1. For which value of x is the expression log base 4 of (x+3) not defined?a. 0
b. -2
c. 3
d. -4

2. If log 7= a, what is the value of log 490 in terms of a?

3. For what value of k will the graph of y=log base 7 of x contain the point (1,k)?

Answers

Answer 1

Answer: 1.
$log_a b \na>0 \hbox{ and } a \not=1 \nb>0 \n \nlog_4 (x+3) \nx+3>0 \nx>-3$

log₄(x+3) is defined for x greater than -3.
0>-3
-2>-3
3>-3
4≤-3
The answer is D. -4.

2.
$\log 7=a \n \n\log 490= \log (7^2 \cdot 10)=\log 7^2 + \log10=2 \log 7 + 1=2a+1$

The formulas I used:
$\log_a (x \cdot y)=\log_a x + \log_a y \n\log_a x^y=y \log_a x \n\log x=\log_(10) x$

3.
$y=\log_7 x \n \n(1,k) \nx=1 \n y=k \n \nk=\log_7 1 \nk=\log_7 7^0 \nk=0$

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How to create a proportional relationship that constant of proportionality equal.to 0.8 ?how to create a proportional relationship that constant of proportionality equal.to 0.9 ?

Answers

Answer:

y = 0.8x
y = 0.9x

Step-by-step explanation:

A proportional relationship is described by the equation ...

y = kx

where k is the constant of proportionality.

For a constant of proportionality of 0.8, the relation is ...

y = 0.8x

For a constant of proportionality of 0.9, the relation is ...

y = 0.9x

Write an expression to represent Steve's height in inches.

Answers

Final answer:

The expression to represent Steve's height in inches can be denoted as 'H'. 'H' is a variable that represents the unknown quantity, which is Steve's height in this context.

Explanation:

We will denote Steve's height in inches as H. This letter represents a variable, a letter that stands for a number we don't know yet, which, in this case, is Steve's height. In Mathematics, we commonly use letters like this to represent unknown quantities or variables. So the expression to represent Steve's height in inches is H.

Learn more about expressions in Mathematics here:

brainly.com/question/35169284

#SPJ3

Answer:

he is as tall as a Mouse.

explanation:

we can't Write an expression to represent Steve's height inches if we don't know what his height is

So what is Steve's height?

Lisa is seven times as old as her brother. She will be four times as old as her brother in three years. Represent the above situation in mathematical form.

Answers

Answer:

Let B = the brothers age now

Let L = Lisa's age now

Then today:

L = 7B

And three years from now, Lisa's current age plus 3 equals 4 times the brothers age plus 3 represented by the following formula

L+3 = 4(B+3)

Now we can substitute the value of L in the first formula for L in the second formula

7B + 3 = 4(B+3)

So the answer is C

Step-by-step explanation:

The value of a dirt bike decreases by 20% each year. If you purchased this dirt bike today for $500, to the nearest dollar how much would the bike be worth 5 years later?

Answers

The value of the bike after a year becomes only 80% of the value a year ago. In this given, the initial amount $500 should be multiplied by 80% 5 times. The answer would be $163.84. Thus, after 5 years the dirt bike would only be $163.84.

Answer:

The price of bike after 5 year in nearest dollars is $ 164

Step-by-step explanation:

We have formula

$A=P(1-R)^t$

Where

A= Price of dirt bike after t years

P= Initial price of bike

R= rate of decrease

t= time in years

It is given that the price of dirt bike today is $ 500, and its price is decreasing by 20% each year. We need to find the price after 5 years

So we have

P = $500

R = 20 % = 0.2

t= 5 years

now we plug these values in the formula, so we have the price of dirt bike after 5 years is given by

$A = 500(1-0.2)^5$

$A= 500(0.8)^5\nA= 500(0.32768)\nA= 163.84$

Hence the price of bike after 5 year in nearest dollars is $ 164

M(x) =5
Find m(2)
I have no idea how to do this help me

Answers

Answer:

Step-by-step explanation:

All this is saying is when there is one x value it is equal to 5

so, applying that logic, 2 fives is equal to 2*5=10

so when x=2, it is equal to 10

Hope this helps you out!!!

if x = 5 then m(2)= 10

Mexine can stack 20 boxes in 15 minutes. how long will it take her to stack 100 boxes

Answers

lets use a rule of three simple with direct proportion to solve:
20 boxes -----> 15 min
100 boxes ----> x
x = (100)(15)/20
x = 75
therefore it takes 75 mins to stack 100 boxes

If we use fractions to solve:
15/20 = x/100
and solve for x.
20/15 = 100/y
solve for y

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