Determine the smallest integer that makes -3x + 7 - 5x < 15 true.

State the smallest possible value for x in the solution set below as a number only.

Answer:

(t x 7) 5 - 2

Step-by-step explanation:

I think that is how it would look, I hope it helps!

We can conclude that log10(7) is irrational using a proof by contradiction with the steps given below.

To prove that log10(7) is irrational using a proof by contradiction, we start by assuming that log10(7) is rational, which means that it can be expressed as a ratio of two integers p and q:

log10(7) = p / q

where p and q have no common factors.

We can then use the definition of logarithms to rewrite this equation in exponential form:

10^(p/q) = 7

Next, we raise both sides of the equation to the power of q to eliminate the denominator:

10^p = 7^q

Now, we can assume the opposite, which is that log10(7) is rational and then find a contradiction. If log10(7) is rational, then 10^p and 7^q are also integers. However, 7 and 10 are relatively prime, which means that they do not share any common factors.

This implies that the prime factorization of 7^q cannot include any factors of 2 or 5, which are the prime factors of 10. But since 10^p is an integer, it must have a prime factorization that includes at least one factor of 2 or 5.

Therefore, we have arrived at a contradiction, which shows that our assumption that log10(7) is rational is false. Hence, we can conclude that log10(7) is irrational.

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Answer:

x

Step-by-step explanation:

Answer:

12 divided by 1 can be 12. If thats what you mean and if not, just tell me by explaining with more detail

Step-by-step explanation:

Putting it all together, we get:
∫ 2tan^4(x) sec^6(x) dx = (2/5)tan^5(x) - (2/3)tan^3(x) + 4sec^3(x) - 4sec^2(x) + C

To evaluate this integral, we can use the substitution u = sec(x), which means du/dx = sec(x)tan(x) and dx = du/u^2.

Using this substitution, we can rewrite the integral as:

∫ 2tan^4(x) sec^6(x) dx = ∫ 2tan^4(x) sec^4(x) * sec^2(x) dx
= ∫ 2tan^4(x) (u^2 - 1)^2 du/u^2

Expanding (u^2 - 1)^2 and simplifying, we get:

∫ 2tan^4(x) (u^4 - 2u^2 + 1) du/u^2
= ∫ 2tan^4(x) u^2 du - ∫ 4tan^4(x) du + ∫ 2tan^4(x) du/u^2

The first integral can be evaluated using u = sec(x), giving:

∫ 2tan^4(x) u^2 du = ∫ 2(sec^2(x) - 1) tan^4(x) sec(x)tan(x) dx
= ∫ 2(sec^2(x) - 1) tan^5(x) dx
= (2/5)tan^5(x) - (2/3)tan^3(x) + C

The second integral can be simplified using the identity tan^2(x) = sec^2(x) - 1, giving:

∫ 4tan^4(x) du = ∫ 4(tan^2(x))^2 du = ∫ 4(sec^2(x) - 1)^2 du
= ∫ 4(u^2 - 2u + 1) du = 4u^3/3 - 4u^2 + 4u + C

Finally, the third integral can be evaluated using the substitution w = tan(x), which means dw/dx = sec^2(x) and dx = dw/sec^2(x).

Using this substitution, we get:

∫ 2tan^4(x) du/u^2 = ∫ 2w^4 dw
= (2/5)tan^5(x) + C

Putting it all together, we get:

∫ 2tan^4(x) sec^6(x) dx = (2/5)tan^5(x) - (2/3)tan^3(x) + 4sec^3(x) - 4sec^2(x) + C

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Answer:

y= P(0.87)^t

Step-by-step explanation:

Given data

Price P=  $24,000

Rate of decay in price= 13%

The expression in terms of y, p and t  is

y=P(1-r)^t

y= P(1-0.13)t

y= P(0.87)^t

Considering the probability concept, a random number table could be used as follows:

C) Read single-digit numbers until finding the first 0 or 1. Count the number of digits needed to get the first 0 or 1.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we want to count the number of spins it takes to reach values of 0 or 1, when there are 10 possible outcomes, hence option C is correct.

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Answer:

38

Step-by-step explanation:

It is 4,10,6,6,6,6 feet so add it up and it is 38

Answer:

x=0

Step-by-step explanation:

2x-9=0

2x=9

x=9/2

4x+10=0

4x=-10

x=-5/2

2(9/2)-9 =0

4(-5/2)+10=10

The angle of 15° in standard position can be sketched as a small angle formed by rotating a ray counterclockwise from the positive x-axis.

In standard position, an angle is formed by rotating a ray counterclockwise from the positive x-axis. The initial side of the angle is the positive x-axis, and the terminal side is the ray after rotation. To sketch the angle of 15°, start with the positive x-axis as the initial side. Then, rotate the ray counterclockwise by 15°. The terminal side of the angle will be the position of the ray after the rotation. The angle will be a small angle that opens up to the left of the initial side.

The sketch of the angle will resemble a small "tick" mark or an acute angle, pointing in the counterclockwise direction. The size of the angle will be 15°, which is relatively small, closer to the size of a right angle (90°). By following this process, you can accurately sketch the angle of 15° in standard position.

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Answer:

78.54 meters

Step-by-step explanation:

circular path

radius = 15 meters

First we have to calculate the circumference of the circular path = 2\(\pi r\)

= 2 * \(\pi * 15\)

= 94.285 meters ( total distance to be covered )

For Ali running at a speed of 8.4 meters/ seconds

It will take him : ( 94.285 / 8.4 ) seconds

= 11.22 seconds

You running at a speed of 7 meters/seconds

hence at 11.22 seconds when Ali must have crossed the finish line you must have covered ;

(11.22 * 7 ) meters

= 78.54 meters

Answer:

x=2  y=-4

Step-by-step explanation:

2x-y=4   solve for x

2x-0=4

2x=4+0

2x=4 . divide both sides by 2

x=2

2x-y=4 .  solve for y

0-y=4

-y=4 . divide both sides by -1

y=-4

The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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Answer: a

Step-by-step explanation: I did the test

Answer:

The total cost is $6.25

Step-by-step explanation:

3/4 of 1 kilo of rect

4/5 of 1 kilo of square

3/5 of 1 kilo of flower

rect = 3 per kilo

square = 3 per kilo

flower = 3 per kilo

First rectangle beads:

3x = y where x is number of kilos and y is full cost

3(3/4) = y

9/4 = y = 2 1/4 = $2.25

Second square beads:

3x = y where x is number of kilos and y is full cost

3(4/5) = y

12/5 = y = 2 2/5 = $2.20

Third flower beads:

3(x) = y where x is number of kilos and y is full cost

3(3/5) = y

9/5 = y = 1 4/5 = $1.80

Add costs together

1.80 + 2.20 + 2.25 = 6.25

The total cost is $6.25

The coordinates of the point that lies between the points C and D is represented by E(x, y) = (- 8 + 17 · k, - 15 + 12 · k), for 0 < k < 1.

In this question we know that the locations of the ends of the line segment CD are known and must determine the location of a point within the line segment, between the points C and D. The coordinates of the points can be found by using the line segment formula:

E(x, y) = C(x, y) + k · [D(x, y) - C(x, y)], where 0 < k < 1.

If we know that C(x, y) = (- 8, - 15) and D(x, y) = (9, - 3), then the location of the point within the line segment is:

E(x, y) = (- 8, - 15) + k · [(9, - 3) - (- 8, - 15)]

E(x, y) = (- 8, - 15) + k · (17, 12)

E(x, y) = (- 8 + 17 · k, - 15 + 12 · k), for 0 < k < 1.

The coordinates of the point that lies between the points C and D is represented by E(x, y) = (- 8 + 17 · k, - 15 + 12 · k), for 0 < k < 1.

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Answer:

25\(x^{6}\)

Step-by-step explanation:

Given

(5x³ )²

= 5x³ × 5x³

= 5 × 5 × x³ × x³

= 25\(x^{6}\)

Answer:

5^2x^6

Step-by-step explanation:

I put it into a algebra calculator and this is what I got so I hope it helps:))

Answer:

491.52

Step-by-step explanation:

1500×.80×.80×.80×.80×.80=491.52

The simplified forms of the given trigonometric expressions in terms of the second expression are as follows:The first expression can be simplified to csc(x) (cosec(x)), which is equal to 1/sin(x)

To simplify the first expression, we can rewrite it as (1 - cos(x))/(1 - cos^2(x)) - cos(x)/(1 + cos(x)). Using the identity sin^2(x) + cos^2(x) = 1, we can simplify the expression to (1 - cos(x))/(sin^2(x)) - cos(x)/(1 + cos(x)). Further simplifying, we get (1 - cos(x))/(sin^2(x)) - cos(x)(sin^2(x))/(sin^2(x)(1 + cos(x))). Combining the terms, we have (1 - cos(x) - cos(x)sin^2(x))/(sin^2(x)(1 + cos(x))). Using the identity sin^2(x) = 1 - cos^2(x), we can simplify the expression to (1 - cos(x) - cos(x)(1 - cos^2(x)))/(sin^2(x)(1 + cos(x))). Finally, simplifying further, we get csc(x).

The second expression is already simplified and can be written as cot(x).

The third expression is cos(x)/1 + sin(x), which can be simplified to cos(x).

