An equilateral triangle has a perimeter of 12x+33. What is the length of each side of the triangle?

Equivalence is a relationship that exists between two statements such that if the two statements are both true or both false, then the affirmation of one and the negation of the other contradicts itself.

Equivalent generally refers to two numbers, terms, or expressions that have the same value. There are many ways to express equivalent quantities. It can be represented by bars or equal signs. "Equivalence" relies on a specific relationship called an equivalence relationship. Any two elements are said to be equivalent if there is an equivalence relation between them. Also, in mathematics, equality is different from equivalent. The same means the same in all respects, and equivalent means similar but not identical. For example, 2 is said to be equal to 2, but it is equivalent to 1 + 1.

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Answer: 24 x 1/2(24) = 288

Step-by-step explanation:

Half of 24 is 12.

Multiply 24 by 12 = 288

Answer:

60+12.5x=160

12.5x=100

x=8

Step-by-step explanation:

There are 4 rows of Soprano. The concept of algebraic manipulation is used to solve the problem.

Given the information that there are 64 fingers in total and 8 fingers in each row of the Tenor, I was able to determine that there are 32 fingers in the Tenor rows by multiplying 8 fingers/row x 4 rows.

Then, We subtracted the number of fingers in the Tenor rows (32 fingers) from the total number of fingers (64 fingers) to find the number of fingers in the Soprano rows, which is also 32 fingers.

Finally, We divided the number of fingers in the Soprano rows by the number of fingers per row (8 fingers/row) to find the number of rows of Soprano, which is 4 rows.

If there are 64 fingers in total and 8 fingers in each row of the Tenor, then there are 8 fingers / row x 4 rows = 32 fingers in the Tenor rows.

Since there are 64 fingers in total and 32 fingers in the Tenor rows, then there are 64 fingers - 32 fingers = 32 fingers in the Soprano rows.

Therefore, there are 32 fingers / 8 fingers/row = 4 rows of Soprano.

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The surface area of the square pyramid is 45.

Given data :

H = 6ft.)

W = 3ft

L = 3ft.

2 × b × s +b. Volume of a Square Pyramid

= 45ft

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The distance from the airplane to the end of the runway will be 45.89 miles.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

An airplane is 45 miles from the end of the runway, AB, and 9 miles high, AC, when it approaches the airport. Then the triangle ABC is a right-angle triangle. Then we have

AC² = AB² + BC²

AC² = 45² +  9²

AC² = 2025 + 81

AC² = 2106

AC = 45.89 miles

The distance from the airplane to the end of the runway will be 45.89 miles.

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(a) The net force equation on q1 is 10.6N towards q2. (b) The acceleration of q1 would be 6.8x10^7m/s^2.

a) The Coulomb's law equation for the force between two charges q1 and q2 is given by:

F = k(q1q2)/r2

Where k is the Coulomb's constant and r is the distance between the two charges.

Using this equation, the force on q1 due to q2 can be calculated as:

F12 = (8.99x109 N m2/C2)(8.00x10-6C)(-5.00x10-6C)/(1.00m)2

F12 = -44.8x10-6 N

Similarly, the force on q1 due to q3 can be calculated as:

F13 = (8.99x109 N m2/C2)(8.00x10-6C)(5.00x10-6C)/(2.00m)2

F13 = 55.2x10-6 N

The net force on q1 can be calculated as the vector sum of F12 and F13:

F1 = F12 + F13

F1 = 10.6N towards q2

b) The acceleration of q1 can be calculated using Newton's second law of motion:

F = ma

a = F/m

Where m is the mass of q1.

Therefore, the acceleration of q1 can be calculated as:

a = (10.6N)/(1.50g)

a = 6.8x107m/s2

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The logarithm of a number with respect to a base is the exponent to which the base must be raised to produce that number. In other words, log_b(x) = y means b^y = x.

To find log_7(x), we can use the change of base formula which is log_b(x) = log_c(x) / log_c(b).

So you can use the logarithm of base 10 (common logarithm) or base e (natural logarithm) and use the above formula to find log7

So for example, log7(49) = log10(49) / log10(7) or log7(49) = ln(49) / ln(7)

You can use a calculator or a logarithm table to find the result.

--The question is incomplete, answering to the question below--

"How can we find log₇(x)?"

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The correct option regarding the solution to the system of equations is given as follows:

It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.

Hence the x-value of the solution is given as follows:

x = 3.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The point of intersection in this problem has a x-coordinate of 3, hence the third option is the correct option.

The complete problem is given as follows:

If x=3 is a solution to f(x)=x²-x and g(x)=2x, why is it also a solution to f(x) = g(x)

(1 point)

O It is a solution to f(x) = g(x) because it is the x-intercept of the two graphs

O it is a solution to f(x) = g(x) because it is the y-intercept of the two graphs.

O It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect

O it is a solution to f(x) = g(x) because both graphs are positive at x = 3.

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There are various rules for plotting a graph which includes having scale over X and Y axis.

The options for vertical bar charts are shown below. For horizontal bar charts, swap out "vertical" for "horizontal" and "horizontal" for "vertical."

1. A title ought to be at the top of the graph.

2. The vertical axis' scale has to be consistent and set to 0.

3. Utilise horizontal gridlines.

4. Each bar's definition ought to be listed on its label.

5. The label for the horizontal axis should include a description of the qualitative variable that the bar chart represents. In the event if the labels on each individual bar are sufficiently illustrative, a horizontal axis label is not required.

6. It should say "Count" or "Frequency" on the vertical axis.

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Zero of the quadratic polynomial whose  X²+3X+2 are -2 and -1.

Sum of zeros ( alpha + beta) = -3

Product of zeros ( alpha × beta) = 2.

Quadratic polynomial = X²-(alpha + beta)X+ Alpha× beta = X²-(-3)X+2.

= X²+3X+2 is the required quadratic polynomial.

A = 1 , b = 3 , C = 2

X²+ 3X +2

X² + 2X+ X + 2

X(X+2) +1 ( X+2)

(X+2). ( X+1)

X+2 = 0. X+1 = 0

X = -2. X= -1

Zero of the quadratic polynomial whose  X²+3X+2 are -2 and -1.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

Find a quadratic polynomial, the sum, and the product of whose zeroes are -3 and 2 respectively. hence find the zero

To multiply mixed numbers, first change them to improper fractions. Next, simplify, or reduce, the fractions by removing common factors. Then multiply the numerators, and multiply the denominators. Simplify, or reduce the answer if possible. Finally, if the answer is an improper fraction, you can change it back to a mixed number.

Now, According to the question:

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

To multiply mixed numbers, first change them to improper fractions. Next, simplify, or reduce, the fractions by removing common factors. Then multiply the numerators, and multiply the denominators. Simplify, or reduce the answer if possible. Finally, if the answer is an improper fraction, you can change it back to a mixed number.

Here's an example of a multiplication problem with three mixed numbers:

[tex]3\frac{1}{3}[/tex] × [tex]5\frac{1}{4}[/tex] × [tex]1\frac{1}{2}[/tex]

= 10/3 × 21/4 × 3/2

By Simplification, we have:

=> 105/4

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Answer:

10.22 kilograms

Step-by-step explanation:

you do 1.48+8.74=10.22

The chef bought 10.22 kilograms of nuts in total.

To find the total amount of nuts the chef bought, we add the number of almonds to the number of pecans:

1.48 kg + 8.74 kg = 10.22 kg

So the chef bought 10.22 kilograms of nuts in total.

