[tex]~~~~~8-x^3 = 0\\\\\implies 2^3 -x^3 = 0\\\\\implies (2-x)(2^2 + 2x +x^2) = 0\\\\\implies (2-x) (4+2x +x^2) = 0\\\\\implies 2-x = 0~~~~~~~~~~~;[\text{The roots of }~ x^2 +2x +4 =0~ \text{ are complex}].\\\\\implies x = 2\\\\\text{Hence,}~ x =2~ \text{ is the only real solution.}[/tex]
The possible values of x in the polynomial is x = 2
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
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 data ,
Let the polynomial equation be represented as A
Now , the value of A is
To find the possible values of x in the equation 8 - x³ = 0, we need to solve for x.
Starting with 8 - x³ = 0, we can add x³ to both sides of the equation:
8 = x³
Now, we can take the cube root of both sides:
∛8 = ∛x³
2 = x
So, the only possible value of x that satisfies the equation is x = 2
We can check this by substituting x = 2 into the original equation:
8 - 2³ = 8 - 8 = 0
Hence , the only possible value of x that satisfies the equation is x = 2
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Solve for the value of x
Answer:
x = 7
Step-by-step explanation:
I've attached my work
- im yellow is what the name of the angle is
- in green is what to do with it
- In blue is me checking my work by plugging x back in
Please give me feedback on my repsomse by commenting,
any way i can improve showing my work?
Hope it helps, let me know if you have questions !
Have a nice rest of your day :)
In a quadrilateral mnpq, <M=48°,<N =80° and P is three times than <Q. Find<P.
Answer:
[tex] \boxed{ \rm\angle P = \tt174{ {}^ \circ} }[/tex]
Step-by-step explanation:
Given,
∠M=48°∠N = 80°∠P = Three Times more than ∠Q.In a quadrilateral.
To Find:
∠PSolution:
We know that in quadrilateral MNPQ,
[tex] \rm \: \boxed{ \rm ∠M +∠ N +∠ P+ ∠Q = 360 ^{ \circ}}[/tex]
[tex] \rm \implies \: 48 {}^ \circ + 80 {}^ \circ + \angle P + \cfrac{1}{3} \angle \: P = 360 {}^{\circ}[/tex]
[tex] \rm \implies \angle P + \cfrac{1}{3}\angle P = 360 { {}^ \circ} - 48{ {}^ \circ} - 80 {{}^ \circ} [/tex]
[tex] \implies \rm \: \cfrac{4}{3} \angle P = 232 {{}^ \circ} [/tex]
[tex] \rm \: \implies \: \angle P = 232 {}^{\circ} \times \cfrac{3}{4} [/tex]
[tex] \rm \implies \: \angle P = 174{ {}^ \circ} [/tex]
Thus, ∠P will be 174° .
What are the solutions of the equation x squared equals 4? Use a graph of the related function.
A. A quadratic function is graphed on a coordinate plane. The parabola passes through the points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: negative 2and 2.
B. A quadratic function is graphed on a coordinate plane. The parabola passes through the points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: plus-or-minus StartRoot 2 EndRoot.
C. A quadratic function is graphed on a coordinate plane. The parabola passes through the points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma 4 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: negative 2and 2.
D. A quadratic function is graphed on a coordinate plane. The parabola passes through the points left parenthesis negative 2 comma 8 right parenthesis, left parenthesis 0 comma 4 right parenthesis, and left parenthesis 2 comma 8 right parenthesis.
There are no real number solutions.
In the graph of quadratic equation, the parabola passes through the points left parenthesis (-2,0) right parenthesis, left parenthesis (0,-4) right parenthesis, and left parenthesis (2,0) right parenthesis.
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here,(a,b, c) is the real numbers and (x) is the variable.
The given quadratic equation is,
[tex]f(x)=x^2+4[/tex]
Equate the equation to zero to solve it further,
[tex]x^2=4\\x^2-4=0\\x^2=4\\x=\sqrt{4}\\x=\pm2[/tex]
Thus, the solution of the equation is +2 and -2. The graph of the equation is attached below.
Hence, in the graph of quadratic equation, the parabola passes through the points left parenthesis (-2,0) right parenthesis, left parenthesis (0,-4) right parenthesis, and left parenthesis (2,0) right parenthesis.
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When you half a whole number that ends in 6, you always get a number
ends in 3."
Answer:
This actually is false, it doesn't always work.
Step-by-step explanation:
Such as,
256 x 1/2 =
128.
The last digit isn't a 3, it's an 8.
Another Example,
176 x 1/2 =
88.
The last digit is also an 8 here, and not a 3.
