Explanation:
The log equation [tex]\text{x} = \log_b(\text{y})[/tex] is equivalent to its exponential form [tex]\text{y} = b^\text{x}[/tex]
For the exponential equation, we can replace x with any real number. We don't have to worry about things like dividing by zero. Therefore the domain of the exponential equation is "set of all real numbers".
The domain of [tex]\text{y} = b^\text{x}[/tex] is the range of [tex]\text{x} = \log_b(\text{y})[/tex]. The domain and range swap roles when going from original to inverse.
Therefore, the range of any logarithmic function is "set of all real numbers".
On a graph notice how the log curve stretches forever upward and downward. The base of the log doesn't matter.
Factorise a³ + b³ + c³ please i need this immediately
Answer:
a³(b-c) + b³(c-a) + c³(a-b) = (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)
This is a factorized form of the polynomial, as you can see it factorizes as a combination of difference of squares and difference of cubes.
here is one way to factorize the polynomial a³(b-c) + b³(c-a) + c³(a-b) step by step:
First, we can factor out a³ from the first term, b³ from the second term, and c³ from the third term:
a³(b-c) + b³(c-a) + c³(a-b) = a³(b-c) + b³(c-a) + c³(a-b)
Next, we can factor out (b-c) from the first and second terms, and (c-a) from the second and third terms:
a³(b-c) + b³(c-a) + c³(a-b) = (b-c)(a³ + b³) + (c-a)(b³ + c³)
We can factor out (a-b) from the first and third terms, and then we can use difference of cubes to factorise out:
(b-c)(a³ + b³) + (c-a)(b³ + c³) = (b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²)
Now we can combine like terms, and we get:
(b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²) = (a-b)(b-c)(c-a)(a + b + c)(a² + b² + c² - ab - bc - ca)
The factorized form of the polynomial is (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)
This is a general formula for the factorization of a polynomial of the form a³(b-c) + b³(c-a) + c³(a-b)
By using difference of cubes we can factorise the above polynomial, hope it helps.
Please helppppp meeeeee !!!!!!
Answer:
There are 7 ounces of applesauce in each of Newton's containers.
Step-by-step explanation:
72.5/2.5= 29
29-8=21
21/3=7
Answer: it is 7 in each container .
Step-by-step explanation: becuase if she has 2.5 times more than her what you want to do is divide 72.5 by 2.5 and get 29 the he ate 8 ounces now take away 8 from 29 and you will get 21 and then divide 21 by 3 and you will get 7.... Easy math hope this helps
The point of intersection of the perpendicular bisectors of the sides of a triangle is called a. circumecentre
b. incentre
c. congruent
d. concurrent
The point of intersection of the perpendicular bisectors of the sides of a triangle is called circumcenter
What are perpendicular bisectors?Lines that cut through the middle of each side of a triangle's perpendicular bisector are perpendicular to the provided side. The circumcenter (Durell 1928), which is also the center of the triangle's circumcircle, is where the triangle's three perpendicular bisectors (Casey 1888, p. 9) meet.Measuring a line segment that needs to be bisected will help you discover a perpendicular bisector. The midway of the measured length can then be determined by dividing it by two. From this center, extend a line at a 90-degree angle.The circumcenter is where the perpendicular bisectors of a triangle's sides meet. It is located in the middle of a triangle's perimeter. The center of a polygon's circle is known as the circumcenter. The polygon's circumcenter, also known as the center of that circle, is the circle that passes through all of the polygon's vertices. Cyclic polygons are the collective name for the circumcircle polygons.To learn more about perpendicular bisectors refer to:
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4. You are standing at point B. Point B is 21 feet from the center of the circular water storage tank and 19 feet from point A. AB is tangent to ⊙O at A. Find the radius of the tank. (Round answer to one decimal place)
The radius of the tank is 28.3 feet (rounded to one decimal place).
What is radius?Radius is a term used to describe the distance from the center of a circle to any point on the circumference. It is a line segment that runs from the center of the circle outwards, perpendicular to the circumference. The radius of a circle is the same for all points on the circumference, and it is always half of the diameter.
The radius of the tank can be determined using the Pythagorean Theorem. Since we are given the distances from the center of the tank (O) to points A and B, we can use the following formula to calculate the radius:
R = √(OA² + OB²).
