Answer:
D. x^6 - x + √6
Step-by-step explanation:
Last option:
⇒ x^6 - x + √6
Cannot be simplified further and has three terms.
Therefore is a trinomial.
The algebraic expression that is a trinomial is 2x³-x².
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A trinomial is a polynomial that has three terms.
In the given options, the only expression that has three terms is "2x³-x²". It has the terms 2x³, -x², and 0x (which is often omitted).
The other options have different numbers of terms or they have terms with fractional or radical exponents, which do not fit the definition of a trinomial.
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1
2
3
at
4
927
5
6
Which graph represents g(x)?
7
8
The graph of f(x) = x² is translated to form g(x) = (x - 5)² + 1. What does the graph look like?
6
10
17. Your friend is betting on a game in which the probability of winning is 1 in 5. He has lost 5 games in a
row, so he says he will double his bet on the next game. What do you tell your friend?
The only problem is you may also go bankrupt before you're able to double your bet enough times.
If the game's events are independent, similar to flipping a coin, then the probability never changes, it's still a 1 out of 5 chance of winning each time.
The coin has no memory, so it will always have the same probability on each flip.
If the games' events are like that, a losing streak doesn't mean a win is now more likely.
But if the events are not independent, it may make sense to increase the bet.
for example, a bag has 10 coins and 2 are worth 100. You reach in and pull out 5 coins, all worth only a penny each.
What is the probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Your odds of getting one of the 2 $100 coins is now much greater than the original 1 out of 5 chance.
You originally had a 2 out of 10 chance on the first draw. But now it's up to 2 out of the remaining 5 or 40% chance of winning.
There is another reason someone may wish to double their bet. If you doubled your bet each time you lost, you would eventually recoup all your losses. It can work.
The only problem is you may also go bankrupt before you're able to double your bet enough times.
That risk is usually considered too great to double your bets on independent events.
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Analyze the conditional statement below and complete the instructions that follow.
If an angle measures 90°, then it is a right angle.
Identify ~q.
O An angle does not have measure 90°.
OIt is not a right angle.
An angle measures 90°.
OIt is a right angle.
Answer: It is not a right angle.
in a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there?
The method for calculating how many arrangements are feasible when only a few items are chosen from a collection of items that are unique is as follows:
[tex]^nC_k=\frac{n!}{k!(n-k)!}[/tex]
Where:
n – the sum of all the elements of a set
k – the number of selected objects (the order of the object may change)
! – factorial
For instance, 3!=1×2×3
So, according to the problem, there are [tex]^7C_3[/tex] possible groups of 3 women out of 7 women. And [tex]^5C_2[/tex] possible groups of 2 men out of 5 men.
Combining we get that there are [tex]^7C_3 ~^5C2[/tex] groups of 3 women and 2 men out of 7 women and 5 men.
Therefore, there are [tex]^7C_3 ~^5C2=\frac{7!}{3!4!}\frac{5!}{2!3!}= 350[/tex] possibilities.
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What are the intercepts of graphed function.
Answer:
x-intercept is (-1,0)
y-intercept is (0,-3)
Step-by-step explanation:
An intercept is where the graph crosses the axis.
Here the graph crosses the x-axis (numbered horizontal line that goes left and right) at the point (-1,0)
The graph crosses the y-axis (numbered vertical line that goes up and down) at the point (0,-3). These are what are called intercepts.
*Will give 30pts*Consider function f. f(x)=2x^2.What is the value of (f•f)(x)?
Answer:
[tex]\textbf {B}[/tex]
Step-by-step explanation:
f(x) = 2x²
f [f(x)]
f [2x²] = 2(2x²)²
f[f(x)] = 2(4x⁴)
f[f(x)] = 8x⁴
What’s the slope of this graph? Can y’all guys help please ! Thank y’all
Answer:
-3
Step-by-step explanation:
/= negative slope; \= positive slope
The y-intercept is 2 because this is where it crosses the y-axis
Then you find the next point that touches the graph on an exact point which is (-2,-4)
So, your points are (0,2) and (-2,-4) then you do the slope formula of y2-y1 divided by x2-x1
-4-2/-2-0 = 3 and because the line is / then it is -3
If you subtract 0. 3 from a certain number, add 0. 4 times the original number to the result, and then add another 2. 78, you'll get 25. What was the original number?
After all the conditions you applied from the statement given you will get the original number as 16.08.
What is the algebraic equation?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.
Given that, if you subtract 0.3 from a certain number, add 0.4 times the original number to the result and then add another 2.78, you'll get 25.
We need to find the original number.
Let us take the original number as x.
Now, subtract 0.3 from the original number.
That is x-0.3.
0.4 times the original number is 0.4x.
Add 0.4 times the original number to the result.
That is, x-0.3+0.4x=1.4x-0.3
Now, add 2.78 to the result. That is 1.4x-0.3+2.78=1.4x+2.48.
As a result, you'll get 25. That is 1.4x+2.48=25
⇒1.4x=22.52
⇒x=16.08
There, the original number is 16.08.
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The function f(x) = ex-3 when evaluated for f(4) is equivalent to?
Answer:
[tex]f(4)=e^{4}-3[/tex] or [tex]f(4)\approx51.5981500331...[/tex]
Step-by-step explanation:
The following is a general explanation of functions, what they mean, and how to evaluate them. The simplifications and calculations at the end are based on the clarification from your comments that [tex]f(x)=e^{x}-3[/tex] . If [tex]f(x)[/tex] is equal to something else, the simplifications/calculation will obviously be a little different, and the answer will likely be different, but the general process will be the same.
Understanding function notation
In the equation [tex]f(x)=e^{x}-3[/tex] , the left side of the equation is saying several things at once.
Names
The first character, "f", is the name of the function.
The name of a function tells you which set of directions you should look for to apply to an input. Some functions have names that are more than one letter, and even might give a hint as to what they do, for instance I might name a certain function [tex]squareroot[/tex], and based on the name, you might guess what the equation for [tex]squareroot(x)[/tex] might look like.
Mathematicians often use "f" as a function name between different problems over and over and over again, unless they come up with a special function that is worth giving a special name to.
Input
The rest of the characters after the name of the function, are "(x)" which is a pair of parentheses to contain the input, and the input itself.
Again, mathematicians often use "x" as a generic input over and over and over again, until we actually know which number we want to put into the function.
Output
Even though we've already discussed every character in the notation on the left, there is actually one more thing that the left side of the equation is saying: Altogether, "f(x)" is the output of the function, when the input "x" is put in. I feel it's worth stating, because it's often glossed over.
The equation itself
Next in the equation is the equals sign, which means that the left side of the equation, which is the output "f(x)", is equal to the stuff on the right.
The right side of the equation is the rule to follow describing what f(x) does to an input, and can help you calculate the output.
For instance, if I asked what p(4) was, it is clear that there is an input of 4, but without knowing what the function "p" does, there's no way to know what the function will give as an output when one inputs "4". This is why the right-hand side of the equation for a function is important.
Evaluating functions
To evaluate any function, we take an input, apply the function, and simplify/calculate the output.
In this case, the question asks for [tex]f(4)[/tex], meaning that the "input" is "4".
In this case, the question gives an explanation of what the function does through a rule given in equation form.
Given your clarification of the given function, [tex]f(x)=e^{x}-3[/tex] , meaning a generic input (in this case "x") is put into the function "f" and the output is found by doing the arithmetic on the right side of the equation (exponentiating the number by "e", and then subtracting 4)
Notice that in the expression [tex]f(4)[/tex], the "x" was replaced with "4". So, we need to substitute "4" where we see an "x" in the rule on the right hand side of the equation rule, and simplify and/or calculate (calculate, like with a calculator)
So, to evaluate the expression [tex]f(4)[/tex], simply substitute, and simplify/calculate.
Simplifying (no calculator)
To simplify without a calculator, we substitute "4". Any time you make a substitution, use parentheses. Then, try to simplify.
[tex]f(4)=e^{(4)}-3[/tex]
[tex]f(4)=e^{4}-3[/tex]
As it turns out, this is as much as we could simplify things here (without a calculator). So, if an exact answer is needed, this would be it.
Calculating (with a calculator)
To calculate with a calculator, we substitute "4". Any time you make a substitution, use parentheses. Then, try to simplify.
[tex]f(4)=e^{(4)}-3[/tex]
[tex]f(4)=e^{4}-3[/tex]
[tex]f(4)=54.5981500331...-3[/tex]
[tex]f(4)=51.5981500331...[/tex]
So calculating with a calculator, the output of the function "f", for an input of "4", is approximately 51.598.
what is the area of a triangle (-4,-5),(3,-3),(3,-7)?
i will give brainliest please help quick
The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.
What is the area of the triangle?The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).
Then the area of the triangle will be
Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|
We have
(x₁, y₁) ⇒ (-4, -5)
(x₂, y₂) ⇒ (3, -3)
(x₃, y₃) ⇒ (3, -7)
Then the area will be
Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]
Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]
Area = 1/2[-18 + 4]
Area = 1/2 × 14
Area = 7 square units
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If f(x) = 5x - 1, then f-1 (x)
Step-by-step explanation:
[tex]f(x) = 5x - 1[/tex]
[tex] \: [/tex]
[tex]y = 5x - 1[/tex]
[tex]5y - 1 = x[/tex]
[tex]5y = x + 1[/tex]
[tex]y = \frac{x + 1}{5} [/tex]
[tex] {f}^{ - 1} (x) = \frac{x + 1}{5} [/tex]
Write the ratio as a fraction in lowest terms.
