The domain of the function h(x) = x² - x - 12 when the function operation f(x) = g(x) is performed is ( - ∞ , ∞ ).
A domain is a collection of potential input values. All input values visible on the x-axis make up the graph's domain. The collection of potential output values represented on the y-axis is known as the range.
Consider the two functions,
f(x) = x - 4 and g(x) = x² - 16
The function operation f(x) = g(x).
g(x) - f(x) = h(x)
x² - 16 - ( x + 4 ) = h(x)
h(x) = x² - x - 16 + 4
h(x) = x² - x - 12
The collection of input or argument values for which a function is actual and defined is known as its domain.
So, the domain of the function h(x) is ( - ∞ , ∞ ) or - ∞ < x < ∞.
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Simplify each number. -(-27)⁻⁴/₃
The result of simplifying the expression -(-27)⁻⁴/₃ using the exponent rules is 1/81
To solve this exercise we have to resolve algebraic operations following the exponent rules.
-(-27)⁻⁴/₃ =
(27)⁻⁴/₃
As we have a negative exponent, you have to pass the exponent to the denominator:
1/(27)⁴/₃
As we have a fractional exponent, you must convert the exponent to root:
1/[tex]\sqrt[3]{}[/tex](27)⁴
1/[tex]\sqrt[3]{}[/tex](531441)
1/81
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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You get your hair cut at a shop that charges $30. They offer you a deal: If you prepay $150 for five haircuts, they'll give you a punch card that entitles you to a sixth haircut free. The punch cared expires in one year. Is this a good deal?
yes, it is a good deal as long as you use the card before a year.
Is this a good deal?Let's see how much you will save if you pay the $150.
If you want 6 hair cuts, you need to pay $30 6 times, so the total cost will be:
C = $30*6 = $180
If instead, you prepay $150, then you get the 6 cuts only for $150, saving a total of $30 (but the downpayment is 5 times larger than in the other case), but only if you plan to use the punch card for the other cut in the year, if you don't then this option does not make sense.
So, yes, it is a good deal as long as you use the card before a year.
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Please answer this I have had this assignment open for 4 days, 9 hours, 30 minutes, and 25 seconds
The value of f(0) = 2 and f(-2) = -2 given the equation that we have in this image.
How to solve for the functionThe function that we have here is given as
[tex]\frac{2x-2}{(x + 1)(x-1)}[/tex]
We have to find the value of f(-2)
= 2(-2) - 2 / (-2 + 1) (-2 - 1)
= - 4 - 2 / -1(-3)
= -6 / 3
= -2
Hence f(-2) = -2
Next we have to find f(0)
2(0) - 2 / (0 + 1) (0 - 1)
= -2 / 1 * -1
= -2 / -1
= 2
Hence we can say that the value of f(0) = 2 and f(-2) = -2 given the equation that we have in this image.
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Valeria has a points card for a movie theater.
She receives 80 rewards points just for signing up.
She earns 7.5 points for each visit to the movie theater.
She needs 185 points for a free movie ticket.
Write and solve an equation which can be used to determine v, the number of visits
Valeria must make to earn a free movie ticket.
According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.
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:
She receives 80 rewards points just for signing up.She earns 7.5 points for each visit to the movie theater.She needs 185 points for a free movie ticket.
then
The linear equation becomes:
The equation that can be used to represent the explanation given in the question is : 185 = 80 + 7.5x
Then
Combine similar terms
185 = 80 + 7.5x
185 -80 = 7.5x
105 = 7.5x
x = 105 /7.5
x = 14.
So, According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.
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harvey porter is a wizard. he waved his wand and made a grain of sand that had a diameter of 0.00002 meters grow to a diameter 0.006meters. approximately how many times as large is the diameter of the grain of sand now as it was before harvey porter waved his wand
Answer:
Step-by-step explanation:
rgvm
Answer:the answer is A haha
Step-by-step explanation:
i just did this kahn academy lesson-
Will mark brainiest help hurry pls
Answer:
d=-2/3f+7
Step-by-step explanation:
Please help I’m gonna cry
ppppppllllllssss hhhhheeeeellllpppppppp
Answer: its a 18
Step-by-step explanation:
Solve each equation.
