The combination of advanced military technology, numerical advantage, and the use of disease as a weapon were critical factors in enabling the Spanish conquistadors to seize control of Tenochtitlán and establish their colonial rule over the Aztec empire.
The Spanish conquest of the Aztec empire in 1521 was a turning point in world history, marking the beginning of Spanish colonial rule in the Americas.
One major factor was the advanced military technology and weaponry of the Spanish. The conquistadors were equipped with steel swords, guns, and armor, while the Aztecs relied on obsidian-tipped weapons and wooden shields.
Another factor was the advantage of numbers. The Spanish arrived in Mexico with a relatively small force of around 500 soldiers, but they were able to recruit indigenous allies and build up their army to around 8,000 soldiers.
A third factor was the use of disease as a weapon. The Spanish brought diseases such as smallpox, which devastated the indigenous populations and weakened the Aztecs, making them more vulnerable to attack.
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Answer this question based on the number line shown.
B
C
D
The distance from a point to point C is 1, and the distance from that same point to point B is 4. The point must be
O between D and A
• between C and A
O point D
L
• point A
Answer:
between D and A of it might be c
What happens to a graph that is representative of exponential decay? The graph goes: a. down and to the right c. up and to the right b. down and to the left d. up and to the left Please select the best answer from the choices provided A B C D
Answer:
A) Down and to the right.
Step-by-step explanation:
Hope it helps! :)
factor the polynomial completely
z^2 + 10z+24
Answer:
(z + 6)(z + 4)
Step-by-step explanation:
z² + 10z + 24
consider the factors of the constant term (+ 24) which sum to give the coefficient of the z- term (+ 10)
the factors are + 6 and + 4 , since
6 × 4 = + 24 and 6 + 4 = + 10 , then
z² + 10z + 24 = (z + 6)(z + 4) ← in factored form
Which graph represents the solution set? 23 ≤ 15 + x 2 4 number lines labeled A, B, C, and D. Line A: At 4, there is a closed circle. To the right of 4, the number line is shaded with an arrow pointing to the right. Line B: At 16, there is a closed circle. To the right of 16, the number line is shaded with an arrow pointing to the right. Line C: At 19, there is a closed circle. To the right of 19, the number line is shaded with an arrow pointing to the right. Line D: At 31, there is a closed circle. To the right of 31, the number line is shaded with an arrow pointing to the right.
The shaded region in the graph represents the possible solution sets to the inequality.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the inequality -
x² + 15 ≥ 23
The given inequality is -
x² + 15 ≥ 23
Refer to the graph attached.
The shaded region represents the possible solution sets to the inequality above.
Therefore, the shaded region in the graph represents the possible solution sets to the inequality.
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Suppose you add or subtract two quadratic trinomials that use the same variable. What are the possible classifications for the sum or difference? Explain.
The sum of a quadratic trinomial with the same variable is twice the individual and the difference will be zero.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
We know a quadratic equation is of the form ax² + bx + c.
The sum will be,
(ax² + bx + c) + (ax² + bx + c).
= 2ax² + 2bx + 2c.
= 2(ax² + bx + c).
The difference will be,
ax² + bx + c - (ax² + bx + c).
= 0.
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A bag of marbles has 3 red, 1 green, and 3 yellow marbles, what is the probability of selecting a green and then a yellow without replacement?
The probability that one selects a green marble and then a yellow marble from a bag of 3 red, 1 green, and 3 yellow marbles without replacement is 7.15%.
What is probability?Probability refers to the chance or odds of making a selection with an expected outcome.
In probability, many possible outcomes are being considered with an expected event.
The number of red marbles = 3
The number of green marbles = 1
The number of yellow marbles = 3
The odds of selecting a green marble = 1/7
The likelihood of selecting a red marble = 3/7
The chance of selecting a yellow marble = 3/7
The probability of selecting a green (1/7) and then a yellow without replacement (3/6) = 0.0715 (0.143 x 0.5)
= 7.15%
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Can someone please figure this out and explain it? I am so confused!
Answer:
Step-by-step explanation:
Brayden is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $1.75 per mile driven. How much would a taxi ride cost if Brayden is riding for 9 miles? How much would a taxi ride cost that is � m miles long?
Cost of 9 miles ride = $19.25
Cost of m miles ride = $3.50 + $1.75m
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Taxi charges $3.50 for pickup and $1.75 per mile.
