Answer: Degree of polynomial (highest degree) =4
Maximum possible terms =9
Number of terms in the product = 5
Step-by-step explanation:
A trinomial is a polynomial with 3 terms.
The given product of trinomial: [tex](x^2 + x + 2)(x^2 - 2x + 3)[/tex]
By using distributive property: a(b+c+d)= ab+ac+ad
[tex](x^2 + x + 2)(x^2 - 2x + 3)=(x^2 + x + 2) x^2+(x^2 + x + 2) (-2x)+(x^2 + x + 2)(3)\\\\=x^2(x^2)+x(x^2)+2(x^2)+x^2 (-2x)+x (-2x)+2 (-2x)+x^2 (3)+x (3)+2 (3)\\\\\\=x^4+x^3+2x^2-2x^3-2x^2-4x+3x^2+3x+6[/tex]
Maximum possible terms =9
Combine like terms
[tex]x^4+x^3-2x^3+3x^2-4x+3x+6\\\\=x^4-x^3+3x^2-x+6[/tex]
Hence, [tex]\left(x^2\:+\:x\:+\:2\right)\left(x^2\:-\:2x\:+\:3\right)=x^4-x^3+3x^2-x+6[/tex]
Degree of polynomial (highest degree) =4
Number of terms = 5
Answer:
Sample Response: To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.
The maximum number of terms in the product of the trinomials is 5.
There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
Explanation:
This is the response on Edge 2020-21. Hope this helps, have a great day!
what is the quotient of the rational expression below x^2-25/x-11÷ x^2+10x+25/4x-44
Answer:
The quotient is 4x-20/x+5
Step-by-step explanation:
The quotient is simply the result of the division
Through factorization, can express x^2 -25 as (x-5)(x+5)
Also x^2 + 10x + 25 as (x+5)(x+5)
and lastly 4x-44 as 4(x-11)
Now when we divide, the numerator of the second fraction will come down while the denominator goes up;
So we have ;
x^-25/x-11 * 4x-44/x^2 + 10x + 25
Now, making use of the factorizations, we have ;
(x-5)(x+5)/(x-11) * 4(x-11)/(x+5)(x+5)
Canceling out like factors, we have
= 4(x-5)/(x+5)
9. Write the number in place value table of 820245
Answer:
Hello! The answer to your question will be below.
Step-by-step explanation:
Attached below....
Number form:820,245
Word form: eight hundred twenty thousand two hundred forty-five
Expanded form: 800,000+20,000+0+200+40+ 5
Place value chart below!!
Hope this helps! :)
⭐️Have a wonderful day!⭐️
Suppose a cube is given. How many different segments can be formed by connecting the vertices of the cube?
Answer:
28 is thee answer
Step-by-step explanation:
A pyramid has a square base with sides 8" and a slant height of 5". Total Area = 144 square units 200 square units 224 square units
Answer:
It's 144 square units
Step-by-step explanation:
The pyramid has a square base with 8 sides and a slant height of 5
a=8
l=5
The total are of the square base pyramid is
A= [tex]a^{2}[/tex]+2al
a is side length of square and l is slant height
A= [tex](8)^{2}+2[/tex] x 8 x 5
A=64+80
A=144
HELP PLEASE ❤️❤️!!!!!!’
Step-by-step explanation:
your answer is C
HOPE IT HELPS YOU MATE
Need help ASAP thank you sorry if you can’t see the picture but you can zoom in :) !!!
Answer:
264 ft³
Step-by-step explanation:
The following data were obtained from the question:
Pi (π) = 3.14
Height (h) = 21 ft
Radius (r) = 2 ft
Volume (V) =..?
The volume of the cylinder can be obtained as follow:
V = πr²h
V = 3.14 × 2² × 21
V = 3.14 × 4 × 21
V = 264 ft³
Therefore, the of the cylinder is 264 ft³
What effect will replacing x with (x+7) have on the graph of the equation y=x^2?
A. slides the graph 7 units down
B. slides the graph 7 units right
C. shrinks the graph by a factor of 7
D. Slides the graph 7 units left
Answer:
D
Step-by-step explanation:
Solution:-
- The given question pertains to the translation of a function f ( x ) over the cartesian coordinate system.