It does work for some equations, but not for most of them, hope this helps!
to
Integrate 4√x^5 directly
Answer:
here the answer ask if theres any prob
I need help please I don’t know how to solve this
Answer:
68 ft^2
Step-by-step explanation:
The shaded region is a square missing a triangle. Thus, the area of the shaded region = area of square - area of triangle
Thus, we get 8*9 - 1/2 * 2 * 4 = 72 - 4 = 68 square feet.
PLS HELP MEEE I NEED TO TURN THIS IN
Answer:
150 laptops because 70% of the total devices are laptop computers and desktop computers so the remaining 30% of the devices are tablet. 500×0.30= 150.
look at this diagram A: what fraction is shaded B:What Percentage Is Shaded 6/9 is shaded
its a triangle:)
Answer:
Fraction is 6 over 9 percentage is 0.54%
Hope This Helped
THIS IS GEOMETRY AND I NEED IMMEDIATE HELP W THIS PROBLEM PLEASE HELP
Step-by-step explanation:
ang acb of arc amb= 130°
ang acb of arc apb = 230°
length of arc = 5*230/360 = 3.19 cm
identify an equation in slope-intercept form for the line parallel to y=1/4x-7 that passes through (-2,-6)
Answer:
D. [tex]y + 6 =- \frac{1}{4} (x+2)[/tex]
Step-by-step explanation:
We are given that a line is parallel to the line y=-1/4x-7 and passes through (-2, -6).
We want to write the equation of this line.
First, we need to know that parallel lines have the same slope.
In y=-1/4x-7, the slope of the line is -1/4; it is also the slope of the line parallel to it.
All of the answers in your system are written in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
As we already know the slope and the point, we can plug these values into the formula.
Starting with the slope; as found above, the slope is -1/4. Therefore, the equation will then be:
[tex]y-y_1=-\frac{1}{4} (x-x_1)[/tex]
Now substitute -2 and -6 as [tex]x_1[/tex] and [tex]y_1[/tex] respectively (note: we have NEGATIVE numbers, and SUBTRACTION in the formula, so we will end up subtracting a negative).
[tex]y--6=-\frac{1}{4} (x--2)[/tex]
We can simplify this to become:
[tex]y+6=-\frac{1}{4} (x+2)[/tex]
Therefore, D is the answer.
Answer:
y+6= -4(x+2)
Step-by-step explanation:
solve for x 8 (x-1) = -4x + 136
I have been stuck on this question for ever and cant seem to figure it out so if it isnt a big deal for one of you can ya please help.
Answer:
[tex]d = 24mm[/tex]
Step-by-step explanation:
[tex]c = \pi d[/tex][tex]c = 75.36mm \\ 75.36mm = \pi d \\ d = \frac{75.36}{\pi} \\ d = 24mm[/tex]Please solve with explanation (high points)
Answer:
∠ACB = 24.35°
Step-by-step explanation:
∠ACB basically means ∠C
tangent = opposite / adjacent
tanx = 5.62 / (3.54 + 3.86 + 5.02)
you are adding all these to get the total of the base length
tanx = 5.62 / 12.42
x = arctan(5.62 / 12.42)
x = 24.34654°
The sum of the measures of five exterior angles of a hexagon is 284. What’s the measure of the sixth angle?
Answer:
76°The sum of the measures of five exterior angles of a hexagon is 284. What’s the measure of the sixth angle?
Step-by-step explanation:
the sum of all exterior angles in any polygon is 360°.So
360° - 284 = 76°
m
Enter the number that belongs in
the green box
Answer:
m<C = 180 - (90+32)
= 180 - 122
= 58°
If 15% of 200 apples are bad, how many apples are bad?
apples= 200
bad apples= 15%
to find:how many apples are bad.
solution:[tex] 200 \times \frac{15}{100} [/tex]
[tex] = 30[/tex]
therefore, there are 30 bad apples.
A principal of $2000 is invested at 7.75% interest, compounded annually. How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
Yearly compounding: 7.75% $5,686.85
Quarterly compounding: 7.978% $5,857.78
Monthly compounding: 8.031% $5,898.27
Daily compounding: 8.057% $5,918.20
Step-by-step explanation:
multiply yearly by 14
l need the answer for this question asap!!!
The domain of a function is the x-values that the graph applies to. This means that the domain is whatever x-values the graph crosses. All vertical parabolas (like the one pictured) have a domain of all reals. This is because any x-value could be plugged into the function and provide a y-value. while it may not seem like it, that graph will cover every single x-value in existence.
