Answer:
The laws of exponents are:
a) (x^n)*(x^m) = x^(n + m)
b) (x^n)/(x^m) = x^(n - m)
c) (x^n)^m = x^(n*m)
Now, let's see the given equations:
1) (x-²)-³ = x⁶ (true)
Here we se the third law, the "c"
(x^(-2))^(-3) = x^(-2*-3) = x^6
Then this equation is correct.
2) (a^m)^n = a^m^n (false)
This law does not exist, this is false.
An example of why this is false is:
Let's use the values:
a = 2, m = 1, and n = 2
then, in the left side we have:
(2^1)^2 = (2)^2 = 4
And in the right side we have:
2^(1^2) = 2^(1) = 2
We can see that we have different things in the left side than in the right side, then that relation is false.
3) a⁰ = 0 (false)
Let's rewrite this as:
a^0 = a^(n - n)
Now we can use the second law to rewrite this as:
a^(n - n) = (a^n)/(a^n)
And we have a number divided by the exact same number, we know that this is equal to 1, then:
(a^n)/(a^n) = 1
this means that:
a^0 = 1.
Then this is also false.
The only correct option is the first one.
HELP PLEASE! I need helpppp!! :(
Write the ratio of ears to toes on an average person? (in simplest form)
type your answering using one of the following... (NO SPACES)
to
Answer:
1:5
Step-by-step explanation:
DivideByTwo
The expression x3 – 64 can be written as (x)3 – (4)3. What is the factorization of x3 – 64?
a3 – b3 = (a – b)(a2 + ab + b2)
A. (x – 4)(x2 + 4x + 8)
B. (x – 4)(x2 + 4x + 16)
C. (x – 64)(x2 + 64x + 16)
D. (x – 64)(x2 + 64x + 4,096)
Answer:
B
Step-by-step explanation:
(x - 4) because a = x and b = 4, subsitute into (a - b)
(x2 + 4x + 16) because if a = x and b = 4, you subsitute them into (a2 + ab + b2) to get your answer
Hi please help. i’ve been stuck on this for 5 minutes
Factor the expression completely. 54 – 24x
Answer:
6(9-4x)
Step-by-step explanation:
Factor 6 out of 54-24x, or group and factor out the GCF. Hope this helps!
The mean for this set of data is 18. Which number could be put in the blank to make this statement true?
16 10 22 ___
A. 84
B. 24
C. 48
D. 72
The mean of the data is 18 and the missing statement is x = 24
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the data be represented as A
Now , the value of A = 16 , 10 , 22 , x
Let the mean of the data be M = 18
To find the mean of the data set, we need to add up all the numbers and divide by the total number of numbers:
(16 + 10 + 22 + x) / 4 = 18
We can simplify this equation by multiplying both sides by 4 to get rid of the fraction:
16 + 10 + 22 + x = 72
Now we can solve for x by subtracting the three known numbers from both sides:
x = 72 - 16 - 10 - 22
x = 24
Therefore, the number that could be put in the blank to make the statement true is 24
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what's the answer step by step please
A runner's distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. One of the runner's times has a z-score of –1.76. What is the runner's time?
Answer:
The runner’s time is 3.18 minutes
Step-by-step explanation:
Mathematically;
z-score = (x-mean)/SD
In this question, we have the z-score but we want to calculate x
From the question
z-score = -1.76
mean = 4.5 minutes
SD = 0.75 minutes
x = ?
Substituting these values, we have that
-1.76 = (x-4.5)/0.75
0.75(-1.76) = x - 4.5
-1.32 = x - 4.5
x = 4.5 -1.32
x = 3.18
Answer:
3.18
Step-by-step explanation:
edg
A cereal company is determining the nutritional information of a new recipe. They took a random sample of 20 servings of the cereal and measured
the number of calories in each serving. The number of calories in each serving are listed.
143, 145, 147, 150, 150, 152, 157, 159, 160, 160, 161, 163, 164, 165, 165, 168, 173, 175, 177, 180
The box plot shown is a summary of the data. Move numbers to the spaces to label the values and complete the box plot.
