For all values of x, f(x)=2x+1 and g(x)=x^2. Solve fg(x)=gf(x). (Mathwatch)
[tex]\text{Given that,}\\\\f(x) = 2x+1,~~ g(x) = x^2\\\\\ \text{now,}\\\\f(g(x)) = g(f(x))\\\\\implies f(x^2) = g(2x+1)\\\\\implies 2x^2+1=(2x+1)^2\\\\\implies 2x^2+1= (2x)^2 +2\cdot 2x + 1\\\\\implies 2x^2 +1 = 4x^2 + 4x +1\\\\\implies 4x^2 -2x^2 +4x +1-1 =0\\\\\implies 2x^2 +4x =0\\\\\implies 2x(x+2)=0\\\\\implies 2x =0~~ \text{or}~~ x+2 =0\\\\\implies x =0 ~~~\text{or}~ x =-2\\\\\ \text{Hence,}~ x =0 ~\text{and} ~ x =-2~ \text{are the solutions.}[/tex]
change percentage to a decimal
52 %
319%
7.9%
4/5%
3 7/8%
6 2/3%
2.
There are six bottles of water. Each bottle contains 0.65 L of water. The capacity of a cup is 0.26 L.How many cups can you fill with all the water.
3.
30.8 m of cloth is needed to make 7 shirts. What is the length needed to make 16 shirts
4.
Mrs Wong buys 0.6 kg of fish balls for $15. Mr Chan buys 0.5 kg from the same shop how much should he pay?
5.
every 0.35 L of mango drink is made of 0.14 kg of mangoes and some soda . Connie wants to buy 3.75 L of mango drink . How many kilograms of mangoes dose she need
Answer:
52%=0.52
319%=3.19
7.9%=0.079
4.5%=80
37/8%=4.652
62/3%=20.67
2. 15 cups
3. 70.4m
4. $12.5
5.
Step-by-step explanation:
52%=52/100=0.52
319%=319/100=3.19
7.9%=7.9/100=0.079
4/5%=(4/5)/100=4/5×100=80
37/8%=4.(5/8)=4.652
62/3%=20.(2/3)=20.67
1 bottle holds 0.65L
1 cup holds 0.26L
6 bottles hold (0.65×6) =3.9L
n cups hold 3.9L
0.26n=3.9
n=3.9/0.26
n=15
30.8m make 7 shirts
ym make 1 shirt
7y = 30.8
y = 4.4m
1 shirt needs 4.4m
16 shirts need 16×4.4=70.4m
0.6kg cost $15
1kg costs $b
0.6b=15
b=$25
1kg costs $25
0.5kg cost (25×0.5)=$12.5
Jae bought 85 tickets to spend on games and rides at an amusement park. Games cost 3 tickets each, and rides cost 8 tickets each. Jae has already used 39 of the tickets. If he uses all of his remaining tickets for rides, how many more times can Jae go on rides?
Answer:
15
Step-by-step explanation:
Jae can go 15 more times on the rides.
Answer:
Jae can ride 5.75 or 5 more times
Step-by-step explanation:
Total of tickets, Jae buys 85
Jae uses (-) 39 tickets
85 - 39 = 46 remaining tickets
Rides: 8 tickets each
46/8 = 5.75
I hope this helps.
Write the equation for the line in slope intercept form
Answer:
y = -x + 5
Step-by-step explanation:
lmk if you want an explanation
A 14-oz iced tea at a certain restaurant has 140 calories. How many calories are there in a 22-oz iced tea?
Answer:
220 calories
Step-by-step explanation:
Cross multiply and then divide:
[tex]\frac{14}{22}= \frac{140}{x}[/tex]
140 x 22 = 3080
3080 / 14 = 220
Estimate the line of best fit using two points on the line.
Answer: i think it's b
Answer:
C.
Step-by-step explanation:
A and D are immediately wrong since the line is increasing.
Using the formula of rise over run, we can find the slope. We then use 40 as the rise and 5 as the run
40/5 is 8.
We can now put 8 as the slope in the y=mx+b equation. We can see the line intersect at 20 at the y-axis, which makes 20 the y-intercept. We can now insert that into the b part of the equation. This leaves us with y=8x+20.
A pancake recipe calls for 4 eggs and 12 cups of flour. How many cups of flour would you need for a single egg?
Answer:
3
Step-by-step explanation:
i'd say 3
i divided 12 by 4 and then multiplied by one, since that is the amount of eggs we want
good luck! <3
The diameter of the sun is about is about 1 390 000 km;
use scientific
notation to represent this diameter.
