In the expression (ax⁶)^(1/n) = 7x³ the values of a and n are
49 and 2 respectivelyHow to solve for a and nThe expression (ax⁶)^(1/n) = 7x³is simplified as follows
Information from the problem
(ax⁶)^(1/n) = 7x³
to make x⁶ to be equal to x³ we use the powers
6 * y = 3
y = 1/2
hence n = 2
substituting n = 2 and solving
(ax⁶)^(1/2) = 7x³
√(a) x³ = 7x³
dividing both sides by x³
√a = 7
squaring both sides of the equation wil result to
√a = 7
(√a)² = 7²
a = 7²
a= 49
We can therefore say that a = 49 and n = 2
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Eliud wa running 125 mile per week. Now, he’ running 20% more mile per week. How many mile i Eliud running per week? Write and olve an equation to determine how many mile Eliud i now running per week, r. A- 25 mile per week
B- 15 mile per week
C-150 mile per week
D- 250 mile per week
Eliud was running 125 miles per week, and now he is running 20% more. To determine how many miles Eliud is now running per week, the equation is 125 plus 125 times 0.2, which equals 150 miles per week.
125 + (125 x 0.2)
=125 + 25
= 150
Eliud was previously running 125 miles per week. To determine how many miles he is now running per week, an equation needs to be solved. The equation is 125 plus 125 times 0.2, which equals 150 miles per week. This is because 20% of 125 is 25, so 125 plus 25 is 150. Therefore, Eliud is now running 150 miles per week, which is an increase of 25 miles per week from his previous running amount. This increase of 25 miles per week is equivalent to 20% more than he was previously running. Solving this equation reveals that Eliud is now running 150 miles per week, which is an increase of 20% from his previous mileage.
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How old is the king, how many children has he, and how long is his boat? Given that the product of three positive integers gives 32118 which answers these questions. The length of his boat is given in metres, the king has sons and daughters, he has more years than his children, but he is not yet one hundred years old. please help fast please
If the product is positive integers is 32118, then the king's age is 53, his number of children is 6 and is length of boat is 101m.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
The puzzle demands for three numbers - x, y, z which represent the king's number of children, age and length of boat respectively.
It will be advantageous to conceive the problem thus: We have but one unknown; this unknown, however, is not a number but a tripartite unknown, a triplet (x, y, z) of numbers.
It is very important to split the condition that is expressed by the statement of the problem into appropriate clauses. This needs careful con-sideration of details and considerable regrouping. After several trials (which we skip to save space) we may arrive at the following two clauses:
(r1), x, y, and z are positive integers different from 1 and such that -
xyz = 32118
(r2) 4 ≤ x < y < 100
Begin with (r1) which leaves only a finite number of possibilities, whereas (r2), which does not restrict z at all, leaves an infinite number.
Therefore, we examine (r1). Now, 32118 is divisible by 6, and so we easily decompose it into prime factors:
32118 = 2 × 3 × 53 × 101
For a decomposition into three factors we have to combine two of the four primes. Therefore, there are only six different ways to decompose the number 32118 into a product of three factors all different from 1:
6 × 53 × 101
3 × 101 × 106
3 × 53 × 202
2 × 101 × 159
2 × 53 × 303
2 × 3 × 5353
Of these six possibilities, the remaining requirement (r2) rejects all except the first one, and so we obtain -
x = 6 , y = 53 and z = 101.
Therefore, the values of x, y and z are 6, 53 and 101 respectively.
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The diagonal PR of a cyclic quadrilateral PQRS bisect ZOPS and ZQRS. Show that PR is a diameter of the circum-circle PQRS.
Let the circum-circle of the cyclic quadrilateral PQRS be O.
