The given equation has 161700 distinct solution.
If a sum of non-negative integers whose values is pre-defined say m is equal to a fixed value say n such that:x1+x2+x3+...+xm=n then the total combination of m non negative integers x1,x2,...xm in mathematical form can be written as: n+m−1Cm−1.
The above problem can also be written as:
x1+x2+x3+x4=100x1≥1x2≥2x3≥0x4≥0
Here x3 and x4 are non-negative integers and there is a restriction on x1 and x2.
Removing the restriction on x1 and x2 as:100 - 1 - 2 = 97
The number of distinct solution that the equation x1+x2+x3+x4=100 has is equivalent to the non-negative solution. of x1+x2+x3+x4=97 and is given by:
97+4−1C4−1=100C3=161700
Hence, the number of distinct solution that the equation x1+x2+x3+x4=100 has is 161700.
To find solution of equationThe solutions of equations basically depends on the power of variables present on it .
The solutions of equations also show that the how much the power of variables Is present that times it cuts the axis .
For example
1.if x+2=0 then x=—2 that means it has one solution and it also means it cut the x -axis one time .
2.if x^2–4=0 then x have two values that is x=+2,x=—2 it also means it cut the x-axis two times
Similar for power is 3 then it have three solution.
And so on for if power is n then it have solutions .
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Write an equation for the line in slope-intercept form.
Answer: y=2+4x
Step-by-step explanation:
The y-intercept is 2, and 4/1 means it goes up 4 right 1.
Consider the graph of the function [tex]f(x)=e^x[/tex]
What is the range of function g if [tex]g(x)=f(x)+3[/tex]?
A. (3, ∞)
B. (-∞, ∞)
C. (-∞, 3)
D. (-3, 3)
The range of the function g is B. (-∞, ∞).
What is function?Function is a mathematical expression that assigns unique output to each input of a given domain. It is a way of mapping one set of values to another set of values to describe the relationship between them. Functions are important mathematical tools used to model and solve a variety of real-world problems.
The range of a function is the set of all possible output values that the function can produce. In this case, the function g is a linear function which means that its graph is a straight line. This means that the function can produce any real number output value, and so the range of the function is (-∞, ∞).
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solve log x base 3 - 3log 3 base x = 2
The value of x from the logarithmic equation are x = 1/3 and x = 27
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the equation be represented as A
Now , the value of A is
log₃ ( x ) - 3 logₓ ( 3 ) = 2 be equation (1)
Applying the logarithm rules , we get
log₃ ( x ) - 3/log₃ ( x ) = 2
Let the value of log₃ ( x ) = t
So , Substituting the values in the equation , we get
t - 3/t = 2
On simplifying the equation , we get
t = 3 and t = -1
Substituting the value of t in the equation , we get
log₃ ( x ) = 3
x = 27
And ,
log₃ ( x ) = -1
x = 1/3
Hence , the value of logarithmic equation is 1/3 and 27
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helpp:D
yall amazing:D
Answer:
30/49
Step-by-step explanation:
Answer:
30/49
Step-by-step explanation:
6/7÷1 2/5
=6/7÷7/5
=6/7*5/7
=30/49
What is the value of (−12) exponet3?
−15
−1,728
−36
−144
Answer: -1728
Step-by-step explanation:
-12^3 = 144 * -12 = -1728
How to do long division step by step grade 6?
Remember to divide, multiply, subtract, and drop down until each digit in the dividend has been divided in long division problems. The solution to the division issue is the quotient.
Long division is explained in the following steps:
Put the dividend and the divisor in their proper places.
Take the dividend's first digit from the left.
If this digit is more than or equal to the divisor, divide it by the divisor and write the quotient on top.
To calculate the difference, write the product below the dividend and subtract the result from the dividend. If this difference is less than the divisor and no numbers remain in the dividend, this is termed the residual and the division is completed. If there are more digits in the dividend to be handed down, we repeat the operation until there are no more digits more digit left in the dividend.
