Let f(x) = (4x^2 - 11)^3 and g(x) = 4x^2- 11.
Given that f(x) = (hºg)(x), find h(x).
Enter the correct answer.
Answers
Answer:
[tex]\large\boxed{h(x)=x^3}[/tex]
Step-by-step explanation:
[tex]f(x)=(4x^2-11)^3\\\\f(x)=(h\circ g)(x)=h\bigg(g(x)\bigg)\to\text{exchange x to}\ g(x)=4x^2-11\\\\f(x)=(\underbrace{4x^2-11}_{g(x)})^3=\bigg(g(x)\bigg)^3=h\bigg(g(x)\bigg)\\\\\text{Therefore}\ h(x)=x^3[/tex]
Answer:
the person on top is correct
Step-by-step explanation:
Related Questions
After working 10 years as a bus driver, Izabel Antocicco was in an accident and became permanently disabled. She was 63 years old at the time and was planning to retire on her 65th birthday. Her final salary was $55,700 per year. Her rate of benefits was 4.5%. What is her monthly disability benefit?
A. $2,506.50
B. $3,458.90
C. $3,508.11
D. $6,458.22
Answers
Answer:
A. $2,506.50
Step-by-step explanation:
Draw a line perpendicular to the line that contains the points
(1, 8)
and
(4, 6)
and passes through the point
(−2, 8)
Answers
Answer:
[tex]y=\frac{3}{2} x+\frac{20}{3}[/tex]
Step-by-step explanation:
First, to find the original line, employ the slope formula.
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{6-8}{4-1} \\\\\frac{-2}{3}[/tex]
The slope of your original line is [tex]-\frac{2}{3}[/tex].
Next, plug in your slope and the third point to the point-slope formula.
[tex]y-y1=m(x-x1)\\\\y-8=-\frac{2}{3} (x+2)\\\\y-8=-\frac{2}{3} x-\frac{4}{3}\\\\y=-\frac{2}{3} x+\frac{20}{3}[/tex]
To find the line which is perpendicular to the line, take the opposite reciprocal of the slope.
To find the opposite, flip the sign. [tex]-\frac{2}{3}[/tex] is negative, so it will become [tex]\frac{2}{3}[/tex], which is positive.
To find the reciprocal, flip the fraction. [tex]\frac{2}{3}[/tex] would become [tex]\frac{3}{2}[/tex].
Your slope for the perpendicular line is [tex]\frac{3}{2}[/tex], so your line is:
[tex]y=\frac{3}{2} x+\frac{20}{3}[/tex]
Point C is the center of the circle. Angle ACB measures 56 . What is the measure of arc AB?
Answers
Answer:
=56°
Step-by-step explanation:
The degree measure of an angle is the measure of the central angle that intercepts the arc at the circumference.
The central angle is bound by two radii.
In the provided question, the central angle ACB=56° and intercepts the circle at A and B, with the vertex at C the center of the circle.
Answer:56
Step-by-step explanation:
Kira swam 17 4/7 laps in the pool on Monday. On Wednesday, she increased
her workout to 23 5/14 laps. Estimate the total number of laps Kira swam on
Monday and Wednesday
14
A.41 laps
B.40 laps
C.31 laps
D.42 laps
Answers
Answer:
A) 41 laps
Step-by-step explanation:
Round 17 4/7 to the nearest whole number:
18
Round 23 5/14 to the nearest whole number:
23
18 + 23 = 41
Final answer:
By rounding the fractional laps to the nearest whole numbers (18 for Monday and 23 for Wednesday), and adding them together, we estimate that Kira swam a total of 41 laps. Option A is the closest answer.
Explanation:
To estimate the total number of laps Kira swam on Monday and Wednesday, we should round the numbers to the nearest whole number and then add them together. Kira swam 17 4/7 laps on Monday, which we can round to 18 laps for estimation purposes. On Wednesday, she swam 23 5/14 laps, which rounds to 23 laps. Adding the estimated numbers together, we get:
Monday: 18 (estimated from 17 4/7)
Wednesday: 23 (estimated from 23 5/14)
Therefore, the estimated total number of laps is 18 + 23 = 41 laps.
The closest answer to our estimation is Option A: 41 laps.
Value of x, -5x-15>10+20x
Answers
Answer:
x<-1
Step-by-step explanation:
-5x-15>10+20x
Add 5x to each side
-5x+5x-15>10+20x+5x
-15> 10+25x
Subtract 10 from each side
-15-10 > 25x
-25 >25x
Divide each side by 25
-25/25 >25x/25
-1>x
x<-1
After graduating from college, Carlos receives a job offer for $62000 per year with a raise of 5% after one year what is his pay
Answers
Step-by-step explanation:
After the raise, his pay is:
62000 + 0.05×62000
62000 (1 + 0.05)
65100
His pay after one year is $65,100.
To calculate Carlos's new salary after a 5% raise on his initial $62,000 salary, you multiply $62,000 by 0.05 to find the raise amount of $3,100, and then add it to the initial salary, resulting in a new salary of $65,100.
The question involves calculating the new salary of Carlos after a 5% raise following his initial year of employment. Carlos's starting salary is $62,000 per year. After one year, he receives a 5% raise. To calculate Carlos's new salary, follow this step:
Find the raise amount by calculating 5% of the initial salary. This can be found by multiplying the initial salary by 0.05 (which is the decimal form of 5%).Add the raise amount to the initial salary to find the new salary after one year.Now, let's do the math:
Raise amount = $62,000 times 0.05 = $3,100.New salary = Initial salary + Raise amount = $62,000 + $3,100 = $65,100.Therefore, after a 5% raise, Carlos's new annual pay will be $65,100.
A tour boat left the dock and traveled west at an average speed of 10 mph. A smaller fishing boat left some time later traveling in the same direction but at an average speed of 12 mph. After traveling for 10 hours, the fishing boat caught up to the tour boat. The tour boat left _______ hours earlier than the fishing boat.
Answers
The Answer is 2.
2x10=20+10x10=100 100+20=120
12x10=120
recall your d = rt, distance = rate * time.
so the tour boat left at a speed of 10 mph, say the fishing boat left "h" hours later, traveling faster at 12 mph in the same direction.
By the time the fishing boat caught up with the tour boat, the distances travelled by both must be the same, say "d" miles, thus the idea of catching up, the distance of the fishing boat is the same as the distance of the tour boat.
Since the fishing boat caught up with the tour boat after going for 10 hours, and had left "h" hours later, then when that happened, the tour boat has already been travelling for 10 + h hours.
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{Tour boat}&d&10&10+h\\ \textit{Fishing boat}&d&12&10 \end{array}~\hfill \begin{cases} d=(10)(10+h)\\ d=(12)(10) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{doing substitution on the 2nd equation}~\hfill }{(10)(10+h)=(12)(10)\implies \cfrac{~~\begin{matrix} (10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(10+h)}{~~\begin{matrix} 10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=12} \\\\\\ 10+h=12\implies h=2[/tex]
Deshawn has five CDs that he is going to give away. He lets his best friend choose three of five CDs. How many different groups of three CDs are possible?
Answers
Answer:
10 different groups of three CDs are possible
Step-by-step explanation:
Total CDs are five and 3 has to be chosen where order doesn't matter.
In these kind of scenarios, combinations are used for calculating different ways in which the CDs can be given.
So,
Number of ways in which groups of CDs are possible = ⁵C₃
[tex]= \frac{n!}{r!(n-r)!} \\= \frac{5!}{3!(5-3)!}\\=\frac{5!}{3!2!}\\=\frac{5*4*3!}{3!2!}\\=\frac{5*4}{2}\\=\frac{20}{2}\\=10[/tex]
Therefore, 10 different groups of three CDs are possible ..
perform the indicated operation 3/4 ÷ 1/3
Answers
Answer:
9/4 or 2 1/4.
Step-by-step explanation:
3/4 / 1/3
=3/4 * 3/1
= 9/4
Answer:
3/4 ÷ 1/3 equals
(3/4 x 3/1) = 9/4
Step-by-step explanation:
If you vertical stretch the quadratic parent function F(x)=x^2By multiplying by seven is what is the equation of the new function
Answers
Answer:
g(x) = 7x^2
Step-by-step explanation:
Given a function f(x), the function kf(x) is stretched by a factor of k. In this case, if we stretch the function f(x) = x^2 by a factor of seven, the new function is going to be the base function multiplied by 7, as follows:
g(x) = 7x^2
The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.
Which function defines the area of the rectangle?
Hint: A=l⋅w
a(x)=2x^2+5x+4
a(x)=3x+5
a(x)=2x^2+9x+4
a(x)=x−3
Answers
Answer:
a(x)=2x^2+9x+4
Step-by-step explanation:
We have been given the length and width, as well as the formula to find the area:
Length: 2x + 1
Width: x + 4
A = l * w
A = (2x + 1)(x + 4)
2x^2 + 8x + x + 4
We can add like terms now:
2x^2 + 9x + 4
Our area is 2x^2 + 9x + 4
Our answer would be a(x)=2x^2+9x+4
Answer:
The correct answer is third option
a(x) = 2x² + 9x + 4
Step-by-step explanation:
It is given that,the length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.
To find the area of the rectangle
Area of rectangle = Length * Breadth
a(x) = l(x) * w(x)
= (2x + 1)(x + 4)
= 2x² + 8x + x + 4
= 2x² + 9x + 4
The correct answer is third option
a(x) = 2x² + 9x + 4
the perimeter of a square is 20 feet how long is each side
Answers
20 feet/ 4 sides= 5 feet
Therefore, each side of the square is 5 feet.
Hope this helps!
The side of the square whose perimeter is 20 feet is given by the equation A = 5 feet
What is the perimeter of a square?The perimeter of a square is given by four times the length of its each side
The equation for the perimeter of the square with the side 'a' is given by
Perimeter of Square = 4a
Given data ,
Let the perimeter of the square be represented as P
Now , the value of P is
P = 20 feet be equation (1)
Now , for a square
Perimeter of Square = 4A , where A is the measure of side
Substituting the values in the equation , we get
20 = 4A
Divide by 4 on both sides of the equation , we get
A = 20/4
A = 5 feet
Therefore , the value of A is 5 feet
Hence , the side of the square is 5 feet
To learn more about perimeter of square click :
https://brainly.com/question/11495285
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3(-4n - 9) = 21 plc solve
Answers
[tex]\huge{\boxed{n=-4}}[/tex]
Explanation:[tex]\begin{array}{cc}\begin{flushright}\text{Divide both sides of the equation by 3.}\end{flushright}&\begin{flushleft}-4n-9=7\end{flushleft}\\\begin{flushright}\text{Add 9 on both sides.}\end{flushright}&\begin{flushleft}-4n=16\end{flushleft}\\\begin{flushright}\text{Divide both sides by -4.}\end{flushrigh}&n=-4\end{array}[/tex]
Answer:
[tex]\Huge \boxed{n=-4}[/tex]
Step-by-step explanation:
First thing you do is divide by 3 from both sides of equation.
[tex]\displaystyle \frac{3(-4n-9)}{3}=\frac{21}{3}[/tex]
Simplify.
[tex]\displaystyle -4n-9=7[/tex]
Then add by 9 from both sides of equation.
[tex]\displaystyle -4n-9+9=7+9[/tex]
Simplify.
[tex]\displaystyle 7+9=16[/tex]
[tex]\displaystyle -4n=16[/tex]
Divide by -4 from both sides of equation.
[tex]\displaystyle \frac{-4n}{-4}=\frac{16}{-4}[/tex]
Simplify, to find the answer.
[tex]\displaystyle 16\div-4=-4[/tex]
[tex]\huge\boxed{\textnormal{N=-4}}[/tex], which is our answer.
-2k-(-5)+1 like terms
Answers
Answer:
-2k + 6
Step-by-step explanation:
-2k - (-5) + 1 //-1 times -5 = 5 ( - - gives +)
-2k + 5 + 1 //Combine like terms
-2k + 6
Remember you can't add or sub -2k with 6 since -2 is multiplying with k (which is constant and you don't know it's value)
//Hope this helps
Answer:
-2k+6
Step-by-step explanation:
How would you do this problem?
Answers
Divide everything by -5
f(x)=t^2-4t-12
(t-6)(t+2)
Set it up to zero
t-6=0. t+2=0
t=6. t=-2
Since you can’t have negative seconds, the answer is 6 seconds
Answer:
6 seconds
Step-by-step explanation:
First: equalize the equation to zero
f(t) = -5t² + 20t + 60
-5t² + 20t + 60 = 0
Second: find its roots
-5(t² - 4t - 12) = 0
-5 (t - 6)(t + 2) = 0
[tex]t - 6 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t + 2 = 0 \\ t = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t = - 2[/tex]
Time can't be negative so the answer is: it takes 6 seconds to hit the ground
ndicate the equation of the line through (2, -4) and having slope of 3/5.
