Consider the equation below. log4 (x+3)=log2 (2x). Which system of equations can represent the equation?
Answers
[tex]log_{4} (x+3) = \frac{log_{2} (x+3)}{log_{2}4} [/tex]
Therefore, given
log₄(x+3) = log₂(2x), obtain
[tex] \frac{log_{2}(x+3)}{log_{2}4}=log_{2} (2x) \\ log_{2}(x+3) = log_{2}4 log_{2}(2x) \\ x+3 = (2x)^{log_{2}4} [/tex]
Because
log₂4 = log₂ 2² = 2 log₂ 2 = 2, therefore
x + 3 = (2x)² = 4x²
4x² - x - 3 = 0
This factorizes into
(4x + 3)(x - 1) = 0
Answer:
4x² - x - 3 = 0
or
4x + 3 = 0, and
x - 1 = 0
Related Questions
A newspaper has more than 30 pages and fewer than 40 pages. The newspaper is divided into sections and each section has 8 pages. How many sections does the newspaper have
Answers
So the newspaper has 4 sections.
Nolan did the following work to solve the problem -14.52 + 7.3. 14.52 - 7.3 7.22 So, 14.52 - 7.3 = 7.22 Which of the statements is true about his work and answer? His answer is correct. His answer is incorrect, because the answer should be negative. His answer is incorrect, because he didn't line up the decimals.
Answers
That what I got when I did the math
Hope this helps have a nice day
The true statement is: His answer is incorrect, because the answer should be negative.
What are Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
Step 1: -14.52 + 7.3
Step 2: 14.52 - 7.3
Step 3: 7.22
So, 14.52 - 7.3 = 7.22
Nolan made a mistake in step 2 because 14.52 is negative and the answer should be negative.
So, His answer is incorrect, because the answer should be negative.
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Can anybody help me with questions 6-9?
Answers
6. z=2a-p
7. w= A/L
8. w= v/Lh
9. t= (A-P)/PR
Good luck!
Have a good mark for this question.
Which statements prove that a quadrilateral is a parallelogram?
Select each correct answer.
Quadrilateral DEFG has one diagonal that bisects the other diagonal.
Quadrilateral DEFG has only one set of opposite angles that are congruent.
Quadrilateral DEFG has two sets of consecutive angles that are supplementary.
Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.
Answers
*Opposite angles are congruent
*Consecutive angles are supplementary
*The diagonals of a parallelogram bisect each other.
Statement 1: This statement does not prove that the quadrilateral is a parallelogram because both diagonals have to bisect each other and not only one.
Statement 2: A parallelogram has two sets of opposite angles not only one. The statement would prove the quadrilateral is a parallelogram if it said that the quadrilateral has two sets of opposite angles that are congruent.
Statement 3: This statement is a property of a parallelogram. However, it doesn't prove that a quadrilateral is a parallelogram.
Statement 4: This statement proves that the quadrilateral is a parallelogram. If the statement, however, said that the quadrilateral has one set of opposite sides that are only congruent or only parallel, then it would not prove the quadrilateral to be a parallelogram.
The statement "Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel" proves that a quadrilateral is a parallelogram.
A quadrilateral has 4 sides and the sum of interior angles are [tex]360^\circ[/tex] where as the parallelogram is a quadrilateral whose oppposite sides are parallel to each other.
The following statements are:
A). The statement "Quadrilateral DEFG has one diagonal that bisects the other diagonal" is incorrect because both diagonals have to bisect each other.
B). The statement "Quadrilateral DEFG has only one set of opposite angles that are congruent" is incorrect because a quadrilateral is a parallelogram when it has two sets of opposite angles that are congruent.
C). The statement "Quadrilateral DEFG has two sets of consecutive angles that are supplementary" is incorrect although it is a property of parallelogram.
D). The statement "Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel" is correct this statement proves that a quadrilateral is a parallelogram.
