Given:
The logarithmic equation is:
[tex]\log x+\log (x-3)=1[/tex]
To find:
The value of x.
Solution:
Properties of logarithm used:
[tex]\log a+\log b=\log (ab)[/tex]
[tex]\log 10=1[/tex]
[tex]\log x[/tex] is defined for [tex]x>0[/tex].
We have,
[tex]\log x+\log (x-3)=1[/tex]
Using properties of logarithm, we get
[tex]\log [x(x-3)]=\log 10[/tex]
[tex]x^2-3x=10[/tex]
Splitting the middle term, we get
[tex]x^2-5x+2x-10=0[/tex]
[tex]x(x-5)+2(x-5)=0[/tex]
[tex](x-5)(x+2)=0[/tex]
[tex]x=5,-2[/tex]
In the given equation, we have a term [tex]\log x[/tex]. It means the value of x must be greater than 0 or positive. So, the only possible value of x is:
[tex]x=5[/tex]
Therefore, the value of x is 5.
Which of the following is equivalent to(x2+6x+9)
(x-3)(x+3)
(x+2)(x-7)
(x-6)(x+3)
(x+3)2
Please help ASAP!!
A turtle and a snail are 360 meters (who counts this again?) apart, and they start to move towards each other at 3 pm. If the turtle is 11 times as fast as the snail, and they met at 3:40 pm, find the speed of each.
Thank you!! :)
Answer:
Turtle = 11 m / min
Snail = 1 m / min
Total approach speed = 12 m/min
360 m / (12 m/min) = 30 min
Separation is 30 min at assumed speed of 1 m/min
But we know the separation is 40 min
So turtle moves at 3/4 * 11 m / min = 33 m/ 4 min
Snail moves at 3/4 * 1 m /min = 3/4 m / mi
Total approach speed = (33 + 3) / 4 = 9 m / min
So in 40 min
9 m / min * 40 min = 360 m
(Leaving out those units, they approach at 12 * unit of speed)
So the unit of speed has to be 360 m / 40 min = 9 m / min
Please answer fast.
what is 15/9 equivalent to
Answer:
1 6/9 or 1 2/3
Step-by-step explanation:
Answer: A lot of fractions
Step-by-step explanation:
Some Examples: 5/3, 10/6, 20/12
HELP ME PLEASE! I need to find the Interquartile range of : 0,0,0,1,1,3,3,3,4,4,4,6,6,7,7,7,8,8,9,10
Answer:
The interquartile range is 5
Light travels at approximately 2.998 x 10^5 kilometers per second. There are 6.048 x 10^5 seconds in one week. About how many kilometers does light travel in one week?
A 1.813 x 10^5
B 1.813 x 10^10
C 1.813 x 10^11
d 1.813 x 10^25
Which graph represents the inequality
X > 15?
this one because x has to be bigger than 15.
The graph with inequality x>15 is (B)
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
x>15
As, x is greater than 15.
So, the graph with x value labelled from the numbers greater than 15 which is represented by graph on right top corner.
Learn more about inequality here:
https://brainly.com/question/20383699
#SPJ2
What is the slope of the line represented by -3x + 5y = 20 ?
Pelaseee help me I’m stuck on thisss
Answer:
[tex]d = \sqrt{122} \: in[/tex]
Step-by-step explanation:
D^2 = x^2 + y^2 + z^2
= (9 in)^2 + (5 in)^2 + (4 in)^2
= 122 in^2
or
[tex]d = \sqrt{122} [/tex]
HELP, I can't figure out the first question
Answer choice for first question
1. linearly
2.quadratically
3.exponentially
find the values of the variables
i will give brainliest to anyone who’s right.
Based on the statment, below which statement could be used to prove <1=<2?
vertical angles are congruent
supplementary angles are congruent
complementary angles are congruent
two angles that form a linear pair are congruent
Answer:
Vertical angles are congruent
WILL MARK BRAINLIEST A bag contains 16 marbles. There are 4 green, 10 red, and 2 blue marbles. One marble is selected at random. Determine whether each statement correctly describes the likelihood of an event based on the given bag of marbles. Select True or False for each statement.
