The number of divisors of 1730 of the form 4n + 1 is 20.
What do you mean by integers?An integer is a whole number, meaning it can be positive, negative, or zero, but it cannot be a fraction or a decimal. Integers are a subset of real numbers, which also include fractional and decimal numbers.
Integers are commonly used in mathematics and computer science for counting and for performing arithmetic operations such as addition, subtraction, multiplication, and division. They are also used to represent the magnitude of a quantity, such as the number of items in a set or the time elapsed in seconds.
In computer programming, integers are often stored as binary numbers, which are sequences of bits that represent positive or negative whole numbers. Different computer architectures have different numbers of bits for representing integers, with common sizes being 8, 16, 32, and 64 bits.
The number (10)10. (11)11. (13)13 is equal to 11 × 13 × 10 = 1730 in decimal.
A divisor of a number can be represented as (4n + 1) where n is a non-negative integer.
To find the number of divisors of 1730 of the form 4n + 1, we need to find the number of factors of 1730 that can be expressed as 4n + 1.
First, we find the prime factorization of 1730:
1730 = 2 × 3 × 5 × 29
Since 1730 is an odd number, one of its divisors must also be an odd number.
The only possible values for n are 0, 1, 2, ..., (number of odd divisors - 1).
In this case, the number of odd divisors of 1730 can be calculated as:
(number of ways to choose 0 odd factors) × (number of ways to choose 1 odd factor) × (number of ways to choose 2 odd factors) × ... × (number of ways to choose 4 odd factors)
= 1 × 4 × 5 × 1 = 20
Thus, the number of divisors of 1730 of the form 4n + 1 is 20.
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(-4mn)³*(-2m²)³ How do I simplify this?
Simplifying the given expression can be rewritten as: [tex](512m^9n^3)[/tex].
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents. Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive. Zero Exponent. When you have an exponent equal to zero, the result must be 1.For simplifying the given expression, it is necessary to apply the presented power rules previously.
The given expression is (-4mn)³*(-2m²)³. Thus,
Applying the rule - Power, you have:(-64m³n³) * [tex](-8m^6)[/tex]
Note that the rule should be apply in numbers and letters.
After that, you should apply the rule of Multiplication. See below:[tex](512m^9n^3)[/tex]
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Find the circumference of the circle
Answer:
C
Step-by-step explanation:
the circumference of a circle is
2×pi×r
r being the radius, which is half of the diameter.
in our case
r = 18/2 = 9 mm
so, the circumference is
2×3.14×9 = 18×3.14 = 56.52 mm
ochala bought a music system on hire purchase. He paid a total of sh 5,200 .if he started by paying a deposit of sh 2,300 for how many months did he pay the remaining money if each monthly installment was sh 2,900
4. You are painting the roof of a
boathouse. You are going to
place the base of a ladder
3.2 feet from the boathouse.
How long does the ladder
need to be to reach the
roof of the boathouse?
K
3.2 ft
12.6 ft
Answer:
ladder has to be at least 13 ft long
Step-by-step explanation:
l = length of the ladder
12.6² + 3.2² = l²
l² = 158.76 + 10.24 = 169
√l² = l = √169 = 13
The ladder is the hypotenuse of a right triangle with sides 12.6 and 3.2
A basketball player has made 13 out of 20 free throws so far this season. How many
consecutive free throws must the basketball player make to raise the free throw average
to 0.75? Justify your answer.
Answer:
Step-by-step explanation:
x=8
Cora is using successive approximations to estimate a positive solution to f(x) = g(x), where f(x)=x2 - 8 and g(x)=2x - 4. The table shows her results for different input values of x. Use Cora's process to find the positive solution, to the nearest tenth, of f(x) = g(x)
The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:
Input the initial value of x, for example x=0.
Calculate f(x) and g(x):
f(x) = x2 - 8 = 0 - 8 = -8 g(x) = 2x - 4 = 0 - 4 = -4If f(x) is less than g(x), then x should be increased and vice versa.
Increase or decrease x accordingly and calculate the new values of f(x) and g(x).
Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.
The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
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If 3 lbs of fertilizer will cover 408 square feet of lawn, how many pounds would be needed to cover 1088
square feet?
