Your teacher asks the class to evaluate the expression (3³)¹. Your classmate gives an incorrect answer of 81. Evaluate the expression. Then find the likely error.
Answers
The most likely error is that, the student multiplied 27 by 3, after the first computation
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the error in the calculation?The expression is given as
(3^3)^1
As a general rule, we start by evaluating the expression in the inner bracket
So, we have
(3^3)^1 = (3 x 3 x 3)^1
Evaluate the products
So, we have
(3^3)^1 = (27)^1
Next, we evaluate the exponent
So, we have
(3^3)^1 = 27
The above implies that the value of the expression is 27 and not 81 as the student solved
The most likely error is that, the student multiplied 27 by 3, after the first computation
Hence, the value of the expression is 27 and not 81 and the most likely error is that, the student multiplied 27 by 3, after the first computation
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Related Questions
There are 76 milligrams of cholesterol in a 3.1 ounce serving of lobster. How much cholesterol is in 5 ounces of lobster
Answers
Answer:
123 milligrams
Step-by-step explanation:
76 : 3.1 = x : 5
76 * 5 = 3.1x
x = 76*5/3.1 = 123 milligrams
Determine whether each number is a perfect square. If it is a perfect square, write
the number as a product of its two factors.
1.) 20
2.) 36
3.) 49
4.) 68
5.) 121
6.) 400
Answers
20 is not a perfect square.
36 = 6 times 6.
49 = 7 times 7.
68 is not a perfect square.
121 = 11 times 11.
400 = 20 times 20.
Hope this helps
Solve |x -2.5| =8 please help
Answers
Answer (it has two solutions):
x = -5.5x = 10.5I hope this helps!
Simplify the given expression. Write your answer with positive exponents. (x−4y3)−5
Answers
Answer: [tex]\frac{x^{20}}{y^{15}}[/tex]
This is the same as writing (x^20)/(y^15)
===================================================
Work Shown:
[tex]\left(x^{-4}y^3\right)^{-5}\\\\\left(x^{-4}\right)^{-5}*\left(y^3\right)^{-5}\\\\x^{-4*(-5)}y^{3*(-5)}\\\\x^{20}y^{-15}\\\\\frac{x^{20}}{y^{15}}[/tex]
In the second step, I used the rule that (a*b)^c = (a^c)*(b^c)
In step 3, I used the rule (a^b)^c = a^(b*c)
In the last step, I used the rule a^(-b) = 1/(a^b)
work out the size of angles x, y and z.
Answers
Answer:
x = 41° , y = z = 74°
Step-by-step explanation:
x and 41 are alternate angles and are congruent , then
x = 41°
the 2 sides of the triangle with vertex = 32° are congruent so the triangle is isosceles with base angles being congruent , then
y = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74°
y and z are vertically opposite angles and are congruent so
z = 74°
Find the values of d given the area of the quadrilateral. A=48 ft2
Answers
Answer:
x=12
Step-by-step explanation:
the area of a triangle is 1/2hb. so half of the shape's area would be:
(1/2)4x12=24
and 24x2=48
what is 12.8% of 1,300?
Answers
Answer:
166.4
Step-by-step explanation:
Percentage of 12.8% of 1300 = ? 12.8% of 1300 is equivalent to multiplying them: 12.8% × 1300. 12.7% of 1300 = ? 12.9% of 1300 = ? 1% of 1300 = ? Detailed ...
Which of the following is a secant?
Answers
Answer:
Line EF is a secant. I hope this helps!
Answer:line ef
Step-by-step explanation:
Solve by factoring the quadratic equation 2x2 + 13x
=
-21.
Answers
Answer:
x = - [tex]\frac{7}{2}[/tex], x = - 3
Step-by-step explanation:
Given
2x² + 13x = - 21 ( add 21 to both sides )
2x² + 13x + 21 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 21 = 42 and sum = + 13
The factors are + 6 and + 7
Use these factors to split the x- term
2x² + 6x + 7x + 21 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) + 7(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = - [tex]\frac{7}{2}[/tex]
95×2 the answer to problem is
Answers
95 times 2 is 190.
