Step-by-step explanation:
An expression obtained from the square of a binomial equation is a perfect square trinomial. An expression is said to a perfect square trinomial if it takes the form ax2 + bx + c and satisfies the condition b2 = 4ac. The perfect square formula takes the following forms: (ax)2 + 2abx + b2 = (ax + b)
Answer:
x2 − 4x + 4
x2 + 10x + 25
Step-by-step explanation:
The average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?.
the percentages of people at different ages in the life span are more similar, creating what is called the
Answer:
it is called rectangularization
Step-by-step explanation:
Please answer quickly
Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
f(x)=x+a/b
g(x)=cx-d
Part 2. Show your work to prove that the inverse of f(x) is g(x).
Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y=x on the same graph.
Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y=x on the same graph.
Task 2
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation
a√x+b+c=d
Part 2. Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation. Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.
Part 3. Explain why the first equation has an extraneous solution and the second does not.
f(x)=(x+a)/b
or bf(x)=x+a
let f(x)=y
by=x+a
flip x and y
bx=y+a
or y=bx-a
or f^{-1}(x)=bx-a
also g(x) is inverse of f(x)
bx-a=cx-d
so b=c,a=d
again let g(x)=y
y=cx-d
flip x and y
x=cy-d
cy=x+d
y=(x+d)/c
or g^{-1}(x)=(x+d)/c
also f(x) is inverse of g(x)
so (x+a)/b=(x+d)/c
so a=d,b=c
so in either case a=d,b=c
take b=c=1
a=d=2
f(x)=(x+2)/1=x+2
g(x)=1x-2=x-2
so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0
g(x) with y-intercept -2 and slope 0
if we take b=c=2,a=d=3
f(x)=(x+3)/2=x/2+3/2
g(x)=2x-3
here f(x) is of slope 1/2 and y-intercept 3/2
g(x) is of slope 2 and y intercept -3
part 3.
f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d
An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.
Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.
Part 2: g(x) = 3x - 2, the inverse.
Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.
What is inverse function?
An inverse function in mathematics exists function which "reverses" the another function.
TASK 1
Part 1
Let y = f(x) = (x + a) / b
x = g(y) = by-a = cy-d,
so c = b and d = a.
Let d = a = 2 and c = b = 3
f(x) = (x+2) / 3 and g(x) = 3y-2.
Part 2
y = f(x) = (x+2) / 3
3y = x+2
x = 3y-2 = g(y)
so g(x) = 3x - 2, the inverse.
Part 3
g(f(x)) = 3
f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,
so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.
x -2 -1 0 1 2
f(x) 0 1/3 2/3 1 4/3
g(x) -8 -5 -2 1 4
Part 4
The graph is given below.
TASK 2
Part 1
(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5
(b) Let a=-1, b=2, c=3, d=4
(a) Multiply both sides by
[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]
[tex]$ x-36+30=-5 \sqrt{x }[/tex]
[tex]$ x-6=-5 \sqrt{x}$[/tex]
Square both sides:
[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].
Part 2
(a) So x=36 or 1 (apparently).
Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.
So x=36 is an extraneous solution.
substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.
(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.
Substitute x=1 in the original equation: -1+2+3=4 is true.
So x = 1 is the solution.
Part 3
(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].
(b) the solution was simpler and there was no ambiguity.
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- 3< t <2
t is an integer.
Write down all the possible values of t.
Answer:
-2, -1, 0, 1
Step-by-step explanation:
-2
-1
0
1
All the possible values of t in the inequality - 3 < t < 2 is,
t = - 2, - 1, 0, 1
Used the concept of inequality that states,
A relation by which we can compare two or more mathematical expressions is called an inequality.
Given that;
The inequality is,
- 3 < t < 2
Here the given inequality means all the values of t are lies between - 3 and 2.
That is,
t = - 2, - 1, 0, 1
Therefore, the value of t are t = - 2, - 1, 0, 1
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Find the distance between the points
a. 4
b. 5
c. 6
d. 7
Answer:
b. 5
Step-by-step explanation:
:) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
:)!!!!!!!!!!!!!!!!!!!
:)
<3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3
find the lcm of 3, 6 and 8
Answer:
24
Step-by-step explanation:
3x8=24
6x4=24
8x3=24
On Tuesday, a restaurant serves iced tea to 24 of its 160 customers. What percent of the customers order iced tea
Answer:
15%
Step-by-step explanation:
24/160 = 0.15
0.15*100 = 15
The quotient of a number x and 4 is at most 5.
Answer:
x ÷ 4 ≤ 5
Step-by-step explanation:
Find the perimeter. Simplify your answer.
Answer:
3z+13
Step-by-step explanation:
Perimeter is found by adding all the sides
z+2+z+2+z+9
3 z variables 2+2+9=13
Simplified equals
3z+13
Hope this helps!
Please mark this answer as brainiest :)
Kate had 50 thousands-blocks in her package of base-ten blocks. How many ten thousands-blocks does that equal?
5
50
500
5000
Step-by-step explanation:
50000÷10
=5000
MARK ME BRAINLIEST1.8 0.087 − 0.947 + 2.2 0.044
Answer:
2
Step-by-step explanation:
im smart
HELPPPPP!!As soon as possible
Answer:
answer is D :
√24 = 4.89
which is the nearest to 5 and possible answer
For 30 minutes you do a combination of walking and jogging. At the end of your workout your pedometer displays a total of 2.5 miles. You know that you walk .05 miles per minute and jog .1 miles per minute. For how much time were you walking
plzzz help?????????????????????
Answer:
Step-by-step explanation:
Pythagorean theorem: base ² +altitude² = hypotenuse²
1) hypotenuse² = base² + altitude²
x² = 6² + 3²
= 36 + 9
= 45
x = √45
x = 6.7 cm
4) base ² +altitude² = hypotenuse²
x ² + 3.7 ² = 4.2 ²
x ² + 13.69 = 17.64
x ² = 17.64 - 13.69 = 3.95
x = √3.95
x = 1.99 cm
10)c ² = a ² + b ²
= 3 ² +4 ²
= 9 + 16
c ² = 25
c = √25 = 5
11) a ² + b ² = c ²
9 ² +b² = 13 ²
81 + b² = 169
b² = 169 - 81 = 88
b = 9.38
12) a² + b² = c²
12² + b² = 22²
144 + b² = 484
b² = 484 - 144 = 340
b =√340 = 18.44
Is that the right answer
Write an equation in slope-intercept form of the line shown. (-6, 4) (-2, 2)
Teacher Kaye is saving ₱2,000 every month by depositing it in a bank that gives an interest of 1% compounded quarterly. How much will she save in 5 years?
Answer:
1,23,098
Step-by-step explanation:
............
If you multplied 5x10, would you get the same answer as 5x5x5? Explain your reasoning. DO NOT G O O G L E THE ANSWER!!!!!!
No because for 5x10, you just add 10 5 times for 50. For 5x5x5, you multiply 5x5 and get 25 then multiply it again with the other 5 and get 125.
Answer:
No
Step-by-step explanation:
No, because 5 × 5 × 5 = 25 × 5 and that does not equal 10×5.
Find HGI, FGH and FGI I’ll mark the brainiest
Answer:
∠FGH = ∠HGI = 29°
∠FGI = 58°
Step-by-step explanation:
GH is marked as an angle bisector, so we have ...
∠FGH = ∠HGI
2x -9 = 3x -28
19 = x . . . . . . . . . . . . add 28-2x to both sides
Of course, the angle FGH is the sum of its parts. Then the angle measures are ...
(2x -9)° = (2·19 -9)° = 29°
∠FGH = ∠HGI = 29°
∠FGI = 58°
3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of
cardboard that is 10 inches by 18 inches. The box will be formed by making cuts as shown in
the diagram and folding up the sides.
a) Write a function that models the volume of the box.
b) What are the dimensions of the box with the maximum volume? Round to the nearest tenth.
el
at
c) What is the maximum volume of the box?
The volume of the box is the amount of space in it.
The dimension of the postcard is:
[tex]\mathbf{Length = 10}[/tex]
[tex]\mathbf{Width = 18}[/tex]
Let x represents the length of the cut.
So, the dimension of the box is:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
(a) The function that represents the volume of the box
This is calculated as:
[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]
So, we have:
[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
(b) The dimension that maximizes the volume
We have:
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]
Set to 0
[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = 7.3,2.1}[/tex]
The value x = 7.3 is greater than the dimension of the box.
So, we have:
[tex]\mathbf{x = 2.1}[/tex]
Recall that:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, we have:
[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]
[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]
[tex]\mathbf{Height = 2.1}[/tex]
Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1
(c) The maximum volume
This is calculated as the product of the dimension of the box
So, we have:
[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]
[tex]\mathbf{Volume = 168.1}[/tex]
Hence, the maximum volume of the box is 168.1 cubic inches
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Please help me! Bots keeps answering my questions and I really need an answer
Answer:
D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft
34.98+12.24=?
answers please
Answer:
Hello!
After reading your question I have calculated the correct answer to be:
47.22
Step-by-step explanation:
The way I solved this equation was I first split the equation into two parts.
I took the two whole numbers, being "34" and "12", and made their own equation:
"34+12=?"
And then I took the two partial numbers "0.98" and "0.24" and made their own equation:
"0.98+0.24=?"
I then solved both equations:
"34+12= 46"
"0.98+0.24= 1.22"
And added those two solutions together to come up with the final solution:
"46+1.22= 47.22"
Hope this helped!
Answer:
47.22 is the answer
Step-by-step explanation:
hope it helps you
PLEASE HELP!
Your class hopes to collect at least 325 of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.
Part 1: Write an equation that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass its goal.
Part 2: How many cans are needed to meet or surpass the goal?
Answer:
Part 1. 325 - (135 + 89) = c
Part 2. ≤ 101
Step-by-step explanation:
Brainliest Please!Planes S and R both intersect plane T .
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
Which statements are true based on the diagram? Select three options.
Plane S contains points B and E.
The line containing points A and B lies entirely in plane T.
Line v intersects lines x and y at the same point.
Line z intersects plane S at point C.
Planes R and T intersect at line y
Answer:
B,D,E
Step-by-step explanation:
Please help me! Im making the first correct answer brainliest!
Answer:
You didn't ask a question.
Step-by-step explanation:
A survey was given to people who own a certain type of car. What percent of the people surveyed were completely satisfied with the car?
Answer:
60% if this is an edge question
NEED ASAP ! WORTH 20 POINTS
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
-1
Step-by-step explanation:
Using the formula to find gradient or slope:
m = (y2 - y1)/ (x2 - x1)
Using any two points from the graph: (-2, 0) (0, -2)
Substitute this into the equation to get the answer of -1.
Enter the value of x that makes the equation 3x + 4 + 2x + 2 = -24
answer? and how would I answer this.
Answer:
x = -6
Step-by-step explanation:
Combine like terms.
5x + 6 = -24
Subtract 6 from both sides.
5x = -30
Divide by 5 on both sides.
x = -6
Follow Me:-
[tex]3x + 4 + 2x + 2 = - 24 \\ \\ = > 5x + 6 = - 24 \\ \\ = > 5x = - 24 - 6 \\ \\ = > 5x = - 30 \\ \\ = > x = \cancel \frac{ - 30}{5} \\ \\ = > x = - 6[/tex]
Hope This Helpswhat is greater: 19/5, 27/5, 10/3, 14/5
Answer:
I think the greater fraction is 27/5
Answer:
27/5Step-by-step explanation:
what is greater: 19/5, 27/5, 10/3, 14/5
fractions are divisions, we divide to see the greater
19/5= 3.8
27/5= 5.4
10/3= 3.33
14/5= 2.8