First simplify the expression into polynomial form,
[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]
[tex]x^4+8x^3-10x^2-104x+105=297[/tex]
[tex]x^4+8x^3-10x^2-104x-192=0[/tex]
Now factor into,
[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]
Which means the solutions are,
[tex]x-4=0\implies\boxed{x_1=4}[/tex]
[tex]x+8=0\implies\boxed{x_2=-8}[/tex]
and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],
[tex]x^2+4x+6=0[/tex]
[tex]x^2+4x+4=-2[/tex]
[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]
Hope this helps :)
Answer:
x=4
Step-by-step explanation:
(4-1)(4-3)(4+5)(4+7)=297
Helppppp, i dont know how to do this problem
Answer:
(3, -5) (4, -5) (2, -7)
Step-by-step explanation:
An integer is any whole number that is not a fraction, they include -10204, -3, 0, 5, and 8592. (random numbers)
A coordinate with integers can be anything such as (0, 4582) and (547, 42)
However, it can not be (0.45846, 4579) or (54.42, 58).
To determine which points have coordinates that look like they are integers, you just have to select 3 points that lie at the intersection of the y and x value tic marks
You can see that (3, -5) is at the intersection of the x value 3 tic mark and the y value -5 tic mark, while also being on the parabola.
University Trailer Sales Company sold 356 utility trailers during a recent year. If the gross annual sales for the company was $328128, what was the average selling price for each trailer?
The average selling price of each trailer was nearly $
(Round to the nearest whole number.)
Answer:
The Answer is 2000$..........
which of the following is equal to the measure of angle c
Answer:
its C
Step-by-step explanation:
Prove a proof please
Answer:
They look similar
A store sells chocolate in the form of letters of the English alphabet. Identical letters have the same price, different letters have different prices. It is known that the word ONE costs $6, the word TWO costs $9, and the word ELEVEN costs $16. How much does the word TWELVE cost?
Answer:
20
Step-by-step explanation:
A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?
Answer:
y = -1/4x+1/2
Step-by-step explanation:
y = 4x - 3
This is in slope intercept form, y = mx+b where the slope is m
The slope is 4
Perpendicular lines have slopes that are negative reciprocals
-1/4 is the slope of the perpendicular line
y = -1/4x+b
Using the point (2,0)
0 = -1/4(2)+b
0 = -1/2+b
b = 1/2
y = -1/4x+1/2
integration of 3^x (1-3^(x+1)^9)dx
Step-by-step explanation:
the answer is in picture
Is this a function help
While walking in the country, you count 39 heads and 116 feet in a field of cows and chickens. How many of each animal are there?
Answer: 58
Step-by-step explanation:
its 58 because chickens have two feet each so divide 2 % 166 and its 58
because each chicken has 2 legs count the 2 legs up to 116 then u get ur answer
What is the congruence correspondence, if any, that will prove the given triangles congruent?
A. ASA
B. SSS
C. SAS
B. HL
Answer:
HLStep-by-step explanation:
The congruence correspondence between the two given triangles is HL as one leg and hypotenuse are given equal.
----------------------
OAmalOHopeO
----------------------
Find the future value of each deposit if the account pays (a) simple interest, and (b) interest compounded annually! $700 at 3% for 6 years
Answer:
NO ANSWER
Step-by-step explanation:
REASON A: Simple interest, and- its not complete
A clothing factory makes small, medium, and large sweaters. Last week, the factory made
1,612 sweaters. The factory made 3 times as many small sweaters as large sweaters. They
made 3 times as many medium sweaters as small sweaters.
How many small sweaters did the factory make last week?
This requires finding the number of small sweaters the company made last week
Number of small sweaters the company produced last week is 372
Total sweaters made = 1,612
Let
Small sweaters = 3x
Medium sweaters = x
Large sweaters = 3(3x) = 9x
Total = small + medium + large
1,612 = 3x + x + 9x
1612 = 13x
Divide by 13
x = 1612/13
Medium sweaters = x = 124
Small sweaters = 3x
= 3(124)
= 372
Read more:
https://brainly.com/question/24326559
Find the greatest rational number r such that the ratios 8/15 ÷ r and 18/35 ÷ r are whole numbers?
The answer is "[tex]\bold{\frac{2}{105}}[/tex]", and the further calculation can be defined as follows:
When the "r" is the greatest common divisor for the two fractions.
So, we will use Euclid's algorithm:
[tex]\to \bold{(\frac{8}{15}) -(\frac{188}{35})}\\\\\to \bold{(\frac{8}{15} -\frac{188}{35})}\\\\\to \bold{(\frac{56-54}{105})}\\\\\to \bold{(\frac{2}{105})}\\\\[/tex]
this is [tex]\bold{(\frac{8}{15}) \ \ mod \ \ (\frac{18}{35})}[/tex]
we can conclude that the GCD for [tex]\bold{\frac{54}{105}}[/tex], when divided by [tex]\bold{\frac{2}{105}}[/tex], will be the remainder is 0. Rational numbers go from [tex]\bold{\frac{2}{105}}[/tex] with the latter being the highest.
