The solution to the system of equation is x = 1 / 5 and y = 4
How to solve system of equation?The system of equation can be solved as follows:
- 5 / 7 - 11 / 7 x = - y
7 + 5x = 2y
let's rearrange the equations
Therefore,
- 11 / 7 x + y = 5 / 7
5x - 2y = -7
Let's multiply equation(i) by 7 to eliminate the fractions
Hence,
-11x + 7y = 5
5x - 2y = -7
Therefore, using substitution method
5x = -7 + 2y
x = -7 / 5 + 2 / 5 y
Hence,
-11(-7 / 5 + 2 / 5 y) + 7y = 5
77 / 5 - 22 / 5 y + 7y = 5
- 22 / 5 y + 7y = 5 - 77 / 5
-22y + 35y / 5 = 25 - 77 / 5
13y / 5 = -52 / 5
cross multiply
65y = -260
y = -260 / 65
y = 4
Hence,
5x - 2(4) = -7
5x - 8 = -7
5x = -7 + 8
x = 1 / 5
Therefore, the solution to the system of equation is x = 1 / 5 and y = 4
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Find the surface area of the cube shown below. A. 66 cm2 B. 121 cm2 C. 726 cm2 D. 1,331 cm2
Answer:
66
Step-by-step explanation:
Translate (3x-1,y+5)
Answer: Three times x minus y is five times the sum of y and two times x.
Step-by-step explanation:
the given equation is: (3x-1,y+5)
The left hand side of the equation may be written as: "Three times x minus y."
The right hand side of the equation may be written as: "Five times the sum of y and two times x."
Hence, the correct option is:
|2x+2| =< 0
If the solution set is”null” also known as the empty set or no solution. Explain why
=========================================================
Explanation:
The output of an absolute value is never negative.
The result of |2x+2| can never be negative, so we will have no solutions for the portion |2x+2| < 0
There will be one solution for |2x+2| = 0 as shown in the steps below
|2x+2| = 0
2x+2 = 0
2x = -2
x = -2/2
x = -1
------------------
Check:
|2x+2| ≤ 0
|2(-1)+2| ≤ 0
|-2+2| ≤ 0
|0| ≤ 0
0 ≤ 0
We get a true statement at the end to fully confirm the single solution of x = -1
Which of the following identifies the individuals in the
set?
The individuals of a set are the various data or variable of a data set.
The study's participants or study subjects are referred to as individuals. The trait of the person being measured or observed is known as a variable. For instance, if we were to do a research on climbers of Mount Everest, the participants would be the real climbers who succeeded in reaching the summit.
A categorical variable places each individual in to a category such as male or female.
A quantitative variable has numerical values that measure some characteristic of each individual, such as height in centimeter or salary in dollars.
The problem deals with the concept of types of variables. We use the definition of variables to identify/determine the type variable from the known information.
The individuals in the data set are vehicles or cars.
The given information is related to the different types of cars and its model, and specifications. Hence, the vehicles or cars are individuals in the data set.
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MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges
$2.50 to rent shoes and $4.50 per game.
a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling
alley B?
Bowling alley A:__ or more games
Bowling alley B:__
or __
games
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)?Explain.
Using linear functions, we have that:
a. For 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.
b. For any number of games, the cost at alley B will be less.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The slope is the cost per game.The intercept is the cost of 2 shoes.Hence they are given as follows:
A(x) = 4x + 7.5.B(x) = 4.5x + 5.The cost for A will be less when:
A(x) < B(x).
Hence:
4x + 7.5 < 4.5x + 5
-0.5x < -2.5
0.5x > 2.5
x > 2.5/0.5
x > 5.
Hence for 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.
For item b, with the increase of $0.5 per game, we have that:
A(x) = 4.5x + 7.5.
Then the costs per game will be the same, while alley B has the lower intercept, meaning that for any number of games, the cost at alley B will be less.
