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Related Questions
What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
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AB=4-1=3
BC=√((7-4)²+(2-(-2))²)=√(9+16)=√25=5
CD=BC=5
DE=4-1=3
AE=6-(-2)=8
Perimeter=3+5+5+3+8=24.
Using the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 24 units.
What is the Perimeter of a Polygon?
Perimeter = sum of all sides of the polygon.
Name the vertices as follows:
A(−2, 1)B(−2, 4)C(2, 7)D(6, 4) E(6, 1)Perimeter of the polygon = AB + BC + CD + DE + EA
Use the distance formula, [tex]d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find the length of each segment:
AB = |1 - 4| = 3 units
BC = √[(2−(−2))² + (7−4)²]
BC = 5 units
CD = √[(2−6)² + (7−4)²
CD = 5 units
DE = |4 - 1| = 3 units
EA = |6 - (-2)| = 8 units
Perimeter of the polygon = 3 + 5 + 5 + 3 + 8
Perimeter of the polygon = 24 units
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Write an additional word problem in which the estimated sum is 14,000
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7,000 + 7,000 = 14,000
The problem is about estimating the total sales sum of 7 TVs sold in a day, each priced at approximately $2,000, which gives us a total estimate of $14,000.
Explanation:The mathematics problem could be something along the lines of this: In a local electronics store, 7 high-definition smart TVs were sold in one day. If each TV is approximately priced at $2,000, what is the estimated total sales sum for that day?
First, analyze the problem. We want to find the estimated total sales sum for the smart TVs.Then, we use estimation to solve it. We know each TV costs around $2,000 and that 7 TVs were sold.Just multiply $2,000 by 7. Thus, $2,000 * 7 = $14,000So, the estimated sum is $14,000This estimation gives us a total sum of $14,000, which is close to the actual total if each TV is priced at $2,000.
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Divide. 42/−8 Enter your answer as a mixed number, in simplified form, in the box.
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Write the following statement as a conditional. All flowers are beautiful.
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A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 minutes. after treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes (based on data from cognitive behavioral therapy vs zopiclone for treatment of chronic primary insomnia in older adults," by silverstein et al., journal of the american medical association, vol. 295, no. 24). assume that the 16 sample values appear to be from a a normally distributed population and construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments. what does the result suggest about the mean wake time of 102.8 minutes before the treatment
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To construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments, use the formula: Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size).
Explanation:To construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments, we can use the formula:
Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size)
Given that the sample mean after treatment with zopiclone is 98.9 minutes, the standard deviation is 42.3 minutes, and the sample size is 16, we need to find the critical value for a 98% confidence level. The critical value can be found using a t-distribution table or calculator.
Once the critical value is obtained, we can plug in the values into the formula to calculate the confidence interval estimate.
How many gallons is 15 percent of 55 gallons?
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Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.
Given:
∠C, ∠F are rt.∠'s; AC = DF; BC = EF
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The two legs, ie the sides adjacent to the right angle, for the two triangles are also given to be congruent to one another
leg AC = leg DF
leg BC = leg EF
Because we have two pairs of legs congruent for these two triangle triangles, we use the Leg Leg Theorem which abbreviates to the LL Theorem, or simply LL.
This is why the answer is choice B) LL
Answer:
LA
Step-by-step explanation:
Odyssey
The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (a) how many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards. (b) express x in terms of s, w, and r. (c) find e[x].
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Given that the game of clue involves 6 suspects, 6 weapons, and 9 rooms.
The number of ways that one of each is randomly chosen is given by:
[tex] ^6C_1\times{ ^6C_1}\times{ ^9C_1}=6\times6\times9=324[/tex]
Therefore, the number of solutions possible is 324.
Part B:
Given that a players is randomly given three of the remaining cards, let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player.
The number of suspects, weapons, and rooms remaining respectively after the player observes his or her three cards are: 6 - s, 6 - w, and 9 - r.
Let x denote the number of solutions that are possible after that player observes his or her three cards, then:
[tex]x={ ^{6-s}C_1}\times{ ^{6-w}C_1}\times{ ^{9-r}C_1}=(6-s)(6-w)(9-r)[/tex]
Therefore, x in terms of s, w, and r is given by x = (6 - s)(6 - w)(9 - r).
