Part A: explain why x coordinates of the points where the graphs of the equations y=4^x and y=2^(x-1) intersect are the solutions of the equation 4^x=2^(x-1). Part B: Make tables to find the solution to 4^x=2^(x-1). Take the integer values of x between -4 and 4. Part C: How can you solve the equation 4^x=2^(x-1) graphically?
Answers
9514 1404 393
Explanation:
A. The given equation will have a solution when the value of x makes the left-side expression equal to the right-side expression.
The value of the left-side expression for a given value of x is the y-value of y=4^x. The value of the right-side expression for a given value of x is the y-value of y=2^(x-1). The left-side expression will be equal to the right-side expression for a given value of x when the graph of y=4^x and the graph of y=2^(x-1) have the same y-value. That is, the graphs will be of the same point for that x-value. That is what we mean when we say the curves will intersect at that point.
The x-coordinate of the point of intersection is the value that makes the expressions equal, hence it is the solution to the equation.
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B. The tables are included in the first attachment. We have used f(x) to represent the left-side expression, and g(x) to represent the right-side expression.
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C. As described in Part A, the graphs will cross at the solution point. Hence the equation can be solved graphically by graphing the left-side expression and the right-side expression and seeing where the graphs cross. (That is at the point (-1, 0.25) on the attached graph.)
Alternate graphical method
The solution can also be found graphically by graphing the difference of the expressions: y = 4^x -2^(x-1). This difference will be zero at the value of x that makes the two expressions equal. That is, the x-intercept of the graph of this difference will be the solution value. The second attachment shows this sort of graphical solution. (It works nicely because many graphing calculators will display the value of the x-intercept.)
Related Questions
ESIGNMENTS
COURSES
Assignment - 12. Project. Dividing Fractions Performance Task B
Attempt tous
SECTION 5 of 5
QUESTION 11 OF 11
5
6
7
8
9 10
11
>
Write a division problem that has a quotient of 9/10
At least one of the numbers you give must be a proper fraction. The other can be a proper fraction, whole number, or
improper fraction. Neither the dividend nor the divisor can be 9/10.
UPLOAD
WRITER
Answers
Answer:
I help you if you help me with this |a+5| if a<-5
Step-by-step explanation:
Factor the quadratic:
2x^2-7x+3
Answers
what percent of the population has an IQ score between 115 and 130?
Answers
Answer:
68% of the individuals in the population have an IQ between 85 and 115. 95% of the population has IQ scores between 70 and 130. 99.7% of the population has IQ scores between 55 and 145.
Step-by-step explanation:
At Jefferson Middle School,
3/5
of the students play a sport. Of those students,
1/3
play soccer. What equation can be used to find what fraction of the students play soccer?
1
3
+
3
5
1
3
÷
3
5
1
3
×
3
5
Answers
explanation: you look at the total [3/5] and multiply that by the total of soccer players [1/3]
Answer:
[tex]\frac{1}{3}[/tex] times [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
The figure shown is created by joining three rectangles. Enter the area of the figure, in square centimeters. Round to the nearest hundredth.
Answers
Answer:
235
Step-by-step explanation:
first, separate the floor into 3 different rectangles to calculate the area and then add them together.
area of rec=L*B
rec 1: 9*12.5=112.5
rec 2: (13.5-5.5)*(19.5-9-7)=28
rec 3:7*13.5=94.5
Then:
112.5+28+94.5=235
A group of students were asked how many sisters they have visited in their lifetime. Below is a lot plot of their responses. How many observants are in this data set?
Answers
The width of a rectangle measures (4d – 8) centimeters, and its length measures
(7d – 3) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
Answers
Answer:
(22d-22) cm
Step-by-step explanation:
perimeter= 2×(4d-8+7d-3)
= 2× (11d-11)
(22d - 22) cm
Answer:
(22d-22)cm
Step-by-step explanation:
Perimeter = 2 x (width + Length)
= 2 x [(4d – 8) + (7d – 3)]
= 2 x (11d-11)
= (22d-22)cm
HELP IM STRUGGLING I DONT WANNA FAIL THIS SCHOOL YEAR
Answers
Answer:
507 cubic m
Step-by-step explanation:
V = l · w · h
V = 13 × 13 × 3
V = 507
What is the equivalent radian measure of 600?