90 times 2 is 180, and 5 times 2 is 10.
180 + 10 = 190.
Given f (x) = x2 + 3x – 4 and values of the linear function g(x) in the table, what is the range of (f + g)(x)?
x –6 –3 –1 4
g(x) 13 4 –2 –17
ℝ
[–3, 3]
(–∞, –9]
[–9, ∞)
Answers
The range of function (f + g)(x) is (-9, ∞) option (D) is correct the linear function g(x) is g(x) = -3x - 5
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x² + 3x - 4
The domain of the f(x) is all real numbers
The range of the g(x) is [-6.25, ∞)
g(x) is shown in the table:
x –6 –3 –1 4
g(x) 13 4 –2 –17
The linear function g(x) is:
[tex]\rm g(x) = \ -13=\dfrac{\left(4-13\right)}{-3+6}\left(x+6\right)[/tex]
g(x) = -3x - 5
(f + g)(x) = f(x) + g(x)
= x² + 3x - 4 - 3x - 5
(f + g)(x) = x² - 9
The domain of the function is all real numbers.
The range of the function (-9, ∞)
Thus, the range of function (f + g)(x) is (-9, ∞) option (D) is correct the linear function g(x) is g(x) = -3x - 5
Learn more about the function here:
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helpp
helpp i need helpw tih thies
Answers
Answer:
20
Step-by-step explanation:
9/g+2h+5
g=3
h=6
=9/3+2(6)+5
=3+12+5
=20
hope dis helps.
pls brainliest!!!!!
Write a linear equation that passes through the points (-3, 3) and (9, -13) in standard form:
Answers
Answer:
4x +3y = -3
Step-by-step explanation:
The standard form equation can be written from ...
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
(-13 -3)x -(9 -(-3))y = (-16)(-3) -(12)(3)
-16x -12y = 12
The standard form has a positive leading coefficient, and all terms mutually prime. We can get that by dividing the equation by -4:
4x +3y = -3
_____
Additional comment
The form we used above for the equation of the line essentially comes from the fact that the slope of a line is the same everywhere:
(y2 -y1)/(x2 -x1) = (y -y1)/(x -x1)
Multiplying by the product of denominators and separating variable terms from constant terms gives the form used above.
One day in the afternoon 3 groups of 8 students got 5 bags filled with pieces of candy.
they ate a certain amount of candy.
how much candy did each student eat?
Answers
There were 5 bags altogether
Do 5/24
Each student got 5/24 bags of candy
SOMEONE PLEASE HELP ME !!! ASAP
Answers
Answer:
a; line BC corresponds to line FG
Step-by-step explanation:
we know that a is correct as after translating BC and FG are on the same side of the rectangle and have the same length
A shadow of a 4 foot pole is 10 feet long. A tower is 200 feet tall. What is the length of the shadow of the tower?
Answers
Answer:
27 feet
Step-by-step explanation:
We can set up a proportion comparing the height of each object to the length of the shadow.
h/s
h/15=18/10
Cross multiply.
10*h=18*15
10h=270
Use the multiplicative Inverse
10/10=270/10
h=27
I DON'T UNDERSTAND THE ENGLISH OF THE QUESTION, WHAT IS 5-!?
Edit: I just realized the grey is part of the picture.
Answers
Answer:
The area of the small square is 1 cm^2
Step-by-step explanation:
The large square consist in four identical rectangles and one small square.
Then the area of the small square will be equal to the difference between the area of the large square and the areas of the rectangles.
