The number line shows the distance in meters of two birds, A and B, from a worm located at point X:

We line up the decimal point so that the place value of other number does not changes.

Adding and subtracting decimal numbers is the same as adding and subtracting whole numbers. The most important thing to remember is to align the decimal places directly on top of each other when stacked. This stacks the digit values ​​so that 1 is above 1, , the tens on the tens, the tenths on the tenths,, and so on. Note that if a number does not have the same number of decimal places as other numbers, you can pad all the digits to the right of the decimal point with zeros. Numerically, this looks like 3.15 = 3.150 = 3.150000000.

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The 3rd degree polynomial equation 2 x³ -16 = 0 has 1 real solution x₁=2 and two imaginary solutions x₂= -1 + √3 i and x₃= -1 - √3 i

The given equation is:

2 x³ -16 = 0

This is a 3rd degree polynomial equation.

Divide both sides by 2, we get:

x³ - 8 = 0

Add both sides with 8:

x³ = 8

Root characteristics: If a 3rd degree polynomial equation has the form

x³ = b

Then, it has 1 real solution and 2 imaginary complex conjugate solutions.

Furthermore,

x₁ = ∛b

x₂,₃ = ½.∛b (-1± √3 i)

Apply this to the given problem, we have:

x₁ = ∛8 = 2

x₂ = ½. 2 (-1 + √3 i) = -1 + √3 i

x₃ = ½. 2 (-1 - √3 i) = -1 - √3 i

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The expression (-1 ,-5) is not a solution to the inequality 4x + y < -3

The inequality is given as

4x + y < -3

The solution is given as

(-1, 5)

Substitiute (-1, 5) for (x, y) in the inequality expression 4x + y < -3

So, we have

4(-1) + 5 < -3

Open the bracket

-4 + 5 < -3

Evaluate the sum

1 < -3

The above inequality is false

Hence, (-1 ,-5) is not a solution to the inequality 4x + y < -3

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An experimental study is used in the given situation.

Observational Study is defined as the type of study where there is no influence on the response of the participant.

Experimental Study is defined as the type of study where the participant is put into a setup and then the participants are observed .

In the given question ,

As the individual are first categorized into to two groups , one on a healthy, moderate diet and the other group not on any diet.

So, we can see that in this a setup has been created , they are put in different conditions  , and then they are observed .

Therefore ,  an experimental study is used in the given situation.

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Answer:

-0.0238095238

Step-by-step explanation:

Answer:

7. 17

8. -7

9. 64/3 or 21 1/3

Step-by-step explanation:

7. 3x-4 and the value of x is 7. Plug 7 into the x values in the expression that is given.

3x-4  --> 3(7) - 4

When simplified, 3(7) - 4 becomes 21-4 which is 17.

8. -5x+8 and the value of x is 3. Same as before, but this time you'll plug 3 into the x values in the given expression.

-5x+8 --> -5(3) + 8

When simplified,  -5(3) + 8 becomes -15+8 which is -7.

9. 10x+18 and the value of x is 1/3. Plug in 1/3 into the x values in the expression.

10x+18 --> 10(1/3)+18

When simplified, 10(1/3)+18 becomes 10/3+18. To solve this, turn 18 in a fraction over 3. 3x18=54 and that gives you the numerator. 10/3+54/3= 64/3. If you wanted it in a mixed fraction, it would be 21 1/3.

Answer:

18-2x=4x is given

18=6x is addition property of equality

3=x is I think division property of equality bc you divided to get x=3

It should be noted that the graph which will correctly show the number of pages which Louise will have left to read after the number of days is D. A graph titled How much Louise has left to read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (2, 270).

It should be noted that he a graph is a diagram that shows the relationships between two or more things.

In this case, it can be seen that Louise is reading a 300-page book and she reads 15 pages every day.

Therefore, the graph that correctly displays the number of pages which Louise has left to read after the number of days is a graph titled How Much Louise Has Left to Read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (2, 270).

In conclusion, the correct option is D.

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Using the properties of logarithm the value of the expression is   [tex]log_{2} 96 - log_{2} 3 = 5[/tex]

A logarithm is the power to which a number must be raised in order to get some other number.

