The work is done in compressing the spring from a length of 15 inches to a length of 13 inches are the 0.897ftlb.
Work Done:According to the paintings-power theorem, the internet paintings performed on an item equals the alternate withinside the power of the item . If the simplest alternate withinside the power located is withinside the capability power (say U) of the item, then the internet paintings performed W=△U.
Answer and Explanation:When a spring is compressed x in with the aid of using a pressure F,
F=kx, where k is the spring constant.
Since it's miles for the reason that the spring is compressed to 8in from 21in, that is, a compression of (21−eight)=13in, we obtain
F=kx⇒k=Fx=10lb1312ft=12013lbft−1.
Using the theorem, the internet paintings performed on an item equals the alternate withinside the power of the item. In this situation the simplest alternate in power is withinside the capability power of the spring while it's miles compressed with the aid of using x gadgets of duration, which is 12kx2. (k is the spring constant.)
The capability power of the spring while it's miles compressed to 15cm=0.5k(21−1512)2
The capability power of the spring while it's miles compressed to 13cm=0.5k(21−1312)2
Work Done equals the alternate withinside the capability power while it's miles compressed from 15in to 13in
=0.5k[(21−1312)2−(21−1512)2]=0.512013[(21−1312)2−(21−1512)2]≈ 0.897ftlb
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Which of the following choices correctly names angles 2 and 3?
alternate interior angles corresponding angles
alternate exterior angles
vertical angles
The choice that correctly names angles 2 and 3 is called the: D. vertical angles.
What is the Definition of Vertical Angles?Two angles are named vertical angles if both angles form a pair of angles that share the same vertex both not the same side, and they are on the opposite sides of two straight lines that intersect each other.
Given the image above, it shows that angle 2 and angle 3 form a pair that shares the same vertex when two straight lines intersect, and both angles are non-adjacent angles, that is they do not share any common side with each other.
Therefore, according to the definition given above, the angles 2 and 3 can be correctly named as: D. vertical angles.
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Remainder Theorem, (refer to attached image) please help
The type of reasoning used to prove the remainder theorem is; Deductive reasoning
How to interpret Logical Reasoning?Logical reasoning involves using a given set of facts or data to deduce other facts by reasoning logically
There are 4 major types of reasoning here and they are;
1) Deductive reasoning; This is defined as a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true.
2) Inductive reasoning; This is a method of drawing conclusions by going from the specific to the general.
3) Abductive reasoning; This is defined as a syllogism in which the major premise is evident but the minor premise and therefore the conclusion only probable.
4) Reasoning by analogy; This involves using a well known situation to assert something about a less well understood situation
In this case, we are told that since (x - 5) is a factor of the polynomial x² - 25, if he performs the long division (x² - 25) ÷ (x - 5), the remainder would be zero.
Now, this is an example of deductive reasoning because it has used the initial premise to draw a conclusion on the remainder.
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Identify the function family to which f belongs. Then identify the domain and range of f.
a. What type of function is shown?
b. What is the domain:
c. What is the range:
-4 -3 -2 -1
2
4
-5
-6
y
2 3 4 x
Answer:A function can be transformed to another through dilation, reflection, translation, and rotation. Belongs to the quadratic family. The following is the comparison of and its parent function
Both functions are quadratic
The parent function is vertically stretched by 2, rotated along the x-axis and then translated up by 3 units.
Step-by-step explanation:
I don't think this is right
What question does the equation 525=25(x-2) help answer
Answer: x=23
Step-by-step explanation:
1. First we need to find how much needs to be multiplied by 25, so 525/25=21.
2. Now that we know that x-2=21, we do 21+2.
3. 21+2=23, so x=23
Please give brainliest.
At Freddy's Eatery, three steak burgers and two orders of fries cost $18. Two steak
burgers and three orders of fries cost $15.75. What is the cost of one steak burger?
A) $5
B) $4.50
D) $6.50
C)
$2.25
To solve this problem, we can set up a system of equations to represent the given information. Let x represent the cost of one steak burger. Then we can set up the following system of equations:
3x + 2(f) = 18
2x + 3(f) = 15.75
Where f represents the cost of one order of fries.
