The value of h(-2), h(4), and h(0) in the given function is 11, 29 and 9 respectively.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.
To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.
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Divide and simplify. 4√162 x⁴ / 4√2 y⁸
After dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.
We are given the expression
4√162 x⁴ / 4√2 y⁸
We need to divide the expression and simplify it.
First, cancelling the terms that are same in the numerator and the denominator:
√162 x⁴ / √2 y⁸
Now , using the properties of the exponents, we get that:
= √81 x² / y⁴
= 9 x ² / y⁴
Therefore, after dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.
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Quadrilateral A has a side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. Draw a sketch of Quadrilateral A or make a chart.
Sides of Quadrilateral A is 6, 9, 9 and 12.
It is given that Quadrilateral B is a scaled copy of Quadrilateral A,
and have shortest side = 2
To find the length of sides of quadrilateral, first we will find the ratio of the shortest side of quadrilateral A to that of quadrilateral B as shown below :
B : A = 2 : 6 = 1 : 3
This shows that the quadrilateral B is 3 times smaller than A.
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Toby picks a 6-digit number.
It is larger than 599,999 and it is a multiple of 5.
How many different numbers could he have picked?
Answer:
80,000 numbers.
Step-by-step explanation:
Since the number is 6-digits and is larger than 599,999, it would be between 600,000 and 999,999.
Between those two numbers (included), there are [tex]999999 - 600000 = 399999[/tex] numbers.
In addition, we know that the number is a multiple of 5. Therefore, we should divide this number by 5 to find how many of the numbers in that group are divisible by 5.
Since it's difficult dividing 399,999 by 5, I would divide 400,000 by 5, as we must also include 600,000.
[tex]\frac{400000}5 = 80000[/tex]
Solve each equation. Check your answers. 3 ln x+ ln 5=7
The solution 'x' of the expressed logarithmic expression is 17.65.
What exactly is the logarithmic expression?A logarithmic equation one in which the variable x contains a logarithm.
The variable in an exponential formula is signified by an exponent. To solve exponential equations, first see if both sides of the equation can be presented as powers of the same number. Because unless you can't, start taking the common logarithm of both equation sides and solve the problem using property 7.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿExponent Rule = e∧lnx = xNow, as per the stated log expression;
3 ln x + ln 5 = 7
Apply the Power Rule on the first term of the given equation;
ln x³ + ln 5 = 7
Now, by the Product Rule, we can re-write the equation in the form;
ln (x³×5) = 7
ln (5x³) = 7
Using the exponent form of the log on both side.
e∧ln (5x³) = e⁷
As, we have the same base for the obtained expression. Use the exponent rule;
(5x³) = e⁷
x³ = e⁷/5
Substitute the value of exponent e = 2.72
x³ = (2.72)⁷/5
x³ = 5507.5
Take cube root on both side;
x = 17.65
Thus, solution for the value of 'x' for expressed logarithmic expression is 17.65.
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what’s 9/9^4 simplified
Answer: 9/9^4 in Simplest form is 1 / 729
help me out with this
Answer:
The graph of g(x) = -|x| - 8.
A pizza shop charges nine dollars for a large cheese pizza. additional toppings cost $1.25 per topping. heather paid $15.25 for her large pizza. how many toppings that you order
Solve—a high school athletic dept. I bought 40 soccer uniforms at the cost of $3,000. After the soccer season, they. returned some of the uniforms but only received $40 per uniform. What was? the difference between what they paid for each uniform and what they got for each return?
Answer: $75 difference per shirt
Step-by-step explanation:
A figure has two pairs of parallel sides and four right angles. The figure is translated 4 units down. How many parallel sides does the image have?
Answer:
4
Step-by-step explanation:
because if it has two Pairs that's 2 on each side of the side of the shape
so, when you have a figure of 2 parallel sides id would be a parallelogram
Billy is planting a square garden that is 48 ft.² what is the closest side length of each side of the garden
The closest side length of each side of the garden is 7 feet .
Area is the space covered by an object. It is the realm occupied by all forms. When measuring the area of a square, we only consider the length of the sides. Since all sides of a square are equal, its area is equal to the square of the sides which is given by [tex]Area=a^2[/tex] ....(1) where "a" is the side of the square.It is given that Billy is planting a square garden that is 48 ft.²
Putting A = 48 ft.² in equation (1) , we get
[tex]48=a^2\\a=\sqrt{48} \\a=6.92[/tex]
which is approximately equal to 7
Hence , closest side will be 7 ft.
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find the value of x and 6
Answer:
x + 6 = -6
Step-by-step explanation:
Assuming x = -6
[tex]x+6=0[/tex]
Subtract 6
[tex]x+6-6=0-6[/tex]
Simplify arithmetic
[tex]x=0-6[/tex]
Simplify arithmetic(again)
[tex]x=-6[/tex]
we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.
Hope this helps, have a great day!
