Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.
Answer:
Spencer and Jeremiah both are correct
Step-by-step explanation:
We have given an equation 6x-2 = -4x+2
In this case spencer and jeremiah both are correct whether we first subtract 6x from both sides or we add 4x to both sides will not lead to any incorrection we will get the same result after simplification from both the methods
If we subtract 6x from both sides we will get 6x-6x-2= -4x-6x+2 after simplification we will get -2 = -10x+2
After further simplification we will get x=4/10=2/5
And if we add 4x on both sides we will get 6x+4x-2= -4x+4x+2 after simplification we will get 10x -2 =2 which eventually gives the result
x=4/10=2/5
Therefore, Both are correct
mary purchased 3 1/2 pounds of bananas. If the loaf of banana bread requires 3/4 pounds of bananas, how many loaves of banana bread can she make with the bananas.
Which statement best explains whether y = 3x + 5 is a linear function or a nonlinear function?
1. It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 8), which are on a straight line.
2. It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 4), which are not on a straight line.
3. It is a nonlinear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.
4. It is a linear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.
Simplify √550
A 5√22
B 10√55
C 5√11
D 25√5
Answer:
A) 5√22
Step-by-step explanation:
I took the K12 quiz and it was right
The simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The number in radical sign is 550 ie.
= √550
The factors of the 550 can be written as:
550 = 5x5x2x11
= √(5x5x2x11)
= 5√(2x11)
= 5√22
Thus, the simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.
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Linda has 4 2/3 yards of material . She is making baby clothes for the bazzaar. Each dress patterns requries 1/16 yards of material. How many complete dresses will she be able to make from the material she has?
in a carnival drawing,a green ticket wins $1,a yellow ticket wins $5,and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. in simplest form, what are the odds in favor of winning $5 or more?
The odds in favor of winning $5 or more at the carnival are 3 to 10.
To determine the odds in favor of winning $5 or more at the carnival, we need to consider the number of tickets that win $5 or more and the total number of tickets.
Identify the tickets that win $5 or more: Yellow tickets win $5 and Blue tickets win $10.
Count the number of these tickets:
Yellow tickets: 25
Blue tickets: 5
Total tickets that win $5 or more:
25 + 5 = 30
Total number of tickets:
100 + 25 + 5 = 130
Odds in favor of winning $5 or more is the ratio of favorable outcomes to unfavorable outcomes:
Winning tickets: 30
Non-winning tickets:
130 - 30 = 100
Simplified odds:
30 to 100 = 3 to 10
Therefore, the odds in favor of winning $5 or more are 3 to 10.
The odds in favor of winning $5 or more in a carnival drawing are 3 : 10. So, the correct option is (B).
To determine the odds in favor of winning $5 or more in a carnival drawing, observe the number of tickets for each prize and calculate the favorable outcomes.
Here are the ticket counts:
Green ticket ($1): 100 ticketsYellow ticket ($5): 25 ticketsBlue ticket ($10): 5 ticketsFirst, calculate the total number of tickets:⇒ 100 (green) + 25 (yellow) + 5 (blue) = 130 tickets
Next, calculate the number of tickets that win $5 or more:⇒ 25 (yellow) + 5 (blue) = 30 tickets
The remaining tickets are the losing tickets or those winning less than $5 (green):⇒ 130 (total) - 30 = 100 tickets
Therefore, the odds in favor of winning $5 or more are 30:100, which simplifies to 3:10. This converts to the following odds as a ratio:
So, the correct option is (B) 3:10.
Complete question:
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5 and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:1
B. 3:10
C. 2:1
D. 1:3
what is the area of a right triangle with side lengths 6, 8, and 10? a. 48 b. 40 c. 30 d. 24
$10,000 is invested at two different rates. $4,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.
Solve. e^(4x) + 5e^(2x) - 24 = 0.
a recipe calls for 2 1/2 cups of flour toake 2 dozen coockies.how many cups of flour would be required to bake 15 dozen cookies?
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Suppose the population of a town is 8,200 and is growing 3% each year.
a. Write an equation to model the population growth.
b. Predict the population after 3 years.