- There are certain guidelines that must be followed when performing any translations of any function f ( x ).
Translation Guideline
Vertical shifts
Up: f ( x ) - > f ( x ) + bDown: f ( x ) - > f ( x ) - bHorizontal shifts
Left: f ( x ) - > f ( x + a ) Right: f ( x ) - > f ( x - a )Where, " a " and " b " are constants for respective horizontal and vertical shifts.
- We can make a generalized form of the translated function f ( x ) to f* ( x ) as follows:
Generalized shift: f ( x ) - > f ( x ± a ) ± b
Where, a: Unit of horizontal shift
b: Unit of vertical shift
- We are given a function f ( x ) defined. We are to replace the variable ( x ) with ( x + 7 ).
[tex]f ( x ) = x^2\\\\f^*(x) = f ( x + 7 ) = (x + 7 )^2[/tex]
- Use the above given guidelines to determine the type of shift. Take a look at the Left shift in the horizontal shift section.
- Left shift : f ( x ) -> f ( x + a ) = f ( x + 7 )
Answer: The function f ( x ) is slided a = 7 units to the left!
Please answer this question now
Answer:
k=180-23-90=67...................
Answer:
< k = 67°
Step-by-step explanation:
HJ tangent to HG => < H = 90°
< K = 180° - (<J + <H)
= 180° - (90° + 23°)
= 180° - 113°
= 67°
Someone please explain
Area of a triangle is 1/2 x base x height.
The graphed triangle has height of 2 and base of 2.
Area = /2 x 2 x 2 = 2 square units.
The triangle gets enlarged by a scale factor of 2, so the new height would be 2 x 2 = 4 and the new base would be 2 x 2 = 4
Area of enlarged triangle = 1/2 x 4 x 4 = 8 square units.
The answer is C) 8
Help pleaseee! Thank you
Answer:
Step-by-step explanation:
width of a rectangle=11 cm=11*5=55 ft
length of rectangle =8 cm= 8*5=40
Area=55*40=2220 ft²
height=3 cm=3*5=15
base=11 cm=11*5=55
Area of a triangle=base*height/2=15*55/2= ft^2
2220+412.5=2632.5 ft^2
this number is close to 2615 if the square unit on the grid =1 cm
What is the solution to this equation? 8 - 5(x - 3) = 18
Answer:
x = 1
Step-by-step explanation:
Given
8 - 5(x - 3) = 18 ( subtract 8 from both sides )
- 5(x - 3) = 10 ( divide both sides by - 5 )
x - 3 = - 2 ( add 3 to both sides )
x = 1
State the number of possible triangles that can be formed using the given measurements.
Answer: 39) 1 40) 2
41) 1 42) 0
Step-by-step explanation:
39) ∠A = ? ∠B = ? ∠C = 129°
a = ? b = 15 c = 45
Use Law of Sines to find ∠B:
[tex]\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o[/tex]
If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°
If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°
Since ∠A cannot be negative then ∠B ≠ 165°
∠A = 36° ∠B = 15° ∠C = 129° is the only valid solution.
40) ∠A = 16° ∠B = ? ∠C = ?
a = 15 b = ? c = 19
Use Law of Sines to find ∠C:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o[/tex]
If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°
If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°
Both result with ∠B as a positive number so both are valid solutions.
Solution 1: ∠A = 16° ∠B = 144° ∠C = 20°
Solution 2: ∠A = 16° ∠B = 4° ∠C = 160°
41) ∠A = ? ∠B = 75° ∠C = ?
a = 7 b = 30 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o[/tex]
If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°
If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°
Since ∠C cannot be negative then ∠A ≠ 167°
∠A = 13° ∠B = 75° ∠C = 92° is the only valid solution.