143
180
not drawn to sale
145
150
151
160.5
160.7
165
166.5
177
Answer:
Minimum is 143, second whisker is 150, median is 160.5, 3rd quartile is 166.5, maximum is 180
Step-by-step explanation:
The first box is fillled with first quartile 151, the second box is filled with second quartile 160.5, and the third box is filled with the third quartile 166.5
How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.
Similarly, second quartile (also called median) is approximately in mid of the data.
Third quartile (also called upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.
Left to right is said in assumption that data was arranged increasingly from left to right
For this case, the data is:
143, 145, 147, 150, 150, 152, 157, 159, 160, 160, 161, 163, 164, 165, 165, 168, 173, 175, 177, 180
It is already sorted. There are 20 values.
We have to find the limits of box and the mid line, which are the three quartiles.
Dividing 20 in 4 equal parts give size of 5
Thus, 5-5-5-5 groups will be made by the three quartiles of this data.
The fifth value is 150, and sixth is 152. Any number between 150 and 152 can be taken as the first quartile, as before it will lie 25% of values and 75% of the data after that value. By tradition, we take average of these two values, so its 151 as the first quartile of the considered data set.
In the similar way, the second quartile or median is mean of 10th and 11th value which evaluates to (160+161)/2 = 160.5
And, the third quartile is the mean of 15th and 16th value of this data set, which evaluates to (165+168)/2 = 166.5
Thus, the first box is fillled with first quartile 151, the second box is filled with second quartile 160.5, and the third box is filled with the third quartile 166.5
Learn more about quartiles here:
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PLEASE HELP I HAVE TO TURN THIS IN SOON
In ∆XYZ, m∠X = 115°,m∠Y = 23°. What is m∠Z?
Answer:
X+Y+Z=180
115+23+Z=180
Z=180-115-23
Z=42°
Step-by-step explanation:
2 1/4w =6 3/4 answers pls hurry
Answer:
3
Step-by-step explanation:
3 * 2 1/4 = 6 3/4
I need help with A,B and c
Step-by-step explanation:
a. D( as it has 7 sides)
b. D(as it has 7 sides)
c. B( as it has 9 sides)
Hope it will help you :)❤
The 1985 Mexico City earthquake measured a magnitude 8.0 on the Richter scale. The Richter scale uses the function M (I) = log (StartFraction I Over I Subscript 0 Baseline EndFraction). Which equation relates the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, Io?
A.) I = 810(Io)
B.) Io = 810(I)
C.) I = 108(Io)
D.) Io = 108(I)
Answer:
The correct option is C: I = 10⁸I₀.
Step-by-step explanation:
The function of the Richter scale is:
[tex] M_{(I)} = log(\frac{I}{I_{0}}) [/tex]
Since the magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, Io, is:
[tex] 8.0 = log(\frac{I}{I_{0}}) [/tex]
[tex] 10^{8} = \frac{I}{I_{0}} [/tex]
[tex] I = 10^{8}I_{0} [/tex]
Therefore, the correct option is C: I = 10⁸I₀.
I hope it helps you!
The equation relates with the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, [tex]I_0[/tex] is [tex]I = 10^8I_0[/tex].
Given that,
The 1985 Mexico City earthquake measured a magnitude of 8.0 on the Richter scale.
The Richter scale uses the function M (I) = log (Start Fraction I Over I Subscript 0 Baseline End Fraction).
We have to determine,
Which equation relates the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, Io.
According to the question,
The function of the Richter scale is:
[tex]M_(_I_) =log[ \dfrac{I}{I_0}][/tex]
The magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, [tex]I_0[/tex] is:
[tex]M_(_I_) =log[ \dfrac{I}{I_0}]\\\\8 =log[ \dfrac{I}{I_0}][/tex]
Taking log base 10 both sides,
[tex]10^8 = \dfrac{I}{I_0}\\\\I = 10^8I_0[/tex]
Hence, The equation relates with the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, [tex]I_0[/tex] is [tex]I = 10^8I_0[/tex].
To know more about the Exponential function click the link given below.
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can someone pls help me with this!!
Answer:
1st one
Step-by-step explanation:
Which is the graph of y -3= -2/3( x+ 6)?
