[tex]f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16[/tex]
[tex]divide \: by \: x - 2[/tex]
[tex]4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} [/tex]
[tex]g(x) = 4x {}^{2} - 16x + 16[/tex]
[tex]4x \: into \: (x - 2) = 4x {}^{2} - 8x[/tex]
[tex]z(x) = - 8x + 16[/tex]
[tex] - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder[/tex]
[tex]f(x) = (x - 2)(4x {}^{2} + 4x - 8)[/tex]
[tex]f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ [/tex]
[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1[/tex]
[tex]x = 2[/tex]
[tex]x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2[/tex]
Answer: B
Step-by-step explanation:
Edge 2023
Which of the following inequality should be graphed with a dashed line? Select all that apply.
(I think B is one of the correct answers?)
Answer:
B, D
Step-by-step explanation:
Any inequality that does not include the "or equal to" case will be graphed with a dashed line.
ApplicationThe "or equal to" case is included when the inequality symbol is one of ≤ or ≥. When symbols > or < are used, the boundary line of the solution space is dashed (or the end point on the number line is an open circle).
The inequalities that will be graphed with a dashed line are ...
2x -4y < 12 . . . . choice Bx +7 > -1 . . . . . . .choice DThe Residential Energy Consumption Survey found in 2001 that 47% of American households had internet access. A market survey organization repeated this study in a certain town with 25,000 households, using a simple random sample of 500 households: 239 of the sample households had internet access. Of the 500 sample households, 7 had three or more large-screen TVs. Among the sample households, 121 had no car, 172 had one car, and 207 had two or more cars. Estimate the percentage of households in the town with one or more cars; attach a standard error to the estimate. If this is not possible, explain why not.
The percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.
According to statement we have given
239 of the 500 households in the sample had internet access.
So, find sample percentage then
Sample percentage= 500/239 =0.478=47.8%
Thus we estimate the percentage as 47.8%.
The box contains 25,000 tickets of which 47.8% are 1's and the remaining 52.2% tickets are 0's. We will draw 500 tickets from the box.
Number of draws=500
Now, find the SD then
[tex]SD= (Big number - Small number) * \sqrt{Fraction with big number * fraction with small number}[/tex]
Substitute the values then
[tex]SD= (1 - 0) * \sqrt{0.478 *0.522}[/tex]
[tex]SD=0.4995[/tex]
Now find the standard error of sum then
The standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.
[tex]SE sum =\sqrt{Number of draws} * SD box[/tex]
[tex]SE sum =\sqrt{500} * 0.4995[/tex]
[tex]SE sum =11.16[/tex]
Now find the standard error of percentage then
The standard error of the percentage is the standard error for the sum divided by the sample size.
SE percentage= SE for number/Number of draws ×100%
= 50011.1692×100%
≈0.022×100%
=2.2%
Thus the percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.
Learn more about STANDARD DEVIATION here https://brainly.com/question/4079902
#SPJ4
On a coordinate plane, triangle K J L is shown. Line segment G H goes from side J K to J L. Point K is at (0, 0), point G is at (e, f), point J is at (2 e, 2 f), point H is at (e + d, f), and point L is at (2 d, 0).
To prove part of the triangle midsegment theorem using the diagram, which statement must be shown?
The length of JK equals the length of JL.
The length of GH is half the length of KL.
The slope of JK equals the slope of JL.
The slope of GH is half the slope of KL.
Based on the triangle midpoint theorem, the statement which must be shown is that: B. the length of GH is half the length of KL.
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.
Based on the triangle midpoint theorem, we can infer and logically deduce that the statement which must be shown is that the length of GH is half the length of KL.
Read more on triangle midpoint theorem here: https://brainly.com/question/16047906
#SPJ1
Answer: B. The length of GH is half the length of KL.
Step-by-step explanation: TRUST ME! The answer is correct on Edge. :)
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
Learn more about Trigonometric functions:
https://brainly.com/question/6904750
#SPJ1
Which multiplication expression is equivalent to
x+8 2x+16
x² 2x² ?
O
O
ㅎ
X + 8
x + 8
32
X + 8
2
x²
DONE
●
●
2x²
2x + 16
2x + 16
2x²
2x²
2x + 16
Answer:
x=0.5×1±√33
Step-by-step explanation:
x+8=x² and 2(x+8)=2x²
x²-x-8=0
helppp i need it cmonn
Answer:
uhhh i think its a carrot
Step-by-step explanation:
The school that Natalie goes to is selling tickets to a play. On the first day of ticket sales the school sold 14 adult tickets and 3 student tickets for a total of $195. The school took in $306 on the second day by selling 15 adult tickets and 14 student tickets. What is the price each of one adult ticket and one student ticket
The price of an adult ticket is 12$.
