A square painting has an area of 81x^2 - 90x + 25. A second square painting has an area of 25x^2 + 30x + 9. Part A: What is an expression that represents the difference of the areas of the paintings? Show two different ways to find the solution.Part B: The paintings have areas of 1,600in^2 and 484in^2, respectively. A potential buyer went to an exhibition and argued that the value of xfor both paintings is the same. Is he right? Prove it.
Answer:
56x² - 120x + 16 ; (9x - 5)² - (5x - 3)²
x in both equations is 5
Step-by-step explanation:
Painting 1 : 81x^2 - 90x + 25
Painting 2 : 25x^2 + 30x + 9
Expression for the difference between the two paintings :
Painting 1 - painting 2
(81x^2 - 90x + 25) - (25x^2 + 30x + 9)
81x^2 - 90x + 25 - 25x^2 - 30x - 9
81x² - 25x² - 90x - 30x + 25 - 9
56x² - 120x + 16
2.)
81x^2 - 90x + 25 = 1600in²
25x^2 + 30x + 9 = 484 in²
Factorizing each equation :
81x^2 - 90x + 25 = 1600 in²
(9x - 5)^2 = 1600 in²
25x^2 + 30x + 9 = 484 in²
(5x - 3)^2 = 484
(9x - 5)² - (5x - 3)²
2.)
(9x - 5)^2 = 1600
Take square root of both sides
9x - 5 = 40
9x = 40 + 5
9x = 45
x = 45/9
x = 5
(5x - 3)^2 = 484
Take square root of both sides
5x - 3 = 22
5x = 22 + 3
5x = 25
x = 25/5
x = 5
Elizabeth purchased a $20 bus pass. Each time she rides the bus $1.25 is deducted from the pass. What equation would represent this scenario? *
12 points
y= 1.25x - 20
y= -1.25x + 20
y= 20x - 1.25
y= 20x + 1.25
Answer:
Y = 1.25x - 20
Step-by-step explanation:
Everytime she rides the bus 1.25 is taken away from that 20.
The x = Every ride
For example
say she rode the bus 5 times so it would be
1.25 × 5 = 6.25 now you take the answer and subtract it from the 20
20 - 6.25 = 13.75
I hope this helped :)
the following relation is a function?
if 10^3x=1/0.001,find the value of x
Answer:
x = 1
Step-by-step explanation:
Firstly, look at the left hand of the equation
1/0.001 = 1000 = 10^3
then
10^3x = 1000= 10^3
then
10^3x = 10^3
then
x= 1
ANYONE GONNA HELP?????
Answer:
1. [tex]\frac{135}{360}[/tex]xπx[tex]11^{2}[/tex]=142.5cm
2a. [tex]x^{2}[/tex] +2x= x(x+2)
2b. [tex]2x^{2}[/tex]-6x= 2x(x-3)
2c. 15x-10[tex]x^{3}[/tex]= 5x(3x-2[tex]x^{2}[/tex])
2d. 9[tex]x^{2}[/tex]+3[tex]x^{3}[/tex]= 3[tex]x^{2}[/tex](3+x)
3a. (x+8) (x+2)
3b. (X+4) (x+3)
3c. (x+12) (x+1)
4a. 4522.145
4b. 278.15
5a. 14.3
5b. 43.19
Answer:more free points yay
Step-by-step explanation:
What is the value of the missing angle ?
Answer:
30
Step-by-step explanation:
? = 180 - 150 = 30
Answer:
30°
Step-by-step explanation:
The line is 180 degrees so all you have to do is subtract 150° from 180°
You should end up with 30°
Whenever you see a straight line (IT HAS TO BE STRAIGHT), it is equal to 180°.
The graph of g(x) shown below resembles the graph of f(x) = x2, but it has
been reflected over the x-axis. Which is the equation of g(x)?
Answer:
A. g(x) = - x²
Step-by-step explanation:
f(x) reflex over x-axis: g(x) = - f(x)
Using translation concepts, it is found that the equation of g(x) is given by:
A. g(x) = -x².
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function f(x) = x² was reflected over the x-axis, that is, it was multiplied by -1, hence the equation for g(x) is given by:
g(x) = -f(x) = -x².
Which means that option A is correct.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ2
40 POINTS!!!!!!!! NEED HELP
Figure ABCD below is transformed to obtain figure A′B′C′D′:
A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 1, B prime at 2, negative 1, C prime at 2, negative 4, D prime at 4, negative 2.
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)
Part B: Are the two figures congruent? Explain your answer. (4 points)
Answer:
Hello! I just did the test this is on
Step-by-step explanation:
Part A-
reflect the shape across x
then move 1 to the right and 4 units down
Part B- Yes
It is still the same shape as well as the same size
3. The area A of a triangle varies jointly as the base b and the altitude h of the triangle. If the area
of a triangle is 70 cm2 when the base is 14 cm and the altitude is 10 cm, find the area if the base is
8 cm and the altitude is 12 cm.
Answer:
48cm²
Step-by-step explanation:
If the area A of a triangle varies jointly as the base b and the altitude h of the triangle, this is expressed as;
A = kbh
k is the constant of proportionality
If A = 70cm², b = 14cm and h = 10cm
Substitute
70 = k(14)(10)
70 = 140k
k = 70/140
k = 0.5
To get the area if base is 8 cm and the altitude is 12 cm;
A = 0.5*8*12
A = 48cm²
Hence the required area is 48cm²
evaluate 4r/ s if r=9 and s=2
Which percent is equivalent to 0.3?
Answer:
30%
Step-by-step explanation:
smart highschooler brain
Edin has £300 in his saving account. His bank offers him a fixed 5% intrest per annum ,for three years.How much interest will he have in three years
Answer:
£45
Step-by-step explanation:
Given data
P= £300
R=5%
T= 3 years
SI= PRT/100
substitute
SI= 300*5*3/100
SI=4500/100
SI= £45
Hence the interest is £45
Carol starts with $50 and saves $10 each week. Bill has $25 and saves $15 each week.
True or false, Carol and Bill will have the same amount of money at week 6.
Answer:
false
Step-by-step explanation:
i dont know dont trust me
false carol gots 110$ and bill gots 115 10 times 6 is 60 and 60 +50 is 110 15 times 6 is 90 + 25 is 115 so no they don't got the same
B
27 m
24 m
18 m
List angles largest to smallest
Answer:27,24,18
Step-by-step explanation:
sorry if it’s wrong but I think so
Which pair of segments in the figures below are congruent?
Answer:
it would be great if I could see the angles
Answer: D- BC and PN
Step-by-step explanation:
I got %100
17+10+9×9:27
[tex]17 + 10 + 9 \times 9 \div 27[/tex]
Answer:
30
Step-by-step explanation:
17 + 10 + 9 * 9 / 27
= 17 + 10 + 81 /27
= 17 + 10 + 3
= 20 + 10
= 30
please helppp!! ill give brainliest <333
Answer:
a
Step-by-step explanation:
Solve for x. 5 = 1/5x − 3
Enter your answer in the box.
x =
what is 6x^2-18x-3 simplified
Answer:
-6x-3
Step-by-step explanation:
Answer:
the ans is in the picture and how i got the ans thg hope it helps
(can i plz have brainlist it will make my day )
Step-by-step explanation:
Which fractions are less than 1 2 ? Select all that apply. A. 1 3 B. 4 6 C. 2 5 D. 5 8 E. 7 12
Answer:
Explanation below
Step-by-step explanation:
1/2 =0.5
1/3 = 0.333
4/6 = 0.667
2/5 = 0.4
5/8 = 0.625
7/12 = 0.583
The fractions less than 1/2 are:
1/3 and 2/5. (A and C).
what is the equation of a vertical line that passes through the points (3,-5)
Answer: x = 3
I hope this helps you and im not to late
An object is dropped from a height of 150 feet. Its heights s at time, t is given by the
equation s(t) =-16t^2+150 ,where s is measured in feet and t is measured in seconds.
Find the average rate of change of the height over the interval [1, 2.5).
O 1) -56 ft/sec
O2) 77 ft/sec
03) 56 ft/sec
O4) -35 ft/sec
Answer:
The average rate of change of the height over the interval [1, 2.5] is - 56 feet per second.
