Answer:
180 cm²
Step-by-step explanation:
x = length
y = width
perimeter of a rectangle is the sum of all sides, so, 2×length plus 2×width.
x = 5y
72 = 2x + 2y
using the first equation as substitute in the second equation
72 = 2×(5y) + 2y = 10y + 2y = 12y
y = 6 cm
x = 5y = 5×6 = 30 cm
area = x × y = 30 × 6 = 180 cm²
Evaluate the function f(x)=x^2+6x+2 at the given values of the independent variable and simplify.
a. f(-8)
b. f(x+2)
c. f(-x)
Answer:
a) 18
b)x^2+10x+18
c)x^2 -6x+2
Step-by-step explanation:
This is a case of plugging in the value into f(x).
a) f(-8)= -8^2 + 6(-8) +2
f(-8)= 64 + (-48) +2
f(-8)=64 + (-46)
f(-8)=18
b) f(x+2)= (x+2)^2+6(x+2)+2
So here I'll take a break to explain what's going on, because x+2 is a binomial meaning two terms and it is being squared I have to multiply the whole thing by itself. Meaning: (x+2) x (x+2), this is also known as foiling!! and for the next part its distributing 6 into x and 2.
f(x+2)= x^2+4x+4+6x+12+2
I'll reorder it
f(x+2)= x^2+4x+6x+12+2+4
f(x+2)= x^2+10x+18
c) f(-x)= -x^2+6(-x) +2
f(-x)= x^2 -6x+2
Please Help! I will give you a lot of points if you do!
--This is Hindu-Arabic math so you have to use their number system
Answer:
47
Step-by-step explanation:
According to the number system 7 lines and 12 dots, a line is 5 and a dot is 1
you do 5*7+12 which is equal to 47
So the answer is 47,
Hope this helps!
First look at the chart and then convert each symbols to their respective numbers
[tex]\\ \tt\longmapsto 6+14+13+4+0+10[/tex]
Now add[tex]\\ \tt\longmapsto 20+17+10[/tex]
[tex]\\ \tt\longmapsto 37+10[/tex]
[tex]\\ \tt\longmapsto 47[/tex]
The height of a candle, in centimeters, can be modeled by the linear equation h = 28 - 2t, where t represents the hours that the candle has been burning.
Interpret the slope of this equation in the context of this problem:
The slope is -2. In context to this problem, the candle will burn away 2cm of its length every hour.
The slope of the equation, -2, means that the height of the candle reduces at a rate of 2 cm per hour.
Given the linear equation of the height of a candle that has been burning as: [tex]h = 28 - 2t[/tex].
This implies that:
28 in the equation represents the initial height of the candle = 28 cm.
-2 in the equation is slope, which is the rate of change at which the candle burns, meaning the height of the candle reduces by 2 cm every hour.
Therefore, the slope of the equation can be interpreted in the context of the problem as:
for every hour that passes, the height of the candle reduces by 2 cm.
Learn more about linear equation here:
https://brainly.com/question/19408983
x – Зу +8x47+ 15 – 4у
Answer:
X-7y+391
Step-by-step explanation:
First multiply
8x47=376
Now group those that are the same together
X-3y -4y+376 +15
X-7y+391
Answer:
x - 7y + 391
Step-by-step explanation:
[tex]x - 3y + 8 \times 47 + 15 - 4y[/tex]
[tex]x - 3y + 376 + 15 - 4y[/tex]
[tex] - 3y - 4y = (- 3 - 4)y = - 7y[/tex]
[tex]x - 7y + 376 + 15[/tex]
[tex] = x - 7y + 391[/tex]
The value of 2 · 5^2 is 100. True or False?
If n = 4, the value of the expression 28 - 12 + ÷ 2 is _____.
A) 15 B) 17 C) 17/2 D) 21
Please answer both!
The coach made the students run for 11 minutes 24 seconds and then walk for 5 minutes 48 seconds. What is the total time the students ran and walked?
The coach made the students run for 11 minutes 24 seconds and then walk for 5 minutes 48 seconds. What is the total time the students ran and walked?
Answer:
17minutes 10sec
Step-by-step explanation:
Total time running and walking
= time ran + time walked
= 11 minutes 24 sec + 5 minutes 48sec
= 16minutes 70sec
( now we know 60 sec = 1 min) so..
= 17minute 10sec
Show algebraically that f and g are inverse functions:
g = sqrt(x+8)-4
f=x^2+8x+8
Answer:
See Below.
