A weight of 6 lb stretches a spring a distance of 12 in. Find the constant k for the spring.
Answer:
Let F = the force (6 lbs) and x be the distance that the spring is stretched (12 inches).
F = kx
6 lb = k*(12 in.)
6/12 = k = 0.5 lb/in.
A weight of 6 lb stretches a spring a distance of 12 in. The constant k for the spring will be 0.5 lb/in.
How to obtain acceleration from force applied on an object?If the object is of mass m kg and force applied on it is of F N in the direction of motion, then the acceleration of that object is evaluated as:
a= F/m
Given; A weight of 6 lb stretches a spring a distance of 12 in.
Also,
Let F = the force and x be the distance that the spring is stretched
F = kx
6 lb = k*(12 in.)
6/12 = k = 0.5 lb/in.
Therefore, the constant k for the spring will be 0.5 lb/in.
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x * 5 * 25 * 4 ÷ 5, if x = 813 simplified form please
Answer:
81,300
Step-by-step explanation:
Quadrilateral JKLM has vertices at J(0,0), K(0,6), L(9,12), and M(12,0). Find the vertices of the quadrilateral after a dilation with scale factor 2/3.
Answer choices
J'(0, 0), K'(0, 9), L'(27/2, 18), and M'(18, 0)
J'(0, 0), K'(0, 4), L'(6, 8), and M'(8, 0)
J'(0, 0), K'(0, −4), L'(−6, −4), and M'(−8, 0)
J'(2/3, 2/3), K'(2/3, 20/3), L'(9/3, 38/3), and M'(38/3, 2/3)
Answer:
The vertices of the quadrilateral after a dilation with scale factor [tex]\frac{2}{3}[/tex] are [tex]J'(x,y) = (0,0)[/tex], [tex]K'(x,y) = (0,4)[/tex], [tex]L'(x,y) = (6, 8)[/tex] and [tex]M'(x,y) = (8,0)[/tex].
Step-by-step explanation:
Let suppose that center of dilation is located at origin, that is [tex]O(x,y) = (0,0)[/tex]. Vectorially speaking, dilation is described by following expression:
[tex]D'(x,y) = O(x,y) + r\cdot [D(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation.
[tex]D(x,y)[/tex] - Original point.
[tex]D'(x,y)[/tex] - Dilated point.
[tex]r[/tex] - Dilation factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]r = \frac{2}{3}[/tex], [tex]J(x,y) = (0,0)[/tex], [tex]K(x,y) = (0,6)[/tex], [tex]L(x,y) = (9,12)[/tex] and [tex]M(x,y) = (12,0)[/tex], then the dilated points are, respectively:
[tex]J'(x,y) = O(x,y) + r\cdot [J(x,y)-O(x,y)][/tex]
[tex]J'(x,y) = (0,0) +\frac{2}{3}\cdot [(0,0)-(0,0)][/tex]
[tex]J'(x,y) = (0,0)[/tex]
[tex]K'(x,y) = O(x,y) + r\cdot [K(x,y)-O(x,y)][/tex]
[tex]K'(x,y) = (0,0)+\frac{2}{3}\cdot [(0,6)-(0,0)][/tex]
[tex]K'(x,y) = (0,4)[/tex]
[tex]L'(x,y) = O(x,y) +r\cdot [L(x,y)-O(x,y)][/tex]
[tex]L'(x,y) = (0,0) + \frac{2}{3}\cdot [(9,12)-(0,0)][/tex]
[tex]L'(x,y) = (6, 8)[/tex]
[tex]M'(x,y) = O(x,y) +r\cdot [M(x,y)-O(x,y)][/tex]
[tex]M'(x,y) = (0,0) +\frac{2}{3}\cdot [(12,0)-(0,0)][/tex]
[tex]M'(x,y) = (8,0)[/tex]
The vertices of the quadrilateral after a dilation with scale factor [tex]\frac{2}{3}[/tex] are [tex]J'(x,y) = (0,0)[/tex], [tex]K'(x,y) = (0,4)[/tex], [tex]L'(x,y) = (6, 8)[/tex] and [tex]M'(x,y) = (8,0)[/tex].
Option B will be the correct option.
Dilation of a point about the origin by a scale factor 'k',If a point (a, b) is dilated by a scale factor 'k' about the origin, coordinates of the image point will be,
(a, b) → (ka, kb)
Following the rule for dilation,
If a quadrilateral J(0, 0), K(0, 6), L(9, 12) and M(12, 0) is dilated by a scale factor [tex]\frac{2}{3}[/tex], coordinates of the image points will be,
[tex]J(0,0)\rightarrow J'(0, 0)[/tex]
[tex]K(0,4)\rightarrow K'(0, 4)[/tex]
[tex]L(9,12)\rightarrow L'(6,8)[/tex]
[tex]M(12,0)\rightarrow M'(8,0)[/tex]
Therefore, Option B will be the correct option.
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is a rectangle a plane shape
Answer:
A plane shape with four straight sides and four right angles for corners is called a rectangle.
Step-by-step explanation:
Is A PQR-AXYZ? If so, name which similarity postulate or
theorem applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answer:
D. Cannot be determined
Step-by-step explanation:
Similarly between given triangles can not be determined because given information are insufficient.
The correct option for the given triangles is D. Cannot be determined
What are similar triangles?Any two triangles will be considered as similar as they have congruent corresponding angles and the corresponding sides are in equal ratios.
Two shapes are Similar when one can become the other after a resize, flip, slide or turn.
Given are two triangle PWR and XYZ we need to determine whether they are similar or not,
So, we only have measurement of a pair of sides and measurement of an angle,
We have some similarity rules by which we can prove two triangles to be similar, they are :-
AA rule, Side Angle Side (SAS), Side Side Side (SSS) and Right-angle Hypotenuse Side (RHS)
Since, we do not enough information to conclude our discussion.
Hence, the correct option is D. Cannot be determined
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Johnisha paid $144 for 36 ice cream cones. She incorrectly calculates the cost per cone
to be $0.25 each.
Which statement identifies the error Johnisha most likely made in determining the cost per
cone and describes the correct method for determining the cost per cone?
if you can help me i’ll make brainliest
Answer:
help me
Step-by-step explanationok so
Answer:
pts
Step-by-step explanation:
Can anyone help me with this please?
Answer: 3/1
Step-by-step explanation:
use the 2 bottom ones
Enter the number that belongs in the green box
Equilateral triangles are triangles whose all sides and angles are equal.
Since the above given triangle has 3 equal sides it is an equilateral triangle.
So, the three angles of this triangle can be 3x.
Which means :
[tex] =\tt 3x = 180[/tex]
[tex] =\tt x = \frac{180}{3} [/tex]
[tex]\hookrightarrow \tt \color{plum}x = 60°[/tex]
▪︎Therefore, x = 60°
Zoltan read 15 pages of his book in 6 minutes. At this rate, how many pages can he read in 10 minutes?
Answer:
25 pages in 10 minutes.
Meena cuts a 287-in. long ribbon into 2 pieces in the ratio 3 : 4. What is the length of the longer piece of ribbon? (ASAP)
Answer:
164 inches
Step-by-step explanation:
First, add 3 and 4
3+4= 7
Then divide 287 by 7
287/7= 41
Then, multiply 4 (from the ratio) by 41
4*41= 164
To get the length of the shorter piece, subtract 164 from 287
287-164= 123
Check your work:
123+164= 287
Hope this helps!
A recipe uses 2 cups of milk to make 4 servings. If the same amount of milk is used for each serving, how many servings can be made from three pints?
Answer:
12 servings
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
1. The number of customers in a restaurant during the peak hour of each day for a month varied
significantly from day to day. Here are pieces of the data on the number of customers served
during the peak hour of each business day:
3 Lowest
25, 32, 37
Q1
45
Mean
48
Median
50
Q3
58
3 highest
69, 70, 75
(a) Are there any outliers in the data set? Justify your answer numerically
Step-by-step explanation:
First we must calculate the interquartile range (IQR), using this equation:
[tex]IQR = Q_{3} - Q_{1}[/tex]
Based on the information provided we fill in:
[tex]IQR = 58 - 45[/tex]
[tex]IQR = 13[/tex]
In order to find what the range for the data set is we need to use the Interquartile Rule:
[tex]Q_{1}-1.5[/tex] × [tex]IQR\\[/tex]
[tex]Q_{3}+1.5[/tex] × [tex]IQR\\[/tex]
[tex]1.5[/tex] × [tex]13 = 19.5[/tex]
Now we plugin in:
[tex]45 - 19.5 = 25.5\\[/tex]
[tex]58 + 19.5 = 77.5[/tex]
Any number below 25.5 is a possible outlier and any number above 77.5 is a possible outlier.
Answer:
Based on the results of the calculations, 25 could be a possible outlier in the data set.
What is the y-intercept of the line shown?
−1
0
0.5
1
Answer:
-1
Step-by-step explanation:
It crosses the y axis at negative 1, the y axis is the vertical line
a cow is tied to a pole fixed at the mid-point of a side of a square field of side 40m by means of a 14m long rope find the area that cow can graze pls explain
Step-by-step explanation:
The area that cow can graze is in the form of semicircle.
Radius of semicircle
Length of rope =14 m
Required area = 1/2 ×πr
=1/2×22/7×r^2
=1/2×22/7×14×14
=308m2
how to solve for mamath
Answer:
2
Step-by-step explanation:
Answer:
X= 20
Step-by-step explanation:
To find x you need to know what are the dimensions
48 divided by 12 = 4
5 x 4 = 20
x = 20
hope this helps
14 Customers into the store over the course of seven minutes how many Internet store after one minute
Answer:
2
Step-by-step explanation:
14 divided by 7 is two customers in one minute
Answer:
After one minute there will be 2 people inside the store.
Step-by-step explanation:
First we put this into a proportion. Aka set up like a fraction.
14 (customers) x
------- ---> ------
7 (minute) 1 minute
In order to find x, we must divide by 7 because in order to make the bottom number one on the bottom, you must divide by 7 , so we do the same to the top.
14/7 is 2.
This means that per minute, there are 2 people inside the store.
After one minute, There will be 2 people inside the store.
the question is: The endpoints of ST are S(2,-2) and T(4,2) what are the coordinates of midpoint of ST?
Answer:
(3,0)
Step-by-step explanation:
If you use a graphing calculator and connect the two points then you would get (3,0) :))
Simplify the expression using order of operations. 15−7×2+23
Answer: 24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Multiplication first:
15 - 14 + 23
Addition and Subtraction:
15 - 14 + 23 = 24
Please answer for kind of a lot of points :D
Answer:
(5.5d + 8) miles27.5 milesStep-by-step explanation:
Lyndsay ⇒ 3d + 5Seth ⇒ 2.5d + 3a) Together they run:
3d + 5 + 2.5d + 3 = (5.5d + 8) milesb) They run 5 days Monday through Friday last week:
5.5*5 = 27.5 mileswrite an equation of the line perpendicular to the given line that contains P in point slope form? P (4,8) y=4x-7
Answer:
y - 8 = -1/4(x - 4)Step-by-step explanation:
Perpendicular lines have negative-reciprocal slopes.
The line contains point P(4, 8)
Point slope form:
y - y₁ = m(x - x₁)Given line:
y = 4x - 7The slope of the perpendicular line is m = -1/4.
The line in point-slope form is:
y - 8 = -1/4(x - 4)Answer:
y - 8 = -1/4(x - 4)
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 4x - 7. Its slope is 4. A line perpendicular to this one will have a slope of -1/4, the reciprocal (opposite) of the given equation.
Plug this value (-1/4) into your standard point-slope equation of y - y₁ = m(x - x₁)
y - y₁ = -1/4(x - x₁)
To find x₁ and y₁, we want to plug in a value that we know is on this line: in this case, it is P (4, 8). Plug in the x and y values into the x₁ and y₁ of the standard equation.
y - 8 = -1/4(x - 4)
This equation is perpendicular to your given equation (y = 4x - 7) and contains point P (4, 8)
Hope this helps!
Identify the shape that is graphed from the points:
A (4, 6)
B (4, 7)
C (8, 6)
D (8, 7)
Answer:
Rectangle
Step-by-step explanation:
It's a rectangle because opposite sides are parallel as you can see , it has 4 right angles , and it has 4 sides .. it's not a square because in a square all sides are equal
Which inequalities have -0.5, 2.5, and 4 as part of the solution set? Select all that apply.
z > -3
z < 5
z < 4
z Less-than-or-equal-to 4
z > 0
Z>-3
Z<5
Z< or = 4
These 3 above have the 3 numbers in the solution set!
You just have to test each number in each inequality, and when all 3 of them work, the inequality is a part of the solution set!
Also Thanks for the 50 Points!
The inequalities are z ≤ 4 and z < 5 that have -0.5, 2.5, and 4 as part of the solution set.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
If the inequality have -0.5, 2.5, and 4 as part of the solution set.
That means, the required value has to be less than or equal to 4.
So, the inequalities are z ≤ 4 and z < 5.
Therefore, the inequalities are z ≤ 4 and z < 5.
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Sara says, "If you subtract 17 from my number and multiply the difference by - 2,
the result is - 22." What is Sara's number?
Answer: 28
28 - 17 = 11
11 * -2 = -22
plzz write with formula and explanation plzzzzzzzz
Given:
[tex]-\dfrac{33}{16}[/tex] should be divided by a number to get [tex]-\dfrac{11}{4}[/tex].
To find:
The unknown number.
Solution:
Let [tex]-\dfrac{33}{16}[/tex] should be divided by x to get [tex]-\dfrac{11}{4}[/tex].
[tex]\dfrac{-\dfrac{33}{16}}{x}=-\dfrac{11}{4}[/tex]
[tex]-\dfrac{33}{16}=-\dfrac{11}{4}x[/tex]
Multiply both sides by 16.
[tex]-33=-44x[/tex]
Divide both sides by -44.
[tex]\dfrac{-33}{-44}=x[/tex]
[tex]\dfrac{3}{4}=x[/tex]
Therefore, the unknown number is [tex]\dfrac{3}{4}[/tex].
tysmmmmmmmmmmmmmmmmmmmmmm
Answer:
The answer is 10
Step-by-step explanation:
To get this you will make the improper fraction into a fraction and then turn that into decimal form
[tex]4 \frac{1}{8} = 4[/tex]
and
[tex]5 \frac{6}{10} = 6[/tex]
That is how you find the estimated answer
Hope this Helped
help pls ;;-;; ye thxs
Answer:
You still need help? :P
Step-by-step explanation:
I really need help with this one or I fail
can some one help me please....
by step by step explanation......
what times what equals 168 besides 84 times 2?
Answer:
12 & 14
Step-by-step explanation:
