Answer:
A / (1 +√5) = A (1 - √5) / (1 - 5) = -A (1 - √5) / 4
Multiply numerator and denominator by (1 - √5)
Find a polynomial function of degree 4 with - 3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function in expanded form is f(x) =
(Use 1 for the leading coefficient.)
Answer:
[tex]f(x) = x^4 + 9x^3 + 27x^2 + 27x[/tex]
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
- 3 as a zero of multiplicity 3
So
[tex]f(x) = (x - (-3))^3 = (x + 3)^3 = x^3 + 9x^2 + 27x + 27[/tex]
0 as a zero of multiplicity 1.
So
[tex]f(x) = x(x^3 + 9x^2 + 27x + 27) = x^4 + 9x^3 + 27x^2 + 27x[/tex]
(Use 1 for the leading coefficient.)
Multiply the polynomial by 1, so it stays the same. The polynomial in expanded form is:
[tex]f(x) = x^4 + 9x^3 + 27x^2 + 27x[/tex]
You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:
V= 4x^3â36x^2+ 80x
Answer:
Step-by-step explanation:
From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.
Thus, from the diagram
the length = 8 - 2x the width = 10 - 2x and the height = x
So, the volume V = L*w*h
Volume (V) = (8 - 2x) (10 - 2x) x
V = (80 - 16x - 20x +4x²)x
V = 80x -36x² + 4x³
By rearrangement:
V = 4x³ - 36x² + 80x
Having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old. They can afford to save $440 per month. They place the money into an annuity that pays 5.5% per year, compounded monthly. How much will they have to spend on a car after 4 years?
Answer:
$26,179.82
Step-by-step explanation:
FVA = PMT * n * (1 + i) ^ (n - 1)
FVA = 440 * 48* (1.00458)^(47)
A line passes through the point (5,6) and is parallel to the line given by the equation y = 2x - 12. Which of these is an equation for the line? O A. y-5=-264-6) B. y - 6 = -2(x - 5) C. y + 6 = 2(x + 5) D. Y- 6 = 2(x - 5)
Answer: D
Step-by-step explanation:
(lines parallel to each other have the same slope)
slope = m = 2
y = mx + b, (5,6)
6 = 2(5) + b
6 = 10 + b
b = -4
y = 2x - 4
y - 6 = 2(x - 5)
y - 6 = 2x - 10
y = 2x -4
Enter the equation of the line in slope-intercept form. Slope is -1/2, and (-9,4) is on the line. The equation of the line is y=
Answer:
[tex]y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
1) Plug in the slope (m)
We're given that the slope is [tex]\displaystyle-\frac{1}{2}[/tex]. In [tex]y=mx+b[/tex], replace m with [tex]\displaystyle-\frac{1}{2}[/tex]:
[tex]y=\displaystyle-\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle-\frac{1}{2}x+b[/tex]
We're given the point (-9,4). Plug this point into the equation as [tex](x,y)[/tex] and solve for b:
[tex]4=\displaystyle-\frac{1}{2}(-9)+b\\\\4=\displaystyle\frac{9}{2}+b[/tex]
Subtract [tex]\displaystyle\frac{9}{2}[/tex] from both sides to isolate b:
[tex]4-\displaystyle\frac{9}{2}=\displaystyle\frac{9}{2}+b- \displaystyle\frac{9}{2}\\\\\displaystyle-\frac{1}{2} = b[/tex]
Therefore, the y-intercept is [tex]\displaystyle-\frac{1}{2}[/tex]. Plug this back into [tex]y=\displaystyle-\frac{1}{2}x+b[/tex] as b:
[tex]y=\displaystyle-\frac{1}{2}x+(\displaystyle-\frac{1}{2})\\\\y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}[/tex]
I hope this helps!
Please help me with this on the picture
Answer:
this is the chapter of linear equations in one variable?
A retailer sold a fan for ra 1800 at 10% loss what is its cost price?
How to do
Answer:
18
thả 5 sao nha.....
Step-by-step explanation:
..................
compute (-12)+(-8)+30
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The distribution of widgets from a production line is known to be approximately normal with mean 2.7 inches and standard deviation 0.25 inches. About 95% of the distribution lies between what two values?
