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Uranium-238 (U-238) has a half-life of 4.5 billion years. Geologists find a rock containing a mixture of U-238 and lead, and determine that 71% of the original U-238
remains; the other 29% has decayed into lead. How old is the rock?
The rock is ___ billion years old.
(Round to three decimal places as needed.)

In order to know the appropriate number divisible by 2, 5 and 10. We need to have a look at what type of numbers are divisible by either of these number. So, let's discuss one by one

Divisible by 2

Divisible by 5

Divisible by 10

Let's have a look at the given numbers and see which ones are divisible by 2, 5 and 10

We'll write "yes" for the number which are divisible and "No" for the number which are not divisible by either of them.

105 - only by 5

183 - No

34 - only by 2

238 - only by 2

54 - only by 2

553 - No

260 - yes

85 - only by 5

450 - yes

365 - only by 5

745 - only by 5

360 - yes

270 - yes

390 -  yes

400 - yes

110 - yes

210 - yes

775 - only by 5

438 - only by 2

565 - only by 5

766 - only by 2

906 - only by 2

321 - No

347 - No

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This question is incomplete. You can have a look at the attached picture to know the complete question.

2)Main Answer: a)1,8,27,64,125,216,343,512

                        b)I,II,III,IV,V,VI,VII,VIII,IX,X,XI                                    

Concept and definitions should be there:

A conjecture is an educated guess that is based on known information. Example. If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

Given data

a)Next five terms 1,8,27,64

b)Next five terms I,II,III,IV,V

Solving part

using conjecture

a)Next five terms 1,8,27,64,125,216,343,512

Notice that the difference between consecutive terms is 7.

Conjecture: n3, n=1,2,3...

Final Answer:1,8,27,64,125,216,343,512

b))Next five terms I,II,III,IV,V,VI,VII,VIII,IX,X,XI

Conjecture: n, n=i,ii,iii,...

Final Answe:I,II,III,IV,V,VI,VII,VIII,IX,X,XI

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3)Quastion incompleted

4)Main answer :The number 14 is even and therefore is divisible by 2. This is the correct statement.

Given data

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

Solving part

The number 14 is even and therefore is divisible by 2. This is the correct statement.

Final Answer:The number 14 is even and therefore is divisible by 2. This is the correct statement.

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5)Main Answer:X = -2

Concept and definitions should be there:This solution deals with linear equations with one unknown.

Given data

18x-2(3x+1)=5x-16

Solving part

We simplify the equation first:

18x−2(3x+1)=5x−16

18x+(−2)(3x)+(−2)(1)=5x+−16 (Distribute)

18x+−6x+−2=5x+−16

(18x+−6x)+(−2)=5x−16 (Combine Like Terms)

12x+−2=5x−16

12x−2=5x−16

Then we cancel out:

12x−2−5x=5x−16−5x

7x−2=−16

7x−2+2=−16+2

7x=−14

7x/7 = −14/7

x = -2

Final Answer:x = -2

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The equation of the parabola that has vertex at the center and focus at the point (6,0) is x = y²/24

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(y - k)² = 4p(x - h)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v (0, 0)

f (6, 0) the focus is on the right so the parabola is of the form X = Y².

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = 6

p = 0 + 6

p= 6

(y - 0)² = 4*6(x - 0)

(Y)² = 24(X)

x = y²/24

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Answer:

b = 99

Step-by-step explanation:

b and 81° are same- side interior angles and sum to 180° , that is

b + 81 = 180 ( subtract 81 from both sides )

b = 99

Answer:

I'll go with the last option. c=√Em

With the help of linear equtions it can be concluded that we downloaded 54 songs in which 28 songs were free and 26 songs were paid.

A linear equation is an algebraic equation in which each term has an exponent of one and when graphed produces a straight line. That's why it is considered a 'linear equation.'

Let a represent paid downloaded songs.

Total cost of songs downloaded = a x cost of each additional download.

a x $0.59 = $0.59a

The overall cost of downloaded songs is $15.34.

$15.34 =   $0.59a

Divide both sides of the equation by  $0.59.

a = 26 songs

We downloaded 26 paid songs.

Total songs downloaded = total free songs + total paid songs

Total songs downloaded = 26 + 28 = 54 songs

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex][tex]~\dotfill\\\\ \stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is -1/3 and it passes through (2 , -6)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +6= -\cfrac{1}{3} (x -2) \\\\\\ y+6=-\cfrac{1}{3}x+\cfrac{2}{3}\implies y=-\cfrac{1}{3}x+\cfrac{2}{3}-6\implies y=-\cfrac{1}{3}x-\cfrac{16}{3}[/tex]

Answer:

335

Step-by-step explanation:

you put -18 in for x

you multiply -18 by -18 because it's the exponent of 2

then add 11

The nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .

According to the given question.

We have a sequence 4, 16, 64, 256, 1024...

As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.

Here,

The first term of the given sequence is 4, or we can say that 4^1 is 4.

The second term of the sequence is 16, or we can say that 4^2 is 16.

The third term of the sequence is 64, or we can say that 4^3 is 64.

The fourth term of teh sequence is 256, or we can say that 4^4 is 256.

So, if we follow the same pattern or the rule we can say that the nth term of the given sequence is 4^n.

Thereofre, the formula for finding the nth term of the given sequence 4,16,64,256,1024, ...... is [tex]a_{n} = 4^{n}[/tex] where n = 1, 2, 3 , 4....

Hence, the nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .

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The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.

Given: 1, 3, 9, 27, ...

Here, 3 - 1 ≠ 9 - 3 ≠ 27 - 9

Since the sequence does not follow the definition of an arithmetic progression, it is not one.

Hence, The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.

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Answer:

W = -57.6         PS: I'm in 8th grade.

Step-by-step explanation:

W/6 + 7.2 = -2.4   Step 1: Use Inverse operations (subtract 7.2 on both sides)

W/6 = -2.4 - 7.2    Step 2: Combine Like terms (-2.4 - 7.2)

W/6 = -9.6            Step 3: Use Inverse Operations (multiply by 6 on both sides)

W = -9.6 x 6         Step 4: Simplify

W = -57.6            

The property that justifies the following statement, 5(3 x+1)=15 x+5 is the distributive property.

Distributive property can be described as one of the properties of multiplication which states that if we multiply two or more values that are added together with a number then the result will be the same even if we multiply each value separately with that number and then add them together. This can be given as:

x(y + z) = xy + xz

Therefore, as 5 x 3 = 15 and 5 x 1 =5, we can write the equation 5(3x+1) as 15x + 5 as the result will be the same in both circumstances.

The distributive property not only justifies the equations when two or more values are added but also justifies the equations in which they are subtracted which can be given as:

x(y-z) = xy - xz

So, according to the distributive property, the statement, 5(3 x+1)=15 x+5 is valid.

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None of the equations are correct.

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. In other languages, the word equation and its cognates may have slightly different meanings. In French, an équation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

For perpendicular equations, the product of slope is -1, but none of the options here is have slope whose product with the given equation is -1.

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Answer: [tex]2x^{2} +17x+36[/tex]

Step-by-step explanation:

FOIL:
[tex]2x^{2} +8x+8x+36[/tex]

Combine like terms:

[tex]2x^{2} +17x+36[/tex]

The following is the absolute value equation for figuring out the maximum and minimum period of time: t = |d/v| + |25/v|.

The parameters provided;

The number of hours required for the plane to travel just at given values is determined as follows:

Time= distance / speed

The equation for calculating the maximum number of hours is as follows:

t = (d + 25)/v = (160 + 25)/150

t = 1.23 hours.

The equation and for shortest number of hours is as follows:

t = (d - 25)/v = (160 - 25)/150

t = 0.9 hours.

Thus, the absolute value equation for determining the maximum and minimum amount of time is as follows:

t = |d/v| + |25/v|.

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An inequality that matches the wingspan of the common sparrow is       9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.

In this question, we have been given a statement 'The common sparrow has a wingspan of 9 to 15 centimeters. '

We need to write an inequality that matches the wingspan of the common sparrow.

Let x represents the wingspan of the common sparrow.

According to given statement, the common sparrow has a wingspan of 9 to 15 centimeters.

So, the required inequality would be,

9 ≤ x ≤ 15

Therefore, an inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.

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By solving a system of equations we can see that the quadratic equation is:

y = x^2 + 3x + 10

A general quadratic equation is given by:

y = a*x^2 + b*x + c

We want this quadratic equation to pase through the points (-2, 8), (1, 14), and (0, 10).

using the last point, we know that when x = 0, we must have y = 10, then:

10  = a*0^2 + b*0 + c

10 = c

So our quadratic equation is:

y = a*x^2 + b*x + 10

Now we use the other two points to write a system of equations:

8 = a*(-2)^2 + b*(-2) + 10

14 = a*(1)^2 + b*1 + 10

If we simplify these, we get:

-2 = 4*a - 2b

4 = a + b

Isolating a in the second equation we get:

a = 4 - b

Now we replace that in the other equation:

-2 = 4*(4 - b) - 2b

-2 = 16 - 4b -2b

-2 - 16 = -6b

-18/-6 = b = 3

Now that we know the value of b, we replace it in the equation for a:

a = 4 - b = 4 - 3 = 1

Then the quadratic equation is:

y = x^2 + 3x + 10

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Answer:

[tex]\frac{613}{1000}[/tex]

Step-by-step explanation:

Which property does the equation 3(g+h)+2 g=(3 g+3 h)+2 g illustrate?

