Answers
The following weights are listed below:
A red circle has a weight of 20 units.A yellow rhombus has a weight of 8 units.A green trapezoid has a weight of 7 units.A dark blue square has a weight of 6 units.A light blue triangle has a weight of 5 units.The sum of the weights of a red circle, a yellow rhombus and a green trapezoid is equal to 35 units.
How to solve a system of linear equation behind a weight system
In this question we find a case of abstract thinking, in which we find a weight system at equilibrium. There are the following variables below:
x - Weight of a red circle.
y - Weight of a purple cross.
r - Weight of an orange star.
u - Weight of a dark blue square.
v - Weight of a yellow rhombus.
w - Weight of a green trapezoid.
z - Weight of a light blue triangle.
And the resulting system of linear equations is:
x + y = 24 (1)
y + v = 12 (2)
u = 6 (3)
2 · r = 6 (4)
1.5 · v + 2 · u = 24 (5)
0.5 · v + w + r + 2 · z = 24 (6)
u = z + 1 (7)
By (3):
u = 6
By (4):
r = 3
By (7):
z = 5
And the reduced system of linear equations is:
x + y = 24 (1)
y + v = 12 (2)
1.5 · v = 12 (5)
0.5 · v + w = 11 (6)
By (5):
v = 8
By (6):
w = 11 - 0.5 · v
w = 11 - 4
w = 7
By (2):
y = 12 - v
y = 12 - 8
y = 4
By (1):
x = 24 - y
x = 24 - 4
x = 20
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Related Questions
what type of solution is y=5x+4+5x-2
Answers
The type of solution to the given simultaneous equations is no solution
What is the solution to the simultaneous equations?When it comes to linear simultaneous equations as given in the question, there are different types such as; one solution, no solution or infinitely many solution.
We are given the simultaneous equations;
y = 5x + 4 ---(1)
y = 5x - 2 ----(2)
Using elimination method, subtract eq 1 from eq 2 to get;
0 = -2 - 4
0 = -6
0 cannot be equal to -6 and as such there is no value of x that makes the simultaneous equations true. Thus, the type of solution to the given simultaneous equations is no solution
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Write an equation in point-slope form
I NEED HELP ASAP
Answers
[tex]\huge\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]
Given a point and a slope, we want to write an equation in point-slope form.
The point-slope form is defined as:
[tex]y-y_1=m(x-x_1)[/tex]
In this equation, [tex](x_1, y_1)[/tex] is a known point on the line and [tex]m[/tex] is the line's slope.
Substitute in the values:
[tex]y-(-2)=-\dfrac{4}{3}(x-3)[/tex]
Finally, simplify. Subtracting a negative number is the same as adding a positive number:
[tex]\large\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]
Sophie borrowed some money from her friend in order to help buy a new video game system. Sophie agreed to pay back her friend $2 per week and originally borrowed $10. Make a table of values and then write an equation for L,L, in terms of t,t, representing the amount Sophie owes her friend after tt weeks.
what is the equation and the 1 2 3 4
Answers
The equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is; L = 2t + 10
How to write an equation in Slope Intercept Form?
The general formula for equation of a line in Slope Intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the given question, the table of values is;
Number of weeks Amount of money owed
0 10
1 8
2 6
3 4
Now, since Sophie agreed to pay back her friend $2 per week and originally borrowed $10, it means that;
Slope = 2
y-intercept = 10
Thus, the equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is;
L = 2t + 10
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What is the answer to this problem?
Answers
Answer:
8
Step-by-step explanation:
Given: x=2
Then,
5x-2 = 5(2)-2
= 10-2
=8
Please answer the two question in the photo [ Brainliest + points ]
Answers
Answer:
i think there both obtuse
The parking garage charges $3 per hour to park for two hours or less.
The garage charges $3 for each additional hour of parking, up to and
including 5 hours. If a car uses the parking garage for more than 5
hours, there is a flat fee of $20.
Fill in the missing domain values for the following situation.
3x
(Value 1) ≤ x ≤2
f(x) = 6 4(x - 2) (Value 2) < r ≤ 5
20
x> (Value 3)
Value 1 =
Value 2 =
Value 3
Answers
The function will become:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
We are given that:
The parking garage charges $ 3 per hour if the car is parked there for less than 2 hours.
