Proposition: Suppose n ∈ Z (n is an integer). If n^2 is not divisible by 4, then n is not even.
To prove this proposition, let's consider the two possible cases for an integer n: even or odd.
1. If n is even, then n = 2k, where k is an integer. In this case, n^2 = (2k)^2 = 4k^2. Since 4k^2 is a multiple of 4, n^2 is divisible by 4.
2. If n is odd, then n = 2k + 1, where k is an integer. In this case, n^2 = (2k + 1)^2 = 4k^2 + 4k + 1. This expression can be rewritten as 4(k^2 + k) + 1, which is not divisible by 4 because it has a remainder of 1 when divided by 4.
Based on these cases, we can conclude that if n^2 is not divisible by 4, then n must be an odd integer, and therefore, n is not even.
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ayuda por favor!!!!!!!!!!!!
La solución de la ecuación de valores absolutos es x = - 1 y la solución de la inecuación de valores absolutos es x ≥ 9/2 ∨ x ≤ 3.
¿Cómo resolver ecuaciones e inecuaciones de valores absolutos por medios algebraicos?
En esta pregunta debemos resolver una ecuación de valores absolutos y una inecuación de valores absolutos, cuya resolución requiere la aplicación de la definición de valor absoluto y procedimientos algebraicos:
|3 x - 1| = |3 · x + 7|
[tex]\left|\frac{3\cdot x - 1}{3\cdot x + 7} \right| = 1[/tex]
Por definición de valor absoluto:
[tex]\frac{3\cdot x - 1}{3\cdot x + 7} = 1\,\lor\,-\frac{3\cdot x - 1}{3\cdot x + 7} = 1[/tex]
[tex]3\cdot x - 1 = 3\cdot x + 7\,\lor \,- 3\cdot x + 1 = 3\cdot x + 7[/tex]
[tex]NaN \,\lor \, 6\cdot x = -6[/tex]
x = - 1
|4 · x + 3| ≤ 15
Por definición de valor absoluto:
- 4 · x + 3 ≥ - 15 ∨ 4 · x + 3 ≤ 15
- 4 · x ≥ - 18 ∨ 4 · x ≤ 12
x ≥ 9/2 ∨ x ≤ 3
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A group of friends wants to go to the amusement park. They have no more
than $325 to spend on parking and admission. Parking is $11, and tickets cost
$39.25 per person, including tax.
Considering the definition of an inequality, the number of friends admitted must be less than or equal to 8, expressed as p ≤ 8
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A group of friends have no more than $325 to spend on parking and admission. Parking is $11Tickets cost $39.25 per person, including tax.Being "p" the maximum number of people who can go to the amusement park, the inequality that expresses the previous relationship is
39.25 p + 11 ≤ 325
Solving:
39.25 p ≤ 325 -11
39.25 p ≤ 314
p ≤ 314÷ 39.25
p ≤ 8
Finally, the number of friends admitted must be less than or equal to 8, expressed as p ≤ 8
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This is confusing someone help please
Answer:
Below in BOLD.
Step-by-step explanation:
5x^2 - 6x - 2 = 0
Quadratic formula for ax^2 + bx + c = 0 is
x = [-b ± √(b^2 - 4ac)]/ 2a
Here we have a = 5, b = -6 and c = -2
so x = [-(-6) ± √((-6)^2 - 4*5*-2)]/ 2*5
= [ 6 ± √(36 + 40)] / 10
= 0.6 ± √76 / 10
= 0.6 ± 0.8718
= 1.4718, -0.2718
= 1.5, -0.3 to one decimal place.
x^2 + 3x = 40
x^2 + 3x - 40 = 0
We can factor this one:
(x - 5)(x + 8) = 0
x - 5 = 0 giving x = 5 and
x + 8 = 0 giving x = -8.
Answer x = -8, 5.
The angle measurements in the diagram are represented by the following expressions.
The angle measurements of angle B as represented in the diagram shown is 150°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the diagram:
∠A = ∠B (alternate interior angles)
Hence:
8x - 10 = 3x + 90
x = 20
∠B = 3(20) + 90 = 150°
The angle measurements of angle B as represented in the diagram shown is 150°
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iteration-Find the first 3 iterates of the function look at pic pls help!!!!!
The first 3 iterates of the function are D. 3, -3, 9.
