[tex]x^2 +16x +13 =0\\\\\implies x^2 + 2 \cdot 8 \cdot x + 8^2 -8^2 +13 =0\\\\\implies (x+8)^2 -64 +13 =0\\\\\implies (x+8)^2 -51 =0\\\\\implies (x+8)^2 =51[/tex]
Suppose that the functions u and w are defined as follows.
u(x) =
=-x-1
w(x) = 2x² +1
Find the following.
Step-by-step explanation:
(a○b)(x) is the same as a(b(x)).
it is really that simple.
first you calculate the result of the inner function, and then that result is the input for the outer function.
that's it.
so,
(w○u)(2) = w(u(2))
u(2) = -2 -1 = -3
w(-3) = 2×(-3)² + 1 = 2×9 + 1 = 19
so, 19 is the first answer.
(u○w)(2) = u(w(2))
w(2) = 2×2² + 1 = 2×4 + 1 = 9
u(9) = -9 - 1 = -10
so, -10 is the second answer.
Is 11:17 the same as 17:11
Answer:
It is a ratio, which could mean yes and no, mattering which side of the ratio the number goes to.
Step-by-step explanation:
Answer:
yes because it is the same
[tex]3\frac{3}{4} +8\frac{3}{4}[/tex]
The arithmetic mean of the heights of five pupils in a class is 164cm if another pupil whose height is 168cm joins the class, calculate the arithmetic mean of the heights of the 6 pupils
Answer:
164.67 cm
Step-by-step explanation:
The arithmetic mean of height of 5 pupils is 164cm . Let the sum of heights of 5 pupils be x . Then , according to the question ,
[tex]\sf\longrightarrow \dfrac{x}{5}= 164cm [/tex]
On solving ,
[tex]\sf\longrightarrow x = 5*164cm =\bf{820cm}[/tex]
When a student of height 168cm is added ,
[tex]\sf\longrightarrow Mean = \dfrac{820cm+168cm}{6}\\[/tex]
[tex]\sf\longrightarrow Mean = \dfrac{988}{6}\\ [/tex]
[tex]\sf\longrightarrow \boxed{\pink{\sf Mean = 164.66 \approx 164.67 cm }}[/tex]
Ayushi wanted to paint a wall of a room of dimensions 6 m × 5 m. It has a window of dimensions 2 m × 0.5 m and a door of dimensions 3 m × 1.5 m. What area of the wall is required to be painted by Ayushi?
Can you guys plz answer this???
Answer:
Required wall to be painted: 24.5 m²Step-by-step explanation:
Wall dimensions: 6 m x 5 m
=> Wall dimensions: 30 m²
Area of window: 0.5 x 2
=> Area of window: 1 m²
Area of door: 3 m × 1.5 m
=> 4.5 m²
Required wall to be painted: 30 - 1 - 4.5
=> Required wall to be painted: 24.5 m²
Therefore, the required paint for the wall to be fully painted is 24.5 m². Hoped this helped.
A bike that weighs 22 pounds and 3 ounces weighs a total of ____ounces.
Answer:
355 ounces
Step-by-step explanation:
Okay! We're going to have to use some conversion factors for this problem, since we're working with two different units (pounds and ounces). We know that there are 16 ounces in a pound - that's our first conversion factor. We can use it to write up a little equation to help us:
[tex]\frac{22lbs}{1} *\frac{16oz}{1lb} + 3 = x[/tex]
"x" is the total amount of ounces. Does everything in that equation make sense? The first multiplication part tells us how many ounces are in 22 pounds, and the second part (+ 3) adds the 3 ounces that were there from the beginning. Now, it's time to calculate.
[tex]\frac{22bs}{1} *\frac{16oz}{1lb} + 3 = x\\[/tex]
[tex]\frac{352oz}{1} + 3 = x[/tex]
[tex]352+3 = x[/tex]
[tex]x=355[/tex]
So, there are 355 ounces in a bike that weighs 22 pounds and 3 ounces. Hopefully that's helpful! :)
Is s = 7 a solution to the inequality below s < 2 yes
Answer:
No
Step-by-step explanation:
No, because s is less then 2. 7 is not less then 2.
‘Hope that helps! :)
Answer:
no
Step-by-step explanation:
s<2
s=7
7>2
A truck rental is $25 plus $.30/mi. Find out how many miles Ken traveled if his bill was $50.20.
Lets start by finding the equation.
25 is the constant, .3 is the slope, and 50.2 is the final.
This means that our equation is:
50.2 = .3x + 25
50.2 - 25 = .3x
25.2 = .3x
25.2 / .3 = x
84 = x
This means that Ken travelled 84 miles if his bill was $50.2.
I hope this helps! :)
Mary wants to buy one large pizza, one medium pizza, and three drinks. The drinks cost $p$ dollars each, the medium pizza costs two times as much as one drink, and the large pizza costs three times as much as one drink. If Mary started with $30$ dollars, how much money would she have left after making all of her purchases? Give your answer as an expression of $p
$ (30-8p)
Step-by-step explanation:
3 DRINKS- 3P
MEDIUM- 2p
large- 3p
so plus 8 p
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST
easy one - giving brainly if correct - show work.
teacher said it was wrong, anyone know the right answer? answer both!
Answer:
$9.68 per Hour, $11.72 per Hour.
Step-by-step explanation:
What you thought of..
10% of original pay wage = $0.80
Sofia's Pay Wage will be incremented by 10% of $8 every 6 Months.
Function:
Sofia's Pay Wage = e
Original Pay Wage = o
Increment = i
6 Months = t
e = o + ti
1 Year = 12 Months
$8 + ($0.80 x 2) = $9.60
In 1 Year, Sofia's Pay Wage will be $9.60 per Hour
$8 + ($0.80 x 4) = $11.20
In 2 Years, Sofia's Pay Wage will be $11.20 per Hour
What I Thought Of..
Sofia's Pay Wage will be incremented by 10% every 6 Months.
Function:
Sofia's Pay Wage = e
Original Pay Wage = o
Increment = i
6 Months = t
e = o + t(ei)
1 Year = 12 Months
($8 + {10% of Sofia's Pay Wage}) = $8.80
($8.80 + {10% of Sofia's Pay Wage}) = $9.68
In 1 Year, Sofia's Pay Wage will be $9.68 per Hour
($9.68 + {10% of Sofia's Pay Wage}) = $10.65
($10.65 + {10% of Sofia's Pay Wage}) = $11.72
In 2 Years, Sofia's Pay Wage will be $11.72 per Hour
Brainly? (I spent a while on this)
Five ballet tickets and 3 musical tickets cost $370.00. 3 musical tickets cost $120. All ballet tickets cost the same and all musical tickets cost the same. What is the ratio of the cost of a ballet ticket to the cost of a musical ticket in simplest form?
Answer:
$50
Step-by-step explanation:
$370 - $120 = $250 ( 5 ballet tickets )
$250 divided by 5 tickets is $50 per ticket
Ratio is 50:40 or 5:4 simplified
STRUCTURE Gustavo sets up tables for a caterer on weekends. Each round table can seat 8 people. Each rectangular table can seat 10 people. One weekend, his boss asked him to set up tables for 124 people. He uses 2 more round tables than rectangular tables. Write a system of equations to find the number of round tables and rectangular tables Gustavo used. Then graph the system on a separate sheet of paper to solve the system.
Gustavo used 8 round tables and 6 rectangular tables.
Since Gustavo sets up tables for a caterer on weekends, and each round table can seat 8 people while each rectangular table can seat 10 people, and one weekend, his boss asked him to set up tables for 124 people, and he uses 2 more round tables than rectangular tables, to find the number of round tables and rectangular tables Gustavo used the following calculation must be performed:
10 x 8 + 8 x 10 = 160 8 x 8 + 6 x 10 = 124
Therefore, Gustavo used 8 round tables and 6 rectangular tables.
Learn more in https://brainly.com/question/25443927
Help Me in my Math Thanks :)
Answer:
Step-by-step explanation:
Asked: How many square tables are needed to place 100 pupils?
Given: Square table each has 4 pupils to sit
operation : Multiplication, subtraction, Division
Solve:
Number of pupils in 9 rectangular tables = 9*8 = 72 pupils
Remaining pupils = 100 - 72 = 28
Number of square table needed =28 ÷ 4 = 7
7 square tables are needed.
Someone please help me!
Answer:
$343.75
Step-by-step explanation:
$5.50 × 125 = $687.50 ÷ 2 = $343.75
Answer:
$343.75
Step-by-step explanation:
Multiply 5.50 by 125 hours to get the amount of money she has earned. Then since she saved half of it divide that amount which is $687.50 by 2 to get $343.75
Choose the mixed number that has not been reduced to simplest form.
7 14/18
5 5/6
5 7/12
4 2/5
Hello there!
7 14/18 is the mixed number that has not been reduced to simplest form.
We can divide the numerator and denominator by 2 to reduce the fraction:
7 7/9
The answer is Option A. Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]SilentNature[/tex]
Work out the percentage change to 2 decimal places when a price of £189 is decreased to £150.
Answer:
20.63%
Step-by-step explanation:
189-20.63%=150,0093
Answer:
20.63%
Step-by-step explanation:
% change = (New Value - Initial Value)/(Initial Value) * 100
= (150-189)/189 * 100
= -20.63%
Though the value comes as negative but it only indicates that it is a percentage decrease. As the question mentioned that the value is decreased, the final answer would be only 20.63%.
Hopefully this helps!!
Find an
angle in each quadrant with a common reference angle with 280°, from
0°
Answer:
Step-by-step explanation:180
Answer:
80
Step-by-step explanation:
i don't know if it is right
Riley is saving up to buy a new television. She needs a total of $1,161.59. Riley has saved $200.39 already and earns $80.10 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answer:
12 weeks
Step-by-step explanation:
I will use x to describe the amount of weeks.
