[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=h-3\\ V=25h\pi \end{cases}\implies 25h\pi =\pi (h-3)^2 h \\\\\\ \cfrac{25h\pi }{\pi h }=(h-3)(h-3)h\implies 25=\stackrel{F~O~I~L}{h^2-6h+9}\implies 0=h^2-6h-16 \\\\\\ 0=(h-8)(h+2)\implies \blacktriangleright h= \begin{cases} 8~~\checkmark\\ -2 \end{cases} \blacktriangleleft ~\hfill \blacktriangleright \underset{radius}{\stackrel{8~~ - ~~3}{5}} \blacktriangleleft[/tex]
notice, we didn't use h = -2, because the height cannot be a negative value.
A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be
determined using the equation
f(0) - 50
(3)
After two days the scientist receives a second shipment of 50 grams of the
same element. The equation used to represent the amount of shipment 2 remaining after t days is R8) - 50
50l
. Which
of the following is an equivalent form of the expression for the amount remaining in shipment 2?
The equivalent expression for the amount remaining is an expression that has equal value
The equivalent form of the expression for the amount remaining in shipment 2 is [tex]f(t)=50(\frac12^\frac{1}{5})^{5t- 1}[/tex]
How to determine the equivalent expressionThe initial equation of the function is:
[tex]f(t)=50(\frac12)^{\frac t{10}}[/tex]
The function after the scientist receives the second shipment after two days is:
[tex]f(t)=50(\frac12)^{t - \frac 2{10}}[/tex]
Simplify
[tex]f(t)=50(\frac12)^{t - \frac 1{5}}[/tex]
Take the LCM of the exponent
[tex]f(t)=50(\frac12)^{\frac{5t- 1}{5}}[/tex]
Express the exponent as a product expression
[tex]f(t)=50(\frac12)^{\frac{1}{5} * [5t- 1]}[/tex]
Rewrite as:
[tex]f(t)=50(\frac12^\frac{1}{5})^{5t- 1}[/tex]
Hence, the equivalent form of the expression for the amount remaining in shipment 2 is [tex]f(t)=50(\frac12^\frac{1}{5})^{5t- 1}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Answer:
D is the correct answer
Step-by-step explanation:
Multiply. Write your answer in simplest form. 2 1/2 × 3 2/3
20.2694 to the nearest tenth
Is x = 3 a solution to the equation 8= 2x + 3
yes or no
Answer:
NO
Step-by-step explanation:
substitute x=3 into the equation
2(3)+3
=9
Therefore x=3 is not a solution
Answer:
No, it is not a solution.
Step-by-step explanation:
x = 3
8 = 2x + 3
8 = 2 (3) + 3
8 = 6 + 3
8 ≠ 9
I need help what is 11 times 34,000
Answer:
374000
Step-by-step explanation:
use a calculator
Gordon starts in the northwest corner of a swimming pool and swims to the southeast corner. Then he swims along the width, a distance of 21 meters, and then along the length, a distance of 28 meters. Once Gordon returns to his starting point, how far has he swum?
Answer:
84 meters
Step-by-step explanation:
northwest corner to southeast corner= 35 meters
width= 21
length=28
total= 35+21+28=84 meters
Can someone please explain how to factor this difficult problem.
The decimal not equivalent to two and three tenths is
Answer:
2.3, 2 3/10
Step-by-step explanation:
an airline is trying to promote its new Boston to Atlanta flight. the usual price for this flight is $315.00. however the airline is offering a 40% discount until the end of the month. how much will the flight cost after the discount?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 315}}{\left( \cfrac{40}{100} \right)315}\implies 126~\hfill \underset{\textit{after discount}}{\stackrel{315~~ - ~~126}{189}}[/tex]
If usual price for flight is $315.00, the airline is offering a 40% discount until the end of the month. then the cost of the flight after the discount is 126.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that an airline is trying to promote its new Boston to Atlanta flight.
the usual price for this flight is $315.00.
The discount offered by airlines is 40%.
We need to find the cost of the flight after the discount.
Convert 40% to decimal by dividing with 100.
40/100=0.4
Now multiply 0.4 with 315
0.4×315
Zero point four times of three hundred and fifteen.
