Simplify the radical √√189².
O 3√2d
O 20³√3
Od√180
3d+√2a

We can see from the graph that the temperature decreases with increasing time. As a result, the two quantities temperature and time are inversely proportional to one another. The necessary relationship between these quantities is  x ∝ 1/y or x = k(1/y)

The two are said to be inversely proportional when one quantity's value increases relative to another's decline or vice versa. It suggests that in nature, the two quantities behave in opposite ways. Taking time and speed as an example, they are inversely related. Speed increases result in a shorter amount of time.

Other names for this type of proportion that are also used in this context are reciprocal proportion, inverse proportion, varying inversely, inverse variation, and inverse variation. Let's use the example of x and y to illustrate the relationship between the two variables.

x ∝ 1/y or  x ∝ y⁻¹

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Answer:7

Step-by-step explanation: 21/3 = 7

Answer:

1/7 km/min

Step-by-step explanation:

Divide/simplify the two values, 3/21 = 1/7

Answer:

(x+8)^2=40

Step-by-step explanation:

x^2+16x+24=0.

Well, to solve for this, you do:

1. (16/2)^2 to find what number should be in place of 24.

That, by the way, is 64.

2. There's no 64! We have to add 64-24 on both sides, which makes the equation

x^2+16x+64=40.

3. Since we know that (16/2)=8, using the completing the square formula, you know that it's going to be a variation of (x+8)^2 or (x-8)^2.

As we are adding for the middle term, it must be (x+8)^2.

4. Answer: (x+8)^2=40.

Sorry if this is too late :)

The values of x that are solutions to the equation 10x²-64 36+6x² are x = 5, x = -5, x = -10, and x = 10.

Equation is a statement of equality between two expressions that states that they have the same value. Equations can be used to solve problems, model real world situations and describe relationships between different quantities. Equations can be expressed in many different forms, such as linear equations, quadratic equations, exponential equations and more. Equations are a powerful tool for understanding and describing the world around us.

The solutions to the equation 10x²-64 36+6x² are B. x = 5, C. x = -5, E. x=-10, and F. x= 10. These values represent the x-coordinates of the points in which the equation cuts the x-axis. The equation does not have a solution for x= -√√5 or x = √√√5, so these answers are incorrect.

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Inconsistent Pair of Linear Equations is the type of system of linear equation which has no solution notice that the two lines are parallel and will never intersect.

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.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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Answer:

C. Functional

Step-by-step explanation:

I hope I helped you,

Alex Martin :)

The original price of the shiny key chain that Zachary wants to buy, can be found to be $ 1.33

The question notes that there is a sale going on where the items on sale are being discounted by 25 %. This means that the current sale price of the shiny key chain as $ 1, is actually 25 % less than the original price.

The original price of the shiny key chain can then be found by the formula :

= Sale price / ( 1 - sales discount percentage )

= 1 / ( 1 - 25 %)

= 1 / 0. 75

= $ 1.33

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The full question is:
A sale says that all items are 25% off. Zachary wants to buy a shiny key chain. The sale price is $1. What was the original price?

The proof that the square root of 2 is irrational can be shown using proof by contradiction.

Assume that the square root of 2 is rational, meaning that it can be expressed as the ratio of two integers (p/q, where p and q are integers and q is not equal to zero).

This means that:

√2 = p/q, where p and q are integers and q is not equal to zero.

Squaring both sides of the equation:

2 = p^2/q^2

multiply both sides by q^2

2q^2 = p^2

Now, since p and q are integers, p^2 and q^2 are also integers.

Therefore, 2q^2 is an even integer.

However, if 2q^2 is an even integer, q^2 is also an even integer, which means that q is even.

Therefore, p and q have a common factor of 2. But, this contradicts the assumption that p and q have no common factors other than 1.

Therefore, our assumption that the square root of 2 is rational must be false.

Hence, we can conclude that the square root of 2 is irrational.

Answer:

To prove that the square root of 2 is irrational, we will use a proof by contradiction. Suppose that the square root of 2 is rational, which means that it can be expressed as a fraction a/b, where a and b are integers with no common factors. Then, we can square both sides of this equation to get:

2 = (a/b)^2 = a^2 / b^2

Multiplying both sides by b^2, we get:

2b^2 = a^2

This means that a^2 is an even number, because it is equal to 2 times b^2. Therefore, a must be an even number, because the square of an odd number is always odd. Let a = 2c, where c is an integer. Substituting this into the previous equation, we get:

2b^2 = (2c)^2 = 4c^2

Dividing both sides by 2, we get:

b^2 = 2c^2

This means that b^2 is an even number, and therefore b must also be an even number. However, this contradicts our original assumption that a and b have no common factors. Therefore, our assumption that the square root of 2 is rational must be false, and the square root of 2 is indeed an irrational number.

