State which property or properties need to be used to write each expression as a single logarithm.
a. log₄5+log₄5

The expanded form of the number 34.576 is A: An expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth.

It should be noted that the correct form of the expression will be:

= (3 × 10) + (4 × 1) + (5 × 1/10) + (7 × 1/100) + (6 × 1/1000)

= 34.576

Therefore, the expanded form of the number 34.576 is an expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth.

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Answer:

THE CORRECT ANSWER'S ARE A,D AND F

Step-by-step explanation:

did the test on edge .

The mass of the bar of chocolate in kilogram, kg is calculated to be 1.8kg

Given data

mass of a bar of chocolate is 1800g

density of the chocolate is 9g/cm

density is defined the ratio of mass and volume. therefore the density of the chocolate will be the ratio of the mass of the chocolate bar to the volume of the chocolate. this represented mathematically as:

The mass of the bar of chocolate is given in grams as 1800g

converting the unit to kg is done as follows

if 1kg is equal to 1000g, then how many kg is 1800g

= 1800 / 1000

= 1.8 kg

hence the mass of the chocolate bar in kg is 1.8 kg

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The unit rate for the turtle crawling is 1 mile per hour

An equation is an expression that shows the relationship between two or more numbers and variables.

Unit rate is the ratio of two different units, and also having a denominator of one.

For every of an hour that the turtle is crawling, he can travel of a mile. Hence:

Unit rate of crawling = 1 mile / 1 hour = 1 mile per hour

The unit rate for the turtle crawling is 1 mile per hour

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[tex]\huge\boxed{\sqrt5}[/tex]

To find the value of [tex]x[/tex], we'll use the Pythagorean theorem.

The following formula applies, with the lengths of the sides with the right angle being [tex]a[/tex] and [tex]b[/tex], and the hypotenuse being [tex]c[/tex]:

[tex]a^2+b^2=c^2[/tex]

Substitute the values in.

[tex]x^2+(\sqrt{11})^2=4^2[/tex]

Square the numbers as possible.

[tex]x^2+11=16[/tex]

Subtract 11 from both sides of the equation.

[tex]x^2=5[/tex]

Take the square root of both sides of the equation to solve for [tex]x[/tex].

[tex]x=\sqrt5[/tex]

Answer:

so simple do it yourself and use the formula when is given in the text book to solve

Answer:

x = 3/5

Step-by-step explanation:

Isolate the x by subtracting 2x from both sides

2x + 3 = 7x

-2x        -2x

3 = 5x, Then divide by 5 on both sides

x = 3/5

Answer:

[tex] \sf \large \: x = \frac{3}{5} [/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+3=7x

Step 1: Subtract 7x from both sides.

2x+3−7x=7x−7x

−5x+3=0

Step 2: Subtract 3 from both sides.

−5x+3−3=0−3

−5x=−3

Step 3: Divide both sides by -5.

−5x/−5 = −3/−5

x=3/5

[tex]\begin{array}{llll} 10x=5y-8\\\\ 15x=-5y-2\\\\ \end{array}\implies \stackrel{\textit{using elimination}}{\begin{array}{llll} 10x-5y=-8\\\\ 15x+5y=-2\\\cline{1-1} 25x+0=-10 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]25x=-10\implies x=\cfrac{-10}{25}\implies x=-\cfrac{2}{5} \\\\\\ \stackrel{\textit{substituting "x" in the 1st equation}}{10\left(-\frac{2}{5} \right)=5y-8\implies }-4=5y-8\implies 4=5y\implies \cfrac{4}{5}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \left( -\frac{2}{5}~~,~~\frac{4}{5} \right) \end{array}}~\hfill[/tex]

If a ≤ b, then it is not true for all real numbers that a²≤ b² .

Consider a ≤ b.

Then squaring on both sides,

⇒ a²≤ b² .

But this is true only when both a and b are non-negative numbers.

For example, if we take a = 2 and b = 5, then clearly,

2² = 4 ≤ 5² = 25

Now we need to prove that this result is not true for all real numbers. So we find two real numbers a and b which does not follow this result.

Let a = -7 and b = 3

So here, a < b

Now a² = (-7)² = 49

and b² = 3² = 9

So here, a² > b².

Thus a = -7 and b = 3 is the required counter example to show that the given result is not true for all real numbers.