One pound of nitrogen or mixed fertilizer is recommended per 1,000 square feet of lawn and your particular fertilizer contains 20% nitrogen.
How many pounds would be needed to cover 1088 square feet?
In order to calculate pounds per square foot you just need to do some simple math. Simply take the area (in square feet) you want to use as a measurement and divide the number of pounds you want to place on the area by that number.Two gallon cans of paint cover up to 800 square feet, which is enough to cover an average size room. This is the most common amount needed, especially when considering second coat coverage. Three gallon cans of paint cover up to 1200 square feet.Pounds or Pounds Force per Square Foot is a British (Imperial) and American pressure unit which is directly related to the psi pressure unit by a factor of 144 (1 sq ft = 12 in x 12 in = 144 sq in). 1 pound per square foot equals 47.8803 pascals.To learn more about pounds refers to:
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a = [1 0 -4 0 3 -2 -2 6 3] b = [4 1 -4] Denote the columns of A by a1, a2, a3, and let W = Span {a1, a2, a3,}. a) is b in {a1, a2, a3,}? how many vectors are in {a1, a2, a3,}? is b in W?
If a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] and we denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,} , then b is not in {a₁, a₂, a₃} .
The Span of set of vectors is set of all linear combinations of those vectors. In other words, it's the set of all possible vectors that can be created by taking a weighted sum of the original vectors.
The span of a set of vectors is a subspace of the vector space in which the vectors lie, and it's the smallest subspace that contains all of the original vectors.
The vector b is not in {a₁,a₂,a₃} because "b" is not equal to any of the column vectors of A. Clearly, there are only 3 vectors in {a₁,a₂,a₃}.
The given question is incomplete , the complete question is
a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] . Denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,}. Is b in {a₁, a₂, a₃} ?
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the sum of eleven and a number c
Answer:
11 + C
Step-by-step explanation:
Sum= +
You add 11 and C
Assume 2. 0 kg of apples is 1 dozen and that each apple has 8 seeds. How many seeds are in 14 kg of apples?.
Answer:56
Step-by-step explanation:
You divide 14kg by 2kg and get 7kg. So then you times 7kg by 8 seeds.
Hope this helps :)
help this is literally due today
If the diameter of the pool is 24ft, the area is 452.16 ft²
How to find the area of the pool?Here we have a circular pool and we want to find its area.
Remember that the area of a circle of radius R is given by:
A = pi*R²
Where pi = 3.14
Here we want to define the diameter as a value between 12 and 24 ft, so I will use 24 ft.
The radius is half of that, then we have:
R = 24ft/2 = 12ft
Then the area of the pool is:
A = 3.14*(12 ft)² = 452.16 ft²
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The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:
Triangle ABC has length of BC equal to 12 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees, and measure of angle DCB is 30 degrees.
What is the length of the wood that is needed to replace AD?
A. 6.2
B. 4.2
C. 6.9
D. 5.1
The length of the side AD that needed to be replaced is D. 5.1
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, tan = opposite/adjacent.
tan30° = DB/12.
DB = 12×tan30°.
DB = 6.93.
Now, m∠BCA = 30° + 15° = 45°.
Therefore,
tan45° = (AD + DB)/12.
AD + DB = 12.
AD = 12 - 6.93.
AD = 5.1.
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Answer:
5.1
Step-by-step explanation: got right on test
I dont understand may you please help me
Answer:4
Step-by-step explanation:
3
A rectangular field, 400 m long, has an area of 6 hectares. Calculate the perimeter of the field [ 1 hectare=10000m2] What's the answer to this question and what is the way to solve it!
The perimeter of this rectangular field is equal to 1,100 meters.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.Note: Area = 6 × 10,000 = 60,000 m^2.
Next, we would determine the width of this rectangle:
60,000 = 400W
W = 60,000 /400
Width, W = 150 m.
Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
Perimeter of a rectangle = 2(L + W)
Perimeter of a rectangle = 2(400 + 150)
Perimeter of a rectangle = 2(550)
Perimeter of a rectangle = 1,100 meters.
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The perimeter of the rectangular field with an area of 6 hectares and length of 400m is 1100 meters.
