The number -1 is its own multiplicative inverse, just like the number 1, because multiplying -1 by itself results in 1.
The number 1 is indeed its own multiplicative inverse because when you multiply it by itself, you get 1. The property of a number being its own multiplicative inverse means that the number multiplied by itself equals 1. There is another number with this property, which is -1. When you multiply -1 by itself (-1 x -1), the result is 1. Therefore, -1 is also its own inverse when it comes to multiplication.
This concept is rooted in the properties of identity elements and inverses within the mathematical field of abstract algebra. When considering the set of numbers 1 and -1, they form an abelian group under the operation of multiplication. In this group, every element is its own inverse, and the identity element for multiplication is 1, as any number multiplied by 1 yields the original number.
What number is a multiple of 12
Good evening ,
______
Answer:
{ ... , -24, -12 ,0 , 12 , 24 , 36 , ... }
___________________
Step-by-step explanation:
Any number that can be written in the form: 12×k is a multiple of 12 , k∈Z
12×0=0 then 0 is a multiple of 12
12×1=12 then 0 is a multiple of 12
12×2=24 then 0 is a multiple of 12
12×3=36 then 0 is a multiple of 12
12×4=48 then 0 is a multiple of 12
.
.
.
etc.
___________
:)
the product of a number and 3 is 6 more than the number which equation models this sentence
Answer:
3x = 6 + x
Step-by-step explanation:
We can express the product of a number and 3 as:
3x
Where x is the number that we don't know.
Now it says that that product is 6 more than the number (x) so we can write it down:
3x (The product of a number and 3) = (is) 6 + x (6 more than the number)
3x = 6 + x
The sentence 'the product of a number and 3 is 6 more than the number' can be translated into the algebraic equation 3x = x + 6.
Explanation:The given statement can be translated into a mathematical equation in the following way: If we let x be the number in question, the first part of the sentence tells us that the product of the number and 3 can be modeled as 3x. The second part of the sentence tells us that this is 6 more than the number itself. This can be translated into the equation as x + 6. Thus, putting the two parts together, we get the algebraic equation 3x = x + 6.
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17) Given f(x) = 2x + 4, if the output is 12, what is the input? (Solve for x)
_ as an ordered pair:(, )
Answer:
the answer is 8 because when you set the equation equal to 12 and solve it you get 12
Step-by-step explanation:
Final answer:
To find the input for f(x) = 2x + 4 when the output is 12, solve the equation 12 = 2x + 4 for x, resulting in the input-value x being 4, with the ordered pair being (4, 12).
Explanation:
The question concerns finding the input for a given function when the output is known. The function provided is f(x) = 2x + 4, and we want to find the input value, or x, that produces an output, or f(x), of 12. To do this, we set up an equation where 12 = 2x + 4 and solve for x.
We first subtract 4 from both sides of the equation to get 8 = 2x. Then, we divide both sides by 2 to isolate x, resulting in x = 4.
The ordered pair representing the input-output relationship for the function when the output is 12 is (4, 12).
PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!
Find the value of x.
Answer:
x = 121
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 7, thus
sum = 180° × 5 = 900°
Sum the given angles and equate to 900
x + 125 + 119 + 117 + 145 + 133 + 140 = 900, that is
x + 779 = 900 ( subtract 779 from both sides )
x = 121
Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114, or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost ?
Answer:
The cost of a shirt is $16 and the cost of a sweater is $33
Step-by-step explanation:
Let
x -----> the cost of a shirt
y -----> the cost of a sweater
we know that
[tex]3x+2y=114[/tex] -----> equation A
[tex]2x+4y=164[/tex]----> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (16,33)
see the attached figure
therefore
The cost of a shirt is $16 and the cost of a sweater is $33
Answer:
The cost of each shirt is 16$ and the cost of each sweater is 33$
Solution:
Let us consider “x” as the cost of each shirt and “y” as the cost of each sweater.
From question, Andrea has bought 3 shirts and 2 sweaters for 114$. Hence we form equation as,
3x + 2y = 114 ------ eqn 1
Similarly, Andrea has bought 2 shirts and 4 sweaters for $164. Hence we form equation as,
2x + 4y = 164 ----- eqn 2
By solving equation 1 and equation 2, we get the value of “x” and “y”.
On multiplying equation 1 by 2,we get
6x + 4y = 228 -------- eqn 3
Now solving eqn 2 and eqn 3
6x + 4y = 228
-2x - 4y = -164
4x + 0y = 64
4x = 64
[tex]x = \frac{64}{4}[/tex]
x = 16
Substituting the value of x in eqn 1, we get
3(16) + 2y = 114
48 + 2y = 114
2y = 114 - 48
2y = 66
[tex]y = \frac{66}{2}[/tex]
y = 33
Thus the values of x and y are 16 and 33. So the cost of each shirt is 16$ and the cost of each sweater is 33$
Each data pair shown is of the form below:
(years since purchase, value of car)
Based on the correlation coefficient, there is a(n)
linear correlation between the
data
Answer:
Each data pair shown is of the form below:
(years since purchase, value of car)
Based on the correlation coefficient, there is a(n) strong linear correlation between the data.
Use the regression equation to estimate the value of the car 8 years after purchase. Round to the nearest dollar. $ 6019
As more years go by, the prediction (extrapolation) becomes less reliable.
Explanation:
the answer are in bold :)
Based on the correlation coefficient, there is a(n) strong linear correlation between the data.
The correlation coefficient, often denoted as "r," measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with:
r = 1 indicating a perfect positive linear correlation (as one variable increases, the other increases proportionally).r = -1 indicating a perfect negative linear correlation (as one variable increases, the other decreases proportionally).r = 0 indicating no linear correlation (variables are not related linearly).The regression equation to estimate the value of the car 8 years after purchase, as more years go by, the accuracy of this prediction becomes less reliable.
Thus, there is strong linear correlation.
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what is the distance between -4 and -1 on a number line
Answer: The distance is 3.
Step-by-step explanation: Start on a number line from 0. Go back 4 and mark it at -4. Then go back to 0 and go back 1 and mark it at -1. If you count the space between -4 and -1 you will get 3 spaces.
8 5/8 + 8 7/8 ????????
Answer:
17 1/2
Step-by-step explanation:
8 5/8 + 8 7/8
=17 1/2
Answer:
17 1/2
Step-by-step explanation:
8 5/8+8 7/8=...
So, let's take away the fractions for now.
What's 8+8?
Well, 8+8=16.
Now, let's take a look at the fractions.
5/8+7/8=...
Well, when we are adding fractions, the denominator will stay the same. So let's pretend that we are adding 5+7.
5+7= 12. So our answer is 16 12/8 Right?
wrong.
you will simplify the 12/8. Since the numerator is more than eight, we will subtract 8 from 12.
12-8=4
we will make the 8/8 a 1 and add it to the 16 to make it 17 4/8. We can still simplify this. The 4/8 becomes 1/2 making the answer: 17 1/2
Hope this helps!!!
Please need help urgent
10x−8/3−4x=6x
whats the value of x?
(20 points!!!)
There is no solution of expression.
We have to given that,
An expression to solve,
⇒ 10x - 8/3 - 4x = 6x
Now, We can simplify as,
⇒ 10x - 8/3 - 4x = 6x
Combine like terms,
⇒ 6x - 8/3 = 6x
⇒ 6x - 6x = 8/3
⇒ 0 ≠ 8/3
Which is not possible.
Thus, There is no solution of expression.
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-15= z/-2 answer please?
Answer:
30
Step-by-step explanation:
[tex]-15=\frac{z}{-2}\\\\(-15)(-2)=z\\\\30=z[/tex]
61/6 to mixed number
Answer:
10 1/6
Step-by-step explanation:
61/6= 10.1666667
Answer: 10 1/6
Divide using long division, the whole number proportion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
How do you round 949999 to the nearest ten thousand
Answer:
950000
Step-by-step explanation:
the rule with rounding is if the number to the direct left is under 5, it stays the same but if it is 5 or above, you round up and everything behind becomes zeroes.
What is a multi step problem?
Answer:
In multi-step problems, one or more problems have to be solved in order to get the information needed to solve the question being asked.
For 32 hours of work, you are paid $244.80. How much would you receive for 37 hours?
You would receive $
. (Round to the nearest cent as needed.)
Answer:
$283.05
Step-by-step explanation:
first divide $244.80 by 32, to find out how much you are making hourly. in this case you are making $7.65 an hour
next, multiply $7.65 by 5, to add the 5 hours, in this case you get $38.25.
next, add $38.25 to $244.80 and you get your answer!
Final answer:
To find out how much you would receive for 37 hours of work, set up a proportion using the given information and solve for x. The result is approximately $283.98.
Explanation:
To find out how much you would receive for 37 hours of work, we can set up a proportion using the information given. Since 32 hours of work pays $244.80, we can set up the proportion: 32/244.80 = 37/x. Cross-multiplying, we get: 32x = 244.80 * 37. Simplifying, we find that x = (244.80 * 37) / 32. Calculating the result, we find that you would receive approximately $283.98 for 37 hours of work.
if chocolate chips have 20 calories in 1 tbsp how many calories are in 1 cup
Answer: 320
Step-by-step explanation:
there are 16 tablespoons in one cup so 20*16=320
To calculate the calories in one cup of chocolate chips, you multiply the number of calories per tablespoon (20) by the number of tablespoons in a cup (16), resulting in 320 calories per cup.
To determine how many calories are in 1 cup of chocolate chips, knowing that there are 20 calories in 1 tablespoon, we first need to understand the conversion between tablespoons and cups. There are 16 tablespoons in a cup.
Therefore, to find out how many calories are in a full cup, you would simply multiply the number of calories in one tablespoon by the number of tablespoons in a cup:
20 calories / tablespoon × 16 tablespoons / cup = 320 calories / cup.
Thus, there are 320 calories in 1 cup of chocolate chips.
write down the coordinates of the point 5 units to the left of the y axis and 3 units above the x axis
The coordinates of the point is (-5,3)
How to determine the coordinates?Let the initial coordinate be:
Initial = (0,0)
5 units to the left of the x-axis represents a horizontal translation left by 5 units.
So, we have:
New = (0 - 5,0)
3 units above the y-axis represents a vertical translation up by 3 units.
So, we have:
New = (0 - 5, 0 + 3)
Evaluate
New = (-5, 3)
Hence, the coordinates is (-5,3)
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Round the following numbers to the nearest 10. 13-21-29
Answer:
13 --> 10
21 --> 20
29 --> 30
Answer:
The correct answer is: 10-20-30
Step-by-step explanation:
13 is between 10 and 20. The closest 10 for 13 is 10, because it's only 3 away (13 the other option would be 20 but it's 7 away, so way more.)
21 is between 20 and 30. The closest 10 for 21 is 20 ( it's only 1 away from 20, the other option would be 30 but it's 9 away, so way more.)
29 is between 20 and 30. The closest 10 for 29 is 30 (it's only 1 away from 30, the other option would be 20 but it's 9 away, so way more.)
A car used 1/64 of a gallon of gas to drive 1/4 of a mile. at this rate, how many miles can the car travel using 1 gallon of gas?
HELP ! SHOW WORK AND I WILL MAKE YOU THE BRAINIEST ANSWER .
Answer: 4/64
Step-by-step explanation:
Since 1/4 * 4 = 1
We just have to multiply 1/64 times 4 to get the answer
1/64 * 4 = 4/64
Answer:
Car will cover 16 miles in 1 gallon of the gas.
Step-by-step explanation:
We can solve this question by unitary method.
∵ A car used [tex]\frac{1}{64}[/tex] gallons of gas to drive the distance = [tex]\frac{1}{4}[/tex] miles
∴ Car used 1 gallons to drive the distance = [tex]\frac{\frac{1}{4} }{\frac{1}{64} }[/tex]
= [tex]\frac{64}{1}\times \frac{1}{4}[/tex]
= [tex]\frac{64}{4}[/tex]
= 16 miles
Therefore, car will cover 16 miles in 1 gallon of the gas.
What is the area of the trapezoid?
13 m
16 m
19 m
232 m2
256 m2
328 m2
352 m2
Answer:
256m2.
Step-by-step explanation:
Answer:
256m^2
Step-by-step explanation:
Find X and Y for both.
Answer:
Second picture: y=4 and x=7
First picture: x=70 degrees y=20 degrees
Step-by-step explanation:
Second picture:
One of the given triangles is an equilateral and the other is an isosceles.
Equilateral triangle has all congruent sides and it's angles are all congruent.
Isosceles triangle has two congruent angles and the opposite sides of those congruent angles are also congruent.
This implies all the side algebraic expression-measurements given are all equal.
5y-4=y+12
Add 4 on both sides:
5y=y+16
Subtract y on both sides:
4y=16
Divide both sides by 4:
y=4
So what is the side measurement for each of the sides given in terms of algebraic expressions?
y+12
4+12
16
Each side given in terms of an algebraic explanation is 16 units.
So we have also the following equation to solve:
3x-5=16
Add 5 on both sides:
3x=21
Divide both sides by 3:
x=7
So x=7 and y=4.
There is only one side in the picture that is possibly not 16. It is the one of the sides in the isosceles, not opposite the base angles.
------------------------------------------
First picture:
We are given x+y=90.
Since that one triangle is an isosceles we know that x+x+(180-40)=180
So let's solve the second equation for x then go back and solve for y in the first equation.
2x+140=180
Subtract 140 on both sides:
2x=40
Divide both sides by 2:
x=20
First equation:
x+y=90
So y=90-x=90-20=70.
Which of the following is a rational equation?
A. 4-2(x-1)=x+3
B. 1/2x-1/3=4-x
C. 0.7x-3=0.09(x-5)
D. 6/x - 1 = 4/(x-2)
Answer:
B and D
Step-by-step explanation:
Since they're the fractions
Option B and Option D represent rational equation.
A rational equation is defined as any equation that can write in p/q form where q not equal to zero.
From given option it is observed that,
Option B, [tex]\frac{1}{2}x-\frac{1}{3} =4-x [/tex]
option D, [tex]\frac{6}{x}-1=\frac{4}{x-2} [/tex]
Both option have fraction term.
Hence, Option B and Represent rational equation.
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the 9s in 9,905,482
Answer:
the 9s are in the millions and hundred thousands
Step-by-step explanation:
Kaleb had 136 songs on his mp3 player. if he deleted 56 songs, what is the ratio of songs he kept to songs he deleted
Answer:
80/56 = 1.42
Step-by-step explanation:
Total songs = 136
Number deleted = 56
Number kept = 136-56 = 80
The ratio of songs kept to songs deleted = 80/56 = 1.42
The proportions or ratio are used to compare quantities with each other, and are usually written with a colon (:) intermediate.
The equation y-5=6(x+1) is written in point-slope form. What is the equation written in slope-intercept form?
A)y = 6x + 11
B)y = 6x – 1
C)y = 6x – 4
D)y = 6x + 6
Answer:
a. y = 6x + 11
Step-by-step explanation:
distribute and rearrange into slope-intercept form.
y - 5 = 6x + 6
add 5 to both sides
y = 6x + 6 + 5 ⇒ y = 6x + 11
Answer: Hello mate!
our equation is y - 5 = 6(x + 1), and we want to rewrite it in the slope-intercept form.
First lets distribute the parenthesis.
y - 5 = 6(x+1) = 6x + 6
now let's add 5 in both sides.
y-5 + 5 = 6x + 6 + 5
y = 6x + 11
Then the correct answer is the option A.
–27x^6b^9 as a cube of a monomial
[tex]\bf -27x^6b^9~~ \begin{cases} -27=&-3^3\\ x^6=&x^{2\cdot 3}\\ &(x^2)^3\\ b^9=&b^{3\cdot 3}\\ &(b^3)^3 \end{cases}\implies (-3)^3(x^2)^3(b^3)^3\implies (-3x^2b^3)^3[/tex]
John made 12 dollars per delivery plus a base pay of 30 dollars.
If he made 150 dollars, how many deliveries did John make
Answer:
10
Step-by-step explanation:
$150 minus the base pay of $30 is $120. Divide this by the $12 he makes each delivery. 120/12=10
Can you help me with number 7?
Answer:
512 in³
Step-by-step explanation:
Given the volume (V) of a cube is calculated using
V = s³ ← s is the side length
When s = 8, then
V = 8³ = 8 × 8 × 8 = 64 × 8 = 512 in³
Answer: 512 in.³
Step-by-step explanation: To find the volume of a cube, first start with writing down the formula for the volume of a cube which is as followed.
Volume = Length × Width × Height
In this problem, our prism is a cube. Since the length, width, and height of a cube are all equal, we can find the volume of a cube by simply multiply side times side times side or s³.
Volume = Length x Width x Height
Volume = (8) (8) (8)
Volume = 512 in³.
Therefore, the volume of the cube is 512 in.³.
y
=
–x + 4
x + 2y
=
–8
How many solutions does this linear system have?
one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions
Answer:
one solution
Step-by-step explanation:
Given two equation
y = -x+4 ... (1)
x+2y = -8 ...(2)
Substituting equation (1) into (2), we will have;
x+2(-x+4) = -8
Opening the bracket up
x-2x+8 = -8
-x = -8-8
-x = -16
x = 16
Substituting x = 16 back into equation 1:
y = -16+4
y = -12
This shows that the linear equation has one solution (16,-12)
Evaluate (4+4×4-5)×2
Answer:
30
Step-by-step explanation:
By following PEMDAS
P - parenthesis | E - exponent | M - multiply | D - divide | A - add | S - subtract
You first work out what is in the parenthesis first. The order of operation would first have you multiply 4×4 = 16, next you will add 4 and subtract 5... 4-16+5 = 15. Finally multiply to what's outside the parenthesis (15)×2. And that's how you arrive to 30 as the final answer.