According to the question we have been given the expression as

                        =  [tex]log_{2} 96 - log_{2} 3[/tex]

The properties of logarithm that we are going to use are :

         [tex]log(\frac{x}{y} ) = logx - logy[/tex]  and [tex]log_{a} a = 1[/tex]

Also we can see that the base are same so we can use the property of logarithm in the given equation.

Now solving this step by step using the properties of logarithm we get

                       [tex]= log_{2} \frac{96}{3} \\= log_{2} 32\\= log_{2} 2^{5}\\ = 5* log_{2} 2\\= 5*1\\= 5[/tex]

Hence using the properties of logarithm the value of the expression is

[tex]log_{2} 96 - log_{2} 3 = 5[/tex]

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Answer:

what?

Step-by-step explanation:

???????????????????

A function that gives the length of the hypotenuse of an isosceles right triangle with side length s is given by h(s)=s√2 and the length of the side of the triangle is approximately 4.24 inches.

The largest side of a right-angled triangle is referred to as the hypotenuse. Additionally, the hypotenuse is situated across from the right angle.

We know from the Pythagorean Theorem that the square of the hypotenuse is equal to the sum of the squares of the triangle's right-angled legs.

The right triangle's given legs are s. Let's think about the hypotenuse's function, h(s).

Therefore we can define the function h(s) as

h(s)=s√2

The inverse of the function can be written as

y=s√2

or, s=y²/2

so the inverse function is:

h⁻¹(s)=s²/2

Now for hypotenuse = 6 inches.

Each side can be calculated using the inverse function h⁻¹(s)=s²/2.

s=6÷√2

or, s=4.242...

Hence the length of the side of the triangle is approximately 4.24 inches.

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Answer:

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

First divide 45 by 9.

After you divide you should have 5.

Next you multiply 5 times 12.

Which gives you 60.

Hope this helps! :)

The length of the third side of the right triangle is 12.65 feet.

It states in a right triangle the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.

We have,

Right triangle:

Side = A = 6 feet

Hypotenuse = h = 14 feet

Let the 3rd side be = M

Applying Pythagoras theorem:

h² = A² + M²

14² = 6² + M²

196 = 36 + M²
M² = 196 - 36

M² = 160

M = √160

M = 2√10

M = 2 x 3.1622

M = 12.649

Rounding to the nearest hundredth we get,

M = 12.65

Thus the length of the third side of the right triangle is 12.65 feet.

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Answer:

11.1111 for 40 km

279.4 for 11 in

Step-by-step explanation:

The area of the computer chip is 2.44 x 10^-15 square units

The area of a shape is the amount of space on the shape

The dimensions of the computer chip are given as

7.18 x 10^-7 and 3.4 x 10^-9

The area of the computer chip is the product of the dimensions of the computer chip

So, we have

Area = Length x Width

This gives

Area = 7.18 x 10^-7 x 3.4 x 10^-9

Rewrite as

Area = 7.18 x 3.4 x 10^-7 x 10^-9

Evaluate the products

Area = 24.412 x 10^-16

Rewrite as

Area = 2.4412 x 10^-15

Approximate

Area = 2.44 x 10^-15

Hence, the area of the computer chip is 2.44 x 10^-15 square units

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x = 512 is not an extraneous solution of the equation.

[tex] \sqrt[3]{x} [/tex] = 8

Cubing both the side of the equation, we get

[tex] { \sqrt[3]{x} }^{3} [/tex]

= 8³

x = 512

Check for extraneous solution by putting the value x = 512 in the original equation

[tex] \sqrt[3]{x} [/tex] = 8

[tex] \sqrt[3]{512} [/tex] = 8

8 = 8

⇒ LHS = RHS

∴ x = 512 is not an extraneous solution of the equation.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is not possible for a triangle to have more than one vertex with internal angle greater than or equal to 90°, or it would no longer be a triangle.

Answer:

X= -4

Step-by-step explanation:

12x+2=5x−26

12+2−2=5−26−2

Answer:

x=−4

Step-by-step explanation:

Subtract  from both sides

Simplify then subtract 5x from both sides

Example:

Do it step by step:

Here is one way of working this out - find out how far the whale can swim in 1 min.

