3x+2=4; 2x-y=5 solve the system of equations algebraically using substitution

There were originally 36 plants in the nursery.

From the question, we have that we can be able to show the total number of the plants as x.

Hence;

When he passes the  1st guard:

x - (0.5x+2)

x -0.5x - 2

0.5x-2 plants left

When he passes the 2nd guard

(0.5x-2) - (0.5(.5x-2)+2)

0.5x - 2 - (0.25x-1+2)

0.5x - 2 - (0.25x+1)

0.5x - 2 - 0.25x - 1

When he passes the 3rd guard

(0.25x-3) - (0.5(0.25x-3)+2) = 1

0.25x - 3 - (0.125x-1.5+2) = 1

0.25x - 3 -(0.125x+.5) = 1

0.25x - 3 - 0.125x - 0.5 = 1

0.125x - 3.5 = 1

0.125x = 1 + 3.5

Then;

x = 4.5/0.125

x = 36 plants

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Answer: As the loan is amortized, Boris will make a series of equal payments each month for the duration of the loan, with each payment comprising of both interest and principal. The amount of interest in each payment will decrease over time, while the amount of principal in each payment will increase.

To calculate the monthly payments, we can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

Where:

M = monthly payment

P = the principal or the loan amount = 91500

i = interest rate as a decimal = 3.3%/12 = 0.00275

n = total number of payments = 40 years x 12 months/year = 480

By substituting the values in the formula:

M = 91500 [ 0.00275 (1 + 0.00275)^480 ] / [ (1 + 0.00275)^480 - 1]

M = $439.65

So the monthly payment that Boris will make is $439.65. This amount will stay the same throughout the loan term, but the proportion of interest to principal in each payment will change as the loan is amortized.

Step-by-step explanation:

Using Pythagorean theorem, AD = 9 units and AC = 25 units.

ΔABC is a right triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using Pythagorean theorem:

AB² = AD² + BD²

AD = √(AB² - BD²)

AD = √(15² - 12²)

AD = 9 units

AC = AD + CD

AC = 9 + 16 = 25 units

For ΔABC:

The hypotenuse is AC = 25.

Using  Pythagorean theorem to confirm if ΔABC a right triangle. That is:

AC² = BC² + AB²

25² = 20² + 15²

625 = 625

Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, ΔABC is a right triangle.

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Answer:

Rolando pays $63 for 20 rides

Step-by-step explanation:

this was the question right???

Correct option is C, The height of triangular prism is not 6 units, it is 15 units.

A triangle base, a translated copy, and three faces that join the appropriate sides make up a triangular prism, a three-sided prism. There are no rectangular sides in an oblique right triangle; it is only a right triangle. A right triangle is a uniform triangular prism, which has square sides and equilateral bases.

In essence, it is a polyhedron with three parallel sides, three surface normals in the same plane, and three surface normals (which is not necessarily parallel to the base planes). These three faces make it a parallelogram. Every cross-section that follows the base faces yields the same triangle.

For the given triangular prism,

The perimeter of base = Side + Side + Side = 13+11+8 = 32 units

The area of base = 1/2 × Base × Height = 1/2 × 11 × 6 = 33 units²

The height of prism = 15 units

The lateral surface area = (side + side + side) × height = 15 × (13 + 11 + 8) = 480 units²

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The probability of randomly drawing seven vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles is low. One time throughout the simulation's 500 iterations, all seven tiles were vowels.

Part A: What is the probability of randomly drawing 7 vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles?

Part B: To imitate one repetition of the process, you would use a table of random digits or a calculator to randomly generate seven digits, each between 0 and 9. The variable you would measure is the number of vowels drawn.

Part C:

Random Digits: 4, 2, 5, 7, 8, 8, 4

Vowels: 2, 8, 8, 4

Part D: This result suggests that it is possible to randomly draw all vowels in one draw, although it is unlikely.

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Answer:

3.5 cups of sugar / 1.75 cups of sugar = 2

3.5 x 2 = 7 cups of flour

Kareem needs 7 cups of flour to make muffins.

Answer:

(-5,-37)

Step-by-step explanation:

Complete the square

(x+5)^2-37

Let x be the number of $1 bills and y be the number of $10 bills.

We know that:

x + y = 59 (the total number of bills)

x + 10y = 239 (the total monetary value of the bills)

We can use the first equation to solve for one of the variables in terms of the other. For example:

x = 59 - y

We can substitute this expression for x into the second equation:

(59 - y) + 10y = 239

59 + 9y = 239

9y = 180

y = 20 (the number of $10 bills)

We can use this value of y to find the number of $1 bills by substituting it back into the first equation:

x + y = 59

x + 20 = 59

x = 39 (the number of $1 bills)

Therefore, the motel clerk has 39 $1 bills and 20 $10 bills.