Answers
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=\cfrac{3}{5}(x-2) \implies y+4=\cfrac{3}{5}x-\cfrac{6}{5} \\\\\\ y=\cfrac{3}{5}x-\cfrac{6}{5}-4\implies \implies y=\cfrac{3}{5}x-\cfrac{26}{5}[/tex]
Answer:
Point-slope form: [tex]y+4=\frac{3}{5}(x-2)[/tex]
Slope-intercept form: [tex]y=\frac{3}{5}x-\frac{26}{5}[/tex]
Standard form: [tex]3x-5y=26[/tex]
Step-by-step explanation:
The easiest form to use here if you know it is point-slope form. I say this because you are given a point and the slope of the equation.
The point-slope form is [tex]y-y_1=m(x-x_1)[/tex].
Plug in your information.
Again you are given [tex](x_1,y_1)=(2,-4)[/tex] and [tex]m=\frac{3}{5}[/tex].
[tex]y-y1=m(x-x_1)[/tex] with the line before this one gives us:
[tex]y-(-4)=\frac{3}{5}(x-2)[/tex]
[tex]y+4=\frac{3}{5}(x-2)[/tex] This is point-slope form.
We can rearrange it for different form.
Another form is the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept.
So to put [tex]y+4=\frac{3}{5}(x-2)[/tex] into y=mx+b we will need to distribute and isolate y.
I will first distribute. 3/5(x-2)=3/4 x -6/5.
So now we have [tex]y+4=\frac{3}{5}x-\frac{6}{5}[/tex]
Subtract 4 on both sides:
[tex]y=\frac{3}{5}x-\frac{6}{5}-4[tex]
Combined the like terms:
[tex]y=\frac{3}{5}x-\frac{26}{5}[/tex] This is slope-intercept form.
We can also do standard form which is ax+by=c. Usually people want a,b, and c to be integers.
So first thing I will do is get rid of the fractions by multiplying both sides by 5.
This gives me
[tex]5y=5\cdot \frac{3}{5}x-5 \cdot 26/5[/tex]
[tex]5y=3x-26[/tex]
Now subtract 3x on both sides
[tex]-3x+5y=-26[/tex]
You could also multiply both sides by -1 giving you:
[tex]3x-5y=26[/tex]
Hiring the bus will cost $25 a day for the driver, $2 per mile traveled, and $3 for gas per mile traveled. The field trip will total 8 miles round trip.
Mrs. Garcia needs to calculate the cost of the bus. Which expression could she write that uses the distributive property?
Answers
Answer:
65
Step-by-step explanation:
25+2x8+3x8
Answer:
25 + 8(2 + 3)
Step-by-step explanation:
Which of the following is a soultion to the quadratic equation below x^2 - 3x - 54 =0
Answers
Answer:
9 or -6
Step-by-step explanation:
To solve, I would suggest factoring.
You need to find two numbers which can be multiplied for 54 and also combined in some way to get 3. In this case, 9 and 6 are perfect.
[tex]x^2-3x-54=0\\(x-9)(x+6)=0[/tex]
Next, you can set both of your terms equal to zero to find your possible solutions.
[tex]x-9=0\\x=9\\[/tex]
or
[tex]x+6=0\\x=-6[/tex]
how to find equation of line passing through the points (x,y)
Answers
First you must acknowledge that you are dealing with a line therefore you must write linear equation or linear function in this case.
Linear function has a form of,
[tex]y=mx+n[/tex]
Then calculate the slope m using the coordinates of two points. Let say A(x1, y1) and B(x2, y2),
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now pick a point either A or B and insert coordinates of either one of them in the linear equation also insert the slope you just calculated, I will pick point A.
[tex]y_1=mx_1+n[/tex]
From here you solve the equation for n,
[tex]
y_1=mx_1+n\Longrightarrow n=y_1-mx_1
[/tex]
So you have slope m and variable n therefore you can write down the equation of the line,
[tex]f(x)=m_{slope}x+n_{variable}[/tex]
Hope this helps.
r3t40
A pedestal for a statue is in the shape of a hexagon, formed by a square and two congruent triangles, with the dimensions shown below. What is the area of the top of the pedestal?