A: y = 8,200 • 3^x ; about 221,400 people
B: y = 8,200 • 3^x ; about 8,960 people
C: y = 3 • 8,200^x ; about 73,800 people
D: y = 8,200 • 1.03^x ; about 8,960 people
Nellie is buying bird seed to put in her bird feeders. She uses about 10 pounds of bird seed each week, but has room to store any extra that she purchases.The bird seed comes in 3 different sizes as given below: 3.5 pounds for $2.52 7.5 pounds for $5.40 11 pounds for $7.92 Nellie is trying to be a smart shopper and get the best deal on the bird seed. Which size bag of bird seed should Nellie buy?
All the bird seed bags Nellie is considering have the same cost per pound ($0.72). She should choose based on her weekly usage and storage preference. Any size will be cost-effective.
To determine the best deal on bird seed, Nellie needs to calculate the unit price for each option. The unit price is the price per pound of bird seed.
For the 3.5-pound bag:
[tex]\[ \text{Unit price} = \frac{\$2.52}{3.5 \text{ pounds}} \approx \$0.72/\text{pound} \]\\For the 7.5-pound bag:\[ \text{Unit price} = \frac{\$5.40}{7.5 \text{ pounds}} = \$0.72/\text{pound} \]For the 11-pound bag:\[ \text{Unit price} = \frac{\$7.92}{11 \text{ pounds}} \approx \$0.72/\text{pound} \][/tex]
Since all three options have the same unit price of approximately $0.72 per pound, Nellie should choose the size that offers her the most pounds of bird seed for the best value, as he has anyway room for storing extra purchase. Here, can choose to buy any of them.
1. A recipe calls for cups of flour, cup of white sugar, and cup of brown sugar. The recipe makes 6 servings.
(a) How many cups of flour are there per serving? Show your work.
(b) How many total cups of sugar (white and brown) are there per serving? Show your work.
(c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe? Show your work
Answer:
abc
Step-by-step explanation:
A=4 B= 26 C= 4 and 2
Suppose z=x^2*sin(y), x=2s^2−4t^2, y=4st.
A. Use the chain rule to find ∂z/∂s and ∂z/∂t as functions of x, y, s and t.
Use the chain rule of differentiation to calculate ∂z/∂s and ∂z/∂t. Start by differentiating the functions z with respect to x and y, then differentiate the functions x and y with respect to s and t. Finally, plug the derived values into the chain rule formula to get the expressions for ∂z/∂s and ∂z/∂t.
Explanation:To solve the problem, we will need to apply the chain rule in order to calculate ∂z/∂s and ∂z/∂t. The chain rule is used in calculus to differentiate a function that has other functions inside of it.
We will differentiate z which is the function of x and y, and x and y themselves are functions of s and t.
The steps are as follows:
Calculate ∂z/∂x and ∂z/∂y by differentiating z with respect to x and y. Calculate ∂x/∂s, ∂x/∂t, ∂y/∂s and ∂y/∂t by differentiating x and y with respect to s and t.Use these calculated values to calculate ∂z/∂s and ∂z/∂t by applying the chain rule formula.
The chain rule formula is:
∂z/∂s = ∂z/∂x * ∂x/∂s + ∂z/∂y * ∂y/∂s
and
∂z/∂t = ∂z/∂x * ∂x/∂t + ∂z/∂y * ∂y/∂t.
This will give you the final expressions for ∂z/∂s and ∂z/∂t as functions of x, y, s, t.
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Find all solutions of the equation 2sin2x−cosx=1 in the interval [0,2π), what is x?
Find all solutions of the equation 2sin2x−cosx=1 in the interval [0,2π), what is x?
How would 0.333333 be classified?
The given number 0.333333 is rational number and real number.
What is the decimal number?A decimal number is said to be irrational if it never repeats. For instance, since there is no repetition, the decimal representation of pi is an estimate. All rational numbers have decimal expansions that either come to an end (in which case all subsequent values are zero) or follow a pattern.
What is the ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What is the rational number?A rational number is defined as a number that can be represented as the ratio of two integers, where the denominator must not equal zero.
A rational number is any number that can be written as a ratio. Think of a ratio kind of like a fraction, functionally at least.
Given number, 0.333333 is a repeating decimal that comes from the ratio of 1 to 3, or 1/3. Thus, it is a rational number.