Plugging in the given values, we get:
R = √(21² + 19²) = √(441 + 361) = √802 = 28.29
Therefore, the radius of the tank is 28.3 feet (rounded to one decimal place).
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Sample 1
ATTCGACGTC
k to add speaker notes
-
acer
Sample 2
GATAGCTAGG
Answer:
Sample 1
ATTCGACGTC
k to add speaker notes
-
acer
Sample 2
GATAGCTAGG
?--?
y = 4/11x + 1
f(5) =
f'(5) =
Answer:
f(5) = 31/11
f'(5) = 4/11
Step-by-step explanation:
y = 4/11x + 1
f(x) = 4x/11 + 1 ==> y = f(x)
f(5) = 4(5)/11 + 1 ==> substitute 5 for x
f(5) = 20/11 + 1 ==> simplify
f(5) = 20/11 + 11/11 ==> make common denominators to simplify easier
f(5) = (20+11)/11
f(5) = 31/11
f'(x) = 4/11
Hence, f'(5) = 4/11 since every value of x will make the derivative 4/11.
Make a the subject of the formula:
4b(5a-2) =2c
Step-by-step explanation:
Firstly you have to open brackets
4b(5a - 2) = 2c
20ab - 8b = 2c
20ab = 2c + 8b
Divide both sides by 20b(coefficient of a)
a = (2c + 8b)/20b
Answer:
[tex]a = \dfrac{2}{5} + \dfrac{c}{10b}[/tex]
Step-by-step explanation:
Expand 4b(5a-2) on the left side
4b(5a-2) = 4b · 5a -4b · (-2)
= 20ab -8b
Therefore we get
20ab -8b = 2c
Add 8b on both sides to get rid of the -8b on the left
20ab - 8b + 8b = 2c + 8b
20ab = 8b + 2c
Divide by 20 both sides:
20ab/20 = 8b/20 + 2c/20
ab = (2/5)b + c/10
Divide by b both sides
==> ab/b = (2/5)b/b + c/10b
==> a = 2/5 + c/10b
The expression
is equivalent to what answer in the picture
Answer:
-4w^6
Step-by-step explanation:
12/-3 = -4
w^9/w^3 = w^6
y^3/y^3 = 1
Answer: -4w^6
Answer:
option 1 = - 4w⁶
Step-by-step explanation:
attached the solution, hope that helps...
Find a1
a2 = 7, а5 = 7/27
A group of numbers in a particular order are called a sequence. For instance: a1, a2, a3, a4,..., an,... The first term is designated as a1, the second term as a2, and the nth term as an.
In math, what does an a1 mean?The sequence's first term is a1 = 1, making it the first term. I = 2 and a2 = 2 if I = 2. I = 3, hence a3 = 3 if I = 3.
The definition of an arithmetic sequence's nth term is: The equation a = a1 + (n - 1)d determines the nth term of an arithmetic sequence with a1 as its first term and d as its common difference.
A group of numbers in a particular order are called a sequence. For instance: a1, a2, a3, a4,..., an,... The first term is designated as a1, the second term as a2, and the nth term as an.
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What is the inverse of an exponential function?.
The inverse of an exponential function is the natural logarithm function. More specifically, if f(x) = a^x, where a is a positive constant and x is a real number, then the inverse function, denoted as f^-1(x), is given by f^-1(x) = log_a(x).
An inverse function is a function that "undoes" the effect of another function. In other words, if we have two functions, f and g, such that g(f(x)) = x for all x in the domain of f, and f(g(x)) = x for all x in the domain of g, then f and g are inverses of each other.
In the case of exponential functions, f(x) = a^x where a is a positive constant and x is a real number, the inverse function is the natural logarithm function, g(x) = log_a(x).
The natural logarithm function "undoes" the effect of the exponential function by taking the logarithm of the output of the exponential function with base 'a' and returns the input value.
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Answer the question below. Be sure to show all of your work.
Naomi earned $45 after babysitting for 5 hours one afternoon. Another day, she babysat for
8 hours and earned $72. Write two equations (one in point-slope and one in slope-intercept)
that represents the number of hours she babysits, x, and the amount of money she earns, y.
Leticia babysat 5 hours on Saturday.
How to calculate?First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. Leticia watched the children for four hours on Friday and for an undetermined period of time on Saturday.
earned $72, Therefore:
8 ( 4 + x ) = 72
( 4 + x ) = 72 / 8
4 + x = 9
x = 9 - 4
x = 5
Leticia babysat 5 hours on Saturday
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Divide 10/2 into equal groups of 1/2 . How many halves can you make?