Total charges can be expressed as
y = $3.50 + $1.75m
where m is the number of miles
For 9 miles
cost y = $3.50 + $1.75×9
= $3.50 + $15.75
= $19.25
Hence, $19.25 will cost for 9 miles ride
For m miles ride will cost $3.50 + $1.75m.
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Simplify the expression. 6q + 7 -2 +4q
Answer:
10q + 5
Step-by-step explanation:
6q+7-2+4q
=10q+5
:]
Hope this helps
Examine thi table of point, which are all on a certain line. X
y
−5
0
−1
−8
1
−12
4
−18
For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.
Given that,
x y
-5 0
-1 -8
1 -12
4 -18
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Then,
Points are, ( - 5,0 ) , ( -1,-8), (1,-12) , (4,-18)
Points are, ( - 5,0 ) , ( -1,-8)
Slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m = [tex]\frac{-8-0}{-1-(-5)}[/tex]
m = [tex]\frac{-8}{-1+5}[/tex]
m = [tex]\frac{-8}{4}[/tex]
m = -2
Points are, ( -1,-8 ) , ( 1,-12),
m = [tex]\frac{-12-(-8)}{1-(-1)}[/tex]
m = [tex]\frac{-12+8}{1+1}[/tex]
m = [tex]\frac{-4}{2}[/tex]
m = -2
Points are, ( 1,-12 ) , ( 4,-18),
m = [tex]\frac{-18-(-12)}{4-1}[/tex]
m = [tex]\frac{-18+12}{3}[/tex]
m = -6/3
m = -2
Then, m = -2
Therefore,
For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.
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For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.
Given that,
x y
-5 0
-1 -8
1 -12
4 -18
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Then,
Points are, ( - 5,0 ) , ( -1,-8), (1,-12) , (4,-18)
Points are, ( - 5,0 ) , ( -1,-8)
Slope
m = -2
Points are, ( -1,-8 ) , ( 1,-12),
m = -2
Points are, ( 1,-12 ) , ( 4,-18),
m = -6/3
m = -2
Therefore,
For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.
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What is the distance between two points A and B whose coordinates are (3, 2) and (9, 7), respectively?
The distance between two points A (3, 2) and B (9, 7) is [tex]\sqrt{61}[/tex] units.
What is meant by distance?The midpoint between a celestial body's greatest and smallest separations from its primary.
The metre is the SI unit for distance (m). Long distances can be measured in kilometres, whereas little distances can be gauged in millimetres (cm) (km).
For instance, you might measure the distance in centimetres between the bottom and top of a piece of paper and the kilometres between your home and school.
You are a long way from anything in space or time if you are far away from it, cannot see it, or cannot recall it.
I need to keep my mum at a distance if I want to manage.
Distance between P and Q if two points are given P([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and Q([tex]x_{2}[/tex], [tex]y_{2}[/tex]) , PQ = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Given:
A (3,2) and B (9,7) are the two points in a plane. We have to find the distance between A and B. Here, [tex]x_{1}[/tex] = 3, [tex]x_{2}[/tex] = 9, [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 7.
AB = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
AB = [tex]\sqrt{(9 - 3)^2 + (7 - 2)^2}[/tex]
AB = [tex]\sqrt{(6)^2 + (5)^2}[/tex]
AB = [tex]\sqrt{36 + 25}[/tex]
AB = [tex]\sqrt{61}[/tex] units.
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How many distinct paths are there from(−1,2,0) to (1,3,7) in Euclidean three-space if each move is one of the following types?
(H):(x,y,z)→(x+1,y,z)
(V):(x,y,z)→(x,y+1,z)
(A):(x,y,z)→(x,y,z+1)
There are 214 distinct paths from (-1,2,0) to (1,3,7) in Euclidean three-space.
We can approach this problem using a combinatorial approach.
Let's say that there are a total of n moves from the starting point (-1,2,0) to the ending point (1,3,7). Then, the number of H moves is nh, the number of V moves is nv, and the number of A moves is na, where nh + nv + na = n.
The starting point (-1,2,0) is (1,1,7) moves away from the ending point in the x, y, and z directions, respectively. Therefore, we have the following constraints:
nh ≥ 1 (to move from x = -1 to x = 1)
nv ≥ 1 (to move from y = 2 to y = 3)
na ≥ 7 (to move from z = 0 to z = 7)
The number of distinct paths from (-1,2,0) to (1,3,7) is simply the number of ways to choose nh, nv, and na moves from n total moves such that the constraints are satisfied. This is equivalent to finding the number of solutions to the equation nh + nv + na = n subject to the constraints.
