Use the Change of Base Formula. What is the value of each expression?
b. log₄18

Answer: h=1

Step-by-step explanation:

multiple 5h and -4 by 7

35h-28-1=14-8h

35h-29=14-8h

add 29 to both sides

35h=43-8h

43h=43

i think this is right...

The given equation is,

→ 7(5h - 4) - 1 = 14 - 8h

Now the required value of h will be,

→ 7(5h - 4) - 1 = 14 - 8h

→ 35h - 28 - 1 = 14 - 8h

→ 35h - 29 = 14 - 8h

→ 35h + 8h = 14 + 29

→ 43h = 43

→ h = 43/43

→ [ h = 1 ]

Hence, the value of h is 1.

The rate at which Riya is applying the mulch to the garden is 250000:1.

It should be noted that rate is simply used to show the relationship between two things. A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the dependent variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Per unit of time is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).

From the information, Riya is applying mulch to the garden and she applied at a rate of 250000cm³ for every m² of space.

Therefore, the rate at which Riya is applying the mulch to the garden is 250000:1.

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The sum of the three numbers 7531, 5252 and 6375 is 19158

The numbers are given as

7531, 5252, 6375

Express the numbers as a summation expression

So, we have

Sum = 7531 + 5252 + 6375

Evaluate the sum

So, we have

Sum = 19158

Hence, the sum of the three numbers 7531, 5252 and 6375 is 19158

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Answer:

10

4 plus 6 is equal to 10 there you go

Answer:

D.

Step-by-step explanation:

Hey there!

In order to find which description of the graph matches the problem, we must first create an equation or an inequality

So, we need to find how much more people the company needs to reach their goal to generate at least $7,300 in monthly revenue

We know that each person adds $300 to the already total of $5,500 per month

Now we can form the equation with this knowledge

[tex]300x + 5,500 \geq 7,300[/tex] where x is the number of people

Now we can simplify the equation

[tex]300x\geq 7500 - 5500\\ 300x\geq 2000\\x\geq 6.67[/tex]

Since we cannot have 6.67th of a person, we must round down because it means that we need more than 6 people

If we round up, it means that you need more 7 people in order to get $7,300 which isn't true

This means, you need more than 6 salespeople per month in order to meet the monthly quota of $7,300 in monthly revenue

Now that we know this, we can make a graph, or find the correct description of the graph

Since they need more than 6 people, the dot that sits on 6 in the number line will not be filled in, indicating that you need more than 6 salespeople

And since we need MORE, not LESS, the line will be pointing to the right

So, the correct answer would be D.

Answer:

constant

Step-by-step explanation:

Answer:

[tex]0.243243[/tex]

1. The constant term of the polynomial is: 8.

2. The exponent of the third term is 1.

A term of a polynomial can include any of the following:

Any of the above is referred to as a term of a polynomial.

Given the polynomial, -y^4 + 2y² + 3y + 8, the polynomial has 4 terms, -y^4, 2y², 3y, and 8.

Thus:

1. The constant term of the polynomial is: 8.

2. The exponent of the third term is 1.

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A graph which represent the solution to this inequality is: graph B.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

Given the following inequality:

-1/4(12x + 8) ≤ -2x + 11

Opening the bracket, we have:

-3x - 2 ≤ -2x + 11

3x - 2x ≤ -11 - 2

x ≤ -13

Note: When the arrow points to the left and shaded, the inequality is either (≤).

In conclusion, a graph which represent the solution to this inequality is graph B.

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Answer:

the answer is false because it will always be a odd number

Answer:

Step-by-step explanation:

well, first you have to add the number to an even number 4+17=21

21 is not an even number 12+17=29 which is also an odd number

answer B is false.

Two consecutive asymptotes are θ = - π / 20 and θ = 3π / 20 and the period is π / 5.

In this question we must look for two consecutive vertical asymptotes related to a trigonometric function. A function becomes undefined when its denominator is zero. Now we proceed to simplify the expression by trigonometric formulas:

y = 4 · csc (5θ - 3π / 4)

y = 4 / sin (5θ - 3π / 4)

y = 4 / (sin 5θ · cos 3π / 4 - cos 5θ · sin 3π / 4)

y = 4 / [(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ]

The function is undefined for (- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0:

(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0

(- √2 / 2) · sin 5θ = (√2 / 2) · cos 5θ

- sin 5θ = cos 5θ

tan 5θ = - 1

5θ = - π / 4 + i · π

θ =  - π / 20 + i · π / 5

θ = (π / 5) · (- 1 / 4 + i)

There are two consecutive asymptotes:

i = 0

θ = - π / 20

i = 1

θ = 3π / 20

And the period is ΔT = 3π / 20 - (- π / 20) = π / 5.