Answer:
1.39×10^6
Step-by-step explanation:
Hide 1 then count how many numbers are after it(6 numbers), that will be the power/exponent you will use
Plz help brainiest to the correct answer!
#1
Current temperature=0°C
Temperature before 1 hour
[tex]\\ \sf{:}\dashrightarrow 0+3°C=3°C[/tex]
#2
Temperature before 3h
[tex]\\ \sf{:}\dashrightarrow 0+3(3)=0+9=9°C[/tex]
#3
Temperature before 4.5h
[tex]\\ \sf{:}\dashrightarrow 0+4.5(3)=13.5°C[/tex]
Adrian, Ben and Charlie share some sweets in the ratio 7.4.11
Charlie got 52 more sweets than Adrian. Work out the total amount of sweets.
Answer:
286 sweets.
Step-by-step explanation:
If Adrian had x sweets, Charlie got x+52 sweets.
The number of parts is 7+4+11 = 22.
So Adrian had 7/22 of the total and Charlie had 11/22 = 1/2 of the total.
This means that Ben had 4/22 = 2/11 of the total.
If y is the total number of sweets:
y = x + x + 52 + 2y/11
9y/11 = 2x + 52
2x = 9y/11 - 52.............(1)
Also x + 52 = y/2
y = 2x + 104
2x = y - 104...............(2)
Equating (1) and (2) - (as there is 2x on left side of both equations):-
9y/11 - 52 = y - 104
52 = 2y/11
y = 52 * 11/2
y = 286 sweets.
kari purchased 3 cherry trees for sale. Each cherry tree cost $9 less than its full price. She paid a total of $135
Answer:
whats the question?
Step-by-step explanation:
Answer:
each tree was $36
Step-by-step explanation:
if the trees are $9 less then the full price and she purchased 3
9 times 3 is 27 135-27 is 108 so then when you divide 108 and 3 to get $36
What is 5 rounded to the nearest whole number, explain why
Answer:
The answer is 10
Step-by-step explanation:
It is
The ratio of taxis to buses to bikes
is 12:5:18.
How many buses are there if there
are 72 bikes?
Answer:
20 buses
Step-by-step explanation:
Using the given ratio, we can see that for every 12 taxis, there are 5 buses and 18 bikes.
To get from 18 bikes to 72 bikes, we multiply by 4. Therefore, to figure out the number of buses, we multiply it by 4.
5 * 4 = 20
Hope this helps! :D
Figure ABCD 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:
Reflected along x axis
Translated 7 units to the right
Step-by-step explanation:
If a point (x, y) is reflected along the x axis, its x coordinate remains the same and the y coordinate is opposite (negated). The new point is at (x, -y)
If a point (x, y) is translated h units to the right, the new coordinate is (x+h, y).The transformation are as follows:
It is reflected along the x axis so that the new coordinates would be at A1 at (- 4, -4), B1 at (- 2, -2), C1 at (- 2, 1), D1 at (- 4, -1)
It is translated 7 units to the right, The new coordinates are A' at (3, -4), B' at (5, -2), C' at (5, 1), D' at (3, -1)
Hope that's better
Can someone please help me with this question
A. Angle 3 is a vertical angle to angle 2 which means they are the same.
Angle 3 = 76 degrees
B. Angle 6 is also the same as angle 2.
Angle 6 = 76 degrees
C. Angle 8 + angle 6 form a straight line which equals 180 degrees
Angle 8 = 180 - 76 = 104 degrees
Answer:
76° , 76° , 104°
Step-by-step explanation:
(a)
∠ 2 and ∠ 3 are vertically opposite angles and are congruent , then
∠ 3 = 76°
(b)
∠ 6 and ∠ 3 are alternate angles and are congruent , then
∠ 6 = 76°
(c)
∠ 6 and ∠ 8 are adjacent angles on a straight line and sum to 180° , then
∠ 8 = 180° - 76° = 104°
what is the slope of the line tha passes through the points (4,-9) and (8,-3)
i suck at this stuff
pls help asap
ty <3
Answer:
12*2=24
Step-by-step explanation:
HELP PLEASE WILL GIVE BRAINLIEST
Answer:
In attachment
Step-by-step explanation:
See the attachment. They are much easier to solve if you set up a spreadsheet template and then copy that template for each problem. The inputs would be the two given points for each graph. Problem 3's slope is undefined, since it is a vertical line and the run is 0, no change in x. Since slope is "Rise/Run," this is dividing by zero, a No-No for mathematicians, as well as us chemists and other mortals.
Gillian can jog 100 metres in 24 seconds. How long will it take her to jog 2 km?
