Answers
Answer:
x = 1 or x = -1
Step-by-step explanation:
Given equation:
[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]
Factor out -1:
[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]
Divide both sides by -1:
[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]
Rearrange the terms:
[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]
[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]
Factor out the common term [tex](x^{98}-1)[/tex] :
[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]
Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):
[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]
Therefore, the solutions to the given equation are: x = 1 or x = -1
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Related Questions
PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
Answers
2. 43 cm
Explanation: take the 15m and subtract 8 cm and for 2 add all the sides together to get 43
Determine whether the given graph is a function or not.
Answers
Answer:
function
Step-by-step explanation:
The graph shows a function since it passes the vertical line test.
cosA/secA+sinA/cosecA=1
Answers
Step-by-step explanation:
please mark me as brainlest
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
Answers
Answer:
The ratio of decay rates is 3:4. So, option D is correct.
Step-by-step explanation:
Concept: The Decay rate for any function can be calculated by the formula Decay rate = Difference in y values / Difference in x values in given interval
Decay Rate for the exponential function in the interval -2 ≤ x ≤ 0 is (4-1) / (-2-0) = 3/2.
Decay rate for quadratic function in same interval = [(4-0) ÷ -(-2-0)] = 2.
Ratio of decay rates = (3/2) : (2) = 3:4
Option D, the exponential function decays at three-fourths the rate of the quadratic function is the correct answer.
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Which expression is equivalent to 2 (14x-37+28x+12.2-5y-17.5)?
A. 84x-16y-10.6
B. 28x-6y-10.6
C. 42x-8y-5.3
D 84x-16y-5.3
Answers
Answer:
A. 84x - 16y - 10.6
Explanation:
[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]
[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]
[tex]\sf \rightarrow 84x -16y-10.6[/tex]
1 2 3 4 5 6 7 8 9 10 11 12 13
Mark this and return
If a new data point at 12 is added to the graph, which will
be true?
O The mean will increase, and the median will stay the
same.
O The median will increase, and the mean will stay the
same.
O The mean will increase more than the median, but
both will increase.
O The median will increase more than the mean, but
both will increase.
Answers
Answer:
The mean will increase more than the median, but both will increase.
[third option listed]
Step-by-step explanation:
the median of a data set is the number in the middle [when listed from lowest to highest in value]
1 2 3 4 5 6 7 8 9 10 11 12 13
is the current median
let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)
1 2 3 4 5 6 7 8 9 10 11 12 12 13
[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]
so, 7.5 is the current median
(this is an increase of 0.5)
--
the mean of a data set is what we commonly refer to as the "average"
[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]
1 2 3 4 5 6 7 8 9 10 11 12 13
mean of original data set:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]
_______________________________________
13
[91 ÷ 13 = 7]
because our number is greater than our original mean [12 > 7], we know that the mean must increase:
[91 + 12 = 103]
[103 ÷ 14 ≈ 9.36]
[we had an increase of 2.36]
so, median increased by 0.5, mean increased by 2.36
so, both values increased, whilst the mean increased by more than the median [as to be expected]
you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]
hope this helps!! :)
I need help on this question
pls help yes
Answers
The arc length of the semicircle is 5π units
Calculating length of an arcFrom the question, we are to calculate the arc length of the semicircle
Arc length of a semicircle = 1/2 the circumference of the circle
∴ Arc length of a semicircle = 1/2 × 2πr
Arc length of a semicircle = πr
Where r is the radius
From the given information,
r = 5
∴ Arc length of the semicircle = 5 × π
Arc length of the semicircle = 5π units
Hence, the arc length of the semicircle is 5π units
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Solve the compound inequality for x and identify the graph of its solution.
x+7> 3 and x-5≤-1
OA. Solution: x<-4 or x ≥ 4
++
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
--
-5-4-3 -2 -1 0 1 2 3 4
OC. Solution: x>-4 and x≤ 4
+
H
-5 -4 -3 -2 -1 0 1
2
4 5
OD. Solution: x2-4 and x < 4
44
-5-4-3 -2 -1 0 1 2 3 4 5
3
5
Answers
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
Let's solve the compound inequality step by step:
x + 7 > 3
Subtract 7 from both sides to isolate x:
x > 3 - 7
x > -4
and, we have,
x - 5 ≤ -1
Add 5 to both sides to isolate x:
x ≤ -1 + 5
x ≤ 4
Now, we have two inequalities for x:
x > -4
x ≤ 4
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.
