Can anyone help me with this

Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

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Answer:

z = 44

Step-by-step explanation:

26/z = 13/22

Using cross products

26 * 22 = 13*z

Divide each side by 13

26/13 * 22 = 13z/13

2 *22 =z

44 =z

Answer:

Z=44

To solve this proportion, you have to isolate z. You have to do what you do on one side of the equal sign to the other as well.

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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The given statement (A-B) ∩ (C-B) = A - (B ∪ C) is False , and the counter example is given below .

In the question ,

it is given that ,

(A-B) ∩ (C-B) = A - (B ∪ C)  ,

we use Boolean algebra to prove it ,

Solving LHS first ,

= (A-B) ∩ (C-B)

= A ∩ B' ∩ C ∩ B'          .....because (A - B) = A ∩ B'

= A ∩ B' ∩ C                  ..... because B' ∩ B' = B'

Solving RHS ,

we get ,

= A - (B ∪ C)

= A ∩ (B ∪ C)'            ....because (A - B) = A ∩ B'  ,

= A ∩ (B' ∩ C')            .....by DE Morgan's Law

= A ∩ B' ∩ C'

we see that , LHS ≠ RHS ,

So , the statement is False .

The counter Example is ,

Let A = { 1, 2, 3} , B = { 1, 2, 4} , C = { 2, 4, 5}

LHS is = (A - B) ∩ (C - B)

Putting the values,

LHS = { 3 } ∩ { 5 } = ∅

and  RHS = A - (B υ C)

Putting  the  values,

RHS = { 1, 2, 3} - { 1, 2, 4, 5}

= { 3 }

So , LHS ≠ RHS

Therefore , we have proved that the given statement is false using a counter example .

The given question is incomplete , the complete question is

Prove that each statement is true and find a counterexample for each statement that is false. assume all sets are subsets of universal set u .

For all sets A,B,C,

(A-B) ∩ (C-B) = A - (B ∪ C)

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Reason:

The scale factor 1.75 is what we'll multiply by each dimension of the blue figure, to get the green figure.

The "3" is multiplied by 1.75 to get 3*1.75 = 5.25 which is the value of x, since both involve the top side of each respective trapezoid.

In other words,

(preimage Length)*(scale factor) = (image length)

(3)*(1.75) = x

5.25 = x

x = 5.25

Therefore , the solution of the given problem comes out to be that one statement is true other than else are false.

In mathematics, inequalities describe the connection between two variables that are not equal. Equal implies to be equal, not. The "not equal symbol ()" is typically used to indicate that two values are not equaivalent. But different inequalities are used to compare the data to see if one is more or less than the other.

Here,

0 < a<1<b

Multiply all terms by b since b>1

0 < ab < b < \(b^{2}\)

Since

b > 1 , then ab > a so then ,

0 < a<ab <  b < \(b^{2}\)  

Given that,

F. 0< ab<a, Never true

G. 0< ab<1, Not always true

H. a< ab<1, Not always true

J. a< ab<b, True

K. b< ab, Never true

Therefore , the solution of the given problem comes out to be that one statement is true other than else are false.

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Looking at the question, I'm assuming it has a mistake.

However, I will first attempt to solve it normally:

Simply combine like terms to get 5x = 180, and thus x = 36, and y = 72

The first mistake possibility is that the first equation should be 3x + 2y = 180

If that is the case, simply substitute in 2x for y, turning the equation into

3x + 2 (2x) = 180

3x + 4x = 180

7x = 180

Thus, x = 25.715 and y = 51.43

Another possible mistake is that the first equation should be 3y + 2x = 180

Solve similar to the first mistake

3 (2x) + 2x = 180

6x + 2x = 180

8x = 180

Thus, x = 22.5, and y = 45

Hope it helps :)

Answer:

\(276\) acres of old-growth trees are there.

Step-by-step explanation:

Given: A forest covers \(69,000\) acres. A survey finds that \(0.4\%\) of the forest is​ old-growth trees.

To find: How many acres of​ old-growth trees are​ there?

Solution:

We have,

A forest covers \(69,000\) acres.

Now, \(0.4\%\) of the forest covers old-growth trees.

So, old-growth trees covers \(=0.4\%\) of \(69,000\).

\(=\frac{0.4}{100} \times69,000\)

\(=\frac{4}{1000} \times 69,000\)

\(=276\)

Hence, \(276\) acres of old-growth trees are there.

Answer:

276 acres in the forest.

Step-by-step explanation:

Total area of the forest = 69000 acres

Old — grown trees = 0.4%

0.4% of 69000 = 69000× 0.4/100

= 69000×0.004= 276

Old grown trees are covered 276 acres in the forest.

Answer:

send a pic, and I will edit this so you can know the answer but send a pic thx

Step-by-step explanation:

Answer:

if it's 5 or more, increase the previous digit by one.

Answer:

4) Dmytro drank more juice

5) Henrietta is older

Step-by-step explanation:

4)

Dmytro drank 7/4 bottles which is 1.75 bottles

Jitka drank 1 1/2 bottles which is 1.5 bottles

So, Dmytro drank more juice

5)

Henrietta is 7 2/3 years old which is 7.66

Jagdeep is 65/12 years old which is 5.41

So, Henrietta is older

Answer:

53 degrees

Step-by-step explanation:

Complementary angles add to 90 degrees

a+b = 90

a=37

37+b = 90

Subtract 37 from each side

37+b-37 = 90-37

b =53

Answer: 53 degrees

Step-by-step explanation: We can find the measure of <b by taking 90 minus the measure of <a which is 90 - 37 or 53 degrees.

Answer:

don't know this answer closely relates to

Answer:

90 + 30+60=180

3y=60

y=60/3

y=20

Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

The exact coordinates of the terminal point (2,y) are (2, 2.06) to two decimal places.

The exact coordinates of the terminal point (2,y) on a circle with radius 3 and an angle of 2.4 radians can be found using trigonometric functions of sine and cosine.

To solve for the y-coordinate, we can use the formula: y = sin(2.4) × 3. Evaluating this expression, we get: y = 3 × sin(2.4) ≈ 2.06. Therefore, the y-coordinate of the terminal point is approximately 2.06.

To solve for the x-coordinate, we can use the formula: x = cos(2.4) × 3. Evaluating this expression, we get: x = 3 × cos(2.4) ≈ 0.621. Therefore, the x-coordinate of the terminal point is approximately 0.621.

Hence, the exact coordinates of the terminal point (2,y) are (2, 2.06) to two decimal places.

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Answer:

Circumference= 84.78 or if needed simplified 85

Step-by-step explanation:

c=2×3.14×r

in this case to get the radius divide the diameter by 2 which would equal 13.5 so the formula would be

2×3.14×13.5=84.78

Answer:

1. 25% 2. 3/4 3. 125% 4. 1.5

Step-by-step explanation:

25% is 1/4 of 100% and 100% aka 4/4 is seen as 1 whole meaning 125% is 1.25 and 1.5 is greater than that.

Answer:She sold 21 magazines on Thursday

Step-by-step explanation:

Step 1

The Total price  of magazine sold on Thursday, Friday and Saturday, she sold $66 .

if she sold $3 more on Thursday than she did on Friday and $6 more on Saturday than she did on Thursday. The expression of the sales can be given as    

Let T represent  Thursday

F represent Friday

S represent Saturday such that

 T + F+ S= 66

T+ T-3 + T+6= 66

Step 2----- Solving

T+ T-3 + T+6= 66

3T - 3+ 6=66

3T+3= 66

3T= 66-3

3T=63

T= 63/3

T= 21

F= T-3= 21-3 =18

S = T+6 = 21+6= 27

She sold 21 magazines on Thursday, 18 on Friday and 27 on Saturday

Answer:

(3x+2)^2+1

Step-by-step explanation:

(f°g)(x) =g(f(x)) =g(3x+2)=(3x+2)^2 +1

Answer:

3(x+1) + 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given polynomial:

Group as follows:

As we see all terms have (x² + 1) as factor apart from the last one.

It means the remainder is - x

Correct choice is C

Option B's equation y = -1/5x + 1/10 has the same slope as the linear function depicted in the table.

One way to describe a linear function is as an algebraic equation with variables raised to the power .A straight line makes up the graph of a linear equation. Y = mx + b, where x and y are variables and m and b are constants, is one of the most typical examples of a linear function.

For instance, if we have the linear function f(x) = 2x + 3, we may calculate the value of f(4) by changing x to 4 and getting f(4) = 2(4) + 3 = 11.

Calculating the difference between y and x for any two points will allow us to determine the slope of the linear function shown in the table. Let's pick the first and last items from the table:

Slope = (change in y) / (change in x) = (0-1/5) / (1/2 - (-1/2)) = (-1/5) / 1 = -1/5

As a result, the table's linear function has a slope of -1/5.

The next step is to find the linear function whose slope is equal to -1/5. Let's look at the possibilities:

A) y = 1/2x + 1/10, slope = 1/2; B) y = -1/5x + 1/10, slope = -1/5 (correct)

C) y = 1/5x - 1/2, slope = 1/5; D) y = 1/2x - 1/10, slope = 1/2

As a result, option B, y = -1/5x + 1/10, is the linear function with the same slope as the one shown in the table.

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The linear function with the same slope as the one represented by the table is: y = -1/5x + 1/10

So the answer is B) y = -1/5x + 1/10.

A linear function is a mathematical function that has a graph that is a straight line.

It can be represented by the equation y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.

To find the slope of the linear function represented by the given table, we can choose any two points and use the slope formula:

slope = (change in y) / (change in x)

Let's choose the points (-1/2, 1/5) and (1/2, 0):

slope = (0 - 1/5) / (1/2 - (-1/2))

= (-1/5) / 1

= -1/5

So the slope of the linear function is -1/5.

Now we need to find the linear function with the same slope.

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept. We know that the slope is -1/5, so we can eliminate answer choices A and D, which have slopes of 1/2 and 1/2, respectively.

To determine the y-intercept, we can use one of the points from the table. Let's use the point (-1/2, 1/5):

1/5 = (-1/5)(-1/2) + b

Simplifying:

1/5 = 1/10 + b

b = 1/5 - 1/10

b = 1/10

So the y-intercept is 1/10.

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer: 375

Step-by-step explanation:

Since we are given the information that there are 250 bricks used to build a wall 20 feet high, the number of brick used per feet will be:

= 250/20

= 12.5 bricks per feet.

Therefore, the number of bricks that will be used to buld a wall that is 30 fet high will be:

= 12.5 × 30

= 375 bricks.

Therefore, 375 bricks would be used.

Answer:

198/0.33= 600

Step-by-step explanation:

Answer:

2.2 kg

Step-by-step explanation:

1000g = 1kg

8700g = 8.7kg

3/4 = 75%

8700 / 100 = 87

87 * 75 = 6525

8700 - 6525 = 2175

2.175kg or if rounded 2.2kg

Answer:

Step-by-step explanation:

The slope-intercept form of a line is y = mx + b, where m is the slope of the line. We can rewrite the given equation y = (13/5)x + (7/6) in this form:

y = (13/5)x + (7/6)

y = (13/5)x + (7/6) * (5/5) // find a common denominator

y = (13/5)x + (35/30)

y = (13/5)x + (7/10)

Comparing this to the slope-intercept form y = mx + b, we see that the slope of the line is m = 13/5.

Therefore, the slope of the line is 13/5.

Hi! I'd be pleased to assist you with your permutations, probability, and position-related query. If a set of 24 children—14 boys and 10 girls—were lined up in a random order, what is the likelihood that the child in the 16th spot is a boy?

Step 1: Compute all possible combinations for the 24 children.

There are 24 children, hence there are 24 possible permutations in all! (Factorial, 24).

Step 2: Determine how many permutations there are with a boy in the sixteenth place.

Consider that there are currently 23 seats available for the remaining 13 boys and 10 girls to do this. The remaining children can be set up in 23! (23 factorial) different ways as a result.

Step 3: Use a to divide the permutations.

Step 4: Calculate the probability.
Probability = (Permutations with a boy in the 16th position) / (Total permutations)
Probability = (14 * 23!) / (24!)

Now, to simplify this expression, we can divide both the numerator and the denominator by 23!:
Probability = (14 * 23!) / (24! * 23! / 23!)
Probability = 14 / 24

Step 5: Simplify the probability.
Probability = 7/12

So, the probability that the person in the 16th position is a boy is 7/12.

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To find the probability that the person in the 16th position is a boy, we need to first calculate the total number of possible permutations in which any person can be in the 16th position. This can be calculated using the formula for permutation, which is n!/(n-r)!, where n is the total number of people and r is the number of positions.

So, the total number of permutations for 24 people in random order is 24!/(24-1)! = 24!

Next, we need to find the number of permutations in which a boy is in the 16th position. Since there are 14 boys and 10 girls, we can choose one of the 14 boys for the 16th position and then arrange the remaining 23 people in any order. This can be calculated using the formula for combination, which is nCr = n!/(r!(n-r)!), where n is the total number of items and r is the number of items chosen.

So, the number of permutations with a boy in the 16th position is 14C1 * 23! = 14 * 23!

Therefore, the probability of a boy being in the 16th position is the number of permutations with a boy in the 16th position divided by the total number of permutations, which is:

(14 * 23!)/24! = 14/24 = 7/12

In conclusion, the probability that the person in the 16th position is a boy is 7/12.

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The approximate number of students awarded a bachelor's degree in 2009 is likely to be around 1,601,000 (option c).

Let's go through each option:

a. 916,000: This option suggests that around 916,000 students were awarded a bachelor's degree in 2009.

b. 685,000: This option suggests that around 685,000 students were awarded a bachelor's degree in 2009.

c. 1,601,000: This option suggests that around 1,601,000 students were awarded a bachelor's degree in 2009.

d. 1,322,000: This option suggests that around 1,322,000 students were awarded a bachelor's degree in 2009.

Now, without any additional context or information, it is difficult to determine the exact number of students who received a bachelor's degree in 2009. However, we can make an educated guess by considering the average number of students who typically graduate each year.

Based on historical data, the number of students awarded bachelor's degrees in the United States has been steadily increasing over time. In 2009, the number of bachelor's degrees awarded was around 1.6 million. Therefore, option c (1,601,000) seems to be the most reasonable estimate among the given options.

In conclusion, the approximate number of students awarded a bachelor's degree in 2009 is likely to be around 1,601,000 (option c).

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Explanation:

The distance between two points (x1, y1) and (x2, y2) is:

In this problem points are (-6, 13) and (8, 13). The distance is:

Answer:

The distance is 14