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H(x)=-4x+3;when h(x)=11
Answers
Then, to solve for x, which is what I am assuming the question is asking, you would subtract 3 from both sides to isolate -4x, which would result in this:
-4x=8
Now, to solve for x, divide both sides by -4, and you get your answer which is x=-2
If an inequality is multiplied or divided by a negative number, the inequality sign should be ___________.
Answers
Answer:
You should change the direction of the sign.
Step-by-step explanation:
This is a general rule for all inequalities. Whenever multiplying or dividing by a negative, always change the direction of the sign
27 is 2/3 of what number?
Answers
Do 27divided by 2/3 to get it
Someone please help me
Find the value of x .
A) 80
B) 100
C) 130
D)120
Answers
130 +145 +65+160+120 = 620
the total inside angles for a 6 sided polygon should = 720
so x = 720-620 = 100
B is the answer
Two numbers have a difference of 24. What is the sum of their squares if it is a minimum?
288
1156
366
576
Answers
a - b = 24
We want to find where a^2 + b^2 is a minimum. Instead of just logically figuring out that the answer is where a=b=12, I'll just use derivatives.
So we can first substitute for "a" where a = b+24
So we have (b+24)^2 + b^2 = b^2 +48b +576 + b^2
And that equals 2b^2 +48b +576
Then we take the derivative and set it equal to zero:
4b +48 = 0
4(b+12) = 0
b + 12 = 0
b = -12
Thus "a" must equal 12.
So:
a = 12
b = -12
And the sum of those two numbers squared is (12)^2 + (-12)^2 = 144 + 144 = 288.
The smallest sum is 288.
The frequency of an AM radio is 1.4 x 106 hertz (cycles per second). Approximately, how many cycles are completed in a minute?
Answers
Answer:
84,000,000
Step-by-step explanation:
Four people share 2 9 pound of peanuts equally. What fraction of a pound of peanuts does each person receive? in simplest form.
Answers
therefore 29 / 4
that fraction is already in its simplest form
your answer is 29/4
Which of the following statements are true? Check all that apply.
The perimeter of a square depends on the length of its sides. A square with a side length of 4 meters has a perimeter of 16 meters. A square with a side length of 6 meters has a perimeter of 24 meters.
A. Perimeter(16) = 4
B. Perimeter(6) = 24
C. Perimeter(24) = 6
D. Perimeter(4) = 16
Answers
Many communities today are concerned with their local government’s ability to appropriately manage the taxes it collects. If a government spends more money on expenditures than it collects in taxes, it may end up with not enough money, called deficit. Which of the following could result in a county government budget in deficit?
a.The government raises sales and property taxes without adjusting expenditures.
b.The county closes a fire station, reducing expenditures, without adjusting taxes.
c.The county gives all public school teachers a $2,000 raise without adjusting taxes.
d.The county collects donations to build a fountain in city hall.
Answers
Answer:
C.The county gives all public school teachers a $2,000 raise without adjusting taxes.
Step-by-step explanation:
100% on edge
The correct answer is Option (C).The county gives all public school teachers a $2,000 raise without adjusting taxes.
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PLEASE HELP
Which linear inequality is represented by the graph?
y ≥ x – 4
y ≤ x – 4
y ≤ x + 4
y ≥ x + 4
Answers
Answer:
y ≤ x – 4 will be the linear inequality is represented by the graph.
Step-by-step explanation:
Given : graph.
To find : Linear inequality equations .
Solution : We have given graph,
We can see from graph here y intercept is -4 and solid line shaded below ,
Since , For shaded below graph we can say equation have less than equal sign. and y intercept -4.
Therefore, y ≤ x – 4 will be the linear inequality is represented by the graph.
Answer:
B
Step-by-step explanation:
because the line goes through -4 evenly
which graph shows the inequality n>-2
Answers
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
in this equation it says that "n is greater than -2" so the equation line has to go to the right. and when the equation has the signs < or >, the circle has to be dotted and when the signs are ≤ or ≥ the circle has to be solid.
so the answer is C.
hope this helps, God bless!