Answer:
5 maybe????????
Step-by-step explanation:
Um, I'm guessing because 10/2=5, and yeah?????
Can someone explain how to solve this please?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionSolution is in the attached photo, do take note when you square a square root, you will get the original expression. (Power 2 x Power Half = Power 1).
Giving 20 points for correct answer
Answer:
Step-by-step explanation:523x2 1323
Elena is 59 inches. Some people are taller than Elena
The height of Andre, given the height of Elena is 63 inches tall.
The height of Lin is 65 .5 inches tall.
The height of Noah is 59 + d inchs tall.
How tall are the people?The height of the other people given which include Andre, Lin, and Noah, are all dependent on the height of Elena.
Andre is 4 inches taller than Elena so the height is:
= 59 + 4
= 63 inches
The height of Lin is:
= 59 + 6 .5
= 65 .5 inches
The height of Noah is:
= 59 + d inches
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What is the sum of the polynomials m'n 3 +( M N 4?.
The sum of the polynomials (m + n + 3) + (m + n + 4) is 2m+2n+7
Sum of given polynomials (m+n+3) +(m+n+4)
Firstly, open the parenthesis we will get m+n+3+m+n+4
After simplification, we will get 2m+2n+7
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 sum of the polynomials (m + n + 3) + (m + n + 4)?
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
Answer:
the answer is 56.58%
Step-by-step explanation:
The first step is to divide 43 by 76 to get the answer in decimal form:
43 ÷ 76 ≈ 0.5658
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.5658 × 100 = 56.58%
Re-write the quadratic function below in Standard Form
y= 9(x - 1)(x + 7)
The value of quadratic function is,
⇒ y = 9x² + 54x - 63
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ y = 9 (x - 1) (x + 7)
Now, We can find the quadratic equation as;
⇒ y = 9 (x - 1) (x + 7)
⇒ y = 9 (x² + 7x - x - 7)
⇒ y = 9 (x² + 6x - 7)
⇒ y = 9x² + 54x - 63
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What type of term 2x 3y is?.
The concept is Binomial distribution, an integer that can be obtained by evaluating a polynomial containing two terms The answer is, a linear equation in two variables.
In probability theory and statistics, a binomial distribution with parameters n and p is a discrete probability distribution of the number of successes in a sequence of n independent experiments, each of which asks a yes-no question and each has its own assessment of the Boolean result: passed or failed.
Data:
A polynomial of form 2x + 3y
The polynomial above is the sum of 2x and 3y.
In the expression, the polynomial is the sum of two terms, each of which is a monomial
Again, we know that a binomial is a polynomial that is the sum of two terms, each of which is a monomial, so the given polynomial is a binomial
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The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.
The expression [tex]x^{3} +3x^{2}[/tex] represents the volume of the prism, in cubic units.
We have given that the,
The height of a right rectangular prism is 3 units greater than the length of the base.
The edge length of the square base is x units.
The volume of a rectangular prism = width*length*height
V=w*l*h ......(1)
We have given that the
h=3 greater than the length of the base
and the length of the base is x
Hence, h=x+3
length of base = x
width = x
Substituting values l h and w into the formula (1) we get,
V=w*l*h
= [tex](x)*(x)*(x+3)[/tex]
= [tex]x^{2}*(x+3)[/tex]
=[tex]x^{3}+3x^{2}[/tex]
Therefore the expression
[tex]x^{3}+3x^{2}[/tex] represents the volume of the prism, in cubic units.
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what is 16 over 16 as a whole number
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
16/16
16 ÷ 16 = 1
So your answer is 1
HAVE A GREAT DAY!
What is the value of tan A?.
The value of tan A is 5/12.
To find the value of tan A, we use the trigonometric function tangent, which is defined as the ratio of the length of the side opposite angle A to the length of the side adjacent to angle A. In a right triangle, these sides are labeled as x and y, respectively. Therefore, to find the value of tan A, we divide the length of the side opposite angle A (x) by the length of the side adjacent angle A (y).
tan A = x/y
Here,
x = 5 y = 12tan A = 5/12
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The complete question is:
Given a right triangle with one angle measuring A, and the lengths of the side opposite angle A and the side adjacent angle A as 5 and 12 respectively, find the value of tan A.
