Answer:
1,-1,4,-3 so D
Step-by-step explanation:
0 = x^4 - x^3 -13x^2 + x + 12
x = 1,-1,4,-3
The final answer is -3,-1,1 and 4
What is the relation between roots and the biquadratic equation?The biquadratic equation is of the form ax⁴+bx³+cx²+dx+e and hence
The sum of roots is -b/a, the sum of the product of two roots is c/a, the sum of the product of three roots is -d/a, and the product of all four roots is e/a.
Solving the given problemThere is no specific method of solving a biquadratic equation, hence we use the trial and error method and also some form of the root.
So finding f(1) = 1-1-13+1+12 = 0 hence 1 is a root.
finding f(-1) = 1-(-1)-13-1+12 = 0 hence -1 is also a root.
So let other roots be p,q
Now we can use sum of roots formula which is p+q+1-1= 1, hence p+q=1
product of roots p*q*1*-1=12, pq= -12 substituting p = -12/q
-12/q+q = 1, multiplying q on both sides
q²-12=q, q²-q-12=0, q²-4q+3q-12 = 0, q(q-4q)+3(q-4)=0
(q-4)(q+3) = 0 hence the roots are 4,-3 also
Hence 1,-1,4, and -3 are the roots of the equation.
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write the slope- intercept form of the equation for the line.
Y=2x-1
Y=1/2x-1
y=-2x-1
y=1/2x+1
Answer:
The answer will be y=2x-1
Step-by-step explanation:
With the graph we are able to use the formula rise/run, which means we count down from the top point, and then over, and then divide.
Going down is 4 points, and over is 2.
4/2 is 2.
This leaves us with two answers. With this information, we look at the direction the graph is going, it is going upwards, making it positive. Which means that your answer is the first one. Plus the line goes through -1.
Thank you, if you need any more help let me know.
Which equation represents an ellipse with foci at (3, 2) and (-9, 2)
that passes through the point (-3, 10)?
Answer:
D, since it horizontal ellipse, a is greater than b
An ellipse has two foci. The correct option is D.
What is the equation of ellipse if its major and minor axis and centre are given?Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Coordinates of its foci would be: (h±c, k) where c² = a² - b²
If its major axis is parallel to the y-axis, then,
coordinates of its foci would be: (h, k±c) where c² = a² - b² and its equation would be:
[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]
Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,
[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]
Hence, the correct option is D.
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(k) 2 cos 16A + 1 = (2 cos 2A - 1).(2 cos 2A + 1).(2 cos 4A-1).(2cos 8A-1).
I need help to prove this......
Qno. k.
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle identity: cos 2A = 2cos²A - 1
We are going to find one factor at a time:
2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)
↓ ↓ ↓ ↓
factor last factor 2nd factor 1st
Proof LHS → RHS:
Given: 2 cos16A + 1
let α = 8A, then 2·cos2α + 1
Identity: 2(2cos²α - 1) + 1
Distribute: 4cos²α - 2 + 1
Simplify: 4cos²α - 1
Factor: (2cosα - 1)(2cosα + 1)
Substitute: (2cos8A - 1)(2cos8A + 1)
let β = 4A, then 2·cos2β + 1
Identity: 2(2cos²β - 1) + 1
Distribute: 4cos²β - 2 + 1
Simplify: 4cos²β - 1
Factor: (2cosβ - 1)(2cosβ + 1)
Substitute: (2cos4A - 1)(2cos4A + 1)
let Ф = 4A, then 2·cos2Ф + 1
Identity: 2(2cos²Ф - 1) + 1
Distribute: 4cos²Ф - 2 + 1
Simplify: 4cos²Ф - 1
Factor: (2cosФ - 1)(2cosФ + 1)
Substitute: (2cos2A - 1)(2cos2A + 1)
(2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) [tex]\checkmark[/tex]
Answer:Use the following Double Angle identity: cos 2A = 2cos²A - 1
We are going to find one factor at a time:
2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)
Step-by-step explanation:
apples are on sale for $3 and 12 per kilogram is the total cost of the apples proportional to the total yes or no
Answer:
yes the apples are porportinal
Step-by-step explanation:
Answer:
apple is proportional
Step-by-step explanation:
How do I solve this
Answer:
-36
Step-by-step explanation:
[tex]-\frac{t}{2} -8 = 10\\-\frac{t}{2} = 18\\\frac{t}{2} = -18\\t = -36[/tex]
Find the value of x.