Describe the following characteristics of the graph of each
parent function: domain, range, intercepts, symmetry,
continuity, end behavior, and intervals on which the graph is
increasing/decreasing. (Example 1)
2. f(x) = /1
5. f(x) = c 6. f(x) = x
1. f(x) = [x]
4. f(x) = x4
3. f(x) = x³
Step-by-step explanation:
-by-step explanation:
y=\frac{2}{x+1}-3y=
x+1
2
−3
asymptotes:
x+1 = 0
x = -1
y = -3
asymptotes: x = -1, y = -3
x int: (-\frac{1}{3}, 0)(−
3
1
,0)
y int: (0, -1)
D: (-infinity, -1) (-1, infinity) x cannot be -1
R: (-infinity, -3) (-3, infinity) y cannot be -3
Write each logarithmic expression as a single logarithm.
5 log₇2-2 log₇y
Expression as a single logarithm of 5 log₇2-2 log₇y is Log (2x/3y).
What is natural logarithm?Log a + Log b = Log ab
Log a - Log b = Log (a/b)
so starting with the bracket, we have;
Log 2 + Log X - Log 3y
Furthermore, we have;
Log 2x - Log 3y
Finally, we have;
Log (2x/3y)
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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8/15% into a fraction
Answer:
2/375
Step-by-step explanation:
We can multiply 8/15 by 1/100 to get
[tex]\frac{8}{15} *\frac{1}{100}=\frac{8}{1500}[/tex]
Now we simplify this fraction into simplest form.
2/375
An amusement park offers a ticket for $12.95 off the original price p. Write and solve an equation to find the original price
The original price of a ticket is a $56.95.
According to the statement
We have to find that the linear equation.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
An amusement park offers a ticket for $12.95 off the original price p.
Then
Discounted price is that the amount of sum that extracted from the initial price when buyers receive some style of leverage from the vendor. during this case, discounted price of the ticket is $44 which was $12.95 but the initial price.
Then the first price would be:
$44 + $12.95 = $56.95
So, The original price of a ticket is a $56.95.
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-3x = -12 need to know the answer because I'm late for my homework
Answer: 4
Step-by-step explanation: Divide both sides by -3 so the x is by itself. When you divide both sides by -3, you get x =4.
Answer:
4
Step-by-step explanation:
Divide -3 on both sides so that x is by itself
-3x = -12
-3 -3
-3 is cancelled out
-12 divided my -3 is 4
Since both numbers are negative it would end up positive.
If the numbers are both positive then it would be positive as well.
And if one number is positive and the other is negative then the answer would be negative.
The answer would be: 4
I hope it helps! Have a great day!
Answer all of these with work please
Here we need to evaluate some mathematic expressions in some given values, we will get:
3x- 4 is equal to 17 when x = 7.
-5x + 8 is equal to -7 when x = 3.
How to evaluate expressions?Here we have some expressions that we need to evaluate. Evaluating an expression means that we replace the variables (usually denoted by letters) with numerical values.
The first expression is:
3x- 4
And we we want to evaluate it in x = 7.
So just replace the x by the number 7 and then do the operations:
3*7 - 4 = 21 - 4 = 17
The expression is equal to 17 when x = 7.
Now let's do it again for second expression:
-5x + 8 with x = 3.
Replacing the variable by the number we get:
-5*3 + 8 = -15 + 8 = -7
So that is the basic procedure to evaluate mathematic expressions.
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Permutation v combination
The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.
How to explain permutations and combination?Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the amount of potential combinations of unrelated objects.
Fir example, if we want to select 2 players from 6. This will be:
= 6! / 2! (6 - 2)!
= 15 ways
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For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=3/√x
Answer to this question is:
Domain of given function is (0,∞),{x|x>0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is 9/x²
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(0,∞)
Set-Builder Notation:{x|x>0}
The set of all valid y values constitutes the range.Graph may be used to find the values.
Interval Notation:(0,∞)
Set-Builder Notation:{y|y>0}
For calculation of inverse:
Interchange the variables x=3/√ySolve for yy=9/x²Replace y with f^-1(x)f^-1(x)=9/x²∴Domain of given function is (0,∞),{x|x>0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is 9/x²
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The denominator of a fraction is 2 more than its numerator. the reciprocal of this fraction is equal to the fraction itself. what is the sum of the numerator and denominator
Answer:
0
Step-by-step explanation:
You want the sum of numerator and denominator such that their difference is 2 and the reciprocal is equal to the original fraction.
SetupWe want a fraction such that ...
x/y = y/x
y = x +2
SolutionSubstituting for y, we have ...
x/(x +2) = (x +2)/x
x^2 = x^2 +4x +4 . . . . . cross multiply
0 = 4(x +1) . . . . subtract x^2, factor
x = -1 . . . . . . . . the value of x that satisfies the equation
Then the denominator is ...
y = x +2 = (-1) +2 = 1
The sum is ...
x +y = (-1) +1 = 0
The sum of numerator and denominator is zero (0).
Suppose that the function f is defined, for all real numbers, as follows.