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.1 hour = 60 mins so multiply how far the whale can swim in 1 min (0.53333333333333333333333333333333) by 60 to get how far the whale can swim in 1 hour. = 60*0.53333333333333333333333333333333 = 32 miles.

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.1 hour = 60 mins so multiply how far the whale can swim in 1 min (0.53333333333333333333333333333333) by 60 to get how far the whale can swim in 1 hour. = 60*0.53333333333333333333333333333333 = 32 miles.Here is another way of working this out - by fractions.

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.1 hour = 60 mins so multiply how far the whale can swim in 1 min (0.53333333333333333333333333333333) by 60 to get how far the whale can swim in 1 hour. = 60*0.53333333333333333333333333333333 = 32 miles.Here is another way of working this out - by fractions.1 hour = 4 quarters hours

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.1 hour = 60 mins so multiply how far the whale can swim in 1 min (0.53333333333333333333333333333333) by 60 to get how far the whale can swim in 1 hour. = 60*0.53333333333333333333333333333333 = 32 miles.Here is another way of working this out - by fractions.1 hour = 4 quarters hours1 and one forth of an hour = 5 quarter hours

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.1 hour = 60 mins so multiply how far the whale can swim in 1 min (0.53333333333333333333333333333333) by 60 to get how far the whale can swim in 1 hour. = 60*0.53333333333333333333333333333333 = 32 miles.Here is another way of working this out - by fractions.1 hour = 4 quarters hours1 and one forth of an hour = 5 quarter hoursit takes the whale 5 quarter hours to swim 40 miles so how far can it swim in 4 quarter hours or 4/5 ths of the time.

Here is one way of working this out - find out how far the whale can swim in 1 min.1 and 1/4 hours = 60 + 15 mins = 75mins.The whale can swim 40 miles in 75 mins. So devide 40 by 75 and this is how far it can swim in 1 min. = 40/75 = 0.53333333333333333333333333333333 miles.1 hour = 60 mins so multiply how far the whale can swim in 1 min (0.53333333333333333333333333333333) by 60 to get how far the whale can swim in 1 hour. = 60*0.53333333333333333333333333333333 = 32 miles.Here is another way of working this out - by fractions.1 hour = 4 quarters hours1 and one forth of an hour = 5 quarter hoursit takes the whale 5 quarter hours to swim 40 miles so how far can it swim in 4 quarter hours or 4/5 ths of the time.ie 4/5*40 = 32miles

Answer:

Total length of the pipe = 125 inches

Let the shorter piece be x inches

So, the longer piece is 4x.4x + x = 1255x = 125x = 25

Therefore, the lengths of the two pieces are 25 inches and 100 inches

Step-by-step explanation:

The value of x = 16, y = 172 and z = 2.

x - 4z = 12x - y - 6z = 42x + 3y - 2z = 8

let x - 4z = 8 be equation (1), 12x - y - 6z = 8 be equation (2) and 42x + 3y - 2z = 8 be equation (3)

x - 4z = 8

x = 8 + 4z

12x - y - 6z = 8

12(8 + 4z) -y - 6z =8

96 + 48z - y - 6z = 8

42z - y = -88

y = 42z + 88

42x + 3y - 2z = 8

42(8+4z) + 3(42z + 88) - 2z = 8

336 + 168z + 126z + 264 - 2z = 8

168z + 126z + 2z = 336+264 - 8

296z= 592

z = 2

substituting the value of z

x = 8 + 4z

= 8 + 4(2)

8+8 = 16

y = 42z + 88

42(2) + 88

84 + 88= 172

The value of x = 16, y = 172 and z = 2.

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Answer:

2.088 x 10^5

Step-by-step explanation:

7.2 x 10 x 2.9 x 10^3 = 20.88 x 10^4

= 2.088 x 10^5

The variable w is as follows:

We have to find the variable w in the equation.

