Answer:
The conjecture cannot work for any negative numbers, It works for x > 1.3.
Step-by-step explanation:
An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."
It only takes a counterexample to show the conjecture is incorrect.
x^5 -2 ?? x
(-2)^5 -2 ?? (-2)
-32 -2 ?? -2
-34 < -2 . . . . . . not greater than
As of 2016 New York City has a population of 8.55 million and a land area of 300 square miles. Manhattan is a section of New York City that has a land area of 23 square miles and a population of 1.64 million.
How much greater is the population density of Manhattan than that of New York City?
Answer:
42,804.35 million people per miles
Step-by-step explanation:
Population density = Number of people / Land area
New York
Population = 8.55 million
Land area = 300 square miles
Manhattan
Population = 1.64 million
Land Area = 23 Square miles
Population density of New York = Number of people / Land area
= 8.55 million / 300 Square miles
= 8,550,000 / 300
= 28,500 people per square miles
Population density of Manhattan = Number of people / Land area
= 1.64 million / 23 miles
= 1,640,000 / 23
= 71,304.35 million people per square miles
Difference between Manhattan and new York City = 71,304.35 - 28,500
= 42,804.35 million people per miles
Therefore,
The population density of Manhattan is greater than that of New York City by 42,804.35 million people per miles
The difference between the population densities of Manhattan and New York is 42,804 people per square mile.
The density of New York is:
= Population / Area
= 8,550,000 / 300
= 28,500 people per square mile
Density of Manhattan:
= 1,640,000 / 23
= 71,304 people per square mile
The difference is:
= 71,304 - 28,500
= 42,804 people per square mile
In conclusion, Manhattan's population density is 42,804 people per square mile higher than New York City's.
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What shape would you get if you cut off one of the corners of a rectangular prism?
Answer:
Different cuts can produce cross sections that are congruent to the base, a side, or even triangles if the cut is through the corner of a prism. A slice that is not parallel to the base and contains points from the four vertical edges of the prism reveals a parallelogram.
Step-by-step explanation:
hope this helps
Answer:
An irregular pentagonal prism
I know that this is a very tricky question: What is the value of 0 to the power 0?
Answer:
just 1
Step-by-step explanation:
It is easy, anything with the power of zero just equals to one
Answer:
1
Step-by-step explanation:
any number including 0 having power 0 will be equal to 1
Which fraction is equal to a whole number?
10/4
7/7
8/4
3/6
Answer:
Step-by-step explanation:
7/7 = 1 whole number
8/4 = 2 whole numbers
both equal to whole number
Mason loves collecting sea glass from the beach. He recorded the weight of each jar full of sea glass. If he decided to distribute the sea glass equally among the jars, how much would each jar weigh? pounds (Write mixed numbers as x y/z.)
The missing weights are:
2 2 2 1 11 12 12 2 24 22 24 3 37 22
Answer:
[tex]Average = 12\frac{4}{7} \ lb[/tex]
Step-by-step explanation:
Given
Weight of sea glass
To solve this question, we have to calculate the mean of the weight of the sea glass as follows;
[tex]Average = \frac{\sum x}{n}[/tex]
Where n = number of sea glass
[tex]n = 14[/tex]
So:
[tex]Average = \frac{\sum x}{n}[/tex] becomes
[tex]Average = \frac{2 +2 + 2 + 1 + 11 +12 +12 +2 +24+22 +24 +3 +37+ 22}{14}[/tex]
[tex]Average = \frac{176}{14}[/tex]
[tex]Average = 12\frac{8}{14}[/tex]
Simplify fraction
[tex]Average = 12\frac{4}{7}[/tex]
Hence; the weight of the sea glass would be [tex]12\frac{4}{7}\ lb[/tex] when evenly distributed...
Suppose you start at the origin, move along the x-axis a distance of 6 units in the positive direction, and then move downward along the z-axis a distance of 3 units. What are the coordinates of your position
Answer:
Coordinates are (x,y,z)= ( 6,0,-3)
Step-by-step explanation:
Because
X = +6units
Y= 0at origin
= -3 units negative because its downwards on the number line
please help ASAP, thank you!
Answer:
5
Step-by-step explanation:
i think
Answer:
The Answer is -5
Step-by-step explanation:
1. C=[tex]\frac{5}{9}[/tex](f-32)
2. Remove parenthesis
c=f−32
3. Add 32 to both sides
c+32=f
4. Switch the sides
f=c+32
Hope this helped!
Please help! x+25=100
Find the zeros of the function.
Enter the solutions from least to greatest.
h(x) = (-4x – 3)(x – 3)
lesser x =
greater x =
Answer:
x = -3/4 or x = 3
Step-by-step explanation:
Solve for x over the real numbers:
(-4 x - 3) (x - 3) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
-4 x - 3 = 0 or x - 3 = 0
Hint: | Look at the first equation: Divide both sides by the sign of the leading coefficient of -4 x - 3.
Multiply both sides by -1:
4 x + 3 = 0 or x - 3 = 0
Hint: | Isolate terms with x to the left hand side.
Subtract 3 from both sides:
4 x = -3 or x - 3 = 0
Hint: | Solve for x.
Divide both sides by 4:
x = -3/4 or x - 3 = 0
Hint: | Look at the second equation: Solve for x.
Add 3 to both sides:
Answer: x = -3/4 or x = 3
Answer:
lesser x = -3/4
greater x =3
Step-by-step explanation:
h(x) = (-4x – 3)(x – 3)
Set the function equal to zero to find the zeros
0 = (-4x – 3)(x – 3)
Using the zero product property
0 = (-4x – 3) 0=(x – 3)
Solve each equation
3 = -4x 3 =x
-3/4=x 3 =x
lesser x = -3/4
greater x =3
F(x-1) = (x-1)^2 + 3(x-1) - 2
Answer:
F(x−1)=x2+x−4
Explanation:
Substitute the given value into the function and evaluate.
How many multiples of 6 are greater than -25, but less than 25?
Answer:
8.
Step-by-step explanation:
They would be -24, -18, -12, -6, 6, 12, 18, 24.
What is 8/12k+3/12k=22?
Greetings from Brasil...
let's multiply both the 1st and 2nd members by 12k:
(8/12K) + (3/12K) = 22 x12K
8 + 3 = 264K
K = 11/264a store offers a 15% discount on all items in the storage on a cell All Star employee gets in the aditional 10% employee discount in the equation below C represents the cost of an item for an employee including tax and x represents the original price of the item
C=0.765x+0.06(0.765×)
Chris is an employee at the store. He plans to buy a coat during the sale. The price of the coat before the discount is 100$. How much will Chris pay for the coat during the sale? Remember,do not include the $ symbol.
Answer:
$81.09
Step-by-step explanation:
C=0.765(100)+0.06(0.765x100)
C=0.765(100)+0.06x76.5
C=0.765(100)+4.59
C=76.5+4.59
C=81.09
Question 1
Solve the equation. Enter only the number into the box below,
22
18+ X
Answer:
no cemma cuhydhfhhdhdhd
Triangle ABC is shown below. Triangle A B C is shown. The length of side A B is 2 x, the length of side B C is 4 x minus 10, and the length of side A C is 3 x minus 7. Angle A B C and B C A are congruent. What is the length of line segment AC? 7 9 14 18
The length of line segment AC of the given triangle is; 14
How to find the length of the line segment?Since Angle ABC and BCA are congruent, it means that they are equal.
An isosceles triangle is a triangle that has two equal sides and two equal base angles.
Now, since Angle ABC and BCA are equal, it means that the triangle is an isosceles triangle. It also means that sides AC and AB are equal. The expression becomes;
3x - 7 = 2x
3x - 2x = 7
x = 7
To determine the length of line segment AC. We will substitute x = 7 into 3x - 7. It becomes
(3 × 7) - 7
= 21 - 7 = 14
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What common error(s) did this student make? What is the correct solution for x? Please help
Answer:
10x - 5(x - 1) = 20
10x - 5x + 5 = 20
5x + 5 = 20
5x = 20 - 5
5x = 15
x = 15/5
x = 3
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
The first error was in the 2nd line: -5(x - 1) is -5x + 5, not -5x - 5 = 20.
Continuing the solution:
10x - 5x + 5 = 20
Combining like terms, we get
5x = 15, and so x = 3
is 7/18 rational or irrational
7/18 is a rational number. A rational number is one that may be expressed as a fraction or as a component of a whole number.
What is a rational number?
Any number that can be stated as a fraction or as a portion of an entire number is considered rational.
The given number in the problem is;
7/18
The number is in the form of p/q and the denominator value is greater than the numerator in fraction form, so that the given number is a rational number.
Hence,7/18 is a rational number.
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Liam's breakfast was an egg and cheese biscuit with a carton of milk. He spent a total of $5.65. Finn spent $7.65 on an egg and cheese biscuit and two cartons of milk. How much was an egg and cheese biscuit?
Answer:
An egg and cheese biscuit was $3.65.
Step-by-step explanation:
Liam's breakfast was:
[tex] P = E + C + M [/tex]
Where:
P: total price
E: egg
C: cheese biscuit
M: carton of milk
[tex] P = E + C + M [/tex]
[tex] 5.65 = E + C + M [/tex] (1)
Now, Finn's breakfast was:
[tex] P = E + C + 2*M [/tex]
[tex] 7.65 = E + C + 2*M [/tex] (2)
By subtracting equation (2) from (1) we have:
[tex] 7.65 - 5.65 = 2M - M [/tex]
[tex] M = 2 [/tex]
Hence, the price of a carton of milk is $2, so by entering this value into equation (1) we can find the price of an egg and cheese biscuit:
[tex] 5.65 = E + C + M [/tex]
[tex] 5.65 - 2 = E + C [/tex]
[tex] E + C = 3.65 [/tex]
Therefore, an egg and cheese biscuit was $3.65.
I hope it helps you!
What two properties are used in the following solution to 4b - 3 17?
4b-3 = 17
45-3+3 = 17+ 3
4b = 20
46 20
4-4
b = 5
A Addition Property of Equality and Division Property of Equality
B Subtraction Property of Equality and Addition Property of Equality
C Multiplication Property of Equality and Distributive Property
D Subtraction Property of Equality and Zero Product Property
h(t) = 4t+20 What is h(_____)=4?
Answer: -4
Step-by-step explanation:
For the function 4t + 20, the value of t is -4.
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
The given value of function h(t) = 4t + 20.
To find the value of t when h(t) = 4.
Substitute, h(t) 4.
4t + 20 = 4
4t = 4 - 20
4t = - 16
t = -4.
The required value of t is -4.
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Suppose it takes you 12 min to walk from home to school at a rate of 260 ft/min. Your friend lives closer to school than you do. Which inequality represents the distance d (in feet) that your friend lives from school? A. d 260 C. d > 3120 D. d < 3120
Answer:
The answer is d < 3120.
Step-by-step explanation:
Please help! This is for geometry
Which expression is equivalent to √ 24 ⋅ √ 2 in simplest form?
Answer:
4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
[tex]\sqrt{24}[/tex] × [tex]\sqrt{2}[/tex]
= [tex]\sqrt{48}[/tex]
= [tex]\sqrt{16(3)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex]
5/7 multiplied by 35
Answer:
25
Step-by-step explanation:
5 / 7 * 35
Cancel 35 by 7 since 7 * 5 = 35
Therefore, you get
5 * 5 = 25
Answer:
[tex] \frac{5}{7} \times 35[/tex]
[tex]divide \: the \: 7 \: from \: 35[/tex]
[tex]you \: will \: get \: 5[/tex]
[tex]now \: 5 \times 5 = 25[/tex]
ANSWER = 25
Hope this is correct and helpful
HAVE A GOOD DAY!
A rectangle has a length that is 8 less than its width, w. The perimeter is 52. Which equation can be used to determine its width?
if one root of the equation is 4x^2- 2x+p-4 be the reciprocal of other. then find the value of p
Answer:
p = 8
Step-by-step explanation:
Let one root of the eqn. be alpha . Other root is 1/alpha .
We know that product of both roots of an quadratic eqn. is c/a where "c" is the co-efficient of the constant & "a" is the co-efficient of x^2.
Here "c" is p-4 & "a" is 4. And the product of roots is 1 ( ∵ prdouct of a number and its reciprocal is 1 )
[tex]\frac{c}{a} = 1\\=> \frac{p - 4}{4} = 1\\=> p - 4 = 4\\=> p = 4 + 4 = 8[/tex]
what is x/-4 + 7 = 9
Answer:
[tex]x[/tex] = 8
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
x = 8
Hope it helps!
Maggie baked a berry pie. The recipe called for 6 ounces of blackberries, 9 ounces of raspberries, and 5 ounces of strawberries. In the supermarket, she only found 12-ounce containers of berries. She bought 1 container of each kind of berry. After she baked the pie, how many ounces of berries did Maggie have left?
Answer:
16 berries
Step-by-step explanation:
Blackberries: 12 - 6 = 6Raspberries: 12 - 9 = 3Strawberries: 12 - 5 = 7 Now we know how many individual berries will be left: 6 blackberries, 3 raspberries, and 7 strawberries.6 + 3 + 7 = 16Ethan buys dough to make fresh bread for his sandwich shop. He pays $11.55 for 25 ounces. What is Ethan's price per ounce of dough?
The cost of dough per ounce is $0.462.
How to calculate the cost per item?In order to calculate the cost of one item, divide the total cost of items by the total number of items.
It is also called the unit rate of that item.
The cost for 25 ounce dough of $11.55.
The price per ounce is equivalent to the unit rate given as,
Unit rate = Total cost ÷ Amount of dough
= 11.55 ÷ 25
= 0.462
Hence, Ethan's price per ounce of dough is $0.462.
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You install 404 feet of fencing along the perimeter of a rectangular yard.
The width of the yard is 100 feet. What is the length of the yard?
Answer:
The length of the yard is 102
Step-by-step explanation:
If the width of the yard is 100 feet, and it's a rectangular, that means the other side of the rectangle is also equal to 100 feet. So so far we have 200 feet of the yard covered. Then we do 404-200=204. So the combined length of both the sides is 204. Since they both equal the same length, we can then do 204/2 to get 102. So one side length is 102 and the L, W, L, W of the rectangle is 102, 100, 102, 100. In other words, the rectangle is 102 by 100.
Answer:
Length of the yard = 102 ft
Step-by-step explanation:
Perimeter of the yard P = 404 ft
Width of the yard W = 100 ft
Find Length of the yard L = ?
Perimeter of a rectangular = 2L + 2W
404 = 2L + 2(100)
2L = 404 - 200
2L = 204
L = 204 / 2
L = 102 ft