Subtracting the second equation from the first equation gives us:
x = 18 - 2(f) - 15.75 + 3(f)
= 18 - 15.75
= 2.25
Therefore, the cost of one steak burger is $2.25, which is answer choice C.
Two companies are trying to sell laptops to a school district. The tables show to total cost for laptops purchased from each of the companies.
Company 1
1=$425
3=$475
5=$525
Company 2
1=$250
3=$350
5=$450
How many laptops would the school district have to purchase for the cost to be the same for both companies?
The school district have to purchase 8 laptops for the cost to be the same for both companies.
What is sequence?
A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is the number of elements.
Given that the company 1 offers:
The cost of 1 laptop is $425.
The cost of 3 laptop is $475.
The cost of 5 laptop is $525.
The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $50
The company 2 offers:
The cost of 1 laptop is $250.
The cost of 3 laptop is $350.
The cost of 5 laptop is $450.
The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $100
Take the cost as a sequence:
The common difference of first sequence is 50/2 = 25.
The common difference of second sequence is 100/2 = 50.
Assume that the school district needs to buy n computer.
The nth term of a sequence is a + (n - 1)d, where a is the first term, d is common difference.
The nth term of the first sequence is 425 + (n - 1) 25
The nth term of the second sequence is 250 + (n - 1) 50
According to question,
425 + (n - 1) 25 = 250 + (n - 1) 50
425 + 25n - 25 = 250 + 50n - 50
25n - 50n = 250 - 50 - 425 + 25
- 25n = -200
Divide both sides by 25
n = 8
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12. Look at this shape:
Which image
shows a reflection and why?
Answer:
Answer is B.
Step-by-step explanation:
Option A seem to look like a rotation of 180°.
Option B is a reflection across the x-axis.
Option C is a translation shift.
500 milliliters =
liters
Answer: 0.5 Liters
Step-by-step explanation:
1 Liter = 1000 milliliters
500 milliliters = 0.5 Liters
I just need to take 500 divided by 1000 = 0.5 Liters
PLEASE HELP FAST ILL GIVE BRAINLIEST IF CORRECT!!!!
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
A. One solution
B. Infinitely many solutions
C. Two solutions
D. No solutions
Answer: (A) One solution
a quadratic function can be used to model the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. according to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. based on the model, what was the height, in feet, of the object 1 second after it was launched?
The height of the object 1 second after it was launched is equals to 243.1 feet.
Let the launching velocity /initial velocity = u ft./s
and final velocity = 0 feet/sec , because at the maximum height, the final velocity of launching is '0'.
Maximum height , s = 3136 feet
time, t = 14 sec
Using the Equation of motion,
v² - u² = -2gs
where, v --> final velocity
u --> initial velocity
g --> acceleration due to gravity and it is a constant with value 9.8 m/sec²
s --> distance ( max. height)
plugging all known values in above formula,
0 - u² = -2 (9.8)(3136) = - 61465.6
=> - u² = - 61465.6
=> u² = 61465.6
=> u = √61465.6 = 247.92 ~ 248
=> u = 248 feet/sec
Now, the height, in feet, of the object 1 second after it was launched is
s = ut + (1/2)(-g)t²
=> s = 248(1) + (1/2)(-9.8)(1)
=> s = 248 - 4.9 = 243.1 feet
So, the required height is 243.1 feet.
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Name the Special Segment that Matches the picture below.
The special segment that matches the picture is the Median.
What is the median segment?
A median is a line segment that connects any triangle vertex to the middle of the opposite side. It is also the path that connects an angle's opposite internal side to its midpoint. At the centroid, they coexist.
From the figure, the given triangle in which segment is concurrent at the centroid. It bisects each side of the triangle into two equal parts.
Hence, the special segment that matches the picture is the Median.
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1. solve 2x-5/7 - 2x-1/2 = 3
2. solve x+1/2 + 2x-1/4 + x+2/3
3. A= 8/x+1 and B=2x+5/x
Given 5-A-B=0
Work out the possible values of x.
Give your solutions to two decimal places.
Answer:
1.
2(2x-5)-7(2x-1)=3
Multiply both sides of the equation by 14, the least common multiple of 7,2.
2(2x−5)−7(2x−1)=42
Use the distributive property to multiply 2 by 2x−5.
4x−10−7(2x−1)=42
Use the distributive property to multiply −7 by 2x−1.
4x−10−14x+7=42
Combine 4x and −14x to get −10x.
−10x−10+7=42
Add −10 and 7 to get −3.
−10x−3=42
Add 3 to both sides.
−10x=42+3
Add 42 and 3 to get 45.
−10x=45
Divide both sides by −10.
x= −10/45
Reduce the fraction to lowest terms by extracting and canceling out 5.
x=− 2/9
2. I don't know this one. Sorry.
3. is in the file
Two number have a difference of 20. How do you find the number if the um of their quare i a minimum?
The first and second numbers are -10 and 10, respectively. because their difference is zero
What is unitary method?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares.
The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.
Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.
According to our question-
Let us consider that first number is x and second number is y.
Hence, The first and second numbers are -10 and 10, respectively.
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Please help me respond this
Answer:i don't know thanks for the brainy money tho
Step-by-step explanation:
950.95 written in expanded form
Answer:
(9 x 100) + (5 x 10) + (0 x 1) + (9/10) + (5/100)
hope this helps brainliest <3
Answer:
Step-by-step explanation:
Need Help!!!!!!!!! Solve for side similar triangle
Answer: root 70
Step-by-step explanation:
starting info:
KL = 2NM
KM = 20
NO = 7
Using the fact the ratio of similar sides must be equal:
KL/NO = KM/NM
Therefore sub in values…
KL/7 = 20/NM
As KL = 2NM
2NM/7 = 20/NM
Rearrange:
2(NM)^2 = 140
(NM)^2 = 70
NM = root(70)
(Obviously take positive as can’t have negative length)
Find the inverse of the function.
y = 3x + 3
Write your answer in the form ax + b. Simplify any fractions.
y =
Submit
Which of the following statements is true regarding a scatter diagram?
a. It provides very little information about the relationship between the regression variables.
b. It is a plot of the independent and dependent variables.
c. It is a line chart of the independent and dependent variables.
d. It has a value between -1 and +1.
e. It gives the percent of the variation in the dependent variable that is explained by the independent variable.
Option B is correct. It is a plot of the independent and dependent variables.
A scatter diagram is a type of plot or graph that uses Cartesian coordinates to display the values of two variables for a set of data. It is a simple yet powerful way to visualize the relationship between two variables.
The points on the plot represent the values of two variables, the independent variable (X-axis) and the dependent variable (Y-axis). Scatter diagrams provide a visual representation of the relationship between the two variables, which makes it easier to identify patterns such as linear or non-linear relationships.
They also can show correlations, or lack thereof, between two or more variables. Additionally, scatter diagrams can provide insight into the strength of the relationship between the two variables as well as how much of the variation in the dependent variable is explained by the independent variable. For example, a correlation coefficient of 1 indicates a perfect linear relationship, while a correlation coefficient of 0 indicates no relationship between the two variables.
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Susie is going to rent an apartment in Smallville, where other monthly expenses will sum up to $2831. Susie makes $8609 each month.
Write the inequality for the possible amounts of money Susie can spend renting her apartment in Smallville in order for Susie to have some money left over each month.
Use x to represent the cost of the rent in Smallville and don't use the $ symbol in the inequality.
Answer:
x = $2351
Step-by-step explanation:
The football team ha a total of 50 jerey. There are 20 medium jerey. What percent of the jerey are medium ize jerey?
the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%
In order to calculate the percentage of medium jerseys, we must divide the total number of medium jerseys (20) by the total number of jerseys (50).
To express this as a percentage, we must multiply the result by 100. Therefore, 20 ÷ 50 = 0.4 and 0.4 x 100 = 40%. Thus, 40% of the jerseys are medium size. the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%
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two buses leave towns miles apart at the same time and travel toward each other. one bus travels slower than the other. if they meet in hours, what is the rate of each bus?
two buses leave towns miles apart at the same time and travel toward each other. then the Rate of first bus = 72 mph and Rate of second bus = 62 mph
let first bust travels at x mph
then, 2nd but will travel at ( x - 10) mph
distance travelled by first bus in 2 hours = 2x
distance travelled by 2nd but in 2 hours = 2( x- 10) = 2x - 20
distance between the two is 268 miles
so we can write
2x + 2x - 20 = 268
4x = 288
x = 288 / 4 = 72 mph
rate of first bus = 72 mph
and second bus = 72 - 10 = 62 mph
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I need help please :)
By using normal distribution of probability, it can be calculated that-
a) When x = 142, z = 1.4
b) When x = 130, z = 0.6
c) When x = 103, z = -1.2
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by
f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}[/tex]
Where z = [tex]\frac{x - \mu}{\sigma}[/tex] , [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
Here Systolic blood pressure is normally distributed
Mean = 121
Standard deviation = 15
a) x = 142
z = [tex]\frac{142 - 121}{15}[/tex] = 1.4
b) x = 130
z = [tex]\frac{130 - 121}{15}\\[/tex] = 0.6
c) x = 103
z = [tex]\frac{103 - 121}{15}[/tex] = -1.2
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Please help!! 45 points!!
A ball is projected into the air. Its height at time, t, is given by the equation h=-16t^2 + 100t + 2. When will the ball return to the ground?
A.0.02 sec
B. 6.3 sec
C. 6.5 sec
D. 16 sec
Answer:
The ball will return to the ground at t = 16 seconds, so the correct answer is D.
Step-by-step explanation:
To find when the ball will return to the ground, we need to find the time at which the ball's height is equal to 0. We can do this by setting the height equation equal to 0 and solving for t.h = -16t^2 + 100t + 2
0 = -16t^2 + 100t + 2
-2 = -16t^2 + 100t
-0.125t = -2
t = 16
Answer:
B. 6.3 sec
Step-by-step explanation:
To find the time when the ball will return to the ground, we need to find the value of t when h is equal to 0 (since height = 0 means the ball is on the ground). We can do this by substituting 0 for h in the given equation and solving for t.
So, let's start by substituting 0 for h:
h = -16t^2 + 100t + 2
0 = -16t^2 + 100t + 2
-16t^2 + 100t + 2 = 0
This is a quadratic equation, which we can solve using the quadratic formula:
t = (-100 +/- sqrt(100^2 - 4(-16)(2)) ) / (-2(-16))
t = (-100 +/- sqrt(10000 + 128)) / 32
t = (-100 +/- sqrt(10128)) / 32
t = (-100 +/- 100.64) / 32
t = (200.64) / 32
t = 6.3125
Since the ball is projected into the air and then falls back down to the ground, the time when it returns to the ground must be a positive value. Therefore, the solution to the problem is t = 6.3 sec
ƒ(x) = √−2x What is the domain of f?
The domain of the function is all negative real number and zero.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The given function
ƒ(x) = √−2x
The domain of the expression is all real numbers except where the expression is undefined.
And here, when x is positive real number then field changes to complex.
That means the function is undefined in real field when x is not negative or zero.
Therefore, the domain of the function is all negative real number and zero.
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a bookcase is 5 feet high and 5 feet wide as shown. two braces are going to be built diagonally across the back of the case. how long is the piece of wood that is needed for each brace?
The piece of wood that is needed to build each brace 5√2 feet.
Let the piece of wood that be needed to build each brace x feet.
A bookcase is 5 feet high and 5 feet wide, so
By condition we can write (5^2)+(5^2)=x^2
⇒25+25=x^2
⇒ 50=x^2
x=√50
prime factors:
50=2 × 5 × 5
50 = 2 × 5^2
√50 = √(25 × 2) = 5√2
The piece of wood that is needed to build each brace 5√2 feet .
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Which of the following is not a type of graph?EulerHamiltonianTreePath
Answer:
Step-by-step explanation:
Answer = D Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler. 32) Which of the following is not a type of graph ? Answer = D Explanation:Path is a way from one node no another but not a graph.
find the general solution of the given second-order differential equation. y'' − 10y' + 26y = 0
The general solution of the given second-order differential equation is
y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).
In the given question we have to find the general solution of the given second-order differential equation.
The given second-order differential equation is:
y'' − 10y' + 26y = 0
We can write this equation as
d^2(y)/dx^2 − 10dy/dx + 26 = 0
Let d/dx = D
then, d^2/dx^2 = D^2
Now the equation is:
(D^2 − 10D + 26)y = 0
Now solving the equation as a quadratic equation.
m^2 − 10m + 26 = 0
m = [tex]\frac{-(-10)\pm\sqrt{(-10)^2-4\times1\times26}}{2\times1}[/tex]
m = [tex]\frac{10\pm\sqrt{100-104}}{2}[/tex]
m = [tex]\frac{10\pm\sqrt{-4}}{2}[/tex]
m = [tex]\frac{10\pm2i}{2}[/tex]
m = 5±1
Now the general equation for quadratic equation is
y = [tex]e^{at}[/tex]([tex]c_{1}[/tex]cosbt + [tex]c_{2}[/tex]sinbt)
As a = 5 and b = 1
Now the general solution of the given second-order differential equation is y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).
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Edgar is putting toys into bags. One bag can hold 6 toys and Edgar has 53 toys. How many bags will Edgar fill? Write the answer as a mixed number AND an improper fraction.
Answer:
[tex]\textsf{Improper fraction}: \quad \dfrac{53}{6}[/tex]
[tex]\textsf{Mixed number}: \quad 8\frac{5}{6}[/tex]
Step-by-step explanation:
Definitions
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.A mixed number is a number consisting of a whole number and a proper fraction.A proper fraction is a fraction where the numerator is less than the denominator.If each bag holds 6 toys and Edgar has 53 toys, to find how many bags Edgar will fill, divide 53 by 6.
Improper fractionTo write this as an improper fraction, place 53 as the numerator and 6 as the denominator:
[tex]\implies \dfrac{53}{6}[/tex]
As 53 is a prime number, its only factors are 1 and 53. Therefore, the improper fraction cannot be reduced any further.
Mixed numberRewrite 53 as the sum of 48 and 5:
[tex]\implies \dfrac{53}{6}=\dfrac{48+5}{6}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}:[/tex]
[tex]\implies \dfrac{48}{6}+\dfrac{5}{6}[/tex]
Divide 48 by 6:
[tex]\implies \dfrac{6 \cdot 8}{6}+\dfrac{5}{6}[/tex]
[tex]\implies 8+\dfrac{5}{6}[/tex]
Write as a mixed number:
[tex]\implies 8\frac{5}{6}[/tex]
What is the prime factorization of 168?
22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7
Answer:
[tex]2^3 * 3 * 7[/tex]
Step-by-step explanation:
Linked below.
Find two factors and break down individually. Circle prime numbers. If there are more than one of the same prime number, write as an exponent:
i.e. 6 x 6 = [tex]6^{2}[/tex]
Observation, experimentation, and mathematics, in combination, produce reliable results. This statement describes a development of thought during which period?.
This statement describes a period known as the Scientific Revolution.
The Scientific Revolution: What Was It?
The 16th and 17th centuries saw a radical shift in scientific ideas that is known as the Scientific Revolution.
During the Scientific Revolution, a new understanding of nature replaced the Greek perspective that had dominated science for nearly two thousand years.
The Scientific Revolution was absent?
The Enlightenment, an intellectual and social movement, was influenced by the scientific revolution, which started in Europe at the end of the Renaissance and lasted until the late 18th century.
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