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Equation 1: m = 6 + n Equation 2: 2m = 8 + 8n Step 1: −2(m) = −2(6 + n) 2m = 8 + 8n Step 2: −2m = −12 − 2n 2m = 8 + 8n Step 3: −12 − 2n = 8 + 8n Step 4: −20 = 10n Step 5: n = −2 In which step did the student first make an error? (4 points) Step 2 Step 3 Step 4 Step 5 4 points Click Save and Submit to save and subm
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Answer:
step three is the incorrect one making step three the answer
Step-by-step explanation:
In the following steps student made the error in the third step.
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
The error occurred in Step 3.
Step 3 should be:
-2(m) = -2(6 + n)
-2m = -12 - 2n
The mistake was that the student distributed the negative sign only to the 6 and not to the n.
The correct next step is to simplify equation 2:
2m = 8 + 8n
So the student made an error in Step 3.
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If you roll a fair six-sided die and a fair four-sided die, what is the probability that neither die shows a 1?
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Answer in decimal form: 0.625
==============================================
Explanation:
There are 5 sides that aren't labeled "1" out of 6 total. So the probability of not rolling a "1" on the six-sided die is 5/6
Similarly, there are 3 sides that aren't labeled "1" out of 4 sides on the four-sided die. The probability of not rolling a "1" for this die is 3/4
Multiply the fractions
(5/6)*(3/4) = (5*3)/(6*4) = 15/24 = 5/8
The answer in fraction form is 5/8 which converts to 0.625 (use long division or a calculator)
Note: the multiplication of probabilities works because the two events (of rolling each die) are independent
2 + 3 × 16 − 2 × 21 − 3
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The order of operations is PEMDAS -
· Parenthesis
· Exponents
· Multiplication
· Division
· Addition
· Subtraction
Thus, we would multiply 3 with 16 and 2 with 21 first.
2 + 3 × 16 - 2 × 21 - 3
2 + 48 - 42 - 3
Now we combine the terms from left to right.
2 + 48 - 42 - 3
50 - 42 - 3
8 - 3
5
Answer:
5
Final answer:
To solve the expression 2 + 3 × 16 − 2 × 21 − 3, we use the order of operations rule, starting with multiplication to get 48 and 42, followed by addition and subtraction to arrive at the final answer of 5.
Explanation:
The student's question requires us to solve a mathematical expression using the correct order of operations. In the expression 2 + 3 × 16 − 2 × 21 − 3, we need to follow the BIDMAS/BODMAS/PEMDAS rule (Brackets, Indices/Orders, Division and Multiplication, Addition and Subtraction). This rule ensures that we perform multiplication and division before addition and subtraction.
First, we calculate the multiplication parts: 3 × 16 and 2 × 21.
3 × 16 = 48
2 × 21 = 42
Substituting these into the original expression gives us:
2 + 48 − 42 − 3
Next, we perform the addition and subtraction in order from left to right:
2 + 48 = 50
50 − 42 = 8
8 − 3 = 5
So, the expression simplifies to the number 5.
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages.
What is the greatest number of packages Tim can make?
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The greatest number of identical packages Tim can make is 13.
The sum of two numbers is 43 . The larger number is 11 more than the smaller number. What are the numbers
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b- second number
a + b = 43 (the sum of two numbers is 43)
(a +11) = b (he larger number is 11 more than the smaller number)
so:
a + b = 43
a + (a + 11) = 43
a + a + 11 = 43
2a = 43 - 11
2a = 32
a = 16
now:
a + b = 43
16 + b = 43
b = 43 - 16
b = 27
that is:
a = 16
b = 27
--------------------------
checking:
b - a = 11
27 - 16 = 11 (TRUE)
identify the two rational numbers. A) √2 B) 1.01 C) 1.010010001... C) -2/5
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So -2/5 and 1.01 are rational.
We have that for the Question "identify the two rational numbers. " it can be said that
Option B,C,D is rational
From the question we are told
identify the two rational numbers.
A)√2
B) 1.01
C) 1.010010001...
D) -2/5
Generally
Rational number are real number that exist is a form where the denominators are not zero
Therefore
A)√2 this is an irratioanl number as its \pm 1
B) 1.01 Rational
C) 1.010010001... rational
D) -2/5 rational
Hence
Option B,C,D is rational
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Your salary is $25,000 you just received a 2.5% pay increase for the year. What is your new salary?
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Here is your answer:
The proper answer to this question is "$25,625".
Reason:
In order to add a 2.5% increase on a pay check you have to multiply 25,000 by 1.025.....
25,000×1.025=$25,625
Therefore my new salary is $25,625!
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
If 2 fluid ounces equals 60 milliliters , how many milliliters are in 7 ounces of cough syrup
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Factor x3 + 2x2 + x completely
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Answer:
x(x+1)²
Step-by-step explanation:
x is a common factor to all terms so the first step is to factor it out:
... x(x² +2x +1)
The quadratic factor is recognizable as the square (x+1)², so the factoring is ...