The fourth expression is (tan(x) + cot(x))/sec(x). Using the identities sec(x) = 1/cos(x), tan(x) = sin(x)/cos(x), and cot(x) = cos(x)/sin(x), we can rewrite the expression as (sin(x)/cos(x) + cos(x)/sin(x))/(1/cos(x)). Simplifying further, we get (sin(x)sin(x) + cos(x)cos(x))/(cos(x)). Using the identity sin^2(x) + cos^2(x) = 1, we have (1)/(cos(x)), which is equal to sin(x)

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Answer:

(2)(9) + 75 = 75+18

Step-by-step explanation:

(2)(9) + 75 = 75+18

The expression written as a product of a number and another sum is 3(25 + 8)

Given the expression 75 + 18, we are to write as a product of a number and another sum.

First we need to find the GCF of 75 and 18

75 = 3 * 25

18 = 3 * 6

Since 3 is common to both D+GCF, we can factor it out from the expression to have:

75 + 18 = 3(25 + 8)

Hence the expression written as a product of a number and another sum is 3(25 + 8)

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Answer:

x = 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

7x - 3 = 39

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 39 does indeed equal 39.

∴ x = 6 is the solution to the equation.

Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.

The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is 303.

1313 - 1010 = 303

Based on this, the two numbers are 1010 and 1313

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Answer: Which of the following ordered pairs is a solution of the inequality 2x + 6y ≤ 10?a. (3, 1) b. (2, 2) c. (1, 2) d. (1, 0)Answer:The correct answer among the choices is letter d. From the following choices of ordered pair, (1, 0) is the set solution of the inequality 2x + 6y ≤ 10. Substituting the given pair order make the inequality a true statement.  To counter check answer, substituting the pair order and solving the linear inequality will result a value to support the correct answer.Step-by-step explanation:a. ( 3,1 ) (x ,y)Substitution2x + 6y ≤ 102(3) + 6(1) ≤ 106 + 6 ≤ 1012  ≤ 10 ( The inequality is False)This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.b. (2, 2) (x ,y)Substitution2x + 6y ≤ 102(2) + 6(2) ≤ 104 + 12 ≤ 1016  ≤ 10 ( The inequality is False)This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.c. (1, 2) (x ,y)Substitution2x + 6y ≤ 102(1) + 6(2) ≤ 102 + 12 ≤ 1014  ≤ 10 ( The inequality is False)This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.d. (1, 0) (x ,y)Substitution2x + 6y ≤ 102(1) + 6(0) ≤ 102 + 0 ≤ 102 ≤ 10 ( The inequality is True)The statement states that 2 is lesser than or equal to 10.

Step-by-step explanation:

Answer:

a= -2b

Step-by-step explanation:

math.

Answer:

k

Step-by-step explanation:

Answer: \(5\pi\)

Step-by-step explanation:

The circumference is \(10\pi\).

Half of this, which is the arc length of the semicircle is \(5\pi\).

Answer:

Yes.

Step-by-step explanation:

The intersection of the two graphs represents the area of all solutions for both inequalities. In this case, (1, -2) is in that area, thus we know that it is a solution to both inequalities.

Answer:

Yes

Step-by-step explanation:

The local maximum value of the function g(x) = x^4 - 3x^3 - 19x^2 occurs at x = -3/4, and its value is 49/16. The local minimum value of the function occurs at x = 2, and its value is -60.

To find the local maximum and minimum values of the function g(x) = x^4 - 3x^3 - 19x^2, we need to first take the derivative of the function and set it equal to zero to find the critical points. The critical points will correspond to the potential locations of local maximum or minimum values.

Step 1: Find the derivative of g(x):

g'(x) = 4x^3 - 9x^2 - 38x

Step 2: Set the derivative equal to zero and solve for x:

4x^3 - 9x^2 - 38x = 0

Step 3: Factor the equation or use numerical methods to solve for x:

x(x + 2)(2x - 19) = 0

From this equation, we can find the critical points at x = 0, x = -2, and x = 19/2.

Step 4: Determine the nature of each critical point:

To determine whether each critical point is a local maximum or minimum, we can use the second derivative test. Taking the derivative of g'(x) gives us the second derivative:

g''(x) = 12x^2 - 18x - 38

Plugging in the x-values of the critical points, we find:

g''(0) = -38 (negative, indicating a local maximum)

g''(-2) = 70 (positive, indicating a local minimum)

g''(19/2) = 1103/4 (positive, indicating a local minimum)

Therefore, we have identified two local extrema: a local maximum at x = -3/4 and a local minimum at x = 2. The corresponding values of g(x) at these points are 49/16 and -60, respectively.

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