Answers
You are told the middle part is a square, so all 4 sides are equal.
The height is shown as 4 feet, so the width of the square is also 4 feet.
This means the height of the 2 triangles is 7 - 4 = 3 feet, so each triangle is 1.5 feet high ( 3 feet / 2 = 1.5).
The area of the square is 4 x 4 = 16 square feet.
The area of 1 triangle is 1/2 x base x height = 1/2 x 4 x 1.5 = 3 square feet.
The total area = 16 + 3 + 3 = 22 square feet.
Which expression is equivalent to 2a+1/10a-5 / 10a/4a^2-1
Answers
Answer:
[tex]\large\boxed{\dfrac{(2a+1)^2}{50a}}[/tex]
Step-by-step explanation:
[tex]10a-5=5(2a-1)\\\\4a^2-1=2^2a^2-1^2=(2a)^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2a-1)(2a+1)\\\\\dfrac{2a+1}{10a-5}\div\dfrac{10a}{4a^2-1}=\dfrac{2a+1}{5(2a-1)}\div\dfrac{10a}{(2a-1)(2a+1)}\\\\=\dfrac{2a+1}{5(2a-1)}\cdot\dfrac{(2a-1)(2a+1)}{10a}\qquad\text{cancel}\ (2a-1)\\\\=\dfrac{2a+1}{5}\cdot\dfrac{2a+1}{10a}=\dfrac{(2a+1)^2}{50a}[/tex]
Answer: The answer is D
Step-by-step explanation: got it right 2023 edge
To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Is Shayla applying the vertical line test correctly?
Answers
Answer:
"No, because using the y-axis tests only whether x = 0 is mapped to multiple values."
Shayla's use of the vertical line test is incorrect because she is only considering the number of y-intercepts, which is not conclusive in determining if a graph is a function. The correct method is to see if any vertical line intersects the graph at more than one point.
Explanation:Shayla is not applying the vertical line test correctly. The correct use of the test involves drawing vertical lines through various points on the graph and checking to see if any vertical line intersects the graph at more than one point. A graph represents a function if, and only if, every vertical line intersects the graph at most once. The number of y-intercepts, or where the graph intersects the y-axis, is not a reliable indicator of whether a graph is a function. For example, a straight line with a slope and a y-intercept, such as in the form y = mx + b, will always be a function, regardless of the number of y-intercepts it has.
which values of x and y would make the following expression represent a real number? (4+5i)(x+yi)
Answers
Answer:
So x=4 and y=-5 would work.
Step-by-step explanation:
When you multiply complex conjugates, you get a real result.
Example:
[tex](a+bi)(a-bi)=a^2-b^2i^2=a^2+b^2[/tex]
I replace [tex]i^2[/tex] with -1 since [tex]i^2=-1[/tex].
[tex]a^2+b^2[/tex] is a real number (there is no imaginary part, no i).
So what is the conjugate of 4+5i?
4-5i
So x=4 and y=-5 would work.
A multiple of the complex conjugate would work as well.
[tex](a+bi)(ca-cbi)[/tex]
[tex]c(a+bi)(a-bi)[/tex]
[tex]c(a^2-b^2i^2)[/tex]
[tex]c(a^2+b^2)[/tex]
This is still a real number; there is no imaginary part,no i.
If statement q is angles ABC and QRT are vertical angles then ~q is angles ABC and QRT are congruent
True or false?
Answers
Answer:
true
explanation:
because vertical angles are congruent.
Find the angle measure C in the parallelogram ABCD.
Answers
Answer:
135°
Step-by-step explanation:
In a parallelogram the opposite angles are congruent, so
∠BCD = ∠BAD = 135°
Which shows the correct solution of the equation, when 1/2a+2/3b=50, when b=50 ?
Answers
Answer:
[tex] a = \frac{100}{3}[/tex]
Step-by-step explanation:
We have the following equation:
[tex]\frac{1}{2} a + \frac{2}{3} b = 50[/tex]
If [tex]b=50[/tex], then:
[tex]\frac{1}{2} a + \frac{2}{3}[/tex]×50 [tex] = 50[/tex]
Solving for 'a':
[tex]\frac{1}{2} a = \frac{50}{3}[/tex]
[tex]\frac{1}{2} a = \frac{50}{3}[/tex]
[tex] a = 2\frac{50}{3}[/tex]
[tex] a = \frac{100}{3}[/tex]
Answer a=60 (3rd option)
Step-by-step explanation:
The equation below has one solution.