The circum-circle of the cyclic quadrilateral PQRSSince PQRS is a cyclic quadrilateral, the four points P, Q, R, S are concyclic. Thus, the line joining any two points among them will pass through the center O of the circum-circle. Since PR bisects ZOPS and ZQRS, it follows that PR passes through the center O of the circum-circle.Therefore, PR is a diameter of the circum-circle PQRS.Let PQRS be a cyclic quadrilateral with PQ bisected at Z, QS bisected at O, RS bisected at P and PS bisected at S. Let PR be the diagonal of the quadrilateral.We have to prove that PR is a diameter of the circumcircle of PQRS.Since the quadrilateral is cyclic, the four angle bisectors all intersect at one point, which is the centre of the circumcircle of the quadrilateral, let us call it O. We know that the angle bisectors divide the angles of the quadrilateral into two equal parts. Therefore, the angles QOP, ROP, POR and QOS are all right angles. This implies that PQRS is a rectangle with the diagonal PR as its diameter.Moreover, the Euler’s theorem states that the sum of the angles of a cyclic quadrilateral is equal to two right angles. This implies that the angles POQ and RQS are equal. So, the line PR bisects the angles POQ and RQS.Thus, we have proved that the diagonal PR of a cyclic quadrilateral PQRS bisects ZOPS and ZQRS, and is a diameter of the circumcircle PQRS.To learn more about the circum-circle of the cyclic quadrilateral PQRS refer to:
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Solve the radical equation.
Check all solutions to eliminate extraneous solutions
and do not include them in your answer.
If your answer is not an integer then type it as a
decimal rounded to the nearest hundredth.
√2x +3-√x+2=0
X =
The radical equation solution is x= -1.
What is radical equation?
The unknown is a component of the radicand of a radical expression in a radical equation. Equations with an uncertain value enclosed by a radical sign are referred to as radical equations (also known as irrational) equations. Radical expressions are those that fall inside the square root. Radical inequality refers to an inequality contained within a radical.
Here the given radical equation is
=> [tex]\sqrt{2x+3} -\sqrt{x+2}[/tex] = 0
=> [tex]\sqrt{2x+3} = \sqrt{x+2}[/tex]
Now taking square on both sides then,
=> [tex](\sqrt{2x+3})^2 = (\sqrt{x+2})^2[/tex]
=> 2x+3 = x+2
=> 2x-x = 2-3
=> x = -1
Hence value of the x is -1.
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What is the standard form of the polynomial function in number 3 *?.
The correct option is A. The standard form of the polynomial function in number 3 is f(x) = 5[tex]x^{7}[/tex] +[tex]x^{4}[/tex] + 3x.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
What is the standard form of the polynomial function in number 3?
A. f(x) = 5[tex]x^{7}[/tex] +[tex]x^{4}[/tex] + 3x
B. f(x) = 5[tex]x^{7}[/tex] + 3x + [tex]x^{4}[/tex]
C. f(x) = [tex]x^{4}[/tex] + 5[tex]x^{7}[/tex] + 3x
D. f(x) = 3x + 5[tex]x^{7}[/tex] + [tex]x^{4}[/tex]
The city of Rock Hill has an approximate population of 70,000. An average of 100 people move in to Rock Hill every month and 150 people move out of Rock Hill each month. The City of Greenville has an approximate population of 61,000. An average of 200 people move into Greenville every month. In how many months will the populations of the 2 cities be the same?
In 36 months the populations of the 2 cities be the same .
What is additive comparison?
In an additive comparison, we question or state how much more (or less) one amount is in contrast to the other to determine the relationship between the two numbers. Additive comparison issues are typically word problems that can be resolved by creating an equation.
The comparison approach is a technique for rewriting each equation with the same variable as the subject in order to solve systems of independent equations. The initial variable to isolate can be any of the variables. Every equation is now an isolated-subject equation with an isolated variable.
Let,
if in about x month, the population of the towns will be equal .
the equation will be;
70,000 + (150-100)x = 61,000 - 200x
⇒ 70,000 + 50x = 61,000 - 200x
⇒ 250x = 9000
⇒ x = 9000/250
⇒ x = 36
So, in 36 months the populations of the 2 cities be the same .
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Is the solution of the equation 2x y 5 and 3x 2y 11 *?.
The value of x = 3 and y = 1 is the solution.
Two or more algebraic equations that have a common variable and are solved simultaneously are referred to as simultaneous equations (that is, simultaneously). For instance, the simultaneous equations x + y = 5 and x - y = 6 are created by concurrently solving two equations that have the same unknown variables, x and y. Multiple techniques, including the substitution method, elimination approach, and visual methods, can be used to solve simultaneous equations.
We have 2 equations,
2x - y = 5 (equation 1)
3x + 2y = 11 (equation 2)
We can solve the given equations simultaneosuly.
Multiplying equation 1 by 2,
4x - 2y = 10
Adding the 2 equations,
4x - 2y = 10
3x + 2y = 11
⇒ 7x = 21
⇒x = 3
Substituting the value of x = 3 in equation 1,
2x - y = 5
⇒ 6 - y = 5
⇒ y = 1
Hence, the values of x and y are 3 and 1 respectively; this is the solution of the equation.
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Which Compression is not correct
-3 < 4
3 < 6
1 > -9
-8> -6
Answer:
5p
6d6errryd6tj4wytejytjwyreyrj
Can you please help me?
9x² + 24x + 16 is equal to (3x + 4)².
This is a perfect square trinomial equation.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
9x² + 24x + 16
This can be written as,
(3x)² + 2 x (3x) x 4 + 4²
This is the perfect square trinomial of (3x + 4)².
[ (a + b)² = a² + 2ab + b² ]
Thus,
9x² + 24x + 16 is a perfect square trinomial equation.
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In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
The required measure of the angles x and y is given as 50°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
As it can be seen, x and y are alternate-opposite equal angles,
x = y
Now,
Adding complementary angles to 180°,
x + 60 + 70 = 180
x = 180 - 130
x = 50°
So,
x = y = 50°
Thus, the required measure of the angles x and y is given as 50°.
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Help me answer all 4 of these please!!!
Step-by-step explanation:
for first image →
Option B ) 8n + 4
for second image →
Option A ) The number of minutes Dylan practises each weekdays
What is the domain of CD X?.
The domain of function, (cd)(x) is all real values of x except x = 2, i.e., (−∞,2)∪(2,∞).
The domain of a function is defined as a set of values accepted by function. In this case, we have a rational function. A rational function will only be defined if the denominator is not equal to zero. We have, two functions, c(x) = 5/ x - 2 and
d(x) = x + 3. We should determine the domain of (cd) (x). The product of two is (cd) (x) = c(x) . d(x)
=> (cd)(x) = (5/(x - 2) )(x + 3) = 5(x+3)/(x -2)
Which is a rational function. So, the function will be defined if the denominator is not equal to zero, i.e., x - 2 ≠ 0 => x ≠ 2. Thus, domain set of function contains all real numbers values except 2. Therefore, the required domain of function (cd) (x) is all real values of x except 2.
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Complete question:
If c(x) = 5 / x - 2 and d(x) = x + 3. What is the domain of (cd)(x)?
what is a devided by a% of a
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE x}\% of \textit{\LARGE y}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE x}}{100} \right)\cdot \textit{\LARGE y} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{a\% of a}}{\left( \cfrac{a}{100} \right)a}\implies \cfrac{a^2}{100} \\\\[-0.35em] ~\dotfill[/tex]
[tex]a\div \cfrac{a^2}{100}\implies \cfrac{a}{1}\div \cfrac{a^2}{100}\implies \cfrac{a}{1}\cdot \cfrac{100}{a^2}\implies \cfrac{a}{a^2}\cdot \cfrac{100}{1}\implies \cfrac{1}{a}\cdot 100\implies \cfrac{100}{a}[/tex]
make me brainalist
I'm in need of it
If you would like to know what is a divided by a% of a, you can write it as follows:
a divided by a% of a:
a/ (a% of a) = a/ (a% a) = a/ (a/100* a) = a/(a^2/100) = a * (100/a^2) = 100 / a
The correct result would be 100/a.
What is the molar mass of nh3?.
Answer:
17.031g/mol
Step-by-step explanation:
pay attention in class
[tex]-4y^{5} +20y^{3}[/tex]
A die ha ix face numbered 1 to 6. On a ingle roll of the die,find the probability of:
a Getting the number 6
b Getting the number 10
c Not getting the number 6
d Getting one of the number 1,2,3,4,5 or 6
PLS WITH EXPLANATION <3
The probability of getting number 6 on a single roll of the fair die is 1/6; not getting 6 is 5/6; getting number 10 is 0 and getting any number of 1-6 is 1.
a) The probability of getting the number 6 on a single roll of a fair die numbered 1 to 6 is 1/6, or approximately 0.17. This is because there is a single outcome (rolling a 6) out of a total of 6 possible outcomes (rolling any number from 1 to 6) that will result in rolling a 6.
b) The probability of getting the number 10 on a single roll of a fair die numbered 1 to 6 is 0, because the die only goes up to 6.
c) The probability of not getting the number 6 on a single roll of a fair die numbered 1 to 6 is 5/6, or approximately 0.83. This is because there are five outcomes (rolling any number from 1 to 5) out of a total of 6 possible outcomes (rolling any number from 1 to 6) that will not result in rolling a 6.
d) The probability of getting one of the numbers 1, 2, 3, 4, 5, or 6 on a single roll of a fair die numbered 1 to 6 is 1 because there is only one outcome out of one possible outcome that is not getting one of the numbers 1, 2, 3, 4, 5 or 6.