Answer:
8 minutes or 480 seconds
Step-by-step explanation:
1 km = 1000 m
100x20=2000
24 x 20 = 480
480/60 = 8
Answer:
Step-by-step explanation:
A bag contains pennies, nickels, nickels, and nickels. There are 50 coins in total. Of the coins, 14% are pennies and 34% are dimes. There are 6 more nickels than pennies. How much money does the bag contain?
answer:
8 pennies,16 dimes,13 nickels,13 quarters
Step-by-step explanation:
total number of coins = 50
16% are pennies
16% of 50
16/100 x 50=(16x50)/100=800/100=8
Pennies = 8
32% are dimes
32% of 50
32/100 x 50=(32x50)/100=1600/100=16
Dimes = 16
5 more nickels than pennies
Pennies = 8
nickels = 8 + 5 = 13
nickels = 13
8+16+13=37
50 - 37 = 13
13 quarters
pennies = 8, dimes = 16, nickels = 13, quarters = 13
A farmer decides to make three identical pens with 88 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?
Answer:
The long fence, AC = 44 feet
4 shorter segments at 11feet each = 44 feet
Area = 484 ft^2
Step-by-step explanation:
The three pens will share one fence section parallel to the barn, we'll call it AB. Each pen will need two side fence segments, from the front fence to the barn. We'll call those portions AC. We need four of them: two for the outer sides and two more to divide up the space equally among the three pens. The total area would be AB*AC.
We know that AC + 4AB = 88 feet.
or AC = (88feet - 4AB)
Area = AB(88feet - 4AB)
Area = 88AB - 4AB^2
To maximize the area, we can take the first derivative and set it equal to zero:
Area' = 88 - 8AB
0 = 88 - 8AB
AB = 11 feet
AC = (88 - 4AB)
AC = (88 - 44)
AC = 44 feet
The fours segments of fence:
AC + 4AB = 88 feet
(44) + 4(11 feet) = 88feet
Area = 44' x 11 ft' = 484 ft^2
21²/0.219 to 2 significant figures
5ab+8c} if a = 3, b = 2, and c = 9.
Step-by-step explanation:
5ab + 8c
Putting values of a = 3 b = 2 and c = 9
5(3)(2) + 8(9)
30 + 72
102
Find the value of x.
75
70
60
80
Answer:
75. is yr correct ans.
Step-by-step explanation:
hope it helps.
stay safe healthy and happy.
Answer:
x = 75
Step-by-step explanation:
The triangle has 2 congruent sides and is therefore isosceles with 2 congruent base angles, both of measure x
The sum of the 3 angles = 180° , that is
x + x + 30 = 180
2x + 30 = 180 ( subtract 30 from both sides )
2x = 150 ( divide both sides by 2 )
x = 75
what is 3x + 4y = 10
6x - 4y = 8
Answer:
x=2
y=1
Step-by-step explanation:
9x+0=18
so it's x=2
6=4y=10
so y=1
please help i'm stuck and it's a unit test if correct i will give brainiest
Which inequality represents this statement?
A number is no more than 5.
a. n≥5
b. n<5
c. n>5
d. n≤5
Answer:
d. n≤5
Step-by-step explanation:
This is the answer
Answer:
D) n≤5
Step-by-step explanation:
No more than 5 means that the number cannot exceed 5, but it's ok to have any number less than 5 or equal to 5. So, this means that D is correct.
Jason has $45.00. He wants to buy equal numbers of soft drinks and sandwiches. A soft drink costs $0.79. A sandwich costs $2.49.
Part A
How much does a sandwich and drink cost together?
$
Part B
How many can he buy with $45.00?
soft drinks and
sandwiches
Part C
How much change will Jason get?
$
Answer:
Step-by-step explanation:
How much does a sandwich and drink cost together?
($0.79 + $2.49) = $3.28
How many can he buy with $45.00?
$45/$3.28 = 13.72 or 13 sandwich/soda combos.
13 soft drinks and
13 sandwiches
How much change will Jason get?
$45 - 13($3.28) = $2.36
Find the missing base.
Write your answer as a whole number.
?^2=36
Answer:
6
Step-by-step explanation:
6^2 = 36
hope this helps! :D
have a miraculous day!! <3
what does x equals to if 3( x + 7 ) =57
3(x + 7) = 57 |÷3
x + 7 = 57/3
x + 7 = 19 |-7
x = 19 - 7
x = 12
--
△XYZ = △KLM,m
Find m
Answer:
<m is equal to the measure of <Z
_______________________________________
Hope this helps!!
Please tell me if I have made a mistake!!
I enjoy learning form them:)