the singleton set {n}, then k must either already belong to n or be equal to n.

The statement "It's obvious that k ∈ n ∪ {n} if and only if k ∈ n or k = n" expresses a relationship between the elements of a set n and the element n itself, along with another element k. In simpler terms, it states that if k belongs to the set obtained by taking the union of n and {n}, then k must either belong to n or be equal to n.

To understand this statement, let's break it down:

- The symbol "∈" denotes membership, indicating that an element belongs to a set.

- The symbol "∪" represents the union of two sets, which combines all the elements from both sets without duplication.

This is essentially highlighting the fact that when you take the union of a set with another set containing a single element (in this case, the set {n}), the resulting set will contain all the elements of the original set along with the additional element.

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Answer:

y = 3 * 9^x

Step-by-step explanation:

To write an exponential function in the form y = ab that goes through the points (0, 3) and (2, 243), we need to find the values of a and b.

Let's start by using the point (0, 3). When x = 0, y = 3. Substituting these values into the exponential function equation, we get:

3 = ab^0

3 = a * 1

a = 3

Now, let's use the second point (2, 243). When x = 2, y = 243. Substituting these values into the exponential function equation, we get:

243 = 3b^2

To find the value of b, we can rewrite the equation as:

3b^2 = 243

Dividing both sides of the equation by 3, we have:

b^2 = 81

Taking the square root of both sides, we get:

b = ±9

Since we are looking for a positive value for b, we can take b = 9.

Therefore, the exponential function that goes through the points (0, 3) and (2, 243) is: y = 3 * 9^x

The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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The total cost of 24 copper hearts is approximately $13.08.

To find the total cost of 24 copper hearts, we need to calculate the total amount of copper used and then multiply it by the cost per pound of copper.

Given:

- Each heart uses 0.75 in³ of copper.

- There is 0.323 pound of copper per cubic inch.

- The cost of copper is $2.25 per pound.

First, we calculate the total amount of copper used by multiplying the copper volume per heart by the number of hearts:

Total copper used = 0.75 in³/heart * 24 hearts = 18 in³.

Next, we convert the copper volume to pounds by multiplying it by the copper density:

Total copper in pounds = 18 in³ * 0.323 lb/in³ = 5.814 lb.

Finally, we find the total cost by multiplying the total copper weight by the cost per pound:

Total cost = 5.814 lb * $2.25/lb = $13.0825.

Therefore, the total cost of 24 copper hearts is approximately $13.08.

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Given statement solution is :- a) T = [tex]A^−1[/tex] b) T - 1.

For suitable values of s = -2 and t = 1, T = [tex]A^−1[/tex] and T - 1.

To show that for suitable values of s and t, T = [tex]A^−1[/tex], and T - 1, let's assume a matrix A and its inverse [tex]A^−1[/tex]. We'll find suitable values of s and t such that T = [tex]A^−1[/tex] and T - 1.

Consider the equation T = [tex]A^−1[/tex]. If T is the inverse of A, then we have A * [tex]A^−1[/tex] = I, where I is the identity matrix. Let's construct a specific matrix A and solve for [tex]A^−1[/tex] to find T.

Let's take the following matrix A:

A = [[1, 2],

[3, 4]]

To find the inverse of A, we can use the formula:

[tex]A^−1[/tex] = (1 / det(A)) * adj(A)

where det(A) represents the determinant of A, and adj(A) is the adjugate of A.

The determinant of A is calculated as follows:

det(A) = 1 * 4 - 2 * 3 = -2

Now, let's find the adjugate of A by interchanging the elements of the main diagonal and changing the sign of the other elements:

adj(A) = [[4, -2],

[-3, 1]]

Finally, we can compute [tex]A^−1[/tex] by multiplying the adjugate by the reciprocal of the determinant:

[tex]A^−1[/tex] = (1 / -2) * [[4, -2],

[-3, 1]]

= [[-2, 1],

[3/2, -1/2]]

Therefore, we have found the inverse of A. We can set T =[tex]A^−1[/tex]:

T = [[-2, 1],

[3/2, -1/2]]

Now, let's show that T - 1 using suitable values of s and t. To do that, we'll assume T - 1 = [tex]A^−1[/tex] and solve for s and t.

