Answer:
The answer is 4x² – x – 4 = 0
Step-by-step explanation:
1st Method Given;Sum of zeroes = α + β = (-b)/a = 1/4Product of zeros = αβ = c/a = 1Where,
a = 4b = 1c = 4So, one quadratic polynomial satisfying is given condition is 4x² – x – 4 = 0
2nd MethodSum of zeroes = 1/4
Product of zeros = 1
Remember this formula
x² – (α + β)x + αβ
x² – 1/4x + 1
4x² – x – 4 = 0
Thus, The quadratic polynomial is
4x² – x – 4 = 0.
A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?
Answer:
See below ↓↓
Step-by-step explanation:
Finding the radius
C = 2πr25 = 2 x 3.14 x rr = 25 / 6.28r = 3.98 cm ≅ 4 cmSurface Area
4πr²4 x 3.14 x 4 x 43.14 x 64200.96201 cm²Volume
4/3πr³ = 4πr² x r/3201 x 4/367 x 4268 cm³Find two numbers whose product is 110, and whose sum is 21.
Step-by-step explanation:
The answer is 10 and 11
10 + 11 = 21
10 × 11 = 110
A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h2 where h and d are measured in feet. What is the rocket's height when the distance between you and the rocket is 100 feet?
Answer:
iam thinking the answer is ""-262,5ft""
The height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.
What is the height?The height is a vertical distance between two points. It is given that A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h² where h and d are measured in feet.
The height will be calculated by forming the two equations from the given data in the question.
25 = 625 + h²
100 = 4 ( 625 + h² )
100 = ( 2500 + 4h² )
By solving both the equations:
100 - 25 = 2500 - 625 + 4h² - h²
3h² = 1800
h = √600
h = 24.49 feet
Therefore the height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.
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He decided to bike from his home to the library to return some books. Ell biked 110 miles when he remembered that he had left a book at home, so he biked back home to get it. After getting the book from home, he biked to the library. What was the total distance, in miles, en had biked when he finally reached the library Show your work. miles Answer
Answer:
2 2/10 miles
but on the part where he realized he forgot his books was he at the library already when he realized cuz if not them it's more than 2 2/10
Determine the area of the following shapes.
a. 144 in
b. 154 in
c. 164 in
A) 144 in
is your answer. good luck
help asap will give brainly .
A drawer is 5 feet wide, 4 feet deep. If the volume is 40, what is the height =
What is the equation of the line that passes through the point (3, 5) and has a slope
of -1/3
Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-intercept (the value of y when the line crosses the y-axis)To determine the equation of a line:
Find the slopePlug the slope into y=mx+bPlug in a point that falls on the line as (x,y)Solve for bSolving the Question
We're given:
[tex]m=-\dfrac{1}{3}[/tex]The lines passes through the point (3,5)[tex]y=mx+b[/tex]
⇒ Plug the slope into the equation:
[tex]y=-\dfrac{1}{3}x+b[/tex]
⇒ Plug in the given point (3,5) and determine the y-intercept:
[tex]5=-\dfrac{1}{3}(3)+b\\\\5=-1+b\\\\b=6[/tex]
⇒ Plug this back into the equation along with the slope:
[tex]y=-\dfrac{1}{3}x+6[/tex]
Answer[tex]y=-\dfrac{1}{3}x+6[/tex]
What's the area of the composite figure?
Answer:
[tex]\huge\boxed{\bf\: 83 \: yd^{2}}[/tex]
Step-by-step explanation:
Consider rectangle ABCD.
Here,
AB = DC = 9 yd (length = l)
AD = BC = 7 yd (width = w)
Area of this rectangle:
= l * b
= 9 * 7
= 63 yd²
[tex]\rule{150pt}{2pt}[/tex]
Now, take rectangle DEGF.
Here,
DE = FG = 5 yd (length = l)
DF = EG = 4 yd (width = w)
Area of this rectangle:
= l * b
= 5 * 4
= 20 yd²
[tex]\rule{150pt}{2pt}[/tex]
Total area of the compisite figure:
= Area of rectangle ABCD + Area of rectangle DEGF
= 63 yd² + 20 yd²
= 83 yd²
[tex]\rule{150pt}{2pt}[/tex]
Refer to the attachment for the labelling of the figure.2. What is the x-intercept of the line that passes
through the point (-5,-9) and has a slope of 3?