The correct representation is:
OC. Solution: x > -4 and x ≤ 4
Graph:
-5 -4 -3 -2 -1 0 1 2 3 4 5
+---|---|---|---|---|---|---|---|---|---+
-4 0 4
The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.
The shaded area between -4 and 4 represents the solution to the compound inequality.
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the number of cows in the field minus 12...
Answers
Answer:
maybe minus 12 there was no number of cows
Answer:
x - 12
Step-by-step explanation:
x represents the number of cows since we do not know the number
then "minus 12"
bada bing bada boom
Help me please, i am dum
Answers
a) 50<x<60
b) 20<x<30
idek
I’m still not sure how the answer would be D (CBA), couldn’t it also be ACB?
Answers
Answer: No it could not be ACB.
Step-by-step explanation:
Angles are named based on the vertex of the angle so this could be referred to as ∠B. The other way to name an angle is by saying the three points, However, when you say the three points the vertex must be in the middle. Hence, the answer is ∠CBA as the middle point of the angle is in the middle of the name.
Could I get some help on this pls, and most importantly how you could solve it.
Thank you.
Using your choice of technology, find the line of best fit using the data below for the women’s 100-meter Olympic records. Interpret the y-intercept, and explain the significance of the slope.
Answers
The equation of the line of best fit is y = -0.03x + 69.94
How to determine the line of best fit?The column headers are given as:
Year Time(s)
To enter the data values in a graphing calculator, we use the following representations:
x ⇒ Year
y ⇒ Time (s)
Using the above representations, we have the following calculation summary from a graphing calculator:
Sum of X = 72209Sum of Y = 432.95Mean X = 1951.5946Mean Y = 11.7014Sum of squares (SSX) = 17242.9189Sum of products (SP) = -514.5997The equation of the line of best fit is:
y = bx + a
Where
b = SP/SSX = -514.6/17242.92 = -0.02984 ≈ -0.03
a = MY - bMX = 11.7 - (-0.03*1951.59) = 69.94497 ≈ 69.94
So, we have:
y = -0.03x + 69.94
A linear equation is represented as:
y = Slope * x + y intercept
So, we have:
Slope = -0.03
y intercept = 69.94
The y-intercept implies that the initial time is 69.94 seconds, while the slope implies that the time decreases by 0.03 seconds each year
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What are the more appropriate measures of center and spread for this data
set?
35 40 45
55
90
hi
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
select two choices: one for the center and one for the spread.
a. better measure of spread: the standard deviation
select two choices: one for the center and one for the spread
Answers
The more appropriate measure of center is mean.
The more appropriate measure of spread is standard deviation.
What is mean and standard deviation?Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.
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Which quadratic inequality does the graph below represent?
Answers
The quadratic inequality represented by the graph is:
y ≤ 2x² - 8x + 3
Which quadratic inequality does the graph below represent?
First, we can see that the shaded region is below the parabola, and the line of the parabola is solid, which means that the points on the parabola are solutions, then the inequality is:
y ≤ quadratic equation.
Now we need to get the quadratic equation.
Now, if you look at the y-intercept, you can see that it happens at y = 3. Then the constant term of the quadratic equation is 3.
The only one that has that (and the ≤ symbol) y-intercept is the first option:
y ≤ 2x² - 8x + 3
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David can you 25/6 meters per hour manually, but using a digging machine he can dig 3 times as fast. how many meters would david be able to dig with the machine in an hour?
Answers
Answer:
12.5 meters
Step-by-step explanation:
1 hour manually = 25/6 meters
1 hour using machine = 25/6 × 3 meters
1 hour using machine = 12.5 meters
Hope this helped and have a good day
given f(x)=2x+2 and g(x) =-5x-3 find (f-g)(x)
Answers
Answer:
(f-g)(x) = 7x+5
Step-by-step explanation:
Given that,
f(x)=2x+2 and g(x) =-5x-3
To Find:
(f-g)(x)Solution:
[tex](f - g)(x)[/tex]
Re-write as:
[tex]f(x) - g(x)[/tex]Now substitute the values on the polynomial/function:
Simplify using this order:BPEMDAS
[tex]2x + 2 - ( - 5x - 3)[/tex][tex]2x + 2 + 5x + 3[/tex][tex]2x + 5x + 2 + 3[/tex][tex] \boxed{ ( f - g)(x) = 7x + 5}[/tex]Hence,(f-g)(x) = 7x+5.