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Answer:

C)  S: {20, 40}

Step-by-step explanation:

Given inequality:

[tex]\dfrac{1}{5}(m-5)\leq \dfrac{1}{10}(m-20)[/tex]

To solve the inequality, multiply both sides by 10:

[tex]\implies \dfrac{10}{5}(m-5)\leq \dfrac{10}{10}(m-20)[/tex]

[tex]\implies2(m-5)\leq m-20[/tex]

Expand the left side:

[tex]\implies 2m-10 \leq m-20[/tex]

Subtract m from both sides:

[tex]\implies m-10 \leq -20[/tex]

Add 10 to both sides:

[tex]\implies m \leq -10[/tex]

Therefore, the true solution set to the given inequality are values of m that are less than or equal to -10.  

Therefore, the integers in the given set that make the inequality false are the values of m that are greater than -10:

Answer:12.57

Step-by-step explanation:

Given that radius of the circle= 2km

as we know the formula of circumference of the circle as

Circumference of the circle= 2* pi * radius

circumference of the circle = 2*pi*2

                                               = 2* 22/7*2

                                               =88/7

                                                =12.57

A function which has the greater initial value include the following: linear function A.

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table of values for linear function A, we can reasonably and logically deduce that its y-intercept (initial value) is equal to 8 when the value of "x" is equal to zero (x = 0).

For linear function B, we would substitute the value of x with zero (0) as follows;

y = 3x + 2

y = 3(0) + 2

y = 0 + 2

y = 0.

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the height of the stamp is 2/5in.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Given that stamp of Height is 3in with 4 1/2 in width.

So 9/2 of width = 3 Height

1 of width = 3/(9/2) Height

So for 3/5 in wide = 3/5* 3/(9/2) = 2/5in

Hence the height of the stamp is 2/5in.

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Answer:

69

Step-by-step explanation:

The central angle is twice the inscribed angle. So the angle that is behind the one equal to 2x is equal to x. We know that the opposite angles in a circle add up to 180. Therefore, we can solve for x:

[tex]x + x + 42 = 180$^{\circ}$\\\\2x = 180$^{\circ}$ - 42$^{\circ}$\\\\2x = 138$^{\circ}$\\\\x = 69$^{\circ}$[/tex]

The multiplication theorem of probability is if  and  be two events associated with the sample space . Then, (∩) = ()⋅() and the addition theorem of probability is For two mutually exclusive events ,

(or ) = () + ().

According to the multiplication theorem of probability, the probability of both events and occurring is equal to the product of the probability of occurring and the conditional probability of event occurrence if event happens.

Let  and  are two events associated with the sample space . ∩ gives the simultaneous occurrence of two events  and

We know that the conditional probability of the event given that has occurred is given by (∣) and is given by

(∣) = (∩)(), () ≠ 0

We can write the above equation as

(∩) = (∣)⋅()⋯()

Also, we can write

(∣) = (∩)(), () ≠ 0

(∩) = (∣)⋅()

Combining () and (), we can write

(∩) = (∣)⋅() = (∣)⋅(), where (),() ≠ 0

According to the addition theorem, if two events and , are mutually exclusive, the probability of either or  occurring is the total of the individual probabilities of  and .

Let event happen in ways, and event happen in ways. Then the total number of happening of events is , which is = +

Thus, the probability of events happening is given by (or ).

By the definition of probability,

() = / and () = /

Adding,

() + () = / + / = + / = / = 1

Therefore,

(or ) = () + ()

--The given question is incomplete; the complete question is

"What is the multiplication and addition theorem of probability? Explain with suitable examples."--

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Answer:

Step-by-step explanation:

The container holds more than 3 cups of sugar, since it holds 3 times the amount used in the recipe.

To calculate the amount of sugar in the container, we need to first determine the amount used in the recipe. The recipe calls for 2 1/3 cups of sugar. This can be converted to a decimal by dividing by 3, resulting in 2.333 cups of sugar used in the recipe. Now that we know the amount used, we can calculate the amount the container holds.