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O Solve questions Pg #61 Prá
1 Correct 78. 4695 to
a) 1 decimal place.
c) the nearest hundredth
The number corrected to 1 decimal place is 78.5
The number corrected to the nearest hundredth is 78.47
EstimationFrom the question, we are to estimate the given number to the nearest 1 decimal place
The given number is
78.4695
Correcting to 1 decimal place
In the given number, we can observe that the hundredth digit is greater than 5, thus we will add 1 to the tenth digit
Thus,
78.4695 corrected to 1 decimal place is 78.5
Correcting to the nearest hundredth
The thousand digit is greater than 5, thus we will add 1 to the hundredth digit
Thus,
78.4695 corrected to the nearest hundredth is 78.47
Hence,
The number corrected to 1 decimal place is 78.5
The number corrected to the nearest hundredth is 78.47
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In a normal distribution the theoretical mean is 30 and the theoretical standard deviation is 5. Find: a) the area below 24, b) the area between 24 and 36, c) the point that has 95% of the area below it.
Answer:
a) P(X < 24) = 0.1151
b) P(24 < X < 36) = 0.7698
c) X value for P(x < X) = 0.95 is X = 38.225
Step-by-step explanation:
a) P(X < 24)
Since μ = 30 and σ = 5 we have:
[tex]\text {z value = } \dfrac{24-30}{5}} = -1.2[/tex]
P(X < 24) = P(Z < -1.2) = 0.1151
You can use a calculator or the standard normal tables to determine P(Z < -1.2)
b) P(24 < X < 36)
First find P(X < 36) using the technique detailed in part a)
For 36, the Z value is
[tex]\dfrac{36-30}{5} = 1.2[/tex]
P(X < 36) = P(z < 1.2) = 0.8849
P(24 < X < 36) = P(X < 36) - P(X < 24) = 0.8849 - 0.1151 = 0.7698
c) X value below which 95% of the area is covered
Using a calculator (or tables) the z value corresponding to P(z < Z) = 0.95 is Z = 1.65(approx)
[tex]\text{We have } \dfrac{X - \mu}{\sigma} = z\\\\\dfrac{X - 30}{5} = 1.645\\\\\text{Multiplying both sides by 5: }\\\\X - 30 = 1.645 \times 5 = 8.225\\\\X = 30 + 8.225 = 38.225[/tex]
So X value is 38.225-
Find the distance between each pair of points
(2,-8) and (5,-6)
(-6,3) and and (5,6)
(1,5) and (7,-3)
(-1,4) and (0,-4)
(1,-3) and (-7,-4)
(-7,-6) and and (1,0)
(-3,-5) and and (-1,-8)
(1,8) and (-6,-1)
(2,-8) and (-4,-1)
Step-by-step explanation:
x1=2 , y1= -8
x2=5 , y2=-6.
distance= rootunder x2-x1 whole square + y2-y1 whole square
=(5-2)whole square + (-6-(-8)) whole square
= root under 9+4
=rootunder 13 units
Antwan determines the distance between the points –7 and 2 on a number line. Maggie determines the difference between the numbers –7 and 2. How are Antwan’s and Maggie’s solutions related?
Maggie’s solution is the absolute value of Antwan’s solution.
Antwan’s solution is the absolute value of Maggie’s solution.
Both solutions are greater than either of the two numbers in the problem.
Both solutions are less than either of the two numbers in the problem.
Antawan's solution is the absolute value of Maggie's solution is the solution related to Antawan's and Maggie's solution.
Given
Antawan determines the distance between two points as 9.
Maggie finds the difference between two numbers ₋ 7 ₋ 2 = ₋9
Hence we notice that Antawan's solution is the absolute value to the Maggie's solution.
The non-negative value of x, regardless of its sign, is the absolute value (or modulus) | x | of a real number x. For instance, 5 has an absolute value of 5 and so does 5, which likewise has an absolute value of 5. One way to conceptualize a number's absolute value is as its separation from zero on the real number line.
hence option 2 is right.
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A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 9 mi north to his place of work. if a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
If a road was made directly from his home to his place of work, its distance will be 16.6 mi.
If a man drives east from his home, makes a left turn at an intersection, and then travels north to his place of work, then the path he travels resembles the sides of a right triangle (see attached photo).
if a road was made directly from his home to his place of work, then this path will be the hypotenuse of the triangular path.
Using Pythagorean theorem, we can solve for the distance of the road.
c^2 = a^2 + b^2
where c is the distance of the road
a is the distance he travels to the east
b is the distance he travels up north
c^2 = a^2 + b^2
c^2 = (14 mi)^2 + (9 mi)^2
c^2 = (196 + 81) mi^2
c^2 = 277 mi^2
c = 16.64331698 mi
distance of the road = c = 16.64331698 mi
Rounding off to the nearest tenth of a mile:
distance of the road = 16.6 mi
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Find the equation of the line that passes through (1,3) and is perpendicular to y = 2x + 3.