Domain = All realsB. Range
The range is similar to the domain but is for y-values. So, the range is whatever y-values the graph applies to and crosses. As you can see from the graph, there are no y-values above 1. This means the range is y≤1.
Range = y ≤ 1C. Increasing Interval
A graph is increasing when the y-values are increasing. So, on the parent function of a parabola, the graph increases to the right and decreases to the left. However, this graph is inverted and shifted to the left, so the interval will also be flipped and shifted. In this case, the graph increases from -∞ to 2.
Increasing Interval = [-∞, 2]D. Decreasing Interval
The decreasing interval is very similar to the increasing interval. This interval applies when the y-values are decreasing as the x-values increase. For a parabola, the increasing and decreasing intervals always meet at the x-value of the vertex, which is 2 on this graph. The y-values decrease during the interval 2 to ∞.
Decreasing Interval = [2, ∞]E. Opening
The direction of a parabola is decided by the sign (+ or -) of the leading coefficient. Positive coefficients open up and negative opens down. As you can see from the graph, the sides of the parabola point downwards. This means that the leading coefficient must be negative.
Opening = DownF. Min and Max
A parabola will always only have a min or a max, never both. If a graph opens up it has a min because there is one y-value which is the minimum possible y-value. Graphs that open downwards have a maximum because there is one y-value that is the largest possible. So, this graph has a maximum of 1 because that is the largest possible y-value.
Max = 1A summer camp rewards campers and counselors with badges. The camp orders 200 badges. They plan to give 25 badges to counselors. They ordreed at least 3 badges for each camper.
a. How many campers could be at the camp?
b. Are all the values on the graph of c is less than or equal to 58 possible solutions? Explain.
correct answer gets a brainless
Answer:
58 campers,
Step-by-step explanation:
you do 200 - 25 then 175 divided by 3
QUADRATIC FORMULA
11. The current World Record for the Track event Shot Put is 23.37 meters - meaning the Shot landed
23.37 meters from where it was launched (DO NOT USE THIS VALUE FOR THE EQUATION).
The path of the Shot thrown by an athlete during a track meet can be modeled by the Quadratic Equation
h(t) = -0.09c2 + 2t + 1.67 where he represents its height in meters and m represents the horizontal
distance in meters. How far did the Shot land from where it was thrown? Substitute 0 for h in your Equation
in order to find the horizontal distance from where this Shot was lauchedlaunched.
Answer:
23.028 meters
Step-by-step explanation:
We presume your quadratic equation is intended to be ...
h(m) = -0.09m² +2m +1.67
where h(m) is the height in meters, and m is the horizontal distance in meters. You want to find the positive value of m when h = 0.
__
The quadratic formula tells you the solution to ...
ax² +bx +c = 0
In your equation, a = -0.09, b = 2, c = 1.67, and the variable is m. The solutions given by the formula are ...
[tex]m=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-2\pm\sqrt{2^2-4(-0.09)(1.67)}}{2(-0.09)}\\\\=\dfrac{2\pm\sqrt{4+0.6012}}{0.18}\approx\{-0.806,23.028\}[/tex]
The shot landed about 23.028 meters from where it was thrown.
_____
Additional comment
The shot was launched at an angle of about 63.4° from the horizontal. Had a shallower angle been used with the same launch speed (about 16.5 m/s), the shot would have traveled farther. At about 45°, the distance might have been in excess of 29 meters.
Volume with fractions is confusing.
Answer:
V≈0.064
Tip:
just to help you for future note with finding volume with fractions is you use a calculator and do the top divided by the bottom and it should give you a decimal
What are the slope and y-intercept in the equation y = 7 + 5x + 2x + 4?
Answer: slope is 7 and y-intercept is 11
Step-by-step explanation:
y = 7 + 5x + 2x + 4
combine like terms
y = 11 + 7x
rearange
y = 7x + 11
slope is 7 and y-intercept is 11
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
What is the slope of the line y=7+5x+2x+4? What about the y-intercept?
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
First, we need to combine like terms:-
[tex]\Large\text{y=7+4+5x+2x}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\Large\text{y=11+7x}[/tex]
[tex]\bigstar[/tex] We can rearrange the terms a little:-
[tex]\Large\textit{y=7x+11}[/tex]
Now we can easily determine the slope and the y-intercept of the line.
Slope = number multiplied by x
y-intercept = a number added to or subtracted from x
Henceforth, we conclude that
[tex]\Large\text{Slope=7 \& y-intercept=11}[/tex]
Good luck with your studies.#TogetherWeGoFar
[tex]\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
The order of rotation for a regular hexagon is?
Answer:
6
Step-by-step explanation:
The rotational symmetry for a hexagon is 6 as it is a regular polygon.
