a = 1, b = 2 is a counterexample, and with that, we conclude that the conjecture is false.
Is the conjecture true or false?Here we have the conjecture:
"For any two integers a and b, (a - b)^2 = (a^2 - b^2)"
Notice that if we find a single pair of integers a and b such that the equality in the conjecture is false, then we have found a counterexample and that is enough to conclude that the conjecture is false.
If we define=
a = 1
b = 2
Replacing that in the equation of the conjecture we get:
(1 - 2)^2 = (1^2 - 2^2)
(-1)^2 = 1 - 4
1 = -3
This is false, then a = 1, b = 2 is a counterexample, and with that we conclude that the conjecture is false.
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Find the population mean or sample mean as indicated. Sample: 16, 17, 5, 6, 16
Answer:
sample mean = 12
Step-by-step explanation:
To find the mean of a sample of items, we can use the following formula:
[tex]\boxed{\mathrm{mean = \frac{sum \ of \ items}{number \ of \ items}}}[/tex].
In this question, we are given the following items: 16, 17, 5, 6, and 16.
• sum of items = 16 + 17 + 5 + 6 + 16
= 60
• number of items = 5
∴ mean = [tex]\frac{60}{5}[/tex]
= 12
Therefore, the sample mean is 12.
Find the value of x.
(6x + 7)º
(8x-17)°
(6x+7) and (8x-17)° are both vertical angles; so, the value of x is 12.
What is verticle angles?When two straight lines cross, the angles that are opposite one another are called vertical angles. (These two lines should technically be on the same plane.)
Angles vertically are congruent.
According to the given value;
Let the angles be A and B; such that:
A = 6x+7
B=8x-17
By theorem of vertical angles
A = B
So, we have:
6x+7=8x-17
Collect like terms
8x-6x=7+17
2x=24
x=12
Hence the value of x is 12.
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Mary bought a pair of jeans for 30$ and a sweater for 20$. if sales tax is 7% of the total how much did she pay for the jeans sweater and tax altogether
Answer:
53.5
Step-by-step explanation:
7% of 50 is 3.5 and you add it
what is the circumfrence of a circle with a diameter of 10 meters
Answer:
31.42m
Step-by-step explanation:
Find[tex]C = (22/7) \times d\\C = 3.14 \times 10\\C = \mathrm{31.42m}[/tex]
CAN SOMEONE EXPLAIN TO ME HOW TO SOLVE 8^15÷8^7×8
So, we are to solve: [tex] {8}^{15} \div {8}^{7} \times 8[/tex]
Using the exponential rule of multiplication and division with the same bases, which are:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
and:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
Therefore:
[tex] {8}^{15} \div {8}^{7} \times {8}^{1} = {8}^{15 - 7 + 1} [/tex]
→[tex] {8}^{9} = 134217728[/tex]
Therefore: 134217728 is the final answer
I hope this helps.The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 240 480 720
Create a description in words for the table.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 240-hour workout, there is 1 calorie burned, and for every 480-hour workout, there are 2 calories burned.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 240-hour workout, there is 1 calorie burned, and for every 480-hour workout, there are 2 calories burned.
Answer: The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
Step-by-step explanation:
By observing the nature of the question, we can decide that the amount of time spent working out dictates the number of calories we burn, making the workout (hours) the independent variable and the calories burned the dependent. This automatically cancels out the answers C and D.
We then just use our knowledge of the table. The hours were assigned 1, 2, and 3, and the calories were 240, 480, and 720. Just make sure the answer reflects that! That gives us answer choice B, The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
Complete the factor tree for 1,575.
Press each hotspot
Label the corresponding number below with the requested factor.
Answer:
See the factor tree in the attached image
Step-by-step explanation:
1575 ÷ 5 = 315
315 ÷ 5 = 63
63 ÷ 7 = 9
Factors of 9 are 3 and 3
15.255 is what percent of 28.25?