126
Hence, the cost of the flight after the discount is 126.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ2
Which two operations are needed to write the expression that represents "five less than the quotient of a number and three"? tin
Answer: The quotient is the result of a division and 'less than is a subtraction.
After a meal, your total bill (before tax) comes to $47.50. If the tax on
your meal is 6%, what is the cost of tax you will have to pay?
6% of 47.50 = 2.85
The tax money is $2.85
Find the selling price of each item.
45) Cost of a car: $43,000.00
Markup: 70%
Solve this question please thanks
Answer:
9
Step-by-step explanation:
if this helped pls give brainliest
PLEASE HELP IM CONFUSED HOW TO FACTORISE THESE
WILL MARK BRAINLIEST
Answer:
These are all quadratics, where the x/y/a/b coefficient has been cancelled out. So it's like factorising a quadratic. What i mean by the x/y/a/b coefficient being cancelled out is for example y^2 - 1, becomes (y - 1)(y + 1). This is equal to y^2 - y + y - 1. You can see that - y + y = 0, to therefore it's not visible in the final equation, but it's there.
c) y^2 - 1 = (y - 1)(y + 1)
d) x^2 - 64 = (x - 8)(x + 8)
g) a^2 - 81 = (a - 9)(a + 9)
h) x^2 - y^2 = (x - y)(x + y)
k) 25 - x^2 = (5 - x)(5 + x)
l) 1 - b^2 = (1 - b)(1 + b)
o) x^2 - 400 = (x - 20)(x + 20)
p) 900 - y^2 = (30 - y)(30 + y)
I hope this makes sense :))
Search
Khan academy
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you
decide to swim 15 minutes longer than she does one day at practice.
Write an equation for the number of minutes you swim, y, when your friend swims a number of minutes.
You swim 55 minutes.
How many minutes did your friend swim?
minutes
Stuck? Review related articles/videos or use a hint.
Report a problem
Determine the slope from the graphs
Answer:
This is solved
Step-by-step explanation:
Hope this helps
Find the area and circumference of a circle of radius 30cm ( use π= 3.14 )
Answer:
Area = 2826 cm^2
Circumference = 188.4 cm
Step-by-step explanation:
Area of a circle = πr^2 3.14 X (30^2) = 2826
Circumference = 2πr or πd 2 X 3.14 X 30 = 188.4
[tex] \mathbb\red{ANSWER} [/tex]
Area Formula :
[tex] \green{\pi {r}^{2} }[/tex]
[tex] \pink{ \pi \times {30cm}^{2} }[/tex]
[tex] \orange{ 3.14 \times 900 {cm}^{2} }[/tex]
[tex] \red{2826 {cm}^{2} }[/tex]
Circumference Formula:
[tex] \green{\pi \times d}[/tex]
[tex] \pink{3.14 \times 60cm}[/tex]
[tex] \orange{188.4cm}[/tex]
[tex] \mathbb\blue{HOPE \:IT\: HELPS} [/tex]
If g(x) = 3x − 4, what is the value of g−1(g(−2))?
x+4/3
2/3
−10
−2
Answer:
C, 2/3, hope this helps
Step-by-step explanation:
sorry if it does not!
Antonio has 2 2/3 of a piece of wood that he wants to cut into 4 pieces. How long should he cut each piece?
A 8 2/3
B 10 2/3
C 8/3
D 2/3
Answer:
D 2/3
explanation:
[tex]\bold{total \ length \ \div \ number \ of \ pieces }[/tex]
solve
[tex]\sf 2\dfrac{2}{3} \div 4[/tex]
reciprocal to change signs
[tex]\sf \dfrac{8}{3} \ * \ \dfrac{1}{4}[/tex]
simplify
[tex]\sf \dfrac{2}{3}[/tex]
Solution:
To find the measure of each piece, divide the total piece of wood (2 2/3) by the number of pieces Antonio wants to cut (4).