A. 2.45 inches and 3.2 inches
B. 2.45 inches and 2.95 inches
C. 2.2 inches and 3.2 inches
D. 1.95 inches and 3.45 inches
Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.
To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81
The formula for calculating the z-score is expressed as;
[tex]z=\frac{x-\overline x}{s}[/tex] where:
[tex]\overline x[/tex] is the mean
s is the standard deviation
z is the z-scores
Given the following
[tex]\overline x[/tex]=2.7 in
s = 0.25
if z = -2.81
[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]
Similarly:
[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]
Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.
Learn more on normal distribution here: https://brainly.com/question/23418254
write any five sentences of fraction?
Step-by-step explanation:
Fractions represent equal parts of a whole or a collection.
Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
a fraction has 2 parts
The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.
There are different types of fraction
unit fractionimproper fractionproper fractionmixed fractionWhich of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = (x - 2)^4 and 8x - y =16 about the line x= 10?
A. Pi integral^4_2 {[10 - (1/8 y + 2)^2] - [10 - (2 + ^4 squareroot y)^2]} dy
B. Pi integral^16_0 {[10 - (1/8 y + 2)] - [10 - (2 + ^4 Squareroot)]}^2 dy
C. Pi integral^4_2 {[10 - (1/8 y + 2)] - [10 - 2 + ^4 squareroot y)]}^2 dy
D.Pi integral^16_0 {[10 - (1/8 y + 2)]^2 - [10 - 2 + ^4 squareroot y)]^2} dy
E. Pi integral^16_0 {[10 - (1/8 y + 2)^2] - [10 - 2 + ^4 squareroot y)^2]} dy
F. Pi integral^4_2 {[10 - (1/8 y + 2)]^2 - [10 - 2 + ^4 squareroot y)]^2} dy
Answer:
[tex]\displaystyle V = \pi \int _0^{16}\left[10-\left(\frac{1}{8}y-2\right)\right] ^2 - \left[10 - \left(2+y^{{}^{1}\!/\!{}_{4}}\right)\right]^2\, dy[/tex]
Step-by-step explanation:
We want to find the volume of the solid obtained by rotating the region between the two curves:
[tex]y=(x-2)^4\text{ and } 8x-y=16[/tex]
About the line x = 16.
Since our axis of revolution is vertical, we can use the washer method in terms of y.
[tex]\displaystyle V = \pi \int _c^d[R(y)]^2 -[r(y)}]^2\, dy[/tex]
Where R(y) is the outer radius and r(y) is the inner radius.
First, solve each equation in terms of y:
[tex]\displaystyle x_1 = \frac{1}{8}y+2\text{ and } x_2 = y^{{}^{1}\! /\! {}_{4}}+2[/tex]
From the diagram below, we can see that the outer radius R(y) is (10 - x₁) and that the inner radius r(y) is (10 - x₂). The limits of integration will be from y = 0 to y = 16. Substitute:
[tex]\displaystyle V = \pi \int_0^{16}\left[\underbrace{10-\left(\frac{1}{8}y+2\right)}_{R(y)}\right]^2 - \left[\underbrace{10-\left(y^{{}^{1}\!/\!{}_{4}}+2\right)}_{r(y)}\right]^2\, dy[/tex]
Thus, our volume is:
[tex]\displaystyle V = \pi \int _0^{16}\left[10-\left(\frac{1}{8}y-2\right)\right] ^2 - \left[10 - \left(2+y^{{}^{1}\!/\!{}_{4}}\right)\right]^2\, dy[/tex]
*I labeled the diagram incorrectly. Let R(x) be R(y) and r(x) be r(y).
Work out how many more skirts were sold on Friday than on Thursday ?
Answer:
15 more were sold on friday then thursday
Step-by-step explanation:
PLEASE HELP ASAP, Thank you
9514 1404 393
Answer:
2.244
Step-by-step explanation:
Your answer looks like it may have a transcription error.
The period is reasonably computed as the difference of the x-values of the given points:
period = 4.114 -1.870 = 2.244 . . . seconds
PLZ ANSWER QUESTION IN PICTURE
Answer:-1
Step-by-step explanation:
The slope would be negative one due the fact that every horizontal box, the line also goes down one vertical box. You can also figure this out by using the slope equation which is slope=y2-y1/x2-x1. Just take the xy coordinates of two different points and plug it into the equation if you would like to use a formula.