Graph the logarithmic equation y= log 5x
Answers
Suppose you have two credit cards. The first has a balance of $415 and a credit limit of $1,000. The second has a balance of $215 and a credit limit of $750. What is your overall credit utilization?
Answers
Explanation:
You have used a total of 415+215=630. You have a total credit limit of 1000+750=1750. This makes your utilization 630/1750=36%.
The data below were obtained from a pulse-chase experiment in which cells were examined at different times during the chase period. the numbers represent the radioactivity (measured in counts per minute) recorded at each of the indicated sites. the higher the number, the greater the radioactivity. time er golgi cytoplasm lysosomes extracellular space 3 minutes 162 7 21 5 4 20 minutes 73 88 17 10 8 60 minutes 9 35 14 112 13 120 minutes 11 23 18 151 10 based on these data, what is the most likely function of the cells in this experiment
Answers
Final answer:
The most likely function of the cells in this pulse-chase experiment is to synthesize, process, and degrade or secrete proteins. This is deduced from the movement of radioactivity from the ER to the Golgi apparatus, then to lysosomes and the extracellular space over time.
Explanation:
Based on the data provided, which stem from a pulse-chase experiment, we can infer the most likely function of the cells. Initially, radioactivity is high in the endoplasmic reticulum (ER), indicating that newly synthesized proteins, likely labeled with radioactive amino acids, are present there.
As time progresses, radioactivity moves to the Golgi apparatus, implying that proteins are being processed and modified.
Eventually, the highest levels of radioactivity are found in the lysosomes and then the extracellular space, suggesting that these proteins are being degraded and secreted respectively.
This sequence of events indicates that the cells are involved in synthesizing, processing, and secreting proteins, with some being targeted for degradation in lysosomes.
This is a fundamental part of the protein secretory pathway in cells. The data reveal the dynamic movement of molecules within the cell, reflecting the pathway from synthesis to secretion or degradation.
Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After reading for 4 hours, he had 330 pages left to read. how long is the book?
Answers
Answer: There are 550 pages in the book
Explanation:
Since we have given that
Number of pages per hour Naoya read = 55
Number of hours he read the book = 4
Total number of pages he read is given by
[tex]55\times 4=220[/tex]
Still there are some pages are left ,
Number of pages left = 330
So, total number of pages in the book is given by
[tex]330+220=550[/tex]
Hence, there are 550 pages in the book .
Answer:
550 pages 10 hours
Step-by-step explanation:
A quiz consists of 20 multiple-choice questions, each with 5 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60 %.
Answers
To find the probability of passing the quiz, we need to determine the minimum number of correct answers needed to achieve a passing grade. The probability of guessing the correct answer for each question is 1/5, so the probability of getting exactly 12 correct answers is calculated using the binomial probability formula.
Explanation:To find the probability of passing the quiz, we need to determine the minimum number of correct answers needed to achieve a passing grade. Since a passing grade is 60%, this corresponds to 12 correct answers out of 20. The probability of guessing the correct answer for each question is 1/5, so the probability of getting exactly 12 correct answers is given by the binomial probability formula:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Using this formula, we can calculate the probability of passing the quiz.
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The problem can be solved using binomial distribution principles where the number of trials is the total number of questions (20), success is answering a question correctly, and the probability of success is 1/5 since the answers are guessed randomly. Calculate the cumulative binomial probability for getting 12 (minimum passing grade at 60%) to 20 (total questions) correct answers. This gives the probability of passing the test.
Explanation:The question asks about the probability of passing a 20 question quiz with each question having 5 possible answers, by making random guesses. To pass the quiz, a grade of 60% is required which means at least 12 questions need to be answered correctly. Since the answers are guessed randomly, the chance of picking the correct answer for each question is 1/5 or 0.2.
