After direct variation y = 2 when x = -3.
What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ 1/-1.5That is y = kx ⇒ y = 1/-1.5 × xWhen x = -3:
1/-1.5 × -3 ⇒ y = 2Therefore, y = 2 when x = -3.
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h3lp
Which graph is the graph of the function [tex]g(x)=\frac{x^{2}-x }{x^{2} -1}[/tex]
see screenshot for answer choices
Answer:
A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.
Step-by-step explanation:
Which expression is equivalent? Please help!
Answer:
I am pretty sure it is y^14/z^14
Answer
y^14 / z^14 (Option 3)
Step-by-step explanation:
The z^-4 adds to the z^3, making z^7
The y^-2 adds to the y^5 making y^7
The negative square flips the equation and essentially doubles it. leaving the Y on the numerator and Z on the denominator, doubling the 7 into 14
Select the correct answer. Which graph best models the inequality? y< - 2/5x + 2 A. A linear function on a coordinate plane passes through (minus 5, 0), (0, minus 2), and (5, minus 4) to form a blue shaded portion at the top. B. A linear function on a coordinate plane passes through (minus 5, 0), (0, minus 2), and (5, minus 4) to form a blue shaded portion at the bottom. C. A linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top. D. A linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the bottom
The linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.
Option (c) is correct.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given inequality is
y< - 2/5x + 2
According to given question we have
The inequality is
y< - 2/5x + 2
To solve the inequation by putting the value of
At x=0
y< - 2/5x + 2
y<-2/5*0+2
y<2
The points are (0,2).
At x= 5
y< - 2/5x + 2
y<-2/5*5+2
y<-2+2
y<0
The points are (5,0).
At x= -5
y< - 2/5x + 2
y<-2/5*-5+2
y<2+2
y<4
The points are (-5,4).
Therefore, the linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.
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Answer: The linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.
Option (c) is correct.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given inequality is
y< - 2/5x + 2
According to given question we have
The inequality is
y< - 2/5x + 2
To solve the inequation by putting the value of
At x=0
y< - 2/5x + 2
y<-2/5*0+2
y<2
The points are (0,2).
At x= 5
y< - 2/5x + 2
y<-2/5*5+2
y<-2+2
y<0
The points are (5,0).
At x= -5
y< - 2/5x + 2
y<-2/5*-5+2
y<2+2
y<4
The points are (-5,4).
Therefore, the linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.
Step-by-step explanation:
Given the algebraic expression ----- create an equivalent expression.
The equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the equivalent expression?The expression is given as
(64x^2/3)^-1/3
Evaluate the product of the exponents
So, we have
(64x^2/3)^-1/3 = 64^-1/3 * x^(2/3*-1/3)
Evaluate the product of the exponents
So, we have
(64x^2/3)^-1/3 = 64^-1/3 * x^-1/9
Evaluate the exponent
So, we have
(64x^2/3)^-1/3 = 1/4 * x^-1/9
Evaluate the product
So, we have
(64x^2/3)^-1/3 = 1/4x^-1/9
Rewrite as
(64x^2/3)^-1/3 = 1/(4x^1/9)
Hence, the equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)
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turn 4 3/5 into a decimal
Answer:
4.6
Step-by-step explanation:
1. Multiply the whole number by the denominator
4 x 5 = 20
2. Add the result of step 1 to the numerator
20 + 3 = 23
3. Divide the result of step 2 by the denominator
23 ÷ 5 = 4.6
Determine which of the following relations is a function.
x
-10
50
-5
50
10
y
10
5
0
-5
-10
D
x
-3
-1
0
0
3
NE
2
1
2
4
0
x
-8
-2
1
2
4
y
-4
-2
3
4
6
x
0
1
2
2
LO
5
92
42
2
6
7
We need to know about the difference between relation and function to solve this problem. Options 1 and 3 are functions but 2 and 4 are just relation not functions.