How to calculate the value?The function given is:
f(x) = -2x + 3
= -2(0) + 3
= 3
When x = 3
f(x) = -2x + 3
= -2(3) + 3
= -6 + 3
= -3
When x = -3
f(x) = -2x + 3
= -2(-3) + 3
= 9
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Which triangle is a translation of triangle P?
(X+m)(c+n) if m=5 and n=-7
Answer: -7/5
Step-by-step explanation:
x = - 5cm^2 - 7m^2 + 35/ m (5c - 7), C = (cross out the equal sign) 7/5 and m = (cross out the equal sign) 0 and n = -7/5
what's y=1/4x-4 on a graph? please helppppppp!!!!
Answer:
Please see attachment.
Step-by-step explanation:
Remember, the 1/4x is the slope, and the -4 is the y-intercept.
Please see attachment for the graph.
Hope this helps!
The school canteen charges rs. 15for lunch and rs. 5for milk for each day.how much money do you spend in 6 dayson these things?also, mention the property of whole numbers that have been used.
120Rs is spend in 6 days on these things and distributive property is used
Properties of whole numbers are defined to operate basic arithmetic operations such as addition and multiplication, in an easy way. Applying these properties helps us to solve such math problems quickly, without even using calculators. These properties are almost similar to the properties of integers, although the definition for whole numbers and integers are different.
Total cost of a single day= 15 + 5 = 20Rs
∴ In 6 days total cost = 20 x 6 = 120Rs
Thus 120Rs is spend in 6 days on these things and distributive property is used.
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Carlos found that the length of the diagonal of his laptop monitor is . If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal
The size of the monitor as measured by the diagonal to the nearest whole inch, 17 inch.
What is square root?A number's square root is a quantity that, when multiplied by itself, yields the original quantity. There are two ways to calculate the square root of a number: method of prime factorization and division strategy.
For example, both 3 and –3 are square roots of 9
The length of the diagonal of his laptop monitor is squared root of 290
Let 'D' be the diagonal of the monitor.
The,
Diagonal = √290
Use long division method to solve the value,(attached in the file)
√290 = 17.029
= 17.03
Therefore, the value of √290 rounds to the nearest whole inch is 17 inch.
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The correct question is -
Carlos found that the length of the diagonal of his laptop monitor is squared root of 290. If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal? 12 17 97 245
ASAP PLEASE I NEED YouR HELP
Subtract − 4 b 2 + 4 b − 4 from 3 b 2 + 2 b − 5 .
Step-by-step explanation:
I assume the question really looks like
-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.
so,
3b² + 2b - 5 - (-4b² + 4b - 4) =
= 3b² + 2b - 5 + 4b² - 4b + 4 =
= 7b² - 2b - 1
Find the nth term of the sequence 4, 7, 10, 13, …
Answer:
3n+1
Step-by-step explanation:
Subtract one from all the values, you get multiples of 3 in the equation 3n=nth term
So when you add one back, your equation is 3n+1=nth term
What is the range of the function f(x) = 6x – 2 over the interval of 3 < x ≤ 8
The range of f(x) = 6x – 2 is [16,46]
According to the statement
we have given the function f(x) = 6x – 2 and the given interval is 3 < x ≤ 8
we know that to find the range of function we have to fill the values in it and then find the range of this function.
So, range is basically a difference between the lowest and the highest value.
Here the given function is f(x) = 6x – 2
when f(3) then
f(3) = 18-2
f(3) = 16.
and when f(8) then
f(8) = 48-2
f(8) = 46.
after put the values we seen that the range of this function is 16,46.
So, The range of f(x) = 6x – 2 is [16,46]
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Answer is :
16 and 46Step-by-step explanation:
Given function
[tex]\sf f(x) = 6x - 2 [/tex]
We need to the find the range of the function over the interval of 3 < x ≤ 8
When, x is 3
Put x = 3 in the given function,
[tex]\sf f(3) = 6(3) +2 [/tex]
[tex]\sf f(3) = 18 - 2 [/tex]
[tex]\sf f(3) = 16 [/tex]
when, x is 8
Put x in the given function,
[tex]\sf f(8) = 6(8) -2 [/tex]
[tex]\sf f(8) = 48 - 2 [/tex]
[tex]\sf f(8) = 46 [/tex]
Hence range of the function f(x) = 6x – 2 is 16 and 46.
Call line that passes through the point x, y with a y intercept of b and a slope of m can be represented by the equation y=mx + b. a line is drawn on the coordinate plane that passes through the .3, -6 and has a slope of four the y-intercept of the line is
Answer: (0, -7.2)
Step-by-step explanation:
Substituting into point-slope form, the equation is
[tex]y+6=4(x-0.3)[/tex]
The y-intercept is when x=0, so substituting in x=0,
[tex]y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2[/tex]
So, the y-intercept is (0, -7.2).
The angle measurements in the diagram are represented by the following expressions.
Answer:
X = 12
<B = 45°
Explanation:
From the diagram above:
Alternate exterior angles are equal. Therefore,
[tex]5x - 15 = 2x + 21 \\ collecting \: liketerms \\ 5x - 2x = 21 \: + 15 \\ 3x = 36 \\ dividing \: bothsides \: by \: 3 \\ \frac{3x}{3} = \frac{36}{3} \\ x = 12 [/tex]
For the measure of angle B
2x + 21°
2(12) + 21 = 24 + 21 = 45
Measure of angle B = 45°
What’s 1/6 to 3 dp does anyone know?
❄ Hi there,
[tex]\sf{\dfrac{1}{6}\approx0.167}[/tex], rounded to 3 DP (decimal places)
[tex]\left\vert\textsf{Decimal Places = Number of digits after the decimal point}\vert[/tex]
Why round? Because the entire number goes on for ever and ever.
So, we need to round. 1/6 rounded to 3 decimal places is 0.167. We have 3 numbers after the decimal point.
❄
The red blood cell counts for a population of adult males can be approximated by a normal distribution with a mean of 5.3 million cells per microliter and a standard deviation of 0.3 million cells per microliter what is the minimum red blood cells count that can be in the top 28% of accounts
The minimum red blood cells count that can be in the top 28% of accounts is 5.61%.
Red blood cells, also called crimson cells, purple blood corpuscles, haematids, erythroid cells, or erythrocytes, are the maximum common type of blood cells and the vertebrate's primary approach of delivering oxygen to the body tissues thru blood drift thru the circulatory device.
A low RBC depends, also called anemia, can have an effect on the frame's capability to transport oxygen and vitamins around the cardiovascular machine. it may reason fatigue, dizziness, and heart palpitations. The maximum not unusual form of anemia is iron deficiency anemia. this can result from blood loss, malnutrition, or kidney problems.
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A wall shaped like a trapezoid needs to be painted. The height of the wall is 16 feet and the bases are 20 feet and 24 feet. If one can of paint covers 20 square feet, how many whole cans of paint will the painter need to buy to paint the wall with one coat
Answer:
18 cans
Step-by-step explanation:
The number of cans of paint will be the least integer greater than or equal to the number required to cover the area of the trapezoid.
Area of a trapezoidThe area of the wall is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the bases, and h is the height.
We are given the values b1=20 ft, b2=24 ft, h=16 ft, so the area is found to be ...
A = 1/2(20 ft +24 ft)(16 ft) = 352 ft² . . . . . area of the wall
Cans of paintEach can of paint covers 20 ft², so n cans of paint will cover 20n square feet. We want to find the minimum integer value of n that satisfies ...
20n ≥ 352
n ≥ 17.6 . . . . . . . . . divide by 20
The next larger integer is 18.
The painter will need to buy 18 cans of paint.
3. A gardener uses 2 packages of lettuce seeds for 3 garden rows, each 5 feet long. How many packages of seeds does the gardener need to plant 45 feet of lettuce rows? Use the table to help.
Seeds (pkg) 2,4
Lettuce (rows) 3, 6
A 27
B 16
C 6
D 80
I need this with explanation please:(
Answer:
C) 6
Step-by-step explanation:
3 garden rows = 3*5 = 15 feet
we know we need 2 packages per each 15 feet
45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages
Select the interval where g is negative.
Choose 1 answer:
A)0B)2C)3
Answer:
A). 0
Step-by-step explanation:
If you look at the graph, you can see that the only time it passes through the X- Axis is at (0, -20). Therefore, the solution to y=g(x) where g is negative, would be 0.
How do we combine like terms with negative coefficients
5n+6+(-7n)
Answer:
- 2n + 6
Step-by-step explanation:
note that + (-) = -
5n + 6 + (- 7n)
= 5n + 6 - 7n ← collect like terms
= 5n - 7n + 6
= - 2n + 6
f(x) = x^2 + 4x + 20 find the real roots. take your time if you want :)
Answer:
No real roots
[tex]x = -2 + 4i, x = -2 - 4i[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the Quadratic Formula.
Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Given our Equation: [tex]f(x) = x^2 + 4x + 20[/tex]
a = 1b = 4c = 20Set the equation to 0 and solve using the formula.
Solve[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-4\pm\sqrt{4^2 - 4(1)(20)}}{2(1)}[/tex][tex]x = \frac{-4\pm\sqrt{16 - 80}}{2}[/tex][tex]x = \frac{-4\pm\sqrt{-64}}{2}[/tex][tex]x = \frac{-4\pm8i}{2}[/tex][tex]x = -2 + 4i, x = -2 - 4i[/tex]There are no real roots to the quadratic.
Gerri purchases a coupon book with discounts for her favorite coffee shop. every coupon for the coffee shop offers the same discount. the table shows her total savings, y, based on the number of coupons, x, used from the book. a table showing coffee shop coupon savings with 2 columns and 6 rows. the first column, x, has the entries, 0, 5, 10, 15, 20. the second column, y, has the entries. negative 20, negative 10, 0, 10, 20.
Slope 2 and y intercept is 10
The question seems to be incomplete and complete and the complete question is shown in the image
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases.
When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.
Y-intercept is the point at which the line intersects the y axis- meaning x = 0
From the table y = -20 when x= 0
y-intercept: -20
To find the slope
m = ΔY/ΔX
m = -20+10/0-5 = 2
Hence the slope is 2 and y intercept is 10
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A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. josh decides to make the house addition smaller, and he changes the scale of the drawing to 1 in. = 1.1 ft. what is the change in the scale factor from the old scale to the new scale? one-third two-thirds 2.2 3
3 is the scale factor that was changed from the previous scale to the new scale.
What is the scale factor?
The scale factor is a way to compare figures that appear to be similar but actually have distinct scales or measurements. Let's say two circles have similar appearances but different radii. A figure's scale factor indicates how much larger or smaller it is than the original figure.
What is the change in the scale factor?
A scale drawing is a condensed representation of an original image, structure, or object in terms of dimensions. The scale drawing is typically shrunk at a fixed dimension.
The change in the scale factor = larger scale / smaller scale
3.3 / 1.1 = 3
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Answer: 3
Step-by-step explanation:
Find the area of each figure as described or shown. Write final answer on blank provided. Show work. Include units as part of your answer. If needed, round answer to 2 decimal places.
Answer:
482.84u², 42.5cm², 51.5ft²
Step-by-step explanation:
1) A = 2(1 + √2)a²
A = 2(1 + √2)(80 / 8)²
A = 482.84units²
2) Square = 5²
Square = 25
T1 = 3 x 5 / 2
T1 = 7.5
T2 = 4 x 5 / 2
T2 = 10
Total = 10 + 7.5 + 25
Total = 42.5cm²
3) Rect = 4(8 + 3)
Rect = 44
T1 = 2 x 3 / 2
T1 = 3
T2 = 3 x 3 / 2
T2 = 4.5
Total = 3 + 4.5 + 44
Total = 51.5ft²
Я
1
Which expression is equivalent to
O
зарко
2,²
345
Зарка
2,²
3x4
44
948
Answer:
I'm sorry mate for helping for nothing but i just need more points to post my question. I am really sorry.
Draw a line segment of length 6.4 cm and divide it in to 4 equal parts.
Write the length of each part.
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The line segment has a length of 6.4 cm. Hence:
Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
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What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
The possible length of the third hallway is between 30 yards and 150 yards.
How to find the third length of a triangle?The hallway forms a triangle .
Therefore, using triangle inequality theorem, It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Hence,
90 + 60 > x
Where
x is the third side
x + 60 > 90
x + 90 > 60
Therefore, the possible length of the third hallway is between 30 yards and 150 yards.
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Answer:
D: between 30 yards and 150 yards
Which of the following shows the power of a power property
Answer: MULTIPLYING THE EXPONENTS!!!
Step-by-step explanation:
Mark me brainliest
0.00000007 as a fraction
Answer:
7/100000000
Step-by-step explanation:
to find this out we can start by saying that 0.7 is 7/10
every 0 in front of 7 after that is adding another 0 to 10
so
0.07 is 7/100
0.00000007 is 7/100000000