Simplify. 4√162 +3 4√32

Answer:15 spoonfuls

Step-by-step explanation:

The required value of x using the properties of exponents and logarithm is 6.362.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation for x

We are given a logarithmic expression: log (1 + 3x) = 3

On applying exponent both sides, we get,

e^[log (1 + 3x)] = e^3

Using the properties of exponents and logarithm, we get,

1 + 3x = 20.0855

3x = 19.0855

x = 6.362

Hence, the required value of x can be 6.362.

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The percent error is 56. 9%

Percent error is defined as the difference between the estimated value and the actual value in comparison to the actual value.

The formula for percent error is expressed as;

Percent error = [tex]\frac{|VA - VE|}{VE}[/tex] × 100/1

Where;

Substitute the values

Percent error = | 612 - 390| / 390 × 100/ 1

Percent error = 222/ 390 × 100/ 1

Percent error = 0. 56 × 100

Percent error = 56. 9%

Thus, the percent error is 56. 9%

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Answer:

Rate of change in y is -6

-3-6 = -9

-9-6=-15

-15-6=-21

Rate of change in x is 1

1+1=2

2+1= 3

3+1 = 4

4-1=5

........And so on

Answer: he was faster the second time

Step-by-step explanation:

1/15 is a smaller fraction and 1/12, 1/15 of an hour is 4 minutes and 1/12 of an hour is 5 minutes, so he took it in 4 minutes the second time which was quicker

[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

Given: [tex]25^{2x+1}=144[/tex]

Taking logarithm on both sides:

log ([tex]25^{2x+1}[/tex]) = log (144)

=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])

=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]

=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]

=> 2x + 1 = 1.544

=> 2x = 0.544

=> x = 0.272

Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

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The simplest form of the following are -

a) 4/7 / (1 3/4) = 16/49

b) 5 3/5 / (2 2/3) = 21/10

The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.

We have been given that

a) 4/7 / (1 3/4)

Rewrite as -

= (4/7) / (1× 3/4)

= (4/7) / (7/4)

= (4/7) × (4/7)

= 16/49

b) 5 3/5 / (2 2/3)

Rewrite as -

= (5× 3/5) / (2× 2/3)

= (5× 3/5) / (8/3)

= (28/5) / (8/3)

= (28/5) × (3/8)

= 7/5 × 3/2

= 21/10

= 2.1

Thus , the following are in order of simplicity:

a) 4/7 / (1 3/4) = 16/49

b) 5 3/5 / (2 2/3) = 21/10

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Answer:

Step-by-step explanation:

no because perenthesis

Answer:

No it is not equivalent because the parenthesis

Step-by-step explanation: When it comes to parenthesis you have to do the problem in them, so you would do 33x33 rather than the whole problem at once. no idea if that makes sense bff it sounded right in my head

Answer:

Step-by-step explanation:

Can somebody simplify this?

(−8) × (-6) − (−5)² =

48 - 25 =

23

When -46 decreased by the difference between -23 and -61, the number becomes -18.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.

According to mathematical rules, when two negative signs are multiplied by each other, the number becomes positive.

The difference between -23 and -61: -61 - (-23)

-61 + 23 = -38

-46 - (-38)

-46 + 28 = -18

Here is the complete question:

-46 decreased by the difference between -23 and -61. What is the value of the number?

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Answer: Distance point is 8.

Step-by-step explanation:

You would do 2 by the power of 2 and double that (8)

the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

In mathematics, the common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm function.

Here, we have the logarithm function as:

( log ₂ 4 )

Now, we can see that:

It has a base of 2.

So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.

Therefore, we get that, the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

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Answer: Using a property of operations, what can you say about the sum of two expressions, Then the temperature changed more on Day 2.

Step-by-step explanation:

Using a property of operations, what can you say about the sum of the two expressions.

Let us assume the table of values is : Sunrise (F) = -11.31 -7.69

                                                              Sunset (F) = 13.49 25.25

           Day 1 and Day 2

Sunrise Temperature (F) = -11.31 -7.69         (eq-1)

Sunset Temperature (F) = 13.49 25.25        (eq-2)

The sum of the two equations are:

Sunrise Temperature (F) = -11.31 -7.69

                                    (F) = -19

Sunset Temperature (F) = 13.49+  25.25

                                   (F) = 38.74

Which day saw the greatest variation in temperature? Describe your thinking. To do this, we only compute the absolute difference in daily temperatures between the times of sunrise and sunset.

So, we can write

Day 1 = |-11.31 - 13.49|

Day 1 = 24.8

Day 2 = |-7.69 - 25.25|

Day 2 = 32.94

 So,      32.94 is greater than 24.8

 Therefore,     Day 2 is greater than the Day 1

Hence, the temperature changed more on Day 2.

