Find the slope of a line perpendicular to the line whose equation is x - 2y = 14.
Fully simplify your answer.

If 4 cm and 7 cm are the lengths of two sides of a triangle then the length of the third side should be 6 cm.

In the given question we have to check 4 cm and 7 cm are the lengths of two sides of a triangle then the length of the third side may be.

Any two sides of a triangle can have a sum of lengths that is always greater than the length of the third side.

Any two triangle sides' length differences will never be greater than the triangle's third side's length.

The sum of 4cm and 7cm is 11cm, and their difference is 3cm.

The third side's possible length must be larger than 3 cm and less than 11 cm to ensure that the aforementioned rule is not broken.

6 cm is therefore larger than 3 cm and less than 11 cm from the possibilities presented.

The triangle's third side measures 6 cm in length.

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Answer:

equation: 2(2w + 2) = 60

length = 16

width = 14

Step-by-step explanation:

width = w

length = w + 2

perimeter = 2(w + w + 2) = 60

equation: 2(2w + 2) = 60

4w + 4 = 60

4w = 56

w = 14

width = 14

length = w + 2 = 14 + 2 = 16

length = 16

Therefore , the solution of the given problem of expressions comes out to be it means to promote peace and love.

It is required to multiply, divide, add, or take away in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical statement, such as multiplication, subtraction, multiplied, or division, etc., include numbers, variables, and functions. It is possible to contrast expressions and phrases.

Here,

Given  : purple peace emoji

Thus,

An easy approach to find a peace sign online is to use the peace symbol emoji,

which is used to signify a variety of emotions such as, well, peaceful, love, unity, harmony, togetherness, and general everyone-getting-along-ness. Sleep well, Divergents Be genuine.

Promote peace and love.

Therefore , the solution of the given problem of expression comes out to be it means to promote peace and love.

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Answer:

15m, 1,800c​m, 7km

Step-by-step explanation:

Ascending order mean from smallest value to largest value

We know

1km = 1000m

1km = 100000cm

1) 15m = 0.015km

2) 7km

3) 1800cm = 0.018km

So, the order is

15m, 1,800c​m, 7km

Answer:

(1,4)

Step-by-step explanation:

The statement that can be represented by the expression, 5m - 12, is B. Twelve less than the product of five and a number.

The expression given is 5 m - 12. In this formula, the value of m is a mystery number that is multiplied by 5 and then the product of these two numbers is reduced by 12.

This means that representing the formula can be done by saying, Twelve less than the product of five and a number. First the product of 5 and the value of m are found, and then twelve is subtracted from the formula.

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As per the unitary method, the cost of 8 pear is at the rate of $12.

The term unitary method is defined as a process of finding the value of a single unit, and based on this value and then we can find the value of the required number of units.

Here we have given that the grocery store the cost of 6 pear is $9.

Let us consider that x be the cost of one pear.

Here we know that the the cost of 6 pear is $9.

Then the cost of one pear is calculated as,

=> x = 9/6

When we simplify this one then we get, the cost of one pear as,

=> x = 1.5

Therefore, the cost of 8 pear is calculated as,

=> 8 x 1.5

=> 12

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The average rate of change for the interval from x = 5 to x = 6 can be calculated by taking the derivative of the quadratic function and evaluating it at the midpoint of the interval (x = 5.5).

Given that the vertex of the function is at (1, 0), the equation of the quadratic function is in the form of:

f(x) = a(x-1)^2 +0

The derivative of the function is:

f'(x) = 2ax - 2a

We know that the vertex of the function is at (1,0), which means that the value of a is 0.

So the derivative of the function is 0.

Therefore the average rate of change for the interval from x = 5 to x = 6 is 0.

The solution of the inequality for n is n > 31/40

Inequality is a statement of an order relationship greater than or equal to less than between two numbers or algebraic expressions.

Inequalities are not only driven by and measured by income but are also determined by other factors including gender origin, ethnicity, disability,  class and religion. Moreover inequalities are determined not only by income but also by other factors.

How to solve the inequality?

The inequality is given as

n minus three eighths is greater than negative two fifths

Rewrite properly as

n - 3/8 > 2/5

Add 3/8 to both sides

n > 3/8 + 2/5

Evaluate the sum

n > 31/40

Hence, the solution of the inequality for n is n > 31/40

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Answer:

1/15

Step-by-step explanation:

Dividing a fraction by a whole number

3/5 ÷ 9

Copy dot flip

3/5 * 1/9

Rewriting

3/9 * 1/5

1/3 * 1/5

1/15

Answer:

1/15

Step-by-step explanation:

3/5 ÷ 9

3/5 × 1/9

1/5 × 1/3

1/15

Answer:

y=mx+c

Step-by-step explanation:

y=mx+c

Answer:

C. 15 and 2

Step-by-step explanation:

The least common denominator (LCD) of 3/4 and 5/6 is 12

To discover the least common denominator, list the multiples of both denominators until you find the smallest multiple that both denominators share. Because 20 is the first shared multiple of 4 and 5, it must be the fractions’ least common denominator.