42) ∠A = ? ∠B = 119° ∠C = ?
a = 34 b = 34 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o[/tex]
If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°
If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°
Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°
There are no valid solutions.
label missing angles 1, 2, 3, 4, and 5 if lines ‘m’ and ‘n’ are parallel
Answer:
see attached diagram
Step-by-step explanation:
1. 1 and 70 are angles on a line (supplementary)
2. vertical angles with 70
3. angles on a line are supplementary
4. 2 and 4 are supplementary interior angles between parallel lines m & n
5. corresponding angle with 70
Find the product.
(5ab3b) (2ab)
PLEASE HELP!!! ASAP!!!
Answer:
10a²b²6ab²
Step-by-step explanation:
Distribute the 2ab the other values
A group of students volunteered to finish a task in 25 days .1 Q of students did not come n the work could b completed in 35 days .find original number of students in group were??
Answer:
p=7Q/2
Step-by-step explanation:
Original number of students:
p students to do 1 job in 25 days.
Let r= the rate for 1 student.
pr*25=1
pr*25=1 is the work rate equation for p students.
Lesser number of students:
p-Q students came to do the job and time required was 35 days.
(P-Q)*r*35=1.
The unknowns are p, Q and r
Equate the original number of students and the lesser number of students
pr*25=(P-Q)*r*35
25rp=35rp - 35Qr
Collect like terms
25rp-35rp = -35Qr
Divide both sides by -5
-5rp+7rp=- 7rp
It can be re written as
7rp-5rp=-7Qr
2rp=7Qr
Make p the subject of the formula
p=7Qr/2r
p=7Q/2
p=7Q/2 is the original number of students
-10rp = -35Qr
The system of these two equations can be solved for p. See the THREE unknown
variables, p, r, and Q. You might assume that either r or Q would be a constant.
Write the equation of a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2(sqrt5)
Answer:
[tex]\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4[/tex]
The foci c is at +/-2√5, using c² = a² + b²:
[tex]c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2[/tex]
Substituting the value of a and b to get the equation of the hyperbola:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]
PLZZ HELPP WILL GIVE 100 POINTS Which ordered pairs are solutions to the inequality −2x+y≥−4? Select each correct answer. (0, −5) (1, −2) (3, −1) (0, 1) (−1, 1)
Answer:
(1, −2) (0, 1) (−1, 1)
Step-by-step explanation:
−2x+y≥−4
Substitute the points into the inequality and see if it is true
(0, −5)
-2(0) + -5 ≥−4
0-5 ≥−4
-5≥−4
False not a solution
(1, −2)
-2(1) -2 ≥−4
-2-2 ≥−4
-4≥−4
True it is a solution
(3, −1)
-2(3) -1 ≥−4
-6 -1 ≥−4
-7 ≥−4
False, not a solution
(0, 1)
-2(0) +1 ≥−4
0+1 ≥−4
1 ≥−4
True it is a solution
(−1, 1)
-2(-1) +1≥−4
2+1≥−4
3≥−4
True it is a solution
Answer:
(1.-2)
(0.1)
(-1,.-1)
Step-by-step explanation:
To solve this we have to plug in each point to see which one would work.
Inequality: -2x + y >= -4
First let's plugin (0,-5):
-2x + y >= -4
-2(0) + (-5) >= -4
0 - 5 >= -4
-5 >= -4 is wrong.
Now let's plugin (1,-2)
-2x + y >= -4
-2(1) + (-2) >= -4
-2 - 2 >= -4
-4 >= -4 is correct
Now let's plugin (3,-1):
-2x + y >= -4
-2(3) + (-1) >= -4
-6 - 1 >= -4
-7 >= -4 is wrong
Now let's plugin (0,1):
-2x + y >= -4
-2(0) + (1) >= -4
0 + 1 >= -4
1 >= -4 is correct
Now let's plugin (-1,1):
-2x + y >= -4
-2(-1) + (1) >= -4
2 + 1 >= -4
3 >= -4 is correct
Would appreciate if you gave me brainliest :)
Please answer this in two minutes
Answer:
Not a triangle
Step-by-step explanation:
Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.
whats the answer to that ?
Answer:
11 and 2/3.
Step-by-step explanation:
6 and 3/12 = 72/12 + 3/12 = 75/12.