Distributive property .

What is distributive property?

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The distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

Two points J(-2 , 6) and K(1 , 4) are given .

We have to find out the distance between two points.

What is the distance formula ?

The distance formula is [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] where two points are ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]).

As per the question ;

J ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) = J (-2 , 6) and K ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = K (1 , 4)

and

The distance formula is ;

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex]

So ,

The distance between points J(-2 , 6) and K(1 , 4) will be ;

= [tex]\sqrt{(-2-1)^{2} + (6-4)^{2} }[/tex]

= [tex]\sqrt{(-3)^{2} + (2)^{2} }[/tex]

= [tex]\sqrt{(9)+ (4)}[/tex]

= √13

= 3.6 ( round to nearest tenth)

Thus , the distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

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The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂)  is given by ;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between A(1,5) and B(-2,-3)

[tex]d = \sqrt {\left( {1 + 2 } \right)^2 + \left( {5 + 3 } \right)^2 }[/tex]

d = 8.544

Roud to nearest tenth ⇒ 8.54  units.

Hence "The distance between A(1,5) and B(-2,-3) is  8.54 rounded to the nearest tenth".

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Using the Factor Theorem, the quadratic functions are given as follows:

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the roots are given as follows:

[tex]x_1 = -3, x_2 = 8[/tex]

Hence:

f(x) = a(x + 3)(x - 8)

f(x) = a(x² - 5x - 24).

It opens upward with a positive leading coefficient, that is, a > 0, hence one example is a = 1 as follows:

f(x) = x² - 5x - 24.

It opens downward with a negative leading coefficient, that is, a < 0, hence one example is a = -1 as follows:

f(x) = -x² + 5x + 24.

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Each subtraction equation as an addition equation is  mathematically given as

a - 9 = 6 ==> a=6+9

p - 20 = -30==> p+30=20

z - (-12) = 15 ==>  z+12=15

x - (-7) = -10 ==> x+17=0

This is further explained below.

Generally, In mathematics, the summation is the process of adding together a string of any form of numbers, which are referred to as operands or summands; the result is the sum or total of the figures.

In conclusion,

a - 9 = 6 ==> a=6+9

p - 20 = -30==> p+30=20

z - (-12) = 15 ==>  z+12=15

x - (-7) = -10 ==> x+17=0

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The Simplified value of the complex fraction 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3) .

A complex fraction is defined as an expression that has fraction in it's numerator and a fraction in its denominator.

For Example : [tex]\frac{\frac{2}{3} }{\frac{5}{7} }[/tex] is an example of complex fraction.

The given question is

=1 + 2/x / 2 + 3 / 2x

[tex]=1+\frac{\frac{2}{x} }{2+\frac{3}{2x} }[/tex]

Taking LCM in the denominator and solving further,

[tex]=1+\frac{\frac{2}{x} }{\frac{4x+3}{2x} }[/tex]

[tex]=1+\frac{2}{x} *\frac{2x}{4x+3}[/tex]

Cancelling out "x" from both numerator and denominator

we get,

=1+(2*2)/(4x+3)

=1+(4)/(4x+3)

Taking LCM as 4x+3 and solving further we get,

=(4x+3+4)/(4x+3)

=(4x+7)/(4x+3)

Therefore , the simplified value of the expression 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3).

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After solving for equation or inequality 4 x+6 ≥ -6, the value of  x ≥ -3

⇒ 4 x+6 ≥ -6

⇒ 4x ≥ -6-6

⇒ 4x ≥ -12

⇒ x ≥  -12/4

⇒ x ≥ -3

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

12°

Step-by-step explanation:

The angles of the shape should all add to 360°.

We divide this by 30, because the shape has 30 angles.

360° ÷ 30 = 12°.

This is the measure of each angle, and also the degree of rotation. The shape will look like the original figure each time it is rotated 12°.

A. For every 4 apples, there are 3 oranges.

B. The ratio of bananas to oranges is 6:3

C. The ratio of apples to bananas is 4 to 6.

D. For every 1 orange, there are 2 bananas.

The approximate length of each side of the park is 85m .

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

According to the question

given that the park is a square

and in square the longest side is it's diagonal and the diagonal is  given to be 120m.

In square all sides of square is same .

let the side be x.

By Applying Pythagoras Theorem in the given ΔABC

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

Substituting the values  we get

[tex]x^{2} +x^{2} =120^{2}[/tex]

[tex]2x^{2} =120^{2} \\ \\ 2x^{2} =14400\\ \\ x^{2} =7200[/tex]

[tex]x=\sqrt{7200} =60\sqrt{2}[/tex] = 84.85 ≅ 85

Therefore ,  the approximate length of each side of the park is 85m .

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