Reflection across X=1
Answers
It should be noted that a reflection is known as a flip and it's a mirror image of the shape.
How to illustrate the reflection?An image will reflect through a line, known as the line of reflection.
Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.
In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.
The reflection is attached.
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What is the inverse of f(x)=5x/3+5
Answers
Answer:
f^-1(x)=8x/5
Step-by-step explanation:
The inverse of f(x)=5x/3+5 is 8x/5
The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
How to determine the inverse?We have:
f(x)=5x/3+5
Rewrite as:
y=5x/3+5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
5y/3 = x - 5
Multiply through by 3
5y = 3x - 15
Divide through by 5
y = 3x/5 - 15
Rewrite as:
f-1(x) = 3x/5 - 15
Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
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A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation
to estimate the number of packages that would need to be randomly selected to find a package that was not
delivered on time. The student assigns the digits to the outcomes.Beginning at line 1, and starting each new trial right after the previou
trial, carry out 5 trials of this simulation.
Based on the 5 trials, what is the average number of packages the
led to be selected in order to find a package
that was not delivered on time?
Answers
The average number of packages the led to be selected in order to find a package that was not delivered on time is 2.2 option first is correct.
What is simple random sampling?With simple random sampling, each component of the population has an equal chance of being selected for the sample.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A shipping company claims that 95% of packages are delivered on time.
From the table:
00- 04 is the package not delivered on time.
05-99 - package delivered on time.
The first simulation's third number, 31, 64, 04, is where you can locate an item that wasn't delivered on time.
The second simulation's second number, 34, 02, is the location of a late-delivered delivery.
The third simulation is equal to 96,00 - the second number, which is the location of a late package.
The second number where to find a shipment not delivered on time in the fourth simulation is 31,04
Where to find a box that wasn't delivered on time in the fifth simulation: 98, 01, second number
The average number = (3 + 2 + 2 + 2 + 2)/5
= 11/5
= 2.2
Thus, the average number of packages the led to be selected in order to find a package that was not delivered on time is 2.2 option first is correct.
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You have a dog walking business. You charge based on the weight of the dogs. For a 45-minute walk your prices are:
For dogs that weight 0 up to 15 lbs. you charge $5.00.
For dogs between 15 lbs. and 45 lbs. you charge $7.00
Dogs over 45 lbs. you charge $9.00.
Answer the following questions:
1. If a customer has a 6 pound Chihuahua how much would you charge?
2. If a customer has a 65 pound Labrador how much would you charge?
3. Define the variables:
4. Write a piecewise function for dog walking business, including the conditional statement for the variables.
5. Graph the function.
PLEASE ANSWER ALL FIVE PLEASEEAAAA
Answers
2:$9
3. Variables and letters and symbols that represent unknown values
5|2x+6|=26...can someone answer this please
Answers
Answer:
x = -2/5 or x = -28/5
Step-by-step explanation:
Let's solve your equation step-by-step.
5(|2x+6|)=26
Step 1: Divide both sides by 5.
5(|2x+6|)/5 = 26/5
|2x+6|=26/5
Step 2: Solve Absolute Value.
|2x+6|=26/5
We know either2x+6= 26/5 r2x+6=−26/5
2x + 6 = 26/5(Possibility 1)
2x+6−6= 26/5 - 6 (Subtract 6 from both sides)
2x = -4/5
2x/2 = -4/5/2 (Divide both sides by 2)
x = -2/5
2x + 6=-26/5 (Possibility 2)
2x+6= -26/5 (Simplify both sides of the equation)
2x + 6 - 6 = -26/5 - 6 (Subtract 6 from both sides)
2x = -56/5
2x/2 = -56/5/2(Divide both sides by 2)
x = -28/5
Answer:
x = -2/5 or x = -28/5
If anyone could help me, it would be greatly appreciated!