The process of converting a quadratic function to vertex form.

In math quadratic function is defined as a polynomial where the highest degree of any variable is 2.

Here we have to write the steps to convert the a quadratic function to vertex form.

Here we have to convert quadratic equation from standard form to vertex form

Let us consider that the given quadratic equation is given as,

=> y = ax² + bx + c { a, b, c € R, a ≠ 0}.

Here from the above equation we have to take a as common from the terms containing x.

then the equation is rewritten as,

=> y = a(x² + bx/a) + c

In order to Complete the square inside the bracket by adding and subtracting (b/2a)², then we get,

[tex]y=a[x^2+\frac{bx}{a} +(\frac{b}{2a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]

When we factorize it, then we get,

[tex]y=a[(x+\frac{bx}{a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]

Rewrite it as follows:

[tex]y=a[x+\frac{bx}{a}]^2 - (\frac{b}{2a})^2+ c[/tex]

Let us consider that the value of

=> h = -b/2a and k = c - b²/4a

Then we get the vertex form of the expression as,

=> y = a(x - h)² + k.

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Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

Answer: can you help me i cant put a q     i have to points

Step-by-step explanation: plssssssssssssssss      

A customer wanted to purchase a video game and realized that they were short $4.28 to be able to pay. Which value is the opposite of being short $4.28

1/2 is not a whole number.

We know that the whole numbers are numbers that include natural numbers and zero.

That is the set of whole numbers is denotes by W = N ∪ {0},

here N represents the set of natural numbers.

And we know that the natural numbers are nothing but the numbers which can be counted and start from 1 and ends at infinity.

i.e., the set of natural numbers N = {1, 2, 3, . . ., ∞}

and the set of whole numbers W =  {0, 1, 2, 3, . . ., ∞}

A set of whole numbers do not include fractions, decimals, or negative integers.

Here, 1/2 is a fraction (number of the form p/q where q ≠ 0)

So, given number 1/2 is not a whole number.

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Option C better choice, the measurement of the line segment RS is equal to x+5.which is difference of segment TR and TS.

A line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints.

There is a point S between the line segments T and R, measure of segment TR is 4x+1 and the measure of segment TS is 3x-4.

we shall find out the measure of RS.

so, length of RS is equal to difference of TR and TS.

Mathematically,

RS=TR-TS

RS=(4x+1) -(3x-4)

RS=4x+1-3x+4

RS=x+5

Hence the length of RS is equal to x+5.

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The area of the regular decagon is 496.7 squared unit.

In geometry, a decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon.

To calculate the area of the decagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

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Answer:

c)   (0,6) and (-5,-9)

Step-by-step explanation:

if you graph the system you will get a line and a parabola

the two points at which they intersect will be (0,6) and (-5,-9)

Answer: 24%

Step-by-step explanation: 48 out of 200 is 24%, meaning that 48 is 24% of 200. To find our answer, we follow two simple steps before we add the percentage symbol, though there can be three steps if we have to round a decimal in a percentage to two digits after the decimal point.

Answer:24%

Step-by-step explanation:

The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)

The formula for the surface area of a square pyramid is given by:

A = a² + a  √(a² + 4h²)

Where:

A = surface area

a = base length

h = height of the pyramid

In the given problem, the side length of the base = W = L = 3 ft.

Hence,

a = 3 ft.

h = 6 ft.

Plug these parameters into the formula:

A = 3² + 3 x √(3² + 4x6²)

A = 9 + 3 x √153

A = 45 ft². (option (A)

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Answer:

3515.3443 grams

Answer:

Price after discount: $33.75

You saved: $11.25

Step-by-step explanation:

Answer:

d) 0.1a

e) -5.2m^2 + 7.8m + 4.5k

f)[tex]4g^{2}[/tex]

g)-3t^2 +4.29t+9

h)4n

i)2.6g^2 -5.4g

Step-by-step explanation:

Hope this helps!

To add two mixed numbers, you can separate the whole number and fraction parts. Add the whole numbers together as you normally would, and then find a common denominator to add the fractions. Once you have your sum, you may need to simplify the fraction for your final answer.

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The given point and parallel to the given line is: y - 5 = 0 (Slope is 0)perpendicular to the given line is: y - 5 = -1/6x (Slope is -1/6).