A. (2,0)
B. (-2,0)
C. (6,0)
D. (-6,0)
Answer:
Step-by-step explanation:
hello :
an equation for the line is : y=ax+b when a is the slope
so : a= 3 y =3x+b
passes
through the point (-5,-9) x=-5 y= -9 means ; -9 =3(-5)+b so: b=6
conclusion : y=3x+6
Answer: B because y=0 3x+6 =0 3x =-6 x= -2
Question 1a:
Compute the Laplace Transforms of
f(x) = { x² +2x +1 , x < 3
{ e⁻⁵ˣ , x ≥ 3
This is made easy if you know the Laplace transform pair
[tex]u(t - c) y(t - c) \mapsto e^{-cs} Y(s)[/tex]
where u(t) is the Heaviside step function and Y(s) is the Laplace transform of y(t).
We rewrite f, g, and h in terms of u :
[tex]f(x) = (x^2+2x+1) (u(x) - u(x-3)) + e^{-5x} u(x-3)[/tex]
[tex]g(x) = \sin(3x) (u(x-5) - u(x-10))[/tex]
[tex]h(x) = (u(x) - u(x-4)) + 2(u(x-4)-u(x-8)) + 3 (u(x-8)-u(x-16))[/tex]
and we also rearrange terms to get the right shift in argument:
[tex]f(x) = (x^2+2x+1) u(x) - ((x-3)^2+8(x-3)+16) u(x-3) + e^{-15} e^{-5(x-3)} u(x-3)[/tex]
[tex]g(x) = [\cos(15) \sin(3(x-5)) + \sin(15) \cos(3(x-5))] u(x-5) \\\\ ~~~~~~~~~~- [\cos(30) \sin(3(x-10)) + \sin(30) \cos(3(x-10))] u(x - 10)[/tex]
[tex]h(x) = u(x) + u(x-4) + u(x-8) - 3 u(x - 16)[/tex]
Now we can apply the known transform pair, along with
[tex]x^n \mapsto \dfrac{n!}{s^{n+1}}[/tex]
[tex]e^{ax} \mapsto \dfrac1{s-a}[/tex]
[tex]\sin(ax) \mapsto \dfrac{a}{s^2+a^2}[/tex]
[tex]\cos(ax) \mapsto \dfrac{s}{s^2+a^2}[/tex]
The transforms of f, g, and h are then
[tex]F(s) = e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-15} e^{-3s}}{s + 5} \\\\ = \boxed{e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-3(s+5)}}{s + 5}}[/tex]
[tex]G(s) = \dfrac{3\cos(15) e^{-5s}}{s^2+9} + \dfrac{s \sin(15) e^{-5s}}{s^2+9} - \dfrac{3\cos(30)e^{-10s}}{s^2+9} - \dfrac{s \sin(30) e^{-10s}}{s^2+9} \\\\ ~~~~~~~ = \dfrac{3(\cos(15)-\cos(30)) + s(\sin(15) - \sin(30))}{s^2+9} \\\\ ~~~~~~~ = \boxed{\dfrac{6\sin\left(\frac{45}2\right)\sin\left(\frac{15}2\right) - 2s \cos\left(\frac{45}2\right)\sin\left(\frac{15}2\right)}{s^2+9}}[/tex]
[tex]H(s) = \boxed{\dfrac{e^{-s} + e^{-4s} + e^{-8s} - 3 e^{-16s}}s}[/tex]
A line has a slope of 2 and a y-intercept of -3/4 which of the following is an equation of the line
Answer:
y = 2x - 0.75
Step-by-step explanation:
Slope-intercept form is:
⇒ y = mx + b
m being the slope and b being the y-intercept.
The given slope and y-intercept:
⇒ Slope ⇒ 2
⇒ Y-intercept ⇒ -3/4
Plug in:
⇒ y = 2x - 0.75 (3/4)
Hi, I need help. What is 4 1/12 + 5 3/12?
Answer:
9 4/12
Step-by-step explanation:
Just add the mixed numbers 4 + 5 = 9
Add the fraction numerators 1 +3 = 4
*Since the denominator is the same, we just add the numerators
9 4/12
Answer:
as decimal 9.33333
Step-by-step explanation:
4 1/12 + 5 3/12 = 28/3 = 9 1/3
13tX 9
7. Dareen's family now wants to Install 1-foot-square terra-cotta tiles in the entryway and kitchen, and 4-inch-square blue tiles on each bathroom floor. The
terra-cotta tiles cost $ each, and the bathroom tiles cost 45€ cach. How many of each kind will they need? What will all the tiles cost?
The total number of terra-cotta tiles needed is 220 tiles.
The total number of blue tiles needed is 4428 tiles.
The cost of all the tiles would be $3,092.60.
What is the total number of tiles needed?The first step is to determine the area of the entryway and the kitchen.