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The base of a right triangle is 48cm and its hypotenuse is 50cm. What will be the areas of the triangle? class 9
The area of a triangle can be found using the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 48cm and the hypotenuse is 50cm. Since this is a right triangle, we can use the Pythagorean theorem to find the length of the height. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So,
c^2 = a^2 + b^2
50^2 = 48^2 + b^2
2500 = 2304 + b^2
b^2 = 2500 - 2304
b = √(2500 - 2304)
b = √(196)
b = 14
So, the height of the triangle is 14cm.
Area = (1/2) * 48 * 14 = 336cm^2
Order from least to greatest
27% 2/10, 0.22, 1/4, 26/100
A) 1/4, 2/10, 27% 0.22, 26/100
B) 2/10, 26/100, 27% 1/4, 2/10
C) 2/10, 0.22, 1/4, 26/100, 27%
D) 27% 2/10, 0,22, 1/4, 26/100
Answer:
0.22 <
1
4
<
26
100
<
272
10
Step-by-step explanation:
What is the multiplicative inverse of 7 /- 9?.
The multiplicative inverse of -7/9 is -9/7
The multiplicative inverse of a number is basically the reciprocal of the number Multiplicative inverse of a is 1/a where a≠ 0
The standard form to represent the multiplicative inverse is as follows:
a * (1/a) = 1
when a number is multiplied by its multiplicative inverse then the result is 1.
The multiplicative inverse is the Reciprocal of a fractional number where the number and denominator are simply interchanged.
Hence multiplicative inverse of 7/9 is
1/(7/-9) = -9/7
The multiplicative inverse of -7/9 is- 9/7.
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In the figure below, C is between A and D, and B is the midpoint of AC. If BC=3 and AD=13, find CD.
The length of CD is 7 units.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
From the figure it is given that C is between A and D.
B is the midpoint of AC
BC=3 and AD=13, we have to find CD.
As B is the midpoint of AC, then BC=AB
BC=AB=3
AC=AB+BC=6
Now to find CD=AD-AC
CD=13-6
CD=7
Hence, the length of CD is 7 units.
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What is the ratio of the 3 sides of a 45 − 45 − 90 triangle?.
The ratios of the sides of a 45-45-90 triangle are 1:1:[tex]\sqrt{2}[/tex].
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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16<21<25, so 21−−√ is between
Answer:
This meant to be a question?
Step-by-step explanation:
Calculator
not allowed
What are the values of m and c?
to task
Bookwork code: P76
Give each of your answers as an integer or as a fraction in its simplest form.
Y
5-
-4-
3
2-
1
-5 -4 -3 -2 -1.0 1 2 3 4 5
Line T
✓ Scroll down
Watch video
0°C Fog w
Answe
ENG
Answer:
m = [tex]\frac{1}{5}[/tex] , c = - 4
Step-by-step explanation:
m is the slope of the line and is calculated using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line
m = [tex]\frac{1-0}{1-(-4)}[/tex] = [tex]\frac{1}{1+4}[/tex] = [tex]\frac{1}{5}[/tex]
c is the value of the y- intercept , where the line crosses the y- axis
the line crosses the y- axis at - 4, then c = - 4
Help please……………………….
This figure and the given statements are important for understanding basic principles of geometry.
Fill in the blanks to write a true statement?(a) Another name for plane P is plane XYZ.(b) T and X are distinct points that are collinear.(c) T, R, X, Y, and Z are distinct points that are coplanar.(d) Suppose line QT is drawn on the figure. Then QT and S are distinct lines that intersect. Line QT is contained in plane P, while line S does not lie in plane P. Therefore, these two lines will intersect at a point outside of plane P.This question is asking for true statements about points and planes in a given figure. Plane P is the plane that contains points T, R, X, Y, and Z. (a) Another name for plane P is plane XYZ. (b) T and X are distinct points that are collinear. (c) T, R, X, and Y are distinct points that are coplanar. (d) Suppose line QT is drawn on the figure. Then QT and SR are distinct lines that intersect. Plane P is a three-dimensional space that contains points T, R, X, Y, and Z. Points T and X are collinear, meaning they lie in the same line. Points T, R, X, and Y are coplanar, meaning they all lie in the same plane. Finally, if line QT is drawn on the figure, it intersects with line SR, meaning the two lines have a common point.To learn more about distinct lines that intersect refer to:
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