Compare in inches.
4 feet to 49 inches
Answer:
48/49
Step-by-step explanation:
divison and multiplcation
Advise the committee of the minimum number of shade tents that must be set up to hold all the balloons so that they don’t fly away ?
The maximum number of spherical balloons that can be held in the canopy will be 30.
What is a canopy?The canopy is the fabric cover that hangs above a bed. It is a covering that is fastened to or carried over a dignitary or a holy item.
The base layer of spheres in a square pyramidal arrangement has n2 balls, where n is the number of balls that make up a square's side.
n=4 inch
The total number of spheres in the pyramid is;
⇒n(n+1)(2n+1)/6
⇒4(4+1)(2×4+1)/6
⇒(4×5×9)/6
⇒30
Hence, in the canopy, 30 spherical balloons are the most that may be accommodated.
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Given functions f ( x ) = 1 √ x and m ( x ) = x 2 − 4 , state the domains of the following functions using interval notation.
Domain of f ( x ) /m ( x ):
Domain of f ( m ( x ) ):
Domain of m(f(x)):
The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 1/√x
m(x) = x² - 4
Domain of f(x)/m(x):
f(x)/m(x) = (1/√x)/(x² - 4)
f(x)/m(x) = 1/√x(x² - 4)
The denominator cannot be zero:
√x(x² - 4) ≠ 0
x(x - 2)(x+2) ≠ 0
x ≠ 0, 2, -2
and x > 0
Domain of f(x)/m(x) is: (0, ∞) - {0, 2, -2} or [tex]\:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]
Domain of f(m(x)):
f(m(x)) = 1/√(x² - 4)
x² - 4 > 0
Domain: [tex]\rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)[/tex]
Domain of m(f(x)):
= ((1/√x)² - 4)
Domain: [tex]\:\left(0,\:\infty \:\right)[/tex]
Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.
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If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?
(f + g(x)>3 for all values of x
(f + g)(x)<3 for all values of x
(f + g)(x)>6 for all values of x
(f + g)(x)<6 for all values of x
Answer: for all values of x
Step-by-step explanation:
[tex](f+g)(x)=|x|+9-6=|x|+3[/tex]
Since the range of y = |x| is [tex]y \geq 0[/tex], adding 3 to this shifts the graph 3 units up, giving us that [tex](f+g)(x) \geq 3[/tex] for all values of x.
Determine the equation of a line passing through the point (2,-6), with a slope of m=-1
Answer:
sub(2，-6)into y=mx+C
-6=-1(2)+C
C=-4
equation=y=-x-4
Answer:
y = -x - 4
Step-by-step explanation:
Given:
a line with a slope of -1, passing through the point (2,-6)
Point-Slope Form: y - y₁ = m(x - x₁)
where:
(x₁, y₁) is the given point
m is the slope
Substitute the given values into the formula:
⇒ y - y₁ = m(x - x₁)
⇒ y - (-6) = -1(x - 2)
⇒ y + 6 = -1(x - 2) [distribute -1 through the parentheses]
⇒ y + 6 = -x + 2 [subtract 6 from both sides]
⇒ y + 6 - 6 = -x + 2 - 6
⇒ y = -x - 4
Check your work:
⇒ y = -x - 4 [substitute 2 for x, and -6 for y]
⇒ -6 = -2 - 4 [simplify]
⇒ -6 = -6 ✔
Therefore, the equation of the line is: y = -x - 4
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unrjdjxbzbwnf c and f f
Answer:
.
Step-by-step explanation:
.
Given the following equation of a circle in general form, find the equation in standard form by completing the square.
4x² + 8x + 4y² + 32y +52 = 0
Provide your answer below:
The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have an equation that represents the circle:
4x² + 8x + 4y² + 32y +52 = 0
Divide by 4 on both the sides:
x² + 2x + y² + 8y + 13 = 0
x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0
x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13
(x + 1)² + (y + 4)² = 4
(x + 1)² + (y + 4)² = 2²
Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
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Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10)
Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
Given, that a hyperbola centred at the origin has vertices at (0, ±9) and foci at (0, ±10).
What is hyperbola?In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The formula for a hyperbola centred at the origin is [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]
Where (h, k) is the center = (0, 0)
Distance from centre to vertices a = 9 ⇒ a² = 81
Distance from centre to vertices which is given from the foci c = 10
⇒ c² = 100
Using the Pythagorean formula, c²= a²+ b²
Substituting the values 100 = 81 + b²
So we get, b²= 100 - 81 = 19
Substituting the values in the standard form [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
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Please helpppp!!!!!!!!!!