The number 0.333333 is also real number.
Hence, the number 0.333333 is rational number and real number.
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In the diagram below, AB is parallel to CD. What is the value of x?
The correct answer is: Option (D) x = 72°
Explanation:
When two lines are crossed by another line, the angles in matching corners are called corresponding angles. When the two lines are parallel, the corresponding angles are equal.
Here in this case, the two lines are "AB" and "CD", and both are parallel and are crossed by the line; therefore, the corresponding angles will be the same.
Since the first corresponding angle is 72°, the second angle x will be 72° as well. The correct answer is: x = 72° Option (D).
In the diagram below, AB is parallel to CD. What is the value of x?
Answer: 72!
Please help! Numbers 16 & 17.. It will be much appreciated! :D
10 POINTS!
Solve.
6 – 3x = 4(3 – x) – 6
A.
0
B.
–6
C.
all real numbers
D.
6
The length of a rectangle is 5 inches less than 3 times the width. The perimeter of the rectangle is 14 inches. Find the length and width of the rectangle.
I did this: Length 3x-5; width 3x Then I did guess and check and came up with X=2 solving the problem with a perimeter of 14. But, the answer is supposed to be length 4inches, width 3inches.
Please explain what I did wrong. I know the answer but not how to get it.
The following list shows the items and prices for a restaurant order. Calculate the total amount if there is 7.5% tax and the customer leaves a 15% gratuity.
1 appetizer: $8.99
2 entrees: $14.99 each
1 entree: $12.99
3 drinks: $1.99 each
a. $70.96
b. $71.62
c. $75.31
d. $75.97
The first thing we are going to do to find the total cost of the meal before tax:
Total cost before tax = $8.99 + 2($14.99) + $12.99 + 3($1.99)
Total cost before tax = $8.99 + $29.98 + 12.99 + $5.97
Total cost before tax = $57.93
Regarding the 15% gratuity, remember that the unofficial rule for tipping at restaurants is to tip according to the actual value of the meal and not the tax, so we calculate the value of the tip first, and then we add it to the total at the end of our calculations.
Tip = 15%($57.93) = $8.69
Now, lets calculate the tax
Tax = 7.5%($57.93) = $4.34
Finally, we can calculate the total cost of the meal
Total cost = cost before tax + tip + tax
Total cost = $57.93 + $8.69 + $4.34 = $70.96
We can conclude that the correct answer is a. $70.96
Answer:
$70.96
Step-by-step explanation:
Cost of 1 appetizer = $8.99
Cost of 1 entrees= $14.99
Cost of 2 entrees= [tex]14.99 \times 2 = 29.98[/tex]
Cost of 1 entree: $12.99
Cost of 3 drinks = 1.99 \times 3 =5.97
Total cost before tax = $8.99 + $29.98 + 12.99 + $5.97
Total cost before tax = $57.93
there is 7.5% tax
So, tax =[tex]7.5 \% \times 57.93 = \frac{7.5}{100} \times 57.93 =4.34[/tex]
The customer leaves a 15% gratuity.
Gratuity=[tex]15 \% \times 57.93 = \frac{15}{100} \times 57.93 =8.69[/tex]
So, Total cost including tax and gratuity = $57.93 + $8.69 + $4.34 = $70.96
So, Option A is true
suppose sin u= x and u is between 0 and pi/2. what is sec u? ...?
The required value will vary Between [1,∞)
What is Trigonometry?It is the branch of science that studies the relation between right-angled triangles.
How to solve?if sin u = x and u varies from 0 to [tex]\frac{\pi }{2}[/tex]
We know, Sec u = [tex]\frac{1}{cos u}[/tex]
Then, for sec u or sec u varying from 0 to [tex]\frac{\pi }{2}[/tex] value will be in between [1,∞)
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Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.
Base 1 1/2 feet, altitude 6 inches.
Area = sq. ft. ...?
Answer:
3/4 sq. ft.
Step-by-step explanation:
Hope it helps.