-61 = 8 - 1 / 3(12w + 42) - w

subtract 8 from both sides of the equation

-61 = 8 - 1 / 3(12w + 42) - w

-61 - 8 = 8 - 8 - 1 / 3(12w + 42) - w

-69 = - 1 / 3(12w + 42) - w

69 = 1 / 3(12w + 42) + w

Therefore,

[tex]\frac{1}{3(12w+42)}+w[/tex] = 69

[tex]\frac{1+3w(12w+42)}{3(12w+42)}[/tex] = 69

[tex]\frac{1 + 36w^{2} +126w}{3(12w+42)}[/tex] = 69

cross multiply

1 + 36w² + 126w = 2484w + 8694

36w² + 126w - 2484w - 8694 + 1 = 0

36w² - 2358w - 8693 = 0

using,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 36

b = -2358

c = -8693

Hence,

[tex]\frac{2358+\sqrt{(-2358)^{2}-4(36)(-8693) } }{2(36)}[/tex]  and [tex]\frac{2358-\sqrt{(-2358)^{2}-4(36)(-8693) } }{2(36)}[/tex]

Therefore,

[tex]w = \frac{393+\sqrt{189221} }{12}[/tex] and [tex]w = \frac{393-\sqrt{189221} }{12}[/tex]

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The fraction of the tank that was full of petrol that he had used is 1/4

From the question, we are to determine the fraction of the tank that was full of petrol that he has used

From the given information,

On Monday, Nassim filled up his tank

and

On Tuesday, his tank was 3/4 full

The fraction of the tank when filled is 1/1, that is, 1

Thus,

The fraction of the tank that he had used = 1 - 3/4

The fraction of the tank that he had used = 1/4

Hence, the fraction of the tank that was full of petrol that he had used is 1/4

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The value of k in function g of x is x-2.

A function in mathematics can be defined which from a set X to a set Y that is to allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and range or sometimes refer to the codomain of the function , respectively.

In mathematics, a function is an expression, rule, or law that establishes the relationship between a single variable (the independent variable).

In the given question,

function of x = (1)* (-x+6)

and function of g = g of x = k

now the solution of equation is,

f (x) = g (x) is x = 4.

taking,  putting x =4 in (1)* (-x+6)

=> x = -4 + 6 = 2

now for g of x to be 4 the value of k should be x-2

as when x = 4 , g of x = x-2 = 4-2 = 2 = f of x

Thus, The value of k in function g of x is x-2.

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The answer is square root of 3

The given equation contains square root forms hence we must simplify it before proceeding further

we know that 12= 2^2 *3

Thus applying it in the equation, the equation becomes

5[tex]\sqrt{3}[/tex]-2[tex]\sqrt{12}[/tex]

Thus writing 12 as 2^2X3

5[tex]\sqrt{3}[/tex]-2[tex]\sqrt{2^2*3}[/tex]

Now taking out square root of 2^2 which is 2,

the equation becomes

5[tex]\sqrt{3}[/tex]-4[tex]\sqrt{3}[/tex]

=[tex]\sqrt{3}[/tex]

Thus the answer is square root of 3

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On day 1 they travel 40 miles , on day 2 they travel 120 miles, on day 3 they travelled 80 miles.

what is  linear equation ?

A linear equation is a kind of equation that has the highest power of the variable is always 1 is also called as a one-degree equation.

By the linear equation, lets assume family travelled x miles on day 1 then, According to the question, family travelled on day 2 is = 3x miles family travelled in day 3 is = 3x - 40 miles now the travel 240 miles in total then by addition x + 3x + 3x -40 = 240

7x -40 = 240,

7x = 280

x = 40 miles

day 1 =40 miles

day 2 = 120 miles

day 3 = 80 miles

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Answer:

$310.59

Step-by-step explanation:

68% of what number is 211.20

.68x = 211.20  Divide both sides by .68

x = 310.5882352968  Round to the nearest cent

x = 310.59

The result to the equation given by rounding this to the nearest ten-thousandth is 4.0000.

Rounding off means simplifying a number by keeping its overall value but moving it closer to the next number. It is used for whole numbers and decimals with tens, hundreds, thousands, and so on.

If the digit in the smallest spot is less than 5, it is left alone. Rounding down occurs when any number of digits then after the number become zero. If the digit inside the smallest place is larger than or equal to 5, it is multiplied by +1.

the equation 3 x=36

3x = 36

x = 36/3

x = 4.0000

the answer to the equation given is =  4.0000

The result to the equation given by rounding this to the nearest ten-thousandth is 4.0000.

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