The least common denominator (LCD) of a group of fractions is the least common multiple (LCM) of their denominators.

In this case, the denominators of the fractions are 4 and 6. The least common multiple (LCM) of 4 and 6 is 12. Therefore, the least common denominator of 3/4 and 5/6 is 12.

You can also find the LCM by finding the prime factorization of the numbers, and then take the highest power of each prime factor and then multiply those.

[tex]4 = 2^2\\6 = 2*3[/tex]

The highest power of 2 and 3 are [tex]2^2[/tex] and 3 respectively, so LCM(4,6) = [tex]2^2 * 3 = 12[/tex]

So the LCD of 3/4 and 5/6 is 12.

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Complete question is: What is the least common denominator of 3/4 and 5/6?

The remainder of given polynomial is 10 . An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. The word "polynomial" is derived from the Greek words "poly" and "nominal," which together translate to "many terms."

Given,

[tex]fx=x^3+2x^2-5x-6[/tex]

By using remainder theorem

[tex]f(2)=2^3+2*2^2-5*2-6\\f(2)=0[/tex]

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According to th given question x³ - 2x² - 5x + 6 is divided by x + 2 it gives remainder zero.

The act of dividing a fraction into further equal portions is known as fraction division. For instance, if you cut a slice of pizza in half and had three-fourths of the pizza left, you would have eaten six slices total, or four of the entire pizza. In mathematics, division is the procedure of dividing a sum into equal parts. For illustrate, we may divide a group of 20 individuals into small groups of 4, 5, 6, and so on.

Given that p(x) = x³ - 2x² - 5x + 6 and g(x) = x + 2

We have to track down the rest.

So let's get started!

Remainder theorem is used;

g(x) = x + 2 = 0

g(x) = x = -2

By substituting the value x = -2

x³ - 2x² - 5x + 6

Substituting the values:

(-2)³ - 2(-2)² - 5(-2) + 6

=  - 8 + 10 + 6

= -16 + 16

= 0

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Answer:

c = 4

Step-by-step explanation:

Solve for c:

2 (c + 1) = 10

Divide both sides of 2 (c + 1) = 10 by 2:

(2 (c + 1))/2 = 10/2

2/2 = 1:

c + 1 = 10/2

The gcd of 10 and 2 is 2, so 10/2 = (2×5)/(2×1) = 2/2×5 = 5:

c + 1 = 5

Subtract 1 from both sides:

c + (1 - 1) = 5 - 1

1 - 1 = 0:

c = 5 - 1

5 - 1 = 4:

Answer: c = 4

Answer:

[tex]\boxed{\sf c=4}[/tex]

Step-by-step explanation:

[tex]\sf 2(c+1)=10[/tex]

Distribute:-

[tex]\sf 2c+2=10[/tex]

Subtract 2 from both sides:-

[tex]\sf 2c+2-2=10-2[/tex]

[tex]\sf 2c=8[/tex]

Divide both sides by 2:-

[tex]\sf \cfrac{2c}{2}=\cfrac{8}{2}[/tex]

[tex]\sf c=4[/tex]

Therefore, c = 4!!!

_________________

Hope this helps!

Have a great day!

The average rate of change of h(x) on the interval [-1, 8] is r = -3.6

For any function, the average rate of change on an interval [a, b] is given by:

r = ( f(b) - f(a))/(b - a)

In this case, the function is:

h(x) = -x^2 + 4x + 12

And we want to find the average rate of change on the interval [-1, 8]

Evaluating the function in these values we will get:

h(-1) = -(-1)^2 + 4*(-1) + 12

h(-1) = -1 - 4 + 12 = 7

h(8) = -(8)^2 + 4*8 + 12 = -20

Then the average rate of change is:

r = ( h(8) - h(-1) )/(8 + 1)

r = (-20 - 12)/9

r = (-32/9) = -3.6

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The simplified expression of 3 (-5 + 2x) is -15 + 4x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3 (-5 + 2x)

The distributive property of multiplication over addition states that,

a x (b + c) = a x b + a x c

Now,

3 x (-5 + 2x)

3 x (-5) + 2 x (2x)

-15 + 4x

Thus,

The simplified expression is -15 + 4x.

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Answer:

y = -2/3x

Step-by-step explanation:

In linear equation, The number of pounds of apples is 12 and the number of pounds of raspberries is 20.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given that, the cost of a pound of apples = $2.25 and the cost of a pound of raspberries = $1.50.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of pounds of apples be x, then the number of pounds of raspberries(y) be y=x+ 12

Now, the total cost of apples = The number of pounds of apples × The cost of a pound of apples

=x × 1.50

= 1.50x

The total cost of raspberries = The number of pounds of raspberries × The cost of a pound of raspberries

=(x+12) × 3

=3x+ 36

So, the total cost = The total cost of apples + The total cost of raspberries

⇒ 72 = 1.50x+ 3x+ 36

⇒  72 = 4.5x + 36

        4.5x = 72-36

            x =  8

So, y= x+ 12 = 20

Therefore, the number of pounds of apples is 12 and the number of pounds of raspberries is 20.