Let's set T - 1 =[tex]A^−1:[/tex]

T - 1 = [[-2, 1],

[3/2, -1/2]]

We can rewrite T - 1 as:

T - 1 = [[s, t],

[u, v]]

Comparing the corresponding elements, we have:

s = -2

t = 1

u = 3/2

v = -1/2

Therefore, for s = -2 and t = 1, we have T - 1 = [tex]A^−1.[/tex]

In conclusion, we have shown that for suitable values of s = -2 and t = 1, T = [tex]A^−1[/tex] and T - 1.

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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Step-by-step explanation:

you shuld us student demos brow it wold grafe that for you easyly

[tex]((x^3) * (x^2))^4[/tex] divided by [tex]3x^4[/tex]simplifies to[tex]x^{16/3[/tex]using the rules of exponents.

To simplify the expression[tex]((x^3) * (x^2))^4[/tex]divided by [tex]3x^4[/tex], we need to follow the rules of exponents.

First, let's simplify the numerator,[tex]((x^3) * (x^2))^4[/tex]. According to the exponent rule for multiplying powers with the same base, when we multiply two powers with the same base, we add their exponents. Applying this rule, we get[tex](x^{(3+2)})^4[/tex], which simplifies to [tex](x^5)^4.[/tex]

Next, we apply the exponent rule for raising a power to another power. When we raise a power to another power, we multiply the exponents. In this case, we have [tex](x^5)^4[/tex], which becomes [tex]x^{(5*4)[/tex] or [tex]x^{20.[/tex]

Now let's simplify the denominator, [tex]3x^4[/tex]. Since division is equivalent to multiplying by the reciprocal, we can rewrite the expression as [tex](x^{20})/(3x^4).[/tex]

To simplify this division, we use the exponent rule for dividing powers with the same base. According to this rule, when we divide two powers with the same base, we subtract their exponents. In this case, we have [tex]x^{20[/tex] divided by x^4, which gives us[tex]x^{(20-4)[/tex]or x^16.

Therefore, the simplified expression for [tex]((x^3) * (x^2))^4[/tex]divided by 3x^4 is[tex]x^{16/3.[/tex] This is the final answer, as the expression has been simplified as much as possible.

In summary,[tex]((x^3) * (x^2))^4[/tex]divided by 3x^4 simplifies to [tex]x^{16/3[/tex] using the rules of exponents.

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The maximum amount of monthly rent payment he could pay would be $755 per month.

Mika has the option of buying a condominium for a monthly payment of $675 or renting it with an option to buy it at the end of 3 years.

If he buys it now, he must pay $7,100 for closing costs. If he rents it, he must pay one month’s rent and a $750 security deposit for move-in costs.

Mika decides to rent instead of buying because it is the cheapest option over the first 3 years. He would still need to pay his first month’s rent on top of these move-in costs.

The maximum amount of monthly rent payment Mika could pay would be $755 per month.

Here's how to determine it: In the case of renting, Mika pays $750 for the security deposit, $675 for the first month’s rent, and $675 for the remaining 35 months of the lease.

So the total cost of renting the condominium for 3 years will be:750 + 675 + (675 × 35) = 24,375 To determine the maximum monthly rental payment that Mika could pay, we must divide the total rental cost by the total number of rental months: 24,375 ÷ 36 = 676.25 Since we are looking for the maximum amount of monthly rent payment, we can round up to the nearest dollar: $677.

Therefore, the maximum amount of monthly rent payment he could pay would be $755 per month.

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To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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The computer can occupy a maximum of 1200 bytes of memory.

To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.

If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.

The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.

Hence, the maximum memory capacity this computer can occupy would be 300 memory words.

To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:

300 memory words * 4 bytes per word = 1200 bytes.