Step-by-step explanation:
By definition, if two functions, f and g, are inverses, then:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
We are given the two functions:
[tex]\displaystyle g(x) = \sqrt{x + 8} -4 \text{ and } f(x) = x^2 + 8x + 8[/tex]
Find f(g(x)) and g(f(x)):
[tex]\displaystyle \begin{aligned} f(g(x)) &= (\sqrt{x + 8} -4)^2 + 8(\sqrt{ x+ 8}-4) + 8 \\ \\ &= ((x+8) -8\sqrt{x + 8} +16) + 8\sqrt{x + 8} - 32 + 8 \\ \\ &= x + (-8\sqrt{x+8} + 8\sqrt{x + 8}) +(16 - 32 + 8 + 8) \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned}g(f(x)) &= \sqrt{(x^2 + 8x + 8) + 8} - 4 \\ \\ &= \sqrt{x^2 + 8x+16 } - 4 \\ \\ &=\sqrt{(x+ 4)^2} - 4 \\ \\ &= (x +4) - 4 \\ \\ &= x \stackrel{\checkmark}{=} x \end{aligned}[/tex]
Hence, f and g are indeed inverses of each other.
11/14 as a repeating decimal using bar notation
Step-by-step explanation:
______
0.7857142
note the first 7 is not included in the bar
Miss Marple’sgrandfather passed away and she attended the reading of the will. The estate was valued at $8,424,000. It was decided that 23of the estate would be given to his children. Of the remainder, 15would be used to create a scholarship for mathematics majors at a local university and the rest would be divided evenly among his fourgrandchildren, of which Miss Marplewas one. a.How much money was used for the scholarship?[3 pts]b.What fractionof the estate did Miss Marpleend up inheriting?
The amount of money used for scholarship and the fraction of the estate gotten by Miss Maple are :
Scholarship amount = $561,600Fraction gotten by Miss Maple = 1/30The entire fraction of the estate = 1/1
Fraction given to children = 2/3
Fraction left = Total - fraction given to children
Fraction left = 1/1 - 2/3 = 1/3
For scholarship :
1/5 of fraction left :
1/5 of 1/3 = 1/5 × 1/3 = 1 /15
Fraction Given to grand children :
1/5 - 1/15 = 2/15
Amount of money used for scholarship :
1/15 × 8424000 = $561,600
B.)
Since There are four grand children and it was equally shared among them:
Miss Maple is one of the grand children:
Fraction each grandchild gets is :
2/15 ÷ 4
2/15 ÷ 4/1
2/15 × 1/4 = 2/60 = 1/30
Hence, miss Maple will get 1/30
Learn more : https://brainly.com/question/18109354
jennifer works at whataburger and earned 168.75 last week. If she worked 22.5 hours, how much does she earn per hour?
Answer:
7.5
Step-by-step explanation:
168.75 divided by 22.5 = 7.5
$7.50 dollars an hour.
7.50 x 22.5 = 168.75
Geometry PLEASE HELP
I’m right? Yes or no?
Answer:
B
Step-by-step explanation:
-2 + 12 = 10
A rectangle has perimeter 92 cm and length 39 cm. What is its width?
f(x)=x2
g(x)=x−3
Find the composition of the two functions and show your process:
g(f(x))
Answer:
g(f(x)) = x² - 3
Step-by-step explanation:
g(f(x))=g(x²)
= x² - 3
Step-by-step explanation:
[tex]f(x) = {x}^{2} \\ g(x) = x - 3 \\ g(f(x)) = g( {x}^{2} ) = {x}^{2} - 3 \\ thank \: you[/tex]
Please helpppppp????
Answer:
hii
Step-by-step explanation:
which question do you want
PICTURE ABOVE ^^ PLEASE HELP
Answer: 4 /15
Step-by-step explanation:
[tex]0.2\overline{6}\\\\=0.2+\dfrac{1}{10} *\dfrac{6}{9} \\\\=\dfrac{1}{5} +\dfrac{1}{15} \\\\\\\boxed{0.2\overline{6}=\dfrac{4}{15} }\\[/tex]
Determine whether the variable is qualitative or quantitative. Explain your reasoning.