Leave your answer in the form ax + by = c Where a, b and c are integers.
The equation of the line that passes through (1,3) and which is perpendicular to y = 2x ₊ 3 is x ₊ 2y = 7.
Given the equation of the which passes through the point is (1,3)
the line is perpendicular to y = 2x ₊ 3
first we need to determine the slope of the equation.
line is perpendicular to y = 2x ₊ 3
perpendicular means slope (m) = ₋1
but given the in the line equation we have
y = mx ₊ c
m = 2
therefore ₋1 = 2
hence slope m = ₋1/2
Then the line passing through (1,3), substitute the coordinates of the point in the equation of the line:
y ₋ y₁ = m(x ₋ x₁)
take (1,3) as (x₁,y₁)
y ₋ 3 = ₋1/2 (x ₋ 1)
y ₋ 3 = ₋1x/2 ₊ 1/2
y ₋ 3 = ₋x ₊ 1/2
2y ₋ 6 = ₋x ₊ 1
2y ₊ x ₋ 6 ₋ 1 = 0
2y ₊ x ₋ 7 = 0
2y ₊ x = 7
x ₊ 2y = 7
which is in the form ax ₊ by = c
Hence we derived the equation of the line as x ₊ 2y = 7 which is in the form of ax ₊ by = c.
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the 5th term of an A.P is 9 and the 8th term is 27.Find the 31st term
Answer:
189
Step-by-step explanation:
The difference between consecutive terms of an arithmetic sequence, known as the common difference is given by
d = a(k) - a(k-1) where k = 1,2,3 ....n
We have the 5th term as a(5) = 9
The 6th term is 9 + d
The 7th term is 9 + 2d
The 8th term is 9 + 3d
Each successive term adds a d to the previous term
We have 8th term = 27
So 9 + 3d = 27
3d = 27 - 9 (subtract 9 from both sides)
3d = 18
Divide above by 3 on both sides to get
d = 18/3 = 6
So the common difference is 6
Let's figure out how to calculate the 31st term
We can see that the 5th term can be expressed as
9 + 0d = 9 + 0.6 = 9
The sixth term is
9 + 1d = 9 + 1(6) = 9 + 6 = 15
The seventh term is 9 + 2d = 9 + 12 = 21 and so on
Therefore the general equation for the nth term, given the 5th term
is
a(n) = a(5) + (n - 5)(6) 9 + 6(n - 5)
So the 31st term is
a(31) = 9 + 6(31-1) 9 + 6 x 30 = 9 + 180 = 189
Answer: 31st term is 189
3. Which statement is true about a translation?
A) A translation takes a line to a parallel line or itself.
B) A translation takes a line to a perpendicular line.
C) A translation requires a center of translation.
D) A translation requires a line of translation.
A) A translation takes a line to a parallel line or itself.
Answer: A) A translation takes a line to a parallel line or itself.
Step-by-step explanation:
Factor completely:
4x2−144
A
4(x2−36)
B
4(x+6)(x−6)
C
(2x−12)(2x+12)
D
(x+12)(4x−12)
Answer:
C
Step-by-step explanation:
(2x - 12)(2x + 12)
4x² + 24x - 24x - 144
4x² - 144
solve the equation tanx+secx=2 given that x is greater than or equal to 0 and less than or equal to 2pie
X = 0.6444
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
tan x +sec x =2
⇒sin x /cosx + 1/ cos x = 2
⇒1+sin x / cos x =2
⇒ (sin² x/2 +cos ² x/2 +2 sin x/2 cos x/2 )/( cos ² x/2 - sin²x/2 ) = 2
⇒(cos x/2 +sin x/2)² / ( cos ² x/2 - sin²x/2 ) = 2
⇒( cos x/2+sin x/2)² / (cos x/2 + sin x/2)(cos x/2-sinx/2) = 2
⇒(cos x/2 +sin x/2)/ (cos x/2-sin x/2) = 2
Dividing by cos x/2 in both numerator and denominator,
⇒(1+tan x/2)/(1-tan x/2) =2
⇒ 1 + tan x/2 = 2 - 2tanx/2
⇒ tan x/2 = 1/3
⇒ x= 0.6444
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The ratio of circumference/diameter for all circles is pie. what is the ratio of force/mass for all freely-falling bodies?