5 and 5/12 = 60/12 + 5/12 = 65/12.
75/12 + 65/12 = 140 / 12 = 70 / 6 = 35 / 3 = 11 and 2/3.
Hope this helps!
Answer: 11 2/3
Step-by-step explanation:
[tex]6\frac{3}{12}+5\frac{5}{12}[/tex]
[tex]Add\:whole\:numbers[/tex]
[tex]6+5=11[/tex]
[tex]Combine\:fractions[/tex]
[tex]\frac{3}{12}+\frac{5}{12}=\frac{8}{12}[/tex]
[tex]Simplify[/tex]
[tex]\frac{8}{12} =\frac{2}{3}[/tex]
[tex]11+\frac{2}{3}[/tex]
[tex]=11\frac{2}{3}[/tex]
What are the coordinates of the vertex of the function f(x)=x2+ 10x-3?
O (-5. -28)
(-5, 28)
O (5,-28)
(5.28)
Answer:
(-5,-28)
Step-by-step explanation:
Use the vertex form y=a(x-h)^2
a=1
h=-5
k=-28
vertex=(h,k)
Answer: A. (-5, -28)
Step-by-step explanation:
f(x) = x² + 10x - 3
a=1 b=10
The axis of symmetry is the x-coordinate of the vertex:
[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(10)}{2(1)}=-5[/tex]
Input x = -5 into the original equation to find the y-coordinate of the vertex:
f(-5) = (-5)² + 10(-5) - 3
= 25 -50 -3
= -28
x, y coordinate of the vertex is: (-5, -28)
Which equation can you use to solve for theta in the figure shown? A right triangle is shown. 2 sides have lengths of 45 feet and 31.2 feet and the hypotenuse has a length of 54.8 feet. The angle opposite to the side with length 45 feet is theta.
Answer:
45/58.4
Step-by-step explanation:
Answer: part 1: 45/54.8.
Part 2: 55.2
Step-by-step explanation:
Edge
length of a rectangle is 3 times its width.If its perimeter is 24 centimetres what is the area of the rectangle?
Answer:
27 cm²Step-by-step explanation:
The length is 3 × width.
l = 3w
The perimeter is 24 centimeters.
P = 2l + 2w
24 = 2(3w) + 2w
24 = 6w + 2w
24 = 8w
3 = w
The width is 3 centimeters.
l = 3(3)
l = 9
The length is 9 centimeters.
Area is l × w.
A = l × w
A = 9 × 3
A = 27
The area is 27 squared centimeters.
Answer:
27
Width= x
Length= x × 3 =3x
so, 3x+3x+x+x=24
8x=24
x=24/8
x=3
so, length=3(3)=9
width=3
therefore,
Area=9×3
=27
A city counsel has a square lot to place a playground. They plan to place a diagonal of trees to create two distinct play areas. To determine if there is enough money in the budget, they needs to know the distance. If the length of each side of the lot is 45 m, how long is the diagonal?
Answer:
66.63
Step-by-step explanation:
To find the diagonal length, use Pythagorean’s theorem.
Diagonal = √45^2 + 45^2 = √2025+2025 = √4050 = 63.63.
Hope this helps
0.90(2.25d + 1.40t + 6).
CHECK THE COMPLETE QUESTION BELOW;
Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza with t toppings, her total cost can be found using this expression: 0.90(2.25d + 1.40t + 6). What is the total cost for Lindy and her friends to order 4 drinks and a medium pizza with 3 toppings? A. $17.28 B. $16.52 C. $15.69 D. $28.40
Answer:
OPTION A. is correct
A)$17.28
Step-by-step explanation:
From the question we were giventhis expression as the total cost for all.
0.90(2.25d + 1.40t + 6).
We know that Lindy and her friends to order 4 drinks and a medium pizza with 3 topping
Then we can say d= 4 and t= 3 ,
Then we can substitute into below expresion
0.90(2.25d + 1.40t + 6).
0.90[2.25(4)+1.40(3)+6]
= 0.90[9+4.2+6]
= 17.8
Hence the total cost for Lindy = $ 17.28
How does the period of f(x)= cos(2x) relate to the period of the parent function cos x?