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What must be known to use the law of sines to find a missing measurement in a triangle?.
If two of the angles and one of the sides of an oblique triangle are known, the Law of Sines can be used to find the missing lengths or angle measurements.
We cannot utilize the formulas specified for right triangles to solve oblique triangles; instead, new formulas must be used. We'll look at how the Law of Sines can be applied to resolve oblique triangles.
The Sine Rule:
The ratios of the length of a side to the sine of the angle opposite the side must all be the same if A, B, and C are the measurements of the angles of an oblique triangle and a, b, and c are the lengths of the corresponding sides.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
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What will be the roots of the equation 3x² 7x 5 0?.
Therefore, there are no solutions to the given quadratic equation. 57 and −2. Yes, there are two real roots in the given equation.
How do I locate an equation's roots?The formula for determining the roots is x = (-b (b2 - 4ac))/2a. D = b2 minus 4ac is the discriminant. The equation has two real and distinct roots if D is greater than zero.
What is the sum of X2 5x7 0's roots?As a result, this equation does not have any actual roots.
What are the three quadratic equation formulas?Quadratic equations can be solved in three basic ways: completing the square, using the quadratic formula, and factoring.
When a given quadratic equation is multiplied by ax 2 + bx + c=0, we obtain a=2, b=7, and c=5.
Now, x x x using the quadratic formula.
= \s2×3 \s−7± \s7 \s2 \s −4×3×−5
= \s6 \s−7± \s49+60
= \s6 \s−7± \s109
= \s6 \s−7+ \s109
\s and x= \s6 \s−7− \s109
=0.57 and x=−2.91
Therefore, 0.57 and 2.91 are the answers to the given quadratic equation.
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Full Question = Solve the following equations.
3x 2 +7x−5=0
Show all your working and give your answer correct to 2 decimal places.
In a certain examination 52 candidate offered biology 60 offered hitory 96 offered mathematic 21 offered biology and hitory 22 offered mathematic and biology 16 offered mathematic and hitory if 7 candidate offered all the three ubject
Satisfying all the given situations, there were 156 candidates in the examination.
We can use the principle of inclusion-exclusion to solve the problem.
The principle of inclusion-exclusion states that the total number of elements in the union of two or more sets is equal to the sum of the number of elements in each set, minus the number of elements in their intersection.
Here, let A be the set of candidates who offered biology, B be the set of candidates who offered history, and C be the set of candidates who offered mathematics.
Using the principle of inclusion-exclusion, the total number of candidates, N, can be found as follows:
N = (A U B U C) = (A + B + C) - (A ∩ B + B ∩ C + A ∩ C) + (A ∩ B ∩ C)
where A U B U C is the union of the three sets, A ∩ B is the intersection of A and B, and so on.
Given that:
|A| = 52, |B| = 60, |C| = 96
|A ∩ B| = 21, |A ∩ C| = 22, |B ∩ C| = 16
|A ∩ B ∩ C| = 7
Therefore,
N = (52 + 60 + 96) - (21 + 22 + 16) + 7
N = 156
Hence, there were 156 candidates in the examination.
The problem seems incomplete, it must have been
"In a certain examination, 52 candidates offers biology,60 offers history,96 offers mathematics, if 21 offered both biology and history,22 offered mathematics and biology, and 16 offered mathematics and history. If 7 candidates offered all the subject. how many candidates were there for the examination?"
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What is the sum of in the interior angles of a 21-gon (21 sides)? S=180 (n -2)
The sum of the interior angles of a 21-gon (21 sides) is 3420°.
What are Interior angles?
Any angle that is created between two of a polygon's adjacent sides is said to be its internal angle. The internal angle of a polygon is what we might refer to as the angle measured at the interior portion of a polygon.
The polygon has 21 sides.
we can find the sum of all interior angles of the polygon by using this formula :
S = 180 ( n - 2)
So, S = 180 (21 - 2)
= 180 × 19
= 3420°.
