Which relation is a function?

A. {(-2,6),(2,-6),(6,-2),(-6,2),(2,6)}
B. {(7,2),(-3,-5),(3,2),(6,7),(-3,4)}
C. {(-8,9),(8,-5),(-8,4),(6,-3),(8,1)}
D. {(-3,5),(6,10),(5,-2),(-6,-5),(3,9)}

The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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Step-by-step explanation:

work he in a department store

Answer:

You will have 28 dollars in 4 hours

Step-by-step explanation:

4 x 7 =28

The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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Answer: The first box in the model is 60. The box above it is 300. The box above 20 is 70. The answer is 74.

Step-by-step explanation: Self-explanatory.

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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ANSWER

Angle PQR

EXPLANATION

We have that PQRS is a scale copy of ABCD.

This means that ABCD was dilated to form PQRS.

What this simply means is that all the sides of PQRS are only larger than those in ABCD by a certain factor.

This also means that all the angles in ABCD are equal with those in PQRS.

In other words, if we observe PQRS, we see that the angle that corresponds with ABC is angle PQR.

The simplification of the trigonometric function tan x csc x is;  sec x

The six trigonometric functions are defined as;

sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Now, we know that;

cot x = cos x/sin x

sec x = 1/cos x = (cos x)⁻¹

csc x = 1/sin x = (sin x)⁻¹

tan x = sin x/cos x

Thus;

tan x csc x = (sin x/cos x) * (1/sin x)

= 1/cos x = (cos x)⁻¹

= sec x

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1. The volume under the surface \(f(x,y)=e^{x+y}\) is given by the double integral,

\(\displaystyle\int_0^1\int_0^1e^{x+y}\,\mathrm dx\,\mathrm dy\)

We split up the integration region into a 2x3 grid of rectangles whose upper right corners are determined by the right endpoints of the partition along either axis. That is, we split up the \(x\) interval [0, 1] into 2 subintervals,

[0, 1/2], [1/2, 1]

with right endpoints given by the arithmetic sequence,

\(r_i=0+\dfrac{i(1-0)}2=\dfrac i2\)

for \(i\in\{1,2\}\), and the \(y\) interval [0, 1] into 3 subintervals,

[0, 1/3], [1/3, 2/3], [2/3, 1]

with right endpoints

\(r_j=0+\dfrac{j(1-0)}3=\dfrac j3\)

for \(j\in\{1,2,3\}\).

Then the upper right corners of the 6 rectangles are the points

(1/2, 1/3), (1/2, 2/3), (1/2, 1), (1, 1/3), (1, 2/3), (1, 1)

generated by the sequence \((r_i,r_j)\).

The integral is thus approximated by the sum

\(\displaystyle\sum_{j=1}^3\sum_{i=1}^2f(r_i,r_j)\dfrac{1-0}m\dfrac{1-0}n=\dfrac16\sum_{j=1}^3\sum_{i=1}^2f(r_i,r_j)=\frac{e^{5/6}+e^{7/6}+e^{4/3}+e^{5/3}}6\)

or approximately 2.4334. (Compare to the actual value of the integral, which is close to 2.952.)

For the midpoint rule estimate, we replace the sampling points \((r_i,r_j)\) with \((m_i,m_j)\), i.e. the midpoints of each subinterval, so the set of sampling points is

(1/4, 1/6), (3/4, 1/6), (1/4, 1/2), (3/4, 1/2), (1/4, 5/6), (3/4, 5/6)

and the integral is approximately

\(\displaystyle\sum_{j=1}^3\sum_{i=1}^2f(m_i,m_j)\dfrac{1-0}m\dfrac{1-0}n=\frac{e^{5/12}+e^{3/4}+e^{11/12}+e^{13/12}+e^{5/4}+e^{19/12}}6\)

or about 2.908.

2. We approach the second integral the same way. Split up the \(x\) interval into 8 subintervals with left and right endpoints given respectively by

\(\ell_i=-2+\dfrac{(i-1)(2-(-2))}8=\dfrac{i-5}2\)

\(r_i=-2+\dfrac{i(2-(-2))}8=\dfrac{i-4}2\)

for \(i\in\{1,2,\ldots,8\}\), and the \(y\) interval into 2 subintervals with

\(\ell_j=0+\dfrac{(j-1)(2-0)}2=j-1\)

\(r_j=0+\dfrac{j(2-0)}2=j\)

for \(j\in\{1,2\}\).

The upper left corners of the rectangles in this grid are given by the sequence \((\ell_i,r_j)\). So the integral is approximately

\(\displaystyle\sum_{j=1}^2\sum_{i=1}^8f(\ell_i,r_j)\frac{2-(-2)}m\frac{2-0}n=51\)

(Compare to the actual value, 32.)

The expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662

The expected population of each country is calculated as:

P(n) = a *(1 + r)^n

Where:

2025 is 25 years since 2000.

This means that:

n = 25

So, we have:

Australia

P(25)= 19169000 * (1 + 0.6%)^25

P(25)= 22261221

China

P(25)= 1261832000* (1 + 0.6%)^25

P(25)= 1465382683

Mexico

P(25)= 100350000 * (1 + 0.6%)^25

P(25)= 116537821

Zaire

P(25)= 51965000* (1 + 0.6%)^25

P(25)= 60347662

Hence, the expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662

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Step-by-step explanation:

distribute the 3

3(w)-5(3)+4w

3w-15+4w

add like terms

7w-15

Answer:

(a): x = 125 yards.

(c): x = 170 yards.

