Answer:
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Step-by-step explanation:
Assuming the desired polynomial has real and rational coefficients, each of the complex and irrational roots has a corresponding conjugate. That is, the roots of p(x) must include ...
{3, 2 -i, 2 +i, √3, -√3}
Each of these roots corresponds to a linear factor. Root p corresponds to factor (x -p), for example.
__
Factored formThen the factored p(x) will be ...
p(x) = k(x -3)(x -(2 -i))(x -(2 +i))(x -√3)(x +√3) . . . . for some scale factor k
Simplifying a bit, we have ...
p(x) = k(x -3)((x -2)² +1)(x² -3) = k(x -3)(x² -4x +5)(x² -3)
__
Scale factorAt x=0, this evaluates to ...
p(0) = k(0 -3)(0² -4·0 +5)(0² -3) = 45k
We want p(0) = -90, so we require ...
45k = -90
k = -2
__
Then the function p(x) factored to integers is ...
p(x) = -2(x -3)(x² -4x +5)(x² -3)
When we multiply this out, we find the standard form equation is ...
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
(b) The volume of water in a container is
directly proportional to the cube of its depth.
When the depth is 12 cm, the volume is 576 cm3.
Calculate
(i) the volume when the m is 1300 cm?. [2]
Answer:
See below.....Something is wrong with your question
Step-by-step explanation:
v = k d^3 or k = v/d^3 = 576/12^3 = 1/3
when depth (??? m??) is 1300 :
1/3 = v / (1300^3) = 732 333 333 .3 cm^3
Natoshia's den is 4 feet longer than it is wide. If the den's area is 320 square feet, what are the dimensions of the room?
Dimensions : 16 x 20
Let the width be xthen the length: x + 4 area of rectangle = Length * Widthsolving steps:
(x+4)(x) = 320x² + 4x = 320x² + 4x - 320 = 0x² +20x -16x -320 = 0x(x + 20) -16(x+20) = 0(x-16)(x+20) = 0x = 16, -20x = 16 [ As length or width can never be negative ]So we found Width = 16 feet
Length:
16 + 420 feetAnswer:
width = 16 ft
length = 20 ft
Step-by-step explanation:
Let width = x
If the length is 4 ft longer than the width, then
⇒ length = x + 4
Area of a rectangle = width × length
Given:
area = 320width = xlength = x + 4Substituting these values into the equation for the area of a rectangle and solving for x:
⇒ 320 = x(x + 4)
⇒ 320 = x² + 4x
⇒ x² + 4x - 320 = 0
⇒ (x - 16)(x + 20) = 0
⇒ x = 16, -20
As distance is positive, then x = 16 only.
Therefore, width = 16 ft and length = 20 ft
[tex]\sqrt[2]{80x^{2}y^{25} }[/tex]
Answer:
4xy^5√5
Step-by-step explanation:
√80 x √x² x √y^25
=4√5 x x x y^5
= 4√5xy^5
Answer:
4xy^12√(5y)
Step-by-step explanation:
Squares under the radical can be factored out.
[tex]\displaystyle \sqrt{80x^2y^{25}}=\sqrt{(4xy^{12})^2\cdot5y}=\boxed{4xy^{12}\sqrt{5y}}[/tex]
_____
Additional comment
Some versions of this question may have different exponents.
May currently has a balance of $1,817.43 on her credit card. if she must make a minimum monthly payment of 3.44% of her total balance, what is her minimum payment, to the nearest cent? a. $5.21 b. $62.52 c. $40.84 d. $51.49 please select the best answer from the choices provided a b c d
She makes a minimum monthly payment of 62.52 dollars. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
May currently has a balance of $1,817.43 on her credit card.
If she must make a minimum monthly payment of 3.44% of her total balance.
Then the minimum payment will be given as
Minimum payment = 0.0344 × 1817.43
Minimum payment = 62.519 ≅ 62.52
More about the percentage link is given below.
https://brainly.com/question/8011401
What is the area of this quadrilateral(Please show a step by step process)
Answer:
40ft
Step-by-step explanation:
What you need to know is the formula for the air of a rectangle:
the long side * the short side.
First calculate the area of the rectangle in the middle: 3*8=24ft
Then we are left with two right-angled triangles, one on the left and one on the right. If we juxtapose them, we realize that it forms a rectangle whose large side measures 8 and the small 2 so 2*8=16ft.
Finally, just add the area of the middle rectangle with the area of our rectangle formed by the two triangles on the right and on the left. So 16+24=40ft
This is urgent I really I need the answers
Thanks in advance
equation: 2y = 3x + 15
If cross y-axis, the x will be 0
2y = 3(0) + 15
2y = 15
y = 7.5
crosses y-axis at (0, 7.5)
(b)
P(-1,10), Q(3,4)
(i) gradient:
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{4-10}{3--1}[/tex]
[tex]\rightarrow \sf \dfrac{-6}{4}[/tex]
[tex]\rightarrow \sf -1.5[/tex]
(ii) midpoint:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
[tex]\rightarrow \sf (x_m, y_m) = (\dfrac{3-1}{2}, \dfrac{4+10}{2})[/tex]
[tex]\rightarrow \sf (x_m, y_m) = (1,7)[/tex]
what is equivalent to 24x + 32y
Answer:
8*(3x-4y)
Step-by-step explanation:
Just did the test
What is the space between two intersecting lines called?.
Answer:
The space between two intersecting lines is called an:
Angle
An angle is formed when two lines meet at a shared point. They are measured in degrees. There are four important types of angle; acute, right, obtuse, and reflex. A full circle has 360 degrees. If you see an angle of 720 degrees, it means it has rotated twice around a full circle.
360 degrees (one time round) x 2 = 720 degrees (two times round)
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
need help with this pls
The volume of the square base pyramid is 588 ft³
The Volume of the rectangular prism is 120 ft³
The Volume of a rectangular pyramid is 360 ft³
What is volume of a shape?Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object.
Volume of a square base pyramid = 1 / 3 × B × h
where
B = base area
Therefore,
Volume of a square base pyramid = 1 / 3 × 7² × 12
Volume of a square base pyramid = 1764 / 3 = 588 ft³
Volume of a rectangular prism = lwh
Volume of a rectangular prism = 6 × 5 × 4 = 120 ft³
Volume of a rectangular pyramid = 1 / 3 lwh
Volume of a rectangular pyramid = 1 / 3 × 10 × 12 × 9 = 1080 / 3 = 360 ft³
learn more on volume here: https://brainly.com/question/1578538
solve pls brainliest
Mary walks to her garage. The distance to the garage as a function of time is shown in this graph
A. Mary starts 8 meters from the garage.
B. Mary walks 8 meters every 4 seconds.
C. Mary arrives at the garage after 4 seconds.
D. Mary walks at a speed of 2 meters per second.
Answer:
d
Step-by-step explanation:
so if you look at the bottom left corner you can see 1 box is the same as saying for every second someone walks its one metre.
thats not how i got the answer though.
if you look at the starting point at 8 because she was 8 meters away you need to see when she comes across her first second which after 2 meters (Goes down two squares before reaching the first second)
now technically soe of the other answers are correct too but heres how i thought about it.
A. its correct but i dont think that's what its asking you for tbh
B. This we don't know for sure. eg she could take 890 seconds walking back to her starting point we just don't know for sure.
C. This is also true but once again it's easily given to you so i dont think that's what you're being asked.
D. This is the only option where you had to do any for of working out because s=d/t so s=8/4=2m/s
SOMEONE PLSLPLSSLSLS HELP ITS JUST 3 QUESTIONS BRO PLEASE ITS SO CONFUSING ILL BRAINLIST.
The length and width of a rectangle is 3x + 4 and x + 3 respectively.
a) write the perimeter of the rectangle in simplified form.
b) find the perimeter of the rectangle if x = 5.
c) the area of a rectangle is given by the formula area = length x width. Find the area of this rectangle when x = 4.
Step-by-step explanation:
a) Perimeter is equal to 2w + 2L
2(3x + 4) + 2(x + 3)
6x + 8 + 2x + 6
8x + 14
b) Put 5 in x's place
8×5 + 14
40 + 14
54
c) Area = (3x + 4) * (x + 3)
Put 4 in x's place
(3×4 + 4) * (4 + 3)
12 + 4 * 7
16 * 7
112
What's the answer pls help
Answer:
x = 8
Step-by-step explanation:
Both these angles are equal because they are equal. So we make this equation:
8x + 36 = 5x + 60
-5x -5x
3x + 36 = 60
-36 -36
3x = 24
Divide both sides by 3:
x = 8
30 POINS Find the measures of the numbered angles in the parallelogram. Please help
Answer:
Is there supposed to be an attachment? if so please send it so I can answer your question.
Find the measure of the missing angle in this triangle.
Answer:
b = 25°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
b + 110° + 45° = 180°
b + 155° = 180° ( subtract 155° from both sides )
b = 25°
Which statement accurately describes the contents of the two boxes in the image?
A. The box on the top consists of a mixture while the box on the bottom consists of a pure substance.
B. Both boxes consist of pure substances.
C. The box on the top consists of a pure substance while the box on the bottom consists of a mixture.
D. Both boxes consist of mixtures.
The statement that describes the content of the two boxes is that the box on the top contains a pure substance, while the one on the bottom contains a mixture.
What is the difference between a pure substance and a mixture?A pure substance often refers to a specific element such as nitrogen, helium, etc. that has not been modified or mixed with others.
On the other hand, a mixture includes two or more elements mixed.
What is the content of the first box?The first box contains only nitrogen, which is a pure substance.
What is the content of the second box?Different from the first box, this box contains two types of substances carbon and oxygen, which is why particles have two different colors. This means the content is a mixture.
Learn more about substances in: https://brainly.com/question/24372098
2x-10=12 what is the value of x+4
Answer:
15
Step-by-step explanation:
if 2x-10=12 then
2x=22 so
X=11
X+4= 15
Answer:
15
Step-by-step explanation:
1. we find what x is by finding out the first equation:
2x - 10 = 12
Add 10 to both sides (it cancels out on the first side)
-10 + 10 = 0 (cancels out)
12 + 10 = 22
2x = 22
Now we divide both sides by 2 to get x alone
22 divided by 2 = 11
X = 11
2. Now we can solve the equation x + 4:
Just fill in x, which as we solved, is 11
x + 4 = 11 + 4 = 15
Therefore, the value of x + 4 is 15.
200 divided by 5 what is the answer
Answer:
40
Step by Step:
200/5 = 40
Consider functions f and g
Answer:
A
Step-by-step explanation:
[tex] f(x) = \dfrac{x - 16}{x^2 + 6x - 40} [/tex]
[tex] g(x) = \dfrac{1}{x + 10} [/tex]
[tex] f(x) + g(x) = \dfrac{x - 16}{x^2 + 6x - 40} + \dfrac{1}{x + 10} [/tex]
[tex] f(x) + g(x) = \dfrac{x - 16}{x^2 + 6x - 40} + \dfrac{(x - 4)}{(x + 10)(x - 4)} [/tex]
[tex] f(x) + g(x) = \dfrac{x - 16 + x - 4}{x^2 + 6x - 40} [/tex]
[tex] f(x) + g(x) = \dfrac{2x - 20}{x^2 + 6x - 40} [/tex]
Answer: A
Evaluate −x^2+4x+1 when x=−2.
Hey there!
In order to evaluate this expression, we need to plug in the value of x (-2)
So we have
-x²+4x+1
plug in -2
-(-2)²+4(-2)+1
-4-8+1
-12+1
-11
Hence, the answer's
[tex]\boxed{\boxed{\bold{-11}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#ILoveLearning
:-)
Explain why 10 to the zero power equals 1
Answer:
Because any number to the power of zero will be one.
x = –8 –6x + 9y = 12 solve for substitution
Answer:
x= -8,y= -4
Step-by-step explanation:
Substitute x= -8
-6(-8)+9y=12
simplify
48+9y=12
isolate for y
y= -4
The solutions to the system of equations are:
x= -8 and y= -4
Please Help!!!!!!!!!!!!!!! I need this ASAP!
HELP.
can someone give me an explanation of how to do this? i just want to know how to apply the explanation to other problems!
Mid point of any two points (x1,y1) and (x2,y2)
is ((x1+x2)/2,(y1+y2)/2)
using this
we get coordinates of d are (a,-2b)
Which statements are true regarding the regular dodecagon? Check all that apply
Answer:
A dodecagon is a shape with 12 sides
Step-by-step explanation:
Decagon is 10 and do is 2 so 12
THIS IS MY LAST QUESTION PLEASE HELP ME
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price
Zion Sun Chairs must sell each chair for to break even if the total annual fixed costs are $17,363.50
and the variable cost per chair is $52.17.
O $57.03
O $64.50
O $81.25
O $79.65
Answer:
81.25
Step-by-step explanation:
A sample of size 38 has s = 15.5 and yields this confidence interval for the mean:
(304.67, 322.48). What's the t* for this confidence interval?
6.29
3.14
2.514
2.026
3.542
Answer:
6338.7
Step-by-step explanation:
a A hole in the shape of a hemisphere is carved into each face of a cube. The holes are identical and centered at the centre of each face. The holes touch their neighbours at only one point. The cube has side 2. What is the diameter of each hole?
Diameter of each hemispheral holes = the diameter of a full sphere = side length of cube = 2 units.
What is a Hemisphere?A hemishpere is half of a sphere. Thus, two hemispheres makes one full sphere.
Given the image as shown below, since the identical hemispheral holes are centered at the center of each fce and they touch each other at only one point, it means that two hemisphere meet to make one full sphere.
Therefore, the diameter of a full sphere = side length of cube.
Thus, diameter of each hemispheral holes = the diameter of a full sphere = side length of cube = 2 units.
Learn more about hemisphere on:
https://brainly.com/question/9280450
What is the area of the quadrilateral
What is a line? What is an angle? How do you describe a line and an angle? How do we know if an angle is right? obtuse? acute? or a full circle?
Answer:
A line is something that goes on endlessly in both directions. An angle is the number of degrees at a point where two rays meet. We know if an angle is right if there is a right angle that measures up to 90°. An obtuse is any angle that measures over 90° and an acute angle is under 90°. Hope this helps! :)
Step-by-step explanation: