A hobby store prices model train track using a proportional relationship between the length of track (in inches) and the cost in dollars.
If 6.4
6
.
4
inches of track costs $16
$
16
, what is the constant of proportionality?
Answers
Answer:
If... 6.4 inches : 16 dollars
Then... 32 inches = 80 dollars.
And, 1 inch of track = 80/32 dollars.
80/32 = 2.5.
So, the answer is: 1 inch of track costs 2.5 dollars.
The constant of proportionality is $2,50.
The equation used to represent direct proportionality is: y = kx
Where:
y = dependent variable
x = independent variable
k = constant of proportionality
Here, the dependent variable is the cost of the track. The independent variable is the length of the tracks.
$16 = 6.4k
k = 16 / 6.4 = $2.5
A similar question was answered here: https://brainly.com/question/17033082
Related Questions
Given: AB tangent at D, AD = OD = 4 Find: Area of the shaded region
Answers
Answer:
1.72
Step-by-step explanation:
AB tangent at D, AD = OD = 4
so triangle OAD is right angle with side of 4 and 4.
area of OAD = 1/2 * 4 * 4 = 8
Angle AOD = DAO = 45 deg.
so circular sector OCD area = area of circle O * 45/360
= pi * 4 * 4 * 45/360
= 2pi
Shade area ACD = trigangle OAD - circular sector OCD
= 8 - 2pi
= 1.72
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Answers
Answer:
3b (3a - 4b)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
9ab - 12b² ← factor out 3b from each term
= 3b(3a - 4b) → C
use order operation
Answers
Answer:
The correct answer is the final option, 2.
Step-by-step explanation:
[(16+4) - 10] - 8
Our first step in this problem, according to the order of operations, is to simplify what is inside the parentheses. Since there are multiple sets of parentheses, we must simplify the innermost group first. If we add 16 and 4, we get:
[20 - 10] - 8
Next, we must perform the subtraction inside the parentheses. This gives us:
10 - 8
Now, we can perform the final operation.
10 - 8 = 2
Therefore, the correct answer is 2.
Hope this helps!
Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE≅EC and BE≅DE Can you prove can you prove that the figure is a parallelogram? Explain. A. Yes; two opposite sides are both parallel and congruent. B. Yes; diagonals of a parallelogram bisect each other. C. Yes; opposite sides are congruent. D. No; you cannot determine that the quadrilateral is a parallelogram.
Answers
Answer:
B. Yes; diagonals of a parallelogram bisect each other.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
Answer: B. Yes; diagonals of a parallelogram bisect each other.
If AE=EC and BE=DE then quadrilateral ABCD is a parallelogram because diagonals of parallelogram bisect each other.
What is parallelogram?A parallelogram is a 2 dimensional figure whose opposite sides are equal to each other and parallel to each other. Area of parallelogram is base*height.
How to prove quadrilateral a parallelogram?To be parallelogram ΔAEB and ΔEDC should be congruent.
Angle AEB= Angle DEC
AE=EC
DE=EB
so both triangles are congruent by side, side, angle.
Similarly AE=EC , DE=EB and vertical angles AED= Vertical angle BEC.
Therefore triangle AED and BEC are congruent and that makes all their corresponding sides are also congruent.
And AB=DC.
Hence both pairs of opposite sides of a quadrilateral are congruent ,then the quadrilateral is a parallelogram.
Learn more about parallelogram at https://brainly.com/question/970600
#SPJ2
Find the LCM of
[tex]14 {a}^{3} {b}^{2} [/tex]
and
[tex]20 {a}^{4} {b}^{2} [/tex]
Answers
Answer:
Hi,
I hope you are searching for this answer.
The lcm of an expression is calculated by taking the common factor and multiply the common factor with the remaining one, alright.
or, simply the lcm of an expression is calculated by the product of common factors and the factors which are not common.
Hope it helps...
Julie had 2730 cards and Kim had 3570 cards at first.
Julie gave some of her cards to Kim. In the end, Kim had thrice as many cards as Julie.
How many cards did Julie give Kim.
Answers
Answer:
1155
Step-by-step explanation:
Total number of cards is 2730+3570=6300
Since Kim now has 3 times the card of Julie so Julie must have 6300/4=1575.
