Which equation has no solution?

4(x + 3) + 2x = 6(x + 2)
5 + 2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)

Answer:

To prove that F = A’BC + A’BC’ + A’B’C + AB’C + ABC is equivalent to F = A'B + C, we can use proof by rewrite to simplify and transform one expression into the other.

Starting with F = A’BC + A’BC’ + A’B’C + AB’C + ABC, we can apply the distributive law to factor out A’ and get:

F = A’(BC + BC’ + B’C) + AB’C + ABC

Next, we can use the law of complementation to simplify A’(BC + BC’ + B’C) as A’B + A’C, and then use the distributive law again to factor out C:

F = A'B + A'C + AB'C + ABC

Finally, we can use the law of idempotence to simplify A'C + ABC as C + A'BC, and then substitute this into the above expression to get:

F = A'B + C

Therefore, we have shown that F = A’BC + A’BC’ + A’B’C + AB’C + ABC is equivalent to F = A'B + C using proof by rewrite. The key to the simplification was applying the distributive law, law of complementation, and law of idempotence, and using the fact that the uniting law allows us to combine terms that have a common variable.

Consider the given equation is \(3-2x=15\) and one of the 6 in the options is -6.

Given:

The equation is

\(3-2x=15\)

To find:

The value of x.

Solution:

We have,

\(3-2x=15\)

Subtracting 3 from both sides, we get

\(3-2x-3=15-3\)

\(-2x=12\)

Divide both sides by -2.

\(x=\dfrac{12}{-2}\)

\(x=-6\)

Therefore, the value of x is -6.

Answer:

Use mathpapa, it's a great calculator and it explains the steps

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Step-by-step explanation:

Answer:122 days

Step-by-step explanation:

To find all functions \(\(f\)\) such that \(\(f(bt)\)\) is a martingale, we can apply \(Itô's\) Lemma to \(\(f(bt)\).\)

The \(Itô's\) Lemma formula in one dimension is:

\(\[df(t) = f'(t)dt + f''(t)dW(t)\]\)

Where:

- \(\(f(t)\)\) represents the function we want to find.

- \(\(df(t)\)\) represents the differential of the function.

- \(\(f'(t)\)\) represents the first derivative of \(\(f\)\) with respect to \(\(t\).\)

- \(\(dt\)\) represents an infinitesimal change in time.

- \(\(f''(t)\)\) represents the second derivative of \(\(f\)\) with respect to \(\(t\).\)

- \(\(dW(t)\)\) represents the differential of the Wiener process (a standard Brownian motion).

Now, let's apply \(Itô's\) Lemma to \(\(f(bt)\):\)

\(\[df(bt) = f'(bt)dbt + f''(bt)dW(bt)\]\)

Where:

- \(\(b\)\) represents a constant.

- \(\(db(t)\)\) represents an infinitesimal change in \(\(b\).\)

To make \(\(f(bt)\)\) a martingale, we require that the drift term in the differential equation is zero. Therefore, we have:

\(\[f'(bt)dbt = 0\]\)

This implies that \(\(f'(bt) = 0\)\) for all \(\(t\)\). Thus, \(\(f(bt)\)\) must be a constant function. Let's denote this constant as \(\(C\).\) Therefore, we have:

\(\[f(bt) = C\]\)

So, all functions \(\(f(bt)\)\) that satisfy the condition of being a martingale are constant functions of the form \(\(f(bt) = C\).\)

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The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.

In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.

Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.

Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.

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The volume of the figure is the sum of the volume of the square prism and the volume of the square pyramid which is 67.2cm³

To calculate the volume of the figure, we need to find the volume of the square prism and the volume of the square pyramid.

The volume of a square prism is given as;

V = L³

V = 4³

V = 64cm³

The volume of the square pyramid is given as;

V = 1/3lh

V = 1/3 * 4 * 2.4

V = 3.2cm³

The volume of the figure is 64cm³ + 3.2cm³ = 67.2cm³

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The approximate value of x in the equation using change of the base of logarithmic rule found as -1.317.

The change of base rule of the log is used to write the given logarithmic number in terms of ratio of two log numbers.

For example,

\(\log_ba=\dfrac{\log_xa}{\log_xb}\)

Here, a,b is the real number and x is the base.

The logarithmic equation given in the problem is,

\(log_5(15) = x+ 3\)

Using the change of base formula, the above equation can be written as,

\(\dfrac{log{15} }{log{5} }= x+ 3\)

Isolate the x variable as,

\(x=\dfrac{log{15} }{log{5} }- 3\\x=\dfrac{1.17609}{0.69897}- 3\\x\cong-1.317\)

Hence, the approximate value of x in the equation using change of the base of logarithmic rule found as -1.317.

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Answer:

B

Step-by-step explanation:

B) -1.317

According to the information the length of x of the boat sail would be 10.5.

To calculate the length of x we must identify the data that we have available. In this case we have the length of the base of both boats sails and the length of the height of one of the boats. According to the above, if these candles have a scale we can apply a rule of thumb to find the length of x. Here is the procedure:

According to the above, the length of x of the boat sail would be 10.5

Note: This question is incomplete. Here is the complete information.

Imagen anexada

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The function is growing exponentially at a rate of 5.5% every year.

The exponential decay equation is given by:-

\(y = (1 \pm r)^n\)

Where r is the rate of decay and A is the initial amount and n is the time period.

The function is given in the question below as:

The function \(f(t) = 1500(1.055)^{60}\) ....(i)

This represents the change in quantity over t days.

As per the given exponential decay equation,

\(\implies f(t) = 1500(1.055)^{60}\)

We can above function rewrite as:

\(\implies f(t) = 1500(1 + 0.055)^{60}\)

\(\implies f(t) = 1500\huge \text(1 + \dfrac{5.5}{100}\huge \text)^{60}\)

\(\implies f(t) = 1500(1 + 5.5\%)^{60}\)

Compare to the standard exponential decay equation, and we get

\(\implies r= 5.5\%\)

Therefore, the function is growing exponentially at a rate of 5.5% every year.

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Step-by-step explanation:

The two angles added together = a right angle = 90 degrees

so  8m+7    + 5m+5   = 90

      13m  + 12 = 90

     13m = 78

      m = 78/13 = 6

Answer:

17,955

Step-by-step explanation:

5% turns into 0.05 multiply the numbers 0.05 and 17100 you end up with 855 then add both since sales tax INCREASES the price and the final answer should be 17,955.

Answer:

17,955.

Step-by-step explanation:

5% divide by 100 = 0.05

0.05 times 17100 = 855

855 + 17100 and the final answer should be 17,995

Answer:

1/2x-18

Step-by-step explanation:

18 subtracted from half of a number

We assume that the "number" is x

so 1/2x is the half of a number

We now need to have 18 subtracted from that so 1/2x-18

From the stem and leaf plot, let's write the data set:

10.9 cm

11.0 cm

11.2 cm

11.2 cm

12.1 cm

12.3 cm

We need to find the range of the data set, which is, the difference between the length of the longest pencil and the shortest pencil.

From the data set, we can see:

• Length of Longest Pencil = 12.3 cm

• Length of Shortest Pencil = 10.9 cm

The difference is

12.3 - 10.9 = 1.40 cm

The approximate change in surface area under the given condition if the radius increases by 0.01 cm is 3.54 cm².

The derived formula using the principles of surface area of a sphere is given as

A = 4πr²

staging the values to calculate the surface area before the increase in radius

A = 4 x π x (12)²

A = 4 x 3.14 x 144

A ≈ 1809.56 cm²

From the given question if the radius increases by 0.01 then new radius is 12.01cm

Therefore, the new surface area derived is

A' = 4π(12.01)²

A' = 4 x 3.14 x(12.01)²

A' ≈ 1813.1 cm²

considering the recent events the change in surface area

ΔA = A'-A ≈ 1813.1 - 1809.56 ≈ 3.54 cm²

The approximate change in surface area under the given condition if the radius increases by 0.01 cm is 3.54 cm².

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Answer:

y + 4x + 2

Step-by-step explanation:

ANSWER

EXPLANATION

We want to find the solution to the system of equations given, using the graph.

On a graph, the solution of a system of equations is the point where the lines of the two equations intersect one another. This means that the ordered pair made up of the x and y coordinates of the point where the two lines meet is the solution to the system of equations.

Therefore, going by that, the solution to the given system of equations is:

Answer:

31/32 or 0.96875

Step-by-step explanation:

first you muliply 5/8 by 3/4 then the answer add it to 1/2

The true statement is the angle XWZ is right angle.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

The complete question is:

Line segment W Y is an altitude in triangle WXZ.

Triangle W X Z is shown. An altitude is drawn from point W to point Y on side Z X, forming a right angle. Angles Z W Y and W X Y are congruent.

If ΔYWZ ~ ΔYXW, what is true about Angle XWZ?

Angle XWZ is an obtuse angle.

Angle XWZ is a right angle.

Angle XWZ is congruent to Angle WXY.

Angle XWZ is congruent to Angle XZW.

As, in triangle WXZ, WY is an altitude.

So, ∠ WYZ = ∠ XYW = 90°

Now, ∠ ZWY = ∠ WXY.

Now, from Δ XYW,

∠ WXY + ∠ YWX = 90°

∠ ZWY + ∠ YWX =  180° {Since, ∠ ZWY = ∠ WXY}

∠ XWZ = 90°

Hence, the angle XWZ is right angle.

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Answer:B

Step-by-step explanation:

y = 25x

the x represents gallons

Step-by-step explanation:

11/4 X 5/12

Lcm of denominators= 12

11 3 33

X =

4 3 12

33/12 X 5/12 = 165/12

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Answer:

cos C = 7/25

Step-by-step explanation:

(cos C = opposite side divided by the hypotenuse)

cos C = 7/25

The final coordinates after the given transformation is:

A)  (-(x + 2), -y)

B) (0, 5)

A) When the coordinate (x, y) is mapped by a reflection about the line x = 2, we note:

(1) The y-coordinate is unaffected.

(2) For reflections the distance from the line of reflection to the object is equal to the distance to the image point.

∴ a = 2 + 2 = 4 units

Thus, the image point is 4 units from the line of reflection

The new coordinate is:

((x + 2), y)

The rule for a rotation by 180° about the origin is: (x, y) → (−x, −y) .

The final transformation is: (-(x + 2), -y)

2) Sequel to the translation, the coordinate is (0, 5).

Now, if the point (x, y) is reflected across the line y = a, then the relation between coordinates of actual point and image point will be:

(x, y) → (x, 2a − y) .

Thus, a reflection around the line y = 5 gives:

(0, 2(5) - 5) = (0, 5)

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Answer:

Every integer greater than 1 is either prime or composite.

Step-by-step explanation:

Let us negate this statement.

Assumption - any number greater than 1, is neither prime nor composite.

A prime number has only 2 divisors, and a composite number has at least 3.

Let a number be X such that X >1.

Now X is divisible by 1 (Any integer is divisible by 1)

And X is divisible by X (X/X = 1, if X is not zero)

So by this, we see X has at least 2 divisors, X is either prime, or composite if it has more divisors!

So our assumption is wrong, and every integer greater than 1 is either prime or composite.

Answer:

2nd option

{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)}

Step-by-step explanation:

For a function to exist, every value of input must have exactly one value of output.

The rest of the relations(1, 3, and 4) have 2 outputs for 1 input so they dont make a function.

Answer:

(B)

Step-by-step explanation:

If you noticed, all the other input values have one input value that has two output values. This doesn't represent a function. Only (B) has one output for each input.

Hope that helps (●'◡'●)

Answer:

36 total cookies

Step-by-step explanation:

2 dozen = 2/3 of the total cookies

24 = 2/3 of the total cookies

24/x = 2/3

cross multiply

24(3) = 2x

72 = 2x

x = 36

Check the math: 2/3 x 36 = 72/3 = 24

Answer:

\(4x^6y^2\)

Step-by-step explanation:

\(x^{m} *x^{n} = x^{m * n}\)

2^2 = 4

(x^3)^2 = x ^3*2 = x^6

y^2 = y^2

Answer:

x = 14

Step-by-step explanation:

2(x + 3) + 5 = 39

2x + 6 + 5 = 39

2x + 11 = 39

2x = 28

x = 14

\(2(x + 3) + 5 = 39 \\ \\ 2x + 6 + 5 = 39 \\ \\ 2x + 11 = 39 \\ \\ 2x = 39 - 11 \\ \\ 2x = 28 \\ \\ x = 14 \\ \\ x = 7\)

Answer:

The probability that Dominik is the goalie given that the goal attempt was blocked is 0.667 or 66.7%.

Step-by-step explanation:

To find the probability of Wayne attempting a shot on goal, we need to count the number of times Wayne appears in the data and divide it by the total number of shots taken:

Number of shots attempted by Wayne: 4

Total number of shots: 10

Probability of Wayne attempting a shot on goal: 4/10 = 0.4 or 40%

Therefore, the probability of Wayne attempting a shot on goal is 0.4 or 40%.

To find the probability of a goal given that Wayne took the shot, we need to count the number of goals scored by Wayne and divide it by the total number of shots he attempted:

Number of goals scored by Wayne: 2

Number of shots attempted by Wayne: 4

Probability of a goal given that Wayne took the shot: 2/4 = 0.5 or 50%

Therefore, the probability of a goal given that Wayne took the shot is 0.5 or 50%.

To find the probability that Dominik is the goalie given that the goal attempt was blocked, we need to count the number of times Dominik appears as the goalie when a shot was blocked and divide it by the total number of blocked shots:

Number of blocked shots where Dominik was the goalie: 2

Total number of blocked shots: 3

Probability that Dominik is the goalie given that the goal attempt was blocked: 2/3 = 0.667 or 66.7%

Therefore, the probability that Dominik is the goalie given that the goal attempt was blocked is 0.667 or 66.7%.