Because we have 4 equal rectangles, if R is the area of one rectangle, and S is the area of the large square, the area of the small square will be:
area = S - 4*R
We know that the area of the large square is 49 cm^2
Then:
S = 49cm^2
Remember that the area of a square of side length K is:
A = K^2
Then the side length of the large square is:
K^2 = 49 cm^2
K = √(49 cm^2) = 7cm
And we know that the diagonal of one rectangle is 5cm.
Remember that for a rectangle of length L and width W, the diagonal is:
D = √(L^2 + W^2)
Then:
D = √(L^2 + W^2) = 5cm
And for how we construct this figure, we must have that the length of the rectangle plus the width of the rectangle is equal to the side length of the large square, then:
L + W = 7cm
L = (7cm - W)
Replacing this in the diagonal equation, we get:
√((7cm - W)^2 + W^2) = 5cm
(7cm - W)^2 + W^2 = (5cm)^2 = 25cm^2
49cm^2 - 14cm*W + W^2 + W^2 = 25cm^2
2*W^2 - 14cm*W + 49cm^2 = 25cm^2
2*W^2 - 14cm*W + 49cm^2 - 25cm^2 = 0
2*W^2 - 14cm*W + 24cm^2 = 0
We can solve this for W using the Bhaskara's formula, the solutions are:
W = [tex]\frac{-(-14)(+/-)\sqrt{14^{2}-4(2)(24) } }{2(2)}[/tex]
Then we have two solutions, and we only need one (because the length will have the other value)
We can take:
W = (14 cm + 2cm)/4 = 4cm
Then using the equation:
L + W = 7cm
L + 4cm = 7cm
L = 7cm - 4cm = 3cm
L = 3cm
Now remember that the area of one rectangle of length L and width W is:
R = L*W
Then the area of one of these rectangles is:
R = 4cm*3cm = 12cm^2
Now we can compute the area of the small square:
area = S - 4*R = 49cm^2 - 4*12cm^2 = 1cm^2
The area of the small square is 1 cm^2
This took me ages to complete so please brainliest
find 3 ratios
s that are equivalent to the given ratio 9 to 15
Answers
Answer:
3:5 & 18:30
Step-by-step explanation:
To find an equivalent ratio, just multiply or divide both terms by the same number. For the two I did, I divided by 3 for one, and multiplied by 2 for the other, but there are infinite possibilities. Hope this helped!
Write the equation of the line that is perpendicular to 3x+2y=8 and goes through the point (-5,2)
Answers
Answer:
[tex]\displaystyle y=\frac{2}{3}(x+5)+2[/tex]
Step-by-step explanation:
We need to find the equation of the line perpendicular to the line 3x+2y=8 and passes through (-5,2).
The given line can be expressed as:
[tex]\displaystyle y=-\frac{3}{2}x+4[/tex]
We can see the slope of this line is m1=-3/2.
The slopes of two perpendicular lines, say m1 and m2, meet the condition:
[tex]m_1.m_2=-1[/tex]
Solving for m2:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{-\frac{3}{2}}[/tex]
[tex]\displaystyle m_2=\frac{2}{3}[/tex]
Now we know the slope of the new line, we use the slope-point form of the line:
[tex]y=m(x-h)+k[/tex]
Where m is the slope and (h,k) is the point. Using the provided point (-5,2):
[tex]\boxed{\displaystyle y=\frac{2}{3}(x+5)+2}[/tex]
the number of people who have read a new book is 300 at the beginning of January. The number of people who read the book doubles each month. what do you notice about the difference in the number of people who read the book from month to month. what do you notice about the factor by which the number of people changes each month. if any people have read the book one month how many people read the book the following month.
Answers
At the end of the fourth month, we would have a total number of 4800 readers. The factor by which the number changes monthly is 2 and we would have 2n number of readers the following month
Data;
Initial Number of Readers = 300Factor of Increase 2The difference in number of people who read from month to monthThe difference in number of people who read from month to month will be
[tex]0 = 300\\1 = 2 * 300 = 600\\2 = 2 * 600 = 1200\\3 = 2 * 1200 = 2400\\4 = 2 * 2400 = 4800[/tex]
At the end of the fourth month, we would have a total number of 4800 readers.