X
10
A. 52
B. 10/2
C. 512
D. 5
А
В
URGENT
[tex] \huge{ \bold{ \bigstar \: pythagoras \bigstar}}[/tex]
Pythagoras :
[tex] {10}^{2} = {x}^{2} + {x}^{2} [/tex]
[tex]100 = 2{x}^{2}[/tex]
[tex]100 \div 2 = {x}^{2} [/tex]
[tex]50 = {x}^{2} [/tex]
[tex]x = \sqrt{50} [/tex]
[tex]x = \sqrt{25 \times 2} [/tex]
[tex] \red{x = 5 \sqrt{2} }[/tex]
Answer:
Step-by-step explanation:
Compare this to a similar figure with hypotenuse √2 and leg lengths all 1.
Write and solve an equation of ratios, as follows:
x 10
------ = ------
1 √2
10√2
'then x = -------- = 5√2
2
abbi invested $1,000 in a certificate of deposit with a simple interest rate of 6% find the interest earned in 4 years. then find the total of principal plus interest.
Answer:
Step-by-step explanation:
Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle_______ more red bottles than plant A. Plant C would recycle________________ more red bottles than plant D.
Answer:
70
80
Step-by-step explanation:
Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle___70____ more red bottles than plant A. Plant C would recycle_____80___________ more red bottles than plant D.
A = We first multiply 150 x 2.333 (2 1/3) = 350 tbottles 60 x 2.333 = 140
B = Then multiply 350/200 = 200 x 1.75 350 tbottles RED = 120 x 1.75=210
First answer = 210-140 = B recycles 70 more than A
C = We first multiply 175 x 2 = 350 tbottles RED = 110 x 2 = 220
D = We first find LCM of 180 and 350
Then find 18x now equals 1/10 x 35x tbottles RED = 72 / 18 = 4 then 4 x 35 = 140
Second answer = 220-140 = C recycles 80 more than D.
Answer:
Plant B would recycle 60 more red bottles than plant A. Plant C would recycle 38 more red bottles than plant D.
Hope this helps!
Sorry for answering so late!
How many ways can 4 people sit in a row of 7 chairs?
[tex]7\cdot6\cdot5\cdot4=840[/tex]
If the Federal Resene sets the reserve rate to 20%, what is the resulting money multiplier?
Answer:
5
Step-by-step explanation:
Money multiplier helps to explain how an economic activity boosts the economic output for the country. It shows how saving in terms of deposit increases the net supply of money in any economy.
Money multiplier = 1/reserve ratio
given reserve ratio = 20% = 20/100 = 0.2
thus,
Money multiplier = 1/0.2 = 5
Please solve the one w the underline please ❤️❤️
Answer:
6 ÷ 6 + 6 x 6
Step-by-step explanation:
Hope this helps :D
Simplify: 15 7/12 x−9 1/3 x
Order matters in a combination.
True
False
Answer:
False
Step-by-step explanation:
So, in Mathematics we use more precise language: When the order doesn't matter, it is a Combination. When the order does matter it is a Permutation.
A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold
Answer:
31 Pikachu bags were sold.
19 peanut bags were sold.
Step-by-step explanation:
Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.
We know that the number of Peanuts sold is 50-x (as the total needs to be 50)
We know that the total revenue is:
Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts
Using our definitions above:
Total Revenue = x * $3.68 + (50-x) * $0.76
We know that the revenue needs to be $128.52.
$128.52 = x * $3.68 + (50-x) * $0.76
Let's remove the $ signs.
128.52 = x * 3.68 + (50-x) * 0.76
Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.
128.52 = x*3.68 + 50*0.76 - x*0.76
128.52 = x*3.68 + 38 - 0.76*x
Subtracting 38 from both sides
90.52 = 3.68*x - 0.76*x
We can simplify the right side.
90.52 = 2.92*x
We can divide both sides by 2.92:
31 = x
And flip it:
x = 31
So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is
50-x = 50-31 = 19
31 Pikachu bags were sold.
19 peanut bags were sold.