The ratio of circumference/diameter for all circles is π. And the ratio of force/mass for all freely-falling bodies will be g.
What is the circumference of a circle?Let d be the diameter of the circle. The circumference of the circle will be
C = πd units
The ratio of circumference to diameter for all circles is pie.
C/D = πd / d
C/D = π
Then the ratio of force to mass for all freely-falling bodies will be
The force acting on a free-falling body of mass (m) is mg. Then we have
Force/Mass = mg / m
Force/Mass = g
Where g is the acceleration due to gravity.
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Hans spent $38 on fruit at the grocery store. He spent a total of $40 at the store. What percentage of the total did he spend on fruit?
Is 168 divisible by 2,3,4,5,6,8,9 or 10 explain why please
Help ASAP
Answer:
2,3,4,6,8
Step-by-step explanation:
prime factorization: 2^3×3×7 which has: 2, 3, 4, 6, 8
Answer:
It is divisible by 1, 2, 3, 4, 6, 7, 8
Step-by-step explanation:
Everything is divisible by one, so this is obvious.
168 is an even number, therefore being able to be divided by 2
1+6+8=15 which is in the 3 times tables (3x5=15)
If the last two digits are divisible by 4 (which 68 is) then you can divide it by 4.
168 doesn't end in 5 or 0 so it can't be divided by 5
This number can be divisible by 2 and 3 so it can be divided by 6
160 is divisible by 8 so if you add 8 it is divisible.
1+6+8=15 again which is not divisible by 9
It doesn't end in 0 meaning it cannot be divisible by 10
Hope this helped! <3
Find the area of a circle with a 15inch diameter in terms of pie
Answer:
56.25π in²
Step-by-step explanation:
The area of a circle is given by πr², where r is the radius of the circle.
Given that the diameter is 15 inch, let's calculate the radius.
Diameter= 2 ×radius
Radius
= 15 ÷2
= 7.5 in.
Applying the formula for area of circle,
area of circle
= π(7.5)²
= 56.25π in²
Since the question requires for the answer to be in terms of π, we have arrived at our answer.
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A circular plate has a circumference of 34.54in. What is the area? Use 3.14 for pie and round to the nearest square inch.
The area of the circular plate is 9234 inches²
How to find area of the circular plate?The plate is circular and have a circumference of 34.54 inches.
Hence, let's find the radius of the circular plate using the circumference of the circular plate.
circumference of the circular plate = 2πr
where
r = radiusTherefore,
34.54 = 2π × r
r = 34.54 / 2π
r = 17.27π
Therefore,
area of the circular plate = πr²
area of the circular plate = π × ( 17.27π)²
area of the circular plate = π³ × 298.2529
area of the circular plate = 3.14³ × 298.2529
area of the circular plate = 9233.65447952
area of the circular plate = 9234 inches²
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the formula for the volume of a cylinder is v = πr2h. The cylinder to the right has an exact volule of 500π cubic meters. Find its height
The height of the cylinder is 20 meters.
What is the volume of a cylinder?The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the material. Check the shape's volume here.
Formula= V = π r² h
According to the given value,
The formula for the volume of a cylinder is V=πr²h.
The cylinder to the right has an exact value of 500π cubic meters.
Its radius is given as 5 meters in the figure.
volume of the cylinder.
V = π r² h
We have,
V = 500π cubic meters
500π cubic meters = πr²h
Find the height of the cylinder.
We have,
500π cubic meters = πr²h
Divide both sides by π
500cubic meters = r²h
We have,
r = 5
500 cubic meters = 5² square meters x h
500cubic meters = 25 square meters x h
Divide both sides by 25
20 meter = h
h = 20 meters
Thus the height of the cylinder is 20 meters.
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someone help please!!!!
Answer:
x = -2
TU = 4
UB = 2
Step-by-step explanation:
you can add x^2 with 4x+10 and equate it to 6:
x^2 + 4x + 10 = 6
x^2 + 4x + 4
then u can use the roots formula : x = (-b ± √ (b2 - 4ac) )/2a
so it'll be x = {-4±[√16 - 4(4)]}/2
x= -2
then u can substitute it and find TU and UB
TU= (-2)^2 = 4
UB= 4(-2)+10 = 2
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system
Answer: The equations are:
X+3=Y;
45X + 75Y = 1455 ;
The variables used are X and Y specifying number of small and large boxes
Step-by-step explanation:
Let X be the number of small boxes
Let Y be the number of big boxes
The first equation is: X+3=Y; ( Since there were 3 more small boxes shipped than large boxes )
The second equation is: 45X + 75Y = 1455 ( this is because the small box weighs 45 pounds and big box weighs 75 pounds. The total weight of the small boxes is 45 times the weight of each individual box. And the total weight of the second boxes is equal to 75Y.)
