A farmer has 64 sheep, and you take 12 now the farmer has 52. How many sheep do you have?

Answer:

You didn't include the following choices. If you would let me know in the comments, I'd be happy to help!

The point on the line y = 5x + 3 that is closest to the origin is (0, 3). This is obtained by minimizing the distance between the origin and any point on the line.

To find the point on the line y = 5x + 3 that is closest to the origin, we need to minimize the distance between the origin (0, 0) and any point on the line.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).

In this case, we want to minimize the distance between (0, 0) and any point on the line y = 5x + 3.

Substituting y = 5x + 3 into the distance formula, we get: √(x^2 + (5x + 3)^2).

To minimize this distance, we need to find the x-value that minimizes the expression inside the square root. Taking the derivative of this expression and setting it equal to zero, we find x = 0.

Therefore, the point on the line y = 5x + 3 that is closest to the origin is when x = 0, which gives us the point (0, 3).

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The sum of the reciprocals of all the positive factors of the perfect number 28 is 2.

A factor is a number that divides another number by itself and leaves no residue. In other words, if multiplying two whole numbers yields a product, the numbers being multiplied are factors of the result since the product is divisible by them. Factors may be found using two methods: multiplication and division. Factors are numbers that may be multiplied together to get another number.

Here,

The sum of the reciprocals of all the perfect number 28's positive elements is 2.

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Answer:

a. 1.5

b 1.6 or 1.7

c. 90

Step-by-step explanation:

a. the initial height is 1.5 m (x=0)

b. the maximum height occurs at x = 20, probably 1.6 or 1.7 m

c. the arrows reaches 90 m when it lands (y=0)

hope this helps.

Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

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The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

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There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.

The following are the steps to find the number of positive factors of a number:

Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:

24 = 2 × 2 × 2 × 3

Step 2: Same bases should be added in powers. So, the factors we can write as

24 = 2³ × 3¹

Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.

I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.

So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.

It is given that, m, p, and t are distinct positive prime numbers.

Then, the number of positive divisors greater than 1 for the number m³pt are

m³× p × t

Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,

N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16

So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.

Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.

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\(tan = \frac{opp}{adj} \)

\(tan = \frac{12}{5} \)

Answer:

it is option C, hope it helps

To prove this \(Rank(AB)â¤min(Rank(A),Rank(B))Rank(AB)â¤min(Rank(A),Rank(B))\) , we use matrices.

If A and B are matrices, then to prove that Rank(AB) ≤ min(Rank(A), Rank(B)), the rank of the matrix is ​​the maximum number of linearly independent rows or columns.

You can use the fact that there is Inside is a matrix.

Suppose A is an m-by-n matrix and B is an n-by-p matrix. In this case, product AB is an m-by-p matrix.

Let rA be the rank of A and rB be the rank of B.

First, note that the column space of AB is a subspace of the column space of A. This is because the columns of AB are linear combinations of the columns of A.

Thus, the column-space dimension of AB is at most equal to the column-space dimension of A equal to rA.

Similarly, the row space of AB is a subspace of the row space of B. This is because the rows of AB are linear combinations of the rows of B.

Therefore, the row-space dimension of AB is at most equal to the row-space dimension of B equal to rB.

Now consider the null space of AB. ABx = 0 if x is a vector in the null space of AB. This means that Bx is in A's null space.

Therefore, the dimension of the nullspace of AB is at least the dimension of the nullspace of A, and by the rank zeroness theorem, the dimension of the nullspace of A is n-rA.

Therefore, the dimension of the null space of AB is at least n - rA.

Similarly, consider the null space of B. ABx = 0 if x is a vector in the null space of B. This means that Ax is in the null space of AB.

Therefore, the dimension of the null space of B is at least the dimension of the null space of AB. By the rank nullity theorem, the dimension of the null space of AB is p − rB.