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F(c)=x+3/2
Find f(2)
F^-1(x)
F^-1(12)
After using inverse function the answers are
a) f(2) = [tex]\frac{5}{2}[/tex]
b) [tex]f^{-1}(x)[/tex] = 2x-3.
c) [tex]f^{-1}(12)[/tex] = 21.
What is inverse function?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
The output of a function is returned by the inverse function, which also returns the initial value.
Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.
Here the given function f(x) = [tex]\frac{x+3}{2}[/tex]
a) Put x= 2 into f(x) then
=> f(2) = [tex]\frac{2+3}{2}[/tex]
=> f(2) = [tex]\frac{5}{2}[/tex]
b) Now to find inverse function , take y=f(x) then
=> y = f(x)
=> y = [tex]\frac{x+3}{2}[/tex]
Now interchange x and y and solve for y then,
=> x = [tex]\frac{y+3}{2}[/tex]
=> 2x= y+3
=> y = 2x-3
Then y = [tex]f^{-1}(x)[/tex]
=> [tex]f^{-1}(x)[/tex] = 2x-3.
c) Now put x=12 into [tex]f^{-1}(x)[/tex] = 2x-3 then
=>[tex]f^{-1}(12)[/tex] = 2(12)-3 = 24-3 = 21.
=>[tex]f^{-1}(12)[/tex] = 21.
Hence the answers are ,
a) f(2) = [tex]\frac{5}{2}[/tex]
b) [tex]f^{-1}(x)[/tex] = 2x-3.
c) [tex]f^{-1}(12)[/tex] = 21.
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Use Pascal's Triangle to expand (5x + 5)³. Express your answer in simplest form.
Submit Answer
Using Pascal's triangle the expansion of the expression [tex](5x+5)^3[/tex] is [tex]125x^3+375x^2+375x+125[/tex].
What is Pascal's triangle?
The triangle can be used to calculate the coefficients of the expansion of [tex](a+b)^n[/tex] by taking the exponent n and adding 1. The coefficient will correspond with line n+1 of the triangle.
Here for [tex](5x+5)^3[/tex] , n= 3 so the coefficient of the expansion will correspond with line 4.
The expansion follow the rule ,
[tex](a+b)^n=c_{0}a^nb^0+c_{1}a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_{n}a^0b^n[/tex]
The values of the coefficients, from the triangle, are 1-3-3-1.
=> [tex]1a^3b^0+3a^2b+3a^1b^2+1a^0b^3[/tex]
Here substitute a=5x and b=5 then,
=> [tex]1(5x)^35^0+3(5x)^25+3(5x)^25^2+1(5x)^15^3[/tex]
=> [tex]125x^3+375x^2+375x+125[/tex]
Hence the expansion of the expression [tex](5x+5)^3[/tex] is [tex]125x^3+375x^2+375x+125[/tex].
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Imagin Math question
The required statements below correspond to the information shown by the graph.
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
According to the given graph, the required solution would be as:
Pool A is filling up "more than" Pool B because the "slope" of the graph for Pool A is "greater than" that of the graph for Pool B.
The "slope" of the graph tells you the unit rate in "gallons per minute".
Thus, the required statements above correspond to the information shown by the graph.
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Use point-slope form to write the equation of a line that passes through the point (- 5, 7) with slope -5.
The equation of the line in point-slope form is y = -5x - 28.
What is the point-slop?
The point-slope form is a way to express the equation of a straight line. It's an alternate form of the slope-intercept form y = mx + b. In point-slope form, the equation of a line is represented as y - y1 = m(x - x1) where (x1,y1) is a point on the line and m is the slope of the line, which represents the steepness of the line and the direction it's going (positive, negative or zero). By using this form, we can find the equation of a line that passes through a given point and has a known slope.
The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
To write the equation of a line that passes through the point (-5, 7) with a slope of -5, we can plug in the given values:
y - 7 = -5(x + 5)
Simplifying:
y = -5x - 35 + 7
y = -5x - 28
Hence, the equation of the line in point-slope form is y = -5x - 28.