Answers
Answer:
[tex] = \frac{ \theta}{180} \times \pi \\ = \frac{600}{180} \times \pi \\ = \frac{10}{3} \pi[/tex]
Which statement best describes the association between variable X and variable Y?
Answers
Answer:
weak, negative association
Step-by-step explanation:
If variables have a strong association, the points will form a clear line/curve. Since the graph's points are scattered and fairly chaotic, we can say the association is weak.
Positive associations trend upwards and negative associations tend downwards. This graph seems to overall tend downwards, so we can say the association is negative.
Hi I’m a tutor ask me if you need help
Answers
Answer:
are you realy a tutor?
Step-by-step explanation:
A triangle has height 4ft and an area 64ft square What is the length of its base?
Answers
Answer:the answer is 60
Step-by-step explanation:
The question is “what is the length” so what I think we are supposed to do is to add since the height is 4 and the area is 64 so the length has to be 6
Hope I helped
determine the discount between the point(-4,2) and the line 4y=3×+6
Answers
Answer:
d = 14/5
Step-by-step explanation:
The point (-4,2) means that;
At x = -4, y = 2
Now general form of a linear equation is;
Ax + By + C = 0
We are given;
4y = 3x + 6
Rearranging to the form of a linear equation gives;
3x - 4y + 6 = 0
Thus, A = 3, B = -4 and C = 6
Thus, at point (-4,2), distance between them is;
d = (3(-4) - 4(2) + 6)/√(3² + (-4)²)
d = -14/5
We will take the absolute value.
Thus; d = 14/5
7. If the total number of books checked out of the library at your high school is 14,400 and the student population
is about 2400. How many books on average does each student have?
Answers
14,400/2,400
= 6
Which is a lot of books to check out from a school, but real life math problems has no logic.
How many different three-letter arrangements can be formed using the letters in the word ABSOLUTE if each letter is used only once?
Ο 112
Ο 168
Ο 336
O56
Answers
Answer:
336 3-letter-arrangements
2) Zack ran 6 miles this weekend. How many feet did Zack run over the weekend?
Answers
Answer:
zach ran 31680 feet over the weekend.
Step-by-step explanation:
1 mile = 5280, so 6 x 5280 = 31680
Solve. *25 points*
1/2 divided by 2/3 =?
Answers
Answer:
The answer is 3/4
Step-by-step explanation:
When you divide two fractions, such as 1/2 ÷ 2/3, you have to flip the second fraction and then you simply multiply the numerators with each other and the denominator with each other.
Find the 30th term of the following sequence. 1, 7, 13, 19, ...
Answers
Answer:
175
Step-by-step explanation:
a30 = a1 + f × (n-1)
f= difference between numbers
Write sin 53° in terms of cosine.
Answers
Answer:
cos(37°)
Step-by-step explanation:
sin(53°) = cos(90° - 53°)
sin(53°) = cos(37°)
find the measure of angles
Answers
Answer:
∠1 & ∠3 = 68°
∠2 & ∠4 = 112°
Step-by-step explanation:
180 degrees is the total sum of the angles in a triangle.
180 - 68 = 112
A custodian plans to repaint some classroom bookcases. She has 5 1/4 gallons of paint. All of the bookcases are the same size and each requires 3/4 gallons of paint. How many bookcases will the custodian be able to repaint with that amount of paint?
Answers
Answer:
7 bookcases
Step-by-step explanation:
Find how many bookcases the custodian can repaint by dividing 5.25 by 0.75:
5.25/0.75
= 7
So, the custodian will be able to repaint 7 bookcases
PLZ ANSWER AND SHOW WORK TY :D
Answers
Answer:
[tex]-\frac{\sqrt{21}}{2}[/tex]
Step-by-step explanation:
ASTC (I use a sentence to memorize: All Students Take Calculus):
Q1 - All functions are positive
Q2 - Sine is positive (Cosecant is positive as well) (all others negative)
Q3 - Tangent is positive (Cotangent is positive as well) (all others negative)
Q4 - Cosine is positive (Secant is positive as well) (all others negative)
Applying ASTC:
Secant is negative, so it can't be in quadrant 1, and quadrant 4.
Quadrant 2 - Sine and Quadrant 3 - Tangent are left.
Cosecant is positive so it can't be in quadrant 3.