Answer:

g(x) = 4x - (1/2)

Second choice

Step-by-step explanation:

Using points: (-2, -8.5) and (-1, -4.5)

            y2 - y1      -4.5 - (-8.5)      -4.5 + 8.5        4

slope = -----------  = ---------------  =  --------------- =   --- = 4

             x2 - x1         -1 - (-2)              -1 + 2            1

Answer:

the answer should be g(x) = 4x - (1/2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x=child number

Let y=adult number

so,    x+y=143

and  6x+9.5y=1089

Form x+y=143, we got x=143-y

so, 6x+9.5y=1089

will be 6(143-y) +9.5y=1089

then we got y=66

We are looking for adult ticket were sold, so it is 66 tickets.

The graph that shows the new position of the rectangle after a translation is; Option C

When it comes to transformation in mathematics, there are different types such as reflection, dilation, rotation, translation.

Now, we are dealing with translation which is defined as a transformation of a shape in a plane that preserves the length, which tells us that the object is transformed without getting its dimensions affected.

In this case, we see the rectangle in the graph and we can conclude that the translation of the rectangle shows the correct translation would be the second option because it shows that the length is preserved without getting its dimensions or shape altered.

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The total cost that he paid for the parking for 5 days is $26.00.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

The graph above shows the cost of parking at the airport,

since the graph is a straight line so it is the condition for a linear equation,

from the graph, the y-axis shows the price in dollars and the x-axis shows the number of days,

line of the graph passes from coordinates (0, 6) and (6, 30)

equation of line is y = mx + c

where c is initial cost when x is 0, y is 6

c = 6

and m = (y₂- y₁)/(x₂ - x₁)

m = (30 - 6)/(6 - 0)

m = 4

equation of line is,

y = 4x + 6

cost for 5 days,

x = 5

y = 4(5) + 6

y = 26

cost is $26.00

Hence cost for 5 days is $26.00, option C is correct.

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The measure of tangent BC from the given figure is 12.6 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, Circle A has radius =5.8 and DC=8.1. BC is tangent line.

Here, AB=AD= 5.8 units and AC=AD+DC =5.8+8.1

= 13.9

Using Pythagoras theorem, we have

AC²=AB²+BC²

13.9²=5.8²+BC²

BC²= 193.21-33.64

BC²= 159.57

BC=12.6 units

Therefore, the measure of tangent BC is 12.6 units.

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Let where is an integer greater than 9. compute the number of values of for which the sum of the squares of the digits of is at most 25.

The question asks us to count the number of values of for which the sum of the squares of the digits of is at most 25. To solve this problem, we can use a loop to iterate through all possible values of starting from 9 and up. For each value of , we can then calculate the sum of the squares of the digits of by using modulo and division operations to extract each digit and square it. If the sum of the squares of the digits of is at most 25, we can add 1 to the count of values. After the loop completes, we will have the total number of values of for which the sum of the squares of the digits of is at most 25.

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a. It is more likely to randomly select square yards of material and finding an average of or more flaws.

b. Normal distribution assumes that the data is continuous and symmetric, but in this case, the number of flaws per square yard is a count data, and it is not symmetric. Therefore, a normal distribution cannot be used to calculate the probability of the first event in part (a).

c. To calculate the probability of the second event in part (a), we would need the mean and standard deviation of the number of flaws per square yard, as well as the specific threshold of "or more flaws" to calculate the area under the curve that is greater than or equal to that threshold. Without that information, I cannot provide an accurate probability calculation.

I determined that it was not possible to calculate the probability of the second event in part (a) without the specific mean and standard deviation of the number of flaws per square yard and the specific threshold of "or more flaws." This is because in order to calculate the probability of an event, you need to know the underlying distribution of the data and the specific cut-off point for the event in question.

In the other part of the question, I stated that it is more likely to randomly select square yards of material and finding an average of or more flaws than it is to randomly select a square yard of material and finding 2 or more flaws.

I came to this conclusion without any calculations because in general, when you are looking for a specific number of flaws (in this case, 2 or more flaws) in a single square yard, it is typically less likely than finding an average of that number of flaws when you look at multiple square yards. This is because the number of flaws per square yard can vary, so even if the average is 2 or more flaws per square yard, it is still possible to find square yards with fewer than 2 flaws.

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Answer:

23

Step-by-step explanation:

just divide 34.5 and 1.5 that gives you the ammount of days she worked on her project

The factorization of three polynomials (x2 - 8x + 15) = (ax + b)(cx + d) is (x-5) (x-3)

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

The general equation of a straight line is given by the expression y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.

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Answer:

We multiply 3/4 with the reciprocal of 3/8 which is 8/3. This leaves us with 3/4x8/3 which equals 24/12. This can be simplified into 2.