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the mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. a random sample of 16 students will be selected and the mean number of pets for the sample will be calculated. what is the mean of the sampling distribution of the sample mean for samples of size 16 ?
The sampling distribution of the sample mean for samples of size 16, then, is 3.2 pets, which is the same as the mean number of pets owned by the population of students at the high school.
The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. To better understand this population, a random sample of 16 students will be taken and the mean number of pets for the sample will be calculated.
This will provide us with the mean of the sampling distribution of the sample mean for samples of size 16.
To calculate this, we will first calculate the standard error of the mean, which is the standard deviation of the sample mean. This is calculated by dividing the population standard deviation (1.7 pets) by the square root of the sample size (16), resulting in a standard error of the mean of 0.43.
This means that the standard deviation of the sample means is 0.43 pets.
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A candy box is shaped like a rectangular prism. The box is 8 inches long, three inches wide, and 2 inches high. How much paper is used to wrap the box?
92 inches² paper would be needed to wrap the prism completely.
What is the Surface Area of a Rectangular Prism?The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.
Given here: The dimensions of the rectangular prism are 8,3,2 in inches.
Total surface area of a rectangular prism = 2(lb + bh + lh)
Thus TSA= 2(24+16+6)
=92 inches²
Hence, 92 inches² paper would be needed to wrap the prism completely.
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What is a formula for the nth term of the given sequence?
8, -4, 2...
PLEASE HELP!!
Formula for the nth term of the given sequence is [tex]a_{n} =8(\frac{-1}{2}) ^{n-1}[/tex]
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
We have to find the nth formula for the sequence 8, -4, 2...
As we observe the sequence we came to know it is a geometric sequence.
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value
In the given sequence the first term is a =8
The common ratio is -4/8=-1/2
The nth formula is [tex]a_{n} =ar^{n-1}[/tex]
[tex]a_{n} =8(\frac{-1}{2}) ^{n-1}[/tex]
Hence, formula for the nth term of the given sequence is [tex]a_{n} =8(\frac{-1}{2}) ^{n-1}[/tex]
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HELP! EASY POINTS!
Explain how to use the value q = 4 to show that q * q^3 is equivalent to q^4.
Answer:
see attached
Step-by-step explanation:
You want to use q=4 to show q×q³ = q⁴.
ExponentsThe attachment shows your calculator can help with this. It will compute and display the powers of values without requiring the intermediate calculations.
4 × 4³ = 4 × 64 = 256
4⁴ = 256 . . . . . . equivalent to 4 × 4³
Repeated multiplication
An exponent signifies repeated multiplication in the same way a coefficient signifies repeated addition.
4 × 4³ = 4 × (4·4·4) = 4·4·4·4 . . . . . using the associative property of multiplication
4⁴ = 4·4·4·4 . . . . . . . equivalent to 4 × 4³
__
Additional comment
In literal terms, ...
q×q³ = q·q·q·q = q⁴
for linear inequalities when your multiplying by (0,0) , etc is it always greater than sign
For linear inequalities when multiplying by (0,0) , it does not exist.
What is linear inequality?Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.
Given statement,
For linear inequalities when multiplying by (0,0) , It is always greater than sign.
Let the inequality be
ax > by
ax - by > 0
Multiplying with (0,0)
(ax - by)(0x + 0y) > 0
(ax - by).0 > 0
0 = 0
LHS = RHS
there is no inequality remained.
Hence, when multiplying by (0,0) there is no existence of inequality.
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What’s 18b=4 anyone know?
Answer: 4.5
Step-by-step explanation: 18b=4
18/4=4.5
4/4=1
4.5/1=4.5
In ΔABC, AB = 4x + 2, BC = 5x - 3, and AC = 2x + 4. The perimeter of the triangle is 36 units. Which angle in the triangle has the largest measure?
==================================================
Explanation:
Add up the three sides. Set the sum equal to the perimeter 36 so we can solve for x.