Using the stars and bars technique, the number of solutions can be calculated as:
C(n - 1, 2) = C(n - 1, n - 3) = C(n - 1, na - 1)
where C(n, k) is the binomial coefficient representing the number of ways to choose k items from a set of n items.
Since na ≥ 7, we can start by setting na = 7 and then increasing it by one to see if there are additional solutions. For na = 7, n = 7 + nh + nv. Therefore, n >= 8 and n <= 14. The number of solutions for each value of n can be calculated using the formula above, and the total number of solutions can be obtained by summing up the results for each value of n.
For example, when n = 8, there are C(7, 2) = 21 solutions, when n = 9, there are C(8, 2) = 28 solutions, and so on. The final answer is the sum of all the solutions, which is:
21 + 28 + 35 + 35 + 28 + 21 + 13 + 6 = 214
Therefore, there are 214 distinct paths from (-1,2,0) to (1,3,7) in the Euclidean three-space.
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Can someone PLEASE help? I will give brainliest if possible
Click on the image to see answers
Answer:
second option
Step-by-step explanation:
vertical angles are situated opposite each other at a vertex. For this reason they are often called vertically opposite angles.
from the diagram the vertical angles opposite to each other at vertex E are
∠ 1 ≅ ∠ 3 and ∠ 2 ≅ ∠ 4
Answer:
∡1 ≅ ∡3 and ∡2 ≅ ∡4
Explanation:
Definition of vertical angles: Each of the pairs of opposite angles made by 2 intersecting lines.
By definition, vertical angles are on opposite sides of the intersection, and are always equal.
Since the pairs ∡1,∡3 and ∡2,∡4 are on opposite sides of the intersection, they are equal.
Proof for the Vertical Angles Theorem: https://www.cuemath.com/geometry/vertical-angles/
Pls help i will give Brain to correct, 5 stars, and thanks
Mallory's Border Collie had 18 puppies in 3 litters. Determine the rate for a ratio of the two different quantities.
18 over 3 puppies per litter
3 over 18 puppies per litter
18 over 21 puppies per litter
1 over 6 puppies per litter
The rate for a ratio of the two different quantities is; ¹⁸/₃ puppies per liter
How to find the ratio between two quantities?Two quantities can be referred to as proportional provided that they can be represented in the general form y = kx,
where k is a constant of proportionality
Now, we have the parameters as;
Number of Puppies = 18 puppies
Number of Litters = 3 litters
Thus, the rate for the ratio between the two quantities is expressed as;
18 puppies/3 Litters
= ¹⁸/₃ puppies per liter
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Is 2X squared +8x-8 a polynomial
The expression 2x² + 8x - 8 represents a polynomial.
When does an expression represent a polynomial?An expression represents a polynomial when these following conditions are satisfied:
Integer exponents.Non-negative exponents.The exponents for this problem are given as follows:
2, 1 and 0.
(as the constant term has an exponent of zero).
Which are both integer and non-negative, hence the expression 2x² + 8x - 8 in fact represents a polynomial.
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Clara has written the following sentence that needs revision.
When students are taking a test, you should keep your eyes on your own paper.
Which of the following is the best revision of the sentence?
Answer: B
Step-by-step explanation:
"When students are taking a test, they should keep their eyes on their own paper" is grammatically correct and the best sounding out of the others.
Johnny charges $10 plus $7.50 per hour to mow lawns.
The linear equation of Johnny's charges is C(x) = 10 + 7.5x
How to determine the linear equationFrom the question, we have the following parameters that can be used in our computation:
Initial charge = $10
Hourly rate = $7.50
Let the number of hours be x and the total cost be C(x)
So, we have the following representation
C(x) = Initial charge + Hourly rate * x
Substitute the known values in the above equation, so, we have the following representation
C(x) = 10 + 7.5x
Hence, the function is C(x) = 10 + 7.5x
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Complete question
Johnny charges $10 plus $7.50 per hour to mow lawns.
Determine the linear equation
In ΔVWX, u = 7.9 inches, m∠V=76° and m∠W=44°. Find the length of x to the nearest 10th of an inch
The length of x to the nearest 10th of an inch is 7.1 inches.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
We have law of sine of triangle, which states that,
sin X / x = sin Y / y = sin Z / z
where X, Y and Z are three angles of a triangle and x, y and z are the sides opposite to X, Y and Z respectively.