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Answer:
Step-by-step explanation:
The variables used are A and B specifying number of small and large boxes
Let the number of small box is A
Let the number of large box is B
The first equation is: A+3=B;
( Since there were 3 more small boxes shipped than large boxes )
The second equation is: 45A + 75B = 1455 ( this is because the small box weighs 45 pounds and large box weighs 75 pounds. The total weight of the small boxes is 45 times the weight of each box. And the total weight of the second boxes is equal to 75B.)
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A number Q is at least -2 and less than 6
Answer:
Q=-8
Step-by-step explanation:
Q-2-6
Atsu and Sabu shared an amount of money in the ratio 3:7 respectively. if Sabu received 20 cedis more than Atsu, how much was shared
Answer:
Step-by-step explanation:
Atsu : Sabu
3 : 7
x : x + 20
x is equal to the number of cedis
cross multiply the ratio above
3(x+20) = 7x
3x + (20×3) = 7x
3x + 60 = 7x
3x - 3x + 60 = 7x - 3x (put - 3x on both sides of the equation)
60 = 4x
60/4 = 4x/4 (divide both sides by 4)
15 = x
What is b in this equation? -16 = 0.2b
Answer:
-16=0.2b
-16/0.2=b
b= -80 answer
Answer:
In the equation "-16 = 0.2b", b is equal to -80.
Step-by-step explanation:
-16 = 0.2b
Turn the decimal into a fraction. This will make solving simpler.
-16 = [tex]\frac{1}{5}b[/tex]
Multiply both sides by 5.
-80 = 1b
Simplify.
b = -80
How can you rearrange two digits in the number 2,957,648 so that the value of the digit 4 is 10 times greater?
Answer:
2,957,468
Step-by-step explanation:
Each digit to the left is worth 10 times more than the same digit one place to the right.
If 2,957,648 becomes 2,957,468, the 4 moves from the tens place to the hundreds place, and now its value is 400 instead of 40, so it's 10 times greater.
In 8 years Jack will be three times as old as he is now. How old is he now?
Answer:
4 years old
Step-by-step explanation:
3x = x + 8
2x = 8
x = 4
Answer:
4 y/o
Step-by-step explanation:
x = age now
add 8 years
x+8 and this equals 3 times as old as he is now, or 3x
x+8 = 3x subtract 'x' from both sides
8 = 2x divide both sides by 2
x = 4 y/o
a) Work out the value of 23 +52
b) Work out the value of 72-33
c) Work out the value of 82 + √100
Answer:
Step-by-step explanation:
One
23 + 52 = 75 This can be done using columns
2 3
5 2 No carries Add.
7 5
Two
72 - 33 = 39
7 2
3 3 You have to borrow a ten from the 7 to make this work
3 9
Three
82 + sqrt(100)
sqrt(100) = 10
82 + 10 = 92
The diagram shows a solid triangular prism with a cylindrical hole of radius r cm drilled through it. (i) The ratio of the volume of solid removed : volume of remaining solid is 1 : 6. Find the value of r. Using your answer in part (i), find the total surface area of the solid shown.
The value of the radius r is 9.35 cm.
The dimensions of the triangular prism is 62 cm × 62 cm × 85 cm.
The volume of the prism will be:
Volume = (1/2) × 62 × 62 × 85
Volume = 163370 cm³
Now,
The volume of solid removed: The volume of remaining solid = 1 : 6
Therefore,
The solid removed = ( 1 / 7 ) of the total volume
Solid removed = ( 1 / 7 ) × 163370
Solid removed = 23338.57 cm³ which is the volume of the cylindrical hole.
Now, the volume of the cylinder is:
V = π (r)² h
23338.57 = π (r)² × (85)
23338.57 = (3.142) × (r)² × (85)
23338.57 = 267.1 r²
r² = 87.38
r = √(87.38)
r = 9.35 cm
The surface area of the triangular prism:
A = (1/2) (b) (h)
A = (1/2) (85)(62)
A = 2653 cm²
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