AB+BC+AC = perimeter
(4x+2)+(5x-3)+(2x+4) = 36
11x+3 = 36
11x = 36-3
11x = 33
x = 33/11
x = 3
Then use this x value to determine each side length.
AB = 4x+2 = 4*3+2 = 14BC = 5x-3 = 5*3-3 = 12AC = 2x+4 = 2*3+4 = 10The sides are
AB = 14BC = 12AC = 10As a check so far: 14+12+10 = 36 which helps confirm we have the correct x value, and correct side lengths.
-------------------------
Rule: The largest angle is always opposite the longest side of a triangle.
We found that AB = 14 was the longest side. The opposite angle is C, which means this angle is the largest angle.
This is why angle C is the final answer.
Which of the following is equivalent p
Answer: The second one on the left
Step-by-step explanation: Its not ant step-by-step but i recently just took this test
What is the value of the expression 5 *( 2 16 )/ 2 4 *( 2 2 )+ 1 4 of 16?
The final answer for the Expression is 33
The following is a list of BODMAS's expansions:
Brackett is abbreviated B. O is short for of. D denotes division. M denotes multiplication. A is for Addition S represents Subtraction.
Additionally, the order of operation is the same as B O D M A S.
Given:
The expression provided is
16 divided by 5*(2+16)/2-4*(2+2)+1/4, where * denotes multiplication.
5×(2 + 16)÷ 2 - 4 ×(2+2) + 1 ÷ 4 of 16
Solution:
5×(2 + 16)÷ 2 - 4 ×(2+2) + 1 ÷ 4 of 16
We shall first solve brackets using BODMAS.
= 5×(18)÷ 2 - 4 ×(4) + 1 ÷ 4 of 16
next of,
= 5×(18)÷ 2 - 4 ×(4) + 1 ÷ 4 × 16
Division follows.
= 5×9 - 4 ×(4) + 0.25 × 16
Next, multiplying
= 45 - 16 + 4
Finally, addition
= 45 + 4 - 16
= 49-16
= 33
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-3x+2c=-3, solve for x
Answer:
x = 1 + [tex]\frac{2c}{3}[/tex]
Step-by-step explanation:
-3x + 2c = -3
Subtract 2c from both sides
-3x = -3 - 2c
Divide by -3
x = 1 + [tex]\frac{2c}{3}[/tex]
Hope this helps! :)
What are the 5 algebraic expressions?
The 5 algebraic expressions are simple linear expression, linear expression, a product of two binomials, quotient of two expressions and quadratic expression.
Here are five examples of algebraic expressions:
1. 2x + 3: This is a simple linear expression that involves a variable (x) and two constants (2 and 3).
2. 4y - 7: Similar to the first example, this is also a linear expression, involving a variable (y) and two constants (4 and 7).
3. 3x^2 + 4x - 5: This is a quadratic expression, involving a variable (x) raised to the power of 2, a constant (3), a variable (x) and a constant (-5).
4. (x + 2)(x - 3): This is a product of two binomials, each one is a linear expression and the result of the product is a quadratic expression.
5. (3x + 4)/(x-2): This is a quotient of two expressions, the numerator is a linear expression and the denominator is a linear expression.
It's important to note that these are just a few examples and there are many different types of algebraic expressions, each with their own unique characteristics and properties. Algebraic expressions can become more complex as the student progresses, but the basic idea remains the same.
Therefore, The 5 algebraic expressions are simple linear expression, linear expression, a product of two binomials, quotient of two expressions and quadratic expression.
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What is the solution to this system of linear equation 2x 3y 3?
In the given question, we have to find the solution to this system of linear equations 2x+3y=3 and 7x-3y=24.