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The average rate of change or the slope is found as 39.

The slope of the line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

The function is given as;

g(x) = 3x³ + 1

The points are; -1 and 4.

Put x = -1

g(-1) = 3(-1)³ + 1

g(-1) = -2

Put x = 4

g(4) = 3(4)³ + 1

g(4) = 193

The points are;

(x₁ ,y₁) = (-1, -2)

(x₂, y₂) = (4, 193)

Put the values in the slope formula;

m = (193 + 2)/(4 + 1)

m = 195/5

m = 39

Thus, the value of the average rate of change is 39; which is also the slope of the function.

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Using breaking apart technique 4 X 23 = 92

To make the multiplication process simpler, you split up one or more of the numbers. It also explains why you would "carry" a number to the following column.

split apart definitions. verb: break anything down into its component parts. substitute words: separate, dismantle, take apart

According to the given question

4×23 = (20×4)+(3×4)

         =80+12

          =92

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Answer: x=5/4

Step-by-step explanation:

−6−(−4x+2)−x=-(5x-2)

−6+4x-2−x=-5x+2

-x+4x-6-2=-5x+2

3x-8=-5x+2

3x-8+8=-5x+2+8

3x=-5x+10

3x+5x=-5x+5x+10

8x=10

x=10/8

x=5/4

Hi there,

I hope you and your family are staying safe and healthy during this anomalous time.

[tex]-6 -(-4x + 2) - x = -(5x-2)[/tex]

The first step is to distribute

[tex]-6 + 4x - 2-x=-(5x-2)[/tex]

Now let's subtract the numbers

[tex]-8 +3x = -(5x-2)[/tex]

[tex]3x - 8 = -(5x-2)[/tex]

[tex]3x - 8 = -5x+2[/tex]

[tex]3x = -5x + 2 +8\\3x = -5x +10[/tex]

[tex]3x + 5x = 10 \\8x = 10\\x = \frac{10}{8}[/tex]

Once we simplify that, we get:

[tex]x = \frac{5}{4}[/tex] as the answer

Happy to help! All the best this semester.

Answer:

1.3

Step-by-step explanation:

(−2 3/5)(−0.5)

=(−13/5)(−0.5)

=−13/5(−0.5)

=1.3

=1.3

Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{21}~,~\stackrel{y_2}{11}) ~\hfill AB=\sqrt{(~~ 21- 5~~)^2 + (~~ 11- (-1)~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16 )^2 + ( 12)^2}\implies \boxed{AB=20}[/tex]

[tex]B(\stackrel{x_1}{21}~,~\stackrel{y_1}{11})\qquad C(\stackrel{x_2}{26}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 26- 21~~)^2 + (~~ -1- 11 ~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 5)^2 + ( -12)^2}\implies \boxed{BC=13} \\\\\\ C(\stackrel{x_1}{26}~,~\stackrel{y_1}{-1})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8}) ~\hfill CD=\sqrt{(~~ 2- 26~~)^2 + (~~ -8- (-1)~~)^2} \\\\\\ ~\hfill CD=\sqrt{( -24)^2 + ( -7)^2}\implies \boxed{CD=25}[/tex]

[tex]D(\stackrel{x_1}{2}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill DA=\sqrt{(~~ 5- 2~~)^2 + (~~ -1- (-8)~~)^2} \\\\\\ ~\hfill DA=\sqrt{( 3)^2 + ( 7)^2}\implies \boxed{DA=\sqrt{58}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{20~~ + ~~13~~ + ~~25~~ + ~~\sqrt{58} ~~ \approx ~~ \text{\LARGE 65.6}}[/tex]

now, as far as the area goes, let's check the picture below, hmmm, there are two triangles, both have a base of 21, and you can see their heights there, well, let's simply get the area of each triangle and sum them up.

[tex]\cfrac{1}{2}(21)(12)~~ + ~~\cfrac{1}{2}(21)(7)\implies 126~~ + ~~73.5\implies \text{\LARGE 199.5}[/tex]

The more economical purchase is the 24-ounce box of cornflakes for $3.89.

The more economical purchase can be determined by calculating the unit rate for each box of cornflakes.