So, the final answer is "[tex]\bold{\frac{2}{105}}[/tex]".
Learn more:
greatest rational number:brainly.com/question/16660879
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! Chapter 11a
Please SHOW YOUR WORK THOROUGHLY!!
9514 1404 393
Answer:
vertical shift: 7 (up)horizontal shift: 2 (right)vertical asymptote: x=2domain: x > 2range: all real numbersStep-by-step explanation:
For any function f(x), the transformation f(x -h) +k represents a horizontal shift of h units to the right and k units upward.
Here, the parent function is log₂(x) and the transformation to log₂(x -2) +7 represents translation 2 units right and 7 units upward.
The parent function has a vertical asymptote at x=0, so the shifted function will have a vertical asymptote at x-2=0, or x = 2.
The parent function has a domain of x > 0, so the shifted function will have a domain of x-2 > 0, or x > 2.
The parent function has a range of "all real numbers." Shifting the function vertically does not change that range. The range of the shifted function is still "all real numbers."
The graph is shown below. The vertical asymptote is the dashed orange line.
_____
The "work" is in matching the pattern f(x -h) +k to the function log₂(x -2) +7.
Diane must choose a number between 49 and 95 that is a multiple of 2, 3, and 9. Write all the numbers that she could choose. If
there is more than one number, separate them with commas?
The set of numbers that Diane can choose is:
{54, 60, 66, 72, 78, 84, 90}
Finding common multiples of 2, 3, and 6:
A number is a multiple of 2 if the number is even.
A number is a multiple of 3 if the sum of its digits is multiples of 3.
A number is a multiple of 6 if it is a multiple of 2 and 3.
Then we only need to look at the first two criteria.
First, let's see all the even numbers in the range (49, 95)
These are:
{50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94}
All of these are multiples of 2.
Now we need to see which ones are multiples of 3.
To do it, we sum its digits and see if that sum is also a multiple of 3.
50: 5 + 0 = 5 this is not multiple of 3.
52: 5 + 2 = 7 this is not multiple of 3.
54: 5 + 4 = 9 this is multiple of 3, so 54 is a possible number.
And so on, we will find that the ones that are multiples of 3 are:
54: 5 + 4 = 9.
60: 6 + 0 = 6
66: 6 + 6 = 12
72: 7 + 2 = 9
78: 7 + 8 = 15
84: 8 + 4 = 12
90:9 + 0 = 9
Then the numbers that Diane could choose are:
{54, 60, 66, 72, 78, 84, 90}
If you want to learn more about multiples, you can read:
https://brainly.com/question/1553674
I really need help with this
Answer:
G=21, F=9, M=6, L=7, E=20, D=15, B=10, R=12.5, T=16, N=13.5, W=18, H=36, Z=12
*I=5*
Step-by-step explanation:
I basically just found the scale factor/proportion from two given sides and then used that to find the remaining sides.
*I'm not sure about 'I' since the edge of the paper was cut off so I want sure if it was a 5 or a 15 on the left most problem in the third row. I assumed it was 15. If it's not, just shout it out in the comments and I'll fix it! :)*
You can fill the letters in at the bottom XD
I hope this helped! :D
3. Solve x^7 - 11x^6 +48X^5 - 120x^4 + 225x^3 - 243x^2 - 162X + 486 = 0. (1 point)
-x=-1, x = +61, x = 3 with multiplicity 4
-x=-1 with multiplicity 5, x = 3 with multiplicity 2
-x = -1, x = + v6i, x = 3 with multiplicity 4
-x = -1 with multiplicity 3, x = V6, X = 3 with multiplicity 2
Answer:
Entrada
{-x = -1, x = +61, x = 3}
Resultado
{-x = -1, x = 61, x = 3}
Alternate form
{x = 1, x = 61, x = 3}
The answer will be [tex]x=-1,\:x=3,\:x=\sqrt{6}i,\:x=-\sqrt{6}i[/tex]
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation.
Given equation:
x^7 - 11x^6 +48X^5 - 120x^4 + 225x^3 - 243x^2 - 162X + 486 = 0.
x^7 +48X^5+ 225x^3+ 486 = 11x^6+ - 120x^4 + 243x^2 + 162x
On solving
[tex]\left(x+1\right)\left(x-3\right)^4\left(x^2+6\right)=0[/tex]
[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0[/tex]
[tex]x+1=0\quad \mathrm{or}\quad \:x-3=0\quad \mathrm{or}\quad \:x^2+6=0[/tex]
Hence, the solution is [tex]x=-1,\:x=3,\:x=\sqrt{6}i,\:x=-\sqrt{6}i[/tex]
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ2
Jason can peel 15 potatoes in 25 minutes. Janette can peel 8 potatoes in 1/10 hour. If they start peeling at the same time how many
minutes will it take them to peel 406 potatoes?
9514 1404 393
Answer:
210 minutes
Step-by-step explanation:
Jason's rate of peeling is ...
(15 potatoes)/(25 minutes) = 15/25 potatoes/minute = 3/5 potatoes/minute
Janette's rate of peeing potatoes is ...