... x(x +1)²
Answer:
Step-by-step explanation:x(x+1)2
at the market,8 apples cost $4.How much do 9 apples cost?
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If you divide 8 by 4, it seem that 2 apple costs $1.00. It also seems that whenever there is an odd number of apples, the cost of those apples have a cent count of 0.50 cents. So if 8 apples are $4.00, then I believe that 9 apples are $4.50.
I hope this helps!
write in short; × + 2× + 13×
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x + 2x + 13x = (1 + 2 + 13)x = 16x
To win at lotto in one state, one must correctly select 5 numbers from a collection of 58 numbers (1 through 58). the order in which the selection is made does not matter. how many different selections are possible?
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A bookstore costs $75 a day to keep open, and it spends $11 for each book that it sells. If each book sells for $16, what is the break-even point for this bookstore?
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Answer:c=11n+75
Step-by-step explanation:
8x+6=5x+9
[tex]8x + 6 = 5x + 9[/tex]
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8x - 5x = 9 - 6
Now combine like terms:
3x = 3
Divide by 3 to isolate the variable x.
x = 1
Final answer:
To solve the equation 8x + 6 = 5x + 9, subtract 5x from both sides to get 3x + 6 = 9, then subtract 6 from both sides to get 3x = 3. Finally, divide by 3 to find x = 1.
Explanation:
The equation given is 8x + 6 = 5x + 9. To solve for x, you first want to get all terms containing x on one side and the constants on the other. This is achieved through the use of addition or subtraction. From LibreTexts™, we know that addition or subtraction of the same number on both sides of an equation maintains equality. So, subtract 5x from both sides:
8x + 6 - 5x = 5x + 9 - 5x
3x + 6 = 9
Next, you subtract 6 from both sides to isolate the x term:
3x + 6 - 6 = 9 - 6
3x = 3
Now, you divide both sides by 3, a step also indicated by LibreTexts™ as multiplication or division by the same number maintains the equation's balance:
3x / 3 = 3 / 3
x = 1
The solution to the equation is x = 1.
√x<4 A.20 B.12 C.2 D.-1 E.5. F. No solution
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If we square both sides of the inequality, we have
x < 4²
x < 16
Thus the whole solution is
0 ≤ x < 16
The following choices are valid solutions to the inequality:
B. 12
C. 2
E. 5
You help build a new play center at a daycare. The play center has a tunnel for the children to climb through. You are painting the outside of the tunnel. Find the approximate surface area of the outside of the tunnel so you know how much area you need to paint. Use 3.14 to approximate pi.
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Simplify
cosx ( tanx+cotx)
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cos(x) × [tex]( \frac{sin(x)}{cos(x)} + cot(x) )[/tex]
Using cot(t) = [tex] \frac{cos(x)}{sin(x)} [/tex],, transform the expression again.
cos(x) × [tex]( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )[/tex]
Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) × [tex] \frac{sin(x)^{2} + cos(x)^{2} }{cos(x)sin(x)} [/tex]
Using sin(t)² + cos(t)² = 1,, simplify the expression.
cos(x) × [tex] \frac{1}{cos(x)sin(x)} [/tex]
Reduce the expression with cos(x).
[tex] \frac{1}{sin(x)} [/tex]
Lastly,, use [tex] \frac{1}{sin(t)} [/tex] = csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)
Final answer:
The expression cosx (tanx+cotx) simplifies to sinx+cosx by using trigonometric identities and recognizing that tanx and cotx can be expressed in terms of sinx and cosx, allowing terms to cancel out.
Explanation:
To simplify the expression cosx (tanx+cotx), we need to use trigonometric identities. Recall that tanx = sinx/cosx, and cotx = cosx/sinx. Therefore, when we multiply cosx by tanx, the cosx in the numerator and denominator will cancel out, leaving us with sinx. Similarly, when we multiply cosx by cotx, sinx in the numerator and denominator will cancel out, leaving us with cosx.
So the simplification process will look like this:
cosx * tanx = sinx
cosx * cotx = cosx
Thus, cosx (tanx+cotx) = sinx+cosx.
This is the simplified form of the expression given. It's important to remember that trigonometric identities are a powerful tool in simplifying expressions involving trigonometric functions.
45 points!!!❤
Northwoods Middle School chorus 3/8 of the members are 11 year olds of the 11 year old chorus members 2/5 are boys what fraction of all the chorus members are 11 year old boys
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Simply do 3/8 times 2/5 to find this
2/5 of the 11 year olds are boys.
so 2/5 of 3/8 are 11 year old boys.
2/5 * 3/8 = 3/20 is da answer.
find (f o g)(2) and (f+g)(2) when f(x)=1/x and g(x)=4x+9
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(f o g) (2)= 1/17 and (f+g) (2)= 17.5
To find (f o g)(2), substitute the value of g(2) into f. To find (f+g)(2), find f(2) and g(2) separately, then add them together.
Explanation:To find (f o g)(2), we need to first find g(2), and then substitute that value into f. To find g(2), we substitute 2 into the expression for g(x). g(2) = 4(2) + 9 = 8 + 9 = 17. Now, we substitute 17 into the expression for f(x), which is 1/x. (f o g)(2) = f(g(2)) = f(17) = 1/17.