True False
1) It is unlikely that a blue marble will be selected.
2) It is certain that a green marble will be selected.
3) It is impossible that a yellow marble will be selected.
4) It is unlikely that a red marble will be selected.
Answer:
1 is FALSE
2 is TRUE
3 is FALSE
4 is FALSE
Step-by-step explanation:
1 is false because the blue marble is 2 only
2 is true because green marble has a 100% you get this.
3 is false because we din't have yellow marble
4 is false because red is has 10 marble so you get this red marbke is has 82% because red marble is 2nd most at the number of color
Mary bought a bag of parsnips that weighed 2 1/4 pounds. She also bought a bag of turnips that weighed 3 times as much as the parsnips. How many pounds of turnips did Mary buy?
Step-by-step explanation:
2 1/4 is improper fraction, because it's 21/4. To simplify;
21/4 = 21/4
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
21/4 = 5 1/4
With 21/4 simplified into 5 1/4, you would then do 5 1/4•3 which would be;
15.75
Conlusion/Answer:
Mary bought 15.75 pounds of turnips.
Determine the function that models the median home price, f (n), in thousands of dollars, n years since
2010.
f(n) =
I need help
.........:...:..:............
PLEASE HELP!!!
!!!!!
Answer:
y=63, x=20, x=47, b=70, c=89, x=133
Step-by-step explanation:
1) y=63- alternate angles are the same
2) 4x+5x=180
9x=180
x=20
3) x=47
4) b=70- angles on a line equal to 180
c=89- angles in a triangle add up to 180
5) x=133- angles that are alternate are the same
Write an expression for the nth term of the geometric sequence. Then find the indicated term. a1 = 3, r = 3 , n = 10
Answer:
[tex]A_{n} =3(3)^n^-^1[/tex]
[tex]A_{10} = 59,049[/tex]
Which is an example of a statistical question?
Questions
Question 1 How many pets does Alisha have at home?
Question 2 How old were you when you got your first pet?
Question 3 Do you like having a pet?
Question 4 What is Alisha’s pet’s name?
A question 1
B question 2
C question 3
D question 4
Answer:
Question 2
Step-by-step explanation:
divdtihcdyuvftujvfujvfubf
Answer:
2
Step-by-step explanation:
Triangle ABC with vertices A(-3, 4), B(0, 2),
and C(-2, 1) is translated 4 units right and 5
units down. Which quadrant is the image?
A(-3, -1)
B(0, -7)
C(-2, -4)
Therefore, the image is in the III quadrant (bottom left).
My little brother spent $5 on comic books and magazines. He bought 4 items. If comic books
cost $1 and magazines cost $2, how many of each item did my brother buy?
comic books
magazines
No links please!
Thank you
Answer: He bought 1 magazine and 3 comic books.
Step-by-step explanation: If comic books cost $1 and magazines cost $3, the equation for the problem should look like this: 2(m) + 1(c) = 5, since you know that the brother spent $5 in total. "m" represents the number of magazines purchased while "c" represents the number of comic books purchased. If you plug in 1 for "m" and 3 for "c", the equation would be true and would equal a total of $5. Also, 1 magazine and 3 comic books would mean that the little brother did, in fact, purchase 4 items.
Question 3 of 10
Which rays form the sides of TUV?
U
A. VT
O B. VU
C. UT
D. TU
E. UV
OF. TV
Kevin has $50 and wants to buy some art paper and paints. One pack of art paper cost $12 and the paints cost $6 per tube. He buys 2 packs of paper. Which inequality should Kevin solve to find the maximum number, n of tubes of paint that he can buy
Answer:
26 ≤ 6
Step-by-step explanation:
$50 is the budget
Art paper = $12
Paints = $6
He gets 2 packs of paper making it $24
$50 - $24 = $26
26 divided by 6 = 4.33333 (he can only get 4)
For some reason this was a little confusing for me so let me know if I helped at all.