(8 potatoes)/(6 minutes) = 4/3 potatoes/minute
Their combined rate is ...
(3/5 +4/3) = (9 +20)/15 = 29/15 . . . . potatotes/minute
Then the time required for 406 potatoes is ...
(406 potatoes)/(29/15 potatoes/minute) = (406×15/29) minutes
= 210 minutes
A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 52 in^2 and a perimeter of 30in. Find the dimensions of the brochure. The longer side is _____in. The shorter side is ______ in.
9514 1404 393
Answer:
9.562 in5.438 inStep-by-step explanation:
The sum of side lengths of a rectangle is half the perimeter, so is 15 inches for this brochure. If x is one of the side lengths, then (15 -x) is the other one, and the area is ...
x(15 -x) = 52
x^2 -15x = -52 . . . . multiply by -1 and expand
(x -7.5)^2 = -52 +56.25 = 4.25 . . . complete the square
x = 7.5 ±√4.25 ≈ {5.438, 9.562} . . . inches
The longer side is 7+√4.25 ≈ 9.562 inches; the shorter side is 7-√4.25 ≈ 5.438 inches.
?
6.2
Divided by 1/2
Answer:
The answer is 3.1
[tex]6.2 \div \frac{1}{2} = 3.1[/tex]
If we were to convert it into a **FRACTION** the answer would be : 31/10.
And that i an improper fraction, but as a **MIXED NUMBER** : [tex]3 \frac{1}{10}[/tex]
All answers would be : 3.1 , 31/10 and 3 1/10
Answer:
0.5167
Step-by-step explanation:
6.2/12 first rewrite 6.2 as an improper fraction or 36/5 then multiply by 1/12 to get the solution of 0.5167.
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
Answer:
540 and 50 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
The property taxes on a house were $1000. What was the tax rate if the house was valued at $125,000
Answer:
The tax rate was 0.8%
Step-by-step explanation:
Set up an equation:
x = tax rate
1000/125000 = x/100
Cross multiply:
1000 × 100 = 125000 × x
100000 = 125000x
0.8 = x
Check your work:
1000/125000 = 0.8/100
0.008 = 0.008
Correct!
Another way to check your work:
1000 × 100 = 125000 × 0.8
100000 = 100000
Correct!
I need help as soon as possible at 20 points
9514 1404 393
Answer:
(15/14)² = 225/196
Step-by-step explanation:
Evaluating the expressions inside parentheses, we can see they are the same, eliminating a bit of work.
[tex](\frac{5}{7}\times\frac{3}{2})^5\div(\frac{5}{2}\times\frac{3}{7})^3=(\frac{15}{14})^5\div(\frac{15}{14})^3=(\frac{15}{14})^{5-3}=\boxed{(\frac{15}{14})^2=\frac{225}{196}}[/tex]
 Solve each system by graphing.
9514 1404 393
Answer:
(x, y) = (4, -4)
Step-by-step explanation:
A graphing calculator makes graphing very easy. The attachment shows the solution to be (x, y) = (4, -4).
__
The equations are in slope-intercept form, so it is convenient to start from the y-intercept and use the slope (rise/run) to find additional points on the line.
The first line can be drawn by staring at (0, -2) and moving down 1 grid unit for each 2 to the right.
The second line can be drawn by starting at (0, 2) and moving down 3 grid units for each 2 to the right.
The point of intersection of the lines, (4, -4), is the solution to the system of equations.
Piecewise functions alg1
Answer:
C. 0
Step-by-step explanation:
Since we are finding f(-4), we use the first function since -4 is less than -2.
f(-4) = (-4) + 4 = 0
Therefore, the answer is C.
Solve for 2x^2=50
Please help
Answer:
Equation:
2x^2 = 50
Divide by 2:
x^2 = 25
Take the square root:
x = 5, or -5.
Let me know if this helps!
Answer:
x=5
x=−5
Step-by-step explanation:
Prove that sin2α = 2sinαcosα
Answer:
Here is your answer . hope this helps.
The width of a rectangle is three units less than the length if the area is 28 square units then find the dimensions of the rectangle
Let
width be xLength=x+3ATQ
[tex]\\ \sf \longmapsto Area=Length\times Width[/tex]
[tex]\\ \sf \longmapsto x(x+3)=28[/tex]
[tex]\\ \sf \longmapsto x^2+3x=28[/tex]
[tex]\\ \sf \longmapsto x^2+3x-28=0[/tex]
[tex]\\ \sf \longmapsto x^2+7x-4x-28=0[/tex]
[tex]\\ \sf \longmapsto x(x+7)-4(x+7)=0[/tex]
[tex]\\ \sf \longmapsto (x-4)(x+7)=0[/tex]
[tex]\\ \sf \longmapsto x=4\:or\:x=-7[/tex]
Ignore negative value[tex]\\ \sf \longmapsto Width=4units[/tex]
[tex]\\ \sf \longmapsto Length=4+3=7units[/tex]
what is the area of rectangle
Answer:
Step-by-step explanation:
What are the odds against picking a red marble from a bag of 10 green marbles, 10 yellow marbles, and 5 red marbles?