Therefore, the dimension of the null space of B is at least p − rB. Combining these inequalities gives:

Disabled (AB) ≥ n - rA

invalid (AB) ≥ p - rB

Adding these inequalities gives:

2nullity(AB) ≥ (n + p) - (rA + rB)

The rank zero theorem tells us that:

Invalid (AB) = n - Rank (AB) = p - Rank (AB)

So the above inequality can be rewritten as

2(Rank(AB)) ≤ (n + p) - (rA + rB)

Adding rA + rB on both sides gives:

2(Rank(AB)) + rA + rB ≤ n + p

Since rank(AB), rA, and rB are all non-negative integers,

2(Rank(AB)) ≤ n + p

Dividing both sides by 2 gives:

rank(AB) ≤ (n + p)/2

Both n and p are non-negative integers, so

(n + p)/2 ≤ min(n, p)

For this:

rank(AB) ≤ min(n, p) = min(rank(A), rank(B))

This completes the proof.

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Step-by-step explanation:

4x-9y=-9 1

2x +3y=3 2

1 - 2(2)

4x -9y=-9

(2)* -4x -6y=6

________

0-15y=-3

15y=3

y=3/15

y=1/5

Answer:

Hope it helps

4x-9y=9

-x+3y=6

The exponential growth function will be:  y = 4000(1 + 0.04)⁴

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.

We are given;,

Initial population = 4000

Rate of increase = 4%

Let current population be p.

Let number of years passed be t.

Thus, the exponential growth function will be:

y = 4000(1 + 0.04)⁴

Complete question is;

A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals make up 3 percent of the town's population.

Part A

Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.

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Answer:

number of emergency response professionals = 3% of population

e = 0.03p

e is a function of p

e(p) = 0.03p

Step-by-step explanation:

edumentum

Mathematical operators are essential tools for expressing mathematical ideas and solving problems in a concise and precise manner. The following parts can be solved the concept of Mathematical operators.

a) Let P(x) be the predicate "x is a negative real number" and Q(x) be the predicate "x is positive". Then the statement "the product of two negative real numbers is positive" can be expressed as:

∀x . ∀y[(P(x) ∧ P(y)) → Q(x . y)]

which reads "For all x and y, if x and y are negative real numbers, then the product of x and y is positive."

b) Let R(x) be the predicate "x is a real number". Then the statement "the difference of a real number and itself is zero" can be expressed as:

∀x[R(x) → (x - x = 0)]

which reads "For all x, if x is a real number, then the difference between x and x is zero."

c) Let S(x) be the predicate "x is a positive real number", and T(x, y) be the predicate "y is a square root of x". Then the statement "every positive real number has exactly two square roots" can be expressed as:

∀x[S(x) → ((∃y(T(x, y) ∧ ∀z(T(x, z) → z=y))) ∧ (∃y. ∃z(T(x, y) ∧ T(x, z) ∧ y ≠ z)))]

which reads "For all x, if x is a positive real number, then there exist exactly two distinct real numbers y and z such that y and z are square roots of x."

d) Let U(x) be the predicate "x is a negative real number", and V(x) be the predicate "x does not have a real square root". Then the statement "a negative real number does not have a square root that is a real number" can be expressed as:

∀x[U(x) → V(x)]

which reads "For all x, if x is a negative real number, then x does not have a real square root.

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It came rude when I typed. so, I took screenshot for your answer.

The given equation are illustrations of trigonometry identities. The value of \(\sin^2\theta + \sin^4\theta\) is 1

Given that:

\(\cos \theta + \cos^2 \theta = 1\)

In trigonometry:

\(\sin^2 \theta + \cos^2\theta = 1\)

Rewrite as:

\(\sin^2 \theta = 1 - \cos^2\theta\)

Make \(\cos \theta\) the subject in \(\cos \theta + \cos^2 \theta = 1\)

\(\cos\theta = 1 - \cos^2 \theta\)

Compare \(\sin^2 \theta = 1 - \cos^2\theta\) and \(\cos\theta = 1 - \cos^2 \theta\)

\(\sin^2 \theta = \cos \theta\)

So:

\(\sin^2\theta + \sin^4\theta\) becomes

\(\sin^2\theta + \sin^4\theta = \sin^2\theta + (\sin^2\theta)^2\)

Substitute \(\sin^2 \theta = \cos \theta\)

\(\sin^2\theta + \sin^4\theta = cos\theta + (cos\theta)^2\)

\(\sin^2\theta + \sin^4\theta = cos\theta + cos^2\theta\)

Recall that: \(\cos \theta + \cos^2 \theta = 1\)

This means:

\(\sin^2\theta + \sin^4\theta = 1\)

Hence, the value of \(\sin^2\theta + \sin^4\theta\) is 1

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The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s

What is a slope-intercept function?

A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that  represents Macario's hourly wage y is shown thus:

y=9x+0.12s

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Answer:

The second one

Answer: The second one i think

Step-by-step explanation:

Answer:

64

Percentage Calculator: 16 is what percent of 25? = 64.

Step-by-step explanation:

PLZ MARK BRAINLIEST I REALLY NEED THEM TO LEVEL UP

Answer:

C. 2/3

Step-by-step explanation:

correct for september 2022

We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

So, the wood we need to make 120 pins:

Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.

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The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

\(h = 4\sqrt{3}\)

Step-by-step explanation:

If the triangle is equilateral, it means that all the sides are the same. Since there are 3 sides in a triangle, each side is 24/3 = 8

Now, in order to find the height, we can use the pythagoeren theroem. Notice that the height bisects(splits the side) into two equal parts, which each part having the length 8/2 = 4

So we have \(h^2 + 4^2 = 8^2\)

\(h^2 = 48\)

\(h = 4\sqrt{3}\)

SOLUTION

From the question

And a poster is in a shape of a rectangle. The area of a rectangle is measured as

So, the expression for the area of the poster becomes

Hence the answer is

Answer:

y = 4/6x - 4

Step-by-step explanation:

y = mx + b, m = slope and b = y intercept

Rise over run

Rise = +4

Run = +6

This means the slope is 4/6.

The y intercept is at -4.

Now, plug in the numbers for y = mx + b

y = 4/6x - 4

Step-by-step explanation:

25-9=16

4x=16

x=4

mask =$4

The 1st box: 14.3

second box: 2.052

Third box: 2

fourth box: 28

fifth box: 13.5

sixth box: 15.1

The 1st box: 14.3

second box: 2.052

Third box: 2

fourth box: 28

fifth box: 13.5

sixth box: 15.1

2/3 + (-1/3) = 2/3 - 1/3 = 1/3

Answer:

x = \(-\frac{3}{8}\)

Step-by-step explanation:

Answer:

your answer is -3/8 or in decimal form its -0.375

Step-by-step explanation:

According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,

To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:

According to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).

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the nominal interest rate per year for a one-month loan of $500 with a 6% fee is 6.4%. It is important to note that this is the nominal interest rate, which does not take into account the effect of compounding

The nominal interest rate is the annual percentage rate (APR) that is charged on a loan, without taking into account the effect of compounding. To calculate the nominal interest rate per year for a one-month loan of $500 with a 6% fee, we need to first calculate the total cost of the loan, which is the sum of the loan amount and the fee.

The fee for a loan of $500 is 6% of $500, which is $30. Therefore, the total cost of the loan is:

Total cost = Loan amount + Fee = $500 + $30 = $530

To calculate the nominal interest rate per year, we need to know the number of months in a year. Since there are 12 months in a year, the nominal interest rate per year can be calculated as follows:

Nominal interest rate per year = (Total cost / Loan amount - 1) * (12 / Number of months)

= ($530 / $500 - 1) * (12 / 1)

= 6.4%

Therefore, the nominal interest rate per year for a one-month loan of $500 with a 6% fee is 6.4%. It is important to note that this is the nominal interest rate, which does not take into account the effect of compounding. The effective interest rate, which does take into account the effect of compounding, may be higher than the nominal interest rate, especially for longer loan terms. It is important for borrowers to carefully consider the terms of the loan and the total cost of borrowing before taking out a loan.

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