Step-by-step explanation:

Given

\(f(x) = x(200 - x)\)

\(x = length\\\\\)

\(f(x) = area\)

Required

Determine the possible length

For a length to be possible or usable, the calculated area must be greater than 0.

(a): x = 125 yards.

\(f(x) = x(200 - x)\)

Substitute 125 for x

\(f(125) = 125 * (200 - 125)\)

\(f(125) = 125 * 75\)

\(f(125) = 9375\)

(b): x = 200 yards.

\(f(x) = x(200 - x)\)

Substitute 200 for x

\(f(200) = 200 * (200 - 200)\)

\(f(200) = 200 * 0\)

\(f(200) = 0\)

(c): x = 170 yards.

\(f(x) = x(200 - x)\)

Substitute 170 for x

\(f(170) = 200 * (200 - 170)\)

\(f(170) = 200 * 30\)

\(f(170) = 6000\)

(d): x = 225 yards.

\(f(x) = x(200 - x)\)

Substitute 225 for x

\(f(225) = 200 * (200 - 225)\)

\(f(225) = 200 * (- 25)\)

\(f(225) = -5000\)

(e): x = 210 yards.

\(f(x) = x(200 - x)\)

Substitute 210 for x

\(f(220) = 200 * (200 - 210)\)

\(f(220) = 200 * (- 10)\)

\(f(220) = -2000\)

From the above calculations, only values of x that are 125 and 170 makes the function true

The molar entropy of mixing is given by the equation S_mix = R(x1lnx1+x2lnx2).

To maximize the molar entropy of mixing, we need to find the value of x1 and x2 that will produce the maximum value of S_mix. Differentiating S_mix with respect to x1 and x2 and setting the derivatives equal to 0 will yield the critical points. The critical points can then be tested to see which one produces the maximum value of S_mix. After differentiating, we get x1 = x2 = 1/2. This implies that the molar entropy of mixing is maximized when the mole fraction of each component is 0.5. The corresponding maximized change in molar entropy upon mixing is Rln2 which is equal to 2.30258509299405 j/mol-k.

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Answer:

7) -1.75

8) 2

Step-by-step explanation:

7) m=-7/4 =-1.75

8)M m=8/4 = 2

Answer:

ln which class's do you are

Answer:

the formula for the volume of a sphere is

\( \frac{4}{3} \pi \: {r}^{3} \)

r is the radius, which is half the diameter. Since the diameter of the whole sphere is 18 the radius would be half of that, which is 9. If you plug 9 into the formula you get 3052.08in.cubed. Now you must find the volume of the smaller core, the diameter of the core is 3, so the radius is 1.5 and if you plug that into the formula you get 14.13in.cubed. Since you're finding only the volume of the outside layer, you would subtract the volume of the core from the whole sphere, so 3052.08-14.13=3037.95

Your answer is 3037.95in.cubed

Answer:

4.20

Step-by-step explanation:

First find the total cost of the nametags

105 * .12

12.60

Then divide by the 3 teachers

12.60/3 =4.20

Each teacher will pay 4.20

h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}\)

Answer:

28.26 in

Step-by-step explanation:

Radius = (1/2) diameter

Radius = (1/2)(9)

Radius = 4.5 in

Circumference = 2πr

Circumference = 2(3.14)(4.5)

Circumference = 28.26 in

What we observe here

Two consecutive sides are equal

Answer:

KITE.

Explanation:

As it has two pairs of adjacent sides and a total of 4 sides.

Sides adjacent to each other:

WZ = WZ

ZY = XY

Answer:

just sub

Step-by-step explanss

Answer:

38.88

Step-by-step explanation:

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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a) The numeric values of each function at x = 3 are given as follows:

b) The division is given as follows: f(3)/g(3) = 5.

c) The domain of f(x)/g(x) is given as all real values except x = -7, as the function g(x), which is the denominator of the division, assumes a value of 0 at x = -7.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Hence the numeric values are found replacing the lone instance of x by 3 in each function, as follows:

Hence the division is given as follows:

(f/g)(3) = f(3)/g(3) = 50/10 = 5.

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Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other

Let \($V_1, V_2$\) be the two subspaces of V. Suppose \($V_1 \cup V_2$\) is a subspace of V.

Then if \($x_1 \in V_1$\) and \($x_2 \in V_2$\) then we must have \($x_1 \in V_1 \cup V_2$\) and\($x_2 \in V_1 \cup V_2$\) so that we must have \($x_1+x_2 \in V_1 \cup V_2$\).

If and only if one of the subspaces is contained in the other, the union of the two subspaces is a subspace.

But this by definition means \($x_1+x_2 \in V_1$\) or \($x_1+x_2 \in V_2$\). Either way, by the existence of additive inverses and the closure properties for the subspaces we have:

\(\left(x_1+x_2\right)+\left(-x_1\right) \in V_1\)

Or

\(\left(x_1+x_2\right)+\left(-x_2\right) \in V_2\)

By the associative/commutative properties, we have:

\(x_2 \in V_1 \text {, or, } x_2 \in V_1\)

Thus we have shown if \($x_1 \in V_1$\) and \($x_2 \in V_2$\) then \($x_1 \in V_2$\) or \($x_2 \in V_1$\). If \($x_1 \in V_2$\) for all \($x_1 \in V_1$\) then we have \($V_1 \subseteq V_2$\). If \($x_2 \in V_1$\) for all \($x_2 \in V_2$\) then \($V_2 \subseteq V_1$\). In either case, we see one subspace is a subset of the other.

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