Answer:
-13-4i
Step-by-step explanation:
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?
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.
__
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.
__
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.)
One dice and one coin are tossed. What is probability that you will see HEAD on coin and dice will show a number
more than 4. Answer should be in reduced fraction format.
Answer:
1/6
Step-by-step explanation:
1/2 multiplied by 1/3
What is the volume of a triangular prism whose base has an area of 38.2mm and heigh of the prism meausers 14mm?
Answer:
534.8
Step-by-step explanation:
Volume= area × height
= 38.2×14
= 534.8
Hence the volumer is 534.8
Answer:
534.8 mm
Step-by-step explanation:
The volume of a triangular prism is given by the relation :
Volume = Base area * height
Base area = 38.2 mm
Height = 14 mm
Hence, the Volume of triangular prism is :
V = 38.2mm² * 14mm
Volume = 534.8 mm
Need answer ASAP
Keiko and Eric each randomly surveyed people with cell phones. They recorded peoples’ ages (a years) and how many texts they send per day on average (t texts). For their respective data, they each drew a line of best-fit and determined its equation. They then compared equations and made inferences based only on the equations they calculated.
Answer:
subject?
Step-by-step explanation:
The inferences given can be concluded as (a) Agree, (b) Disagree, (c) Agree, (d) Disagree and (e) Disagree
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given two equations made each by Keiko and Eric. They are,
Keiko : t = -1.63a + 92.14
Eric : t = -1.05a + 80.97
(a) As the value of a increases, the value of t decreases for both of the equations.
So the first statement is true.
(b) When a = 20 and 30, t = 59.54 and 43.24 in the equation of Keiko.
When a = 20 and 30, t = 59.97 and 49.47 in the equation of Eric.
On an average, Eric's equation gives more t.
So second statement is false.
(c) t = 92.14 and t = 80.97 when a = 0.
A person with 0 years old cannot end texts.
So y intercept does not have a relevant meaning.
So c is also true.
(d) -1.63 and -1.05 is the slope of the corresponding lines.
This means that for every 1 year increase in age, the number of text messages decreased by 1.63.
So this is false.
(e) Similarly, in case of Eric's equation, for very 1 year increase in age, the number of text messages decreased by 1.05.
This is also false.
Hence the inferences are either agreed or disagreed as explained.
Learn more about Equations here :
https://brainly.com/question/16038959
#SPJ2
A plot of land is 5,824 square feet. It is divided into 4 equal sections.
Answer:
1456!!!!!!!!!!!!!!!
Step-by-step explanation:
5824 ÷ 4 = 1456
Answer: 1,456!
Step-by-step explanation: divide 5,824 ÷ 4 = 1456
What is the inverse function of f(x) = -2?
Hurry please
Answer:
A
Step-by-step explanation:
2x/x-1
Proper angle for a ladder is about 75° from the ground. Suppose you have a 10 foot ladder. How far from the house should you place the base of the latter? Round to the nearest hundredth
Answer:
The base of the ladder is 2.58 m.
Step-by-step explanation:
Given that,
The angle of elevation for a ladder from the ground is 75°.
The length of a ladder, H = 10 foot
We need to find the distance from the house should you place the base of the latter. Let the base of the ladder is b. Using trigonometry,
[tex]\cos\theta=\dfrac{B}{H}\\\\B=H\times \cos\theta\\\\B=10\times \cos(75)\\\\B=2.58\ m[/tex]
So, the base of the ladder is 2.58 m.
A model of a house is created by putting a square pyramid on a cube. The resulting figure has a surface area of 165 square inches 5 in. What is the height of one of the triangular faces? O 2 inches O 4 inches O 5 inches O 6 inches
Answer:
Is 4 inches or B
Step-by-step explanation:
I can't really break it down but I did get it right on Edge 2021.
Just wanted to make sure I got the right answer
Answer:
D
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEEE
Answer:
The correct answer is 6
Step-by-step explanation:
42 = 7r
R = 42/7 = 6
Answer:
r=6
Step-by-step explanation:
Divide both sides of the equation by the same term
simplify
Solve the equation. 18 = m - 18
Answer:
n = 36
Step-by-step explanation:
18 = n - 18
add 18 to both sides
36 = n
n = 36
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
36
Step-by-step explanation:
18 + 18 = 36
36 - 18 = 18
Mark as Brainliest
Co...
1.2 m
2.5 m
3.5 m
The front of a house needs to be painted black. The garage door is 1.5 m high and 2 m wide.
