Answer:
ANSWER
C.
3 {x}^{4} - {x}^{3} + 3{x}^{2} + 18x + 43x
4
−x
3
+3x
2
+18x+4
EXPLANATION
We want to multiply;
(3 {x}^{2} + 5x + 1)( {x}^{2} - 2x + 4)(3x
2
+5x+1)(x
2
−2x+4)
We use the distributive property to obtain:
3 {x}^{2} ( {x}^{2} - 2x + 4) + 5x( {x}^{2} - 2x + 4) + 1( {x}^{2} - 2x + 4)3x
2
(x
2
−2x+4)+5x(x
2
−2x+4)+1(x
2
−2x+4)
We expand to get:
3 {x}^{4} - 6 {x}^{3} + 12 {x}^{2} + 5 {x}^{3} - 10 {x}^{2} + 20x + {x}^{2} - 2x + 43x
4
−6x
3
+12x
2
+5x
3
−10x
2
+20x+x
2
−2x+4
Regroup similar terms:
3 {x}^{4} - 6 {x}^{3} + 5 {x}^{3} + 12 {x}^{2} - 10 {x}^{2} + {x}^{2} + 20x - 2x + 43x
4
−6x
3
+5x
3
+12x
2
−10x
2
+x
2
+20x−2x+4
Combine similar terms:
3 {x}^{4} - {x}^{3} + 3{x}^{2} + 18x + 43x
4
−x
3
+3x
2
+18x+4
The correct choice is C.
What is the height of the pyramid ???
Answers:
A: 7cm
B: 5cm
C: 14 cm
D: 10 cm
Given:
[tex]m\angle ACD=45^\circ[/tex]
Point B is the center of the base.
Each side of the base = 10 cm
To find:
The height of the pyramid.
Solution:
It is given that the measure of each side of the base is 10 cm. It means the base is square. The length of the diagonal of a square is:
[tex]d=a\sqrt{2}[/tex]
Where, a is the side length of the square.
Putting [tex]a=10[/tex] in the above formula, we get
[tex]d=10\sqrt{2}[/tex]
It is given that point B is the center of the base. It means point B bisect each diagonal of a base. So,
[tex]BC=\dfrac{d}{2}[/tex]
[tex]BC=\dfrac{10\sqrt{2}}{2}[/tex]
[tex]BC=5\sqrt{2}[/tex]
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In triangle ABC,
[tex]\tan (45^\circ)=\dfrac{AB}{BC}[/tex]
[tex]1=\dfrac{h}{5\sqrt{2}}[/tex]
[tex]5\sqrt{2}=h[/tex]
[tex]7.0710678=h[/tex]
Round the value to the nearest integer.
[tex]h\approx 7[/tex]
The height of the pyramid is about 7 cm. Therefore, the correct option is A.
The picture is above I’ll mark as brainliest.
Answer:
8
Step-by-step explanation:
32 ÷ 4 = 8
32 ÷ 8 = 4 :D
4x8 = 32
32 divided by 4 is 8. 8 is your answer.
A population of mice is increasing exponentially. On Monday there were 120 most. One month later there were 132 most. Ready function tomorrow the situation. Determine the percent increase of the population of most of each month.
Answer:
[tex]y=120 * 1.1^x[/tex] --- function
The monthly rate is 10%
Step-by-step explanation:
Given
Let
[tex]x \to months[/tex]
[tex]y \to mice[/tex]
So, we have:
[tex](x_1,y_1) = (0,120)[/tex] --- Monday
[tex](x_2,y_2) = (1,132)[/tex] --- One month later
Required
The function
The function is represented as:
[tex]y=ab^x[/tex]
In [tex](x_1,y_1) = (0,120)[/tex], we have:
[tex]120 = a * b^0[/tex]
[tex]120 = a * 1[/tex]
[tex]120 = a[/tex]
[tex]a=120[/tex]
In [tex](x_2,y_2) = (1,132)[/tex], we have:
[tex]132 = a * b^1[/tex]
[tex]132 = a * b[/tex]
Substitute: [tex]a=120[/tex]
[tex]132 = 120 * b[/tex]
Solve for b
[tex]b = \frac{132}{120}[/tex]
[tex]b = 1.1[/tex]
So, the function is:
[tex]y=ab^x[/tex]
[tex]y=120 * 1.1^x[/tex]
To calculate the monthly rate (r), we have:
[tex]y =a(1 + r)^x[/tex]
Compare to: [tex]y =ab^x[/tex]
[tex]1 + r = b[/tex]
Make r the subject
[tex]r = b-1[/tex]
Substitute [tex]b = 1.1[/tex]
[tex]r = 1.1-1[/tex]
[tex]r = 0.1[/tex]
Express as percentage
[tex]r = 0.1*100\%[/tex]
[tex]r = 10\%[/tex]
HELPP HELPPP PLEASEEE
the table shows the result of a survey asking 48 students what type if pet they prefer.
if one student in the survey Is selected at random, what is the probability the student will prefer cat or dog?