Answers
Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]
Step-by-step explanation:
All radii of a circle are congruent, so by the base angles theorem
z = y = (180-50)/2 = 65.Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.
5b+a-2c when a=2,b=1&c=3
Answers
5b+a-2c when a=2,b=1&c=3
5(1) + 2 - 2(3)
5 + 2 - 6
7-6
Answer: 1
The graph below shows the solution to which system of inequalities?
Answers
Answer:
C
Step-by-step explanation:
The horizontal line, y=2, is solid and shaded above, so it represents
[tex]y \geqslant 2[/tex]
The slanted line, y=x is dashed and shaded below, so it represents y<x.
Answer
Answer is A
Step-by-step explanation:
If area of a circle is 49/64 pie cm square,then find the circumference of the circle?
Answers
Answer:
7/4 * pi
Step-by-step explanation:
Area of circle = pi * r^2
Find radius:
pi * 49/64 = pi * r^2
49/64 = r^2
7/8= r
Circumference of circle = 2pi * r
2 * pi * (7/8) = 7/4 * pi
Assuming that the answer is in terms of pi as the question is in terms of pi
LCM of 18 , 25 , 35, 40 ,80 81 , and 72
Answers
Answer:
the LCM of 18 25 40 80 81 and 72 is 226800
i hope this helps you
Step-by-step explanation:
by which method
prime factorization , division or defination method
The table shows the probability of how a certain score will
compare to a listed score on a popular video game. Use the
probability distribution to find the variance, o².
Answers
The variance of the probability distribution is 400
The Variables of X and their Probability Distribution.
To find Variance, first we should find out Mean and then Variance
The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)
The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.
Step – 1: Calculation of Mean Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)
Mean = X * P(X) Variance = Sum of (X – Mean)²*P(X)
X P(X) X*P(X)
-50 0.029 -1.45
-30 0.121 -3.63
-10 0.210 -2.1
10 0.485 4.85
30 0.145 4.35
50 0.010 0.5
Mean 2.52
X P(X) X - Mean (X – Mean)² (X – Mean)²*P(X)
-50 0.029 -52.52 2758.35 79.99216
-30 0.121 -32.52 1057.55 127.9636
-10 0.210 -12.52 156.7504 32.91758
10 0.485 7.48 55.950 27.13594
30 0.145 27.48 755.1504 109.4968
50 0.019 47.48 2254.35 22.5435
Variance=400.00
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22*90 what 2+2 3 +3 3+3
Answers
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{ASSUMING: }\\\mathsf{22\times90}\\\mathsf{= 90 \times 22}\\\mathsf{= 1,980}[/tex]
[tex]\mathsf{ASSUMING: }\\\mathsf{2 + 2 + 3 + 3 + 3 + 3}\\\mathsf{= 2\times 2 + 3\times4}\\\mathsf{= 4 + 12}\\\mathsf{= 16}[/tex]
[tex]\huge\textsf{Answer \#1. 1,980 }\huge\checkmark\\\\\\\huge\textsf{Answer \#2. 16 }\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). a point is at (negative 3, 1). what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)? y – 1=negative three-halves(x 3) y – 1=negative two-thirds(x 3) y – 1= two-thirds(x 3) y – 1= three-halves(x 3)
Answers
The equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
Equation of a lineA line is the distance between two points. The equation of a line in point-slope form is expressed as:
y - y0 = m(x-x0)
Given the coordinates (-2, -4) and (2, 2) on the line, the slope is expressed as:
Slope = 2-(-4)/2-(-2)
Slope = (6)/4
Slope = 3/2
Find the equation of the line
y -(1) = 3/2(x-(-3))
y - 1 = 3/2(x+3)
Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
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Answer:
d
Step-by-step explanation:
Simplify this radical
[tex]\sqrt{84} \\\\A: 2\sqrt{21} \\B: 2\sqrt{42} \\C: 4\sqrt{21} \\D: 4\sqrt{42} \\[/tex]
Answers
The given radical root 84, the simplification is option B; [tex]2\sqrt{21}[/tex].
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given radical;
[tex]\sqrt{84} \\\\\sqrt{42 \times 2} \\\\\sqrt{7\times3\times 2 \times 2} \\\\2\sqrt{21} \\[/tex]
Thus, the correct option is B; [tex]2\sqrt{21}[/tex].
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