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]
Let the number of peanut bags be x
Then, Number of pikachu bags = 50 - x
Given,
Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68Then,
⇛ Total cost he gets from peanut bag = $0.76 × x
⇛ Total cost he gets from pikachu bag = $3.68(50 - x)
According to question,
⇛ $0.76x+ $3.68(50 - x) = $128.52
Solving this equation,
⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)
⇛ 184 - 2.92x = 128.52
⇛ 184 - 128.52 = 2.92x
⇛ 55.48 = 2.92x
Flipping the equation,
⇛ 2.92x = 55.48
⇛ x = 55.48 / 2.92
⇛ x = 19
Then,
⇛ 50 - x = 50 - 19 = 31
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━
You are planning to use a tile design in your new room. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 11 cm, what will be the exact area of each hexagonal shape? A. 3,993 cm^2 B. 181.5 root 3 cm^2 C. 132 root 3 cm^2 D. 33 cm^2
Answer:
B. 181.5√3 cm^2
Step-by-step explanation:
The area of a regular hexagon with side length s is given by ...
A = (3√3/2)s²
For side length s = 11 cm, the area is ...
A = (3√3/2)(11 cm)² = 363√3/2 cm²
A = 181.5√3 cm²
Factor the following expression completely:
32
z
4
+
8
z
3
−
4
z
2
Answer:
40z + 5
Step-by-step explanation:
I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2
32z + 8z ( since they both have the same variable ) = 40z4 + 3 - 4 + 2 ( since they have to variables ) = 5Hope this helped
Answer:
The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)
Step-by-step explanation:
In the problem, we a re given an equation.
32z⁴ + 8z³ - 4z²
We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.
A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.
4(8z⁴ + 2z³ - z²)
So, this is your factored expression from the given equation.
Help pls will give brainliest
Answer:
The surface area of the rectangular prism is 292 cm²
Complete the statement. The line x = −2 is _______.
Answer:
see explanation
Step-by-step explanation:
The line x = - 2
Is a vertical line parallel to the y- axis
It passes through all points with an x- coordinate of - 2
What is the domain of the function shown in the graph below? answer type: interval, all real values except one, all real values except two, all real numbers Interval:
Answer: the domain is negative infinity to positive infinity
Step-by-step explanation:
the graph covers all x values
PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5
Answer:
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since there is no constant value. This must be a special case.
So,
(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
a contractor is in charge of hiring people for construction project the number of days it would take to complete a project with ex full time workers can be found using the function f (x) equals 1 26/x.assume once workers are assigned to the project no workers may be added or taken out the project until it is finished find and interpret the given function values and determine an appropriate domain for the function
This is about understanding domain of a function.
The domain of the function is x is a set of positive integers.
We are given the function;f(x) = 126/x
Where;
f(x) is the number of days it would take to complete a project with x number of workers
x is number of workers it will take to complete the project.
We want to find the domain for the given function.Domain is defined as the set of all possible input values for which the function is defined.
Let's try x = 0 workers.
f(x) = 126/0 ; this is undefined and so x cannot be zero.
Let's try x = 1 worker
f(x) = 126/1 = 126 days
Let's try x = 10 workers
f(x) = 126/10 = 12.6 days
Let's try x = 100 workers
f(x) = 126/100 = 1.26 days
We see that every positive integer is a possible value of x that can make the function defined. Since 0 and negative numbers will make the function invalid.
Thus, the domain of the function is x is a set of all positive integers.
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A formula to find the period, T, of cyclic phenomena based on the frequency, F is T= 1/F
Solve the formula for F in terms of T
Answer:
F = 1/T
Step-by-step explanation:
In order to solve for F, you would need to isolate F.
(F)T = 1/F (F) --> multiply F on both sides to cancel out the F on the right side
FT/(T) = 1/(T) --> divide T on both sides to cancel out the T on the left, so the F is isolated
F = 1/T
Hope this helps!
Answer:
F = 1/T
Step-by-step explanation:
T= 1/F
USING CROSS MULTIPLICATION TECHNIQE
T(F) = 1
DIVIDE BOTH SIDES BY T
F = 1/(T)
URGENT!!!! PLEASE HELP NOW!!! WHO EVER GIVES THE CORRRECT ANSWER WILL GET BRAINLIEST!!!
Items Sold at a Clothing Store
The bar graph shows the number of each item sold at a clothing store. Which
statement about the graph is true?
Answer:
The correct ans is..... ( which i believe )
3rd option
Hope this helps...
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
Answer:
3rd option
Step-by-step explanation:
because 2/5 of 40 is equal to 16, and thats the equivelent of the pants sold.
A diver dives 17 2/3 yards and then comes back to the surface. Then, she dives 9 3/8 yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?
(giving the points this website is allowed to give me)
The total depth covered by the diver is 27(1/24) yards.
What is yard?Yard is a unit to measure length. 1 yard is equal to 36 inches.
1 yard= 3 feet or (0.9144 meter)
What is
Given that,
First time depth reached by diver = 17(2/3) yards
In the second time, the depth reached by the diver is 9(3/8) yards more than the first time,
To find total depth,
Add depth covered by first time and second time,
Total depth = 17(2/3)+9(3/8)
=53/3+75/8
= 27(1/24)
The total depth covered by the diver is 27(1/24) yards.
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Find the total surface area of this square based
pyramid.
10 in
5 in
Answer:
125 in²
Step-by-step explanation:
Each triangular face has a base of 5 in and a height of 10 in. The area of it is given by the formula ...
A = (1/2)bh
A = (1/2)(5 in)(10 in) = 25 in²
The square base has an area given by the formula ...
A = s² . . . . . where s is the side length
A = (5 in)² = 25 in²
The total area is the sum of the areas of the 4 faces and the base:
total area = 4 × (area of 1 face) + (area of base)
total area = 4 × (25 in²) + 25 in²
total area = 125 in²
Answer: The Surface Area is 125 in^
Step-by-step explanation:
Surface area = 4 × (area of 1 face) + (area of base)
total area = 4 × (25 in²) + 25 in²
Surface area = 125 in²
Help plz, thx urgent
Answers:
5. Quadrilateral
6. Rhombus
7. Rectangle
8. Parallelogram
=============================
Explanations:
5. We don't know much about this other than it has 4 sides, so we simply say it is a quadrilateral. Quad = 4, lateral = side
-----------
6. The four sides are the same length as shown by the similar tickmarks. Therefore we have a rhombus. A rhombus is any quadrilateral with four equal sides. A square is a special type of rhombus, though in this case it appears to be a non-square type of rhombus, as the angles are not 90 degrees.
-----------
7. A rectangle has 4 angles that are all 90 degrees. Visually the tiny little square angle marker tells the reader we have a 90 degree angle.
-----------
8. We have a parallelogram here because the opposite sides are the same length. In addition, the opposite angles are the same measure. Through using the SSS congruence rule, we can do a bit of work to show that the alternate interior angles are congruent, leading to the opposite sides being parallel. So in short, the given info here is enough to prove we have opposite sides being parallel which is what makes a parallelogram possible.
Perform the following calculation and express the answer in scientific
notation: 1.2 x 10^-2 m x 3.0 x 10^-6 m =
Answer:
Hey there!
1.2 x 10^-2 times 3.0 x 10^-6 = 3.6 x 10^-8 m^2.
Hope this helps :)
CAN SOMEWON HELP ME PLZ I NEED HELP
Answer:
1.791875241e13
Step-by-step explanation:
5.67811 x 10⁵ = 567811
3.15576 x 10⁷ = 31557600
31557600 x 567811 = 1.791875241e13
Answer:
1.791875241e13
Plzz help I’ll mark brainliest
Answer:
6cot 50
Step-by-step explanation:
Tan 50=6/x
x= 6/(tan 50)
x= 6cot 50°
Answer:
? = 6 cot 50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 50 = 6 /?
? tan 50 = 6
? = 6 / tan 50
We know that 1 / tan 50 = cot 50
? = 6 cot 50
write an equation of the line that passes through the given points
(-2,9) and(1,-3)
Answer:
Y = -4x + 1
Step-by-step explanation:
1. We know the equation of a line is y=mx+b.
2. using the slope formula, [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], to find the slope. -12 / 3 = -4, so the slope is -4.
3. we need to find the Y intercept, or the Y coordinate at X=0. if at x=1 the Y is -3, and the slope is -4, then if we go down to x=0 then the Y would be 4 higher. therefore the Y intercept is 1.
4. now we can make the equation; Y = -4x + 1