Therefore, angle x is in Quadrant 2 or QII
Secant is hypotenuse / adjacent
5 = hypotenuse (hypotenuse is never a negative number)
-2 = adjacent
use pythagorean theorem to solve for opposite (bc tan = opp / adj)
[tex](-2)^2+o^2=5^2;4+o^2=25;o^2=21;o=\sqrt{21}[/tex]
tanx = [tex]\frac{\sqrt{21}}{-2}=-\frac{\sqrt{21}}{2}[/tex]
PLEASE HELP ASAP
The data set gives heights, in inches, of a group of students.
71 60 72 70 60 63 64 68 59
Create a stem display for this data.
Answers
Answer:
5 | 9
6 | 0 0 3 4 8
7 | 0 1 2
Step-by-step explanation:
The stems (to the left of the vertical line) are the first digits of the data, the leaves (to the right of the line) are the second digits)
7 | 0 1 2 represents the data 70, 71, 72
What is the value of x?
Answers
Answer:
98 degrees
Step-by-step explanation:
first find angle G
53 + 45 + G = 180
subtract 45 and 53 from both sides
G = 82
angle g is supplementary (add up to 180) to x
x +82 = 180
subtract 82 from both sides
x = 98
Answer:
x = 98°
Step-by-step explanation:
There are 180° in a triangle, and 180° on a line.
180° - 53° - 45° = 82°
180° - 82° = 98°
Four classmates collect data by conducting a poll. They ask students chosen at random how many states they have visited . Gabriel interviews 72 students. Morgan interviews 36 students. . Elle interviews 12 students. • Connor interviews 41 students, Whose results are probably the most trustworthy? O A. Morgan's B. Gabriel's C. Elle's D. Connor's
Answers
Answer:
B: Gabriel's
Step-by-step explanation:
Question 11
A card game is being played and the 5 of spades and 10 of clubs are drawn. In order to win the
hand, the next card must be higher than the highest card already on the table. Assuming the
game is played with a single deck, what is the chance that the next card drawn will win the
hand? (An ace has a value of 1.)
A.3%
B.12%
I
C.24%
D.25%
Answers
Answer:
24%
Step-by-step explanation:
trust me and get blessed
The probability of drawing a card that could win the hand and actually winning the hand is 12%.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
There are 50 cards left in the deck after the 5 of spades and 10 of clubs are drawn since there are 4 suits with 13 cards each, and 2 of those cards have already been drawn.
Out of the remaining 50 cards, there are 16 cards that could win the hand: the 9 remaining cards higher than the 10 of clubs in any suit, and the 6 remaining cards in the spade suit (since the 5 of spades is already on the table).
Therefore, the probability of drawing a card that could win the hand is 16/50, which simplifies to 8/25. This is approximately 0.32 or 32%.
However, we need to subtract the probability of drawing the 5 of clubs, 10 of spades, or any of the 8 remaining cards that would not win the hand.
The probability of drawing one of these cards is 10/50, which simplifies to 1/5 or 20%.
The probability of drawing a card that could win the hand and actually winning the hand is:
(16/50) x (1/5)
= 0.32 - 0.2
= 0.12 or 12%.
Thus,
The probability of drawing a card that could win the hand and actually winning the hand is 12%.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ2
Write and solve using a proportion to find the missing length
Answers
Answer:
n = 2.6
Step-by-step explanation:
6.5 : 5
n : 2
6.5/5 = 1.3
2 x 1.3 = 2.6
n = 2.6
i hope this helps
Solve for n: 8n = 56
n=1/7
n = 7
n = 48
n = 64
n= 448
Answers
Answer:
The answer is number 7
Step-by-step explanation:
56÷8=7
n= 7
You divide by 56
Please help what does A equal
Answers
Answer:
26°
Step-by-step explanation:
∠a and the 154° angle are both supplementary, so their sum is equal to 180°.
[tex]a+154=180[/tex]
[tex]a=26[/tex]
So, m∠a=26°.
Answer:
If i'm not wrong it should be 26
Step-by-step explanation:
I'm so sorry if I am wrong.
What is the probability that a randomly chosen student is a boy that prefers comedy movies?
I NEED HELPPO ASAP
Answers
Expiation I don’t got one
Answer:
12/35
Step-by-step explanation:
i don’t know the decimal but you can figure that out quickly