Answer: [tex]\huge\boxed{x=3\frac{1}{3} \quad ;\quad y=-3}[/tex]
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol+\ \left \{ {{6x+4y=8} \atop {-4y=12}} \right. \Longrightarrow\\\\\\ 6x+ 4y\!\!\!\!\!\diagup-4y\!\!\!\!\!\diagup=12+8 \\\\6x=20 \\\\x=\frac{20}{6} =\frac{10}{3} =3\frac{1}{3} \quad ; \quad y=-3[/tex]
A rectangular sheet of paper is 12 1/2 cm long and 10 2/3 cm wide.Find it's perimeter
Answer:
Given
length of rectangular sheet of paper is 12 (1/2) i.e. (25/2)
Breadth of rectangular sheet of paper is 10 (2/3) i.e. (32/3)
But we know that perimeter of rectangle = 2 (length + breadth)
Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]
LCM of 2 and 3 is 6,
by taking this and simplifying we get
Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]
= 2[(75/6) + (64/6)]
= 2(139/6) = (139/3)
= 46 (1/3) cm
Answer:
Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]
LCM of 2 and 3 is 6,
by taking this and simplifying we get
Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]
= 2[(75/6) + (64/6)]
= 2(139/6) = (139/3)
= 46 (1/3) cm
Step-by-step explanation:
A square pyramid is inscribed in a rectangular prism. A cone is inscribed in a cylinder. The pyramid and the cone have the same volume. Part of the volume of the rectangular prism, 1 V 1 , is not taken up by the square pyramid. Part of the volume of the cylinder, 2 V 2 , is not taken up by the cone. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?
Answer:
V₂ = V₁
Step-by-step explanation:
Let the height of the rectangular prism = h
Let s represent the side length of the base of the square prism, we have;
The volume of the prism, [tex]V_{prism}[/tex] = s²·h
The volume of the square pyramid, [tex]V_{pyramid}[/tex] = (1/3)·s²·h
∴ V₁ = The area not taken up by the square pyramid = [tex]V_{prism}[/tex] - [tex]V_{pyramid}[/tex]
∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h
Similarly, for the cylinder, we have;
Let h represent the height of the cylinder
Let r represent the radius of the base of the cone, we have;
Therefore;
The volume of the cylinder, [tex]V_{cylinder}[/tex] = π·r²·h
The volume of the cone, [tex]V_{cone}[/tex] = (1/3)·π·r²·h
∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h
V₂ = (2/3)·π·r²·h
[tex]V_{cone}[/tex] = [tex]V_{pyramid}[/tex]
Therefore;
(1/3)·π·r²·h = (1/3)·s²·h
∴ π·r² = s²
Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁
V₂ = V₁.
Jin completed 8 pages in his math workbook and
12 pages in his science workbook. This is 25% of the
total number of pages in both workbooks together.
If there are 32 pages in his math workbook, how
many pages are there in his science workbook?
A. 20
B.
48
C. 80
D. 128
Need answer :))))))))
Answer:
cost per serving can be used as a result of using your head to think
The sum of four consecutive numbers is two more than three times the greatest of these numbers. Find the numbers.
Answer:
9, 10, 11, 12
Step-by-step explanation:
Let the consecutive numbers be:
x, x+1, x+2, x+3
Greatest of the numbers will be: x + 3
x+x+1+x+2+x+3 = 3(x+3) + 2
4x + 6 = 3(x+4) + 2
4x + 6 = 3x + 12 + 2
4x + 6 = 3x + 14
Collect like terms
4x - 3x = 14 - 6
x = 8
x +1 = 8+ 1 = 9
x + 2 = 8 + 2 = 10
x + 3 = 8 + 3 = 11
x + 4 = 8 + 4 = 12
A boy bought an article for £9. He spent £4
repairing it and sold it for £18. Calculate the gain
percent on his total costs. (to nearest %)
Help
Answer:
Profit % = 39%
Step-by-step explanation:
Cost price of the article = 9
Price for repairing = 4
Therefore, Total cost of the article = 9 + 4 = 13
Selling price of the article = 18
Profit = 18 - 13 = 5
Hence,
[tex]Profit \% = \frac{Profit}{Cost \ price} \times 100\\\\[/tex]
[tex]= \frac{5}{13} \times 100\\\\=38.46 \%\\\\=38.5 \%[/tex]
Profit percent (to the nearest %) = 39%
which country won
the last world cup
Answer:
The country is France.
The correct answer is France
What is the equation of the line graphed below?
5
-5
5
(1, -3)
-5
O A. y = 3x
B. y=-3x
c. y=-5
D. y =
-X
Answer: y = -3x this is the answer.
PLEASE HELP, I WILL GIVE YOU BRAINLIEST!
Find the equation of a line that results in one real solution as part of a system with f(x)=x^2+2
Step-by-step explanation:
i hope this will help you
Answer:
give that person brainliest
Step-by-step explanation:
I am tired bestie. You are lucky we are friends. want sleep but homeworrkkk
Use the elimination method to solve the system of equations.
A. Infinitely many solutions
B. (10, 10)
C. (16, 18)
D. No solution
Answer:
they are the dame line...
A. Infinitely many solutions
Step-by-step explanation:
2log₃4-log₃8+log₃9/8
hurry im timedd
Answer:
[tex]2(1 - log_{3}(2) )[/tex]
Step-by-step explanation:
I have attached the explanation above, hopefully this help
what is the length of KM ? no links . HELP
Answer:
40 units
Step-by-step explanation:
9x-5=7x+7
9x-7x=7+5
2x=12
x=6
6x+4
6(6)+4
36+4
40
A²,b²,c² are consecutive perfect squares.How many natura numbers are lying between a² and c², if a>0
Answer:
The quantity of natural numbers between [tex]a^{2}[/tex] and [tex]c^{2}[/tex] is [tex]2\cdot (a + b) + 1[/tex].
Step-by-step explanation:
If [tex]a^{2}[/tex], [tex]b^{2}[/tex] and [tex]c^{2}[/tex] are consecutive perfect squares, then both [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are natural numbers and we have the following quantities of natural numbers:
Between [tex]b^{2}[/tex] and [tex]c^{2}[/tex]:
[tex]c^{2} = (b+1)^{2}[/tex]
[tex]c^{2} = b^{2}+2\cdot b + 1[/tex]
[tex]c^{2}-b^{2} = 2\cdot b + 1[/tex]
And the quantity of natural numbers between [tex]b^{2}[/tex] and [tex]c^{2}[/tex] is:
[tex]c^{2}-b^{2}-1 = 2\cdot b[/tex]
Between [tex]a^{2}[/tex] and [tex]b^{2}[/tex]:
[tex]b^{2} = (a + 1)^{2}[/tex]
[tex]b^{2} = a^{2} +2\cdot a + 1[/tex]
[tex]b^{2}-a^{2} = 2\cdot a + 1[/tex]
And the quantity of natural numbers between [tex]a^{2}[/tex] and [tex]b^{2}[/tex] is:
[tex]b^{2}-a^{2}-1 = 2\cdot a[/tex]
And the quantity of natural numbers between [tex]a^{2}[/tex] and [tex]c^{2}[/tex] is:
[tex]Diff = 2\cdot a + 2\cdot b + 1[/tex]
Please observe that the component +1 represents the natural number [tex]b^{2}[/tex]
hshsjshshsjsksjjsbsbbs bc hd
Answer:
its b b b
Step-by-step explanation:
Helppp and explain too
Answer:
the first option
Step-by-step explanation:
I have attached the explanation. hope this help
PLEASE SHOW ALL WORK
The function s(t) = t2+2t+5shows the height s(t), in feet, of a water balloon after t seconds. A second water balloon moves in the air along a path represented by p(t)=11+3t where p(t) is the height, in feet, of the balloon from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the two functions. What is the solution for s(t) = p(t)? How do you know? Include the table in your answer.
Part B: Explain what the solution from Part A means in context of the problem.
Answer:
t = 2,3
Step-by-step explanation:
s (t) = t^2 + 2 t + 5
p (t) = 11 + 3 t
A:
s (1) = 8
s (2) = 13
s (3) = 20
s (4) = 29
Now
[tex]t^2 + 2 t + 5 = 11 t + 3t \\\\t^2 - t - 6 = 0\\\\t^2 - 3 t - 2 t - 6 = 0 \\\\(t-2)(t-3)=0\\\\t = 2, 3[/tex]
(b) The values are same at t =2 an t =3.
Which of the following
is most likely the next step in the series?
Answer:
B.
Step-by-step explanation:
The numbers are always in the blue side, and the blue side starts at facing right, left, right, and then left.
The probability that Caroline wins a raffle is given by the expression
m/n.
Write down an expression, in the form of a combined single fraction, for the probability that Caroline does not win.
Answer: [tex]\frac{n-m}{n}[/tex]
This is the same as writing (n-m)/n
Don't forget about the parenthesis if you go with the second option.
==================================================
Explanation:
The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.
For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.
The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.
We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".
Doing a bit of algebra would have these steps
[tex]1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\[/tex]
and now the expression is one single fraction.
Which of the following options results in a graph that shows exponential growth? (2 points)
f(x) = 0.4(3)x
f(x) = 3(0.5)x
f(x) = 0.8(0.9)x
f(x) = 0.9(5)−x
Answer:
Step-by-step explanation:
The formula for exponential equations is
[tex]y=a(b)^x[/tex] where a is the initial value and b is the growth rate. If b is greater than 1, we have growth; if 0 < b < 1, then we have decay. The only choice that shows a b value greater than 1 is the first one where b = 3. (The last one is also a decay as it can be written as
[tex]f(x)=0.9(\frac{1}{5x})[/tex] which isn't even exponential!)