200.39 (amount already have) + 80.10x (amount per week) = 1161.59 (total amount needed)
Now, just solve for x.
80.10x = 961.2
x = 12
You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet
cost $18 per square yard. How much will the carpet cost?
Answer:
27360
Step-by-step explanation:
38x40=1520
1520*18=27360
plz help will mark as brainliest
Answer:
18⁰
Step-by-step explanation:
As AOB is a line so it's is 180 ⁰
Hence,
5y+3y+2y=180⁰
10y=180⁰
y=180⁰/10
y=18⁰
HELP ASAP!!!!!!!!! IM SO PUZZLED
, leisan can drive 32 miles on every gallon of gasoline. if she fills up her tank for $2.39 per gallon, how much will it cost her to drive 448 miles?
Answer:
It will cost her $33.46
Step-by-step explanation:
She drives 32miles per gallon
In 448miles, she will use: (448 × 1)/32
= 14gallons
If a gallon costs $2.39
Then 14gallons will cost, 14×2.39
= $33.46
Calibri
11 -
BI USA
f* Average Annual Weather Statistics
B
с
Average Annual Weather Statistics
D
E
F
G
H
J
K
L
M
N
1
2
3
Atlanta
1050
Average
1616.833333
4
5
89
Boston Dallas Orlando Phoenix SanteFe Total
20 430 91 1110 7000
69 96 82 86 70
44 37 62 59 43
42.53 21.32 47.7 7.3 14
41
6
0
0 32
Altitude
High Temp
Low Temp
Rain (in.)
Snow (in.)
6
7
33.5
50.19
0
8
9
10
11
12
13
14
15
16
17
Alt. Diff. ->
Atlanta & Dallas
Alt. Diff. Answer Here ->
18
19
20
21
Answer: were you born yesterday
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Answer:
= -3x +3
Step-by-step explanation:
like terms (7x) -(4x)
or 7x + -4x = -3x
no like terms to condense 3
Which of the following is(are) the solution(s) to |11x +3 = 6 ?
Hey there!
11x + 3 = 6
SUBTRACT 3 to BOTH SIDES
11x + 3 - 3 = 6 - 3
CANCEL out: 3 - 3 because it gives you 0
KEEP: 6 - 3 because it helps you solve for your x-value
11x = 6 - 3
11x = 3
DIVIDE 11 to BOTH SIDES
11x/11 = 3/11
CANCEL out: 11/11 because that gives you 1
KEEP: 3/11 because it simplifies for the x-value
SOLVE
x = 3/11
Therefore, your answer should bed x = 3/11
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The sale of cars in a particular month is decreased by 20% is $3060. What was the sale of cars before reduction.
Answer:
$3672
Step-by-step explanation:
3060 x 20% = 612
612 + 3060 = 3672
What is the answer of this question please reply!
0.00536 by 25
Answer:
0.134
Step-by-step explanation:
"By" means multiplied by, so the question is, what's 0.00536 multiplied by 25?
In the first step, we multiply all the numbers in the decimal by 5, and we get 0.02680. In the second, we multiply all the numbers in the decimal by 20, and we get 0.10720. Then we add the two together and get 0.134.
I hope that helped :)
State the domain and range of the relation:
{(1,3), (2, 4), (3,5), (-1,3), (-2, 4), (-3,5))
Answer: Domain is {-3, -2, -1, 1, 2, 3}. Range is {3, 4, 5}
Step-by-step explanation:
Domain in x values and therefore -3, -2, -1, 1, 2, 3. The range is y-values and you don't have to repeat same values making the range 3, 4, 5
can someone help me solve this 11
[tex]\dfrac{\sin \alpha}{\cos \alpha + \sin \alpha} - \dfrac{\cos \alpha}{\cos \alpha - \sin \alpha}\\\\\\=\dfrac{\sin \alpha(\cos \alpha - \sin \alpha) - \cos \alpha(\cos \alpha + \sin \alpha)}{(\cos \alpha + \sin \alpha)(\cos \alpha -\sin \alpha)}\\\\\\=\dfrac{\sin \alpha \cos \alpha - \sin^2 \alpha - \cos^2 \alpha - \cos \alpha \sin \alpha}{\cos^2 \alpha - \sin^2 \alpha}\\\\\\=\dfrac{-(\sin^2 \alpha + \cos^2 \alpha)}{\cos 2 \alpha}\\\\\\=-\dfrac{1}{\cos 2 \alpha}\\[/tex]
[tex]=-\left(\dfrac{1}{\tfrac{1- \tan^2 \alpha}{1 + \tan^2 \alpha}} \right)~~~~~~~~~~~~~~~~~~; \left[\cos 2\theta = \dfrac{1 - \tan^2 \theta}{1+ \tan^2 \theta} \right]\\\\\\\ = -\left(\dfrac{1+ \tan^2 \alpha}{1- \tan^2 \alpha}\right)\\\\\\= \dfrac{1+\tan^2 \alpha}{\tan^2 \alpha -1}[/tex]