When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used.
Which property listed below is used in all of these proofs?

The difference in the rate of change of both functions is: 15.

Rate of change of a linear function = change in y / change in x.

Function A is given as: y = 35x. The rate of change for function A is 35.

From the graph of function B, using two points, (1, 50) and (2, 100):

Rate of change = (100 - 50)/(2 - 1)

Rate of change = 50.

Therefore, the difference in the rate of change of both functions = 50 - 35 = 15.

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Answer:

510

Step-by-step explanation:

Assume 2 numbers 500,500.. with a mean of 500

so if we add 10 to each of the two numbers, mean will be:

[tex]\frac{510+510}{2}=510[/tex]

Of course you can vary the set and the numbers and still get the same mean

There are 7,800 different passwords.

Here we need to count the number of options for each of the digits of the password.

The first character has 26 options (26 letters in the alphabet).

The second character has 10 options (ditis from 0 to 9), and also does the third character

The fourth character has 3 options (%,*, or #)

The total number of different passwords that can be generated is given by the product between the numbers of options, so we have:

C = 26*10*10*3 = 7,800

There are 7,800 different passwords.

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The reason that would support that is ∠B ≅ ∠B , the reflective property of equality.

Similar triangles are triangles that have their corresponding angles equal and the ratio of their corresponding lengths also equal.

Analysis:

triangle BDE and BAC share the same angle B

which means ∠DBE = ∠ABC.

The reflective property of equality says a number is always equal to itself. Therefore, ∠B ≅ ∠B

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Answer:

b. 4.5 cm

a. 42 mm is the answer

The product of 12, x, and y written in an algebraic expression is 12xy.

Algebraic expressions are mathematical expressions containing variables, coefficients, and their arithmetic operators such as addition, subtraction, multiplication, and division.

An algebraic expression can be used to interpret and solve mathematical word problems.

From the information given:

The algebraic expression can be translated as 12x × y = 12 xy.

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The algebraic expression that can be translated as product of 12, x and y is 12 xy.

Expressions are used to interpret mathematical problems

From the question given we are to translate the product of 12, x and y.

The product of 12 and x is 12x

The product of 12x and y is 12xy, hence the algebraic expression that can be translated as product of 12, x and y is 12 xy.

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The amount of money that is saved by purchasing the projector at Office and beyond is $144.

The first step is to determine the price of the projector at The Office spot.

Discounted price : (1 - 0.20) x $1200

0.80 x $1200 = $960

The second step is to determine the price of the projector at the Office and Beyond.

Discounted price : (1 - 0.15) x $960 = $816

Difference in price : 960 - 816 = $144

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Answer:

h(-8)= -14

Step-by-step explanation:

[tex]h(-8)=-2(-8+5)^2+4 \\h(-8)=-18+4=-14[/tex]

[tex]\huge\boxed{-14}[/tex]

We have the following equation:

[tex]h(f)=-2(f+5)^2+4[/tex]

Substitute in [tex]-8[/tex] for [tex]f[/tex] and simplify.

[tex]\begin{aligned}h(-8)&=-2(-8+5)^2+4&\textsf{Substitute.}\\&=-2(-3)^2+4&\textsf{Add.}\\&=-2\cdot9+4&\textsf{Simplify the power.}\\&=-18+4&\textsf{Multiply.}\\&=\boxed{-14}&\textsf{Add.}\end{aligned}[/tex]

The company should use the median to support their claims.

Measures of average commonly used are mean and median.

Mean is the sum of the numbers divided by the total number

Mean : (5 + 6 + 6 + 6 + 7 + 8 + 8 + 8 + 8 + 11) / 10 = 7.3

Median is the number at the center of the dataset when it is arranged either in ascending or descending order.