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Answer:

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

Step-by-step explanation:

Given function:

[tex]\text{g}(x) = -2|x+3|[/tex]

Parent function:

[tex]\text{f}(x) = |x|[/tex]

A parent function is the simplest form of a family of functions.

The graph of g(x) is related to the graph of f(x) by a series of transformations.  To determine the series of transformations, work out the steps of how to go from f(x) to g(x).

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Step 1

Translation left by 3 units:

[tex]\implies f(x+3) =|x+3|[/tex]

Step 2

Stretch in the direction of the y-axis (vertically) with scale factor 2:

[tex]\implies 2f(x+3) =2|x+3|[/tex]

Step 3

Reflection in the x-axis:

[tex]\implies -2f(x+3) =-2|x+3|[/tex]

Conclusion

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

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Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

The fourth point of the parallelogram is (10, -3).

What is Parallelogram?

A Parallelogram is a quadrilateral with opposite sides parallel.

Given that;

Three points of a parallelogram are (4,3), (-4,3) and (2,-3).

Now, Take Two points at one diagonal of parallelogram are (4, 3) and

(2, -3).

Let fourth point of a parallelogram is (x, y).

Take (-4,3) and (x, y) on the another diagonal of a parallelogram.

Since, Midpoint of both diagonal is same.

Hence, Midpoint of (4, 3) and (2, -3) is calculated as;

(4+2/2, 3+(-3)/2) = (6/2, 0/2) = (3, 0)

So, Midpoint of (4, 3) and (2, -3) = (3, 0)

And, Midpoint of (-4,3) and (x, y)  = (-4+x/2, 3+y/2)

Since,  Midpoint of both diagonal is same.

Hence, (-4+x/2, 3+y/2) = (3, 0)

Equating coordinates we get;

⇒-4+x/2 = 3

⇒ -4 + x = 6

⇒ x = 6 + 4

⇒ x = 10

And, 3+y/2 = 0

    ⇒3 + y = 0

    ⇒y = -3

So, The fourth point of the parallelogram is (10, -3).

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No extraneous solution to the equation.

The equation is

[tex](x + 5)^{1/2}[/tex] - [tex](5 - 2x)^{1/4}[/tex] = 0

To know whether the equation is an extraneous solution we first need to find the value of x.

So we have,

[tex](x + 5)^{1/2} = (5 - 2x)^{1/4}[/tex]

Multiply both sides with the power of 4, then we have

[tex]((x+ 5)^{1/2})^{4}[/tex] = [tex]((5 - 2x)^{1/4} )^{4}[/tex]

[tex](x+ 5)^{2}[/tex] = 5 - 2x

[tex]x^{2}[/tex] + 10x + 25 = 5-2x

[tex]x^{2}[/tex] + 12x + 20= 0

[tex]x^{2}[/tex] + 10x + 2x + 20 = 0

x(x + 10 ) + 2(x + 10) = 0

(x + 10)(x+2) = 0

x = -10, -2

Now we have to put the value of x in the equation

x = -10

[tex](-10 + 5 )^{1/2}[/tex]-[tex](5 - 2 * -10)^{1/4}[/tex] = 0

[tex](-5)^{1/2}[/tex] - [tex]25^{1/4}[/tex]= 0

[tex](-5)^{1/2}[/tex] - [tex]5^{1/2}[/tex] = 0

Which has not possible as we don't have negative number in the square root.

x = -2

[tex](-2 + 5)^{1/2}[/tex] -[tex](5-2*-2)^{1/4}[/tex]=0

[tex]3^{1/2}[/tex]- [tex]9^{1/4}[/tex]=0

[tex]3^{1/2}[/tex]- [tex]3^{1/2}[/tex]=0

0 = 0

Therefore there is no extraneous solution to the equation

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The dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

We are told that the dimensions of the rectangular plot of land is 120yd x 53yd.

Now, you want to draw this rectangular plot on a scale of 1 inch : 5 yards. This means that 1 inch will represent 5 yards.

Thus, for the side of 120 yards, using the scale gives us;

1/5 * 120 = 24 inches

For the side of 53 yards, using the scale gives us;

1/5 * 53 = 10.6 inches

Thus, the dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

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Answer:

Step-by-step explanation:

Step-by-step explanation:

500.000 evvie was on the digit card

The solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] is called a quadratic equation.

The formula for the roots of the quadratic equation is found by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The equation is:

√x + 4 = √3 x

√x = √3 x - 4

Squaring both sides:

x = (√3 x - 4)²

x = 3x² - 8√3 x + 16

2x² - 8√3 x + 16 = 0

x² - 4√3 x + 8 = 0

After solving with the quadratic formula:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\rm x = \dfrac{-(-4\sqrt3) \pm\sqrt{(-4\sqrt3)^2-4(1)(8)}}{2(1)}[/tex]

x = 2(1 + √3) or x = 2(1 - √3)

Thus, the solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).

