What is the equation in point-slope form of the line passing through (1, 9) and (−1, 11)?
Which of the following shows the extraneous solution(s) to the logarithmic equation? log4 (x) + log4(x - 3) = log4 (-7x + 21)
A. x= -7
B. x= -3
C. x= 3 and x= -7
D. x=7 and x= -3
Answer: The correct option is C, i.e., x=3 and x=-7.
Explanation:
The given equation is,
[tex]log_4(x)+log_4(x-3)=log_4(-7x+21)[/tex]
Using product property of logarithm [tex]log_a(mn)=log_am+log_an[/tex]
[tex]log_4(x(x-3))=log_4(-7x+21)[/tex]
[tex]log_4(x^2-3x)=log_4(-7x+21)[/tex]
On comparing both sides,
[tex]x^2-3x=-7x+21[/tex]
[tex]x^2-3x+7x-21=0[/tex]
[tex]x^2+4x-21=0[/tex]
Using grouping method 4x can be written as (7x-3x). Because the product of 7 and -3 is equal to the constant term -21 and the addition of 7 and -3 is equal to the coefficient of x.
[tex]x^2+7x-3x-21=0[/tex]
[tex]x(x+7)-3(x+7)=0[/tex]
[tex](x-3)(x+7)=0[/tex]
Equate each factor equal to 0.
The value of x is 3 and -7. Therefore, the option C is correct.
The extraneous solutions are x=3 or x=−7.
We have the equation; log4 (x) + log4(x - 3) = log4 (-7x + 21) we can write;
log4[x(x - 3)] = log4 (-7x + 21)
log4 can be cancelled out from both sides and we have;
x^2 - 3x = -7x + 21
To have a proper quadratic equation;
x^2 + 4x -21 = 0
The solutions of the quadratic equation therefore are x=3 or x=−7.
Learn more about quadratic equations; https://brainly.com/question/4390345
which point of the following ordered pairs is represented by a point located on the y- axis
a. (1,1)
b. (-2,0)
c. (4,-4)
d. (0,3)
Find all solutions to the equation. cos x = sin x
A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 +672t. After how many seconds does it reach its maximum height?
Answer: 21 seconds
Step-by-step explanation:
We know that a parabola with equation [tex]y=ax^2+bx+c[/tex] attains its maximum height at :-
[tex]x=\dfrac{-b}{2a}[/tex]
The given function: [tex]h=-16t^2 +672t[/tex]
It will attain its maximum height at :
[tex]t=\dfrac{-672}{2(-16)}=21[/tex]
Hence , after 21 seconds the projectile will reach its maximum height .
Need help please!!!!
I can't see the question...maybe I would be better at helping if I knew what to assist with.
;)
You cut a 90 cm long rope into two pieces. the longer piece is 2 times as long as the shorter piece. what is length of the longer piece and the shorter piece respectively?
what should be the first step in solving the equation 1.2 W -3.8 equals 12.4
Answer:
Step 1 would be to add 3.8 on both sides.
Step-by-step explanation:
The Equation mentioned in the question is a simple Algebra Equation. We need to solve for W. To do so, we need to get the variable W alone on one side.
Initial Equation: [tex]1.2W-3.8 = 12.4[/tex]
Step 1: Add 3.8 on both sides. [tex]1.2W = 16.2[/tex]
Step 2: Divide 1.2 on both sides. [tex]W = 13.5[/tex]
This gives us the answer of W = 13.5.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
ASAP!!
Shortly before a 1992 mayoral election, a local radio station conducted a Internet survey of voters. Based on the results of the survey, the magazine predicted that the Democratic candidate would beat the Republican candidate by a landslide. In fact, exactly the opposite happened. The trouble with the survey was that the radio station was a largely liberal station and few Republicans visited its Web site. This is a classic example of an error in which phase of inferential statistics?
A.Data gathering
B.Data analysis
C.Probability-based inference
D.Data organization
This is a classic example of an error in data gathering phase of inferential statistics.
What is data gathering?Data gathering is the process of collection and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes.
Learn more about data gathering here
https://brainly.com/question/17538970
#SPJ2
A tennis racket normally costs $6060. the tennis racket is on sale for 60 60% off. what is the sale price of the tennis racket?
the length of a rectangle is 2 inches less than twice its width. If the perimeter of the rectangle is 74 inches, what is the area of the rectangle
Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root 3
The area of a regular hexagon is mathematically given as
A=665.1 sq units
What is the area of a regular hexagon whose side length is 16 in.?Question Parameter(s):
a regular hexagon whose side length is 16 in.
and the apothem is 8 square root 3
Generally, the equation for the area is mathematically given as
A=(3√3)/2 *a^2
Therefore
A = 6*(0.5*16*8√3)
A= 384√3 sq units
A=665.1 sq units
In conclusion, the area of a regular hexagon
A=665.1 sq units
Read more about Area
https://brainly.com/question/24487155
#SPJ2
When asked to factor the trinomial 4x2 + 20x + 25, a student gives the answer (2x - 5)(2x - 5). what is one thing wrong with this answer?
Answer:
The minus signs should be plus signs
The required factor of the given trinomial is (2x+5)(2x + 5).
Given that,
When asked to factor the trinomial 4x² + 20x + 25, a student gives the answer (2x - 5)(2x - 5). the mistakes in the solution is to be justified.
What is the factors?
factors can be defined by splitting the value into multipliable values.
