Step-by-step explanation:
puhhh ! that way of typing can be misleading.
let me sum up what equations I think the problem definition specified :
1)
6x + 2y = 82
x - y = 3
2)
y = 4x - 1
x + y = 9
3)
4x + 3y = 17
y = 5 - x
solving 1)
x - y = 3 => x = y + 3
putting this into the first equation
6×(y+3) + 2y = 82
6y + 18 + 2y = 82
8y +18 = 82
8y = 64
y = 8
x = y + 3 = 8 + 3 = 11
solving 2)
using the first equation in the second equation
x + (4x - 1) = 9
5x - 1 = 9
5x = 10
x = 2
y = 4x - 1 = 4×2 - 1 = 8 - 1 = 7
solving 3)
using the second equation in the first equation
4x + 3×(5 - x) = 17
4x + 15 - 3x = 17
x + 15 = 17
x = 2
y = 5 - x = 5 - 2 = 3
find the sum 38+39+40+41...+114+115
It seems like you want to find the sum of 38 to 115:
[tex] \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}[/tex]
If we notice, this is arithmetic series or the sum of arithmetic sequences.
To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.
[tex] \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }[/tex]
This formula only applies to the sequences that have the common difference = 1.
Given that a1 = first term of sequence/series, n = number of terms and a_n = last term
We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.
To find the n, you can use the following formula.
[tex] \displaystyle \large{n = (a_n - a_1) + 1}[/tex]
Substitute an = 115 and a1 = 38 in the formula of finding n.
[tex] \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}[/tex]
Therefore the number of sequences is 78.
Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.
[tex] \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}[/tex]
Hence, the sum is 5967.
if a stone is dropped from a cliff that is 122.5m high then its height in meters after t seconds is h=122.5-4.9t^2. find its velocity after 2s
Answer:
Step-by-step explanation:
Let t = 2
h = 122.5 - 4.9·2² = 122.5-19.6 = 102.9
A survey on Internet usage was conducted among a group of 200 students in the school cafeteria. It was found that 100 students spend at least two hours online every day. Which of these is an example of descriptive statistics? a.) 50% of the students in the cafeteria spend at least two hours online each day. b.) 50% of the students in the school spend at least two hours online each day. c.) 50% of the students in a class spend at least two hours online each day. d.) 50% of the students surveyed spend at least two hours online each day.
Answer:
D) 50% of the students surveyed spend at least two hours online each day.
50% of the students surveyed spend at least two hours online each day.
Hence option d is correct.
Given that,
Number of students who spend at least two hours online = 100
Total number of students surveyed = 200
To calculate the percentage of students who spend at least two hours online each day,
we can use the formula:
percentage = (number of students who spend at least two hours online / total number of students surveyed) x 100%
Plugging in the values from the problem, we get:
percentage = (100 / 200) x 100% = 50%
Therefore, we can conclude that 50% of the students surveyed spend at least two hours online each day.
Learn more about the percent visit:
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Someone please help me with this
Answer:
Step-by-step explanation:
Question 7 plz show ALL STEPS
Answer:
Function C is the only one that matches both definitions for the domain and range.
Step-by-step explanation:
First let's understand what the domain and range definitions mean in plain English.
The following statement means x is defined such that x can be any real number except for 1.
[tex]\{x | x \ne 1, x \epsilon R \}[/tex]
The following statement means y is defined such that y can be any real number except for 3.
[tex]\{y | y \ne 3, y \epsilon R \}[/tex]
So let's see what functions match those definitions. Take a look at the denominator of the functions in question 7, if we plug in x = 1 for any of them, we would be dividing by zero, which we know we can't do since the function would not be defined at that value. Therefore the domain definition is correct for all functions, we cannot use x = 1 for any of them.
Let's move on to the range. Our goal is to find a function where plugging in y = 3 would give us an undefined result. Simply plugin y = 3 into all of the given equations and simplify.
(A) We find that x = 0, and since the function is defined, we know that the range definition does not match.(B) We get the expression -12x + 9 = -3x, where x = 1. Once again the function is defined here, so the range does not match.(C) We get 3x - 3 = 3x, which simplifies to -3 = 0. But clearly -3 does not equal 0, which means the function was not defined for y = 3, which means our range definition matches.(D) We get -3x = 0, which simplifies to x = 0, which means our function is defined, and our range definition does not match.Therefore the function C is the only one that matches both definitions for the domain and range.
The perimeter of a rectangle is 360 centimetres. If the ratio of its length to its width is 11:4, find the dimensions of the rectangle.
Answer: Length 132cm, Breadth 48cm
Explanation:
Perimeter = 360cm
Let the length and breadth be x
ATQ
2(11x + 4x) = 360
22x + 8x = 360
30x = 360
x = 360/30
x = 12
Length = 11×12
= 132 cm
Breadth = 4×12
= 48cm
Must click thanks and mark brainliest
Solve the following system of equations for x: xy = 6
3y = x - 3
Answer:
B
Step-by-step explanation:
xy=6
y=6/x (1)
substitute (1) into 3y=x-3 and solve
Add :-
a+2b-3c, -3a+b+2cand 2a -3b+c
Answer:
[tex]a + 2b -3 c + - 3a + b + 2c + 2a - 3b + c \\ = a - 3a + 2a + 2b + b - 3b - 3c + 2c + c \\ 0a + 0b + 0c \\ thank \: you[/tex]
a+2b-3c+(-3a+b+2c) +(2a-3b+c)
=a+2b-3c-3a+b+2c+2a-3b+c
=a-3a+2b+2b+b-3b-3c++2b+c
=0a+0b+0c
=0
Therefore, the addition of the expressions, a+2b-3c+(-3a+b+2c) +(2a-3b+c) is zero or 0.
To know more about algebraic expressions
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point C is located at (-4,3) on the coordinate plane. Point C is reflected over the x-axis to create point C'. What ordered pair describes the location of C'?
Answer:
(-4,-3)
Step-by-step explanation:
When a point (x,y) is reflected over the x-axis, you take the opposite so it becomes (x,-y).
(-4,3) --> (-4,-3)
The figure below is a rectangular prism.
Which edge is parallel to segment BD?
A. HK
B. BM
C. DK
D. AH
How much can 1/2 go into 25
Answer:
50
Step-by-step explanation:
please mark me as brainliest
Answer:
50
Step-by-step explanation:
Hi there!
Determining how much 1/2 can go into 25 is the same as solving for 25÷1/2:
[tex]25\div\frac{1}{2}[/tex]
Dividing by a fraction is the same as multiplying its reciprocal:
[tex]=25\times\frac{2}{1}\\=25\times2\\=50[/tex]
I hope this helps!
Given: ABCD is a trapezoid,
AB= 13, CD = 14,
BC = 5, and AD= 20.
Find: A
ABCD
Answer:
A=13×13
=169sqr.units
pls help :c if anyone knows what to do
To compare the teaching methodologies of two of its eighth-grade math teachers, a school decides to compare student test scores from the two classes throughout the year.
Which type of statistical study is the school conducting?
a) Matched-pair design study
b) Meta-analysis
c) Retrospective observational study
d) Prospective observational study
Answer:
D) Prospective observational study
Step-by-step explanation:
A study which gathers data moving forward is called a prospective study. Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design.
business/multivariable calc question
help needed asap!!!!
I solved and got a max of (8/5,8) at 64/5
Answers:
There is a max value of 81/8 located at (x,y) = (9/8, 9)
=============================================================
Explanation:
Solve the second equation for y
8x+y = 18
y = 18-8x
Plug this into the first equation
f(x,y) = x*y
g(x) = x*(18-8x)
g(x) = 18x-8x^2
This graphs out a parabola that opens downward, and has a max point at the vertex.
If you apply the derivative to this, you get g ' (x) = 18 - 16x
Set this equal to zero and solve for x
g ' (x) = 0
18 - 16x = 0
18 = 16x
16x = 18
x = 18/16
x = 9/8
Use this x value to find y
y = 18 - 8x
y = 18 - 8(9/8)
y = 18 - 9
y = 9
So the max is x*y = (9/8)*9 = 81/8
Or we could say
g(x) = 18x-8x^2
g(9/8) = 18(9/8)-8(9/8)^2
g(9/8) = 81/8
----------------
To summarize,
There is a max value of 81/8 located at (x,y) = (9/8, 9)
When saying "max value of something", we're basically talking about the largest f(x,y) value. Which in this case is the largest x*y value based on the fact that 8x+y = 18.
A practical real world example of a problem like this would be if you wanted to max out a certain rectangular area based on constraints of how much building material you have for the fence.
One time Maria took 27 minutes to walk 1.8km to school. She left home at 07:48 . Write down the time Maria arrived at school
Answer:
8:15
Step-by-step explanation:
Graph the line for y+1=-3/5(r-4) on a cordinate plane.
Answer: Screenshot attached
Step-by-step explanation:
Simplify: (3x2 − 5xy + 2y2) − (7x2 − 3xy − 3y2) (5 points)
−4x2 + 8xy − y2
−4x2 − 8xy + y2
−4x2 + 2xy − 5y2
−4x2 − 2xy + 5y2
Answer:
-4×2-2xy+5y2
Step-by-step explanation:
(6-5xy+2y2)-(14-3xy-3y2)
=6-5xy+2y2-14+3xy+3y2
=(6-14)+(-5xy+3xy)+(2y2+3y2)
=-4×2-2xy+5y2
Answer:
−4x2 − 2xy + 5y2
Step-by-step explanation:
Each wagon in the Parley
Company of Travelers wagon
train was about 3.65 meters long.
If 12 wagons traveled end to
end, how long would the wagon
train be?
Answer:
43.8 meters
Step-by-step explanation:
12 x 3.65
2. Troy went to see a Monster Truck show. Before the show, Troy got to see
the trucks close up. He noticed that each monster truck tire had a radius of
about 3 feet. Based on the radius, what would be the distance around each
tire?
Monster Truck show. Before the show, Troy got to see
the trucks close up. He noticed that each monster truck tire had a radius of
about 3 feet.
A man starts repaying a loans with first insfallameny of rs.10 .If he increases the instalment by Rs 5 everything months, what amount will be paid by him in the 30the instalment.
Answer:
30×5=150
so 150+10=160
thus his payment in the 30th installment is
rs.160
Please answer ASAP will be greatly appreciated!!
The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length of the garden is 24 ft longer than the width of the garden what is the area of the garden in sq ft
Answer:
297 square feet
Step-by-step explanation:
Let w represent the width of the garden.
Since the length is 24 ft longer than the width, it can be represented by w + 24.
Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and w + 24 as l, then solve for w:
p = 2l + 2w
84 = 2(w + 24) + 2w
84 = 2w + 48 + 2w
84 = 4w + 48
36 = 4w
9 = w
So, the width is 9 ft. Add 24 to this to find the length:
24 + 9 = 33
So, the length is 33 ft.
Find the area of the garden with the formula A = lw:
A = lw
A = (33)(9)
A = 297
The area of the garden is 297 square feet.
In Example 9.2 (p. 214), if you instead carried the suitcase by the handle so that the suitcase was hanging directly at your side, how much work would you do on the suitcase as you carried it forward at a constant walking speed
9514 1404 393
Answer:
none
Step-by-step explanation:
No work is required to maintain an object at a constant speed with no change in direction. Work is only done when an object is accelerated, or moved some distance in the direction of the net force applied.
you would do no work
Find the area of the triangle with the following measurements: B = 67°, a = 13 cm, c = 21 cm
9514 1404 393
Answer:
125.6 cm²
Step-by-step explanation:
The relevant area formula is ...
Area = (1/2)ac·sin(B)
Area = (1/2)(13 cm)(21 cm)·sin(67°) ≈ 125.6 cm²
If two chords of a circle are congruent then they are equidistance from the
A. secant.
B. center.
c. tangent.
D. edge of the circle.
Answer:
I think
The choose B. center.
I hope I helped you^_^
Please Help Polygons
Step-by-step explanation:
5.25....................
The quotient of three times a number and 4 is at least -16.
If anyone can help me I need to Define the variable and write an inequality, then solve.
Answer:
3x4≥−16
3x≥−64
x≥−643
x≥−2113
The answer is x≥−2113
look at the image below
Answer:
SA = 153.9m^2
Step-by-step explanation:
SA = 4[tex]\pi[/tex][tex]r^{2}[/tex]
r = 3.5
SA = 4[tex]\pi[/tex][tex](3.5)^{2}[/tex]
SA = 4[tex]\pi[/tex](12.25)
SA = 49[tex]\pi[/tex]
SA = 153.9m^2
fill in each balance???
Answer:
Step-by-step explanation:
Take the beginning number and add or subtract each transaction to get a new balance. For example,
349.45
- 23.42 = 326.03
- 14.95 = 311.08
+ 276.50 = 587.58
- 219.93 = 367.65
- 76.84 = 290.81