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Answer: x=-5

Step-by-step explanation:

first answer

Plane mirrors and convex mirrors only produce virtual images.

A mirror is a surface that nearly always images the light that strikes it. Mirrors are divided into two types: Plane mirrors and the second one is spherical mirrors. As the name says, plane mirrors have a plain, polished surface, while spherical mirrors are curved throwback surfaces.

Spherical mirrors are further divided into convex and concave mirrors based on their curves. Yet, to distinguish between Concave and Convex Mirror, it is fundamental to understand what they are and how they differ.

To put it simply, mirrors with a reflecting surface that bump outwards are convex mirrors, whereas concave mirrors have a reflecting surface that bulges inwards.

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The Function after reflection over x-axis is D) g(x) = -4IxI.

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

Here The graphs of g may be obtained from the graph of f by shifting up c units. The graph moves downward if we take c out of f(x). Let h(x) = f(x)-c shifting downward c units yields this graph of h from the graph of f.

Now given function f(x)= 4IxI.

It is stated that its graph of  is obtained by reflecting a graph of f(x)= 4IxI over the x-axis.

When a figure is reflected across the x-axis, the rule for reflection is

(x,y)=>(x,-y)

Then g(x)=-f(x),

=> g(x) = -(4IxI)

=> g(x) = -4IxI

Hence the correct option is D)g(x) = -4IxI.

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Answer:

x = 3

pt = 18

I used a calculator

=)

Answer: v would be root2 and u would be 2

Step-by-step explanation:

Angle CAS is another name for Angle SAC. It is necessary to come up with another name for Angle SAC.

A line is a one-dimensional straight shape with no thickness that extends endlessly in both directions. A line is made up of a series of points that stretch in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

Given:

Given a ray diagram,

Ray RS is given and point A & T are on between R & S.

Another ray DC cuts the ray RS at point A.

The ray AS cuts the point A.

One more ray is AB ,there is no any point to cut.

<SAC, we can also write this angle in form < CAS.

So,

∠SAC = ∠CAS (same angle)

Angle SAC is also known as Angle CAS. Angle SAC requires a new name.

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Diagram is missing

Therefore , the solution of the given problem of arithmetic mean comes out to be  a 5000th term = 44995

The sum of all values in a list multiplied by the total no. all items in the list yields the arithmetic average, often known as the group's means. The growth in arithmetic follows a similar pattern. The following equation + 7 + 9 equals 21, but 21 multiplied by 3 (there's several currently three numbers) equals 7, proving that the mean of the numbers 5, 7, while 9 is 4, and the median of the real numbers 5, 8, and 9 is 3.

Here,

Given : sequence is -

=> 4, 13, 17, 18,21...….

a = 4

d = 9

for

=>  a 5000th term  =  a + 4999d

=> a 5000th term  =  4 + 4999*9 = 44995

Therefore , the solution of the given problem of arithmetic mean comes out to be  a 5000th term = 44995

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Answer:

x=47 degrees

Step-by-step explanation:

We can use trigonometry to solve this problem.

the sine of the angle is equal to the side opposite the angle divided by the hypotenuse

so we have [tex]sin(x)=\frac{19}{26}[/tex]

now, in order to get x by itself, we have to take the inverse sine of both sides.

[tex]x=sin^{-1} (\frac{19}{26} )[/tex]

now we can plug this into a calculator.

we get 46.95 degrees

I think there is a typo in option D. because it says to find the nearest whole number but 4.6 is not a whole number.

The

hypotenuse's square

of a right triangle is equal to the sum of its legs' squares.

What is Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in

Euclidean

geometry.

According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.

This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the

hypotenuse

c.

There are several ways to generalize the theorem, including to higher-dimensional spaces, non-Euclidean spaces, objects other than right triangles, and even things that are not triangles at all but n-dimensional solids.

Hence, The hypotenuse's square of a right triangle is equal to the sum of its legs' quares.

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The length of the diagonal of the rectangle is 6.4 meters

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

Length = 5 meters

Width = 4 meters

The length of the diagonal can be calculated as

diagonal = √(length² + width²)

substitute the known values in the above equation, so, we have the following representation

diagonal = √(5² + 4²)

Evaluate

diagonal = 6.4

Hence, the diagonal is 6.4 meters

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The midpoint formula is used to calculate elasticity because it overcomes the limitations of the traditional method.

The old point-slope method has significant drawbacks that are overcome by the midpoint formula, which determines the elasticity of demand. The elasticity of demand refers to how sensitively a good's quantity desired is to a price shift. Inelastic goods are those in which a little price shift causes a large change in quantity demanded, while elastic goods are those in which a small drop causes a small change in quantity demanded.

The conventional point-slope formula for elasticity employs the change in quantity and price at a particular point, which might be deceptive in some circumstances. Contrarily, the midpoint formula determines the elasticity of demand by averaging the quantity and price at the beginning and end and utilising the percentage change in both.

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