Median = 8

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Answer:

required expression = 11x-5

Step-by-step explanation:

We have information about the following things :

Since units digit is 5 less than the tens digit, then the unit digit will become

x-5

Now we have these two things:

Now let us look at some two digit numbers like 29 , 43 and 78

in 29, tens digit is 2 and units digit is 9

29 is formed by multiplying the tens digit by 10 and multiplying the units digit by 1 like this : 29 = (2×10) + (9×1)

Similarly;

43 = (4×10) + (3×1)

78 = (7×10)+(8×1)

Now to get out two digit number from the question, we similarly need to multiply the tens digit with 10 and units digit with 1 and add them like this:

tens digit : x

Units digit : x-5

Hence the number is (x × 10) + [(x-5)×1] = 10x + x-5 = 11x-5

hence the required algebraic expression is 11x-5

Hello,

"perpendicular to the line y= - 1/2x +4 "

so y = -1/2x + p

-1/2 × 6 + p = 4 ⇔ -3 + p = 4 ⇔ p = 4 + 3 = 7

y = -1/2x + 7

Answer:

4^2+4

Step-by-step explanation:

one 2 and two 4s

so 4^2+4=16+4=20

so 4^2+4

(calculation)

Answer:

Yes

Step-by-step explanation:

They are equivalent as 12d + 36 is the expanded form of 12(d + 3)

Answer:

Yes,

just factorize 12d+36 and since 12 is common

12(d+3)

x is powering both numbers so it can be outside the parenthesis.

We have given that 3^x.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

The first one isn't an answer because 3^x is exponential while x^3 is a cubic function.

If you draw them you will see that they are very different.

B is correct because we can divide both numerator and denominator by 6 and we get 3^x.

C is not correct because x is not powering 3 so we cannot divide both by 6D is correct because 3^(x-1) is the same as

and when multiplied by 3 we get 3^x

3^x*3^(-1) = 3^x/3

E is not correct.

will understand after the explanation in DF is correct.

x is powering both numbers so it can be outside the parenthesis.

The question is incomplete the complete question is,

Which expressions are equivalent to the one below? Check all that apply.

3^x

A. x^3

B.(18/6)^x

C.18^x/3

D.3(3^(x-1))

E.3(3^(x+1))

F.18^x/6^x

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Answer:

x = 0.76556443         x = -3.26556443

Step-by-step explanation:

You can use the quadratic formula to find the roots.

The required  exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x

The standard exponential function is expresses as y = ab^x

Given the coordinate points (3,24) and (4,48), the equivalent equations are:

24 = ab^3 ......... 1

48 = ab^4

Take the ratios

48/24 = b^4/b^3

2 = b

Substitute b = 2 into equation 1

24 = a(2)^3

8a = 24

a = 3

Hence the required  exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x

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The economic order quantity is 385 and reorder point is 254.

a. Economic order quantity (EOQ)

EOQ=√2×D×C÷H

Where:

D =Annual Demand

S = Cost of Ordering

H=Holding cost

Hence:

EOQ=√2×5300×70÷.25×20

EOQ=√742,000÷5

EOQ=√148,400

EOQ=385

b. Reorder point

Reorder point=5300/250×12 days

Reorder point=254

c. Reorder point

Reorder point=5300/250×35 days

Reorder point=742

d. Reorder point

Reorder point=742-385

Reorder point=357

Therefore the economic order quantity is 385 and Reorder point is 254.

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The complete question is:

a. If the cost of the part is $20 per unit, what is the economic order quantity?

b. Assume 250 days of operation per year. If the lead time for an order is 12 days, what

is the reorder point?

c. If the lead time for the part is seven weeks (35 days), what is the reorder point?

d. What is the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?

Answer:

913

Step-by-step explanation:

cylinder:

radius=5.6 height=7

first lets find the volume of the cylinder the formula for the volume of a cylinder is pi times radius squared times height. so after plugging in the height and radius you get 689.64242

cone:

radius=5.6 height=6.8

now the volume of the cone, the formula for the volume of a cone is pi times radius squared times height/3. so after plugging in the height and radius of the cone you get 223.31278

so 689.64242 + 223.31278= 912.9552 and that rounded to the nearest tenth is 913

The expression which gives the area of triangle QRS is [tex]\frac{1}{2} (9)(15)sin(20^{o} )[/tex].

We need to find the area of triangle QRS.

The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of Δ = ½ ab sin C.

Now, the area of the triangle QRS[tex]=\frac{1}{2} (9)(15)sin(20^{o} )[/tex]

Therefore, the expression which gives the area of triangle QRS is [tex]\frac{1}{2} (9)(15)sin(20^{o} )[/tex].

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Another way to summarize this proof is to say vertical angles are congruent.

Lines are shortest distance between two point and angles are forned from the intersection of two lines.

From the given figure, they are trying to prove that the angles ANR and VNE are equal. Since these angles are formed at the point of intersection, hence another way to summarize this proof is to say vertical angles are congruent.

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A function assigns the values. The number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.

A function assigns the value of each element of one set to the other specific element of another set.

In the given function y = 30 + 20(x - 1), the number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.

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The value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

The standard error of the estimated mean:

[tex]\rm = \dfrac{2.5}{\sqrt{400}}[/tex]

= 0.1125

x = 6.0–6.2 = 0.2

[tex]\rm Z = \dfrac{0.2}{0.1125}[/tex]

Z = 1.778

This is not significant at the 5% level.

This would have been significant at the 5% level if the same sample means had been found using a sample size of merely 500.

Thus, the value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.

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The measure of arc ECF in circle G is 98°. The correct option is the second option 98°

From the question, we are to determine the measure of arc ECF

By using the one of the circle theorems

The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference

In the given diagram,

∠F = 1/2 ×104°

∠F = 52°

∠D + ∠E + ∠F = 180° (Sum of angles in a triangle)

∠D + 79° + 52° = 180°

∠D = 180° - 79° - 52°

∠D = 49°

m arc ECF = 2 × m ∠D

m arc ECF = 2 × 49°

m arc ECF = 98°

Hence, the measure of arc ECF in circle G is 98°. The correct option is the second option 98°

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Step-by-step explanation:

as speed is always

distance/time

we need to multiply speed by the time traveled to get the distance traveled.

so,

d = 95t + 65

after all, until it reached the city it traveled already 65 miles (we don't know the speed, but it does not matter for the question about the total distance traveled), which we need to add to get the total distance.

Answer:

let's playthe games questiontag

Using a calculator to find the approximate value of e in

F(e)=e^{2e} we have F(e)=229.6516. This is further explained below.

Generally, To approximate a function f (x) f (x) f (x) for values of x near to zero, one may use a power series known as a Maclaurin series.

In conclusion, Using your calculator to find the approximate value of e in

F(e)=e^{2e}

We have

F(e)=e^{2e}

F(e)=229.6516

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Answer:

288

Step-by-step explanation:

[tex]26 * 8+(2^{6} +2^{4} )\\\\208+(64+16)\\208+80[/tex]

Answer:

288

Step-by-step explanation:

PEMDAS

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Parentheses and Exponents:

(26) x 8+(64+16)          (28) x 8+(80)

Multiplication:

26 x 8 + 80       208+80

Addition:

208+80= 288

Answer:

1 deer

Step-by-step explanation:

18 deer minus 17 eaten leaves 1 deer

The total length of the segment AC is the sum of AB and CB, which gives, CB = 9

The given parameters are;

Required: CB

Solution:

AC = AB + CB by segment addition property

Therefore;

AC = 17 = 32 + 3•x + 57 + 6•x = 89 + 9•x

17 = 89 + 9•x

[tex]x = \frac{17 - 89}{9} = - 8[/tex]

CB = 57 + 6•x = 57 + 6 × (-8) = 9

Therefore;

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Answer:

the last option

Step-by-step explanation:

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