A relation is a relationship between two or more sets of values. A function is an expression that defines the relationship between two variables. The main difference between a relation and a function is that a relation can have multiple output for a single input but a function only has single output for a single input. Every function is a relation but every relation is not a function. In this question x is the input variable and y is the output variable,for option (1) all the input values have single output values, for option (2) the value x=0 has two different output values so this relation is not a function, for option (3) all input values have single output values, so it is a function and for option (4) the input value x=2 has two different output values so it is not a function.
Therefore we found out that options (1) and (3) are functions and the rest are just relations.
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Answer:
its simply a, and c
Step-by-step explanation:
yiippeeeeee
which option/graph
PLEASE PLEASE HELP
Solve for w.
0.43 +2.7w = 3.7w - 0.47
Answer:
w = 0.9
Step-by-step explanation:
What I did is I subtracted 2.7 from 3.7 bc it was the least number and that gave me 1 so that left me with 0.43 = w - 0.47. Then I added 0.47 to 0.43 and that gives me 0.9 which would be the answer
If you don't understand how I got it I can try to explain a little better, but hopefully, you understand:)
Please helppppp nowwwwww
Answer:
It has 2 angles right and acute
Oona likes only red,yellow and blue markers. 1/6 of OONA'S markers are red and 1/4 of the markers are yellow and the rest are blue. She has 8 red markers. How many blue markers does she have?
Answer:
28
Step-by-step explanation:
If 1/6 of the markers are red (8) then 8 * 6 = 48 meaning Oona has 48 markers, 8 of them being red.
1/4 of 48 is 12, so 12 yellow markers
If the rest are blue, then 8+12 = 20 and 48-20=28
There are 28 blue markers
Quotients Great and Small
Diving fractions
Thanks so much please show work!
1. 5/6 ÷ 5/8 or. 5/6 x 8/5=
2. 5/9 ÷ 1/2 or. 5/9 x 2/1 =
3. 9/10 ÷ 3/5 or. 9/10 x 5/3=
Step-by-step explanation:
GOOD RIGHT?
Which equation justifies why ?
The equation that justifies [tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] is [tex](7^{\frac{1}{3} } )^{3} = 7^{\frac{1}{3} .3} = 7[/tex]
How to find the equation that justify another equation?The equation is as follows;
[tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex]
using laws of indices, the equation can be simplified.
[tex]a^{1 / b} = \sqrt[b]{a}[/tex]
Therefore,
[tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] are the same.
Hence, it means the equation that justifies [tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] is as follows:
[tex](7^{\frac{1}{3} } )^{3} = 7^{\frac{1}{3} .3} = 7[/tex]
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A square with side length ppp has an area of 169169169 square centimeters. The following equation shows the area of the square.
p^2 = 169p
2
=169p, squared, equals, 169
What is the side length of the square in centimeters?
The side length of the square in centimeters is 13 centimeters
What are areas?The area of a shape is the amount of space on the shape
How to determine the side length?The equation of the area of the square is given as
p² = 169
The area of a square is the product of its length
This means that we simply take the square root of both sides of the equation to determine the side length
Next, we take the square root of both sides of the equation
So, we have
√p² = √169
Evaluate the square roots
So, we have
p = 13
Hence, the side length of the square in centimeters is 13 centimeters
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describe some possible random variables (other than the ones mentioned previously) and discuss whether they are continuous random variables or discrete random variables.
Random variables can be either discrete or continuous.
Sample spaces need not consist of numbers. In statistics, we are most often interested in numerical outcomes such as the "count" of an occurrence. We call X a random variable because its values vary when the phenomenon is repeated. We use capital letters near the end of the alphabet like X or Y.
A random variable is a variable whose value is a numerical outcome of a random phenomenon. When a random variable describes a random phenomenon the sample space S just lists the possible values of the random variable. There are two ways of assigning probabilities to the values of a random variable that will dominate our application of probability as we study statistical inference.