Slope-intercept is a form of linear equation which is written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form of equation is useful for graphing linear equations, as it allows the user to quickly determine the slope and the y-intercept of the equation, which makes it much easier to plot on a graph. It is also helpful for solving linear equations, as the slope and the y-intercept can quickly be determined.

(a) The slope-intercept form of the equation of the line through the given point and parallel to the given line is y = 5. This is because the given line has a slope of 0 and the given point has a y-coordinate of 5, which is the same as the y-intercept of the parallel line.

(b) The slope-intercept form of the equation of the line through the given point and perpendicular to the given line is y = -6x + 5. This is because the given line has a slope of 0 and the line perpendicular to it has a slope of -1/0, which is -infinity. This means that the slope of the perpendicular line is -6 and its y-intercept is 5, which is the same as the given point's y-coordinate.

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There are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The number of non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the number of solutions to the equation x1 + x2 + x3 + x4 = 6, which is the number of ways to place 6 distinguishable balls into 4 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the equation x1 + x2 + (x3/2) + (x4/2) = 6. The variables x1, x2, x3 and x4 are non-negative integers, thus (x3/2) and (x4/2) are also non-negative integers.

The number of solutions to x1 + x2 + (x3/2) + (x4/2) = 6 is equivalent to the number of ways to place 6 distinguishable balls into 3 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20.

Because each of x1 and x2 are integers and (x3/2) and (x4/2) are integers, it ensures x1, x2, x3, and x4 are also integers. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

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The values of angles are  m∠1 = 39° and m∠2 = 51° from the given kite.

What is triangle ?

triangle can be defined in which it consists of three sides , three angles and sum of the angles is 180 degrees

Given figure is a kite.

The diagram is not drawn to scale.

We have to find the measure of angle 1 and 3 in the kite.

From the figure,

Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.

So, sides AB and AD are equivalent adjacent sides.

m∠1 = 39°

AC and BD are diagonals.

Diagonals of a kite always meet at right angles.

Let the diagonals intersect at point O.

From right triangle AOB,

m∠1 + m∠2 + m∠O = 180°

39° + m∠2 + 90° = 180

m∠2 = 180° - 90° - 39°

m∠2 = 90° - 39°

m∠2 = 51°

Therefore, m∠1 = 39° and m∠2 = 51°.

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Answer:

6.3

Step-by-step explanation:

70+7x=114.1

7x=44.1

x=6.3

mark brainliest

To plot the graph of the given quadratic function y = 2x², evaluation the value of the function for several values of x  at the left and right side of the origin, then plot the data.

The standard form of a quadratic function is:

y = f(x) = ax² + bc + c

Steps to plot the graph of a quadratic function includes:

However, in the given function y = 2x²,  x-intercept, y-intercept, and the extreme point are all (0,0) or the origin. Hence, we need to use auxiliary points.

Evaluate the value of y for several values of x in the left and right of the extreme value, (0,0). The results are given in the following table.

x  y

-5  50

-4  32

-3  18

-2  8

-1  2

0  0

1  2

2  8

3  18

4  32

5  50

Plot the data and we get the graph of y = 2x² ( as in the attached picture)

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The units that is appropriate for the time the number of bacteria is 300 is seconds.

The population of bacteria in a petri dish doubles every 40 seconds. The population of the bacteria is initially 400 organisms.

Therefore, the units that is most appropriate for the time at which the number of bacteria is 300 can be calculated as follows:

The bacteria population doubles every 40 seconds. Therefore, the units appropriate for when the population of the bacteria is 300 is second.

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Answer:

x=1

Step-by-step explanation:

If y=6x+1, we can substitute that into the original equation, so it would look like 3x+6x+1=10.

Now we just solve for x. Add 3x and 6x to get 9x, and subtract 1 from both sides of the equation, now we have

9x=9, divide both sides by 9 and we end up with x=1.

PS. sorry for the bad handwriting but i attached a photo of how i solved it.

Answer:  (x*4) - 3= 11.   X = 3.5

Step-by-step explanation

(4x) - 3 = 11 or (x*4) - 3 = 11.

11 + 3 = 14

So then,

14 = x * 4 (or 4x)

14 / 4 = 3.5

so,

X = 3.5

Answer:

For f(1), it's -14. For determining x, x = -1.

Step-by-step explanation:

For f(1), just plug in 1 to x. -6(1) is -6, + -8 is -14.

For determining x, if you plug in -1, you get -6(-1), which is +6. +6 -8 is -2.