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[tex]1/2 (x-5)=9[/tex]
What is the answer to this
The expression that represents the shaded length of the number line would be = 3/20 × 9/20. That is option C.
What is a number line?A number line is defined as the graduates line that is used to represent the position of both positive and negative real numbers.
The shaded length of the number line contains 20 bars with a total of 9 shaded bars.
There are a total number of 3 per each bar of the number line, therefore, the shaded length of the number line would be = 3/20 × 9/20.
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Consider the following rational function fff. f(x)=\dfrac{6x^3-x^2+7}{2x+5}f(x)= 2x+5 6x 3 −x 2 +7 f, left parenthesis, x, right parenthesis, equals, start fraction, 6, x, cubed, minus, x, squared, plus, 7, divided by, 2, x, plus, 5, end fraction Determine fff's end behavior. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to -\inftyx→−∞x, \to, minus, infinity. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to \inftyx→∞x, \to, infinity.
The end behavior of the rational polynomial function [tex]f(x) = \frac{6x^3 - x^2 + 7}{2x + 5}[/tex] is,
{x → ∞, y → ∞ and x → - ∞, y → ∞}.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
Given, A rational polynomial function [tex]f(x) = \frac{6x^3 - x^2 + 7}{2x + 5}[/tex].
Now A cubic function divided by a linear function would result in a quadratic function, And as the coefficients of the highest degree terms of both the highest terms are positive the coefficient of the highest term of the quadratic function will also be positive and it's graph will be a parabola that opens upwards and symmetric about the y-axis.
Therefore, The end behavior will be when x tends to positive infinity y goes to positive infinity and when x tends to negative infinity y goes to positive infinity.
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Find the value of k. Then find the angle measures of the polygon.
2kº
45°
к
Sum of angle
measures: 180°
Answer:
67.5°
Step-by-step explanation:
180 -45 = 135
135 / 2
k= 67.5
How to solve a function?.
Answer: When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function f(x)=5−3x2 f ( x ) = 5 − 3 x 2 can be evaluated by squaring the input value, multiplying by 3, and then subtracting the product from 5.
Step-by-step explanation:
Functions is an important branch of math, which connects the variable x with the variable y. Functions are generally represented as y = f(x) and it states the dependence of y on x, or we say that y is a function of x.
5x / √5
help me please
Answer:[tex]\sqrt{5x[/tex]
Step-by-step explanation:
Is log inverse and antilog same?.
Yes, the anti-logarithm which is also called an antilog is the inverse of the logarithmic transform.
The antilogarithm, also referred to as an antilog, is the inverse of the logarithm transform. Since the base-10 logarithm of 1000 is 3, the anti-logarithm of 3 is 1000. To find the anti-logarithm of a base-10 logarithm, raise it by ten.
We are aware that an exponential is the inverse of a log function. We know that f(x) = log sub(x) has the inverse, f(y) = b, as a result (y). When working with the natural log, the inverse of f(x) = ln(x) is f-1(y) = ey if the base is e.
A logarithm's and an antilog's basis is 2.7183. The natural logarithm and antilog should be calculated by multiplying the logarithm and antilog, whose bases are 10 and 2,303, respectively.
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5x=15 solution for math problem math
Answer: 3
Step-by-step explanation:
5x = 15
Divide both sides by 5:
x = 3 :>
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5x = 15}[/tex]
[tex]\textbf{DIVIDE 5 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{5x}{5} = \dfrac{15}{5}}[/tex]
[tex]\textbf{SIMPLIFY it}[/tex]
[tex]\mathsf{x = \dfrac{15}{5}}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
5,3,1.8 geometric sequence
Answer:
Step-by-step explanation:
3. Rule: output = input +29. Additional practice 7-4 use tables to represent input/output relationships
output of the given input/output relationships is 36 and 25.
What is the input-output table's rule?To illustrate a function, an input-output table can be used, as in the example below. The same function rule connects every pair of numbers in the table. To find each output number, multiply each input number (-value) by 3. ( -value).
Input-output analysis table: what is it?
The table of input-output analysis measures the flows of outputs from one industry as inputs into another (in rows) (in columns). In the input-output analysis paradigm, the original demand shift and its direct, indirect, and induced implications can be used to examine the overall economic impact of an event.
output = input +29
input= 7
output = input +29=7+29=36
input= -4
output = input +29= -4+29=25.
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