Using this,
Sin V / v = Sin W / w = Sin X / x
Given that, m ∠V = 76° and m ∠W = 44°
m ∠V + m ∠W + m ∠X = 180°
76° + 44° + m ∠X = 180°
m ∠X = 180° - ( 76° + 44° )
m ∠X = 60°
Also, given that, v = 7.9 inches
Sin V / v = Sin X / x
sin (76°) / 7.9 = sin (60°) / x
x = [sin (60°) × 7.9] / sin (76°)
x = [0.866 × 7.9] / 0.970
x = 7.051 ≈ 7.1
Hence the length of the x is 7.1 inches to the nearest 10th of an inch.
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Help please!!
You are building a plant stand with three equally spaced circular shelves.
The diagram shows a vertical cross section through the diameters of the shelves.
What is the diameter of the middle shelf?
The diameter of the middle shelf is solved using similar triangle to get
7.5 inHow to find the diameter of the middle shelfThe middle shelf is in the mid segment hence Using the concept of similar triangle the proportions are as follows
The proportions
1 / 2 = x / 15
cross multiplying
15 = 2x
rearranging the equation
2v = 15
isolating x by dividing through by 2
2v / 2 = 15 / 2
x = 7 1/2
x = 7.5
The diameter of the middle shelf is equal to x which is calculated to be 7.5
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Hana is using a square piece of cardboard to make a box without a lid. She cuts 5-inch squares from each corner and folds up the edges. The finished box has a volume of 2,000 cubic inches. Which equation can be used to find the dimensions of the original cardboard piece?.
The equation is 2000=5[tex](L-10)^{2}[/tex] to find the dimensions of the original cardboard piece.
If she is using a square piece of cardboard, then have in mind that we are dealing with a square of unknown length "L".
Now, consider that you are removing from each corner of that square a smaller square of surface 5 . Once the small 5 in size square pieces are cut, the four flaps that are left (see attached image) are bent through the lines pictured in grey so they form the final box.
Notice that the dimensions of this box will be:
For the base now we have a smaller square that has length L minus the quantity "two times five" inches. That is: each side of the square base is now L-10 inches long.Notice as well that the height of the box will be exactly 5 inches (the length of the square cutting).
The final volume of the box (which according to the problem should equal 2000 cubic inches) will be given by the product of the box's three dimensions : "L-10" times "L-10" times "5", that is in mathematical terms:⇒Volume of the box =Length*Breadth*Height.
⇒2000=(L-10)*(L-10)*5
⇒2000=5[tex](L-10)^{2}[/tex]
Therefore, the equation is 2000=5[tex](L-10)^{2}[/tex] to find the dimensions of the original cardboard piece.
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The function f(x)=log2(-x+3)-4 is graphed below. Plot all lattice points of the inverse. Use the labeled points as your guide.
The lattice point of the inverse is (3, 0).
How to determine the lattice pointsTo find the lattice points of the inverse of the function f(x), we need to find the points where both x and y are integers.
To find the inverse of the function, we switch the x and y values, then solve for y:
y = log2(-x + 3) - 4
x = log2(-y + 3) - 4
y = 3 - 2^(x + 4)
For x and y to be integers, both 2^x and - 2^(x + 4) must be integers.
This occurs when y is a positive integer and y <= 2, since 2^y becomes larger than 3 for y > 2.
Thus, the only lattice point of the inverse is (3, 0).
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what is the equation asking you do? what is your plan to solve?
These questions are going to help while you are doing a problem! so use them often!
This statement is TRUE. When we are doing a problem, we could use these questions " what is the equation asking you do? what is your plan to solve?" as the part of starting solving the problem in math about equation matter.
About equationIn mathematics, an equation is an equation statement that contains one or more variables. Solving equations consists of determining which variable values makes an equality true. The variable is also called "unknown" and the value of an "unknown" that satisfies the equation is called the equation solution. There are two types of equations: identity and conditional equations. True identity for all variable values. The conditional equation is true only for certain variable values.
An equation is a mathematical statement in the form of a symbol which states that two things are exactly the same. Equations are written with an equal sign (=), as follows:
x + 3 = 5, which states that value x = 2.
2x + 3 = 5, which states that the value x = 1.
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juan made 1/2 of a quart of hot chocolate each mug holds 1/8 of a quart how many mugs will juan be able to fill
Answer:
Juan can fill 4 mugs.
Step-by-step explanation:
Take the total amount of hot chocolate and divide by the amount each mug will hold.
1/2 ÷ 1/8
Copy dot flip.
1/2 * 8/1
8/2
4
Juan can fill 4 mugs.