We can treat this problem as a binomial distribution problem, where the success is answering a question correctly. In this case, the number of trials is n=20 (the total number of questions), the number of success k is 12 or more (the minimum number of correct answers required to pass), and the probability of success p is 0.2 (since there are 5 multiple choice options per question).
Calculating the cumulative binomial probability for k=12 to n=20, we get the required probability of passing the test. Given that we have to calculate multiple probabilities and sum them, this problem might be easier to solve if you have statistical software or a calculator that can compute binomial distributions.
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A box has dimensions of 19 inches long, 1.7 feet wide, and 6 inches high. What is the volume of the box? The formula for the volume is V = l ⋅ w ⋅ h.
a.193.8 cubic inches (in^3)
b.2325.6 cubic inches (in^3)
c.1.35 cubic inches (in^3)
d.16.15 cubic inches (in^3)
Answers
hope this helps!
AOB and BOC are _____.
complementary angles
supplementary angles
right angles
vertical angles
Answers
A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.
Answers
We can put x as the price of a student ticket so that an adult ticket will be 2x.
64(2x)+132x=1040
260x=1040
x=4
Student=4
Adult=8
Have a good day!
The perimeter of a given is an integer. the length of side one is 4 times the length of side 2. side three is 33. what is the largest and smallest possible perimeter
Answers
the sum of two sides of a triangle has to be larger than the third side, and the difference has to be smaller than the third side
the two unknown sides are x and 4x
x+4x>33 => x>6.6
4x-x<33 => x<11
6.6<x<11
because the perimeter is an integer, the smallest x is 7 and the largest is 10
therefore the largest perimeter is 10+40+33=83
the smallest perimeter is 7+28+33=68
help picture attached !!
Answers
= (7 2/3) / (1 1/3)
= (23/3) / (4/3)
= 23/3 * 3/4
= 69/12
= 23/4
= 5 3/4
= 5 9/12
What is the slope of the line containing (–2, 5) and (4, –4)?
A. 2
B. –3/2
C. –2
D. 3/2
Answers
The point with the bigger x value is (x2,y2)
Next, plug the two points into the formula: (-4 - 5) / (4 -(-2))
Note: 4-(-2) = 4+2 = 6
Simplify: -9 / 6 = - 3/2
The answer is B.
Hope this helps, and May the Force Be With You!
-Jabba
The slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].
What is slope of the line?A slope of a line is the change in y coordinate with respect to the change in x coordinate.
What is the formula for finding the slope of line from two points?[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where,
m is the slope of line.
[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2},y_{2})[/tex] are the two points.
According to the given question.
We have two points (-2,5) and (4,-4).
Therefore, the slope of the line containing the points (-2, 5) and (4, -4) is given by
[tex]m = \frac{-4-5}{4-(-2)}[/tex]
⇒[tex]m = \frac{-9}{6}[/tex]
⇒[tex]m =\frac{-3}{2}[/tex]
Hence, the slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].
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Greg is opening a car wash. He estimates his cost equation as C = 9000 + 0.09x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit.
Answers
9000+0.09x = 1.85x
subtract 0.09x from each side
9000 = 1.76x
divide both sides by 1.76
x = 9000/1.76
x = 5113. 64
he needs to wash 5114 cars to make a profit.
What is x percent of y percent of z, in terms of x, y, and z?
Answers
Solve for x and y please !!
Answers
y = 72 yd
x^2 = 72^2 + 72^2
x^2 = 2(72^2)
x = 72√2 yd
since both inside angles are 45, the height and the base would be the same
the height is 72 yd
so the base (y) would also be 72 yd
Y = 72
and x would equal y * sqrt(2)
so x = 72sqrt(2)
Determine if the lines are parallel, perpendicular, or neither 4x+5y=10 and 5x - 4y =28
Answers
For the second problem you subtract 5x from both sides and are left with -4y=-5x+28 and then you divide both sides of the equation by -4 to get y alone and that leaves you with y=5/4x-7
So looking at the slopes -4/5 and 5/4 which they are reciprocals of each other so these lines are perpendicular.