The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:
f(x) = (x + 1)² + 2
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the function is:
f(x) = x² + 2x + 3
Completing the squares, we find the equation in vertex form, as follows:
f(x) = (x + 1)² + 2
As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.
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QUESTION 8 - 1 POINT
The median monthly rent in 1994 was $499 and $633 in 2001. What was the percent increase in the
median monthly rent prices from 1994 to 2001? Round to the nearest tenth of a percent.
Answer:
26.85%
Step-by-step explanation:
first you find the difference in price increase
633-499=134
*percentage increase=increase value/original value x100
so;=134/499x100=28.85%
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A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is
Answer:
0.5km or 500m
Step-by-step explanation:
Given Distance = Speed x Time
In this case, we should use the difference in speed and time of the 2 scenarios.
Difference in Time = 20 mins(late) + 10 mins(early)
= 30 mins or 0.5 hour
Difference in Speed = 4km/h - 3km/h = 1km/h
Distance = 1km/h x 0.5 hr = 0.5km or 500m.
3(x-5)² +14(x-5)-24
Answer:
3x^{2} -16x-19
Step-by-step explanation:
If we are going to be simplying this problem, then we need to take it step by step.
Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.
Answer:
(3x - 19) • (x + 1)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((3•((x-5)2))+14•(x-5))-24
STEP
2
:
Equation at the end of step 2
(3 • (x - 5)2 + 14 • (x - 5)) - 24
STEP
3
:
Trying to factor by splitting the middle term
Factoring 3x2-16x-19
The first term is, 3x2 its coefficient is 3 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is -19
Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57
Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .
-57 + 1 = -56
-19 + 3 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3
3x2 - 19x + 3x - 19
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-19)
Add up the last 2 terms, pulling out common factors :
1 • (3x-19)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x-19)
Which is the desired factorization
What does the ratio 4: 18 represent in this situation?
Answer:
2:9 or 2/9
Step-by-step explanation:
I guess this question asks the simplest form of ratio 4:18
so I divided it by two and since they cannot be divided further that's the answer
you can either choose to write it in ratio form or fraction form that's your choice good day.
Calcula el valor del lado "c" en el triángulo
rectángulo, que se proporciona en la figura;
aplicando las funciones trigonométricas:
Usando relaciones en un triángulo rectángulo, se encuentra que el valor del lado c es c = 35.5 unidades.
¿Cuáles son las relaciones en un triángulo rectángulo?Las relaciones en un triángulo rectángulo se dan de la siguiente manera:
El seno de un ángulo está dado por la longitud del lado opuesto al ángulo dividida por la longitud de la hipotenusa.El coseno de un ángulo está dado por la longitud del lado adyacente al ángulo dividido por la longitud de la hipotenusa.La tangente de un ángulo está dada por la longitud del lado opuesto al ángulo dividida por la longitud del lado adyacente al ángulo.El lado opuesto de el ángulo de 26º48' = 26.8º es de 16, de esa forma, puede-se encontrar el lado c de la siguiente manera:
[tex]\sin{(26.8^\circ)} = \frac{16}{c}[/tex]
[tex]c = \frac{16}{\sin{(26.8^\circ)}}[/tex]
c = 35.5º.
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document attached. please help!!
Answer:
The answers to different parts for ratio are - 3:5,3:5,3:5,9:25,graph C respectively .
Step-by-step explanation:
A ratio is a relationship between two quantities, normally expressed as the quotient of one divided by the other, or the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
a) The ratio of the median weekly earnings of the holder of a high school diploma only to the median weekly earnings of the holder of a bachelor's degree - 750/1250 = 3:5
b) The ratio of the area of the red rectangle to the area of the blue rectangle - 750 x 1 / 1250 x 1 = 3:5
c) The ratio of the area of the red square to the area of the blue square in graph B - 3:5
d) the ratio of the volume of the red cube to the volume of the blue cube in graph C - 750 x 750 /1250x 1250 =9:25
e) The most misleading graph is graph B because the distribution of values , depth, and shapes differ.
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What is the result of M x H?????
I have asked 4 tutors and none of them know how to answer this.
Answer: m x H = [ -9 36 - 9/2 ]
Step-by-step explanation:
Need help!!!!!!!!!!!!!!!!!
what are x and 8 in the linear equation? 8/x+5=50/25
A.One is variable and one is a coefficient
B.One is a constant and one is a coefficient?
C.Both are variables.
D.both are constants.
find arc length
x=t^(3)-2t
y=t^(2)-3
-2>t<2
Answer:
72
Step-by-step explanation:
I got it right .......