What is the perimeter of the field?The perimeter of a rectangle is expressed as;
P = 2( length + width )
Given the data in the question;
Length of the field = 400m Area of the field = 60,000m²Width of the field = ?First, we determine the width of the field using the area formula.
Area = Length × width
Plug in the values and solve for width
60,000m² = 400m × width
60,000m² / 400m = Width
Width = 150m
Now, the perimeter will be;
P = 2( 400 + 150 )
P = 2( 550 )
P = 1100 meters.
Therefore, the perimeter is 1100 meters.
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Find the best approximation to a solution of the following systems of equations. What the value for x? 4x 2y = 0 x +y = 11 -2 2 1
The best approximation to a solution of the system of equations is x = -11 and y = 22.
A system of equations is a collection of two or more equations with the same variables. Solving a system of equations means finding the values of the variables that satisfy all the equations in the system.
In this case, you have a system of two equations:
4x + 2y = 0 and x + y = 11.
To find the best approximation to a solution of the system, we can use substitution or elimination methods.
First, we can isolate one of the variables in one of the equations.
=> 4x + 2y = 0.
Dividing both sides by 2, we get:
=> 2x + y = 0.
Now we have one equation in terms of one variable, which is y.
Next, we can substitute the expression for y from this equation into the second equation:
=> x + y = 11.
Replace y with -2x
=> x + (-2x) = 11.
=> -x = 11.
=> x = -11.
Finally, we can substitute the value for x back into one of the original equations to find the value of y.
Let's substitute x = -11 into the first equation:
=> 4(-11) + 2y = 0.
=> -44 + 2y = 0.
=> 2y = 44.
=> y = 22.
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Caroline has two pieces of fabric, one is 90 inches wide and the other is 36 inches wide. If she wishes to cut the fabric into equal pieces that are as wide as possible, how wide should she cut the pieces?
Caroline should cut the fabric into 63 inches wide each
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
For example if a number is added to 20 and gives 50. what is the numbers
x+20 = 50
x = 50-20
x = 30
The total width of the pieces of fabrics = 90 + 36 = 126 inches
To cut the pieces into two equal part with maximum width, we divide the total width by 2
= 126/2
= 63 inches
therefore the fabric should be cut into 63 inches wide each
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Which meaurement repreent the ide length of a right triangle?
Right Triangle
NOT a Right Triangle
6 cm, 8 cm, 10 cm
12 cm, 35 cm, 37 cm
4 cm, 6 cm, 10 cm
10 cm, 24 cm, 26 cm
6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.
Which dimension best describes a right triangle?A right triangle, like the triangle below, is one in which one of the angles measures 90 degrees (a right angle). In most cases, right angles are shown by drawing a square at the angle's vertex.
For a right triangle, where c is the hypotenuse and a and b are the smaller sides, the Pythagorean Theorem gives us a2 + b2 = c2.
The hypotenuse is usually the longest. Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be 6, 8, and 10.
a2 + b2 = c2.
= 6^2 + 8^2 = 10^2
36 + 64 = 100.
so,
6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.
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The function f(x)=x√ is horizontally stretched by a factor of 2 to form function g(x).
What is the equation of g(x)?
The solution is , The equation of g(x) is g(x) = 2*x^(1/2).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
The original function f(x) is defined
as f(x) = x^(1/2)
which is the square root of x.
When the function is stretched horizontally by a factor of 2,
the x term becomes 2x.
So the new function g(x) is defined
as g(x) = 2*x^(1/2)
Hence, The solution is , The equation of g(x) is g(x) = 2*x^(1/2).
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Compare the rates to find which is greater.
49 meters in 28 hours or 56 meters in 40 hours
Answer:
Step-by-step explanation:
Equivalent rates can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate. The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour
If 5 glue sticks cost $9.65., then which equation would help determine the cost of 21 glue sticks?
.
5/$9.65 =21/
.
21/5=$9.65/
.
5/=21/$9.65
.
21/= $9.65/5
The equation which would help determine the cost of 21 glue sticks is 5 / 9.65 = 21 / x, where x is the cost of 21 glue sticks.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Given that,
Cost of 5 glue sticks = $9.65
Let x be the cost of 21 glue sticks.
