Why is the sum of three consecutive even integers always a multiple of 3
Answer:
Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6 = 108.
Evaluate the function.
ƒ(x) = 2x + 1
f(x) = 7
Answer:
Read below
Step-by-step explanation:
Step 1: Multiply 2 by x: 2x
Step 2: Add 1 to 2x: 2x + 1
Step 3: Substitute x with 7: 2(7) + 1
Step 4: Multiply 2 by 7: 14 + 1
Step 5: Add 1 to 14: 14 + 1 = 15
Can someone please help my daughter. It's on a timer so she has 10 minutes left. No links people no links no links. The question is in the picture. It's the question Number 2.
Answer: 108° ; 165°
Step-by-step explanation:
180(n - 2) is the formula to figure out the total degrees in a polygon.
A pentagon has 5 sides, so:
180(5-2) = 180(3) = 540°
Divide the total degrees by the number of angles (a pentagon has 5 angles):
540° ÷ 5 = 108°
24-gon:
180(24 - 2) = 180(22) = 3960°
3960° ÷ 24 = 165°
Answer: 108° ; 165°
Step-by-step explanation:
180(n - 2) is the formula to figure out the total degrees in a polygon.
A pentagon has 5 sides, so:
180(5-2) = 180(3) = 540°
Divide the total degrees by the number of angles (a pentagon has 5 angles):
540° ÷ 5 = 108°
24-gon:
180(24 - 2) = 180(22) = 3960°
3960° ÷ 24 = 165°
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Four points are drawn on the coordinate plane and connected with straight lines to form a rectangle. Three of the
vertices of the rectangle are located at (2, 1), (2,4), and (-4,4).
a. What are the coordinates of the fourth vertex of the rectangle?
b. What are the dimensions of the rectangle?
c. What is the area of the rectangle?
Answer:
Step-by-step explanation:
the two diagonals of a rectangle have the same middle point
middle point
x = (2-4)/2 = -1
y = (1+4)/2 = 5/2
The diagonal BD must have the same middle point, so we can find vertex D in this way
(x +2)/2 = -1
x+2 = -2
x = -4
(y+4)/2 = 5/2
y+4 = 5
y = 1
fourth vertex : (-4, 1)
2) for find the first dimension we can use this formula
|y2 - y1| = |4-1| = 3
for find the second we can use this one:
|x2-x1| = |-4-2| = |-6| = 6 (a dimension can’t be negative)
3)
A = dimension 1 x dimension 2 = 3 x 6 = 18
Answer:they for it right
Step-by-step explanation:
....
Hi!
ik -2x+9 is x=4.5 so are the number 4.5 apart and if so what do i do after that
The function y = -2x + 9 have ordered pairs (-4, 17), (-2, 13), (0, 9), (2, 5) and (4, 1)
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Given that:
y = -2x + 9
When x = -2; y = -2(-2) + 9 = 13
When x = 0; y = -2(0) + 9 = 9
When x = 2; y = -2(2) + 9 = 5
When x = 4; y = -2(4) + 9 = 1
The function y = -2x + 9 is a linear equation
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What is 5 1/4 as a single fraction greater than 1
Answer:
21/4
Step-by-step explanation:
(5 * 4) + 1
20 + 1
21/4
Find the ratio of the volume of the cone to the volume of the cylinder. Express your answer as a common fraction.
The ratio of the volume of the cone to the cylinder is 1:3.
A cone has a circular base and the base is made of a radius and diameter.
The volume of a cone is defined as the amount of space a cone occupies. The formula of the volume of a cone is given as one-third the product of the area of the circular base and the height of the cone. If the radius of the cone is "r" and the height is "h", the volume of a cone is given as V = (1/3)πr²h.A cylinder is a three-dimensional solid shape that makes of two parallel bases linked by a curved surface.
Thus, the volume (V1) of a right circular cylinder, using the above formula, is,V1= πr²h
Here,
'r' is the radius of the cylinder
'h' is the height of the cylinder
π is a constant whose value is 22/7.
The ratio of the volume of the cone to the cylinder is
= (1/3)πr²h : πr²h
= 1 : 3
So, the ratio is - 1:3.
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What is numerical coefficient in 3xy?