The unit rate can be calculated by the division of the total ounce of the box by the price of the box

Hence the unit rate for the 18-ounce box is calculated as,

unit rate of 18-ounce box = 18 / 3.49

unit rate of 18-ounce box = 5.16 ounce/$

The unit rate for the 24-ounce box is calculated as,

unit rate of 24-ounce box = 24 / 3.89

unit rate of 24-ounce box = 6.17 ounce/$

As the rate of 6.17 ounce/$ is more economical than 5.16 ounce/$, the more economical purchase is the 24-ounce box of corn flakes.

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Answer: X^3 / Y^5

The first answer choice

Step-by-step explanation:

Step-by-step explanation:

it is a ratio, and as such it is simply a fraction.

we can also write it

A/B = 6/7

and it gives us the same information.

and so,

30/B = 6/7

30 = 6B/7

210 = 6B

B = 210/6 = 35

The radius of the tank should increase √ 2 times.

We are given that:

To fill a pond whose volume is given as V₁ = 1 / 2 (4 / 3 π r₁³), we need a cylindrical tank whose volume is given by V₂ = 12 π r₂².

This means that the volume of the pond should be equal to the volume of the cylinder.

So, we get that:

1 / 2 (4 / 3 π r₁³) = 12 π r₂².

4 / 3 π r₁³ = 24 π r₂²

r₁³ = 18 r₂²

r₂ = √ ( r₁³ / 18)

r₂ = r₁ / 3 √r₁ / 2

Now, we will double the radius of the pond.

So, r₁ will become 2 r₁

Substituting it, we get that:

R₂ = 2r₁ / 3 √2r₁ / 2

R₂ = 2r₁ / 3 √r₁

So, we can see that:

R₂ / r₂ = 2r₁ / 3 √r₁ / (r₁ / 3 √r₁ / 2)

R₂ / r₂ = 2 / √2 = √ 2

Therefore, the radius of the tank should increase √ 2 times.

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Answer:

I THINK ITS B

Step-by-step explanation:

CORRECT ME IF I'M WRONG!!!

Answer:

-1.7 = rational

1.083 = rational

1.22345721 = rational

-1.090909 = rational

Step-by-step explanation:

The domain of the result f/g(x) is (7 /x ) + (5/x^2).

The two functions are:

f(x) = 7x + 5

and

g(x) = x^2

For calculating f/g(x)

f/g(x) is equivalent to f(x) / g(x)

Hence (f / g)(x) = f(x) / g(x)

                        = 7x + 5 / x^2

                        = (7 /x ) + (5/x^2)

the domain of the result f/g(x) is (7 /x ) + (5/x^2).

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Answer: Izzy's speed is [tex]6\frac{9}{10}[/tex] mph.

Step-by-step explanation: You have to divide the number of miles by the number of hours.

[tex]4\frac{3}{5} / \frac{2}{3}\\[/tex]

Convert the mixed fraction [tex]4\frac{3}{5}[/tex] to an improper fraction.

[tex]\frac{4 * 5 + 3}{5} / \frac{2}{3} = \frac{23}{5} / \frac{2}{3}[/tex]

Multiply the first fraction by the reciprocal of the second fraction (the second fraction upside down).

[tex]\frac{23}{5} / \frac{2}{3} = \frac{23}{5} * \frac{3}{2} = \frac{23 * 3}{5*2} = \frac{69}{10}[/tex]

Convert the result into a mixed fraction.

69 / 10 = 6 with a remainder of 9

A: [tex]6\frac{9}{10}[/tex]

Values of x y z for system of equation are

x=[tex]\frac{565}{54}[/tex]

y=[tex]\frac{703}{54}[/tex]

z=[tex]\frac{-23}{6}[/tex]

we have system of equation as follows

x + 2y+3z = 25

z=(25-x-2y)/3..........(A)

3x - 3y + 4z = -23

z=(3y-3x-23)/4........(B)

-4x+y-z = -25

z=(25-4x+y)..............(C)

Equating we get

(25-x-2y)/3=(3y-3x-23)/4=(25-4x+y)

Solving this we get

x=[tex]\frac{565}{54}[/tex]

y=[tex]\frac{703}{54}[/tex]

z=[tex]\frac{-23}{6}[/tex]

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Answer:

18

Step-by-step explanation:

[tex] \sf( \frac{ ∛125 \: - \: 14 }{2})(3 - 5)2[/tex]

Apply rule: ([tex] a[/tex]) = [tex] a[/tex]

