How do you explain irrational numbers to children?

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=1\\ y=27 \end{cases}\implies 27=ab^1\implies 27=ab \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=2\\ y=243 \end{cases}\implies 243=ab^2\implies 243=abb\implies \cfrac{243}{ab}=b \\\\\\ \stackrel{\textit{substituting from the 1st equation}}{\cfrac{243}{27}=b\implies \boxed{9=b}} \\\\\\ 27=ab\implies \cfrac{27}{b}=a\implies \cfrac{27}{9}=a\implies \boxed{3=a}~\hfill {\Large \begin{array}{llll} y=3(9)^x \end{array}}[/tex]

Answer:

The figure isn't there brother

Answer:

49/4 is the answer

Step-by-step explanation:

................

Answer:

The number that should be added on both sides is the square of half the coefficient of x. That is (7/2)²

Step-by-step explanation:

The length of HI will be;

⇒ 6 units.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

HIJK is a square.

The length of KI = 6√2

Now,

Since, HIJK is a square.

Hence, There are all sides are equal.

Let the side of square = x

So, By Pythagoras theorem, we get;

⇒ KI² = HI² + HK²

Substitute the given values, we get;

⇒ (6√2)² = x² + x²

⇒ 72 = 2x²

⇒ x² = 36

⇒ x = √ 36

⇒ x = 6

Thus, The length of HI = 6 units

Learn more about the Pythagoras theorem visit:

https://brainly.com/question/343682

#SPJ1

Answer:

4th picture is the correct one :)

The cost of a pack of gum bought by Lionel is $2.1.

Let the variable g represent the cost of a pack of gum.

Let the variable c represent the cost of a candy bar.

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation that models this situation is;

4c + 2g = 9.80    ......equation (1)

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation (2)

c = 2g/3     ......equation (3)

Substituting equation (3) in equation (1), we get:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

= 29.4/14

= $2.1

The cost of a pack of gum is $2.1.

Read more about the equation:

brainly.com/question/15527616

#SPJ4

The complete question is -

Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?

No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.

The equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.

The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.

On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.

Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ4

Answer:

2.5/1

Step-by-step explanation:

mark me brainliest pls

Answer:

It would be .841

Step-by-step explanation:

There are 1000 meters in a kilometer, and since 841 meters is 841/1000 kilometers, that is how many kilometers you would ride.

Hope this helps!

Answer:

SeeStep by Step explanation

Step-by-step explanation:

Currently, light bulbs need nominal voltage in their operation ( that is if your system is 120 V  phase-neutral ) they will have a nominal voltage 120 (v). For that reason, all of them need this voltage for their proper operation, which follows that in any circuit the bulbs must be installed in parallel.

If you install them in series, the first will get most of the 120 (v) let´s say  90 (V), and  maybe work, but the next one won´t work because the voltage will drop and between the terminals of the second bulbs you surely measure 20 (V) or less, the third one will be working with 10 (V) according to kirchhoff´s second  law

[tex]83 {p}^{3} {q}^{2} {r}^{2} + 83p {q}^{2} {r}^{3} [/tex]

Answer:

83p^9 + q^7 + r^6 + 83p + r^6

Step-by-step explanation:

^9 means to the power of 9

^7 means to the power of 7

^6 means to the power of 6

i can't do step-by-step, it's too complicated to explain. im sorry

<3

Answer:

a=8

b=⅛

c= 2.6

d= 0.26

that's all the answers

Answer:

-65

Step-by-step explanation:

Median = middle number

-76, -74, -67, -65, -63, -58, -48

out of the numbers I am shown, from the photo, I would say "-65" is the answer, but if there is another number I'm missing, add it to the row of numbers above and add the two numbers together and divide by 2

I hope this helps!

No, isosceles triangles do not always have to have 90-degree angles.

An isosceles triangle is a triangle with two sides of equal length. While the two sides are equal, they can be of any length. This means that the angles of the isosceles triangle can vary, and the triangle does not always have to have 90-degree angles. In fact, an isosceles triangle can have angles that range from 0 to 180 degrees. The only requirement for an isosceles triangle is that it must have two sides of equal length. As such, an isosceles triangle can have angles that are greater than 90 degrees, angles that are less than 90 degrees, or even angles that are equal to 90 degrees.

Learn more about isosceles triangles here

https://brainly.com/question/2456591

#SPJ4

On solving the provided question, we can say that it is right angle triangle provided, so  cos 60 = 3/H => 1/2 = 3/H => H = 6

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

it is right angle triangle provided,

so

cos 60 = 3/H

1/2 = 3/H

H = 6

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Using the regression concept to find the equation and applying derivative, The rate of change is 10.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. The dependant variable's predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. 