And the price of a student ticket is 9$.
Let ‘x’ be the price of an adult ticket.
Let ‘y’ be the price of a student ticket.
On the first day of ticket sales, the school sold 14 adult tickets and 3 student tickets for a total of $195 i.e
14x + 3y = 195$ i)
15x + 14y = 306$ ii)
from equation i) we get the value of y,
y = (195 - 14x)/3
put this value of y in equation ii) we get,
= 15x +14{(195 - 14x)/3} = 306
= (45x +2730 - 196x)/3 = 306
= (45x +2730 - 196x) = 918
= -151x = -1812
= x =12$
then value of y we get ,
put value of x in y,
y = (195 - 14*12)/3
= 27/3
= 9$
hence, the price of an adult ticket is 12$.
And the price of a student ticket is 9$.
Learn more about solving equations here
https://brainly.com/question/1202328
#SPJ4
A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.09. In a sample of 260 graduates, 20 students have a GPA of 3.00 or below. The value of the test statistic and its associated p-value are __________.
The test static value is 1.44 and its associated p-value is 0.1335.
Given that the problem deals with the concept of test for single proportion. The parameter of the interest is the population proportion of graduates with GPA of 3.00 or below is less than 0.09.
Let the population proportion be p=0.09.
Let the number of graduates in a sample be n=260.
Let the number of students have a GPA of 3.00 or below be x=20.
Based on the known data, the null and alternative hypothesis are,
H₀:p≥0.09
H₁:p<0.09
The sample proportion of students have a GPA of 3.00 or below is,
[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{20}{260}\\ &=0.07\end[/tex]
Under the null hypothesis, the test static value is,
[tex]\begin{aligned}z&=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.07-0.09}{\sqrt{\frac{0.09(1-0.09)}{260}}}\\ &=\frac{-0.02}{0.018}\\ &=-1.11\end[/tex]
The p-value for the left-tailed test is
p-value=p(z<-1.11)
p-value=0.1335
Hence, the value of the test statistic and its associated p-value for the proportion of graduates with a GPA of 3.00 or below is less than 0.09. are 1.44 and 0.1335.
Learn more about null hypothesis from here brainly.com/question/9954556
#SPJ4
The population of classroom grows x squared in one year. the current population of classroom is 12. in one year. one the las day of the year, each person in the classroom eats 3 slices of pizza. if an entire pizza cost $26.60, how much money does a class spend per year on pizza. a pizza has 8 slices. (sorry if this makes no sense teacher made up on the spot)
The class spends $1436.4 per year on pizza. Since the population grows x² in one year, the strength of the class on the last day of the year is 12² = 144.
How to find the total population of the class in one year?It is given that,
The current population of the classroom is 12. I.e., x = 12
So, at the end of the year, the population of the class = x²
⇒ 12² = 144
Thus, the population of the classroom on the end day of the year is 144.
How many slices of pizza are required for this population in the class?It is given that,
On the last day of the year, each person in the classroom eats 3 slices of pizza.
So, 144 persons eat,
144 × 3 = 432 slices of pizza
Thus, 432 slices of pizza are required for the given population.
How much money does a class spend per year on pizza?It is given that,
A single pizza has 8 slices and every single pizza costs $26.60.
Since there are 432 slices, then the number of pizzas
= 432/8
= 54 pizzas
Then, the cost of 54 pizza's = 54 × $26.60 = $1436.4
Therefore, $1436.4 was spent on pizza per year.
Refer to more such problems here:
https://brainly.com/question/12024841
#SPJ4
Can someone help me out on this problem and show work
A coordinate plane is labeled Street on the x-axis and Avenue on the y-axis. Ping is at point (3, 6) and Ari is at point (21, 18). A line is drawn from Ping to Ari.
Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym Two-thirds the distance from Ping's home to Ari's home.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
Where is the gym?
9th Street and 10th Avenue
12th Street and 12th Avenue
14th Street and 12th Avenue
15th Street and 14th Avenue
The place where the gym is located based on the information given about the coordinate plane is D. 15th Street and 14th Avenue
How to illustrate the information?From the information given, the coordinate plane is labeled Street on the x-axis and Avenue on the y-axis. Ping is at point (3, 6) and Ari is at point (21, 18) and a line is drawn from Ping to Ari.
In this case, the place where the gym is located based on the information given about the coordinate plane is the 15th Street and 14th Avenue.
The graph is attached to illustrate this.
Learn more about coordinate plane on:
brainly.com/question/10737082
#SPJ1
You run around the perimeter of a baseball field at a rate of at most 8 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
The possible amount of time is 90 seconds that it takes you to run around the baseball field
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)
The options are missing.