9x-10 = 3x+2
What is the solution to the equation?
1) -2
2)-1
3) 1
4) 2
Answers
Answer:
x = 2
Step-by-step explanation:
Given
9x - 10 = 3x + 2 ( subtract 3x from both sides )
6x - 10 = 2 ( add 10 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Answer:
x=2
Step-by-step explanation:
Given
9x - 10 = 3x + 2 ( subtract 3x from both sides )
6x - 10 = 2 ( add 10 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Match the polynomial to the correct description :
(X+4)(x-1)(x-2)(x-4)
A. The related polynomial equation has a total of four roots;all four roots are real.
B. the related polynomial equation has a total of four roots,all four roots are real and one root has a multiplicity of 2.
C. The related polynomial equation has a total of four roots, two roots are complex and two roots are real.
D. The related polynomial equation has a total of two roots, both roots are real and have a multiplicity of 2.
E. The related polynomial equation has a total of three roots, two roots are complex and one root is real.
F. The related polynomial equation has a total of four roots, two roots are complex and one root is real with a. Multiplicity of 2.
Answers
Answer:
A
Step-by-step explanation:
The polynomial (x+4)(x-1)(x-2)(x-4) has zeros at x=-4,1,2,4.
The related polynomial equation is (x+4)(x-1)(x-2)(x-4)=0.
In order for this equation to be true at least one of the factors must by 0 that is the only way a product can be zero (if one of it's factors is).
So you wind up needing to solve these 4 equations:
x+4=0 x-1=0 x-2=0 x-4=0
x=-4 x=1 x=2 x=4
First equation, I subtracted 4 on both sides.
Second equation, I added 1 on both sides.
Third equation, I added 2 on both sides.
Fourth equation, I added 4 on both sides.
-4,1,2,4 are all integers
Integers are real numbers.
So A.
The polynomial (X+4)(x-1)(x-2)(x-4) corresponds to option A: The related polynomial equation has a total of four roots; all four roots are real, with no root having a multiplicity. Hence the correct answer is A.
To match the polynomial (X+4)(x-1)(x-2)(x-4) to the correct description, we can look at its factors to determine the roots. Each factor of the form (x - c) represents a real root at x = c. For this polynomial, the factors indicate there are four roots: -4, 1, 2, and 4. These roots all come from different factors, so there is no repeated root, implying no multiplicity among them. Hence, the correct description must state that there are four real roots and none of them is repeated.
Since options B, C, E, and F suggest either roots with multiplicity, a mixture of real and complex roots, or fewer than four roots, they are not correct. Therefore, this leaves us with option A as the correct match: The related polynomial equation has a total of four roots; all four roots are real. None of the roots are repeated, there are no complex roots, and all roots can be identified directly from the given factors of the polynomial.
A woman bought a dress at a discount of 16 2/3%. If the woman paid $32.50, what was the original price of the dress?
Answers
Answer:
$39
Step-by-step explanation:
Let original price be x, so we need to subtract 16 2/3 % from that to get 32.50
So we can write:
[tex]100x-16\frac{2}{3}x=3250\\83\frac{1}{3}x=3250\\x=39[/tex]
So basically, the original price was $39.
Determine the solution for x²-3x-28≥0
Answers
Answer:
(- ∞, - 4 ] ∪ [7, + ∞ )
Step-by-step explanation:
Determine the zeros by equating to zero, that is
x² - 3x - 28 = 0 ← in standard form
(x - 7)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 4 = 0 ⇒ x = - 4
The zeros divide the domain into 3 intervals
(- ∞ , - 4 ], [ - 4, 7 ], [ 7, + ∞)
Choose a test point in each interval and compare value with required solution
x = - 5 : (- 5)² - 3(- 5) - 28 = 25 + 15 - 28 = 12 > 0
x = 0 : 0 - 0 - 28 = - 28 < 0
x = 10 : 10² - 3(10) - 28 = 100 - 30 - 28 = 42 > 0
Solutions are the first and third interval, that is
x ∈ (- ∞, - 4 ] ∪ [ - 7, + ∞)
Answer:
it's C on edge
Step-by-step explanation:
got it right:)