Here,
Given trionomial,
= 4x² + 20x + 25,
= 4x² + 10x + 10x + 25
= 2x(2x + 5) + 5 (2x + 5)
= (2x + 5)(2x + 5)
Thus, the required factor of the given trinomial is (2x+5)(2x + 5).
Learn more about Factors here:
https://brainly.com/question/24182713
#SPJ5
Please help me answer this math question.
all 3 angles in a triangle need to equal 180 degrees
62 +73 = 135 degrees are known
180-135 = 45
so angle B = 45 degrees
What are the rules for dividing signed numbers
Final answer:
In dividing signed numbers, the answer's sign depends on the signs of the numbers involved: same signs result in a positive answer, different signs yield a negative answer. Additionally, the final answer should have the same number of significant figures as the number with the fewest significant figures in the problem.
Explanation:
Rules for Dividing Signed Numbers
The rules for dividing signed numbers are similar to the rules for multiplication. When dividing numbers, it is important to consider both the sign of the numbers involved as well as the significant figures in the result. Here are the key rules to remember:
When two positive numbers divide, the answer has a positive sign, e.g., 6 ÷ 2 = 3.When two negative numbers divide, the answer also has a positive sign, e.g., (-6) ÷ (-2) = 3.When the numbers being divided have opposite signs, the answer has a negative sign, e.g., (-6) ÷ 2 = -3 or 6 ÷ (-2) = -3.As for the significant figures, the final answer should have the same number of significant figures as the number with the fewest significant figures before the division. For example, if you are dividing 23 by 448, limit the final reported answer to two significant figures.Remember, when performing calculations, significant figures are important for maintaining accuracy based on the precision of the data you start with.
Andrea can clean a house 4 times as fast as Denise. When they work together, Andrea and Denise can clean a large house in 8 hours. How many hours would it take Denise to clean the house by herself?
20
15
40
5
Answer:
8 hours
Step-by-step explanation:
A&D can clean a house in 8 hours together.
Proportionally, Denise works at x. Andrea works at 4x. There is a total of 5x.
Out of the 5x, Denise accounts for x.
x/5x = 1/5 of the work over 8 hours.
1/5 ( Denise's time for cleaning the whole house) = 8 hours.
Multiply both sides by 5:
5(1/5)(Denise's time for cleaning the whole house) = 5*8
Denise's time for cleaning the whole house = 40 hours
I like this method better...
That means in ONE hour, they get 1/8 of the job done.
Let's say Denise takes x hours to clean the house.
In one hour, she would do 1/x of the job (x can't be 0 hours).
Since Andrea does the house 4 times as fast as Denise, who takes x hours to do the job, Andrea takes x/4 hours.
In one hour, Andrea does 4/x of the job.
In one hour the part of the job Andrea does, plus the part of the job Denise does, must total 1/8.
(4/x) + (1/x) = 1/8
5/x = 1/8
Cross multiply:
x = 40
So it would take Denise 40 hours to clean the house by herself. (She's not really that efficient, or the house was REALLY dirty.
Andrea takes x/4 hours or 40/4 = 10 hours to clean the house by herself.
So with a little help from Denise, Andrea decreases her time to clean the house from the 10 hours it would take by herself to 8 hours.
The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6. Applying Newton's cooling model, the temperature of the tea after 2 hours will be ºF
Answer:
T = 109 degrees f
Step-by-step explanation:
The sum of the first three terms of a convergent geometric series is 19. the sum of the series is 27. find the first term and the common ratio.
Jessica is baking a cake. the recipe says that she has to mix 96 grams of sugar into the flour. jessica knows that 1 cup of this particular sugar has a mass of 128 grams. she added 1/2 of a cup of sugar into the flour. should jessica add more sugar to make the exact recipe, or did she go over by what amount?
Answer:
she needs to add 32 grams. this is 1/4 cups
Step-by-step explanation:
Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month? (2 points)
19779 - 57(11) = 19779 - 627 = 19152
m = 19152*2/(56*57)
m = 12
she saved $12 more every month
solve the inequality -5.3≥6.7+4.3+q
A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
If 1/3 of an office staff is on vacation and 1/4 of those not on vacation are out sick, what fraction of the staff is in the office
Newton currently has a balance of $1,716.18 in an account he has held for 29 years. He opened the account with an initial deposit of $784. What is the simple interest rate on the account?
Devon is trying to find the unit price on a six pack of drinks on sale for $2.99 his sister says that at that price each drink should cost over $2 is she correct and how do you know if she's not how would Devon's sister find the correct price
10 points! I will thanks, rate, and give best answer!!
Find the 4th term if the sequend in which a 1 = 2 and a n+1 = -4a n + 2
Find four consecutive positive integers such that the product of the first and fourth is four less than twice the first multiplied by the fourth.
A new computer virus can enter the system through an email or through a webpage. there is a 30\% chance of receiving this virus through the email. there is a 40\% chance of receiving it through the webpage. also, the virus enters the system simultaneously through the email and the webpage with probability 0.15. what is the probability that the virus does not enter the system at all?
The top of a 15-foot ladder touches the edge of the roof of a building, and the base of the ladder is 6 feet from the building. What assumptions are made about the building and the ladder when using the Pythagorean Theorem to solve real world problems like this?
Find the length of EF. Round to the nearest hundredth.
to find EF multiply 31 by tan(72)
31 * tan(72) = 95.4082
rounded to nearest hundredth = 95.41