The numerical coefficient in 3xy is 3.
In algebraic expressions, terms are made up of coefficients and variables. A coefficient is a numerical value that multiplies a variable or a set of variables. In the term 3xy, the numerical coefficient is the number that appears in front of the variable (x and y) and it's 3 in this case.
It is used to indicate the degree of the term or the number of times the variable is present in the term. In this case, it is indicating that the variable x and y are present three times in the term.
It's important to note that if there is no coefficient before the variable, it is assumed to be 1. It's also noteworthy that the coefficient can be a whole number, a fraction, or even a variable, but in this case it is a whole number. Understanding the concept of coefficient is very important in understanding algebraic equations and expressions.
The numerical coefficient in 3xy is 3.
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Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of % in hr
The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.
How to illustrate the expression?From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.
An expression have at least two terms which have to be related by through an operator.
Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:
2 - (25% × h)
= 2 - 0.25h
h = number of hours.
The expression is 2 - 0.25h.
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Complete question
Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression
In a poll, 411 students voted. Nominee C received 2 3 of the votes. How many votes did Nominee C receive?
Answer: 274 votes
Step-by-step explanation:
Since we are informed that in a a poll that 411 students voted and Nominee C received ⅔ of the votes.
Therefore, the number of votes that Nominee C received will be:
= ⅔ × 411
= 274
Therefore, Nominee C got 274 votes
Please help!!! This is WAY overdue and I need to submit it by tonight or it won't be accepted!!!!
Answer:
D
Step-by-step explanation:
It's the most logical of them all, it can't be A, it wouldn't make sense if it's C, and for D it says 6 if -5<x<-1 and it has the little line on 6 for y, it sounds a little complicated but that's my logic
Trina is the age of her grandfather, less 5 years. Their combined age is 95 years. How old is Trina? How old is her grandfather?
Answer:
Trina is 45 years old.
Her grandfather is 50 years old.
Step-by-step explanation:
Trina is 5 years younger than grandfather, therefore:
45+50 = 95
Jane spent $40 on flowers. Each small flower cost $2, and each large flower cost $3. Write an equation that describes the relationship between cost and number of flowers purchased, where X is the number of small flowers and Y is the number of large flowers.
Answer:
Step-by-step explanation:
he small ones cost $2 and the bigger ones cost $3. So to get the answer you will need to multiply the number of flowers with the cost. In this case 2 times x and 3 times y. x represents the small flowers and y represents the big flowers.
Answer:
2x + 3y = 40
Step-by-step explanation:
to simplify the expression 3+5×3-8÷4
Answer:
f) 5x 3
Step-by-step explanation:
You do multiplication first
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What is a minimum of 3 examples of polynomials?
Answer:
4x + 3
10x² - 7x + 3
18x² - x + 5
Step-by-step explanation:
A polynomial must consist of 2 terms, one with a variable ( x ) and one as a constant ( any number )
An example of a number with a variable is 4x
An example of a constant is 3
add the two together 4x + 3 and you get a polynomial
More examples are 5x + 9 or -2x - 8
Polynomials can have more than 2 terms. ( the third term has an exponent and variable )
An example of a polynomial with more than 2 terms is 10x² - 7x + 3
Here are the first 4 terms of a sequence.
85 81 77 73
a) (i) Write down the next term in the sequence.
(ii) Explain how you got your answer.
b) Work out the 10th term of the sequence.
Answer:
a) (i) Next term = 69a) (ii) Subtract 4 from each term to get the next term. For example, 85-4 = 81 and 81-4 = 77, and so on.b) The 10th term is 49 The work for part (b) is shown in the next section below.==================================
a1 = 85 = first term
d = -4 = common difference
an = a1 + d(n-1)
an = 85 - 4(n-1)
an = 85 - 4n + 4
an = -4n+89
a10 = -4*10+89
a10 = 49 is the tenth term
What is the length of EH
Answer:
It could be 3x - 3
Step-by-step explanation:
What is == and === in Python?
The == operator determines if two operands are equivalent in terms of value. The === operator determines if two operands are equivalent in terms of value and datatype.
The assignment operator = is straightforward. The left side operand receives values from the right side operands.
On the other hand, == determines whether or not the values of two operands are equal.
The Python is operator determines if two variables point to the same memory item as opposed to the == operator, which compares the value or equality of two objects. This implies that you should almost always employ the equality operators == and != Difference between == and = in Python.
A single equal sign is used to assign a value to a variable in Python and many other programming languages, whereas two successive equal signs are used to determine if two expressions provide the same result.
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HELP!! Find the value of… (picture)
Answer:
C. 94
Step-by-step explanation:
|A| = [tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
det(A) = a * [tex]\left[\begin{array}{ccc}e&f\\h&i\\\end{array}\right][/tex] - b * [tex]\left[\begin{array}{ccc}d&f\\g&i\\\end{array}\right][/tex] + c * [tex]\left[\begin{array}{ccc}d&e\\g&h\\\end{array}\right][/tex]
OR
det(A) = aei - afh - bdi + bfg + cdh - ceg
|A| = [tex]\left[\begin{array}{ccc}-2&-2&-5\\2&7&-3\\8&9&9\end{array}\right][/tex]
det(A) = -2 * [tex]\left[\begin{array}{ccc}7&-3\\9&9\\\end{array}\right][/tex] - (-2) * [tex]\left[\begin{array}{ccc}2&-3\\8&9\\\end{array}\right][/tex] + (-5) * [tex]\left[\begin{array}{ccc}2&7\\8&9\\\end{array}\right][/tex]
OR
det(A) = (-2)(7)(9) - (-2)(-3)(9) - (-2)(2)(9) + (-2)(-3)(8) + (-5)(2)(9) - (-5)(7)(8)
det(A) = 94
The distance from Earth to the moon is 384,400 kilometers. What is this distance expressed in scientific notation?
Answer:
3.844 x 10 to the power of 5 is the answer i think
Step-by-step explanation:
Answer:
If the other person is correct then it should be 3.844 x 10^5 and 3.844E5 as well
Step-by-step explanation:
Jacqueline is buying grapes and apples from the Walmart produce section. Grapes are $3
per pound and apples are $4 per pound. Jacqueline’s mother gave her $20 to spend. To
determine the combinations of grapes and apples that she can afford to purchase,
Jacqueline wrote the inequality 3 + 4 ≤ 20.
1. Define the variables Jacqueline used based on the context.
Let represent _______________________________________________.
Let represent _______________________________________________.
2. Explain why the inequality sign ≤ makes sense in this context.
3. Graph the inequality 3 + 4 ≤20.
4.The ordered pair (3, −4) is a solution to the inequality 3 + 4 ≤ 20.
Explain why
this is not a viable solution in the context of buying grapes and apples.
5. The ordered pair (4, 2) is a point on the boundary line. Explain what the ordered
pair represents in the situation.
Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c: ordered pair (3, −4) isn't solution.
What is inequality, exactly?An unbalanced connection between two expressions or values is referred to in mathematics as an inequality. So, inequity results from imbalance. In mathematics, an inequality defines the connection between two non-equal quantities. Egality and inequality do not mean the same thing. Use the not equal sign whenever two values are not equal (). It is possible to compare values of any size using a variety of inequalities. By changing both sides until only the variables are left, it is possible to solve many straightforward inequality problems.
Here,
Given : 3x + 4y ≤ 20.
where x is the no of apples
and y is the no of grapes
Thus,
Part a:
where x is the no of apples
and y is the no of grapes
Part b:
Inequality signs means that 20 will be the maximum amount of the no of apples and no of grapes summation.
Part c: ordered pair (3, −4)
Thus,
putting in the inequality we find:
=> 3(-3)+ 4(-4)
=> -6 -16
=> -22
Thus , it is not a solution for inequality.
Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c: ordered pair (3, −4) isn't solution.
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Solve for x and show work. Round to the tenths place.
Given the line y = − 2 5 x + 3, determine if the given line is parallel, perpendicular, or neither. Select the correct answer for each lettered part. A. y = 2 5 x + 7 A Parallel B Perpendicular C Neither B. 5y + 2x = −10 A Parallel B Perpendicular C Neither C. −5x + 2y = 4 A Parallel B Perpendicular C Neither
Answer:
(a) Neither
(a) Perpemdicular
Step-by-step explanation:
Required
Determine the relationship between given lines
(a)
[tex]y = -\frac{2}{5}x + 3[/tex]
and
[tex]y = \frac{2}{5}x + 7[/tex]
An equation written in form: [tex]y=mx + b[/tex] has the slope:
[tex]m \to slope[/tex]
So, in both equations:
[tex]m_1 = -\frac{2}{5}[/tex]
[tex]m_2 = \frac{2}{5}[/tex]
For both lines to be parallel
[tex]m_1 = m_2[/tex]
This is false in this case, because:
[tex]-\frac{2}{5} \ne \frac{2}{5}[/tex]
For both lines to be perpendicular
[tex]m_1 * m_2 = -1[/tex]
This is false in this case, because:
[tex]-\frac{2}{5} * \frac{2}{5} \ne -1[/tex]
(b)
[tex]5y + 2x = -10[/tex]
and
[tex]-5x + 2y = 4[/tex]
Write equations in form: [tex]y=mx + b[/tex]
[tex]5y + 2x = -10[/tex]
[tex]5y = -2x +10[/tex]
Divide by 5
[tex]y = -\frac{2}{5}x +2[/tex]
[tex]-5x + 2y = 4[/tex]
[tex]2y = 5x + 4[/tex]
Divide by 2
[tex]y = \frac{5}{2}x + 2[/tex]
In both equations:
[tex]m_1 = -\frac{2}{5}[/tex]
[tex]m_2 = \frac{5}{2}[/tex]
For both lines to be parallel
[tex]m_1 = m_2[/tex]
This is false in this case, because:
[tex]-\frac{2}{5} \ne \frac{5}{2}[/tex]
For both lines to be perpendicular
[tex]m_1 * m_2 = -1[/tex]
This is true in this case, because:
[tex]-\frac{2}{5} * \frac{5}{2} = -1[/tex]
Cancel out 2 and 5
[tex]-1 = -1[/tex]
Can you Please help me
Answer: 290 yd^2
Step-by-step explanation:
Tip: split the shapes into areas that are easier to compute
Rectangle 1 = bh = 10yd x 28 yd = 280 yd^2
Rectangle 2 = bh = 2yd x (10-5)yd = 10 yd^2
280 yd^2 + 10 yd^2 = 290 yd^2
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Answer:
d. Atlantic Ocean
Answer:
Atlantic Ocean
Water boils at 100 ° C 100°C100, degree, start text, C, end text. This is 400 % 400%400, percent more than my room's temperature.
Answer:
The temperature of the room is 25 degree Celsius
Step-by-step explanation:
The complete question is
Water boils at 100 ° C. This is 400 % percent more than my room's temperature. What is the temperature of room
Solution
Temperature at which water boils is 100 degree Celsius
Temperature of room is 400 % of X
[tex]100 = \frac{400}{100} * X\\100 = 4 * X\\X = \frac{100}{4} = 25[/tex]
Hence, the temperature of the room is 25 degree Celsius
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Use Distribute Property to rewrite the algebraic expression.
5(x - 10)
Answer here _________
The value of the expression using the distributive property is 5x + 50.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
5 (x - 10)
The distributive property of multiplication over addition states that,
a x (b + c) = a x b + a x c
Now,
5 (x - 10)
= 5x + 5 x 10
= 5x + 50
Thus,
The expresssion is 5x + 10
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Allison is comparing prices of different cell phones. She made a dot plot to show the prices. How can she find the most common price?
Answer:
The answer is "Find the tallest stack of dots".
Step-by-step explanation:
In this question, we assume that the prices of the plot area on the X (horizontal), and the Y (Vertical) axis are on the cell phone. This price is 90 dollars. Whenever the price is X1, she sets a dot there. When brand X2 is that price also, it places a coordinate point ($90, X2) well above point on either brand at the same price. Therefore, the bigger pile of teams overall that the rates are more mobile phones.
Which represents the solution set of 5(x+5) <85?
Ox< 12
O x> 12
O x < 18
O x> 18
Answer: O x<12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+25<85
Step 2: Subtract 25 from both sides.
5x+25−25<85−25
5x<60
Step 3: Divide both sides by 5.
5x/5 < 60/5
x<12