Area of the entryway = length x width
(22 - 18) x 10 = 40 ft²
Area of the kitchen = 10 x 18 = 180ft²
Sum of the areas of the entryway and the kitchen = 180 + 40 = 220 ft² = 220 tiles
Total cost = 220 x $5 = $1100
Areas of the bathroom floors = (10 x 6) + (7 x 9) = 123ft²
Convert ft² to in²
1 ft² = 144in²
123 x 144 = 17,712 in²
Number of tiles needed = 17,712 / 4 = 4428 tiles
Total cost = 4428 x 0.45 = $1992.60
Total cost = $1992.60 + $1100 = $3,092.60
Here is the complete question: Dareen's family now wants to Install 1-foot-square terra-cotta tiles in the entryway and kitchen, and 4-inch-square blue tiles on each bathroom floor. The
terra-cotta tiles cost $5 each, and the bathroom tiles cost 45€ cach. How many of each kind will they need? What will all the tiles cost?
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A computer loses half of its value every two year. If the computer costs $75 after 6 years, how much
did the computer cost initially?
Answer:
$600
Step-by-step explanation:
This can be modeled as an exponential equation.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial valueb is the growth factorx is the independent variabley is the dependent variableTherefore:
a = initial cost of computerb = 0.5 (since the computer loses half its value)x = t/2 where t is the number of years ⇒ 3y = $75[tex]\implies 75=a(0.5)^3[/tex]
[tex]\implies 75=0.125a[/tex]
[tex]\implies a=\dfrac{75}{0.125}[/tex]
[tex]\implies a=600[/tex]
Therefore, the computer initially cost $600.
Simplify the expression
Step-by-step explanation:
for me it is best as a first step to combine this all to one big fraction, and then simplify the whole expression.
you do know that when multiplying the same variable with exponent we simply add the exponents. and she we divide the same variable with exponents, we subtract them from each other (as the overlapping exponent parts cancel each other out).
(3ac³f³)/(8a²bcf⁴) × (12ab²c)/(18ab³c²f) =
= (3×12a²b²c⁴f³)/(8×18a³b⁴c³f⁵) =
= (3×12c)/(8×18ab²f²) = 12c / (8×6ab²f²) =
= 2c / (8ab²f²) = c / (4ab²f²)
Given: AD || BC and AD = BC.
Prove: AB || DC
Answer:
Step-by-step explanation:
okay okay what is emoji aaaaa
okay okay what is emoji aaaaa
guy is half as old as Gerald, who is three times older than gill. If the sum of their ages is 99, what are their ages?
Answer:
Step-by-step explanation:
gerald=2x
guy=x
gill= aproximately 0.3x
2x+x+0.3x=99
2.3x=99
x=43.04
The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
The equation according to the given statement will be,
The age of Gerald is 2x,
The age of the guy is x and the age of the gill is 0.33x.
So, the equation will be,
x + 2x + 0.33x = 99
3.33x = 99
x = 99/3.33
x = 29.72
Age of Gerald, 2x = 2(29.72) = 59.44 years.
Age of guy, x = 29.72 years and,
Age of gill, 0.33x = 0.33(29.72) = 9.8 years.
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Solve for X
5х – 1 = 6x — 9
Answer:
5x-1=6x-9
5x-1-6x= -9
5x-6x= -9+1
-x= -8
(-1)*(-x)= (-1)*(-8)
x=8
Kai randomly surveys eighth graders at his school and learns that 7 of 35 respondents own a video gaming system. Based on these data, how many of the 150 eighth-grade students in Kai's school would be expected to own a video gaming system? A 15 students B 25 students C 30 students D 50 students
The correct answer for this question is 30 students
Sure hope this helps you :)
help please. I don't know it
Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before delivering the bill to each customer, the waitress selected one of the index cards without reading it and wrote on the bill the same message that was printed on the card. Twenty of the cards had the message "The weather is supposed to be really good tomorrow. I hope you enjoy the day!" Another 20 cards contained the message "The weather is supposed to be not so good tomorrow. I hope you enjoy the day anyway!" After the customers left, the waitress recorded the amount of the tip (percentage of bill) before taxes. The tips for those receiving the good‑weather message are as follows.
20.8 18.7 19.9 20.6 21.9 23.4 22.8 24.9 22.2 20.3
24.9 22.3 27.0 20.5 22.2 24.0 21.2 22.1 22.0 22.7
The tips for the 20 customers who received the bad weather message are as follows.
18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 14.0
17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 18.2 19.4
Click to download the data in your preferred format.
CSV Excel JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt!
Back‑to‑back stemplots of the tips are shown.
Good Weather Tips Bad Weather Tips
13 6
14 0
15
16 1 8
17 0 5
7 18 0 0 2 4 5 8 8
9 19 0 1 2 4
8 6 5 3 20 0 2
9 2 21
8 7 3 2 2 1 0 22
4 23 2
9 9 0 24
25
26
0 27
Because the distributions are reasonably symmetric with no extreme outliers, the procedures will work well.