Evaluate the following equations
Step-by-step explanation:
A....
Solution ,
[tex] = \frac{h - 3}{3} = 3h \\ [/tex]
[tex] = h - 3 = 9h[/tex]
[tex] = h - 3 - 9h = 0[/tex]
[tex] = h - 9h = 3[/tex]
[tex] = - 8h = 3[/tex]
Change the sign of both side
[tex] = 8h = - 3[/tex]
[tex] = h = - \frac{3}{8 } \\ [/tex]
B....
Solution,
[tex] = \frac{t}{2} = \frac{t + 1}{5} \\ [/tex]
Multiply the both side by the least common multiple to eliminate the fraction...
[tex] = 5t = 2t + 2[/tex]
[tex] = 5t - 2t = 2[/tex]
[tex] = 3t = 2[/tex]
[tex] = t = \frac{2}{3} \\ [/tex]
PLS HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 600 tickets. There is one $1,000 grand prize, two $400 second prizes, and ten $20 third prizes. You just bought a ticket. Find the expected value for your profit
The expected value of the profit is $-1 when the student council is hosting a drawing to raise money for scholarships
What is probaility?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event
The expected value of any discrete variable X is calculate as:
E(X)=X1*P(X1)+X2*P(X3)+...+X3*P(X3)
Where X1, X2, ..., X3 are the values that the variable can take and P(X1), P(X2), ..., P(X3) are their probabilities.
In this case the variable X is the dollars that can win, so:
X1=$2,000
X2=$300
x3=$20
X4=$0
Then the probabilities can be calculate as:
[tex]P(X_1)=\dfrac{1}{600}\\\\\\P(X_2}=\dfrac{3}{600}\\\\\\P(X_3)=\dfrac{15}{600}\\\\\\P(X_4)=\dfrac{581}{600}[/tex]
Replacing the variables and probabilities on the equation of expected value we get:
[tex]E(X)=(2000\times \dfrac{1}{600})+(300\times \dfrac{3}{600})+(20\times \dfrac{15}{600})+(0\times \dfrac{581}{600})[/tex]
E(X)=$4
Additionally, the student bought a ticket by $5, so the expected profit can be calculate as:
Expected Profit = Expected Earnings - Cost = $4 - $5 = $-1
Finally, the expected value of the profit is $-1
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Determine the solution set for x.
X + 300 < 450
The solution set for the inequality X + 300 < 450 is X∈ (-∞, 150) when X is less than 150.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have inequality:
X + 300 < 450
X < 450 - 300 (subtract 300 on both sides)
X < 150
X ∈ (-∞, 150)
Thus, the solution set for the inequality X + 300 < 450 is X∈ (-∞, 150) when X is less than 150.
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Can Wendell make a triangular garden using pieces D, E, and F? Why or why not?
If the sides of the triangle are given. Then Wendell can make a triangular garden using pieces D, E, and F.
What is the construction of the triangle?The process of making a triangle is known as the construction of the triangle.
Wendell makes a triangular garden using pieces D, E, and F.
Where D, E, and F may be a side of the triangle or angle of the triangle.
To make a triangle we need at least one side of the triangle.
If all the angles of the triangle is given then we can not make a triangle because the side of the triangle is unknown.
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Answer:
If the sides of the triangle are given. Then Wendell can make a triangular garden using pieces D, E, and F.
Step-by-step explanation:
Work out 15% of £24 please
Answer:
£3.6
Step-by-step explanation:
24 = 100% ; x = 15%
Let's make it simple
[tex]\frac{x}{24 } = \frac{15}{100} ; x = 24.15/ 100 ; x=3.6[/tex]
a football team won 65% of the total matches they played during the year. if they lost 21 matches in all and no matches were drawn, find the number of matches played during the year.
[tex]\large\bold{{Question :}}[/tex]
A football team won 65% of the total matches they played during the year. if they lost 21 matches in all and no matches were drawn, find the number of matches played during the year.
[tex]\large\bold\red{\underline{Solution:}}[/tex]
Here, let's assume no. of matches played be = x
Given,
[tex]\longmapsto{}[/tex](100-60)[tex] \%[/tex] of x = 24[tex]\longmapsto{}[/tex]40 [tex]\% [/tex]of x = 24[tex]\longmapsto{}[/tex][tex]\frac{2x}{5}[/tex] = 24[tex]\longmapsto{}[/tex]x = [tex]\frac{24 \times 5 }{2}[/tex][tex]\longmapsto{}[/tex]x = 60
Hence, the number of matches played during the whole year is [tex]\large\bold\red{\underline{60}}[/tex].
Happy Learning : )