So, we get that:
Parking fees = 3 x for 0 ≤ x ≤ 2
Now, we get that, if the car is parked for more than 2 hours and less than 5 hours, then the parking fee is
6 + 4 ( x - 2) for 2 < x ≤ 5
Now, we are given that it charges a fixed fee of $ 20 if car is parked for more than 5 hours. So, the parking fee will be
20 for x > 5
So, the function becomes:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
Therefore, we get that, the function will become:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
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How to solve the inequality -20 ≤5a-10 <25
Answers
Answer:
-4[tex]\leq[/tex]a<7
Step-by-step explanation:
-20[tex]\leq[/tex]5a -10<25 add 10
+10 +10 +10
-20 [tex]\leq[/tex]5a<35 Divide all the way through by 5
-4[tex]\leq[/tex]a<7
Consider a cube with an inscribed sphere. The function can be used to find the radius, r, of a sphere given the volume, v. The function can be used to find the side length of the cube, s, depending on the radius of the sphere. The function can be used to find the surface area, a, of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
Answers
The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The function used to find the radius r of a sphere given volume V,
r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]
The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r
The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²
We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)
We have, A(s) = 6s²
Substituting function for s to A(s)
⇒ A(s(r)) = 6(2r)² = 24r²
Substituting function for r into A(s(r)),
⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The question is incomplete. Find the complete question below:
Consider a cube with an inscribed sphere. The function r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area, A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
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Answer:
Answer is D
Step-by-step explanation:
will give u brainliest
Need 2 submit by tonight need help asap please <3
Three angles add up to 180 degrees, angle one has a measure of 7x+6, angle two has a measure of 2x+3 and angle three has a measure of 10x+9.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
Answers
Step-by-step explanation:
please find attached file for the problem. hope it will help you , let me know if you have any further query
note: enter your answer and show all the steps that you use to solve this problem in the space provided. simplify the expression 8 2 9 ( 12 ÷ 3 ⋅ 2 ) − 7 . 82 912÷3·2-7. explain each of your steps.
Answers
129 is the value of expression .
What is PEMDAS?
The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.We use , P/E/M/D/A/S (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract)
8^2 + 9(12/3*2) - 7
= 64 + 9(8) -7
= 64 + 72 - 7
= 129
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Select all of the equations that represent linear relationships.
5+2y=13
y=1x²³+7
y-5=2(x-1)
=x+7
x=-4
Answers
A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.
(1). 5+2y= 13
2y=13-5
2y= 8
y=4.
So this is the form of mx+b
Where b=4 and x=0.
(2). y = x²³+7
It is the form of mx+b .
where mx = x²³ and x=7
(3). y-5= 2(x-1)
y-5 = 2x-2
y=2x-2+5
y=2x+3
It is completely the form of mx+b .
where m= 2 and b = 3.
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Expressed as a product of its prime factors in index form, a number n is n = 3 times 5 squared times x cubed. express 5n squared as a product of prime factors in index form. give your answer in terms of x.
Answers
5n² can be expressed as, 5n² = 3² x 5⁵ x x⁶
Given that n can be written as the product of the primes as
n = 3 x 5² x x³
This expression for n is called the prime factorization of n.
We need to express 5n² as such a product of primes.
For that taking square of n, add the power 2 with the existing powers of 3,5 and x,
So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶
So 5n² = 5(3² x 5⁴ x x⁶)
Multiplying 5 with the existing power of 5, 5⁴,
⇒ 5n² = 3² x 5⁵ x x⁶
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20 points can someone lmk the answer ty
Answers
Answer:
a c e
Step-by-step explanation:
how many significant digits are there in the number 2.25x10 using significant digits
Answers
Answer:
3
Step-by-step explanation:
2.25×10=22.5
If there is 0 in front of the number:eg(02.25) 0 does not count but it counts if it comes after nonzero digits.
I need help asap!! (Geometry)
Answers
Answer:
Below
Step-by-step explanation:
Flower bed A
C = 2πr
C = 2π(5)
C = 2(5)π
C= 10π
A= πr²
A= π(5)²
A= π25
A= 25π
____________________________________________________
Flower bed B
C = 2πr
C = 2π(6)
C = 2(6)π
C = 12π
A = πr²
A = π(6)²
A = π36
A = 36π
find the angle between a diagonal of a cube and an adjacent edge. (enter your answer in degrees. round your answer to two decimal places.)
Answers
The angle between a diagonal of a cube and an adjacent edge is 54.75°;
Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;
a = (1, 0, 0)
b = (0, 1, 0)
c = (0, 0, 1)
The diagonal is given by the vector, v = (1, 1, 1)
The angle between the diagonal and one edge of the cube is given by
cos θ = v. a / |v|.|a|
v. a = (1, 1, 1).(1, 0, 0)
= 1(1) + 1(0) + 1(0
= 1 + 0 + 0
v. a = 1
Magnitude of vector V = √[(1)² + (1)² + (1)²]
|v| = √3
Similarly, |a| = √1;
So, |v|.|a| = √3.√1 = √3
Now, cos θ = 1/√3
So, θ = cos¹(1/√3)
θ = 54.75°
Therefore, the required angle is 54.75°.
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Please help!! Graph the image of the trapezoid
below using a scale factor of
k= 1/4
Answers
If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;
F'(-2/4, 8/4) = (-1/2, 2)
G'(4/4, 8/4) = (1, 2)
I'(-6/4, -4/4) = (-1.5, -1) and;
H(8/4, -4/4) = (2, -1)
Reduction and enlargement of figures using scale factors.A scale factor is is a number used to enlarge a shape and each side is multiplied by the same number.
The given trapezoid has the coordinate points F(-2, 8), G(4, 8), I(-6, -4) and H(8, -4).
If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;
F'(-2/4, 8/4) = (-1/2, 2)
G'(4/4, 8/4) = (1, 2)
I'(-6/4, -4/4) = (-1.5, -1) and;
H(8/4, -4/4) = (2, -1)
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.
...........................
Answers
You did a great job!
in exercises 13–17, the position d of a bicyclist (measured in kilometers) is a linear function of time t (measured in minutes). at time t
Answers
The position of the bicyclist at t=8 minutes is 3.2 km
Speed is the rate of change of position of an object in any direction.
position the way in which something or someone is placed or arranged.
when time t = 6 position d = 5
when time t = 5 position d = 2
when time t = 8 position d = x
therefore we can say
8 / x = 5 / 2
x = 8 * 2 /5
= 3.2 km.
Hence the position of the bicyclist at t=8 minutes is 3.2 km.
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complete question:
The position "d" of a bicyclist (measured in kilometers) is a linear function of time "t" (measured in minutes). At time t=6 minutes, the position is d=5 km. If the bicyclists travels at 2 km for every 5 minutes, find the position of the bicyclist at t=8 minutes.
Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3.50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80?
h + c ≤ 80
3h + 3.5c ≤ 100
h + c ≤ 80
3h + 3.5c ≥ 100
h + c ≤ 100
3h + 3.5c ≤ 80
h + c ≤ 100
3h + 3.5c ≥ 80
Answers
The system of inequalities are:
h + c ≤ 100
3h + 3.5c ≥ 80
What are the system of inequalities?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toHere are the system of inequalities :
number of hamburgers sold + number of cheeseburger sold ≤ total number of buns
(cost of one hamburger x number of hamburger sold) + (number of cheeseburger sold x number of cheeseburger sold) ≥ $80
h + c ≤ 100
3h + 3.5c ≥ 80
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100 points HELP!
A group of friends want to go to the amusement park. They have $416.75 to spend on parking and admission. Parking is $15.25, and tickets cost $36.50 per person including tax. Which equation could be used to determine x, the number of people who can go to the amusement park
A. 36.5 (15.25 + x) = 416.75
B. 416.75 = 36.5x + 15.25
C. 15.25x = 416.75 - 36.5
C. 15.25x + 36.5 = 416.75
Answers
Answer:
tyyyy is my final answer
The angle below measures
__ degrees.
Answers
What is the range of the numbers below?
8.1
5.2
-8.4
0.9
-4.7
-8.1
Answers
lowest number: -8.4
range = highest number - lowest number
range = 8.1 - (-8.4) = 8.1 + 8.4 = 16.5
A private jet flies the same distance in 7 hours that a commercial jet flies in 5 hours. If the speed of the commercial jet was 99 mph less than 2 times the speed of the
private jet, find the speed of each jet.
Answer
Answers
Answer:
Private jet - 165 mphCommercial jet - 231 mphStep-by-step explanation:
Let the speed of the private jet is p and commercial jet is c.
Set equations7p = 5cc = 2p - 99Solve by substitution7p = 5(2p - 99)7p = 10p - 49510p - 7p = 4953p = 495p = 495/3p = 165Find c:
c = 2*165 - 99 = 330 - 99 = 231Do number 8 please thank you
Answers
Answer:
a) true
b) false
c) false
Step-by-step explanation:
Here are these 4 sets in order of including more numbers to including fewer numbers.
R = all real numbers
Z = all integers
W = all whole numbers
N = all natural numbers
a) true
b) false
c) false
find the equivalent fractionsss with large denominatorsss
Answers
Answer:
12
Step-by-step explanation:
[tex] \frac{3}{8} = \frac{?}{32} [/tex]
8*4=32
3*4=12
Please help me with this question I don't understand it. Please it must be easy for yall genius's
Answers
Answer:
Range is 12 and mean is -6
Step-by-step explanation:
To find the mean, add together all the numbers and divide by 7.
solve -15.4+25.2+(-10.4)=
Answers
Answer:The answer is -0.6
Step-by-step explanation: -15.4-10.4 is -25.8
-25.8+25.2 is -0.6
So therefore the answer is -0.6
The coordinates of the point
of the way from A to B are____
Answers
The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).
How to find the coordinates of a point within a line segment
In this problem we find a line segment whose endpoints are known: A(x, y) = (- 3, - 6), B(x, y) = (10, 4), and of which we need to find a point C such that it is 3 / 10 of the way from point A to point B, whose exact location can be found by means of the line segment formula:
C(x, y) = A(x, y) + (3 / 10) · [B(x, y) - A(x, y)]
C(x, y) = (- 3, - 6) + (3 / 10) · [(10, 4) - (- 3, - 6)]
C(x, y) = (- 3, - 6) + (3 / 10) · (13, 10)
C(x, y) = (- 3, - 6) + (3.9, 3)
C(x, y) = (0.9, - 3)
The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).
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a tv show had 4,320,000 viewers for its season premiere. express this number using scientific notation.
Answers
Answer:
Step-by-step explanation:
See attachment