Random variables can be either discrete or continuous. A discrete random variable X has a "countable number of possible values. The probability distribution of X lists the values and their probabilities in table form. The probabilities must satisfy two requirements:
1) every probability pi is a number between 0 and 1
2) p1 + p2 +,,,+pk = 1.
The probability of any event is found by adding the probabilities pi of the particular values xi that makes up the event.
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Simplify each expression. (x¹/₅)¹⁰
The answer to the expression is [tex]= x^{2}[/tex]
The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.
The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.
Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.
apply exponent rule [tex](a^{b} )^{c} = a^{bc}[/tex]
assuming a≥ 0
[tex]x^{1/5} . 10[/tex]
[tex]\frac{1}{5} .10 =2[/tex]
[tex]= x^{2}[/tex]
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For the function f(x)=∛2x , find f⁻¹(x) . Then determine the value of x when f(x)=16 .
The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex] when f(x) = 16 is [tex]x=2^\frac{11}{3}[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f^-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the functionWe have given a function [tex]f(x)=x\sqrt[3]{2}[/tex]. ....(1)
Let y = f(x)
[tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]y=\frac{x}{\sqrt[3]{2} }[/tex]
[tex]f^{-1}(x)=y[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]
It is given that f(x) = 16 on comparing it with equation (1) , we get
[tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]
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how can i solve this one (37) pls i really need help
The vehicle travels 55 miles per hour, so for each hour "t" we will travel 55 miles.
[tex]d(t) = 55t[/tex]
Each 20 miles take 1 gallon, so for each gallon of fuel, we can travel 20 miles
[tex]d(g) = 20g[/tex]
Part bIn each hour we travel 55 miles, and each 20 miles require 1 gallon of fuel.
So,
[tex]55t = 20g \\ g = \frac{55}{20} t \\ g = 2.75t[/tex]
or you could set both d(t)=d(g) since they both are distance traveled.
Part c[tex]g = 2.75(6) = 16.5 \: gallons[/tex]
[tex]d(6) = 55(6) = 330 \: miles \: \\ or \: \\ d(16.5) = 20(16.5) = 330 \: miles[/tex]
Each ordered pair is from an inverse variation. Find the constant of variation. (√2, √18)
The value of constant variation is √16.
What is a constant?A mathematical constant is a significant integer that has a steady value and is specified by a precise definition.
What is inverse variation?relationship between two variables in mathematics that may be represented by an equation where the product of their products equals a constant
Inverse variation is y = k. 1/x
given y = √18
x = √2
So, √8 = k. 1/√2
So, the value of k = √16
We can conclude that the value of constant variation is √16
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2. The product of √5 and which of the following numbers will result in an irrational number? A. √5 B. -√5 C. √2 D. 3√5
Answer:
C
Step-by-step explanation:
The radicands have at least one prime-factor that is not in common.
Simplify. (3⁻²) (3⁵) .
Find the midpoint of the segment with the following endpoints (4,6) (1,3)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]
-5; -1/2; -0.05; -45% least to greatest
Answer:
-5, 1/2, -0.45, -0.05 would be the solution
REMEMBER: f(2
1) If f(x) = 2x - 3,
a) f(-2) =
10,645 divided by 5?
Answer:
2,129
5 times 2129 = 10645
Step-by-step explanation:
Hope it helps! =D
Solve. Check for extraneous solutions. 5√x+7=8
The answer is x = [tex]\frac{1}{25}[/tex].
5√x + 7 = 8
⇒ 5√x = 8 - 7
⇒ 5√x = 1
⇒ √x = [tex]\frac{1}{5}[/tex]
Squaring both sides, we get,
⇒ x = [tex]\frac{1}{25}[/tex]
Answer) x = [tex]\frac{1}{25}[/tex]
An extraneous solution refers to the roots of the transformed equation. This root is not the root of the original equation, as the original equation has been transformed to create another equation from which the answer has been found. The original equation has been excluded from the domain of the function.