In the Spring of 2021 the statistics course did a survey of the average number of parking tickets students received by gender. Which has been shared below. Based on the data below which statement would be the best null hypothesis?
Gender # of hours
male 6
female 8
female 8
male 3
female 7
female 5
male 3
male 2
female 9
female 7
female 2
female 3
male 9
female 0
female 2
male 4
male 9
female 12
female 15
female 3
female 6
male 7
female 3
female 8
male 3
male 6
female 7
female 8
Answer:
There is no difference between the two groups.
Step-by-step explanation:
The test hypothesis (null and alternative) are usually employed in evaluating if there is a statistical significance in a claim about the mean, standard deviation or variance of a sample and it's population parameter.
When comparing two independent variables, The null hypothesis usually establish that there is no difference between the mean value of samples, while the alternative hypothesis is the opposite.
The data given shows values for two independent groups ; Male and Female.
The null hypothesis will be:
H0 : There is no difference between the two groups.
H0 : μ1 - μ2 = 0
A window has the shape of a semicircle. The base of the window is measured as having diameter 64 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.
a. 1.3π cm^2
b. 2.4 πcm^2
c. 2.6 πcm^2
d. 3.2 πcm^2
e. 1.6 πcm^2
f. 1.2 πcm^2
Answer:
e. 1.6π cm²
Step-by-step explanation:
Since the window is in a semi-circular shape, its area A = πD²/4 ÷ 2 = πD²/8 where D = diameter of window = 64 cm
Now, the error in the area dA = dA/dD × dD where dD = error in the diameter = 0.1 cm and dA/dD = derivative of A with respect to D.
So, dA/dD = d(πD²/8)/dD = 2 × πD/8 = πD/4
So, the differential dA = dA/dD × dD
dA = πD/4 × dD
Substituting D = 64 cm and dD = 0.1 cm into the equation, we have
dA = πD/4 × dD
dA = π × 64 cm/4 × 0.1 cm
dA = π × 16 cm × 0.1 cm
dA = π × 1.6 cm²
dA = 1.6π cm²
So, the maximum error in computing the area of the window is 1.6π cm²
5765865876+5737555586=
Answer:
5765865876+5737555586=11503421462
Analyze the diagram below and complete the instructions that follow. Find a, b, and c.
Answer:
The correct answer is the letter C.
Step-by-step explanation:
We can use the following trigonometric identity:
[tex]cos(60)=\frac{6}{b}[/tex] (1)
[tex]cos(45)=\frac{c}{b}[/tex] (2)
Solving each equation by b and equaling we have:
[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]
[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]
Let's recall that:
[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]
[tex]cos(60)=\frac{1}{2}[/tex]
Then we have:
[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]
[tex]c=\frac{2*6}{\sqrt{2}}[/tex]
[tex]c=\frac{12}{\sqrt{2}}[/tex]
[tex]c=6\sqrt{2}[/tex]
Using equation (1) we can find b.
[tex]cos(60)=\frac{6}{b}[/tex]
[tex]b=12[/tex]
Finally, we can find a using the next equation:
[tex]tan(60)=\frac{a}{6}[/tex]
[tex]a=6*tan(60)[/tex]
[tex]a=6\sqrt{3}[/tex]
Therefore, the correct answer is the letter C.
I hope it helps you!
For rehab after an injury a patient walks 200m on the first day each day he will increase the amount walked by 100m. How many total kilometers will the patient have walked after 12 days
Answer:
3.3km
Step-by-step explanation:
200m on first day
Increase 200 by 100 = 300 (200+100)
From 2nd day to 11th day
300×11
3300m
If 1000m = 1km
3300m =?
3300/1000
3.3km
I hope it helps
The lengths of two sides of the right triangle ABC shown in the illustration given
b= 8ft and c= 17ft
Answer:
15ft
Step-by-step explanation:
By Pythagorean theorem
[tex] {a}^{2} + {b}^{2} = {c}^{2}\\ {a}^{2} + {8}^{2} = {17}^{2} \\ {a}^{2} + 64 = 289 \\ {a}^{2} = 289 - 64 \\ {a}^{2} = 225 \\ \sqrt{ {a}^{2} } = \sqrt{225} \\ a = 15ft \\ [/tex]
x(x+3)(x+3)=0 Plz I need this fast!
