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.
solve:
100^x=10^(2x+5)
Answer:
[tex]100^x=10^{2x+5}\\100 = 10^2[/tex]
simplifies to
[tex]10^{2x}=10^{2x+5}\\2x = 2x+5\\0=5[/tex]
no solution
WHAT IS THE MEDIAN pls help
A café's annual income depends on x, the number of customers. The function /(x) = 4x2 – 20x
describes the café's total annual income. The function C(x) = 2x2 + 5 describes the total amount
the café spends in a year. The café's annual profit, P(x), is the difference between the annual income and the amount spent in a year.
Which function describes P(x)?
A. P(x)= 2x^2 - 20x - 5
B. P(x)= 4x^3 - 20x^2
C. P(x)= 6x^2 - 20x + 5
D. P(x)= 8x^4 - 40x^3 - 20x^2 - 100x
Answer:B
Step-by-step explanation:
The value of P(x) the difference between the annual income and the amount spent in a year is,
⇒ P(x) = 2x² - 20x - 5
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The function f (x) = 4x² – 20x describes the café's total annual income. And, The function C(x) = 2x² + 5 describes the total amount the café spends in a year.
Hence, The value of P(x) the difference between the annual income and the amount spent in a year is,
⇒ P(x) = 4x² - 20x - 2x² - 5
⇒ P (x) = 2x² - 20x - 5
Thus, The value of P(x) the difference between the annual income and the amount spent in a year is,
⇒ P(x) = 2x² - 20x - 5
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ2
Please Help! The diagram shows the graph of y=2x+c, where c is a coonstant. Find the value of k.
Answer:
k = 6.5
Step-by-step explanation:
The question relates to the association of the association of the equation of a graph point(s) on the graph
The given equation of the graph, is y = 2·x + c
The value of 'c' is a constant
We note that the value of 'c' can be found when x = 0, as follows;
y = 2·x + c = 2 × 0 + c = c
∴ When x = 0, y = c
From the graph, when x = 0 we have the y-intercept, the point the graph crosses the y-axis, which is the point y = -3
Therefore;
When x = 0, y = -3 = c
∴ c = -3
The equation of the graph becomes, y = 2·x + (-3) = 2·x - 3
y = 2·x - 3
The other given point on the graph is the point (k, 10)
The value k is the x-value when y = 10
Substituting y = 10 in the equation for the graph gives the x-value at the point y = 10 as follows;
10 = 2·x - 3
2·x = 13
x = 13/2 = 6.5
x = 6.5 (when y = 10)
Therefore the point (k, 10) = (6.5, 10)
By comparing the two equal coordinates, we have;
k = 6.5.
pls pls pls, I beg you to answer this question only if you know the correct answer please please please I beg you please I beg you no n no no no link
Answer:
use ma th wa y (its all together)
Step-by-step explanation:
Answer:
10. The number of cupcakes Sheldon would have to buy to recieve the same number of cupcakes in a package would be 30 cupcakes in a package.
Step-by-step explanation: Find the least common denominator (LCD) of six and ten which is, 30.
11. The greatest number of necklaces Samuel would have to make is four.
Step-by-step explanation: Divide 148 necklaces by 36 strings and the answer will be four necklaces.
12. The greatest length, in feet, of each piece of ribbon Karen, would have to cut is six feet.
Step-by-step explanation: Find the greatest common denominator (GCD) of 18 and 12 which is, six.
13. Find the least common denominator of five and three which is, 15 minutes.
Step-by-step explanation:
Jacob will finish his laps in these following minutes, supposing he starts at zero.
3 minutes, 6 minutes, 9 minutes, 12 minutes, 15 minutes...
That is, all instants of time which are multiples of three.
Betty
5 minutes, 10 minutes, 15 minutes, 20 minutes, 25 minutes, ...
That is, all instants of time which are multiples of five.
Для изготовления макета космической ракетыбыло куплено d м алюминевых проводов по цене 150 тг k стеклопластикапо цене 340 тг сколько всего денег изасходовали на изготовления космической ракеты
Answer:
I do not understand ummmm
What percent of the ninth grade students scored between 78 and 96?
Answer:
30%
Step-by-step explanation:
Answer: Its 18%
Step-by-step explanation: To get the answer subtract 96 from 78
A 3ft child casts a 2ft shadow at the same time a tree casts a shadow that is 6ft long how tall is the tree?