4^{3 x}=64
value of x in given exponential equation is = 1
What is exponential equation ?In, mathematics a exponential function or equation is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a is the base of function
x is the expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponents :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^0 =1[/tex]According to given statement,
4^3x = 64
=> 4^3x = 4³
=> 3x = 3
=> x = 1
Thus solution for this equation is x =1.
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Perimeter of
6x-2
2x + 4
2y + 4
The right response is Perimeter, x - 2y = 9.
The parameters listed in the question are:
A rectangle's perimeter is equal to 6 x – 2, its length to 2 x + 4, and its width to 2 y + 4.
The perimeter is calculated using the following formula: 2(L) + 2 (W)
6x - 2 = 2(2x + 4) + 2(2y +4) = 4x + 8 + 4y + 8
The result is: x - 2y = 9 and 2x - 4y = 18.
Consequently, the right response is x - 2y = 9.
What is a perimeter?The sum of a polygon's sides is what is referred to as its perimeter. For the perimeter calculation, the shape must be closed. And the polygonal shapes are either one- or two-dimensional.
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If triangle is rotated 90° clockwise about the origin what will be thr new coordinates of vertex B?
(-1,-4)
(1,4)
(4,1)
(4,-1)
Answer:
The answer to your question is going to be c
1. Which square-large, medium, or small-covers more of the plane? Explain your reasoning.
The large square covers more
(See attachment below)
Explanation- The large square has the highest dimension and by extension, it has the highest area.
This means that, less large squares will be needed to cover more areas compared to other sizes of the squares
Area of the square =(side)².
square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle and a special kind of parallelogram.
By observation,
9 small squares are equivalent to one large square, implying that the 5 large squares are giving us 45 small squares.
4 small squares can fit into one medium square, implying that the 10 medium squares are giving us 40 small squares.
There are only 10 small squares.
Hence, the large square covers more of the plane
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a cyclist is traveling north down the road at 23 ft per second as he approaches his destination 20 minutes (minutes need to be changed to seconds) later he comes to a complete stop. what is his acceleration?
PLEASE HELP ME ASAP!!! THIS IS DUE IN A FEW MINUTES!!!!!!
Answer:
A
Step-by-step explanation:
we need to find what they equal so we put them as equations against each other
Choose the reasonable product of each expression Explain your reasoning 3.14×7
Based on the product expression, the estimate of the product expression 3.14 x 7 is 22
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 evaluate the expression?The expression is given as
3.14 x 7
Rewrite 3.14 as a rational expression
So, we have
3.14 x 7 = 314/100 x 7
Evaluate the product of 314 and 7
So, we have
3.14 x 7 = 2198/100
Evaluate the quotient of 2198 and 100
So, we have
3.14 x 7 = 21.98
Approximate the above expression
So, we have
3.14 x 7 = 22
Hence, the estimate of the product expression 3.14 x 7 is 22
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The length of a bacterial cell is about 4 x 10−6 m, and the length of an amoeba cell is about 2.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
The bacterial cell length is 62.5 times smaller than the amoeba cell.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The length of a bacterial cell is about 4 x 10⁻⁶ m, and the length of an amoeba cell is about 2.5 x 10⁻⁴ m
Hence:
Ratio of Amoeba length to bacteria length = (2.5 x 10⁻⁴ m) / (4 x 10⁻⁶ m) = 62.5
The bacterial cell length is 62.5 times smaller than the amoeba cell.
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Answer:
the answer in scientific notation with the significant amount of digits is 6.25 x 10^2.
Step-by-step explanation:
you have to solve the equation and divide 0.00025 by 0.00004
you will get 6.25
and if you divide 2.5 by 4 you get 0.625 you have to move the decimal over to the right by 2 so you get the exponent of 2
The answer in scientific notation with the significant amount of digits is 6.25 x 10^2
Suppose the function f(x)=0.15 x represents the number of U.S. dollars equivalent to x Chinese yuan and the function g(y)=14.07 y represents the number of Mexican pesos equivalent to y U.S. dollars.
b. Find the value in Mexican pesos of an item that costs 15 Chinese yuan.