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

from the given data,

y= a + bx is our regression line.

a=8 and b =10

y=8+10x is the line.

derivate the line , we get,

[tex]\frac {dy}{dx} = 10[/tex]

To learn more about regression visit:

https://brainly.com/question/14313391

#SPJ1

Answer:

First use the formula of diamete which is d by 2

Step-by-step explanation:

which the answer comes 6 and after that use formula of area of a semcicle that is pie into radius square and the answer comes 113.14

Answer:

i think it’s B

Step-by-step explanation:

Answer:

$45

Step-by-step explanation:

Answer:

50 grams

Step-by-step explanation:

36 grams = 72%

→ Find 1% by dividing both sides by 72

0.5 grams = 1%

→ Times both sides by 100 to find 100%

50 grams = 100%

Answer: Hello the lengths of the pieces of wood is missing but I will provide the format for drawing a line plot which you can now plug in your own values .

answer :

First draw a number line containing all the values in the given data set

Place a dot on top every value contained in the given data set

place as many dots as possible representing the frequency of the value in the given dataset

Step-by-step explanation:

A line plot is simply a method of displaying given data on a number line

steps :

First draw a number line containing all the values in the given data set

Place a dot on top every value contained in the given data set

place as many dots as possible representing the frequency of the value in the given dataset

attached below is an example

Step-by-step explanation:

Let's check

Circumference:-

➜2πr

➜2πx

New Circumference:-

➜2πr

➜2π3x

➜6πx

Taking ratio:-

➜2πx/6πx

➜1/3

➜1:3

If we quadruple the radius Circumference will also be quadrupled.

Answer:

[tex]\displaystyle x < \frac{12}{7}[/tex]

Step-by-step explanation:

This is an inequality, not an equation. Notice the sign is a "less than" sign and not an "equal" sign. You still solve it like a normal equation, however:

[tex]\displaystyle 7x-2 < 10\\\\\rightarrow 7x < 12\\\\\rightarrow x < \frac{12}{7}[/tex]

Answer: Choice A

False, because a logarithmic function is defined only for positive real numbers.

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

Explanation:

Using your calculator, you should see that ln(0) is undefined or it leads to some kind of error. The same happens when you try ln(-1) or any other negative number. So ln(x) only allows x > 0. This applies to any log function, and not just the natural log function.

This is why choice A is the answer. Choice B is close, but the use of "non-negative" is not correct because that means 0 is involved. But as explained above, 0 is not allowed as part of the domain.

-----------------

Extra info (optional section)

As for why 0 and negative numbers are not allowed, you have to look carefully at what logs are designed for. They were formed to help solve exponential equations. Consider the following equation

2^x = 16

We could do guess and check to see which value would replace x. You should find that x = 4 is the solution. Though another way to solve is to use logs. The given equation converts to the log form of [tex]x = \log_2(16)[/tex]; note how the number inside the parenthesis is positive. We can't have 2^x equal to a negative value, due to powers of a positive number being a positive result. So that's why we rule out negative numbers as part of the domain. Zero is excluded for similar reasoning.

Answer:

negative infinity

positive infinity

Step-by-step explanation:

edg 2022

The inequality equation ( x ≥ 4 ) is given as ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

x ≥ 4   be equation (1)

On simplifying the equation , we get

Divide by 4 on both sides of the equation , we get

( x / 4 ) ≥ 1

Adding x on both sides of the equation , we get

x + ( x/4 ) ≥ 1 + x

Now , adding ( 1/4 ) on both sides of the equation , we get

x + ( 1/4 ) + ( x/4 ) ≥ 1 + x + ( 1/4 )

On simplifying the equation , we get

( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x

Therefore , the value of A is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x

Hence , the inequality equation is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Answer:

--------------------------------------------------

Permutation of 5 mountain photographs:

Since all are next to each other, the mountain photographs count as one item along with the other 3 + 4 = 7 photographs and therefore the permutation for this is:

Total arrangements is:

Answer:

128cm²

Step-by-step explanation:

Formula to find area of rectangle is l×b

In order to find the area of the rectangle we need to apply that formula

[tex]A =lb[/tex]

[tex]A = 16[/tex]×[tex]8[/tex]

[tex]A = 128[/tex][tex]cm[/tex]²

Hence ,  the area of the given rectangle is 128cm²

Answer:

12

Step-by-step explanation:

According to the Pythagorean Theorem,

5^2 + X^2 = 13^2, OR

25 + X^2 = 169

X^2 = 169, SO X = √144, or 12

The unknown side has length 12.