The Factor by which the number changes monthlyThe factor by which the number changes monthly is 2. From the pervious calculation, we can see a constant increase by a factor of 2 month to month.
If n number of people are reading this month, the number of readers in the next month would be?Since we already established that the factor by which the readers increase is by two, we can simply say that at the next month, we would have 2n number of readers.
[tex]next month = 2 * n = 2n[/tex]
Learn more on linear equations here;
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A group of 49 hikers registered for an 8-day trekking trip. The organizers arranged food to last for the entire trip. A few last minute registrations saw more hikers join the expedition. As a result, the food lasted only for 7 days. How many hikers in all went trekking?
Answers
Answer:
56 people
Step-by-step explanation:
49 times 8= 392
392 divided 7= 56
In 72,165 give the value of the
digit in the thousands place?
Answers
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Subtract 7a
2
-4ab+2b
2
from 3ab+7a2+2b2
Answers
Answer:
Step-by-step explanation:
3ab + 7a² + 2b² - (7a² - 4ab + 2b²) = 3ab + 7a² + 2b² - 7a² + 4ab - 2b²
Now combine like term. Like terms have same variable with same power.
= 3ab + 4ab + 7a² - 7a² + 2b² - 2b²
= 7ab
You were 20 inches tall at birth, and 65 inches tall on your 10th birthday. Create a linear equation to
represent this situation. According to your equation, how tall will you be at age 20?
Answers
Answer:
At age 20, you will be 90 in
what is the lie fact about sociology
Answers
Answer: Social science or sociology is considered as science but it is a pseudoscience.
Step-by-step explanation:
The sociology is considered as science as the study of social class, ethnicity, and religion abide by people of the society. Like, other factual sciences like chemistry, biology, and physics the facts cannot be rectified or verified by experimental trials. Instead, it is based on assumption and day to day experience with surrounding social environment. Thus, we can say that sociology is a science is a lie.
A(n) ______ can be used to make hand measurements of angles of interest with the joint centers forming the vertices of the angles between adjacent body segments.
Answers
Answer:
The blank should say 'protractor'.
Step-by-step explanation:
I do not have one sorry,
The cash price for a car was £7460. Mr Roberts bought the car on the
following hire purchase terms: A deposit of 20% of the cash price and 36 monthly payments of £191.60. Calculate the total amount Mr Roberts paid.
Answers
The for the total of the 36 months you’ll do 191.60*36 which is 6897.60.
Then to get the total amount Mr. Roberts paid you’ll add the two totals we have 6897.60+1492 which would give the total amount paid of £8389.60.
work out (7×10^5) ÷ (2×10^2)
Answers
Answer:
3500 is the correct answer .Step-by-step explanation:
( 7×10^5) ÷ (2×10^2)= (7 × 100000) ÷ ( 2×100)= 700000 ÷ 200= 3500Mark BRAINLIEST
Thank you ☺️☺️
What is the measure of the
hypotenuse of a right triangle
if the legs measure 10 and 24?
Answers
Answer:
hypotenuse= 26
Step-by-step explanation:
c= a^2 + b^2
10^2 + 24^2= 26
1/2 of Cindy's money is equal to 2/3 of Emily's money. They have $105 altogether. How much money does each of them have?
Answers
Answer:
Cindy has $45 and Emily has $60
Step-by-step explanation:
let x be the amount of money , then
[tex]\frac{1}{2}[/tex] x + [tex]\frac{2}{3}[/tex] x = 105
multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
3x + 4x = 630 , that is
7x = 630 ( divide both sides by 7 )
x = 90
Cindy has [tex]\frac{1}{2}[/tex] × 90 = $45
Emily has [tex]\frac{2}{3}[/tex] × 90 = $60