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Answer:

9

Step-by-step explanation:

[tex]\frac{3^4}{3^2}=3^{4-2}=3^2=9[/tex]

Answer:

[tex]\textsf{25)} \quad y=6\cdot 2^x[/tex]

[tex]\textsf{26)}\quad y=3\cdot 7^x[/tex]

Step-by-step explanation:

The general form of an exponential function is:

[tex]\boxed{y=ab^x+c}[/tex]

where:

As the asymptote is y = 0 for both equations, the general function to use is:

[tex]\boxed{y=ab^x}[/tex]

To write the equation of an exponential function that passes through the given pairs of points, substitute both points into the exponential function and solve to find the values of a and b.

[tex]\hrulefill[/tex]

Given points:

Substitute point (0, 6) into the formula and solve for a:

[tex]\begin{aligned}y&=ab^x\\\implies 6&=ab^0\\6&=a(1)\\a&=6\end{aligned}[/tex]

Substitute the found value of a and the point (3, 48) into the formula and solve for b:

[tex]\begin{aligned}y&=ab^x\\\implies48&=6b^3\\8&=b^3\\b&=\sqrt[3]{8}\\b&=2\end{aligned}[/tex]

Therefore, the exponential equation with asymptote y = 0 that passes through points (0, 6) and (3, 48) is:

[tex]\boxed{y=6\cdot 2^x}[/tex]

[tex]\hrulefill[/tex]

Given points:

Substitute point (1, 21) into the formula, and point (2, 147) into the formula, to create two equations:

[tex]21=ab^1 \implies ab=21[/tex]

[tex]147=ab^2 \implies ab^2=147[/tex]

Divide the second equation by the first equation to eliminate a and solve for b:

[tex]\dfrac{ab^2}{ab}=\dfrac{147}{21}[/tex]

 [tex]\dfrac{b^2}{b}=7[/tex]

   [tex]b=7[/tex]

Substitute the found value of b into the first equation and solve for a:

[tex]\begin{aligned}ab&=21\\7a&=21\\a&=3\end{aligned}[/tex]

Substitute the found values of a and b into the formula to write an exponential equation with asymptote y = 0 that passes through points (1, 21) and (2, 147):

[tex]\boxed{y=3\cdot 7^x}[/tex]

The boat will arrive at the other port at 12:45 p.m.

To determine the time the boat arrives at the other port, we can use the formula:

Time = Distance / Speed

Given:

Distance = 80 km

Speed = 32 km/h

Calculate the time it takes for the boat to travel the given distance:

Time = Distance / Speed

Time = 80 km / 32 km/h

Time = 2.5 hours

Convert the time to minutes:

Since the time is given in hours, we need to convert it to minutes.

1 hour = 60 minutes

2.5 hours = 2.5 * 60 = 150 minutes

Add the calculated time to the departure time:

The boat leaves the port at 10:15 a.m. We need to add 150 minutes to this time to find the arrival time.

10:15 a.m. + 150 minutes = 12:45 p.m.

Therefore,​ the boat will arrive at the other port at 12:45 p.m.

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Answer:

835.66m^2 (to 2d.p)

Step-by-step explanation:

Firstly split the shape up so you get a rectangle and 2 circles.
Find the area of the circle:
formulae = πr^2
14/2=7
7^2=49
49π*2 (as there is two circles)= 98
98π=307.876
Find the circumference of the circle
formulae = dπ
14π=43.98
43.98 is the height of the rectangle
43.98*12=527.79 (rounded to 1d.p)
Area of rectangle is 527.79
Area of two circles is 307.876
Add them together = 835.66m^2 (to 2d.p)

Answer:

836cm^2

Step-by-step explanation:

For the sides, do 14/2 to find the radius (r) which is 7.

7^2 x pi = 153.9380400259 (formula for area of a circle is pi x r^2)

Multiply this by 2 to account for both sides of the cylinder.

For the cross-section of the cylinder, do 2 x pi x the radius (7) x 12 (the length, or l) which gets you 527.787565803085.

527.787565803085 + (153.9380400259 x 2) = 835.663645854885, rounded to 836 centimetres squared.