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The transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

A transformation is a general term for four specific ways to manipulate the shape or position of a point, a line, or a geometric figure.

We have,

Coordinates of a pentagon Q.

(2, 4), (3, 7), (7, 5), (5,4), and (4,2).

Coordinates of pentagon Q'.

(-2, -4), (-3, -7), (-7, -5), (-5,-4), and (-4,-2).

We see that the coordinates of each point of the pentagon Q have changed their position as negative coordinates in pentagon Q'

The coordinates of pentagon Q are in (x, y) which can be assumed to be in the first quadrant of the coordinate plane.

The coordinates of pentagon Q' are in (-x, -y) which is in the 3rd quadrant.

From the first quadrant to 3rd quadrant there is a rotation of 180°.

Thus the transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

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Answer:

the answer is 1

Step-by-step explanation:

trust mehhhh

Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.

Since Point T is on line segment SU, then S, T, and U are collinear.

Collinear points refers to the points that lies on the same straight line.

IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.

ST + TU = SU

Given:

ST = 3x + 2

TU = 3x + 4

SU = 5x + 9

Substitute the expressions in the equation and solve for x.

ST + TU = SU

3x + 2 + 3x + 4 = 5x + 9

3x + 3x - 5x = 9 - 2 - 4

x = 3

Substitute the value of x in the expression for SU.

SU = 5x + 9

SU = 5(3) + 9

SU = 24

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Answer:

Heya, your answer would be 52 horses, and 42 chickens.

Step-by-step explanation:

By doing the long, long and I mean long process of adding 2 + 2 or 4 + 4 (due to the fact chickens have 2 legs and horses have 4), we get to 52 horse legs, and 62 chicken legs.

Adieu

Answer:

There are 9 horses and 29 chickens.

Step-by-step explanation:

a = animals

a = 38

h = horses

c = chickens

l = legs

l = 94

Equation 1: h + c = 38

Horses have 4 legs. Chickens have 2 legs.

Equation 2: 4h + 2c = 94

Manipulate the equations so that one of the coefficients are the same.

We will multiple Equation 1 by 2 so that both equations have 2c.

Equation 1: 2h + 2c = 76

Equation 2: 4h + 2c = 94

Subtract Equation 1 from Equation 2.

Equation 2 - Equation 1

(4h + 2c) - (2h + 2c) = 94 - 76

(4h - 2h) + (2c - 2c) = 94 - 76

2h = 18

h = 9

Substitute h into either equation to solve for c.

Equation 1: 2h + 2c = 76

Equation 1: 2(9) + 2c = 76

Equation 1: 18 + 2c = 76

Equation 1: 2c = 76 - 18

Equation 1: 2c = 76 - 18

Equation 1: 2c = 58

Equation 1: c = 29

Equation 2: 4h + 2c = 94

Equation 2: 4(9) + 2c = 94

Equation 2: 36 + 2c = 94

Equation 2: 2c = 94 - 36

Equation 2: 2c = 58

Equation 2: c = 29

There are 9 horses and 29 chickens.

The linear function f(x) with a slope of -8 and that f(1) = 2 is f(x) = 10 -8x

From the question, we are find a linear function with slope of -8 and that f(1) = 2

If f(1) = 2, then the line passes through the point (1, 2)

Using the point-slope form of the equation of a straight line

y - y₁ = m(x - x₁)

Where m is the slope

Then,

y - 2 = -8(x - 1)

Simplify

y - 2 = -8x + 8

y = -8x + 8 + 2

y = -8x + 10

∴ f(x) = -8x + 10

f(x) = 10 - 8x

Hence, the linear function is f(x) = 10 -8x

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Answer: f(-2) = - 4

Step-by-step explanation:

Answer: Emily's in total journey is 15.045 kilometers.

Step-by-step explanation:

Given data,

Emily traveled a certain distance on a horse = 10.98 kilometers

Emily traveled a certain distance on a bike = 4.06 kilometers

The overall distance traveled by Emily on her horse and bike needs to be determined.

For "Total Distance" , we will use addition operation:

So, Total distance covered by Emily's journey is given by equal to

Emily traveled a certain distance on a horse + Emily traveled a certain distance on a bike

Let us assume,

Total distance covered by Emily's journey is represented by 'x'

Then we can write,

                          x = 10.981 kilometers + 4.064 kilometers

                          x = 15.045 kilometers

Therefore, Emily's in total journey is 15.045 kilometers.

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20 people likes movies, such that  12 of these also like music, then the probability is just the quotient between:

Q = 12/20 = 0.6

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.

So the quotient between 12 and 20, that will gave us the probability we want to find.

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

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