Answer:
x=0,-3
Step-by-step explanation:
x(x+3)(x+3)=0
Using the zero product property
x=0 x+3=0 x+3 =0
x=0 x=-3 x=-3
5 less than three times a number is 37 what is the number
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
3x - 5 = 37
Step 2: Solve for x
[Addition Property of Equality] Add 5 on both sides: 3x = 42[Division Property of Equality] Divide 3 on both sides: x = 14What is the value of g(-4)?
Answer:
A
Step-by-step explanation:
(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)
[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]
solve on calculator 6x+8-8x=-8
Answer:
x = 8
Step-by-step explanation:
6x + 8 - 8x = -8
-2x + 8 = -8
-2x = -8 - 8
-2x = -16
x = 8
Bob has 40 cents in his pocket. If Bob has no pennies, how many different combinations of quarters, dimes, and/or nickels could he have.
dime: 5 cents
nickel: 10 cents
quarter: 25 cents
let's start with quarters, (2)
25 + 10 + 5
25 + 5 + 5 + 5
nickels, (4)
10 + 10 + 10 + 10
10 + 10 + 10 + 5 + 5
10 + 10 + 5 + 5 + 5 + 5
10 + 5 + 5 + 5 + 5 + 5 + 5
dimes, (1)
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
7 combinations.
hope it helps :)
if x=2 and y=3. What is x*y/xy+x*y
Answer
its uhhhhh i dont know
Step-by-step explanation:
Please help!!! what is x: |6n+7|=8
Answer:
-5/2, 1/6
Step-by-step explanation:
|6n+7|=8
6n+7=8
n=1/6
6n+7=-8
n=-5/2
Answer:
[tex]n=-\frac{5}{2}[/tex] and [tex]n=\frac{1}{6}[/tex]
Step-by-step explanation:
There is no x variable present in the question, but if you are asking for the value of n, I can help with that.
The absolute value function always results in a positive number, so that means 6n+7 can equal 8 or negative 8, and the absolute value function takes care of the rest. First, we will solve for 6n + 7 equaling 8.
[tex]6n+7=8[/tex]
Subtracting 7 from both sides gets us
[tex]6n=1[/tex]
Dividing by 6 from both sides is equal to
[tex]n=\frac{1}{6}[/tex]
Now we will solve for 6n + 7 equaling negative 8.
[tex]6n+7=-8[/tex]
Subtracting 7 from both sides is equal to
[tex]6n=-15[/tex]
Dividing by 6 from both sides gets us
[tex]n=-\frac{15}{6}[/tex]
Simplifying, we have
[tex]n=-\frac{5}{2}[/tex]
The cost of producing x units of a particular commodity is 2 C(x) = x' +6x +45 shillings, and the production level t hours into a particular production run is x(1)=0.312 +0.04 units. At what rate is cost changing with respect to time after 5 hours?
Complete question is;
The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?
Answer:
dC/dt = 49.45
Step-by-step explanation:
Since C(x) = ⅔x² + 6x + 45
And x(t) = 0.3t² + 0.04t
This means that;
C(x) = C(x(t))
The rate at what cost is changing with respect to time is given as;
dC/dt
Thus, from chain rule;
dC/dt = (dC/dx) × (dx/dt)
dC/dx = (4/3)x + 6
dx/dt = 0.6t + 0.04
Now, when t = 5, then;
x(5) = 0.3(5)² + 0.04(5)
x = 7.7
Thus;
dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267
At 5 hours,
dx/dt = 0.6(5) + 0.04 = 3.04
Thus;
dC/dt = 16.267 × 3.04
dC/dt = 49.45
find the slope of the line
Answer:
from one point to another, it increases by 1 and right by 2
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Pick two points on the line
(0,1) and (2,2)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (2-1)/(2-0)
= 1/2
What are vertices of the conic 16x² - 25y² = 400 ?
Answer:
(-5, 0) and (5, 0)
Step-by-step explanation:
This equation fits the form for a hyperbola with x-intercepts. The standard form for such an equation is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
To get the equation in the question into this standard form, divide each term by 400.
[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]
To find the x-intercepts, make y = 0.
[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]
The vertices are located at the points (-5, 0) and (5, 0).
Note: There are no y-intercepts; making x = 0 produces no real solutions for y.