Using proportional concept,
5 / 9.65 = 21 / x
Hence the equation is 5 / 9.65 = 21 / x
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solve for x
2x-24 4x+6
Answer:
x=33
Step-by-step explanation:
[tex]180=2x-24+4x+6[/tex]
[tex]180=6x-18[/tex]
[tex]198=6x[/tex]
[tex]x=33[/tex]
[02.03]
Solve for x: -3|2x + 61 = -12 (1 point)
O x = 1 and x = 5
O x = -1 and x = -5
O x = -9 and x = 3
O No solution
For, -3 |2x + 6| = -12 the value of x = -1 and - 5
Correct option is: x = -1 and x = -5. This can be solved using the concept of equation.
What is an equation?Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
-3 |2x + 6| = -12
or, 2x + 6 = 4
or, 2x + 6 = ± 4
or, 2x + 6 = 4
or, 2x = -2
or, x = -1
on the other hand,
2x + 6 = -4
or, 2x = - 10
or, x = -5
So, the value of x = -1, and -5
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Mr adbul made tuna and curry potato filling for ome puff. 3/5 of the filling he made wa tuna and the ret wa curry potato
Answer is 2 5/8 tuna filling at first.
How much tuna filling did he make at first?At first, he made 2 5/8 kg of tuna filling.
M r Abdul made tuna and curry potato filling for some puffs.
3/5 of the filling he made was tuna and the rest was curry potato.
So, amount of curry potato = 1- 3/5 = 2/5
Ratio of tuna & curry potato = tuna : curry potato
= 3/5 : 2/5 = 3 : 2
Let amount of tuna = 3x & amount of curry potato = 2x
After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.
According to the question, he then had equal amounts of tuna filling and curry potato filling left.
So, 3x - 1/8 = 2x + 3/4
Multiplying 8 in both sides we get,
⇒ 24x - 1 = 16x +6
⇒ 24x - 16x = 7
⇒ 8x = 7
⇒ x = 7/8
So, 3x = (3×7/8) = 21/8 kg = 2 5/8 tuna filling at first.
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X^2-5x+2=0 select the two values of x that are roots of this equation
Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.
what is discriminant ?When use the formula to solve a problem, the "discriminant" is the value that helps in recognizing the various sorts of solutions. In a mathematical formula (a quadratic equation), it is a special function of a cross that reveals information out about bases of the equation. The "b" term must be square-rooted before the "a" term and "c" term may be isolated by four times to calculate the discriminant. It has a (delta) next to the letter "D" that stands for discrimination. Positive discriminant describes a quadratic equation with two unique real number solutions. Repeated positive integer solutions exist for a quadratic equation with a characteristic of zero. A negative discriminant reveals that none of the solutions is a real number.
given
x2 - 5x + 2 = 0
the roots of the equation
x = -b ±[tex]\frac{\sqrt{b^{2} - 4ac} }{2a}[/tex]
x = 5 ± [tex]\sqrt{17} / 2[/tex]
Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.
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Ellen has maxed out her credit card at $19,500 and vows not to make any other credit card purchases. Her credit card company charges 1. 5% interest per
month, and the minimum monthly payment is all interest due plus 3% of the principal balance. How much of the balance can Ellen pay down if she pays the
minimum payment only for 3 months? Round the answer to the nearest cent.
After three months, Alan would have paid off how many dollars?
Answer:
$538
Step-by-step explanation:
The minimum payment in the first month would be:
Minimum payment = 1.5% * $19,500 + 3% * $19,500 = $292.25
At the end of the first month, the balance would be:
Balance = $19,500 + $19,500 * 1.5% - $292.25 = $19,318.375
In the second month, the minimum payment would be:
Minimum payment = 1.5% * $19,318.375 + 3% * $19,318.375 = $291.26
At the end of the second month, the balance would be:
Balance = $19,318.375 + $19,318.375 * 1.5% - $291.27 = $19,138.89
In the third month, the minimum payment would be:
Minimum payment = 1.5% * $19,138.89 + 3% * $19,138.89 = $290.26
At the end of the third month, the balance would be:
Balance = $19,138.89 + $19,138.89 * 1.5% - $290.26 = $18,961.62
So, Ellen would have paid off $19,500 - $18,961.62 = $538.38. The answer rounded to the nearest cent is $538
Given A(2,1), B(6,3), C(8,1), D(4,2) and E(5,1), shown below, prove that.