Favorite types of food
The variable is_____
because types are____
find the constant term in the expansion of (x +1/x)'8
[tex]\left( x+\frac{1}{x}\right)^{8} =\sum _{k=0}^{8}\binom{8}{k} \cdotp x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k}\\\\\\ \begin{array}{l}\text{We\ wish\ to\ find\ } x^{0} :\\\\x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k} =x^{0}\\\\\Longrightarrow x^{8-k} \cdotp x^{-k} =x^{0}\\\\\Longrightarrow \cancel{x}^{8-2k} =\cancel{x}^{0}\\\\\Longrightarrow 2k=8\\\\\Longrightarrow k=4\end{array}\\\\\therefore \binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8!}{( 8-4) !\cdotp 4!}[/tex]
[tex]\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8\cdotp 7\cdotp 6\cdotp 5\cdotp \cancel{4!}}{\cancel{4!} \cdotp 4\cdotp 3\cdotp 2\cdotp 1}\\\\\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4}=70\\\\\therefore \boxed{\boxed{\text{The\ constant\ term\ is\ } 70}}[/tex]
A recipe for pancakes calls for 2 eggs, 1 cup of flour, and 1/2 cup of milk.
a) How much flour do you need if you use 5 eggs?
b) How much milk do you need if you use 5 eggs?
Answer:
a: 2 1/2 cups of flour
b: 1 1/2 cups of milk
Answer:
I think 10 cup flour beacuse 1 cup flour is double than that of eggPLEASE HELP it’s been an hour and I can’t figure this out it’s about rate of change algebra 2 I can give brainlist
Answer:
part b is B
Step-by-step explanation:
not sure about the first part i dont want you to get it wrong i kind of forgot about it
Multiply (-14/21) x5/9 Enter your fraction as a fraction, in simplest form.
Please help
Answer:
simplifed -10/27
Step-by-step explanation:
A forest contains 20 elks, of which 5 are captured, tagged, and then released. A certain time later 4 of the 20 elks are captured. What is the probability that 2 of these 4 have been tagged?
Answer:
Step-by-step explanation:
P{2 of 4 tagged}=(52)(152)(204)
=0.2167
if i pour 1/4 gallon of tea in each of the 4 pitchers. how many gallon in each pitcher
convert 69 m 26cm into cm solv
Answer:
View explanation
Step-by-step explanation:
1 meter = 100cm, so with this logic
100 x 69 = 6,900cm
We have a standby 28 cm, so:
6,900 + 28 = 6,928
If this is the incorrect unit of measurement, let me know in the comments section so I can revamp my answer.
Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...
The Answer is:
an = -15 + 9(n - 1)
-3x + 6y = 18
-3x = 6y+14
a) What is the slope of the 1st equation?
b) What is the slope of the 2nd equation?
c) Are they parallel, perpendicular, or neither?
Step-by-step explanation:
-3x + 6y = 18
-3x = 6y+14
a) the slope of the 1st equation = -(-3)/6 = ½
b) the slope of the 1st equation = -3/6 = -½
c) they are niether parallel nor perpendicular
#1
-3x+6y=18-x+2y=62y=x+6y=x/2+3slope=1/2
#2
-3x=6y+146y=-3x-14y=-1/2x-7/3slope=-1/2
#3
Neither
What is percent 10 1/4 of 66?
Whitewater Rentals has 39 canoes and 25 solo kayaks. The canoes rent for $45 for a six-hour trip. The solo kayaks rent for $49 for the same trip. One day 8 canoes and 4 kayaks were not rented. How much money was collected for rent-als that day?
what insect is this??
Answer:
it's either an ant, small beetle, black termite, or something
Step-by-step explanation:
4. The sum of Mr. and Mrs. Bergen's ages is 100. The difference between their ages is 10. How old are Mr. and Mrs. Bergen?
100-10=90
90÷2=45
Mr Bergen's age=45+10
=55 years old
Mrs Bergen's age=45 years old
Help please help help please please please
Answer:
C. [tex] \frac{5}{4} [/tex]
D. [tex] \frac{6}{7} [/tex]
Step-by-step explanation:
C. [tex]2 - \frac{12}{16} [/tex]
[tex] = 2 - \frac{3}{4} [/tex]
[tex] = \frac{8 - 3}{4} [/tex]
[tex] = \frac{5}{4} [/tex]
D. [tex] \frac{20}{22} \times \frac{33}{35} [/tex]
[tex] = \frac{10}{11} \times \frac{33}{35} [/tex]
[tex] = 10 \times \frac{3}{35} [/tex]
[tex] = 2 \times \frac{3}{7} [/tex]
[tex] = \frac{6}{7} [/tex]