A) How many square meters of black paint will be needed to paint the house not including the
garage door?
Show your work
Answer:
16
Step-by-step explanation:
Multiplecation by the length width, and the height, then divide and its 16.
I need some help!! I will try to give brainliest!!!
Answer:
x = 35
y = 95
Step-by-step explanation:
(For y) The measure of a line is 180 degress. 180 - 95 - 50 = 35.
(For x) The measure of a triangle is 180 degress. 180 - 50 - 35 = 95.
Answer:
x = 85, y = 45
Step-by-step explanation:
solving for x:
180 - 95 = 85
solving for y:
85 + 50 = 135
180 - 135 = 45
Good luck on your schoolwork
Can anyone give me some advices for my sis cause she is going to high school soon and I'm worried- even tho she is older then me, she is Autism and ofc I'm worried-
Don't worry I'm sure there'll be great people that would love to be friends with her!, you can also try to call everyday after she finishes her classes^^
Step-by-step explanation:
Advice;
Talk to her, let her know of the things she could be facing, yes we can give her as much advice as needed but it won't stop her from facing other rude teenagers.If she has a temper you guys should come up w coping mechanisms to use during school when she'll be alone. It's good practice to growing up.Ask for a tour around the school, it'll help her be more aware of her surroundings when she starts to attend.If she's nervous about entering a whole different nd new place it's fine, assure her it's going to be okay it'll just be a little adjustment.Advice for you; ( I know it wasn't asked of )
Calm down. Don't stress, I mean I know you're gonna, she's your sister but worrying about her is just gonna be a whole other problem you don't need. She's fine, she'll be fine, you don't want her to see you worry nd make her feel the same way, right?Alright, hope this was helpful! Need a little more insight? Feel free to ask.
find the number of terms in the series for the series given below.
help me find the answer
100 point if u help
Answer:
maybe it is 3600 m not sure though
i don’t need any work for it i just need the answer
HELP WILL GIFT 30 EXTRA POINTS IF SOLVE ANSWER ALL QUESTIONS PLEASE!!!
Answer:
Question 1: The amount of students that Yolanda kept track of doesn't add up to her sample space.
Question 2: The sample space is 237. I know this because it said in the question she was asking all of the students at their Middle School which happened to be 237. A sample space is the group that you are taking information from. They are taking information from 237 students.
I need the coordinates like ASAP
Show that the sum of two irrational numbers can be rational
Answer:
Hint: We will have to know about the rational numbers and irrational numbers. ... So, the sum of the given two irrational numbers is equal to 6 which is a rational number in the form of p/q where p=6 and q=1 both are integers. Therefore, it is proved that the sum of the two given irrational numbers is a rational number.
Step-by-step explanation:
Hope it helps u
FOLLOW MY ACCOUNT PLS PLS
What is the perimeter of this shape? Use numbers only.
Answer:
30 m
Step-by-step explanation:
You simply add the lengths of all the sides. 3 m is not needed for this.
Answer:
10+5+4+6+5 = 30m
Step-by-step explanation:
a marrow plants 0.5 m long. every week it grows by 20%. a find the value of the common ratio. b calculate how long the plant is after 12 weeks. e comment on the predicted length of the marrow after one year.
Answer:
The common ratio is 1.2.
After 12 weeks the plant will be 4.46 meters long.
After one year the plant will be 6,552.32 meters long.
Step-by-step explanation:
Given that a marrow plants 0.5 m long and every week it grows by 20%, to find the value of the common ratio, calculate how long the plant is after 12 weeks and comment on the predicted length of the marrow after one year must be performed the following calculations:
0.50 x 1.2 ^ X = Y
Therefore, the common ratio is 1.2.
0.50 x 1.2 ^ 12 = Y
0.50 x 8.916 = Y
4.4580 = Y
Therefore, after 12 weeks the plant will be 4.46 meters long.
0.50 x 1.2 ^ 52 = Y
0.50 x 13,104.63 = Y
6,552.32 = Y
Therefore, after one year the plant will be 6,552.32 meters long.
Mika is a local farmer who is interested in how often residents in her town go to a farmer's market each month. She surveys 124 families and finds that, on average, those families visit a farmers' market 4.2 times per month with a sample standard deviation of 1.3. If Mika wants to be 99% confident (z=2.58) using this sample, what should her margin of error be and what does it mean?
Answer:
The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.
Step-by-step explanation:
Margin of error
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Standard deviation of 1.3
This means that [tex]\sigma = 1.3[/tex]
She surveys 124 families
This means that [tex]n = 124[/tex]
Margin of error and meaning:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 2.58\frac{1.3}{\sqrt{124}}[/tex]
[tex]M = 0.3012[/tex]
The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.
! + 3 − 5 = 0; by completing the square
Answer:
x = 1.19258 and x = −4.19258
Step-by-step explanation:
The given equation is :
[tex]x^2+3x-5=0[/tex]
Keep x terms on the left and move the constant to the right side by adding it on both sides.
[tex]x^2+3x=5[/tex]
Take half of the x term and square it.
[tex](3\times \dfrac{1}{2})^2=\dfrac{9}{4}[/tex]
then add the result to both sides
[tex]x^2+3x+\dfrac{9}{4}=5+\dfrac{9}{4}\\\\(x+\dfrac{3}{2})^2=\dfrac{29}{4}\\\\(x+\dfrac{3}{2})=\sqrt{\dfrac{29}{4}}\\\\x=\dfrac{-3}{2}+\sqrt{\dfrac{29}{4}}\\\\x=\dfrac{-3}{2}-\sqrt{\dfrac{29}{4}}[/tex]
So,
x = 1.19258 and x = −4.19258
Hence, this is the required solution.
Find the solution of the following equation whose argument is strictly between 90° and 180°.
Answer:
180degreesStep-by-step explanation:
Given the complex value
z² = -81i
z = (-81i)^1/2
Get the argument of -81i
theta = arctan(y/x)
theta = arctan(-81/0)
theta = -90degrees
theta = -π/2
Since tan is negative in the secind quadrant
theta = π - π/2
theta = π/2
According to demoivres theorem
theta = 1/2 * π/2
theta = π
theta = 180degrees
Construct a histogram for the following data set: 11, 17, 13, 2, 22, 18, 16, 14, 16, 21, 17, 9, 9, 7, 3
Does anyone know how to do this plz help if u can.
Answer:
1. Positive
2. I can't read the second question...
Step-by-step explanation:
1. When you graph this equation and look at the quadrant 2, you see that the graph makes a happy face which means that it's positive
2. Give me brainliest
1. For a one-tailed test (lower tail) at 93.7% confidence, Z =
2. For a one-tailed test (upper tail), a sample size of 24 at 90% confidence, t =
3. In a one-tailed hypothesis test (lower tail=left tailed test) and where the population standard deviation is known, the test statistic is determined to be -2.5. What is the p-value for this test?
Answer:
1) Z = -1.8592
2) t = 1.7139
3) p = 0.0062
Step-by-step explanation:
1) Area: (93.7+100)/2 = 193.7/2 = 96.85
Z = invNorm(0.9685,0,1) = 1.8592, but since the test is one-tailed at the lower tail, Z is actually -1.8592
2) Area: (90+100)/2 = 190/2= 95 where df=n-1=24-1=23
t = invT(0.95,23) = 1.7139
3) Since the population standard deviation is known, our test statistic is z=-2.5, making the p-value for the test p=normalcdf(-1e99,-2.5,0,1) = 0.0062
There are 12 paintings at an art show. Three of them are chosen randomly to
display in the gallery window. The order in which they are chosen does not
matter. How many ways are there to choose the paintings?
Answer:
220
Step-by-step explanation: a p e x
There are 220 ways to choose the paintings.
What is combination in mathematics?"Combination determines the number of possible arrangements in a collection of items where the order of the selection does not matter."
Formula for combination:[tex]^{n}C_r=\frac{n!}{r!(n-r)!}[/tex]
For given example,
There are 12 paintings at an art show.
⇒ n = 12
Three of them are chosen randomly to display in the gallery window.
⇒ r = 3
So, using the formula for combination, the number of possible ways to choose the paintings would be,
[tex]\Rightarrow~ ^{n}C_r=\frac{n!}{r!(n-r)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!(12-3)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!\times 9!}\\\\\Rightarrow~^{12}C_3=220[/tex]
Therefore, there are 220 ways to choose the paintings.
Learn more about combination here:
https://brainly.com/question/13387529
#SPJ2
Elijah has
1/2
bag of candy. A bag of candy weighs
5 pounds. How many pounds of candy does Elijah have?
Answer:
2.5 pounds of candy
Step-by-step explanation:
5 / 2 = 2.5
In other words 5 divided by 2 is 2.5 pounds of candy