Answer:
12/5
Step-by-step explanation:
The total number of students divided by the number of students who prefer dogs.
Mathematically:
48/20
=12/5
Therefore, that's the probability
What is the inverse fraction of f(x)=x/x-2
Answer:
[tex]inverse \ of \ f(x) : \frac{2x}{x-1}[/tex]
Step-by-step explanation:
[tex]y = \frac{x}{x-2}\\\\swap\ x\ and \ y\\\\x = \frac{y}{y-2}\\\\x(y -2) = y\\\\xy - 2x = y\\\\xy - y = 2x\\\\y(x-1)= 2x\\\\y = \frac{2x}{(x-1)}[/tex]
Step-by-step explanation:
Given two one-to-one functions f(x)f(x) and g(x)g(x) if
(f∘g)(x)=xAND(g∘f)(x)=x(f∘g)(x)=xAND(g∘f)(x)=x
then we say that f(x)f(x) and g(x)g(x) are inverses of each other. More specifically we will say that g(x)g(x) is the inverse of f(x)f(x) and
denote it by
g(x)=f−1(x)g(x)=f−1(x)
Likewise, we could also say that f(x)f(x) is the inverse of g(x)g(x) and denote it by
f(x)=g−1(x)
Given the function f(x)f(x) we want to find the inverse function, f−1(x)f−1(x).
First, replace f(x)f(x) with yy. This is done to make the rest of the process easier.
Replace every xx with a yy and replace every yy with an xx.
Solve the equation from Step 2 for yy. This is the step where mistakes are most often made so be careful with this step.
Replace yy with f−1(x)f−1(x). In other words, we’ve managed to find the inverse at this point!
Verify your work by checking that (f∘f−1)(x)=x(f∘f−1)(x)=x and (f−1∘f)(x)=x(f−1∘f)(x)=x are both true. This work can sometimes be messy making it easy to make mistakes so again be careful.
Explanation:
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is,
f−1(x)=2xx−1
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is, it is the inverse of function f(x).
That is,
f−1(x)=2xx−1
as required.
i need help with this
Answer: x=32
Step-by-step explanation:
The angles in a triangle add up to 180 degrees.
Since we know a=10 the other two angles must add up to 170 degrees.
[tex]2x+3x=170[/tex]
We can now solve for x
[tex]2x+3x=170\\5x=170\\\frac{5x}{5} =\frac{170}{5}\\x=34[/tex]
We can sub in x to both angles to see if they angles add up to 180
[tex]2(34)+3(34)+10=180\\68+102+10=180\\180=180[/tex]
What is the solution to this system?
x - y = 6
y = 2x - 5
Which word describes the slope of the line?
O Positive
O Negative
O Zero
O Undefined
Answer:
Option (1)
Step-by-step explanation:
Slope of a line is defined by the rule,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
Here, Rise and Run of the line are positive.
Therefore, sign of the slope of the line will be positive.
Option (1) will be the correct option.
Select the correct answer.
What is the slope of the line represented by the equation f(x) = -3x + 7?
ОА.
-7
OB. 3
O C. 3
OD. 7
Answer:
The slope should be -3.
Step-by-step explanation:
:)
If a = 27, b = -10 and c = 40, show that a-(6-c) +(a - b)-C.