WILL GIVE BRAINLIST!
What is the slope of the line graphed on the coordinate plane?
A graph with a line running through coordinates (0, 6) and coordinates (1, -2)
Work Shown:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (-2-6)/(1-0)
m = -8/1
m = -8
The slope is -8
We can think of it like saying "go down 8 and move to the right 1 unit", since -8 = -8/1.
Put another way: slope = rise/run = -8/1
rise = -8 and run = 1.
Answer:
-8
it's easy just use the equation y2-y1 ÷ x2-x1
question on the image
(with the steps)
Answer:
40°
Step-by-step explanation:
The given triangle is a isosceles triangle . And we know that in a isosceles triangle opposite angles are equal . Therefore ,
> x + 70° + 70° = 180°
> x + 140° = 180°
> x = 180° - 140°
> x = 40°
Answer:
40 degrees
Step-by-step explanation:
We know that the base angles are congruent (a fancy word for equal) because of the slash marks. This means that both of the base angles are 70.
Every triangle adds up to 180 degrees.
So, You can just do 180 - (70+70)
Algebra version:
70 + 70 + x = 180
140 + x = 180 (subtract 140 on both sides)
x = 40
hope this helps :)
the ratio of boys to girls is 4:3 .if there are 24boys ,how many are there?
Answer:
[tex]{ \bf{total \: ratio = 4 + 3 = 7}} \\ { \tt{let \: population \: be \: p}} \\ \frac{4}{7} \times p = 24 \\ 4p = 168 \\ p = 42 \\ { \bf{there \: are \: 42 \: people}}[/tex]
Boys to girls- 4:3
Boys and girls- 24 and x (let the girls be x)
4/3=24/x
=4x= 72
= x= 72/4
= x= 18 girls
Ans: There are 42 children (24+18)
The length, breadth and height of an object are 20cm, 15cm and 25cm respectively. Its mass is 7kg. Find its volume and density. vers F. 1.1.3.4m ii. 65000g iii. 24.325 hrs iv. 7500m 00cm', 0.933g/cc st Work a brick and measure its length, breadth and height. alate its volume by using formula. Find its mass by using a balance. Calculate its density. Does it float or sink in the r? Why? Explain. ence & Environment Books
Answer:
the above answer help you.
if the slope of one of these perpendicular lines is -4/5 the slope of the other line is ____
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
Answer:
There is no actual question here, this is just a statement.
re-read the question .... i assume it says "what is the highest that she will get during a dive?"
highest point is at t = 33/32
– 16(33/32)^2 + 33(33/32) + 4 =
62.015625
Step-by-step explanation:
Lindsey will be 30 feet in the air at approximately 1.09 seconds and 2.48 seconds.
To find the time at which Lindsey will be 30 feet in the air, we need to solve the quadratic equation y = -16x² + 33x + 45 for x when y = 30.
Setting y equal to 30, we have:
30 = -16x² + 33x + 45
Rearranging the equation, we have:
16x² - 33x - 15 = 0
To solve this quadratic equation, we can factor or use the quadratic formula. In this case, factoring might be more challenging, so we'll use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values from our equation, we have:
x = (-(-33) ± √((-33)² - 4(16)(-15))) / (2(16))
Simplifying, we get:
x = (33 ± √(1089 + 960)) / 32
x = (33 ± √(2049)) / 32
Calculating the square root of 2049, we have:
x = (33 ± √(2049)) / 32
x ≈ 1.09 or x ≈ 2.48
To learn more about quadratic equation click on,
https://brainly.com/question/27958207
#SPJ2
Complete question is:
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x² + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
At what time will Lindsey be 30 feet in air?
− 0.32 + 0.18 = 0.25 − 1.95
Answer:
Step-by-step explanation:
0.18-0.32 = .25-1.95
-0.14 = 1.70
obviously that equation above is not true, I suspect that there were some "x" variables on some of those numbers?
What is the gradient of a line perpendicular to a line with a gradient of -6?
Answer:
1/6
Step-by-step explanation:
Gradient of a line perpendicular to a line with a gradient of m = -1/m
Gradient of a line perpendicular to a line with a gradient of -6 = -1 /-6 = 1/6
What is the difference between calculating the area and calculating the perimeter of a rectangle?
Answer:
For perimeter you add up the side lengths to get the perimeter but for area you multiply the length times width (L x W )to get area.
Step-by-step explanation:
seventy of myra’s classmates are traveling by the bus to a football game in another town. they hired 2 buses, but there were only 64 seats. the remaining 6 students had to travel in a separate van the equation 2b+6=70 represents the given scenario. what does b represent
Answer:
The b represents the people on each bus.
Step-by-step explanation:
Answer:
C.the number of students who rode on each bus.
Step-by-step explanation:
define complementary angles .
Answer:
A pair of angles is known as complementary angles when the sum of their angles is 90°.