Note that the hint to demonstrating the above proof (that ΔABC ≅ ΔADE) is to compare the slopes of DE and BC. See the computation below.
What is a slope?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
Comparing both slopes, we have:
Slope of DE = 2-1/4-5 = 1/-1 = -1
Slope of BC = 3-1/6-8 = 2/-2 = -1
Since the slope of DE and BC are the same an they are not intersection, it means they are parrallel lines.
Since DE || BC
In ΔABC and ΔADE
∠DAE = ∠BAC
∠ADE ≈ ∠ABC (Correspoinding Angle)
∠AED = ∠ACB (Corresponding Angles)
Thus, ΔABC ≅ ΔADE.
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Full Question:
Given A(2,1), B(6,3), C(8,1), D(4,2) and E(5,1), shown below, prove that ΔABC ≅ ΔADE
The population of a city grew from 23,000 in 2010 to 25,000 in 2015. What was the average rate of change during this time interval
The average rate of change for a city population of the city was growing steadily and can be used to predict future population growth.
The average rate of change for a city can be calculated by subtracting the initial population (23,000 in 2010) from the final population (25,000 in 2015) and then dividing that number by the total number of years (five). The equation for this calculation is:
(Final Population - Initial Population) / (Number of Years)
Using this equation, the average rate of change for the city is calculated as follows:
(25,000 - 23,000) / 5 = 2,000 / 5 = 400
Therefore, the average rate of change for the city between 2010 and 2015 was 400 people per year. This means that on average, the population of the city increased by 400 people each year during this time interval. This calculation shows that the population of the city was growing steadily and can be used to predict future population growth.
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Solve for x in the diagram below
The value of the variable x in the given right angle expression is; x = 11
How to solve right angle problems?We know that a right angle simply means an angle that is equal to 90 degrees.
Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.
Thus;
5x + 35 = 90
Subtract 35 from both sides to get;
5x = 55
x = 55/5
x = 11
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how many faces edges and vertices does a rectangular prism have
A rectangular prism has 6 faces, 8 vertices and 12 edges.
What is rectangular prism?
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.
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Inverse Variation
Independent Practice
Suppose a camper took 2 h to ride around a resevoir at 10 mi/h at the beginning of the summer. By the end of the summer, she can ride around the resevoir in 1
h. What is her rate at the end of the summer?
A. 30 mi/h
B. 0.35 mi/h
C. 13.3 mi/h
D. 9.5 mi/h
Her rate at the end of the summer is 20 miles per hour.
What is her rate at the end of the summer?We can define the rate in this case as the change in position as a function of the time.
So, the rate would be something like a speed (exactly a speed, actually).
Initially, the camper travles at a rate of 10mi/h in 2 hours, so the total distance is:
d = (10mi/h)*2h = 20mi
And at the end of the sumer, the camper travels that distance in one hour, so the rate at the end of the summer is:
R = 20mi/1h = 20mi/h
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-1 = 2x - y, 8x - 4y = -4 using substitution
Answer:
Infinitely many solutions
Explanation:
1) subtract “1” from both sides to get y by itself
Y=-2x-1
2) 4y+8x=-4 share a gcf of “4” so you can divide the whole equation by 4
y+2y=-1
Now substitute “-2x-1” as y
(-2x-1)+2x=-1
-2x and 2x cancel each other and so does -1 and -1
Hence, this system has infinitely many solutions
Answer:
x = 0, y = 1.
Step-by-step explanation:
We can solve for the variables x and y by using substitution. Let's start by solving the first equation for one of the variables:
-1 = 2x - y
y = 2x + 1
Next, we'll substitute y = 2x + 1 into the second equation:
8x - 4y = -4
8x - 4(2x + 1) = -4
Expanding the second equation:
8x - 8x - 4 = -4
-8x - 4 = -4
-8x = 0
x = 0
Finally, we can use one of the equations to find y:
y = 2x + 1
y = 2(0) + 1
y = 1
So, the solution is x = 0, y = 1.