Answer:
[tex] { x^2+3x-4} [/tex]
Step-by-step explanation:
Factor top and bottom.
The numerator is a difference of two squares, and the denominator is a quadratic.
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} } [/tex]
= [tex]\frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}[/tex]
= [tex] \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)} [/tex]
If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give
= [tex] { (x-1)(x+4)} [/tex]
= [tex] { x^2+3x-4} [/tex]
Answer:
The answer is
x² + 3x - 4Step-by-step explanation:
[tex] \frac{9 {x}^{2} - ( { {x}^{2} - 4})^{2} }{4 + 3x - {x}^{2} } [/tex]
To solve the expression first factorize both the numerator and the denominator
For the numerator
9x² - ( x² - 4)²
Expand the terms in the bracket using the formula
( a - b)² = a² - 2ab + b²
(x² - 4) = x⁴ - 8x² + 16
So we have
9x² - (x⁴ - 8x² + 16)
9x² - x⁴ + 8x² - 16
- x⁴ + 17x² - 16
Factorize
that's
(x² - 16)(-x² + 1)
Using the formula
a² - b² = ( a + b)(a - b)
We have
(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)
For the denominator
- x² + 3x + 4
Write 3x as a difference
- x² + 4x - x + 4
Factorize
That's
- ( x - 4)(x + 1)
So we now have
[tex] \frac{(x + 4)(x - 4)( 1 - x)(1 + x)}{ - (x - 4)(x + 1)} [/tex]
Simplify
[tex] \frac{ - (x + 4)(1 - x)(1 + x)}{x + 1} [/tex]
Reduce the expression by x + 1
That's
-( x + 4)( 1 - x)
Multiply the terms
We have the final answer as
x² + 3x - 4Hope this helps you
Pete earns graduated commission on his sales each month. He earns 7% commission on the first $35,000 in sales and 9% on anything over that. If Pete had $43,000 in sales this month, how much commission did he earn?
a. $2,610
b. $3,170
c. $3,870
d. $6,880
Please select the best answer from the choices provided A B C D
Answer:
b.$3170
Step-by-step explanation:
43,000-35,000=8,000
SO you would find 9% commission on 8,000
8,000x.09=720
then, you would find his normal commission if he only made 35,000
so you would do 35,000x.07=2450
you would, then, add the two together to get his entire commission, which is $3170
Answer:
b
Step-by-step explanation:
A scout troop consists of 10 boys and 10 girls. The total weight of their backpacks is 600 pounds. All the boys have to carry backpacks that weigh the same amount. All the girls, too, must carry bags of equal weight, but the girls' backpacks are 1.5 times lighter than the boys' backpacks. How heavy is one boy's backpack?
Answer:
36 lbs
Step-by-step explanation:
let the weight of each boy's backpack be B and the weight of each girl's backpack be G.
Given that the total weight of all (i.e 10 boys' and 10 girls') backpacks equals 600 lbs, i.e.
10B + 10G = 600 (simplifying by dividing both sides by 10)
B + G = 60 ------- eq 1
Also given that a girl's backpack is 1.5 times LESS than a boy's backpack.
written another way, we can say that a boy's backpack is 1.5 times MORE than a girl's backpack, or:
B = 1.5G (rearranging)
B - 1.5G = 0 ------ eq 2
We can solve eq 1 and eq 2 by elimination,
(eq 1) - (eq 2)
(B + G) - (B - 1.5G) = 60 - 0
B + G - B + 1.5G = 60
G + 1.5G = 60
2.5G = 60 (divide both sides by 2.5)
G = 60 / 2.5
G = 24 lbs (substitute this into equation 1)
B + G = 60
B + 24 = 60
B = 60 - 24
B = 36 lbs
Factorise : x²-17x+ 60 Step by Step
Answer:
Step-by-step explanation:
x^2 - 17 x + 60
we should find two numbers such that their sum is equal to -17 and product is equal to 60
The two numbers are -12 and -5
now, x^2 - 12 x - 5 x + 60 { splitting the middle term }
x ( x- 12 ) - 5 ( x - 12 )
= ( x - 5 ) ( x - 12 )
hope this helps
plz mark as brainliest !!!!!!
Answer:
x² - 17x + 60 = (x - 12)(x - 5)Step-by-step explanation:
[tex]x^2-17x+60\quad \implies\quad a=1\,,\quad b=-17\,,\quad c=60\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot1}=\dfrac{17\pm\sqrt{289-240}}{2}=\dfrac{17\pm\sqrt{49}}{2}\\\\x_1=\dfrac{17-7}{2}=5\quad,\qquad x_2=\dfrac{17+7}{2}=12\\\\\\x^2-17x+60=(x-5)(x-12)[/tex]
or:
x² - 17x + 60 =
= x² - 12x - 5x +60 =
= x(x - 12) - 5(x - 12) =
= (x - 12)(x - 5)
the maximum value of 3/5sinx-12cosx+19
Answer:
Step-by-step explanation:
The given trigonometric expression is :
11 cos^2 x +3 sin^2 x+6sinx cosx +5
or, we can write it as,
(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5
Again, after rearranging the terms, we can write the whole expression as,
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
Then if you factor the following underlined section as you would with a polynomial:
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
You get:
(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5
Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.
So, now the whole expression becomes,
(3 cos x + sin x)^2 +7
Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),
The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.
So, I've attached a screenshot from a relevant document below:
Here, a=3 and b=1,
So, R= √10
As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.
Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.
i.e., in our case between (-√10) to √10.
Again, coming back to our original expression,
(3 cos x + sin x)^2 +7
The value of the term in bracket will lie between (-√10) and √10.
But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.
So, the minimum value will be,
(0)^2 + 7=7
and the maximum value will be,
(√10)^2 +7 = 17
PLEASE ANSWER QUICKLY ASAP
READ QUESTIONS CAREFULLY
Answer:
Increase in profit = 531.52
Step-by-step explanation:
I'll take your word for it.
What you'd need to do for each kind of pizza and price, multiply the number sold and profit/loss for each, and add them up.
Calculations have been tabulated and shown in the attached diagram.
Answer
Increase in profit
= 2221.88 - 1690.36
= 531.52
how many seconds are there in a month of 30 days express it in scientific notation
Calculate the perimeter of a semi-circle
whose diameter is 14cm
perimeter of a semicircle is [tex]\frac{2\pi r}{2}+2r=\frac{d\pi}2 +d[/tex]
$d=14$
so, perimeter= $14\cdot\frac{22}7\cdot \frac{1}2+14=22+14=36$ cm
Answer:
Perimeter of semi-circle = 36 cm
Step-by-step explanation:
diameter = d = 14 cm
Perimeter of semicircle = Circumference of semi-circle + diameter
= [tex]\frac{1}{2}\pi d + d[/tex]
= [tex]\frac{1}{2}*\frac{22}{7}*14 +14\\[/tex]
= 22 + 14
= 36 cm
PLEASE ANSWER!!! Select the correct answer from each drop-down menu. Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
Function transformation involves changing the position of a function.
The graph of g(x) is the graph of f(x) translated 2 units right, and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]
The function is given as:
[tex]\mathbf{f(x)=3x + 1}[/tex]
The graph of g(x) passes through (2,1) and (0,-5).
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{-5-1}{0-2}}[/tex]
[tex]\mathbf{m = \frac{-6}{-2}}[/tex]
[tex]\mathbf{m = 3}[/tex]
The equation is then calculated as:
[tex]\mathbf{g(x) = m(x -x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]
By comparing [tex]\mathbf{f(x)=3x + 1}[/tex] and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]
The graph of f(x) is shifted 2 units to the right
Read more about function transformation at:
https://brainly.com/question/13810353
CAN ANYBODY HELP ME OUT
Answer:
Correct option is
b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.
Step-by-step explanation:
Here, we are given the line RQ, which is divided in two equal parts by a line PS which is perpendicular to RQ.
The foot S of PS is on the line RQ.
First of all, let us do a construction here.
Join the point R with P and P with Q.
Please refer to the attached image.
Now, let us consider the triangles PQS and PRS:
Side QS = RS (as given)[tex]\angle PSR = \angle PSQ = 90^\circ[/tex]Side PS = PS (Common side in both the triangles)Now, Two sides and the angle included between the two triangles are equal.
So by SAS congruence we can say that [tex]\triangle PRS \cong \triangle PQS[/tex]
Therefore, the corresponding sides will also be equal.
RP = QP
RP is the distance between R and P.
QP is the distance between Q and P.
Hence, to prove that P is equidistant from R and Q, we have proved that:
b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.
which of these correctly rearranges the terms in this polynomial so like terms are next to each other ? 3-6x+4x^2+3x-6x^2-4 PLEASE HELP!!
Answer:
A is the answer
Step-by-step explanation:
Answer:
the answer is A.
Step-by-step explanation:
Suppose the graph in part A can be represented by the function f(x)=1.5x+750/x . What is the domain of this function? Consider the context of the function in your answer.
Answer:
Domain:
( − ∞ , 0 ) ∪ ( 0 , ∞ ) , { x | x ≠ 0 }
Step-by-step explanation:
i used math. way for help
I need help with 3 and 4
Answer:
Step-by-step explanation:
3) G
Step-by-step explanation:
Q(-1,-1) R(3,1) S(2,-4)
x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)
Q -1+2 -1+3 (1,2) (-1,-2)
R 3+2 1+3 (5,4) (-5,-4)
S 2+2 -4+3 (4,-1)
The width of a rectangle measures (2.3a + 9.9) centimeters, and its length
measures (6.3a - 2.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
12.2a +3.7
O 7.3 + 8.60
O 17.2a + 14.6
O 7.4 +24.4a
Answer:
17.2a+14.6
Step-by-step explanation:
A. X>0
B. xis all real numbers.
C. O sxs 5
D. -5 sxs 5
Answer:
B
Step-by-step explanation:
The domain of a function is all of the x values of a function. Since there seem to be no constraints on the values of x (we know this because the function is continuous and it goes on forever in both sides), the answer is B.
Answer:
B. All real numbers
Step-by-step explanation:
Hey there!
Well the domain is all the x-values in the graph and by looking at where the lines are going we can tell that the graph domain is all real numbers.
Hope this helps :)
Evaluate -3(8).
I know the answer is -24 but I don’t know who to work it out, can someone please help me
Answer:
-24
Step-by-step explanation:
-3 multiply 8 = -24
Because when ever you multiply a negative number with a positive number result will always be negative and 3 multiply 8 is 24.
Answer: -24
Step-by-step explanation: When you're asked to multiply
positives and negatives together, the rules are simple.
positive times a positive is a positive
positive times a negative is a negative
negative times a positive is a negative
negative times a negative is a positive
One way that I think will help you is to think
about the problem in terms of the signs.
If the signs are the same, the product will always be positive.
For example, (+3) · (+6) = +18 and (-6) · (-2) = +12.
If the signs are different, the product is negative.
So (+6) · (-4) is -24 and (-10) · (+5) is -50.
So don't get caught up on the signs.
Do the problem first, then determine if the
signs are the same or if they are different.
Which geometric figure has 120 rotational symmetry?
Answer:
Triangle
Step-by-step explanation:
Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry
Write the other side of this equation so it's true for all values of x: 1/2(6x-10)-x=?
Answer:
2x 5
Step-by-step explanation:
1/2(6x - 10) - x =
= 3x - 5 - x
= 2x - 5
The other side of the given equation so it's true for all values of x is 2x-5.