[tex] \sf( \frac{ ∛125 \: - \: 14 }{2}) = \: \sf\frac{ ∛125 \: - \: 14 }{2}[/tex]

[tex] = \sf \frac{∛125 \: - \: 14 }{2}(3 - 5)2[/tex]

Substract the numbers (3-5) = (-2)

[tex] = \sf \frac{∛125 \: - \: 14 }{2}( - 2)2[/tex]

Change 2 to fraction: [tex] \sf \frac{2}{1} [/tex]

[tex] = \sf \frac{∛125 \: - \: 14 }{2} \times \frac{2}{1} ( - 2)[/tex]

Cross- cancel common factor 2

[tex] = \sf \frac{∛125 \: - \: 14 }{1} ( - 2)[/tex]

Let's calculate [tex] \sf \frac{∛125 \: - \: 14 }{1} [/tex]

[tex] = \sf \frac{∛125 \: - \: 14 }{1} [/tex]

Apply a fraction rule = a/1 = a

[tex] = \sf ∛125 \: - \: 14 [/tex]

[tex] \sf = - 9[/tex]

[tex] \sf \: = - 9( - 2)[/tex]

[tex] \sf \: = 18[/tex]

If the sprinter ran the race for 13.245 seconds, if we are to represent it in tenth then it would be written as 13.2

This is the term that is used to refer to the place value that would come immediately after the decimal point that we have in a group of digits that are a decimal.

In the question, the rule I followed is the one that I have explained above. The number that is after the decimal value is given as 2.

Hence we can say that the the answer after it has been rounded to the nearest tenth is  13.2

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Answer:

[tex](x+7)(x+2)[/tex]

Step-by-step explanation:

We have the equation:

[tex]x^{2} +9x+14[/tex].

The factors of 14 are 1, 2, 7 and 14.

Now, all we have to do is find two numbers that add up to 9.

We see that 2 and 7 add up to 9.

Therefore,

[tex]x^2+9x+14=(x+7)(x+2)[/tex]

Hope this helped! Have a great day!

Answer:

(x+7)(x+2)

Step-by-step explanation:

x^2+2x+7x+14           (Because 7 and 2 add to give 9 and multiply to give 14)

x(x+2) +7(x+2)            (Take out common factors, factorising)

(x+2)(x+7)                   (Put the things common in a bracket together and the bits that are outside in another bracket)

Answer:

$50 = 5 days

$40 = 4 days

$30 = 3 days

$20 = 2 days

$10 = 1 day

Step-by-step explanation:

hope this helps = )

Answer: Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.

Step-by-step explanation:

Define Decimal number :

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

Example: the numbers we use in everyday life are decimal numbers, because they are based on 10 digits (0,1,2,3,4,5,6,7,8 and 9). "Decimal number" is often used to mean a number that uses a decimal point followed by digits that show a value smaller than one. Example: 45.6 (forty-five point six) is a decimal number.

Define Rational numbers :

Rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

Example : a rational number is a type of real number, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.

So, Given data,

Use Structure Why do you multiply by a power of 10 when writing a repeating decimal as a rational number?

Then we can write,

Let us assume to multiply by some number (10, 100, 1000, etc.)

so that,

when we subtract the original number from the multiple, the repeating part cancels out.

If we multiply by 10.

we get 10x = 2

              x = 2/10

              x = 1/5

Therefore ,

x = 1/5 is Rational number.

So,

Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.

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The simplest rational exponent form is [tex]x^\frac{3}{4}[/tex] .

We have given a rational exponent [tex]\sqrt{x} .\sqrt[4]{x}[/tex] .     ...(1)

By formula [tex]\sqrt[4]{x}[/tex] can be written as [tex]x^\frac{1}{4}[/tex] and [tex]\sqrt{x}[/tex] can be written as [tex]x^\frac{1}{2}[/tex] .

Put in equation (1) , we get

    [tex]\sqrt{x} .\sqrt[4]{x}=x^\frac{1}{2} .x^\frac{1}{4} \\[/tex]              ...(2)

Using formula [tex]a^\frac{m}{n} \times a^\frac{p}{q} = a^{\frac{m}{n} +\frac{p}{q} }[/tex]  

Equation (2) can be written as

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

Hence , on simplification , we get  [tex]x^\frac{3}{4}[/tex] .

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