Prove: the midpoint of the hypotenuse of a right triangle is equidistant from three vertices
From the picture attached,
Coordinates of point A → (0, 0)
Coordinates of point M → [tex](\frac{a}{2}, \frac{b}{2} )[/tex]
Coordinates of point A → (0, b)
Coordinates of point A → (a, 0)
Since, we have to prove that midpoint (M) of the hypotenuse BC is equidistant from all three vertices A, B and C,
AM = BM = CM
Use the expression for the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AM = [tex]\sqrt{(\frac{a}{2}-0 )^2+(\frac{b}{2}-0)^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2} )^2}[/tex]
BM = [tex]\sqrt{(a-\frac{a}{2} )^2+(\frac{b}{2})^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
CM = [tex]\sqrt{(0-\frac{a}{2} )^2+(b-\frac{b}{2})^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
Therefore, AM = BM = CM = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
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YES, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices -
AM = CM = BM.
We have a right - angled triangle → ΔABC.
We have to prove that midpoint of the hypotenuse of a right triangle is equidistant from three vertices.
What is Right Angled Triangle?A right angled triangle is a triangle with one of the angles as 90 degrees.
According to the question -
Consider the hypotenuse BC. The mid - point of BC has the coordinates as -
M([tex]\frac{a}{2} , \frac{b}{2}[/tex]).
Now -
Length AM →
AM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Length CM →
CM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2} - b) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Length BM →
BM = [tex]\sqrt{(\frac{a}{2} -a) ^{2} + (\frac{b}{2} ) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Therefore -
AM = CM = BM
Hence, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices.
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write a fraction that is equivalent to 7/10 = _ /_
A degree is larger than 30 arc minutes. ...?
true or false
Answer:
True
Step-by-step explanation:
Given : Statement - 'A degree is larger than 30 arc minutes'.
To find : True or False ?
Solution :
We know that,
1 degree is [tex]1^\circ=\frac{1}{360}[/tex] of a circle
1 arc minute is [tex]1^'=(\frac{1}{60})^\circ[/tex] of degree.
So, 30 arc minutes is [tex]30^'=(\frac{30}{60})^\circ[/tex] of degree.
30 arc minutes is [tex]30^'=(\frac{1}{2})^\circ[/tex] of degree.
Which clearly means,
[tex]1^\circ>(\frac{1}{2})^\circ[/tex]
[tex]1^\circ>30^'[/tex]
Therefore, The given statement is true.
'A degree is larger than 30 arc minutes'.
Complete y^2+15y+56=(y+7)(y+?) ...?
y² + 15y + 56 = (y + 7)(y + a)
y² + 15y + 56 = y² + (7 + a)y + 7a
We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.
15 = 7 + a; a = 8
OR
56 = 7a; a = 8
Second factor is (y + 8)
what is the largest perfect square of 45? ...?
The largest perfect square less than or equal to 45 is 36, which is the square of 6. Squaring numbers less than 7 shows that 36 is the perfect square closest to, but not exceeding 45.
Explanation:The largest perfect square that is less than or equal to 45 is the result of the greatest integer squared that does not exceed 45. To find this, you would look for the highest whole number whose square is less than or equal to 45. The numbers less than 45 are 1, 2, 3, ..., and so on. Squaring these: 12=1, 22=4, 32=9, 42=16, 52=25, 62=36. The next number, 7, squared is 49, which is greater than 45. Therefore, 62=36 is the largest perfect square less than or equal to 45. This concept is essential when simplifying square roots or in problems dealing with areas of squares.on a number line: What does a closed circle mean and what does an open circle mean?
On a number line, closed circle on a point indicates that point is also included and the open circle indicates that point is not included.
What is a Number Line?Number lines are represented as straight lines drawn horizontally on which integers are written in equal intervals.
This line is extended to infinity on both sides.
Number line includes positive numbers, zero and negative numbers.
Closed circles and open circles are used in number line to represent linear inequalities in one variable.
Let 'n' be any number on the number line.
We use open circles on 'n' to denote inequalities like x < n and x > n.
We use closed circles on 'n' to denote inequalities like x ≤ n and x ≥ n.
Hence, open circles are used to numbers which are greater than or less than ( > or < ) and closed circles are used to numbers which are greater than or equal to and less than or equal to ( ≥ or ≤ ).
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Factor the expression.
x^2 -12x +36 =
I really need help and no one will help..!
solve each system by substitution. explain step by step
r + s = -12
4r - 6s = 12