1. 2 1/3 cups = 2.33 cups

2. 3 x 2.33 cups = 6.99 cups

The container holds 3 times the amount used, so we can multiply 2.333 cups by 3, resulting in 6.999 cups of sugar in the container. This is more than 3 cups of sugar, so the container holds more than 3 cups of sugar.

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Answer: Transversal

Step-by-step explanation:

Altitude is in the triangle as it has vertexes shown by the line, Hypotenuse is the longside of the triangle which is shown, and the legs, every single triangle has legs, which leaves us with transversal which means a straight line that cuts a parrel line. Which isn't shown so that's the answer. Have a good day ;)

The population of the town after 10 years will be, 5933

The decrease rate of a value measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.

Given that, the population of a small town is decreasing at a rate of 7% per year. If the town's population is 12,259 now,

The decrease rate =

A = P(1-r)ⁿ

A = final population

P = initial population

r = rate

n = time

A = 12259(1-0.07)¹⁰

A = 5933

Hence, the population of the town after 10 years will be, 5933

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The quadratic formula is an algebraic formula that provides the solutions to a quadratic equation. A quadratic equation is an equation of the shape ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula gives the values of x that satisfy the equation and is expressed as:

x = (-b ± √ (b^2 - 4ac)) / (2a)

In other words, the quadratic formula provides a method for finding the two roots of a quadratic equation, even if the equation cannot be solved by factoring or other methods.

The formula works for all quadratic equations and is a widely used tool in mathematics and various scientific and engineering fields.

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Answer:81, 384

Step-by-step explanation:

9x2 is 18

you can count 9+9 which would be the same as 9*2. 24x16 is 384.

Answer: List 2

Mark the midpoint between 1/6 and 1/2 (see diagram below)

======================================================

Explanation:

There are 3 meats (ham, turkey, bologna) and 2 vegetables (carrots, celery).

This gives 3*2 = 6 different combos of meat plus a vegetable. This is where we can only pick one of each type.

The 6 different combos are shown in  list 2  

List 1 is not correct because you can choose one vegetable only, and not have both.

----------

Look through list 2 and circle the options that say "ham, carrots" and "turkey, carrots". There are 2 items that are circled. This is out of 6 total.

We arrive at the probability 2/6 = 1/3

The fraction 2/6, aka 1/3, is located at the halfway point between 1/6 and 1/2. This is because 1/6+1/2 = 1/6+3/6 = 4/6, which divides in half to get 2/6.

See the diagram below.

The solution for the equations is at x = -1 and y = -3.

2: the system of equations has the same slope and the same y-intercept so the system of equations has infinitely many solutions.

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.

Given the equations,

-2x + 4y = -10

2x + 2y = -8

adding both the equations so -2x and +2x will be eliminated

-2x + 4y + 2x + 2y = -10 - 8

6y = -18

y = -18/6

y = -3

substitute the value of y in equation 2x + 2y = -8

2x + 2(-3) = -8

2x = -8 + 6

x = -1

2: Given equations y = -x + 5 .........(1)

y + x = 5 .........(2)

equation 2 can be written as,

y = -x + 5

so both the equations have the same slope and the same value of y-intercept,

so the line overlaps each other and has infinitely many solutions.

Hence the solution s at x = -1 and y = -3.

2: Equations have infinitely many solutions.

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Answer: 1

Step-by-step explanation:

The required coordinates of point Q are (-46/13, 50/13) lie on line PR.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,

Let the coordinate of Q be (x, y)
Given PR with P(-6, -6) and R(-2, 10), it is on PR such that the ratio of PO to PR is 5:8,

Apply the Section formula.

x = mx₂ + nx₁ / m + n   ; y = my₂ + ny₁ / m + n

m = 5 and n = 8

Put the values in the section formula along with points.
x = 5 × -6 + 8×-2 / 5 + 8 ; y = -6×5 + 8 × 10 / 8 + 5
x = -46/13                        ; y = 50/13

Thus, the required coordinates of point Q is (-46/13, 50/13) lie on line PR.

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