The number of calories burned while jogging varies directly with the number of minutes spent jogging. If george burns 150 calories by jogging for 20 minutes, how many calories does he burn by jogging for 30 minutes
The area of a rectangular field is 7371 m2. If the length of the field is 91 meters, what is its width?
Answer:
81 m
Step-by-step explanation:
From the question given above, the following data were obtained:
Area (A) = 7371 m²
Length (L) = 91 m
Width (W) =?
Area of a rectangle is given by the following equation:
Area = Length × Width
A = L × W
With the above formula, we can obtain the width of the rectangular field as follow:
Area (A) = 7371 m²
Length (L) = 91 m
Width (W) =?
A = L × W
7371 = 91 × W
Divide both side by 91
W = 7371 / 91
W = 81 m
Thus, width of the rectangular field is 81 m
The temperature at midnight is -5°C and is expected to drop 12°
by sunrise. What is the expected temperature at sunrise?
Answer:
-17 degrees Celsius.
Step-by-step explanation:
If the temperature at midnight is -5, and it is supposed to drop 12 more by sunrise, the 12 degrees are subtracted from the initial temperature.
-5 - 12 = -17 degrees by sunrise.
The perimeter of a rectangular garden is 68 feet. The length
of the garden is 2 feet more than double the width. What is the
width of the garden?
Answer:
10 2/3 ft or approximately 10.67 ft
Step-by-step explanation:
Let the width = w
The length is L = 2w + 2.
The perimeter is:
P = 2(L + w)
P = 2(2w + 2 + w)
P = 2(3w + 2)
P = 6w + 4 = 68
6w = 64
w = 64/6
w = 32/3 = 10 2/3
Answer: 10 2/3 ft or approximately 10.67 ft
The area of the rectangular school garden is 24 square units. The length of the garden is 8 units. What is the length of the fence needed to enclose the entire garden?
Jamal launched a website for his custom shoe store. On the first day, 3 visitors registered on the website. On the third day, 27 visitors registered on the website. If Jamal uses an exponential function to model the data from the first and third days, how many visitors will he predict to register on the fifth day.
Answer:
Jamal predicts that 243 people will visit his site on the fifth day.
Step-by-step explanation:
Since Jamal launched a website for his custom shoe store, and on the first day, 3 visitors registered on the website, while on the third day, 27 visitors registered on the website, if Jamal uses an exponential function to model the data from the first and third days, to determine how many visitors will predict to register on the fifth day, the following calculation must be performed:
Day 1 = 3
Day 2 = 3 ^ 2 = 9
Day 3 = 3 ^ 3 = 27
Day 4 = 3 ^ 4 = 81
Day 5 = 3 ^ 5 = 243
Therefore, Jamal predicts that 243 people will visit his site on the fifth day.
Help me please! I need to get this done to go outside :(
Answer:
98ft.
Step-by-step explanation:
Question is asking for the total square feet of laminate wood to cover the entire retail store. Add all the sides together to get your answer.
Two cyclists , A and B , are going on a bike ride and are meeting at an orchard . They left home at the same time . Functions A and B give their distance from the orchard , in miles , after riding for x hours . The functions are defined by these equations
Answer:
Cyclist A lives farther from the Orchard
Step-by-step explanation:
Given
[tex]A(x) =48.5 -21x[/tex]
[tex]B(x) =42 -16.8x[/tex]
Required:
Who lives farther from the Orchard.
To do this, we simply calculate the y intercept.
This represents the total distance traveled to get to the Orchard
To calculate y intercept, we set [tex]x = 0[/tex]
So:
[tex]A(x) =48.5 -21x[/tex]
[tex]A(0) = 48.5-21*0 =48.5-0 =48.5[/tex]
[tex]B(x) =42 -16.8x[/tex]
[tex]B(0) = 42 - 16.8*0 =42-0 =42[/tex]
From the above computation:
[tex]A(0) > B(0) \to 48.5 > 42[/tex]
Hence;
Cyclist A lives farther from the Orchard