Find f(−4), f(−2), and f(3).
The values of f(−4), f(−2), and f(3) for given piecewise function are 0, -4, and -3.5 respectively.
What is piecewise function ?
Whenever the summation of two functions is different over different intervals, the sum is a piecewise function.
Here, the given piecewise function f(x) is :
[tex]\begin{aligned}f(x)&=\left\{\begin{matrix}\frac{-1}{2}x-2 \text{ if} \:x \neq -2&\\-4 \:\:\:\:\:\:\;\;\text{ if }x = -2\end{matrix}\right.\end{aligned}[/tex]
Now, let us find the value of f(-4) :
for x = -4 the function f(x) is (-1/2)x -2, substituting x = -4 in place x :
f(x) = (-1/2)x - 2
f(-4) = (-1/2)*(-4) - 2
f(-4) = 2 - 2
f(-4) = 0
similarly, for f(-2) :
for x = -2 the function f(x) is -4 only that is :
f(-2) = -4
For, let us find the value of f(3) :
for x = 3 the function f(x) is (-1/2)x -2, substituting x = 3 in place x :
f(x) = (-1/2)x - 2
f(3) = (-1/2)*(3) - 2
f(3) = -3/2 - 2
f(3) = - 3.5
Therefore, the values of f(−4), f(−2), and f(3) are 0, -4, and -3.5 respectively.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer: A, C and F
Step-by-step explanation:
5−10∣3x+3∣<95
Please give an explanation. I will mark brainliest.
The value of x in the absolute value inequality is given as5 - 10|3x + 3| < 95 is all set of real numbers
How to determine the values of the absolute inequality?The absolute value inequality is given as
5 - 10|3x + 3| < 95
Subtract 5 from all sides of the absolute value inequality
So, we have
- 10|3x + 3| < 90
Multiply -1/10 to all sides of the absolute value inequality
So, we have
|3x + 3| > -9
This means that the value of x is all set of real numbers
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A stock decreases $11 a day for 5 days. Which integer represents the total decrease?
Group of answer choices
55
-16
16
-55
Answer:-55
Step-by-step explanation:
-11 times 5= -55
Solve each equation.
log₈2=x
The value of x for the equation log₈2=x is 0.333
What are the properties of logarithmic functions?Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties. These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.
Given,
log₈2=x
It can be expressed in the form -
2 = 8ˣ
2 = 2³ˣ
As base is same -
1 = 3x
x = 1/3
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The following ordered pairs represent a relation.
{(1,3) , (5,15) , (2,6), (4,12) , (3,9)}
What are the range values from least to greatest!
A.) {3}
B.) {3, 15, 6, 12, 9}
C.) {3, 6, 9, 12, 15}
D.) {1, 5, 2, 4, 3}
Answer: its C because when you put it in order you should easily find it in the question. So, 1, 2, 3, 4, 5, 6, 9, 12, 15 is the full order but C is the closest answer to the question. Hope its right!
All 385 tickets for a high-school play sold in 10 days. The ticket receipts totaled $ 1960 . If the cost of a child's ticket was $ 4 and the cost of an adult's ticket was $ 6 , how many adult tickets were sold?
Adult tickets that were sold were 210 .
Let the no. of children be x and no. of adults be y .
According to ques .
x + y = 385 - eq 1
4 x + 6 y = 1960 - eq 2
Solving linear equation in 2 variable by method of substitution ,
multiply - eq 1 by 4 ,
4 x + 4 y = 1540 - eq 3
multiplying - eq 3 by - 1
- 4 x - 4 y = - 1540 - eq 4
Adding - eq 2 and - eq 4
2 y = 420
y = 210
Hence , 210 adult tickets were sold .
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15 = 1/2 + 3/2x + 10
Answer:
x=3
Step-by-step explanation:
Sam chose to buy the BLT bond rather than the stock. Based on Sam's purpose for making the investment, which
sentence provides a valid reason for his investment decision?
O Sam wants an investment that offers capital gains.
Sam wants a steady income from his investment.
O Sam wants an investment that he can quickly sell to raise cash.
Sam wants an investment that offers a higher return than stocks.
The statement that shows Sam's purpose for making the investment, is; Sam wants an investment that offers a higher return than stocks.
What are bonds?We know that bonds refers to a type of investment that could be held for a while the hope of making returns. Both the bonds and the stocks are common types of investments that are traded in the equities market. They are held by buyers with the sole hope that they could yield returns.
However, the bonds tend to be more secure than the stocks. The stocks are actually an overly volatile kind of investment. The bonds when mature tends to provide a high return on investment for the investor compared to the stocks.
Hence, the statement that shows Sam's purpose for making the investment, is; Sam wants an investment that offers a higher return than stocks.
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Identify the like terms in the list.
15x 2, 17x, 12x 3, 3x
17x and 3x
15x2 and 12x3
15x2 and 3x
12x3 and 3x
Answer:
17x and 3x
Step-by-step explanation:
like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.