The given equations are:
2x+3y=3...…….(1)
7x-3y=24...…….(2)
To solve these equations we add equation 1 and 2,
2x+3y+7x-3y = 3+24
9x = 27
Divide by 9 on both side, we get
x = 3
Now putting the value of x in equation 1, we get
2(3) + 3y = 3
6 + 3y = 3
Subtract 6 on both side, we get
3y = -3
Divide by 3 on both side, we get
y = -1
The solution to this system of linear equations 2x+3y=3 and 7x-3y=24 is (3, -1).
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The complete question is:
What is the solution to this system of linear equations 2x+3y=3 and 7x-3y=24?
Bao has been notified by his electric company that his rates are going up on his graduated fee schedule. He currently pays: standard use plan 6. 5 cents/kwh for the first 600 kwh 12 cents/kwh for the next 600 kwh if his rates go up 1 cent in each category, find how much he will pay if he uses 875 kwh per month. Round to the nearest dollar. A. $72 b. $105 c. $66 d. $81 please select the best answer from the choices provided a b c d.
If he uses 875 kwh per month, he will pay about $81
The correct answer is an option (d)
Current use plan:
6.5 cents/kwh for the first 600 kwh
12 cents/kwh for the next 600 kwh
If the rates go up 1 cent in each category, the new rates would be:
7.5 cents / kWh for the first 600 kWh
13.0 cents / kWh the next 600 kWh
Given that he he uses 875 kwh per month.
We need to find the amount he will pay.
For first 600 kwh he will pay 7.5 cents/ kWh.
Then remaining rates would be 875 kWh - 600 kWh = 275 kWh
so, the expression for the total cost would be,
(600 × 7.5) + (275) × 13.0
= 4500 + 3575
= 8075 cents
= $ 80.75,
≈ $ 81
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QUICK!! if the simple interest on $3,000 for 6 years is 1,440 then what is the interest rate
Answer:
Step-by-step explanation:
I=Prt so
1440 = 3000r(6) and
1440 = 18000r so
r = .08
As a percentage, which rates are, this is 8%
Whats number 11 algebra 1
Answer:
C
Step-by-step explanation:
think of this… y-intercept is usually on the right and usually slope is in the middle of the equation
Answer:
Step-by-step explanation:
C might be the answer
Solve the system.
y = -x +3
2x + 2y = 4
Answer:
no solution
Step-by-step explanation:
So first, you want to have one of the variables able to cancel out when you add the equations together.
To do this, divide the second equation by two
2x+2y=4
divide by 2
x+y=2
Next, get the variables on the same side on the both equations, so the second thing you do is add x to both sides on the top equation
y=-x+3
+x +x
y+x=3
Now you times one of them by -1 so a variable will cancle out.
y+x=3
x+y=2
*-1
y+x=3
-x-y=-2
Since all the variables cancel out, there is no solution
The time, t, for a pendulum to swing varies directly as the square root of its length, l. When l=9, t=6. (a) Find a formula fort in terms of l. (b) Find t when l = 2.25.
Use the properties of radicals to simplify the expression. Explain.
Because both 2 and 72 under the radical are positive numbers, we can apply this rule:
[tex]\sqrt{2}\cdot\sqrt{72} = \sqrt{2\cdot72}[/tex]
Now that new version, [tex]\sqrt{2\cdot 72}[/tex] is the same thing as [tex]\sqrt{144}[/tex], because [tex]2\cdot72=144[/tex].
And [tex]\sqrt{144}=12[/tex].
12 is your answer.
The rule we used is [tex]\sqrt{a}\cdot\sqrt{b} = \sqrt{a\cdot b}[/tex], but it only works if both [tex]\sqrt{a}[/tex] and [tex]\sqrt{b}[/tex] are real numbers (AKA if a and b are both non-negative).
Which describe all decimal that te rational number
Type the correct answer in each box. Use numerals instead of words.
Consider this expression. (x + 5) (x - 7)
Complete the box to show the distributive property applied to this expression.
The correct number in the box is,
x - 7
x x² -7x
+ 5 5x - 35
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ (x + 5) (x - 7)
Now, We can simplify as;
x - 7
x x² -7x
+ 5 5x - 35
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