From the following, we obtained:
[tex]\rightarrow 2 \dfrac{2}{3} \div 4[/tex]
Convert 2 2/3 into an improper fraction:
[tex]\rightarrow 2 \dfrac{2}{3} \div 4[/tex]
[tex]\rightarrow \dfrac{2 \times 3 + 2}{3} \div 4\\[/tex]
[tex]\rightarrow \dfrac{6 + 2}{3} \div 4\\[/tex]
[tex]\rightarrow \dfrac{8}{3} \div 4\\[/tex]
Simplifying the expression:
[tex]\rightarrow \dfrac{8}{3} \div 4\\[/tex]
[tex]\rightarrow \dfrac{8}{3} \times \dfrac{1}{4} \\[/tex]
[tex]\rightarrow \dfrac{8}{3 \times 4}[/tex]
[tex]\rightarrow \dfrac{8}{12} = \boxed{\dfrac{2}{3}}[/tex]
Thus, Antonio should cut 2/3 of wood for each piece.
The rectangle and a trapezoid have the same area what is the length L of the rectangle?
Answer:
Step-by-step explanation:
Area of rectangle = 9 * L
Area of trapezoid = (24 + 12)*9/2 =9 * 18
Same area, so
9 * L = 9 * 18
L = 18 ft
The graph shows two accounts with the same principal and annual interest rate. Use the graph to estimate the answer to each question.
About how much more compound interest than simple interest is earned after 35 years? Remember to show your work.
About how much more compound interest than simple interest is earned after 45 years? Remember to show your work.
Answer:
The amount of compound interest than simple interest that is earned after 45 years:
$300 is invested.
After 45 years, it will grow to be about $700.
If invested using compound interest, it will grow to be about 1110.
Find the sum of the whole numbers from 1
to 820
Answer:
There is no way to solve this..
Step-by-step explanation:
What is the missing value
Answer:
18
Step-by-step explanation:
I did my method that I was taught but if you do (-5) - (-2), you get 3. So you subtract 39 by the -21 to get 18.
Answer:
-52.5
Step-by-step explanation:
Simplify the expression (5x2 + 5x – 32) – 3(x2 + 2x +11)
Answer:
2x^2 - x - 65
Step-by-step explanation:
hope this helps
brainliest pls
have an awesome day -TJ
Answer:
2x² - x - 65
Step-by-step explanation:
[tex]5x^2+5x-32+(-3)(x^2)+(-3)(2x)+(-3)(11)[/tex] [tex]5x^2 + 5x - 32 - 3x^2 -6x-33[/tex] [tex](5x^2-3x^2)+(5x-6x)+(-32-33)[/tex] [tex]2x^2-x-65[/tex]A rectangle has a perimeter of 8x3 + 7x2 - 10x + 3 and a length of x. Find the width of the rectangle
when the length is 21 inches.
The width is
inches.
Answer:
22091
Step-by-step explanation:
hope this helps
What is the radical of 23.5
Answer:
The result can be shown in multiple forms.
Exact Form:
√
23.5
Decimal Form:
4.84767985
…
Step-by-step explanation:
Which expression shows the prime factors of 220?
O A. 22 x 10
O B. 2x2x5x11
O c. 2x2 x 5 x 11 x 22
O D. 2 x 5 11
B. 2×2×5×11=220
if you divid 220 by 2=110
110÷2=55, 55÷5=11, 11÷11=1
2, 2,5, 11
A pattern follows the rule: obtuse triangle, obtuse triangle, right triangle, obtuse triangle... It also follows the rule isosceles, scalene isosceles, scalene. Draw a triangle that could be the fifth shape in the pattern and explain
The triangle gotten from this pattern is an isosceles obtuse triangle.
What is a pattern?A pattern is a repeated arrangement of numbers, shapes, colours and other items.
Using the rule, we have two obtuse then one right triangle. Hence the fifth would be an obtuse triangle.
For the second, we have isosceles and scalene changing, hence the fifth would be isosceles.
The triangle gotten from this pattern is an isosceles obtuse triangle.
Find out more on pattern at: https://brainly.com/question/17386984
Write story context for the equivalent shown
3/7x28=12?
(Please help)
have a good day/night!
Thank you for helping
Answer:
is 12=12 but need more context
Express as a sum.
15-7
(its not 8)
Answer:
-7+15. this is what i think it is.
Step-by-step explanation:
Answer:
-7+15 is correct answer. Please Mark it as brainlist answer.