Given that, 1/2(6x-10)-x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 6x/2 - 10/2 -x
= 3x-5-2
= 2x-5
Therefore, the other side of the given equation so it's true for all values of x is 2x-5.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
1) UN MOVIL A SE MUEVE DESDE UN PUNTO CON VELOCIDAD CONSTANTE DE 20m/s EN EL MISMO INSTANTE A UNA DISTANCIA DE 1200m, OTRO MOVIL B SALE Y PERSIGUE AL MOVIL A CON VELOCIDAD CONSTANTE DE 40m/s.¿ EN QUE TIEMPO Y A QUE DISTANCIA B ALCANZA a
Answer:
El móvil B necesita 60 segundos para alcanzar al móvil A y le alcanza una distancia de 2400 metros con respecto al punto de referencia.
Step-by-step explanation:
Supóngase que cada movil viaja en el mismo plano y que el móvil B se localiza inicialmente en la posición [tex]x = 0\,m[/tex], mientras que el móvil A se encuentra en la posición [tex]x = 1200\,m[/tex]. Ambos móviles viajan a rapidez constante. Si el móvil B alcanza al móvil A después de cierto tiempo, el sistema de ecuaciones cinemáticas es el siguiente:
Móvil A
[tex]x_{A} = 1200\,m+\left(20\,\frac{m}{s} \right)\cdot t[/tex]
Móvil B
[tex]x_{B} = \left(40\,\frac{m}{s} \right)\cdot t[/tex]
Donde:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Posiciones finales de cada móvil, medidas en metros.
[tex]t[/tex] - Tiempo, medido en segundos.
Si [tex]x_{A} = x_{B}[/tex], el tiempo requerido por el móvil B para alcanzar al móvil A es:
[tex]1200\,m+\left(20\,\frac{m}{s} \right)\cdot t = \left(40\,\frac{m}{s} \right)t[/tex]
[tex]1200\,m = \left(20\,\frac{m}{s} \right)\cdot t[/tex]
[tex]t = \frac{1200\,m}{20\,\frac{m}{s} }[/tex]
[tex]t = 60\,s[/tex]
El móvil B necesita 60 segundos para alcanzar al móvil A.
Ahora, la distancia se obtiene por sustitución directa en cualquiera de las ecuaciones cinemáticas:
[tex]x_{B} = \left(40\,\frac{m}{s} \right)\cdot (60\,s)[/tex]
[tex]x_{B} = 2400\,m[/tex]
El móvil B alcanza al móvil A a una distancia de 2400 metros con respecto al punto de referencia.
a hotel manager wants miriam to tile their lobby using the dame design she created for Mr.Rivera.The lobby measures 45 feet by 45 feet. he wants the outer edge to be the same color as the center tile. will this occur ? justify your answer
Answer:
Yes it will occur
Step-by-step explanation:
The lobby measures 45 feet by 45 feet
Area of the lobby = 45 * 45
=2025 ft^2
So, the lobby has 2025 tiles
subtract 1 black tile in the center
2025 tiles - 1 black tile =2024 tiles
The number of blue tiles and black tiles is 2024 tiles
He wants the outer edge to be the same color as the center tile so, divide by 2
2024/2 = 1012 tiles
The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles
Please I Need Help :(
Answer:
D, 9^4 * 8^4
Step-by-step explanation:
The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.
I confirmed D is right on a calculator also.
Answer:
D
Step-by-step explanation:
How to find the area of the shaded region
Answer:
61 cm^2.
See below.
Step-by-step explanation:
I need helpp!! match the building block of geometry to the statement that defines it.
1)DIAGRAM
A)a formal statement declaring the meaning of
a word
2)DEFINITION
B)a visual tool representing mathematical
ideas to be interpreted
3)THEOREM
C)a mathematical statement proven using
postulates and definitions
4)POSTULATE
D)a mathematical statement taken as a fact
Answer:
1) [tex]DIAGRAM \mapsto B[/tex]
2) DEFINITION [tex]\mapsto A[/tex]
3) THEOREM [tex]\mapsto C[/tex]
4) POSTULATE [tex]\mapsto D[/tex]
Step-by-step explanation:
1) DIAGRAM B) A visual tool representing mathematical ideas to be interpreted
A diagram is the depiction or representation of information using symbols
2) DEFINITION A) A formal statement declaring the meaning of a word
A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign
3) THEOREM C) A mathematical statement proven using postulates and definitions
A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates
4) POSTULATE D) A mathematical statement taken as a fact
An assumed truth taken as the foundation for further reasoning
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
Answer:
83 adult tickets and 217 student tickets.
Step-by-step explanation:
Let number of adult tickets sold = [tex]x[/tex]
Given that total number of tickets = 300
So, number of student tickets = 300 - [tex]x[/tex]
Cost of adult ticket = $15
Cost of student ticket = $11
Total collection from adult tickets = $[tex]15x[/tex]
Total collection from student tickets = [tex](300-x)\times 11 = 3300-11x[/tex]
Given that overall collection = $3630
[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]
So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.
Now , collection = $3632
X+2/x-2 - x+3/x-1 solve
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Hi my lil bunny!
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[tex]x+\frac{2}{x} -2-x+\frac{3}{x} -1[/tex]
[tex]= \frac{-3x + 5}{x}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
(3)/(22)+(-(1)/(11) find the sum without use of a number line
Answer:
1/22
Step-by-step explanation:
Simplify it.
It becomes 3/22-1/11
Change the denominator to 22 becasue that is the LCM.
It becomes 3/22-2/22 which is 1/22. :)
P(x) =2x3 -11x2 -4x +1 g(x) =2x +1
Answer:
see explanation
Step-by-step explanation:
If (2x + 1) is a factor then x = - [tex]\frac{1}{2}[/tex] is a root and P(- [tex]\frac{1}{2}[/tex] ) = 0 ← Factor theorem
P(- [tex]\frac{1}{2}[/tex] )
= 2(- [tex]\frac{1}{2}[/tex] )³ - 11(- [tex]\frac{1}{2}[/tex] )² - 4(- [tex]\frac{1}{2}[/tex] ) + 1
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{11}{4}[/tex] + 2 + 1
= - [tex]\frac{12}{4}[/tex] + 3
= - 3 + 3
= 0
Since P(- [tex]\frac{1}{2}[/tex] ) = 0 then g(x) is a factor of P(x)
PLS HELP I REALLY NEED IT
Answer:
x=9
Step-by-step explanation:
<B = <E from the concurrency statement
5x = 45
Divide by 5
5x/5 = 45/5
x = 9
Answer:
Hey there!
These are similar triangles, and similar triangles have congruent angles.
Thus, we have 5x=45
Simplifying, we have x=9
Let me know if this helps :)
Let f(x) = 4x - 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.
Answer:
7x + 2
Step-by-step explanation:
Answer:
All real numbers
Step-by-step explanation:
Adding f(x) and g(x) together gets you, (4x-5) + (3x-7) = 7x - 12
If you graph this function you get a slanted line, which extends forever so the domain will be all real numbers.
Please Help!!! What is 2x = 40?
Answer:
Friend your answer is 20
Step-by-step explanation:
You divide 40 by the co-efficient of 2=20
[tex]\boxed{x = 20}[/tex]
There is only one step to this equation. We use inverse operations to isolate the x by dividing 2 on both sides; because 2 is being multiplied by x, and the inverse operation for multiplication is division.
2x/2 = x
40/2 = 20
The equation now looks like:
x = 20
This is your answer.
A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 mark
Answer:
The fraction filled with water is 7/40
Step-by-step explanation:
Okay.
Here we start by calculating the volume of the cylindrical tank.
Mathematically, that would be;
V = π * r^2 * h
From the question
r = 80 cm = 80/100 = 0.8 meters
h = 1.4 meters
π = 22/7
Plugging these values into the volume equation, we have;
V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3
But mathematically;
1 m^3 = 1000 liters
So 2.816 m^3 = 2.816 * 1000 = 2816 liters
So the fraction filled with water will be;
492.8/2816 = 0.175 = 175/1000 = 7/40