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Answer:

Step-by-step explanation:

1.

IF THE SHADED REGION IS THE WANTED AREA then the inequality is

y > 2x + 1

BUT IF THE SHADED REGION IS THE UNWANTED AREA then the in equality is

y < 2x + 1

2.

You have to figure out the equation of the dotted line.

Since the line is dotted, it means less than or greater than, it cant be less than equals to or greater than equal to

The gradient of the line is 2 as

rise / run = 14/7 = 2

and y intercept is 1

y > 2x + 1

3.

this is used in economics and for planning to maximize profits and minimize costs.

The amount of markup on a single rose is $2.74.

The markup formula is defined as the profit per unit cost of an item and is given as,

Markup = 100 * profit/cost

We multiply by 100 because we express it as a percentage, not as a fraction.

Now it is given that,

Cost Price of a dozen roses = $2.96

Number of roses = 12

Thus, Cost Price of 1 rose = 12.96/12 = $.108

Now it is also given that, the these dozen roses are sold at $48.48

So, Selling price of 1 rose = 48.48/12 = $4.04

Thus, Profit = Selling Price - Cost Price

⇒  Profit = $4.04 - $1.08

⇒  Profit = $2.96

Thus,Amount of Markup of single rose = Profit/Cost of 1 rose

⇒ Amount of Markup of single rose = 2.96/1.08

⇒ Amount of Markup of single rose = 2.74

Thus, the amount of markup on a single rose is $2.74.

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Answer:

Cube = 8 vertices

Pyramid=5 vertices

Step-by-step explanation:

Cube = 8 vertices

Pyramid=5 vertices

Answer:

1.5 meters per second

Step-by-step explanation:

90 meters divided by 60 seconds is 1.5

The algebraic expression become 3n-16<8.

According to the statement

We have to find that the numerical expression.

So, For this purpose, we know that the

Algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

From the given information:

the difference between three times a number and 16 is at least 8

Then

From 1st statement it become 3n -16

And with other statement and combining

Then  the equation become

3n-16<8

Now solve the expression for the value of the n

then it becomes

3n<24

n<8.

The value becomes is 8.

So, The algebraic expression become 3n-16<8.

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Answer:

2

Step-by-step explanation:

8+14 = 22

22-5 = 17

17-7 = 10

10+3 = 13

13-7 = 6

6-4 = 2

Answer:

d) 2

Step-by-step explanation:

Answer:

-2x-5=4x-29

-2x-4x=-29+5

-6x =-24

x=-24/-6

x=4

hence proved

It depends on what you mean "simplify". Chances are the goal here is to resolve any exponents that are improper fractions, meaning we don't want exponents larger than 1, like 4/3, for instance, but smaller than 1, like 2/3, is okay.

Now, by the distributive property of exponentiation,

[tex]\left(x^4 y\right)^{2/3} = \left(x^4\right)^{2/3} y^{2/3}[/tex]

Since [tex](x^a)^b = x^{ab}[/tex], we have

[tex]\left(x^4 y\right)^{2/3} = x^{4\cdot2/3} y^{2/3} = x^{8/3} y^{2/3}[/tex]

Convert the improper fraction to a mixed number.

[tex]\dfrac83 = 3 + \dfrac23[/tex]

Then we can write

[tex]x^{8/3} = x^{3 + 2/3} = x^3 x^{2/3}[/tex]

since [tex]x^{a+b}=x^ax^b[/tex].

Finally, we group together the factors with the same power.

[tex]\left(x^4 y\right)^{2/3} = x^3 x^{2/3} y^{2/3} = \boxed{x^3 (xy)^{2/3}}[/tex]

The nth term of this given G.P. is  [tex]T_n =5\times[3]^{n-1}[/tex].

Given that

To find

So, according to the question

We have,

            5 15 45 135​

From this G.P.

So, we know that

                        [tex]T_n =ar^{n-1}[/tex]

Where,

Now, putting the all given values

                        [tex]T_n =5\times[3]^{n-1}[/tex] -----------------(1)

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The inverse of function f( x ) = ( 2x - 3)² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].

A function that can reverse into another function is known as an inverse function or anti-function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.

We have the function,

f(x) = y = ( 2x - 3 )²

x = ( 2y - 3 )²

2y - 3 = ±√x

Adding 3 from each side.

2y - 3 + 3 = ±√x + 3

2y = ±√x + 3

Dividing each side of the equation by 2.

[tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex]

Hence, the inverse of function f( x ) = ( 2x - 3 )² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].

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Given data,

A piece of brass has a volume v cm'.

there were 6 cm'

mass would be 200 g

So,

We can write,

                       volume V = 6cm

                brass mass M = 200g

                        Find density d.

Define Density :

Density, mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centi meter.

                                  d = M/V

Where,

M: It is the mass

V: It is the volume

According to the data of the statement we have:

                                [tex]V = 6 cm^{1}[/tex]

                                [tex]M = 200g[/tex]

So, the density is given by:

                                d = M/V

                                d = [tex]\frac{200g}{6cm^{1} }[/tex]

                                d = [tex]33.33\frac{g}{cm^{1} }[/tex]

Therefore,

The density of the brass ornament is d = [tex]33.33\frac{g}{cm^{1} }[/tex]

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Step-by-step explanation:

I guess, the equation is meant to be in slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y intercept (the y value when x = 0).

in a situation like this, where we have the slope and one point of the line, we can start with the point-slope form

y - y1 = a(x - x1)

"a" is again the slope, and (x1, y1) is the given point.

and then we transform this over to the slope-intercept form.

so, in our case here

y - 2 = 5/6 × (x - 5) = 5x/6 - 25/6

let's simplify this by multiplying everything by 6 :

6y - 12 = 5x - 25

6y = 5x - 13

y = 5/6 x - 13/6

or

y = 1/6 × (5x - 13)

If the total price is $307.32 and tip rate is 20%, the original price given the total amount and tip rate is $256.10

What is the sum of the percentage of the original price and tip rate?

First and foremost, the tip rate is an added layer on the original price of 100%, which means that when the original price and the tip rate are added together, it gives 120%, hence, the total price of $307.32 is 120% of the original price

120% of original price=$307.32

1% of original price=$307.32/120

1% of original price=$2.561

100% of original price=$2.561*100

100% of original price=$256.10

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In the expression 2x + 5 at x = 3 Brett is wrong as the correct answer is 11.

An expression is written in the form of numbers and variables with arithmetic operations.

According to the given question we have to evaluate 2x + 5 at x = 3 and match our answer with Brett which is 41.

To obtain the value of 2x + 5 at x = 3, we have to substitute x with 3 in the given expression which is,

= 2(3) + 5

= 6 + 5.

= 11.

So, our answer is correct which is 11 and Brett is wrong.

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For Vertical asymptotes at x=0 and x=3 , horizontal asymptote at y=0 , a zero at -4, the rational function will be - (x+4) / (x)(x-3)

Asymptote, a line or curve that serves as the boundary of another line or curve in mathematics. An example of an asymptotic curve is a descending curve that approaches but does not reach the horizontal axis, which is the asymptote of the curve.

Given,

Vertical asymptotes at x=0 and x=3 , it means that these both factors are included in the denominator.

horizontal asymptote at y=0, it means means highest degrees in both numerator and denominator is 0.

zero at -4, it means we have this as factor in numerator.

The required rational function will be -

(x+4) / (x)(x-3)

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Answer:

the answer is the 20⁰ ok that

Using the midpoint concept and the distance between two points, the correct statement is given by:

[tex]\sqrt{(0 - a)^2 + (2b - b)^2} = \sqrt{(2a - a)^2 + (0 - b)^2} = \sqrt{(a - 0)^2 + (b - 0)^2}[/tex]

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

Hence the coordinates of the midpoint of the hypotenuse are given as follows:

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

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

Hence the distance from the midpoint of the hypotenuse to any vertex is given by:

[tex]\sqrt{(0 - a)^2 + (2b - b)^2} = \sqrt{(2a - a)^2 + (0 - b)^2} = \sqrt{(a - 0)^2 + (b - 0)^2}[/tex]

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Answer:

Angle A is 20°

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°.  

90 + 10x + x +13 = 180  Combine like terms

103 + 11x + 180  Subtract 103 from both sides

11x = 77  Divide both sides by 11

x = 7

Angle A is 13 + x.  X is 7, so 13 + 7 = 20