The options are:
90 seconds100 seconds110 seconds120 secondsWe have a radius of the circle is:
r = 150 ft
The perimeter of the circle = 2πr = 2π(150) = 300π ft
The running path distance = 40% of the perimeter of the circle
= 40% of 300π
= 120π ft
Assume the tape length is 50 m
Total distance = 200 + 200 + 120π - 50 = 726.99
The rate is 8 feet per second.
Time = distance/rate = 726.99/8 = 90.87 ≈ 90 seconds
Thus, the possible amount of time is 90 seconds that it takes you to run around the baseball field
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
The problem: take two solutions and plug them into the original equation. To check for extraneous solutions.
Answer: х=3.
Step-by-step explanation:
А point is missing here: determining the allowable values of x for this equation.
1. Consider the right side of the equation:
The root expression 2x+3 must be greater than or equal to 0.
2x+3≥0
2x≥-3\ |:2
x≥-1,5.
2. Consider the left side of the equation:
the left side of the equation must be greater than or equal to 0.
x≥0.
We get x≥0. ⇒
х=3 ∈ х≥0
х=-1 ∉ х≥0.
If you don’t know the answer don’t answer it pls help me out if you do tho!
Answer: x = 8
Step-by-step explanation:
Hello again XD.
This is a coordinate plane and all the angles on a coordinate plane add up to 360°
Divide 360 by 4 to get the measurement of the section we are working in.
360/4 = 90°
This means it is complementary and complementary angles state that both separate angles added together = 90°
therefore,
6x + 2 + 40 = 90
combine like terms:
6x + 42 = 90
now subtract 42 from both sides
6x = 48
divide 6 from both sides to get:
x = 8
Let me know if you have any more questions you want answered and I hope I explained this well.
i need help fast please
Answer:
D
Step-by-step explanation:
Triangle PQR is scaled 3x the size of Triangle LMN. This means that if length LM is 3cm, just multiply it by 3 to get length PQ, 9cm
People leaving a movie were randomly asked their age. The results are show below. What graph would best display the data, if you were only concerned about the shape and spread of the data, and not specific data? Select all that apply.
7, 37, 45, 78, 24, 97, 12, 17, 43, 56, 69, 63, 76, 23, 50, 38, 45, 57, 4
dot plot
box plot
stem-and-leaf plot
histogram
The graphs to use are box plots, histogram and dot plots
How to determine the graph?From the question, the most important factors are:
Shape of distributionSpread of dataUsing the box plots, histogram and dot plots, one would see the shape and the spread.
While the stem and leaf plot would show specific data values
Read more about graphs at:
https://brainly.com/question/24461724
#SPJ1
anybody know the solution?
The reciprocal relationship of the graph is graph (a)
How to determine the reciprocal relationship?The reciprocal relationship implies that:
The x and the y axes are swapped.
When the x and the y axes are swapped, the value on both axes swap their positions
As per the given graph, the reciprocal relationship is represented by graph (a)
This is shown in the attached graph
Read more about reciprocal relationship at:
https://brainly.com/question/2321596
#SPJ1
Kamal sells 240 ice creams for a total of £640
1/3 of the ice creams he sells are large.
The cost of each large ice cream he sells is £3.80
All the other ice creams he sells are small.
He sells each small ice cream for the same cost.
Work out the cost of each small ice cream.
Answer:
2.10
Step-by-step explanation:
# of large ice creams: 240/3 = 80
# of small ice creams: 240 - 80 = 160
Total large ice cream cost: 80*3.8 = 304
Total small ice cream cost: 640 - 304 = 336
Cost of one small ice cream: 336/160 = 2.1
PLEASE HELP QUICK I WILL MAKE BRAINLIEST: Put the following four numbers in order from least to greatest:
$A.\ 4 \cdot \sqrt{5}\\ B.\ 6 \cdot \sqrt{2}\\ C.\ 5 \cdot \sqrt{3}\\ D.\ 9$
Write your answer as a list of letters, separated by commas. For example, if you believe A is the smallest, B is the next-smallest, C is the next-smallest, and D is the largest, you would write A, B, C, D.
Answer: D, B, C, A
Step-by-step explanation:
A: [tex]4^5 = 1024[/tex]
B: [tex]6^2=36[/tex]
C: [tex]5^3=125[/tex]
D: [tex]9[/tex]
D, B, C, A
Mr. Thompson has a 1-meter-square whiteboard. He creates a square with sides on his whiteboard to post a weekly puzzle. How many square meters of whiteboard space does he use for the weekly puzzle?
Answero
Step-by-step explanation:
i dont know
y Ask...
Find the value of x.
5 in
10 in
OA. 5√3 in
OB. 2√41 in
C. 9
OD. 5√5 in
Answer:
OPTION A [ 5√3 in ]- Please see the attached picture for full solution!:)
--------------- HappY LearninG <3 ------------
What is the answer to this
Answer:
i need help
Step-by-step explanation:
The vertex of a parabola is at -25 what is its equation
The equation of the parabola described by means of its vertex in the task content is; y = x² -25.