Answer:
58
Step-by-step explanation:
a = 27, b = -10 and c = 40
= a - (6 - c) + (a - b) - C
= 27 - (6 - 40) + (27 - (-10)) - 40
= 27 - (-34) + (37) - 40
= 27 + 34 + 37 - 40
= 58
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{a - (6 - c) + (a - b) - c}[/tex]
[tex]\large\textsf{= 27 - (6 - 40) + (27 - (-10)) - 40}[/tex]
[tex]\large\textsf{6 - 40 = \bf -34}[/tex]
[tex]\large\textsf{= 27 - (-34) + (27 - (-10)) - 40}[/tex]
[tex]\large\textsf{= 27 + 34 + 27 + 10 - 40}[/tex]
[tex]\large\textsf{27 + 34 = \bf 61}[/tex]
[tex]\large\textsf{= 61 + 27 + 10 - 40}[/tex]
[tex]\large\textsf{61 + 27 = \bf 88}[/tex]
[tex]\large\textsf{88 + 10 - 40}[/tex]
[tex]\large\textsf{88 + 10 = \bf 98}[/tex]
[tex]\large\textsf{98 - 40}[/tex]
[tex]\large\textsf{= \bf 58}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 58}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
more help im dum lol
Answer:
32780
Step-by-step explanation:
Answer:
32,780
Step-by-step explanation:
It should be 30,000
hello i give points!
Describe how the data is dispersed in a box plot with the following data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.
Answer:
i would say that the box plot will look somewhat in the middle between 18 and 36 with 36 being the largest and 18 as the smallest
the data will also wont have a major difference in them
hope this helps<3
can someone please help me with this i dont have much time left
Answer:
Step-by-step explanation:
sin A = opposite/hypotenuse
=5/13
cos A =adjacent/hypotenuse
=12/13
tan A =opposite/adjacent
=5/12
cosec A = hypotenuse/opposite
=13/5
sec A = hypotenuse/adjacent
=12/5
cot A = adjacent/opposite
=12/5
Two complementary angles have measures 4x and x + 50. Find x.
Answer:
x =17
Step-by-step explanation:
Complementary angles add to 90
4x+ x+5 = 90
Combine like terms
5x+5 = 90
Subtract 5 from each side
5x+5-5 = 90-5
5x = 85
Divide by 5
5x/5 = 85/5
x =17
if f(x) = 3x + 2, what is f(5)?
Answer:
f(x)=3x+2 what is f(5)
f(5)=3(5)+2 = 17
Step-by-step explanation:
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]f(5)=17[/tex]
»»————- ★ ————-««
Here’s why:
Replace the 'x' with the given value (in this case 5) and solve.⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer....}}\\\\\rightarrow f(x)=3x+2; f(5)\\-------------\\\rightarrow f(5)=3(5)+2\\\\\rightarrow f(5)=15+2\\\\\rightarrow \boxed{f(5)=17}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
which of the following is equivalent to the quotient below
Answer:
B
Step-by-step explanation:
Hope it helps and if you need explanation let it in the comments
Answer:
B
Step-by-step explanation:
please help me if you can. please show how you got the answer.
Answer:
Step-by-step explanation:
The area of a circle is A = πr², where r is the radius. That means in order to solve this we have to find the value of x, which is the diameter of the lake, and then divide it in half to get the radius. To find x we will use similar triangles and proportions. x is the height of the big triangle and 4.5 is the height of the smaller triangle; 15.3 + 7.4 is the hypotenuse of the big triangle and 7.4 is the hypotenuse of the smaller triangle. Setting up our proportion:
[tex]\frac{x}{4.5}=\frac{15.3+7.4}{7.4}[/tex] which simplifies a bit to
[tex]\frac{x}{4.5}=\frac{22.7}{7.4}[/tex] and cross multiply to solve for x:
7.4x = 102.15 so
x = 13.8 That is the diameter of the lake. Divide it in half to get 6.9, the radius. Applying the area formula for a circle:
A = (3.14)(6.9)² and
A = 3.14(47.61) so
A = 149.5 which rounds to 150, Choice C
Any help on this please ?
Answer:
x=35
Step-by-step explanation:
because the angles are next to each other they are supplementary, which makes the total of the angle 180 degrees.
the equation would be:
180=x+14 +4x -9
add the like terms
180=5x =5
then subtract 5 from both sides
175=5x
then divide five from both sides
x=35
PLEASE HELP!!! If the quadratic equation has the form y = ax 2and y = ax 2+ c, then their axis of symmetry must always be?
Answer:
axis of symmetry , x = 0
Step-by-step explanation:
For the quadratic equation of the form [tex]ax^2 + bx + c[/tex],
the axis of symmetry is the straight line [tex]x =- \frac{b}{2a}[/tex]
( i) Given equation y = ax² + 0x + 0
b = 0, therefore axis of symmetry is x = 0
( ii ) Second equation y = ax² + 0x + c
b = 0, therefore axis of symmetry is x = 0
help asap Please show working
Answer:
(a) -12
(b) 37
(c) -840
Step-by-step explanation:
We simply have to plug in the values for each expression.