Answer:
[tex]h_t=9ft[/tex]
Step-by-step explanation:
From the question we are told that:
Height of child [tex]h_c=3ft[/tex]
Height of child's shadow [tex]h_c_s=2ft[/tex]
Height of tree's shadow [tex]h_t_s=6ft[/tex]
Since position of Sun remains constant
Generally the equation for Height of tree h_t mathematically given by
[tex]h_t=f_{ts}\frac{h_c}{h_c_s}[/tex]
[tex]h_t=6*\frac{3}{2}[/tex]
[tex]h_t=9ft[/tex]
help me its due in 13 mins i forgot about it
Answer:im so sorry but i cant see the page you should take a more clear picture and send it again
Step-by-step explanation:
Walter's home was originally valued at $29,275. Due to some home improvements, its value is now $56,176. How much more is Walter's home worth now?
Answer: $26901
Step-by-step explanation:
From the information given, we are informed that Walter's home was originally valued at $29,275 but that after some improvement, it is now valued at $56,176.
Therefore, the increase in the worth of Walter's home will now be the difference in the values given above. This will be:
= $56,176 - $29275
= $26901
Plz help will give brainliest
Answer:
what do u need help with there isn't anything attached
Step-by-step explanation:
Answer:
please put correct question
Sarah goes to dinner with two friends the total cost of dinner is $61.92 her friends pay 2/3 of the total cost exactly how much does Sarah pay
Answer:
the amount paid by Sarah is $20.64
Step-by-step explanation:
Given that
The total cost of the dinner is $61.92
And her friends pay 2 by 3
We need to find out the amount paid by Sarah
Since her friends pay 2 by 3 of the total cost
That means the remaining should be paid by Sarah i.e. 1 by 3
So, we need to multiply 1 by 3 with the total cost of the dinner i.e.
= 1 ÷3 × $61.92
= $20.64
Hence, the amount paid by Sarah is $20.64
Which expression gives the volume of a sphere with radius 16?
O A. $ r (262)
B. 47(262)
O C. (163)
O D. 4t(153)
Answer:
16,384π/3
Step-by-step explanation:
V = (4/3)πr³
V = (4/3)π(16³)
V = 16,384π/3
Answer:
Step-by-step explanation:
Equation
V = (4/3) pi r^3
Givens
r = 16
Solution
V = (4/3) pi 16^3
V = (1.3333) * 3.14 * 4096
V = 171148.5
None of those answers agree with mine. Are those the real choices?
Five angles of a hexagon measure 119, 129, 104, 139 and 95 degrees. What is the measure of the sixth angle?
I need help only in number 3
Answer:
I believe they're the same because the last part of the equation is the same
Step-by-step explanation:
because 3/x-4+4 they both are the same
There are 126000 people living in a town. 52920 people in the town own a car. A local environmental group proudly announces 'fewer than 40% of residents own a car'. Is this statement accurate? Give a reason for your answer.
Answer:
False
Step-by-step explanation:
Given that
There are 126000 people living in a town
Out of which 52920 people in the town own a car
So based on this, the group announces that fewer than 40% of residents own a car
We need to find out the statement is correct or not
So here we determine the percentage
= 52,920 ÷ 126,000
= 42%
Since it is more than 40%
So the given statement is false
Find the largest area of the circle enclosed in a square, provided the area of
the square is 324 sq. cm. A.254 sq.cm
B.255 sq.cm
C.256 sq.cm
D.257 sq.cm
Given m and n are parallel lines, t is a transversal
crossing both m and n, and m48 = 100 degrees,
what is the measure of 3?
Answer:
they would measure 74 meters
Question Below! 20 points!
Answer: 20
Step-by-step explanation:
In ΔMNO, the measure of ∠O=90°, MO = 24, NM = 25, and ON = 7. What ratio represents the cosecant of ∠N?
Answer:
\csc N = \frac{\text{hypotenuse}}{\text{opposite}}=\mathbf{\frac{25}{24}}
cscN= opposite
hypotenuse = 24/25
Step-by-step explanation:
Each of the four shapes shown below has been made from four unit cubes.
For each shape, Max takes eight copies of the shape and tries to fit them together to make a
2
×
4
×
4
cuboid.
How many of the shapes can be used to make a cuboid of that size in this way?