What is the equation big the parabola?It follows from the task content that the equation of the the parabola can be determined from.its vertex.
Hence, the equation of the parabola from by virtue by virtue big the vertex given is;
y = (x-0)² -25
Hence, it follows that the equation of the parabola is;
y = x² -25.
Read more on vertex of a parabola;
https://brainly.com/question/1480401
#SPJ1
Write the product in its simplest form:
c•9c
Which equation represents the function graphed on the coordinate plane? g(x) = |x 1| 3 g(x) = |x 3| – 1 g(x) = |x – 1| 3 g(x) = |x 3| 1
The equation that represents the graph is g(x) = |x – 1| + 3. Then the correct option is C.
A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph is shown.
In the graph, the mode function is given.
If the subtracts 1 from the variable then the function gets shifted toward the right and if 3 is added to the function then it gets shifted upwards.
Then the correct equation that represents the graph is g(x) = |x – 1| + 3.
Learn more about function at
brainly.com/question/5245372
#SPJ4
Answer:
Step-by-step explanation:
The equation that represents the graph is g(x) = |x – 1| + 3. Then the correct option is C.
What is a function?
A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph is shown.
In the graph, the mode function is given.
If the subtract 1 from the variable then the function gets shifted toward the right and if 3 is added to the function then it gets shifted upwards.
Then the correct equation that represents the graph is g(x) = |x – 1| + 3.
More about the function link is given below.
brainly.com/question/5245372
#SPJ2
The coordinates of the vertices of quadrilateral ABCD are (0,-4) (-4,3) (3,4) (6,-1)
Based on the given coordinates of the quadrilateral ABCD, the slopes of the lines given at:
Slope of AB = -7/4Slope of BC = 1/7Slope of CD = -5/3Slope of AD = 1/2What are the slopes of the line?The slope of AB is:
= (3 - (-4)) / (-4 - 0)
= -7/4
The slope of BC:
= (4 - 3) / (3 - (-4))
= 1/7
The slope of CD:
= (-1 - 4) / (6 - 3)
= -5/3
The slope of AD:
= (-1 - (-4)) / (6 - 0)
= 1/2
The rest of the question is:
The slope of AB ¯ ¯ ¯ ¯ ¯ is , the slope of BC ¯ ¯ ¯ ¯ ¯ is , the slope of CD ¯ ¯ ¯ ¯ ¯ is , and the slope of AD ¯ ¯ ¯ ¯ ¯.
Find out more on the slope of line at https://brainly.com/question/3493733.
#SPJ1
hola alguien habla español parece que en esta region hablan ingles
Answer:
yo si apenas me lo descargue
There are 8 kids at a birthday party. If there are 5 girls and 3 boys at a party, what fraction of the kids are girls?
Answer:
5/8 fraction of kids are girls
Tell whether you can reach each type of conclusion below using coordinate
methods. Give a reason for each answer.
6. AB = CD
9. AB bisects CD.
12. LA is a right angle.
15. Quadrilateral ABCD is a rhombus.
8. ABL CD
11. LA LB
14. AABC is isosceles.
16. AB and CD bisect each other.
7. AB || CD
10. AB bisects LCAD.
13. AB + BC = AC
The answer to all of them is yes.
6) The lengths of AB and CD using the distance formula. (because congruent segments have equal length)
7) The slopes of AB and CD are equal using the slope formula. (because parallel segments have equal slopesL
8) The slopes of AB and CD are negative reciprocals using the slope formula. (because perpendicular lines have slopes that are negative reciprocals)
9) The two segments that CD is split into by AB have equal length using the distance formula. (because a segment bisector splits a segment into two congruent segments, and congruent segments have equal length)
10) Angles CAB and DAB have the same measure using the angle between two lines formula. (Because an angle bisector splits an angle into two congruent angles, and congruent angles have equal measure)
11) Angles A and B have the same measure using the angle between two lines formula. (Because an angle bisector splits an angle into two congruent angles, and congruent angles have equal measure)
12) The lines that form angle A have slopes that are negative reciprocals using the slope formula. (because perpendicular lines have slopes that are negative reciprocals, and perpendicular lines form right angles)
13) The lengths of AB and AC combined equal the length of AC using the distance formula.
14) Two sides of triangle ABC have equal length using the distance formula.
15) All four sides of ABCD have the same length using the distance formula.
16) Letting AB and CD meet at E, the distance formula says AE=BE and CE=DE.
What can be concluded from the statement ∠1 + ∠2 = 90°?
The sum of measures of angles A and B is 90°
Hence the angles are complementary
As complementary angles have sum 90°