To find (f+g)(2), we first need to find f(2) and g(2) separately. f(2) = 1/2, and g(2) = 17. Now, we add them together. (f+g)(2) = f(2) + g(2) = 1/2 + 17 = 1/2 + 34/2 = 35/2 = 17.5.
Minimze the product of a positive rational number and a negative rational number, given that the positive number is exactly 8 greater than the negative number. what is the final product?
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x(x+8)
This describes an upward-opening parabola whose vertex is (-4, -16).
The numbers are -4 and +4, and the final product is -16.
What is the measure of ∠N?
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180( n - 2 ), n = number of sides in the polygon.
this one is a QUADrilateral, so it has 4 sides, thus its interior angles add up to 180( 4 - 2), or 360°.
thus 75 + 104 + 59 + ∡N = 360, ∡N = 360 - 75 - 104 - 59.
Hey can you please help me posted picture of question
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7*2*4*4
14*4*4
64*4
244
There are 244 combinations
Let f(x) = -6x + 3 and g(x) = 5x + 4. Find f*g and state its domain.
-18x2 - 39x + 20; all real numbers except x = 1
-30x2 - 9x + 12; all real numbers
-18x2 - 39x + 20; all real numbers
-30x2 - 9x + 12; all real numbers except x = 4
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We are given that:
f (x) = -6x + 3
g (x) = 5x + 4
To get f*g, we will simply multiply the two functions as follows:
f (x) * g (x) = (-6x+3)(5x+4)
f (x) * g (x) = -30x² - 24x + 15x + 12
f (x) * g (x) = -30x² - 9x + 12
2- getting the domain:
The domain is all the values of x that can be used in the given equation.
In the equation calculated from part 1, we can note that all real numbers can be considered as the domain.
Hope this helps :)
-1+7n
A. Quadratic monomial
B. Quadratic trinomial
C. Linear binomial
D. fifth degree binomial
E. none
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A. Quadratic monomial
B. Quadratic trinomial
C. Linear binomial
D. fifth degree binomial
E. none
The correct answer is:
C. Linear binomial
Linear binomial is a polynomial of the first degree: ax+ b. If to divide a polynomial, containing a letter x, by a linear binomial x – b, where b is a number ( positive or negative ), then a remainder will be a polynomial only of zero degree, i.e. some number N , which can be found without finding a quotient.
Jordan worked out at a gym for 2 hours. His workout consisted of stretching for 21 minutes, jogging for 45 minutes, and lifting weights for the remaining amount of time. What percentage of Jordan’s workout was spent lifting weights?
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A rectangular prism has a volume of 96ft3. The area of the base is 24ft2. What is thw height of the prism? answer soon please
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The height is 4ft.
hey can you please help me posted picture of question
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Graph using selected points:
\Falls to the left and falls to the right:
x y
-2 -12
-1 3
0 4
1 3
2 -12
Then plot the points given:
See attached picture:
As observed in the provided picture, the graph shows that the function G(x)= 4-x^4 has the same graph in the given problem.
So the relation between two graphs can be written as:
G(x) = F(x) + 1
Using the value of F(x), we get:
G(x) = 3 - x⁴ + 1
So,
G(x) = 4 - x⁴
Thus, option A gives the correct answer.
what is the median number for the numbers 4,8,10,5,9?
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The median is the number in the middle when the numbers go from least to greatest. This would be 4, 5, 8, 9, 10. The middle number would be 8. A way to find the middle number is to mark off the end number on the right and left side until you are left with 1 number. If you are left with 2, add the numbers up and divide. The answer to this is 8.
I hope this helps!
Hello There!
Median: The middle number when all the numbers are listed in oder from least to greatest.
To find the median, place the numbers in order from least to greatest.
In this case, the numbers would be 4, 5, 8, 9, 10
The middle number would be 8 so the median for this set of numbers is 8.
(n+8)+(n−12) =
what is the answer
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The simplification of ( n + 8) + ( n -12 ) is 2(n -2)
algebraic expression are expression with unknown.
This unknown is represented by letters and in linear algebraic equations , the highest power of the unknown is 1.
Simplifying (n + 8) + (n-12)
n + 8 + n -12
collecting like terms
n + n + 8 -12
2n -4
we can further Factorize
2( n -2)
Therefore, the simplification of ( n + 8) + ( n -12 ) is 2(n -2)
2,5,11,20 32,47 what is the next number in the series
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+3,+6, +9,+12,+15,+18, +21,
The next number in the series is 65. To identify the pattern in the given series and find the next number, let's look at the differences between consecutive terms.
5 - 2 = 3
11 - 5 = 6
20 - 11 = 9
32 - 20 = 12
47 - 32 = 15
As we observe, the differences between consecutive terms are increasing by 3 each time. So, to find the next difference, we add 3 to the last difference:
15 + 3 = 18
Now, to find the next number in the series, we add this difference to the last number in the series:
47 + 18 = 65
Therefore, the next number in the series is 65.
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