8 is not a perfect number as sum of its proper divisors is not equal to 8.
A perfect number is a positive integer that is equal to the sum of its proper divisors, which are the divisors of the number excluding the number itself. In other words, a perfect number is a number that can be written as the sum of its divisors, excluding itself.
For example, the number 6 is a perfect number because its divisors are 1, 2, and 3, and 1+2+3 = 6.
8 is not a perfect number because it is not equal to the sum of its proper divisors. The divisors of 8 are 1, 2, 4, and 8, and 1+2+4 = 7, which is less than 8.
Therefore, 8 is not a perfect number. To this date, only 49 known perfect numbers have been found, they are all even numbers and the largest known perfect number is 2^(74,207,281) − 1, it has over 22 million digits.
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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.
Find the value of X. Round to the nearest tenth HELP ASAP!!!!
Answer: 22.5
Step-by-step explanation:
[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]
Compare [tex]99![/tex] and [tex]50^{99}[/tex].
Hint: Identity [tex](a+b)(a-b)=a^2-b^2[/tex].
50^99 is greater than 99!
How to compare the numbers?The numbers are given as:
99! and 50^99
When the above numbers are estimated using a calculator, we have:
99! = 9.332622e+155
50^99 = 1.577722e+168
Next, we compare the exponents
168 and 155
168 is greater than 155
Hence, 50^99 is greater than 99!
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Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.
The cost of 2 chairs is = $30
The cost of 1 table = $60
Step-by-step explanation:
Let a table represent x
A chair represents y
4x + 3y = 225.......eq 1
3x + 4y = 195........eq 2
Use elimination method
x - y = 30
x= 30 + y...... Eq 3
Substitute the value of x into equation 1
4(30+ y) + 3y= 225
120 + 4y + 3y= 225
7y + 120= 225
7y= 225-120
7y= 105
y= 15
Substitute the value of y in eq 2
3x + 15 = 195
3x= 195-15
3x= 180
x= 60
Therefore, the cost of 2 chairs is 15 * 2= $30
The cost of 1 table = $60
Answer:
65
Step-by-step explanation:
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 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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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 of the following shows the power of a power property
Answer: MULTIPLYING THE EXPONENTS!!!
Step-by-step explanation:
Mark me brainliest
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
Compared to the graph of f(x) = x², the graph of g(x) = (x − 2)² +3
is the result of translating f(x)
Answer:
Vertical shift up 3
Horizontal shift to the right 2
Brainliest, please :)
Answer:
Step-by-step explanation:
f(x) is moved 2 units to the right followed by 3 units up,
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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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
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:
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
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.
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.
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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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
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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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.
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
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).
Help me with alg 2 please!
The probability that 5 boys would be selected would be 5/6720
How to determine the probabilityFrom the information given, the probability can be calculated using permutation
The formula for permutation is given as;
Permutation = [tex]\frac{n!}{n - r!}[/tex]
Where;
n is number of sets = 8r is the number of objects selected = 5Substitute the values into the formula
Permutation = [tex]\frac{8!}{8 - 5!}[/tex] = [tex]\frac{8!}{3!}[/tex] = [tex]\frac{40, 320}{6}[/tex] = 6720
The probability that 5 boys would be selected is 5/6720
Thus, the probability that 5 boys would be selected would be 5/6720
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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.
❄
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
Rewrite each equation in factored form and solve using zero product property. Find the solutions of each equation. Use the notes about r * k = c and r + k = b. In the first problem c is 6 and b is -7. So you need the same r and k that multiply to be 6 but also add to be -7. The numbers you find will be the solutions
The factored form of the equation are as follows;
(d - 6)(d - 1) = 0(x + 9)(x + 9) = 0(u + 12)(u - 5) = 0How to write equation in factored form?Converting a quadratic function to factored form is called factoring.
Therefore,
let's factor the equation,
a.
d² - 7d + 6 = 0
d² - d - 6d + 6 = 0
d(d - 1) - 6(d - 1) = 0
(d - 6)(d - 1) = 0
b.
x² + 18x + 81 = 0
x² + 9x + 9x + 81 = 0
x(x + 9) + 9(x + 9) = 0
(x + 9)(x + 9) = 0
c.
u² + 7u - 60 = 0
u² - 5u + 12u - 60 = 0
u(u - 5) 12(u - 5) = 0
(u + 12)(u - 5) = 0
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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
can someone help me i know nothing about graphs
Answer:
The answer is B.
Step-by-step explanation:
The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.
if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.
if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.
(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