Answer:
Step-by-step explanation:
32
The angle of elevation to a building in the distance is 22°. You know that the building is approximately 450ft tall. Estimate the distance to the base of the building
Answer:
1114 ft
Step-by-step explanation:
tan 22°=450/d
==>d=450/tan 22°=1113.7890... ≈1114 (ft)
Select the correct answer.
What is the purpose of the IRS?
A.
to collect taxes and enforce tax laws
B.
to provide a collection of domestic and foreign securities
C.
to foster cooperation between nations to solve economic issues
D.
to ensure fair global trade practices
Answer:
I think A ................
HELP PLEASE. urgent help needee
Answer:
123 cm^2
Step-by-step explanation:
for the rectangles its
#1 5(4)=20 cm^2
#2 5(7)= 35 cm^2
#3 5(8) = 40 cm^2
for the triangles its
4(7)(.5)(2)= 28 cm^2
4(7)= 28 cm^2
I get the .5 from the triangle area formula
and since the triangles are equal I multiplied it by 2 again so the .5 cancels out.
in the end you add them all up which is 20+35+40+28 = 123 cm^2
Is QRST at the right a rectangle? Explain.
Answer:
Right rectangle.
Step-by-step explanation:
The rectangle will be a right rectangle only if the opposite sides are parallel to each other.
This means that RQ should be parallel to ST
And RS should be parallel to QT
Each side can be represented by a line with a restricted domain, and we know that two lines are parallel only if they have the same slope.
Remember that the slope relates to how a change in the x-value makes a change in the y-value.
Then if two segments have, for a fixed change in the x-value, the same change in the y-value, we can conclude that those segments are parallel.
So here to see if the lines are parallel, we just need to compare the changes between the endpoints of each segment.
Let's start with segments QR and TS
First let's look at the segment QR, and let's try to find the difference in the coordinates between R and Q.
In the graph, we can see that R is 3 units above and one unit to the right of Q.
Now let's do the same for the other segment:
In the graph, we also can see that S is 3 units above and one unit to the right of T.
So these two lines will have the same slope:
Only with this, we can conclude that sides QR and TS are parallel.
Now with the other two segments: RS and QT.
Similar to the above case, for the segment RS we can see that S is 4 units at the right and 1 unit below R.
For the segment QT, we can see that T is 4 units at the right and one unit below Q.
So segments RS and QT have the same slope, thus, the segments are parallel.
Then we can conclude that this is a right rectangle.
Cindy feeds her dog 1/3 pound of food each day after 6 day,how many pounds of food has she given to her dog?
Answer: 2 pounds
Step-by-step explanation: if each day the dog gets 1/3 pounds, then after two days the dog would get 2/3 pounds. 3 days would be 1 pound, so after 6 days that would be 2 pounds.
Which is the graph of y – 3 = -2/3 (x + 6)?
answer is in attachment!
The outside of a round swimming pool is 40ft. How far is it to swim from the center to the outside?
Answer:
20ft.
Step-by-step explanation:
The perimeter is 40ft. You are starting at the perimeter of the pool swimming inward, you will have to swim half of that distance to reach the center.
Write 5.3421 (bar on 21) in p/q form
Answer:
[tex]\frac{52887}{9900}[/tex]
Step-by-step explanation:
We require 2 equations with the repeating 21 placed after the decimal point.
let x = 5.34212121 ( multiply both sides by 100 and 10000 )
100x = 534.2121... → (1)
10000x = 53421.2121... → (2)
Subtract (1) from (2) thus eliminating the repeating 21
9900x = 52887 ( divide both sides by 9900 )
x = [tex]\frac{52887}{9900}[/tex]
Due to delays a company had to extend a project from 28 days to 76 days. What was the percentage increase in time to complete the project. Round your answer to the nearest tenth.
Answer: [tex]171.4\%[/tex]
Step-by-step explanation:
Given
Time is extended from 28 days to 76 days
The percentage increase is given by
[tex]\Rightarrow \dfrac{\text{New-original value}}{\text{original value}}\times 100[/tex]
Putting values
[tex]\Rightarrow \dfrac{76-28}{28}\times 100=\dfrac{48}{28}\times 100\\\\\Rightarrow 171.4\%[/tex]
Thus, the percentage increase in time is [tex]171.4\%[/tex]