In the given equation, I have tried to take the equation in the value of x, and hence, after squaring the value, the root has been found.
Since the square root function is used, we get a single value for the variable x.
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Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of 3000feet and height of 1200 feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle 10 inches.
What scale is Alexander using?
The scale of the drawing is 1 inch represents 300 feet .
What is the scale of the drawing?A scale drawing is a smaller image of a larger diagram or object in terms of dimensions. The scale drawing is usually reduced at a constant dimension.
In order to determine the scale of the drawing, divide the base of the actual Federal triangle by the base of the drawing.
Scale of the drawing = original dimensions / dimensions of the scale drawing
3000 / 10 = 300
1 inch represents 300 feet
1 inch : 300 feet
The scale of a drawing is usually written in this format - one a colon (:), the result of the division of the original dimension and the dimension of the scale.
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How much water would you have if you combine all wars together of 1/2 ,1/3 and 1/6 but you have to rewrite with common denominators and then solve
The addition of the fractions means that the value when combined is 1.
How to calculate the fraction?It should be noted that based on the information given, we simply have to add the fractions that are given and this will be:
= 1/2 + 1/3 + 1/6
= 3/6 + 2/6 + 1/6
= 6/6
= 1
Therefore, the addition of the fractions means that the value when combined is 1.
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If one-third of the girls and one-half of the boys attend the Senior Dance, there will be a total of 205 students. If half the girls and all the boys attend, there will be 370 students.
How many students are in the Senior class?
The number of girls and boys in the senior class is 240 and 150 respectively.
How to find the number of studentslet
Number of girls = xNumber of boys = y1/3x + 1/2y = 205
1/2x + y = 370
From (2)
y = 370 - 1/2x
Substitute into (1)1/3x + 1/2y = 205
1/3x + 1/2(370 - 1/2x) = 205
1/3x + 185 - 1/4x = 205
1/3x - 1/4x = 205 - 185
(4x-3x) / 12 = 20
x/12 = 20
x = 20 × 12
x = 240
Substitute the value of x into (2)1/2x + y = 370
1/2(240) + y = 370
120 + y = 370
y = 370 - 120
y = 150
Therefore, the number of girls and boys in the senior class is 240 and 150 respectively.
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ok i help and answers
Combining the like terms, the equivalent expressions are given as follows:
-15a - 3b + 16a + 4b = a + b.2a - 4b - 3a + 6b + 6 = -a + 2b + 6.2a + 2b - 6a -3 - 2b + 6 = -4a + 3.3a - 6b - 6 + 2a + 6b + 2 = 5a - 4.3a + 4a + 2b - 4 - 5b - 10 = 7a + 7b - 14.How do we add and subtract symbolic expressions?To add or subtracted symbolic expressions, in which the terms are accompanied by letters, we combine the like terms, that is, we add or subtract terms that have the same letter.
One example is:
a + b + 3a + 20b = 4a + 21.
As 1 + 3 = 4, 1 + 20 = 21.
Hence the equivalent expressions for the first space is:
-15a - 3b + 16a + 4b = a + b.
For the second space, it is:
2a - 4b - 3a + 6b + 6 = -a + 2b + 6.
For the third space, it is:
2a + 2b - 6a -3 - 2b + 6 = -4a + 3.
For the fourth space, it is:
3a - 6b - 6 + 2a + 6b + 2 = 5a - 4.
For the fifth space, it is:
3a + 4a + 2b - 4 - 5b - 10 = 7a + 7b - 14.
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Make r the subject of the formula t= r/r-3
The Subject formula for r= 3t/ ( t- 1)
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
t= r/r-3
Now, writing the above equation for r
tr - 3t = r
tr - r= 3t
r( t - 1)= 3t
r= 3t/ ( t- 1)
Hence, the Subject formula for r= 3t/ ( t- 1)
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