Hope this helps :D

Answer: 2/90 = 1/45

Step-by-step explanation:

Answer:

It will take approximately 9 years to take investment *o reach the value of $940

The transformation from the function f(x) to g(x) is:

The graph was shrunk vertically by a factor of ¹/₉ and then moved downwards by 2 units

Multiplying the outside of a function would lead to multiplying the y-values.

Multiplying a function by a number greater than 1 means that the graph is stretched vertically.

Multiplying the function by a number between 0 and 1 makes the graph shrink vertically.

Thus, since we have f(x) = x transformed to g(x) = ¹/₉x - 2, then it means that the graph was shrunk vertically by a factor of ¹/₉.

Now, when we shift, move, or translate vertically, shifting upwards by "c" units means we add c to the function.
Moving downwards by c units means we subtract c from the function.

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The measure of x in the circle is 21 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

The measure of x can be calculated using the fact that the angle in a semicircle is 90 degrees

So, we have

4x + 6 = 90

Using the above as a guide, we have the following:

4x = 84

Evaluate

x = 21

Hence, the value of x is 21

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The solution to the equation 4 |x + 7| + 8 = 32 is x = -1 and x = -13.So, the correct answer is: B. x = -1 and x = -13

To solve the equation 4 |x + 7| + 8 = 32, we can follow these steps:

1. Subtract 8 from both sides of the equation:

  4 |x + 7| = 24

2. Divide both sides by 4:

  |x + 7| = 6

Now we have two cases to consider, one for when x + 7 is positive and one for when x + 7 is negative.

Case 1: x + 7 ≥ 0

In this case, the absolute value simplifies to x + 7:

  x + 7 = 6

  Subtract 7 from both sides:

  x = -1

Case 2: x + 7 < 0

In this case, the absolute value simplifies to -(x + 7) since x + 7 is negative:

  -(x + 7) = 6

  Remove the negative sign:

  x + 7 = -6

  Subtract 7 from both sides:

  x = -13

Therefore, the solution to the equation 4 |x + 7| + 8 = 32 is x = -1 and x = -13.

So, the correct answer is:

B. x = -1 and x = -13

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The given information tells us that Terry's wins-to-races ratio is 2:3, but we cannot determine the exact number of races he has won without additional information about the total number of races he has participated in.

If the ratio of the number of times Terry has won to the number of races he has swum in is 2:3, we can set up a proportion to determine the number of races he has won.

Let's denote the number of times Terry has won as x, and the total number of races he has swum in as y. According to the given ratio, we have:

x/y = 2/3

To find the value of x, we need to solve for x when y is known. Since y represents the total number of races, we don't have that information in the given problem. Therefore, we cannot determine the exact number of races Terry has won without knowing the total number of races he has participated in.

The ratio tells us the relationship between the number of wins and the total number of races, but without knowing the denominator (total races), we cannot find a specific value for the numerator (number of wins). We can only determine the ratio between the two quantities.

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The current yield of the corporate bond is 14.23%.

1. To calculate the current yield, we need to divide the annual coupon payment by the market price of the bond.

2. The annual coupon payment can be calculated by multiplying the coupon rate by the par value of the bond.

  Annual coupon payment = Coupon rate * Par value = 13.41% * $1,000 = $134.10

3. The market price of the bond is given as $943.01.

4. Now, divide the annual coupon payment by the market price of the bond and multiply by 100 to convert it to a percentage.

  Current yield = (Annual coupon payment / Market price of the bond) * 100

  Current yield = ($134.10 / $943.01) * 100

  Current yield ≈ 0.1423 * 100 ≈ 14.23%

5. Round off the current yield to two decimal points, and that gives us the final answer.

  The current yield of the corporate bond is 14.23%.

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Answer:

Step-by-step explanation:

Surface area of a cone = surface area of a circle = pi r^2

250 = pi r^2

[tex]r = \sqrt{ \frac{250}{2} } = 5 \sqrt{5} \: cm[/tex]

Because the height (h) of the cone is double the length of its radius

Then

h = 2r

[tex]h \: = 2 \times 5 \sqrt{5} = 10 \sqrt{5} = 22.36 \: cm[/tex]

The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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