2 + -3(3) - 5 = 2 + -9 - 5 = -7 - 5 = -12
5(2) - 4(-3) + 3(5) = 10 - -12 + 15 = 10 + 12 + 15 = 22 + 15 = 37
7(2^3)(-3)(5) = 7(8)(-15) = 56(-15) = -840
select the right answer
Answer:
Blurry po
Step-by-step explanation:
Pwede kunan nyu ulit
What is the y-intercept of the function f(x) = -4.2^x
Answer:
[tex](0,-1)[/tex]
Step-by-step explanation:
The y-intercept always occurs when [tex]x=0[/tex]. To find the y-value of the y-intercept, substitute [tex]x=0[/tex] into your equation:
Given [tex]f(x)=-4.2^x[/tex], when [tex]x=0[/tex]:
[tex]f(x)=-4.2^0,\\f(x)=-(1)=-1[/tex]
Recall that [tex]n^0=1[/tex] for [tex]n\in \mathbb{R}[/tex]Therefore, the y-intercept of this function is [tex](0, -1)[/tex].
The mean sustained wind velocity, v, can be determined by the equation v = 6.3 StartRoot 1013 minus p EndRoot, where p is the air pressure, in millibars, at the center of the hurricane. What is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second? 103 millibars 194 millibars 363 millibars 910 millibars
Answer:
910 millibars
Step-by-step explanation:
According to the Question,
Given That, The mean sustained wind velocity equation [tex]v=6.3*\sqrt{1013-p}[/tex] And The mean sustained wind velocity is 64m/s (v=64) . where, p is the air pressure(in millibars).Now, the air pressure at the center of a hurricane when the mean sustained wind velocity is 64 m/s is
[tex]64=6.3*\sqrt{1013-p}\\\frac{64}{6.3} = \sqrt{1013-p}\\[/tex]
on squaring both sides we get,
(10.1587)² = 1012 - p ⇒ p = 908.80≈910millibar
p = 910millibars air pressure .
Answer: 910
Step-by-step explanation: Did the review and got it right
Pls help I don’t know how to do this
Answer:
the answer is D
BECAUSE it satisfied the conditions
HELP HELP HELP HELP HELP HELP HELP HELP
Answer:
first option is correct
Step-by-step explanation:
3x+12+x=180 degree (being linear pair)
4x+12=180
4x=180-12
x=168/4
x=42
answer please? a girl needs help like right now:))
Answer:
No
Step-by-step explanation:
Which of the following are equivalent to
a^2•a^10
Select all that apply
A) a^8•a^4
B) a^4•a^5
C) a^12
D) a^7•a^5
E) a^20
F) a^2•a^6
find the volume of the larger one pls
Answer:
284 u^3
Step-by-step explanation:
a b c d e f g h i j k l m n o p q r s t u v w x y z
Como se encuentra la mediana?
Answer:
Para encontrar la mediana: Organice los puntos de datos de menor a mayor. Si el número de puntos de datos es impar, la mediana es el punto de datos intermedio de la lista. Si el número de puntos de datos es par, la mediana es el promedio de los dos puntos de datos intermedios de la lista.
Step-by-step explanation:
que tenga un lindo día
expand and simplify (x-5)^2
^2= to the power of 2
Step-by-step explanation:
thats my answer thankyou
mark me as BRAINLIEST
follow me
carry on learning
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
[tex] \large{ \tt{✤ \: FIRST ,\: MEMORISE \: THESE}} : [/tex]
[tex](a + b)^{2} = {a}^{2} + 2ab + {b}^{2} [/tex][tex] (a - b) ^{2} = {a}^{2} - 2ab + {b}^{2} [/tex][tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex][tex] {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab \: [/tex] or [tex] {(a - b)}^{2} + 2ab[/tex][tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]
[tex] \large{ \tt{⋆ \: (x - 5) ^{2} }}[/tex]
Use the formula of ( a - b ) ². Assume ' x ' as ' a ' & ' 5 ' as ' y ' :[tex] \large{ \tt{↦ {x}^{2} - 2 \times x \times 5 + {5}^{2} }}[/tex]
[tex] \boxed{ \large{ \tt{↦ \: {x}^{2} - 10x + 25 }}}[/tex]
Hence , the required answer is x² - 10x + 25And we're done! ♡
[tex] \large{ \# \: \mathfrak{StayInAndExplore \: ☂}}[/tex]
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