The polynomial-like expression is satisfied by the real value x = 1.
How to determine the real solution of a polynomial-like expression
In this question we must apply the concepts of logarithms and algebra properties to solve the entire expression. Initially, we expand the right part of the expression:
[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (4^{x}+2^{x}-6)^{3}[/tex]
[tex](2^{x}-4)^{3} + (4^{x}-2)^{3} = [(2^{x}-4)+(4^{x}-2)]^{3}[/tex]
[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (2^{x}-4)^{3}+3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2}+(4^{x}-2)^{3}[/tex]
[tex]3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2} = 0[/tex]
[tex]2^{x}-4 + 4^{x}-2 = 0[/tex]
[tex]2^{x}\cdot 2^{x} + 2^{x}-6 = 0[/tex]
[tex]u^{2}+u - 6 = 0[/tex]
[tex](u+3)\cdot (u-2) = 0[/tex]
Hence, the roots of the pseudopolynomial are [tex]u_{1} = -3[/tex] and [tex]u_{2} = 2[/tex]. Only the second one have a real value of x. Hence, we have the following solution:
[tex]2^{x} = 2[/tex]
[tex]x\cdot \log 2 = \log 2[/tex]
[tex]x = 1[/tex]
The polynomial-like expression is satisfied by the real value x = 1. [tex]\blacksquare[/tex]
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Find the Circumference ddddddddddddddddddddddddddddd
Answer:
25.12
Step-by-step explanation:
C = π2r
C = 3.14*2*4
C = 25.12
Hope this helps :)
help please thank you!!!
Answer:
3/4 · 1/4 = 3/16
Step-by-step explanation:
We can see from the picture that
yellow is
4 boxes out of the entire group of 16 boxes, hence 4/16
OR simplified
1 horizontal strip out or 4 total same horizontal strips, hence 1/4
blue is
12 boxes out of the entire group of 16 boxes, hence 12/16
OR simplified
3 vertical strips out or 4 total vertical strips, hence 3/4
The multiplication problem is
1/4 · 3/4 = 3/16 or 3/4 · 1/4 = 3/16
The result is 3 green boxes out of all 16 boxes.
(3/16 can not be simplified)
Mr. Wilson bought a bag of birdseed and put half of it in his bird feeder. He split the other half equally among his 4 pet birds. How much of the bag did each pet bird get?
Answer:
each pet bird got 1/8 of the bag of birdseed
Step-by-step explanation:
the easiest way to do this is to divide the bag into eighths. if you divide the bag into eighths, 4/8 of the bag, being half, goes into the bird feeder. the other 4/8 of the bag is divided among Mr. Wilson's four pet birds, leaving each bird to get 1/4 of the bag when split evenly.
hope this helps
Translate the following phrase to an expression: the difference between twenty and twice a number.
Answer:
20 - 2n
n = a number
Spencer owns a taxi cab company. He charges customers a base fee of $5 and an extra $2 for each mile traveled. If F represents a customer's fare (in dollars) and d represents the distance traveled (in miles draw a graph representing the relationship between F and d
Answer:
Let F = customer's fare (in dollars)
Let d = distance traveled (in miles)
Given:
Base fee = $5Charge per mile = $2 per mileCreating an equation from given information:
F = 2d + 5
This is a linear equation, with slope of 2 and y-intercept of (0, 5)
**see attached graph**
Answer:
See below ↓
Step-by-step explanation:
Given :
Base fee = $5Per extra mile = $2Solving :
With F as the total customer fare and d is the distance covered the equation will be :-F = 2d + 5In terms of x and y, it can be written as :y = 2x + 5Graph is given belowFind the distance between the two points in simplest radical form.
Answer:
13 units
Step-by-step explanation:
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is ...
d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 units.
_____
Additional comment
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
A board-game club meets each week at the local library. People bring different board games to play, like checkers and chess. Out of the 50 people that meet each week, 67% prefer to play checkers over chess. Construct an 83% confidence interval for the population mean of people that prefer to play checkers over chess.
Using the z-distribution, as we are working with a proportion, it is found that the 83% confidence interval is (0.5789, 0.7611).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have an 83% confidence level, hence[tex]\alpha = 0.93[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.83}{2} = 0.915[/tex], so the critical value is z = 1.37.
The other parameters are [tex]n = 50, \pi = 0.67[/tex].
Then, the bounds of the interval are given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 - 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.5789[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 + 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.7611[/tex]
The 83% confidence interval is (0.5789, 0.7611).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Answer:
CI = (57.89%, 76.14%)
Step-by-step explanation:
First, solve for the 83% critical z-value (za/2). Second, solve for the margin of error. Third, solve for the confidence interval by subtracting and adding the margin of error with the sample probability of success.
Mary walks to her garage. The distance to the garage as a function of time is shown in this graph
A. Mary starts 8 meters from the garage.
B. Mary walks 8 meters every 4 seconds.
C. Mary arrives at the garage after 4 seconds.
D. Mary walks at a speed of 2 meters per second.
Answer:
d
Step-by-step explanation:
so if you look at the bottom left corner you can see 1 box is the same as saying for every second someone walks its one metre.
thats not how i got the answer though.
if you look at the starting point at 8 because she was 8 meters away you need to see when she comes across her first second which after 2 meters (Goes down two squares before reaching the first second)
now technically soe of the other answers are correct too but heres how i thought about it.
A. its correct but i dont think that's what its asking you for tbh
B. This we don't know for sure. eg she could take 890 seconds walking back to her starting point we just don't know for sure.
C. This is also true but once again it's easily given to you so i dont think that's what you're being asked.
D. This is the only option where you had to do any for of working out because s=d/t so s=8/4=2m/s
if you could just tell me what I should say in the presentation, that would be great :) thx
Answer:
we're u asking for this
What is ur statistical question
which is larger 0.849 or 1.08
Answer:
the answer to this question is 1.08
Paul is running Tennis shop. He sells balls and rackets. Rackets (R) cost $1.20 each and Balls (B) cost $2:0 each. At the end of a month, Paul made a total of $70 and sold a total of 90 Rackets and Balls combined. Which system of equations represents this situation?
A. 2R + 1.20B = 90, B - R = 160.
B. 1.20R + 2B = 90, R - B = 90
C. 1.20R + 2B = 70, and R + B = 90
D. 1.20B + 2R = 90 and 2B + R = 70
The system of equations that represent the situation are 1.20R + 2B = 70, and R + B = 90.
What are the system of equations?
The system of equations are sets of equations that have to be solved simultaneously in order to determine their required values. They are often referred to as simultaneous equations.
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Researchers randomly surveyed people at two amusement parks, Funland and Thrillville, to find out how many times they visit the park per year. Following are the data from the two surveys.
Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2
Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8
How many more times per year, on average, do people visit Thrillville than Funland?
On average, people visit Thrillville 2 more times per year than Funland.
AveragesTo determine how many more times per year, on average, do people visit Thrillville than Funland, the following calculation must be performed:
Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2 = 4545 / 15 = 3Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8 = 100100 / 20 = 55 - 3 = 2Therefore, on average, people visit Thrillville 2 more times per year than Funland.
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There are 777 students in a class: 222 boys and 555 girls. If the teacher picks a group of 333 at random, what is the probability that everyone in the group is a girl?
The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
The probability that everyone in the group is a girl is 2/7.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
Total number of students in a class = 7
Number of boys students = 2
Number of girls students = 5
The probability that everyone in the group is a girl is;
[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]
Hence, the probability that everyone in the group is a girl is 2/7.
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1) Find the slope of the line
2) find the slope between the two points
help please, thank you
Answer:
1 = 3/2
2 = -1/14
Step-by-step explanation:
The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.
For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.
For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.
You can plug all 4 numbers in to get (2-1)/(-17- -3)
2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.
HELLLPPPPPPPP!!!!!!!!
An experiment consists of randomly drawing a card from a standard deck and recording its color, then rolling a die and recording its value.
The following tree diagram shows the possible outcomes.
A 2-column tree diagram: card & die. The card column has B & R. B & R each branch to the numbers 1 through 6 in the die column.
What is the probability of selecting a red card and rolling a number less than 3?
Enter your answer as a reduced fraction, like this: 3/14
The experiment of rolling the dice and selecting a card is an illustration of probabilities
The probability of selecting a red card and rolling a number less than 3 is 1/6
How to determine the probability?From the figure, we have:
Total outcomes = 12
Red card with a number less than 3 = 2
So, the probability of selecting a red card and rolling a number less than 3 is:
p = 2/12
Simplify
p = 1/6
Hence, the probability of selecting a red card and rolling a number less than 3 is 1/6
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Find the solution of the system of equations.
8x – 2y = -30
–9x + 4y = 18
Step-by-step explanation:
8x – 2y = -30 } ×2
16x - 4y = -60
–9x + 4y = 18
___________
7x=-42
x=-6
8(-6)-2y=-30
-2y=-18
y=9
Answer:
(-6,-9)
Step-by-step explanation:
The quickest way is to solve with elimination. Multiply the top equation by 2.
2(8x – 2y = -30)
16x-4y=-60
16x-4y=-60
–9x + 4y = 18
7x=-42
x=-6
8x – 2y = -30
8(-6) – 2y = -30
-48-2y=-30
-2y=18
y=-9
All digits in a dropdown number are different and one of the digits is the average of all the digits. it has at least two digits. for example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number.
The dropdown numbers is an illustration of combination
The smallest dropdown number is 1025
How to determine the smallest dropdown number?From the question, we have the following parameters:
The dropdown number is 4-digitThe digits are different.We start counting from 1023, 1024, 1025, 1026...........
The sum of digits in 1023 is 6, and the average is 1.5The sum of digits in 1024 is 7, and the average is 1.75The sum of digits in 1025 is 8, and the average is 2The number 1025 satisfies the given conditions
Hence, the smallest dropdown number is 1025
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UNIQUE
SIZE
What Does Cate Often
Call Her Twin Sister?
Answer:
a dupli-CATE
Step-by-step explanation:
HAHAHAHA OMG THIS IS ACTUALLY FUNNY
7k^2=21,952
Volume of cylinders, cones, and spheres
What is the answer please
Answer:56Step-by-step explanation:7k²=21952
k²=21952/7
k²=3136
k=√3136
k=56
PLS MARK ME AS BRAINLIEST
Estimate the difference.
Answer:
498. 498/6 = 83.
Step-by-step explanation:
Given the function g(x)=√x+4, which of the following values cannot be the domain of g?
A. X=1
B. X=2
C. X=12
D. X=-5
Answer:
D. x = -5
Step-by-step explanation:
The square root function is only defined for non-negative arguments. For the function ...
[tex]g(x)=\sqrt{x+4}[/tex]
this means we must have ...
x +4 ≥ 0
x ≥ -4 . . . . . . subtract 4 from both sides
All of the numbers on your answer choice list are more than -4 except -5.
x = -5 is not in the domain of g(x)
i am stuck on this question please help me
Answer:
h = 8 units, b = 20 units
Step-by-step explanation:
h = 2 units
2 x 4 = 8
b = 5 units
5 x 4 = 20 units
Therefore, h = 8 units and b = 20 units
Hope this helps :)
giving brainlist please help me out
Answer:
681 m^3
Step-by-step explanation:
Winder only found part of the volume. He also needs to find the volume of the hemisphere.
I would first find the volume of the cylinder like Winder, then proceed to calculate the volume of the hemisphere, which is V = 4/3π(4^3)=27.16 m^3. The total volume inside the storage tank is 681 m^3 when rounded to the nearest cubic meter.
please help
i added a picture
ILL MARK BRAINILEST !! 80 POINTS
Question 1: 11 pts
Find the vertex of the parabola y = x2 - 10x + 16.
A. (-5,91)
B. (-9,5)
C. (5,-9)
D. (8,0) and (2,0)
[tex]\\ \rm\rightarrowtail y=x^2-10x+16[/tex]
[tex]\\ \rm\rightarrowtail y=x^2-10x+16+9-9[/tex]
[tex]\\ \rm\rightarrowtail y=x^2-10x+25-9[/tex]
[tex]\\ \rm\rightarrowtail y=(x-5)^2-9[/tex]
Vertex form
y=a(x-h)^2+kSo
vertex:-
(h,k)=(5,-9)Given g(x)=5x-3g(x)=5x−3, find g(-4)g(−4).
g(x)=5x-3
g(x)=5x−3
g(\color{green}{-4})=5(\color{green}{-4})-3
g(−4)=5(−4)−3
Plug input into x
-20-3
−20−3
Multiply
-23
−23
Answer:
the answer is 529
Step-by-step explanation:
see the explanation photo
A triangular bandana has an area of 38 square inches. The height of the triangle is 9
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
Answer:
Base=8.4 inches
Step-by-step explanation:
Area of triangular bandana is 38sq inches
Height of triangle is 9 inches
Area of ∆ =½×b×h
38=½×b×9
38×2=b×9
76/9=b
b=8.4 inches
What is the rule and how do you find n? 100 points and brainliest to answer!
Answer:
n = 6
Step-by-step explanation:
Let's convert the x and y values into (x,y) form.
(x, y) ⇒ (3, 5), (4, 7), (n, 11), (8, 15)
Now, let's find the rule in slope intercept form. To find the equation in slope intercept form, pick any two points. Then find the slope of the line.
⇒ (3, 5) and (4, 7)
Now, find the slope using the slope formula.
[tex]\dfrac{y_{2} - y_1}{x_2 - x_1} = \text{Slope}[/tex]
[tex]\rightarrow \dfrac{7 - 5}{4 - 3} = \text{Slope}[/tex]
[tex]\rightarrow \dfrac{2}{1} = 2 =\text{Slope}[/tex]
Now, let's use point slope form to find the equation in slope intercept form.
[tex]y - 5 = 2(x - 3)[/tex]
[tex]\rightarrow y - 5 = 2x - 6[/tex]
[tex]\rightarrow y = 2x - 1 \ \ \ \ \ (\text{Rule})[/tex]
Now, substitute the value of y into the equation.
[tex]11 = 2x - 1[/tex]
[tex]\rightarrow 12 = 2x[/tex]
[tex]\rightarrow \boxed{x = n = 6}[/tex]
Take two points find equation
(3,5)(4,7)Slope:-
m=7-5/4-3=2Equation in point slope form
y-5=2(x-3)y=2x-6+5y=2x-1Now put n
11=2n-12n=12n=6What is the measure of arc XZ if the angle equals 135 and the radius is 17 km
now, let's make the assumption that the arcXZ has a central angle of 135° and a radius of 17.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=17\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (17)}{180}\implies s=\cfrac{51\pi }{4}\implies s\approx 40.06[/tex]
Amy earns £10.00 per hour. She gets a raise, and her new hourly rate is £11.50 What is the percentage change in her hourly rate?
Percentage Change = (new rate - old rate) / (old rate)
New Rate = 11.5
Old Rate = 10
(11.5 - 10) / 10
1.5 / 10 = 15 / 100 = 0.15 = 15%
The percentage change in her hourly rate is 15%.
Hope this helps!