Answer:
y= −2/3x−1
Step-by-step explanation:
I WILL MARK THE BRAINEST
1.How many exterior angles are there at each vertex of the triangle
2.How many exterior angles does a triangle have in all
Answer:
blank 1: 2
blank2: 6
hope this helps
I need this ASAP PLSS help
Answer:
I think d.) 1
Step-by-step explanation:
1/2 and 3/4 is a 1/4 difference bc 1/2= 2/4
3/4 + 1/4 is a cup. I may be wrong
Answer:
1 1/8 cups
Step-by-step explanation:
ratio is x1.5
Use the system of equations to answer the question.
x + y = 3
y = x - 5
What is the solution to the system of equations?
Answer:
the answer to the system of equation is (4, -1)
If you can anserw both of them that’ll be great if not that’s okay too !! I need this as fast as possible thank you !!!!
Answer:
Step-by-step explanation:
Slope intercept formula: y = mx + b
m = slope
b = y-intercept
Substitute
14.) y = 1x + 0
Basically y = x
15.) y = 2x + (-7)
y = 2x - 7
Please answer quick 20 points and if answer is right I will give Brainly
Answer:
216*64/8=1728....
Step-by-step explanation:
12³ is the appropriate answer
Write an equation in the form ax? + bc+c=0 if the roots are r1= - 7 and r2 = -5
Answer:
A
Step-by-step explanation:
Use the coordinate plane to write the ordered pair for each plotted point. Help fast
Answer:
a is ( 4,8) B is ( 6,5) and c is ( 2.3)
Step-by-step explanation:
A, B, C, and D are the four angles of a parallelogram. a.Show that angle A = angle C
b.Show that angle B = angle D
Answer:
look at the pictures
Step-by-step explanation:
HOPE THIS helps
Jason’s current age is 1/4 his mom’s current age. In 16 years, Jason’s age will be 1/2 his mom’s age. The equation below can be used to determine x, Jason’s current age. What is Jason’s current age, in years
Answer:x=8
Step-by-step explanation: if you download Math-way you’ll get a lot of answers I was doing a test and I seen u didn’t have an answer so I decided to help you
Mike is purchasing fabric for a school project. He needs to cut out circles with an area of 314 square inches. The fabric at the store is precut into squares, each of which has a whole number of inches for the length of its side. What is the smallest square piece of fabric Mike can purchase to use to cut out one of the circles?
The school's copier can
make 30 copies in 12a
minute. How many
copies can it make in 18
minutes?
Answer: 45 copies in 18 minutes
Step-by-step explanation:
i figured it out ;)
I'm in need of assistance here, please answer ASAP!
What u need help with?
Answer: where do you need assistance
Step-by-step explanation:
Simplify the expression 2(5r + 8) - 4
(Please help ASAP!! Giving brainliest to whoever gives the answer!)
Answers pleasee this stuff is hard
Answer:
According to the integral root theorem the only possible real, integral zeros are +/- factors of (10*3 - 8)
... or factors of 992(+/-). you can test by direct substitution. No positive values are roots ... try 1, 1332, but as x increases so does y ... so there are no positive roots.
Roots, means y = 0 ... so (x + 10)^3 = 8 ... take cube root ... x + 10 = 2 .. x = -8
x = -8 is a root
Testing other negatives and the y values are not zero but tend toward - infinity.
So the only real zero is x = -8
Answer:
it helps you
Step-by-step explanation:
this is for y = (x-10)^3 - 8
According to the integral root theorem the only possible real, integral zeros are +/- factors of (10*3 - 8)
... or factors of 992(+/-). you can test by direct substitution. No positive values are roots ... try 1, 1332, but as x increases so does y ... so there are no positive roots.
Roots, means y = 0 ... so (x + 10)^3 = 8 ... take cube root ... x + 10 = 2 .. x = -8
x = -8 is a root
Testing other negatives and the y values are not zero but tend toward - infinity.
So the only real zero is x = -8
Similarly for y = (x + 7)^3 +2 = 0
(x + 7)^3 = -2
x + 7 = cube root (-2)
x = -7 + cube root (-2) <<< the only real root
Combine like terms to simplify the following expression : 12x+4y-3x+2-8y^2+9
−
8
2
+
9
+
4
+
1
1 fgdfgdfgdfgdfg