Find the perimeter of triangle XYZ with vertices X(3,7), Y(-1,-5) & Z (6,-4)

Evaluated solution of the expressions as (A) 7 and (B) 17.11.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

⇒ 15 - 35/7 - 2 + 3 - 4

⇒ 15 - (35/7) -2 + 3 - 4

Apply the division operation,

⇒ 15 - 5 - 2 + 3 - 4

Rearrange the terms in the above equation

⇒ 15 + 3 - 5 - 2 - 4

⇒ 18 - 11

Apply the subtraction operation,

⇒ 7

⇒ 10 + 2 (9-5) - 16/18

⇒ 10 + 2(4) - 8/9

⇒ 10+8 - 8/9

Apply the addition operation,

⇒ 18 - 8/9

⇒ 162/9-8/9

Take the LCM,  

⇒ 154/9

Apply the division operation,

⇒ 17.11

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By setting up an equation based on the fact that K is between J and L, we found that x = 6. Substituting this value back into the expression for KL, we determined that KL = 8.

To find the value of x and KL, we'll first set up an equation using the fact that K is between J and L, which means JL = JK + KL. Substituting the given expressions:

5x - 10 = 2x + (x + 2)

Now, solve for x:

[tex]\[5x - 10 = 2x + x + 2\][/tex]

[tex]\[5x - 10 = 3x + 2\][/tex]

[tex]\[5x - 3x = 2 + 10\][/tex]

[tex]\[2x = 12\][/tex]

[tex]\[x = 6\][/tex]

Now that we have found the value of [tex]\(x\)[/tex], we can find [tex]\(KL\)[/tex] by substituting \(x = 6\) into the expression for KL:

[tex]\[KL = x + 2 = 6 + 2 = 8\][/tex]

So, x = 6 and KL = 8.

The question probable maybe:

Find the value of x and KL if K is between J and L. JK=2x, KL=x+2, and JL=5x-10.

Answer:121

Step-by-step explanation:

sum = 10000(10000-1)/2

sum = 10000(100001)/2

sum = 100010000/2

sum = 50,005,000

The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

The statement is given as: "the difference of two numbers less than the greater number"

Let the numbers be x and y, where x > y.

So, the interpretation of the statement is:

x - y < x

Add x to both sides

-y < 2x

Rewrite as:

y > -2x

This means that the statement is true only when the smaller number is greater than twice the additive inverse of the greater number

Hence, the counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

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Answer:

(-12)^2 = -12 * -12 = 144

The correct expression after adding a value 1 to variable x is 1 + x.

Used the concept of expression that states,

A mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that,

Add a value of 1 to variable x.

Here, the number is 1 and the variable is x.

Hence add the number 1 and x is written as,

1 + x

So, the expression is, 1 + x

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To frame a cabin:

Lee will take 6.47 days and Ron will take 10.47 days.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

Lee can frame a cabin in 4 days less than Ron.

Ron can frame,

= 1 cabin/(x+4) days.

Lee can frame,

= 1 cabin/(x) days.

When they work together, they will do the job in 4 days.

That means,

4/x+4 + 4/(x) = 1

4(x+4+x)/x(x+4) = 1

x²-4x-16 = 0

Solving the quadratic equation,

x = 2 ± 2√5

Then,

x = -2.47 and x = 6.47.

Therefore, Lee can frame a cabin in  6.47 days and Ron will take 10.47  days.

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It’s 83

Step-by-step explanation:

Answer:

circle, line segment, and parallel lines

Step-by-step explanation:

A circle is the set of all points a given distance from a fixed point called a center.  This only uses the undefined term "point."

A line segment is a portion of a line with two distinct endpoints.  This uses the undefined terms "line" and "point."

Parallel lines are lines that never intersect.  This uses the undefined term "line."

An angle is two rays joined at a common point called the vertex.  While this does use the undefined term "point," it also uses the defined term "ray."  This is not one of our options.

An arc is a portion of the circumference of a circle.  This uses the term "circle," so it is not one of our options.