Step-by-step explanation:
Let [tex]s(t) = -16\cdot t^{2} + 150[/tex]. Geometrically speaking, average rate of change over a given interval ([tex]\bar v[/tex]), measured in feet per second, is determined by definition of secant line, which is defined:
[tex]\bar v = \frac{s(t_{2})-s(t_{1}) }{t_{2}-t_{1}}[/tex] (1)
Where:
[tex]s(t_{1})[/tex], [tex]s(t_{2})[/tex] - Initial and final position of the object, measured in feet.
[tex]t_{1}[/tex], [tex]t_{2}[/tex] - Initial and final times, measured in seconds.
If we know that [tex]t_{1} = 1\,s[/tex] and [tex]t_{2} = 2.5\,s[/tex], then the average rate of change over the interval [tex][1,2.5][/tex]:
[tex]s(1) = -16\cdot (1)^{2}+150[/tex]
[tex]s(1) = 134[/tex]
[tex]s(2.5) = -16\cdot (2.5)^{2}+150[/tex]
[tex]s(2.5) = 50[/tex]
[tex]\bar v = \frac{50\,ft-134\,ft}{2.5\,s-1\,s}[/tex]
[tex]\bar v = -56\,\frac{ft}{s}[/tex]
The average rate of change of the height over the interval [1, 2.5] is - 56 feet per second.
PLEASE ANSWER QUICK
George has 4 pounds of ham to make 16 sandwiches. He puts the same amount of ham on each sandwich. Which statement about George’s sandwiches is true?
Answer:
There is no photo
Step-by-step explanation:
I cant see the photo therefore I cant help
Answer:
Can u put the answer choices
Step-by-step explanation:
what is the amount of 839k in thousands
Nick spent 34 minutes on the phone while routing 17 phone calls. In all, how many phone calls does Nick have to route to spend a total of 50 minutes on the phone? Assume the relationship is directly proportional.
Answer:
25 phone calls
Step-by-step explanation:
Create a proportion where x is the number of phone calls for 50 minutes on the phone:
[tex]\frac{34}{17}[/tex] = [tex]\frac{50}{x}[/tex]
Cross multiply and solve for x:
34x = 850
x = 25
So, Nick would have to make 25 phone calls
How is pi calculated
Answer:
Pie is forever but the first 3 numbers re 314
Step-by-step explanation:
i need some assistance
Answer:
Given that,
Height of dougal is 1.84 meters and height of seb is 1.7 meters. We need to find the height of dougal as a fraction of the height of seb.
Let x is height of dougal as a fraction of the height of seb. So,
If we divide 1.7 on both sides of above equation, then,
On removing decimal, we get,
Hence, this is the required solution.
Step-by-step explanation:
Hi,, i saw this answer here in brainly because i had this one too so i hope this one helps
Simplify: 4 x 3^2 - 3+ 5x2 = 0 OA. 33 OB. 43 O c. 36 O D. 58 O E 34
4 x 3^2 - 3+ 5x2
4 x 9 - 3 + 10 = 0
36 - 3 + 10
33 + 10
43
Answer : 43
X + 12 >7
HELP YOU NOW PLEASE
Answer:
x>−5
Step-by-step explanation:
Verify [(1+tanx)/sinx] - secx = cscx. Show your work and identities you used.
Answer:
let's start.
Step-by-step explanation:
[tex]\frac{(1+tanx)}{sinx} -secx = cscx\\[/tex]
we can write it as
[tex]\frac{(1 + tanx)}{sinx} = cscx + secx[/tex]
starting with left hand side
LHS
[tex]\frac{(1 + tanx)}{sinx}[/tex]
[tex]\frac{1}{sinx} + \frac{tanx}{sinx}\\\\cscx + tanx *\frac{1}{sinx}\\\\cscx + \frac{sinx}{cosx} *\frac{1}{sinx}\\\\cscx + \frac{1}{cosx}\\\\cscx + secx[/tex]
∴ LHS = RHS
hence, proved
Answer:
See below
Step-by-step explanation:
(1 + tanx)/sinx - secx = cscx1/ sinx + tanx/ sinx - 1/cosx = cscx1/ sinx + sinx/ cosx × 1/sinx - 1/ cos x = cscx1/ sinx + 1/cosx - 1/cosx = cscx1/ sinx = cscxcscx = cscx