Answer: 54%
15.25500 is 54% of 28.25
Step-by-step explanation: i might be wrong but let me know if i am right (:
1.268 multiplied by 100
The tile floor in a restaurant is being replaced. The dimensions of the floor are shown. What is the total area of the new tile floor in the restaurant? 15 ft 12 ft 20 ft 17 ft
The total area of the new tile floor in the restaurant = 240 ft².
What is geometric figure?A geometric figure is any arrangement of points, lines, or other planes. Depending on the proportions of the figure, geometric figures are frequently categorized as space figures, plane figures, lines, line segments, rays, as well as points.
What do geometric forms look like?Geometric forms are any open or closed structures with specific shapes and attribute dreamed up of lines, curves, and points. Geometric shapes include square, rectangles, circles, cones, cylinders, sphere, and so on. All of these forms have characteristics that distinguish them from others.
According to the given data:Length of rectangle = 15ft
width of rectangle = 12ft
hypotonus = 17ft
First finding the area of the rectangular part:
area = L x B
= 15 x 12
= 180 ft²
First finding the area of the triangular part:
Area = 1/2 *(B *h)
= 1/2 * (8 * 15)
= 1/2 * 120
= 60 ft²
The total area of the new tile floor in the restaurant = 180 + 60
= 240 ft²
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Can somebody pls help me with this question? Giving lots of points!
Answer:
x^2
Step-by-step explanation:
A number is automatically X. X is any number that is unknown, and the number is unknown in this problem
Answer:
x^2
Step-by-step explanation
x is the number, and since its raised to the second power its x^2
Help me answer Thank for helping
Answer:
1.6
Step-by-step explanation:
first we want to figure out the square roots. the square root of 12 would be 3.5. while the square root of 3 is 1.7
after figuring out the square roots, our equation is -3.5 + 3(1.7)
first we want to multiply 3 by 1.7
this would give us 5.1
leaving our equation as -3.5 + 5.1
our final step is to add 5.1 to -3.5
although i find it easier to just subtract 3.5 from 5.1 since 3.5 is a negative.
this would give us 1.6
Write 1668 in scientific notation
Answer:
Tabla de contenido
Cuando separamos el número 1668 en un coeficiente y una potencia de 10, se obtiene el número 1668 en forma exponencial, pero hay un número indefinido de posibilidades.
Como probablemente desees expresar el número 1668 en notación científica normalizada, el coeficiente o significando de 1668 debe estar en el intervalo de 1 a 10.
En otras palabras, el coeficiente debe ser mayor o igual a 1 y menor a 10, es decir, 1 ≤ |m| < 10.
En esta publicación nos referimos al número 1668 en la versión normalizada, a menos que se indique lo contrario.
No es una convención, pero esto refleja el uso del término en la vida diaria.
Por lo tanto: 1668 = 1.668 × 10^3.
También puedes encontrar el resultado de la conversión numérica en los campos de salida de nuestro convertidor en la parte superior del artículo.
Step-by-step explanation:
*Lets see who will get brainiest*
A quadrilateral in the third quadrant is rotated 90° clockwise about the origin. Which quadrant will the transformed quadrilateral be in?
A.
first quadrant
B.
second quadrant
C.
third quadrant
D.
fourth quadrant
Answer:
B
Step-by-step explanation:
Since the quadilateral rotated 90° from the third quadrant it then lands back on the second quadrant.
Find the error in the calculations below, if there is one:
Line (1): 8x4 = 2(4x + 1) -6
Line (2): 8x - 4 = 8x +1-6
Line (3): 8x - 4 = 8x - 5
Line (4): -4 = -5
Line (5): Based on the calculations above, there are no solutions.
O The error occurred from line (1) to line (2).
The error occurred from line (2) to line (3).
The error occurred from line (3) to line (4).
O The error is in line (5).
The error occurred from line (2) to line (3) i.e., option(b) is correct.
Given that, Line (1): 8x-4 = 2(4x+1)-6, so we will procced to solve line (1) accordingly and then with the steps we will find where the error exactly occur. Let's proceed to solve this question.
8x-4 = 2(4x+1)-6
Now, open or simplify the bracket in RHS, we get
8x-4 = 8x+2-6
Now, simplify RHS accordingly, we get
8x-4 = 8x-4
Now add 4 both sides, we get
8x-4+4 = 8x-4+4
8x = 8x
Now, divide both sides by 8, we get
x = x
Now, subtract x from both sides, we get
0 = 0
Both sides are equal.
⇒ True for all x.
So, from the above calculation steps we can easily concluded that the error occurred from line (2) to line (3).
Hence, option(b) is correct.
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Which diagram shows lines that must be parallel lines cut by a transversal?
The first diagram shows the parallel lines cut by a transversal.
According to the statement
We have to explain all about the parallel lines cut by a transversal.
So, For this purpose, we know that the
A transversal line is a line that passes through two lines in the same plane at two distinct points.
And
Parallel lines are lines in a plane that are always the same distance apart.
From the given information:
In the given pictures we see that there are the presence of the two parallel lines and a one line is passes through these lines and cut the two parallel lines and there is a formation of the some angles in it.
And by property and the behavior of the transversal line to the parallel lines.
The diagram in first option shows a perfect lines that must be parallel lines cut by a transversal.
So, The first diagram shows the parallel lines cut by a transversal.
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The graph below shows the ages of the top five male finishers in the Mt. Washington Auto Road Bicycle Hillclimb each year from 2017 through 2021.
1. Write the relation of this situation as a set of ordered pairs in terms of (age, finishing place).
2. Identify the domain and range of the relation.
3. Do the ordered pairs represent a function? Explain.
From the given table, we have that:
1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
What is the relation of this situation?
To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:
(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
What are the domain and the range?The domain of a relation is the set that contains all possible input values for the values, that is, the values of x.The range of a relation is the set that contains all possible output values for the values, that is, the values of y.Hence, for the given relation:
The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output.
For this problem, we have that:
There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
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Find C that is 1/5 the distance from A(4, 2) to B(8, 7).
The coordinate of C that is 1/5 the distance from A(4, 2) to B(8, 7) is C(x,y) = {(44/6, (37/6)}
Midpoint of a lineThe formula for calculating the point on a line divided into ratio a:b is expressed as;
C(x,y) = {(ax₁+bx₂)/2, (ay₁+by₂)/2}
Given the following coordinate points A(4, 2) to B(8, 7) divided in the ratio 1:5 is expressed as:
C(x,y) = {(1(4)+5(8))/1+5, (1(2)+5(7))/1+5}
C(x,y) = {(44/6, (37/6)}
Hence the coordinate of C that is 1/5 the distance from A(4, 2) to B(8, 7) is C(x,y) = {(44/6, (37/6)}
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4 + 10(5 − 3) ÷ 4 + 6²
Answer:
45
Step-by-step explanation:
=4+10×2÷4+36
=4+5+36
=45
Determine whether the lines are parallel, perpendicular, or neither . Y=20x+9, y=6x-4
Answer:57368
Step-by-step explanation:
put all them on top like this 573 you can do this 68
S(-2, 4) and T (3,9).
The midpoint is MC). The distance between S and T is about
We get the distance between the coordinates of the point S and T as 5 √2 units.
We are given the coordinates of two points as:
S = ( - 2, 4 )
T = ( 3, 9 )
We have to find the distance between the points S and T.
We will use the distance formula for this.
Distance = √(x₂ - x₁)² + ( y₂ - y₁)²
Here, we have:
x₁ = -2
x₂ = 3
y₁ = 4
y₂ = 9
Substituting the values in the formula, we get that:
Distance = √(3 + 2)² + ( 9 - 4)² units
Distance = √(5)² + ( 5)² units
Distance = √25 + 25 units
Distance = √50 units
Distance = 5 √2 units
Therefore, we get the distance between the coordinates of the point S and T as 5 √2 units.
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If 4x + 8 = 28, then x = 5. choose inverse
Answer:
What do you mean by choose inverse?
Step-by-step explanation:
What are the zeros of f(x) = x2 + x - 12?
9.
4
Rena is building a model of a castle using a scale of 1inch = 60 yards. Her model has a rectangular base that is 3 inches wide and 4 inches long.
What is the area of the actual base of the castle in square yards?
The area of the actual base of the castle in square yards is 43200 yards².
How to calculate the area?From the information, Rena is building a model of a castle using a scale of 1inch = 60 yards. Her model has a rectangular base that is 3 inches wide and 4 inches long.
The normal width will be:
= 60 × 3 = 180
The length will be:
= 4 × 60 = 240
Therefore, the area will be:
= Length × Width
= 240 × 180
= 43200 yards²
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Find a 3-by-3 magic square using the numbers 4, 5, 6, 14, 15, 16, 24, 25, and 26.
Fill in the magic square.
Please so work.
A 3-by-3 magic square :
5 24 16
26 15 4
14 6 25
A square array of numbers, often positive integers, is referred to as a magic square in recreational mathematics if the sums of the numbers in each row, each column, and both main diagonals are the same.
The following values are listed in the question:
The numbers are 4, 5, 6, 14, 15, 16, 24, 25, and 26.
A 3-by-3 magic square is required.
Since the numbers are 4, 5, 6, 14, 15, 16, 24, 25, and 26.
Now the sum of all numbers is :
4 + 5 + 6 + 14 + 15 + 16 + 24 + 25 + 26 = 135
There are now 3 rows and 3 columns, thus the total number is divided by 3.
5 24 16
26 15 4
14 6 25
5 + 24 + 16 = 45
5 + 26 + 14 = 45
26 + 15 + 4 = 45
24 + 15 + 16 = 45
14 + 6 + 25 = 45
5 + 15 + 25 = 45
So, the total of each row and each column is therefore 45.
Therefore, this is a 3-by-3 magic square that satisfies the conditions :
5 24 16
26 15 4
14 6 25
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simplify 7(x+1)+-7(-6x+-9)
Answer:
49x=70
Step-by-step explanation:
Solve{3x-4}={3x-5} i am totaly confused
Answer:
They are not equal.
Step-by-step explanation:
Because the equation is {3x-4}={3x-5} the equation is saying that the two equations are equal, but it is false. {3x-4} is less than {3x-5}, and {3x-5} is greater.
Answer:
This Equation has no soulution
Step-by-step explanation:
3x-4=3x-5
3x - 4 - 3x = 3x -5- 3x Simplify___-4 = -5
Find The Slope of the Line?
Answer: 3
Step-by-step explanation:
To find the slope you have to divide y over x: y/x or most commonly known as rise/run.
We start at the point where the line is touching a point, in this case it's -8 in the y axis.
Then we count up until we find another point that the blue line is touching. In this case at the coordinates (2, -2). So there's 6 values up from -8 and we have to move to the right 2 values to reach the point the blue line is touching.
So we use the formula rise/run or y/x:
6/2 = 3
This is very hard to explain in just text! I hope you understand
What is the solution to the following equation?
15+ x = -2
OA. x=17
O B. x = -17
OC. x=13
OD. x=-13
Answer:
x = -17
Step-by-step explanation:
You can plug in answer choices, or you can get x by itself.
I got x by itself because it is faster. Simply subtract 15 from both sides.
So, you would get x = -2 - 15. Keep change change to subtract negative numbers => -2 + -15 which equals to -17.
So x = -17.
You can also plug it in: 15 + -17 does equal -2.
Carolyn says that point a and point b represent opposite integers what is the opposite of the integer represented by a point ?by b point
The value of integer a is (-a).
To solve this problem first of all we have to understand the concept of opposite integers.
The opposite integers are nothing but an integer with two different sign but has same numerical value.
Suppose there is an integer y then the opposite of integer is -y. And the opposite of an integer -h is +h.
Here it is asked to find the opposite integer of a.
The opposite of integer a is given to be b but the value of integer is -a.
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