So, Julie gave 2730-1575=1155
Answer:
1155 cards
Step-by-step explanation:
3(2730-x)=3570+x
8190 - 3x = 3570 + x
4620 - 3x = x
4620 = 4x
1155 = x
For which system of inequalities is (3,-7) a solution? A. x + y < -4 3x + 2y < -5 B. x + y ≤ -4 3x + 2y < -5 C. x + y < -4 3x + 2y ≤ -5 D. x + y ≤ -4 3x + 2y ≤ -5
Answers
Answer:
The correct option is;
D x + y ≤ -4, 3·x + 2·y ≤-5
Step-by-step explanation:
A. For the system of inequality, x + y < -4, 3·x + 2·y <-5
We have;
y < -4 - x, When x = 3, y < -7
y < -2.5 - 1.5·x, When x = 3, y = -7
B. For the system of inequality, x + y ≤ -4, 3·x + 2·y <-5
We have;
y ≤ -4 - x, When x = 3, y ≤ -7
y < -2.5 - 1.5·x, When x = 3, y < -7
C. For the system of inequality, x + y < -4, 3·x + 2·y ≤-5
We have;
y < -4 - x, When x = 3, y < -7
y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7
D. For the system of inequality, x + y ≤ -4, 3·x + 2·y ≤-5
We have;
y ≤ -4 - x, When x = 3, y ≤ -7
y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7
Therefore, the system of inequality for which (3, -7) is a solution is D, x + y ≤ -4, 3·x + 2·y ≤-5.
The graph of a linear system is shown
Answers
Answer:
The coordinates of the point of intersection is (2, 7)
Step-by-step explanation:
From the graph, we have the two intersecting straight lines each described as follows;
The first straight line graph from the left, we have;
y-intercept = (0, 5), x-intercept = (-5, 0) therefore, the slope, m = (0 - 5)/(-5 - 0) = 1
The equation of the graph is slope-intercept form is y - 5 = 1×(x - 0)
Which gives;
y = x + 5.........................(1)
The second lie graph has y-intercept = (0, 9), x-intercept = (9, 0) therefore, the slope, m = (0 - 9)/(9 - 0) = -1
The equation of the graph in slope-intercept form is y - 9 = -1×(x - 0)
Which gives;
y = -x + 9.......................(2)
To find the point of intersection, we equate equation (1) to equation (2), which are the y-value function of x, we have;
x + 5 = -x + 9
x + x = 9 - 5
2·x = 4
x = 4/2 = 2
x = 2
From either equation (1) or equation (2), we can find the value of y as follows;
y = -x + 9, where x = 2 gives;
y = -2 + 9 = 9 - 2 = 7
y = 7
The coordinates of the point of intersection is (2, 7).
How many solutions does the following equation have? 4(y-30)=4y+124(y−30)=4y+12
Answers
Answer:
A. No solution
Step-by-step explanation:
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions
Solution
Given:
4(y-30)=4y+12
Open parenthesis
4y-120=4y+12
Collect like terms
4y-4y=12+120
0=142
There is no solution to the equation, therefore, the answer is A
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement. Triangle LKJ≈____
Answers
Answer: C) similar, SAS similarity, triangle LQR
==============================================
Explanation:
The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.
KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".
The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.
La fuerza necesaria para evitar que un auto derrape en una curva varía inversamente al radio de la curva y conjuntamente con el peso del auto y el cuadrado de la velocidad del mismo. Supongamos que 400 libras de fuerza evitan que un auto que pesa 1600 libras derrape en una curva cuyo radio mide 800 si viaja a 50mph. ¿Cuánta fuerza evitaría que el mismo auto derrapara en una curva cuyo radio mide 600 si viaja a 60mph ?
Answers
Answer:
768 libras de fuerza
Step-by-step explanation:
Tenemos que encontrar la ecuación que los relacione.
F = Fuerza necesaria para evitar que el automóvil patine
r = radio de la curva
w = peso del coche
s = velocidad de los coches
En la pregunta se nos dice:
La fuerza requerida para evitar que un automóvil patine alrededor de una curva varía inversamente con el radio de la curva.
F ∝ 1 / r
Y luego con el peso del auto
F ∝ w
Y el cuadrado de la velocidad del coche
F ∝ s²
Combinando las tres variaciones juntas,
F ∝ 1 / r ∝ w ∝ s²
k = constante de proporcionalidad, por tanto:
F = k × w × s² / r
F = kws² / r
Paso 1
Encuentra k
En la pregunta, se nos dice:
Suponga que 400 libras de fuerza evitan que un automóvil de 1600 libras patine alrededor de una curva con un radio de 800 si viaja a 50 mph.
F = 400 libras
w = 1600 libras
r = 800
s = 50 mph
Tenga en cuenta que desde el
F = kws² / r
400 = k × 1600 × 50² / 800
400 = k × 5000
k = 400/5000
k = 2/25
Paso 2
¿Cuánta fuerza evitaría que el mismo automóvil patinara en una curva con un radio de 600 si viaja a 60 mph?
F = ?? libras
w = ya que es el mismo carro = 1600 libras
r = 600
s = 60 mph
F = kws² / r
k = 2/25
F = 2/25 × 1600 × 60² / 600
F = 768 libras
Por lo tanto, la cantidad de fuerza que evitaría que el mismo automóvil patine en una curva con un radio de 600 si viaja a 60 mph es de 768 libras.
In the figure shown, what fractional part of the circle is shaded?
1. 4/15
2. 3/8
3. 5/8
4. 11/15
Answers
Answer:
4/15
Step-by-step explanation:
Add up the unshaded part
1/3 +2/5
Get a common denominator
1/3 *5/5 + 2/5 *3/3
5/15 + 6/15
11/15
Subtract this from 1 for the entire circle
15/15 -11/15
4/15
4/15 is shaded
Answer:
answer is
[tex] \frac{4}{15} [/tex]
Step-by-step explanation:
explanation is in the picture!
Write (25x^2 + 30x + 12) in the form (ax + b)^2 + c.
Answers
Answer:
25 x^2 + 30 x + 12
Parcelas
Plots
Parcelas
Figura geométrica
parabola
Formas alternativas
x (25 x + 30) + 12
(5 x + 3)^2 + 3
5 x (5 x + 6) + 12
Raíces complejas
x = -1/5 i (sqrt(3) + -3 i)
x = 1/5 i (sqrt(3) + 3 i)
Step-by-step explanation:
Divide. Write your answer as a decimal.
8.722÷(−3.56)=
Answers
Answer:
-2.45
Step-by-step explanation:
Answer:
-2.45
Step-by-step explanation:
Figure a is a scale image of figure b. Figure a maps to figure b with a scale factor of 0.75 What is the value of x? please answer asap!
Answers
Answer:
x = 7.5
Step-by-step explanation:
Step 1: Create a fraction with the known sides
[tex]\frac{x}{10}[/tex]
Step 2: Set the fraction equal to the scale factor
[tex]\frac{x}{10}=\frac{0.75}{1}[/tex]
Cross multiple to solve for x
[tex]x = 7.5[/tex]
Therefore x is equal to 7.5
Answer:
7.5
Step-by-step explanation:
did it on khan
An octagonal pyramid ... how many faces are there, how many vertices and how many edges? A triangular prism ... how many faces are there, how many vertices and how many edges? a triangular pyramid ... how many faces are there, how many vertices and how many edges?
Answers
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Answer:.
Step-by-step explanation:.
Can u guys answer these 2 questions pls
Answers
Answer:
14) answer is 4
15) proved
Step-by-step explanation:
x=7-4√3 , √x +1/√x
√(7-4√3) +1/√7-4√3)=
8-4√x/√(7-4√3)= 4 ( use calculator)
(81/16)^-3/4*[(25/9)^-3/2 ÷(5/2)^-3]=(81/16)^-3/4= (9²/4²)^-3/4=(4^6/4)/(9^6/4)=8/(27)=8/27(25/9)^-3/2= (9^(3/2))/(25^3/2)=27/125(5/2)^-3=2³/5³ =8/125put the number to find the result:8/27[(27/125)÷(8/125)=8/27[(27/125)×125/8)]= 125 in nominator and dinaminotor=18/27[27/8]=1 provedLast week, 17 employees exceeded their sales quota, 13 employees met their sales quota, and 3 employees didn't meet their sales quota. Express the number of employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota. Question 11 options: A) 3:13 B) 16:17 C) 17:16 D) 17:33
Answers
Answer:
17:16
Step-by-step explanation:
Number of employees exceeded their sales quota = 17
Number of employees met their sales quota = 13
Number of employees didn't exceed their sales quota = 3
Now, we need to find the ratio of the number employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota.
. If the market price of a dozen eggs at the local farmers market is 72 cents per dozen, will Brenda make an economic profit? Explain how you determined your answer. (4 points)
Answers
Cost of dozen eggs = 72 cents
Cost of 1 egg = 72÷12
= 6cents
Please click thanks and mark brainliest if you like
Do these pairs of values (x and y) represent two quantities that are proportional?
X: 4, 6, 10, 14
Y: 2, 3, 5, 7
Answers
Answer:
No
Step-by-step explanation:
In a proportional relationship, it will be a straight line (it is here) that goes through the origin (it does not). It would not go through (0.0), but would go through (2, 0)
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100 100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 8 88 finishers in the final round of the 2012 20122012 Olympics. The lower dot plot shows the times of the same 8 88 swimmers, but in the semifinal round. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.) Choose all answers that apply: Choose all answers that apply:
Answers
Answer:
The center of the semifinal round distribution is greater than the center of final round distribution.
The variability in the semifinal round distribution is less than variability in the final round distribution.
Step-by-step explanation:
The mean value of each distribution set is not calculates as the center of semifinal round distribution is greater than the final round distribution. MAD Mean Absolute Deviation is calculated from the dotted graph plot, the distribution of semifinal round is less spread out than the final round distribution.
Answer:
correct answer is None of the above i understood nothing the other person was trying to say...
Step-by-step explanation:
mark me brainliest please...
Look for a pattern in the first three diamonds below. For the fourth diamond, explain how you could find the missing numbers if you know the two numbers
Answers
Answer:
See below.
Step-by-step explanation:
The top number is the product (multiplication) of the two side numbers. The bottom number is the sum (addition) of the two side numbers.
I'll do problem a as an example:
Can someone please help me on these 4 questions PLEASE HELP ME!!
Answers
Answer:4 ans x is -32/10
7 ans b is 6
10 ans x is 25/7
13 ans x is 9/2
Step-by-step explanation:
please mark this answer as brainlist
Hey, please help solve the question.
Answers
Answer:
75%=x-125
90%=x+250
subtract the second from the first
15%=375
100%=?
100%×375/15
100%=2500marked price is 2500
2500+250=2750
90%=2750
100%=?
cost price=3055.56
l= 6 ft, w = 2 ft, h= 5 ft what is the surface area of the rectangular prism
Answers
104 ft^2
Explanation:
The surface areaa of a rectangular prism is given by the formula:
2 (lw + hl + hw)
l = length
w = width
h = height
Substitute the formula with the givsn dimensions:
2 ([6 x 2] + [5 x 6] + [5 x 2])
= 2 (12 + 30 + 10)
2 (52)
= 104
So the SA is 104 square feet or ft^2
Hope this helps!
What is the x-value of the solution to the system of equations? 5x + 4y = 8 2x − 3y = 17 −3 −2 4 5
Answers
Answer:
x = 4Step-by-step explanation:
5x + 4y = 8 ⇒ 4y = 8 - 5x ⇒ y = (8 - 5x)÷4
2x − 3y = 17
2x - 3(8 - 5x)÷4 = 17
×4 ×4
8x - 3(8 - 5x) = 68
8x - 24 + 15x = 68
+24 +24
23x = 92
÷23 ÷23
x = 4
Answer:
it is 4
Step-by-step explanation:
i did it on edge hope it helps.:)
how do you find class width pliz help mi
Answers
Answer:
Class width refers to the difference between the upper and lower boundaries of any class (category)....
To find the width:Calculate the range of the entire data set by subtracting the lowest point from the highest,Divide it by the number of classes.Round this number up (usually, to the nearest whole number).Hope this helps you ❤️MaRk mE aS braiNliest ❤️-56 divided by -8 find the quotient
Answers
Answer:
7
Step-by-step explanation:
We can see that we have a negative number divided by a negative number, so the negatives cancel each other out.
[tex]56\div8[/tex]
We know that 8 will go into 56 7 times, so [tex]-56\div-8=7[/tex].
Hope this helped!
Answer:
7
Step-by-step explanation:
Match each number to the letter that represents its
position on the number line.
HELP ASAP
Answers
Answer:
Step-by-step explanation:
Answer
answer bellow
Step-by-step explanation:
24, C
25, D
26, B
27, A
What is the answer?