Answer: where is the expression

Step-by-step explanation:

The augmented matrix for the linear system corresponding to the matrix equation Ax = b is |1 2 4 0| |-2 2 9| |0 1 4 1| |2 -1| |-2 -4 -3 -1| |9 -1|. Solving the system yields the solution vector (x, y, z) = (5, -1, 4).

The augmented matrix for the linear system Ax = b is a way of combining the two matrices into one matrix. In this case, it is the combination of the coefficient matrix A and the constant matrix b. This new matrix contains all of the information needed to solve the linear system, as it contains both the coefficients of the variables and the solutions of the equations. We can solve the linear system by performing row operations to the augmented matrix, which is equivalent to solving the equations in the original matrix equation. After performing the row operations, we will be left with the solution vector (x, y, z) = (5, -1, 4). This solution vector represents the values of the variables that satisfy the original equation.

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The correct option regarding the relationship between the population of the village and time is given as follows:

A. The population is decreasing over time.

The variables of the scatter plot are given as follows:

From the points on the scatter plot, we have that when the value of t increases, the value of P decreases.

This means that the scatter plot shows a decreasing relationship, and thus the correct option is given by option A.

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The biggest number of children in the group would be 14 boys and 14 girls.

Basic division is an arithmetic operation that involves two numbers. It is used to find out how many times one number can be divided into another. It is sometimes referred to as division or division by a divisor.

Division is the inverse operation of multiplication. This means that division is the opposite of multiplication. When a number is multiplied by another number, the result is the product of the two numbers. When a number is divided by another number, the result is the quotient of the two numbers.

The process of division involves finding the number of times that one number can be divided into another. Division is performed by dividing the dividend (the number being divided) by the divisor (the number that divides the dividend). The result of the division is the quotient.

Division can be done using a variety of methods. Long division is a traditional method of division, often taught to students in elementary school. It involves breaking down each number into individual digits and then dividing them one at a time.

Another type of division is short division, which is a simpler and faster method of division that can be done in one step. Short division can be used when the divisor is a single-digit number.

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One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.

This set is closed under scalar multiplication as if a and (x,y) are in u, a*(x,y) will also be in u because rational numbers are closed under multiplication.

A subset can be described with different properties, one of them is closure, a subset U is closed under an operation if the operation is applied to any two elements of U, and the result is also an element of U.

In mathematics, a subset is a set that is completely contained within another set. It is defined as a set U that is a part of a set S, such that every element of U is also an element of S. The notation used to indicate that U is a subset of S is U ⊆ S.

However, this set u is not a subspace of R^2 because it doesn't contain the zero vector (0,0) and it doesn't close under addition, as the sum of two rational numbers may not be a rational number.

Therefore, One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.

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In order yo calculate the perimeter of a triangle, one should add the length of its sides. For example, if the triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangle, sum of the three sides equals the perimeter.

Units are always a part of the final response. The final answer should be given in centimeters if the triangle's sides are in that unit.

An overview was given as your information is incomplete and couldn't be found.

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The inequality equation for the given graph is option B: y ≤ 1/3x - 4.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality equations are -

y ≥ 1/3x - 4

y ≤ 1/3x - 4

y ≤ 1/3x + 4

y ≥ 1/3x + 4

In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.

Now, write the inequality in equation form -

y = 1/3x - 4

y = 1/3x + 4

Substituting the values of x and y with origin (0,0) -

0 = 1/3(0) - 4

0 = -4

0 = 1/3(0) + 4

0 = 4

Putting the inequality symbol back -

y ≥ -4

This statement is false as seen in the graph.

y ≤ -4

This statement is true as seen in the graph.

y ≤ 4

This statement is false as seen in the graph.

y ≥ 4

This statement is false as seen in the graph.

Therefore, the equation for the graph is y ≤ 1/3x - 4.

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a) The expected annual rainfall is 15 million tons.

b) The standard deviation is the square root is 15 million tons.

c) Pgamma(4, shape = 3, scale = 5)

d) Pgamma(5, shape = 3, scale = 5) - Pgamma(2, shape = 3, scale = 5)

a) The expected annual rainfall accumulated in this lake is given by the mean of the gamma distribution, which is alpha * gamma. In this case, the expected annual rainfall is 3 * 5 = 15 million tons.

b) The standard deviation of the annual amount of rainfall in this lake is given by the square root of the variance, which is the square root of alpha * gamma². In this case, the standard deviation is the square root of 3 * 5² = 15 million tons.

c) To find P(X < 4), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.

pgamma(4, shape = 3, scale = 5)

This will return the probability that X is less than 4, which is the cumulative probability.

d) To find P(2 < X < 5), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.

pgamma(5, shape = 3, scale = 5) - pgamma(2, shape = 3, scale = 5)

This will return the probability that X is between 2 and 5, which is the cumulative probability.

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