Answer:
Both have the same period which is 2π
Step-by-step explanation:
Simplify (2^3)^–2. PLEASE I NEED HELP U WILL GET 10 POINTS
Answer:
I won't give you the answer straight away so you take the time to read my answer and understand
Step-by-step explanation:
We knoe that 2 to the third is 8. when you square to a negative power, you do squaring normally, and then take the reciprocal of that number. so 8 to the second power is 64, and we flip it over, sp the answer is 1/64
Sorry for the bad Angle, anyways if anyone could help me out that be great, I would do the question myself if I'd know how to do it, have a nice day
Answer:
210 students
Step-by-step explanation:
The total number of students surveyed was
19+14+30+23+14 = 100
The fraction that picked Yosemite is 14/100
Multiply that fraction by the total number of students
1500* 14/100 = 210
Answer:
210 students
Step-by-step explanation:
vote me brainliest plz
what is the value of x if e^3+6=8
Answer:
A
Step-by-step explanation:
-4x-7+10x=-7+6x−4x−7+10x=−7+6xminus, 4, x, minus, 7, plus, 10, x, equals, minus, 7, plus, 6, x Choose 1 answer: Choose 1 answer: (Choice A) A No solutions (Choice B) B Exactly one solution (Choice C) C Infinitely many solutions
Answer:
(Choice C) C Infinitely many solutions.
Step-by-step explanation:
First of all, let us learn about solutions of linear equations in one variable.
The linear equations in one variable usually have one solution.
For example:
[tex]2x =x+3[/tex]
When we solve this:
[tex]2x-x=3\\\Rightarrow x=3[/tex]
One solution is [tex]x = 3[/tex]
But there can be situations when there are
1. No solutions:
For example:
[tex]x =x+9[/tex]
It means that value x is equal to value of x+9 which can never be true.
Truth is the term on Right Hand Side is always 9 greater than the value of Left Hand Side.
Such situations are called Contradictions.
Here, no solution exists.
2. Infinitely many solutions:
For example:
[tex]x+2x+8=3x+8[/tex]
The Right hand Side is just the simplification of the LHS.
And LHS is always equal to RHS no matter what is the value of variable [tex]x[/tex].
It means there are infinitely many solutions for this equation.
-----------------------------------------------------
Now, let us have a look at the given equation in the question:
[tex]-4x-7+10x=-7+6x[/tex]
Taking LHS: [tex]-4x-7+10x[/tex]
Taking the terms with [tex]x[/tex] on one side:
[tex]-7+10x-4x\\\Rightarrow -7+6x[/tex]
which is equal to Right Hand Side.
Hence, as we discussed in case 2 above.
For every value of [tex]x[/tex] the equation holds true.
[tex]\therefore[/tex] There exists infinitely many solutions to the given equation.
Correct answer is:
(Choice C) C Infinitely many solutions
Answer:
C Infinitiy solutions
Step-by-step explanation:
Solve for the roots in simplest form using the quadratic formula:
4x2 – 12x = -5
Answer:
x=2.5&.5
Step-by-step explanation:
The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a
12+or-sqrt((-12^2)-4(4)(5))
12+or-sqrt(144-80)
12+or-sqrt(64)
(12+8)/8 and (12-8)/8
x=2.5 and x=.5
Answer: [tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex] or [tex]x=2.5,\:x=0.5[/tex]
Step-by-step explanation:
[tex]4x^2-12x=-5[/tex]
[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]
[tex]4x^2-12x+5=-5+5[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]4x^2-12x+5=0[/tex]
Solve with Quadratic Formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]a=4,\:b=-12,\:c=5:\quad x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]
[tex]\frac{-\left(-12\right)+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]\frac{12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]
[tex]12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=12+\sqrt{64}[/tex]
[tex]\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=\sqrt{64}[/tex]
[tex]\sqrt{64}=8[/tex]
[tex]=\frac{12+8}{8}[/tex]
[tex]=\frac{20}{8}[/tex]
[tex]=\frac{5}{2}[/tex]
[tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex]