Answer:
x^4+x^3-3x^2-12x
Step-by-step explanation:
0,-4,√3 are the zeros of polynomial. P.
If x=√3 is a zero and P has integer coefficients, then x=-√3 is also a zero. Both of these results come from solving the equation x^2=3 or x^2-3=0 so x^2-3 is a factor of P.
x=0 is a zero, means x-0 or x is a factor.
x=-4 is a zero, means x-(-4) or x+4 is a factor.
So the polynomial, P, in factored form is
x(x^2-3)(x+4)
Let's write in standard form.
I will begin by multiplying the last two factors.
x(x^3+x^2-3x-12)
Distribute x
x^4+x^3-3x^2-12x
vanessa will sell yogurt for $2.50 a cup fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt
answer: 47.5 cups
Step-by-step explanation:
2.50 x 19 = answer
Por cada 3 quetzales hay cuatro ajolotes y por cada 8 ajolotes hay 5 lobos mexicanos si hay unapoblacion de 150 quetzales ¿cuantos ajolotes hay?Y cuantos lobos mexicanos hay?
Answer:
Step-by-step explanation:
For every 3 quetzals there are four axolotls and for every 8 axolotls there are 5 Mexican wolves, if there is a population of 150 quetzals, how many axolotls are there? And how many Mexican wolves are there?
Lee can type 300 words in 6 minutes what is his rate per minute
Answer:
300 words in 6 minutes
300/6 words in 1 minutes
50 words in 1 minutes
Therefore,Lee can type 50 words in 1 minute.
6 2/3 times 12 simplest form
Answer:
80
Step-by-step explanation:
[tex]6\frac{2}{3} *12[/tex]
First, write the fractions as improper fractions.
[tex]\sf\frac{20}{3} *\frac{12}{1}[/tex]
Multiply.
[tex]\sf\frac{240}{3}[/tex]
Divide.
80
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6\dfrac{2}{3}\times 12}[/tex]
[tex]\mathsf{= \dfrac{6\times3+2}{3}\times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{18 + 2}{3} \times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{20}{3} \times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{20\times12}{3\times1}}[/tex]
[tex]\mathsf{= \dfrac{240}{3}}[/tex]
[tex]\mathsf{= 240\div 3}[/tex]
[tex]\mathsf{= 80}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{80}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
PLEASE HELP ME ILL BRAINLIEST YOU
Answer:
7
Step-by-step explanation:
a^2 + b^ = c^2
x^2 + 24^2 = 26^2
x^2 = 100
x=10
Can i have brainliest please
Answer:
x = 10
Step-by-step explanation:
This is a right triangle problem
use the Pythagorean Theorem
a^2 + b^2 = c^2
x^2 + 24^2 = 26^2
x^2 + 576 = 676
Subtract 576 from both sides
x^2 = 100
Take the square root of both sides
x = 10
Point lies on the diagonal of square with . Let and be the circumcenters of triangles and respectively. Given that and , then , where and are positive integers. Find .
Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],
where a and b are positive integers.
The value of a + b is 96.
Let mid-point of DC be E and mid-point of AB be F.
Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.
Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]
Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]
Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]
Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference
Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.
Using the above information and symmetry,
[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]
Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)
and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)
Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]
And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]
Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]
[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]
And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]
[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]
Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.
BF = DE = [tex]\frac{12}{2}[/tex] = 6
[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]
And PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]
Now, Let x = AP
Using law of cosine on [tex]$\triangle[/tex]ABP, we have
[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]
[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]
[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]
Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]
Therefore a + b = 72 + 24 = 96
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Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )
Solve this problem
Step by step
The measure of the missing length of the trapezoid is equal to 3√39 units.
How to determine the missing length of a trapezoid
Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:
D = d + 2 · c
Where c is the length of the horizontal leg of the right triangle in a trapezoid.
And the missing leg can be found by means of Pythagorean theorem:
x = √(r² - c²)
Where:
r - Hypotenusec - Shortest legx - Longest legFirst, determine the length of shortest leg: (D = 40, d = 26)
40 = 26 + 2 · c
14 = 2 · c
c = 7
Second, find the longest leg by Pythagorean theorem:
x = √(20² - 7²)
x = 3√39
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Solve. -3 + 9x = 24 (quick)
Answer: x = 3
Step-by-step explanation:
-3 +9x = 24
9x= 24+3
9x=27
9x/9= 27/9
x=3
Answer:
x = 3
Step-by-step explanation:
-3 + 9x = 24
rearrange:
9x - 3 = 24
Add 3 to both sides of the equation:
9x - 3 + 3 = 24 + 3
9x = 27
Divide both sides by 9:
9x/9 = 27/9
x = 3
Have a nice day!
90 minus 10x
ill give 25 points and brainiest
Answer:
80x
Step-by-step explanation:
There is no substitution for the variable so the expression is 80x
where is the vertex located on the graph of y=(x+7)(x+1)
Answer:
The vertex is (-4, -9)
Step-by-step explanation:
The two roots are located at x = -7 and x = -1, which come from (x + 7) and (x + 1). The axis of symmetry is located halfway between these values, at x = -4. This axis passes through the vertex. The y-value at the vertex is (-4 + 7)(-4 + 1), or -9. The graph is a parabola that opens up. The vertex is (-4, -9).
IM GIVING GOOD REVIEWS! EASY MATH!
Answer:
40,000
Step-by-step explanation:
can I have branliest
Answer: 40,000
Step-by-step explanation: Well it doubles every 440 minutes. Since it is asking for the size after 880 minutes, and the starting size is 20,000 just double 20,000 because 440 times 2 equals 880.
What is the surface are of the triangular prism?
Answer:
114.12
Step-by-step explanation:
ANSWER BOTH!!!!
A. In a recent year, 22% of all college students were enrolled part-time. If 7.8 million college students were enrolled part-time that year, what was the total number of college students?
Round your answer to the nearest million.
B. Last year, Mai opened an investment account with $6200. At the end of the year, the amount in the account had increased by 24.5%. How much is this increase in dollars? How much money was in her account at the end of last year?
Increase in amount:$
Year-end amount:$
Answer:
A. 35 million
B. $1519 increase
$7719 year end
Step-by-step explanation:
How to solve 40 50 90 triangles
The 40 50 90 triangle can be solved using Pythagoras theorem.
What is the 40 50 90 triangle?A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.
Given:
We have 40 50 90 triangles.
A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.
Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.
So, Such type of Triangles can be solved using Pythagoras theorem.
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Help please,I’ll give 20points (if I can)
On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
y = 2x +1
y = 3x - 1
x- 1 = 0
x = 1, y = 2
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What are the factors of this quadratic function?
A. (x - 1) and (x - 5)
B. (x + 1) and (x + 5)
C. (x - 1) and (x+5)
D. (x + 1) and (x - 5)
Hello. Please answer!
The measures of the three sides of a triangle are 21 feet, 28 feet, and 35
feet. Determine whether the triangle is a right triangle.
Answer:
yes
Step-by-step explanation:
according to pythagoras theorem = hypotenuse² = √ base²+perpendicular²
so 21² + 28² = 35²
What is the range of this function?
(-9, 10) (19, 18) (0,7) (20,3)
A triangle has sides with lengths of 12 feet, 16 feet, and 18 feet. Is it a right triangle?
Answer:
Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Right triangle fulfill the pythagorean theorem:
[tex]a^2+ b^2 = c^2[/tex]
Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.
[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]
A cylindrical potato chip container has a diameter of 3.5 inches and a height of 12 inches. What is the volume of the chip container? Use 3.14 for pi. Round your answer to the nearest hundredth.
57.73 in3
115.40 in3
350.65 in3
461.81 in3
Answer:
V = 38.47 in^3
Step-by-step explanation:
The container base radius is half the diameter, that is, 1.75 in, and the height is 12 in. The formula for the volume of a cylinder of radius r and height h is V = (1/3)(pi)(r)^2h, which in this particular case comes out to:
V = (1/3)(3.14)(1.75 in)^2*(12 in), or
V = 38.47 in^3
Answer:
115.40 in3
that is the correct answer to this question.
Please help with math assignment
Answer:
a = 4√2, h = 2√3
David went shopping for a new phone because of a sale. The price on the tag was $46, but David paid $39. 10 before tax. Find the percent discount
The percent discount on the new phone is 15%.
Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.
To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.
Discount = Original Price - Sale Price
Discount = $46 - $39.10
Discount = $6.90
Percent Discount = (Discount / Original Price) x 100
Percent Discount = ($6.90 / $46) x 100
Percent Discount = 15%
Therefore, the percent discount is 15%.
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Can a/the variable in a algebraic expression be a base?
Answer:
yes
Step-by-step explanation:
yes
yes
yes
yes
yeyed
yes
An earth day even will cost 15$ for 3 people to attend. If there are four people attending, how much will the Earth Day fun event cost? Pls, Help me!!!!
Answer: 20$
5$ for each person attending. Hope it helps.
Answer:
$20
Step-by-step explanation:
the unit rate (cost per person) is
$15
-------------- = $5/person
3 people
For four people the total cost would be (4 people) ($5/person) = $20
How many solutions
y=10x+2
y=8x+2x+2
Answer:
Infinutely many solutions
Step-by-step explanation:
y = 10x + 2 --------- (1)
y = 8x +2x +2
=> y = 10x + 2---------- (2)
(1) -> 10x -y + 2 = 0
(2) -> 10x -y + 2 = 0
a1=10 ; b1=-1 ; c1 = 2
a2=10 ; b2=-1 ; c2= 2
a1/a2 = 10/10 = 1
b1/b2 = -1/-1 = 1
c1/c2 = 2/2 = 1
therefore, a1/a2 = b1/b2 = c1/c2
Therefore the line coincides and there are infinitely many solutions.
Find the midpoint of A and B where A has coordinates (2,3) and B has coordinates (8,9)
Step-by-step explanation:
[tex]midpoint = ( \frac{(2 + 8)}{2} , \frac{(3 + 9)}{2} ) \\ = (5,6)[/tex]
Answer:
√(x2-x1)²+(y2-y1)²
√(8-2)²+(9-3)²
√6²+6²
√36+36
√72
8.48528137424≈8.5
Step-by-step explanation:
nter (A,B,C,D)in order below if $A$, $B$, $C$, and $D$ are the coefficients of the partial fractions expansion of $$12\cdot\frac{x^3 4}{(x^2-1)(x^2 3x 2)}
The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.
A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.
The denominator is
(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)
(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)
So by partial fraction expansion
(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))
(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²
A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4
(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4
Thus from coefficients of x³, x², x and 1,
A + B + C = 1
2A + 4B + C + D = 0
-A + 5B - C + D = 0
-2A + 2B - C - 2D = 4
Solving
A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2
--The question is not clear, the question is given below--
"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of
[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex] "
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no links, pls help!!
Answer:
look at the photo x is the red and y is the blue
answer correct and u get brainliest if u are able to answer this u r a math god
Answer:
184ft^2
Step-by-step explanation:
W have to find the area of triangles and rectangles and add them together to get the total area of the figure:
Area of triangles = 1/2(b)(h)
Area of rectangles = l x w
6 x 10 = 60
1/2(6)(4) = 12 (We can make this 12 a 24 because there are two of these triangles)
5 x 10 = 50 (We can also make this 50 a 100 because there are two of these rectangles)
100 + 24 + 60 = 184ft^2