The value in Mexican pesos of an item that costs 15 Chinese yuan is 0.474 x.
What is the value in Mexican pesos of an item that costs 15 Chinese yuan?
x yuan to y dollars = f(x)
f(x) = 0.15 x
y dollars to x yuan =
y= 0.15 x
x = [tex]\frac{y}{0.15}[/tex]
y dollars to x pesos =g(y)
g(y) =14.07 y
x pesos to y dollars
x = 14.07 y
y = [tex]\frac{x}{14.07}[/tex]
Substituting the result of second into first,
pesos → dollars → yuan
Lets call this function, h(x) = converts x pesos into y yuan.
h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15
= 0.474 x
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Assessment
Practice
11. On a recent homework assignment, Eli needed to solve the equation
g² = 49. He incorrectly wrote g = -7.
PART A
What is the correct solution?
PART B
Critique Reasoning What error did Eli likely make?
He did not take the square root of 49 correctly since (-7)2 49.
® He did not solve the equation completely since there is a positive
solution as well.
He did not solve the equation completely since there are two positive solutions.
He did not solve the equation completely since there are two
negative solutions.
Answer:
Step-by-step explanation:
Answer:
what is the correct solution
Step-by-step explanation:
Give me a entire guide for 3.82 x 0.63 (my teacher wants me to show work on paper so I need every little step)
The product of 3.82 x 0.63 is 2.4066.
What is multiplication?One of the four fundamental mathematical operations, along with addition, subtraction, and division .In mathematics refers to the continual addition of sets of identical size Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication is called as multiplication.
Given that,
The product of
3.82
x 0.63
1146
2292 x
000 x x
2.4066
Therefore, the product of 3.82 x 0.63 is 2.4066.
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What is the answer to this: ( Image below) Pls help, thanks!
The perimeter of the polygon is 232 units
Perimeter of a polygonFrom the question, we are to determine the perimeter of the regular polygon
From the diagram,
One of the polygon's side length is (4/3)x - 1/3
and another side length is x + 7
Since the figure is a regular polygon, we can write that
(4/3)x - 1/3 = x + 7
Now, solve for x
(4/3)x - 1/3 = x + 7
Multiply through by 3
4x - 1 = 3x + 21
4x - 3x = 21 + 1
x = 22
One of the polygon's side length is x + 7
∴ One side length = 22 + 7
One side length = 29
Since the polygon has 8 sides,
The perimeter of the polygon will be
8 × 29
= 232 units
Hence, the perimeter of the polygon is 232 units
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Answer the 3 question in the photo
[easy points]
Answer:
answer below
Step-by-step explanation:
1.the shape below has 4 edges
2.the shape below has 5 faces
3.the shape below has 8 edges
To the nearest tenth, estimate √67.
Answer:
Step-by-step explanation:
8.2
Answer: 8.2
Step-by-step explanation:
sqrt(67) is more than sqrt(64) which is 8, but far from sqrt( 81) which is 9. It is less than half the disnatce between the two and therefore is less than 8.5.
Just put it in a calculator.....
Which statement about the function y = −14x − 2 is true? A. As the value of x increases, the value of y increases. B. As the value of x decreases, the value of y stays the same. C. As the value of x increases, the value of y decreases. D. As the value of x decreases, the value of y decreases.
The statement about the function y = −14x − 2 that is true is that A. As the value of x increases, the value of y increases. B.
How to illustrate the information?It should be noted that the information is to get the dtatement about the function y = −14x − 2 that is true.
y = −14x − 2
Let's use x = 1
y = −14x − 2
y = -14(1) - 2 = -16
When x = 2, y = −14x − 2.
y = -14(2) - 2 = -40
It shows that as x increases, y will also increase.
Therefore, the correct option is A.
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write two ratios that are equvilent to 3:11
Answer:
6:22, 9:33
Step-by-step explanation:
When writing equivalent ratios, you use two of the numbers from the original ratio and multiply them evenly to get an equivalent ratio.
[tex]\mathrm{p:q~or~\frac{p}{q} = \frac{x(p)}{x(q)}}\\\mathrm{\frac{6 \times 2}{11 \times 2} = 6:22}\\\mathrm{\frac{6 \times 3}{11 \times 3} = 9:33}[/tex]
Answer:
6:22 and 9:33
Step-by-step explanation:
Answer: 6:22 and 9:33
Think of the ratio like a fraction, one way to find an equivalent ratio is to simplify the current ratio. But in this case, we are unable because we can divide 3 by 3 to get one, but not 11 by 3.
3 divided by 3 = 1
11 divided by 3 = does not evenly divide
Another way is to multiply both numbers by the same number.
3 times 2 = 6
11 times 2 = 22
And we can just keep doing the same with different numbers.
3 times 3 = 9
11 times 3 = 33
Please help
--------------------------
Answer:
Step-by-step explanation:
Answer:
y = 8.40x
y = the total amount that he earned and x = the number of hours that he worked.
Step-by-step explanation:
1. 4 times the sum of x and 2
4(x+2)
hope this helps
A rectangular box with top WXYZ and base ABCD has AB=6 cm, BC=8 cm and WA=3 cm
Calculate:
a) the length of AC
b) the angle between WC and AC
The length of the AC is: 10cm
Rectangle length : since, a rectangle is a 2-D shape, it is characterized by two dimensions, length, and width. Length is the longer side of the rectangle and width is the shorter side.
So we have to find the length of AC in which AB=6cm and BC=8cm
Step by step explanation :
AC2= 6²+8²= 100
So AC= 10cm
The angle between WC and AC is 16.7°
Angle: .The space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet
So we have to find the angle between WC and AC , so here is a step by step solution:
tan θ=3/10 θ= 16.7°
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SportCo manufactures basketballs. The fixed expenses are $46,270 and the variable expenses are $6.50 per basketball produced. How many basketballs did they produce if their expenses total $87,870?
SportCo manufactured 6400 basketballs
SportCo manufacturers fixed expenses for producing basketballs = $46,270
Variable expense incurred per basketball produced = $6.50
Total expenses incurred by SportCo for producing basketballs= $87,870
Fixed costs are costs that remain constant regardless of whether more or fewer goods or services are produced or sold.
An expense for the company that varies according to how much is produced or sold is called a variable cost. Depending on a company's production or sales volume, variable costs grow or fall. They climb as production rises and reduce as production declines.
Let x be the number of basketballs produced by the manufacturer SportCo.
Formulating the equation we get:
Fixed cost + Variable cost*Number of basketballs produced = Total expenses incurred by the manufacturer
46270 + 6.5(x) = 87870
6.5(x) = 41600
x = 6400
Therefore, the number of basketballs produced is 6400 by the manufacturer.
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There are 496 black sedans in the parking lot and 640 non-black sedans in the parking lot. what is the ratio of non-black sedans to black sedans? write your answer as a simplified fraction.
There are 496 black sedans in the parking lot and 640 non-black sedans in the parking lot. The ratio of non-black sedans to black sedans is
40 : 31
Define Ratio ?
the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
There are 496 black sedans in the parking lot and 640 non-black sedans in the parking lot.
what is the ratio of non-black sedans to black sedans
divide by 2 , both the terms
640 : 496
320 : 248
160 : 124
80 : 62
40 : 31
Hence , There are 496 black sedans in the parking lot and 640 non-black sedans in the parking lot. Then the ratio of non-black sedans to black sedans is 40 : 31
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x) / g(x)
The given values f(x) / g(x) =2 x+5 / x²-3 x+2
What are the domain of the function f(x) / g(x)Given: f(x)=2 x+5 and g(x)=x²-3 x+2
f(x) / g(x) =2 x+5 / x²-3 x+2
The function operation of f(x) / g(x) =2 x+5 / x²-3 x+2
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