The value of afrom the expression [tex]G = 4ca - 3ba[/tex] is [tex]\boxed{a = \frac{G}{{\left( {4c - 3b} \right)}}}.[/tex]

Further explanation:

PEDMAS rule is use to solve the grouping of multiplication, addition, subtraction and division.

P denotes the parenthesis, E denotes the exponents, M denotes the multiplication, D denotes the division, A denotes the addition and S denotes the subtraction.

Given:

The expression is [tex]G = 4ca - 3ba.[/tex]

Explanation:

The associative property is defined as a grouping of multiplication, addition, subtraction and division.

The given expression is [tex]G = 4ca - 3ba.[/tex]

The factors of [tex]4ca[/tex] can be expressed as follows,

[tex]\begin{aligned}A&= 4ca\\&= 4 \times c \times a\\\end{aligned}[/tex]

The factors of [tex]3ba[/tex] can be expressed as follows,

[tex]\begin{aligned}B &= 3ba\\&= 3 \times b \times a\\\end{aligned}[/tex]

The common factor between [tex]4ca[/tex] and [tex]3ba[/tex] is [tex]a[/tex].

The value of a can be obtained as follows,

[tex]\begin{aligned}G&= a\left( {4c - 3b} \right)\\\frac{G}{{\left( {4c - 3b} \right)}} &= a\\\end{aligned}[/tex]

The value of [tex]a[/tex] from the expression [tex]G = 4ca - 3ba[/tex] is [tex]\boxed{a = \frac{G}{{\left( {4c - 3b} \right)}}}.[/tex]

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: place value, base value, decimal expansion, whole number, natural number, division, multiplication, solve the equation, solution, linear equation.

The value of x, which is the time delay between the two stones' projections, is 1.4 seconds. The velocity of the second stone 6 seconds after the first stone's projection (so 1.4 seconds after its own projection) is 11.32 m/s.

This question involves physics concepts, particularly with motion under gravity, velocity, and displacement. We need to use these principles of Physics to solve the problem.

First, let's calculate the displacement of the first stone 6 seconds after it is thrown. Since the stone is thrown downwards, its final displacement (S1) is given by the equation of motion:

S1 = ut + 0.5gt2, where u is initial velocity (8 m/s), g is acceleration due to gravity (9.8 m/s2), and t is the time (6 seconds).

Therefore, S1 = 8*6 + (1/2)*9.8*6*6 = 48 + 176.4 = 224.4 m.

The first stone is thrown from a tower of height 248 m, so its displacement from the base of the tower is

248 - S1 = 248 - 224.4 = 23.6 m.

The second stone is thrown upwards from the base of the tower, Therefore, after t=x seconds, it travels upward by S2 = ut - 0.5gt2 (=25x - 0.5*9.8*x2).

At t=6 seconds, it must be at a the same height as the first stone (23.6 m). So we set 25x - 0.5*9.8*x2 = 23.6, and solve this quadratic equation to find x = 1.4 seconds.

The second part of the question asks for the velocity of the second stone at this instant. The velocity of an object thrown upward-moving object is given by

v = u - gt, here u = initial velocity = 25 m/s, g = 9.8 m/s2 and t=x=1.4 seconds. Plugging in these values, we find that v = 25 - 9.8*1.4 = 11.32 m/s.

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The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.

Here,

The number is 633,248.

We have to compare the values of each 3 in the number 633,248.

What is Place value?

The value represented by a digit in a number on the basis of its position in the number is called the place value.

Now,

The number is 633,248.

From right the first 3 has place in Thousand place.

So, place value of this 3 is thousands place.

And, From right the second 3 has place in Ten thousands place.

The difference of each 3 is that they have different place values.

Therefore, The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.

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Answer:16 3/10

Step-by-step explanation:

The required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

A company added a new oil thank that holds 350 barrels of oil than its old oil tank . Together they hold 3650 barrels of oil.

According to given question we have

Let the  Capacity of old oil tank = x barrels

Let the Capacity of New oil tank = x + 350 barrels

So,

x + x + 350 = 3650

2x = 3300

x = 1650 barrels

∴Capacity of old oil tank = 1650 barrels

Capacity of New oil tank

=  x + 350

=1650 +350

=2000 barrels

Therefore, the required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.

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