Is there good evidence that the two different messages produce different percentage tips?
Bruce Rind and David B. Strohmetz, "Effect of beliefs about future weather conditions on restaurant tipping," Journal of Applied Social Psychology, 31 (2001), pp. 2160–2164.
Carry out a two‑sample test. What is the test statistic? Give your answer to three decimal places.
=
What is the -value? Give your answer to three decimal places.
-value:
The test statistic and p-value of the given data are 6.274 and 0.0001 respectively.
Test StatisticThe test statistic can be calculated using the formula below
[tex]t = \frac{x-\mu}{\sigma / \sqrt{n} }[/tex]
Solving for the mean and standard deviation, we can substitute the values into the above equation which will be
[tex]t = \frac{x-\mu}{\sigma / \sqrt{n} } = 6.274[/tex]
P-ValueUsing the data from the test statistic, we can calculate the p-value of the data
[tex]p-value = p(z < 6.274)= 0.0001 = 0.00[/tex]
From the calculation above, the test statistic and p-value of the given data are
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Determine the most appropriate model for the data in the table. (0,4)(1,8)(2,15.9)(3,32)(4,65.2)(5,128) Select from the drop-down menu to correctly complete the statement. A(n)____model is the most appropriate model for the given data.
A quadratic model would be the most appropriate model for the given data set.
What is a quadratic model?A quadratic model can be defined as a mathematical model which represents a quadratic equation with a single variable of degree 2.
Aso, a quadratic model is mainly symmetrical because the relationship between its variables when plotted on a graph forms a parabola.
In this scenario, the value of the graph at y(1) is equal to y(2) and y(0) is approximately equal to y(3) as shown in the image attached below, which simply means it is symmetrical about this axis.
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HELP QUICK PLEASE!!!
Answer:
19
please make this answer brainliest If I helped you!
Answer:
c=19
Step-by-step explanation:
110-91=19
129-110=19
148-129=19
4x19 = 76 (91-76=15)
76+15 =91
5x19= 95 ( 110-95=15)
95+15= 110
6x19 = 114 (129-114 =15)
114+15=129
7x19=133 ( 148-133 =15)
133+15 = 148
Of 11 possible books you plan to take 4 with you on vacation how many different collections of 6 books can you take
The number of different collections of 6 books which can be taken on vacation of 11 possible books is 462.
What is combination?Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.
Here, in the original problem, the number of book selection is6.
Of 11 possible books, one plans to take 6 with on vacation. The number of different collections of 6 books can be taken has to be found out.
The total number of books=11.The total number of selection of book=6.Thus, the number of combination to select 6 books collection from 11 is,
[tex]^{11}C_6=\dfrac{11!}{(11-6)!6!}\\^{11}C_6=\dfrac{11\times10\times9\times8\times7\times6!}{5\times4\times3\times2\times1\times6!}\\^{11}C_6=462[/tex]
Thus, the number of different collections of 6 books which can be taken on vacation of 11 possible books is 462.
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2 + 8p - 3(12 - 5p) - (2 - 3p)(4)
[tex]2+8p-3(12-5p)-(2-3p)(4)\\\\=2+8p-36+15p-8+12p\\\\=35p-42[/tex]
A triangular prism has a triangular end with a base of 9 inches and a height of 7 inches.
The length of each side of the triangle is 9 inches and the width of the entire prism is 7 inches.
What is the surface area of the prism?
HELP
Answer:
259.15
Step-by-step explanation:
. Carlee surveyed customers as they left a convenience store. She asked them, “How many items did you
purchase?” The results are shown in the line plot.
(a) How many customers were surveyed?
(b) What was the greatest number of items purchased by a customer?
(c) How many customers purchased 9 items?
(d) How many customers purchased at least 5 items?
(e) What was the median number of items purchased?
Answer:
We need the line plot in order to solve the questions.
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write [tex](8a^{-3})^{-2/3}[/tex] in simplest form.
Answer:
[tex] \frac{1}{64 {a}^{2} } [/tex]
Step-by-step explanation:
[tex](8 {a}^{ - 3} {)}^{ \frac{ - 2}{3} } [/tex]
[tex](8 a {)}^{ - 2} [/tex]
[tex] \frac{1}{ {8}^{2} {a}^{2} } [/tex]
[tex] \frac{1}{64 {a}^{2} } [/tex]
please help solve this math question
Answer:
4# | 267
Step-by-step explanation:
There are 3 numbers in the 40's in the data:
42, 46 and 47.