Answer:
4 mugs
Step-by-step explanation:
If each mug holds 1/8 of a quart, and Juan has 1/2 of a quart of hot chocolate, then he can fill:
[tex]\sf:\implies{1/2 ÷ 1/8 = 4 \: mugs.}[/tex]
So, Juan will be able to fill 4 mugs.
given a and b in exercises 11 and 12, write the augmented matrix for the linear system that corresponds to the matrix equation a x=b. then solve the system and write the solution as a vector.
If A is a m × n matrix, with columns a1, . . . , an, and if b is in R
m,
then the matrix equation
Ax = b
has the same solution set as the vector equation
x1a1 + x2a2 + · · · + xnan = b
which, in turn, has the same solution set as the system of linear
equations whose augmented matrix is
a1 a2 · · · an b.
The equation Ax = b is consistent if−2b1 + b3 = 0.
(equation of a plane in R3)
x1a1 + x2a3 + x3a3 = b
if and only if b3 − 2b1 = 0.
Columns of A span a plane
in R3 through 0
Instead, if any b in R3
(not just those lying on a particular line or
in a plane) can be expressed as a linear combination of the
columns of A, then we say that the columns of A span R3
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Eric's freezer has a volume of 20,000 cubic inches. He freezes 30 cartons of strawberries in the freezer. Each carton is 10 inches long, 4 inches wide, and 5 inches high.
Answer: 120 inches cubed
Step-by-step explanation:
the probability of a rainy day is .25. assuming this probability holds for every day, what is the probability that in the next ten days, exactly three are rainy days? ( hint binomial)
The probability that in the next ten days, exactly three are rainy days will occur is 0.25028.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes
Probability p of a rainy day is 0.25
Using binomial theorem,
The Probability that in the next ten days, exactly three are rainy days will occur:
= 10c₃ p³(1-p)¹⁰⁻³
= 10c₃ (0.25)³(0.75)⁷
= 0.25028
Thus, The probability that in the next ten days, exactly three are rainy days will occur is 0.25028.
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two more after this one
The amount of money that Lisa would have after 9 years is equal to $5,183.2.
How to calculate the future value?Mathematically, compound interest can be calculated by using this formula:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.T represents the time measured in years.Substituting the given parameters into the compound interest formula, we have;
Future value, A(t) = 4,000(1 + 0.029/2)^{2 × 9}
Future value, A(t) = 4,000(1 + 0.0145)^{18}
Future value, A(t) = 4,000(1.0145)^{18}
Future value, A(t) = 4,000(1.2957968642629875)
Future value, A(t) = $5,183.2.
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Please help me with this question.
Answer:
Expression: 0.75m + 4.50
$8.25
Step-by-step explanation:
0.75m + 4.50
0.75(5) + 4.50
3.75 + 4.50
8.25
Given the sequence of numbers, a4=8, a5=12, a6=16, a7=20, and a8=24.
Which recursive rule can be used to find the nth term of the sequence, an?
a1=4; an=2an−1
a1=4; an=an−1+4
a1=−4; an=an−1+4
a1=−4; an=−2an−1
Answer:
[tex]a_1=-4, \,a_n=a_{n-1}+4[/tex]
Step-by-step explanation:
Clearly, our common difference is [tex]d=4[/tex], and we can see that the first term if we work backward from [tex]a_4[/tex] is [tex]a_1=-4[/tex].
Hence, by using the recursive formula [tex]a_n=a_{n-1}+d[/tex], we have our final formula as [tex]a_n=a_{n-1}+4[/tex]
Jose buy s shares for a social media company at $114.95 per share. He later sells the shares at $135.29 per share. Write an equation to show how much money (m) Jose has made on 5 shares.
The total amount of money Jose made on 5 shares is given by the equation A = $ 101.70
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of money Jose made on 5 shares be A
Now , the equation will be
The amount at which Jose buys the share = $ 114.95
The amount at which Jose sells the share = $ 135.29
So , the amount of money Jose made = amount at which Jose sells the share - amount at which Jose buys the share
Substituting the values in the equation , we get
The amount of money Jose made = $ 135.29 - $ 114.95
On simplifying the equation , we get
The amount of money Jose made = $ 20.34
Now , the amount of money Jose made on 5 shares = 5 x amount of money Jose made
On simplifying the equation , we get
The amount of money Jose made on 5 shares A = 5 x 20.34
The amount of money Jose made on 5 shares A = $ 101.70
Hence , the amount of money Jose made is $ 101.70
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