Part C:
The expected value E(x) of a data set [tex]x_i[/tex] with probabilities [tex]p(x_i)[/tex] is given by [tex]E(x)=\Sigma xp(x)[/tex]
There are [tex] ^{3+3-1}C_{3-1}={ ^5C_2}=10[/tex] possible combinations s, w and r. They are (3, 0, 0), (0, 3, 0), (0, 0, 3), (2, 1, 0), (0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 2, 0), (0, 1, 2), (1, 1, 1)
Thus the expected value is given by
[tex]E(x)=3\cdot6\cdot9p(3, 0, 0)+6\cdot3\cdot9p(0, 3, 0)+6\cdot6\cdot6p(0, 0, 3) \\ 4\cdot5\cdot9p(2, 1, 0)+6\cdot4\cdot8p(0, 2, 1)+5\cdot6\cdot7p(1, 0, 2)+4\cdot6\cdot8p(2, 0, 1) \\ +5\cdot4\cdot9p(1, 2, 0)+6\cdot5\cdot7p(0, 1, 2)+5\cdot5\cdot8(1, 1, 1) \\ \\ = \frac{1}{ ^{21}C_3} (162\cdot{ ^6C_3}\cdot{ ^6C_0}\cdot{ ^9C_0}+162\cdot{ ^6C_0}\cdot{ ^6C_3}\cdot{ ^9C_0}+216\cdot{ ^6C_0}\cdot{ ^6C_0}\cdot{ ^9C_3} \\ \\ +180\cdot{ ^6C_2}\cdot{ ^6C_1}\cdot{ ^9C_0}+192\cdot{ ^6C_0}\cdot{ ^6C_2}\cdot{ ^9C_1}[/tex]
[tex]+210\cdot{ ^6C_1}\cdot{ ^6C_0}\cdot{ ^9C_2}+192\cdot{ ^6C_2}\cdot{ ^6C_0}\cdot{ ^9C_1}+180\cdot{ ^6C_1}\cdot{ ^6C_2}\cdot{ ^9C_0} \\ \\ +210\cdot{ ^6C_0}\cdot{ ^6C_1}\cdot{ ^9C_2}+200\cdot{ ^6C_1}\cdot{ ^6C_1}\cdot{ ^9C_1} \\ \\ =\frac{1}{1,330}(324\cdot20+216\cdot84+360\cdot90+384\cdot135+420\cdot216+200\cdot324) \\ \\ =\frac{1}{1,330}(6,480+18,144+32,400+51,840+90,720+64,800) \\ \\ =\frac{1}{1,330}(264,384) \\ \\ =\bold{198.78}[/tex]
Answer:
(a) 324 solutions are possible
(b) (6 - s)(6 - w)(9 - r)
(c) 198/78
Step-by-step explanation:
Just a pure guess and also give brainliest to the other person
It took Leo 3.5 hours to complete a route walking at a rate of 4.2 mph. How long would it take Leo to complete the same route walking at a rate of 2.8 mph?
plz give exact answer
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3.5 hrs * 4.2 mph = 14.7 mi
t = S/V
14.7 mi/ 2.8 mph = 5.25 hrs
The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by 40x - 0.0002x^2, what is an expression for the profit?
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The profit function is given by [tex]\( P(x) = -0.0002x^2 + 26x - 120,000 \).[/tex]
To find the expression for the profit, we need to subtract the cost function from the revenue function.
Given:
Cost function: [tex]\( C(x) = 14x + 120,000 \)[/tex]
Revenue function: [tex]\( R(x) = 40x - 0.0002x^2 \)[/tex]
The profit function, ( P(x) ), is given by:
[tex]\[ P(x) = R(x) - C(x) \][/tex]
Substitute the given functions into the profit function:
[tex]\[ P(x) = (40x - 0.0002x^2) - (14x + 120,000) \][/tex]
Now, let's simplify:
[tex]\[ P(x) = 40x - 0.0002x^2 - 14x - 120,000 \][/tex]
[tex]\[ P(x) = 26x - 0.0002x^2 - 120,000 \][/tex]
This is the expression for the profit:
[tex]\[ {P(x) = -0.0002x^2 + 26x - 120,000} \][/tex]
So, the profit function is given by [tex]\( P(x) = -0.0002x^2 + 26x - 120,000 \).[/tex]
Find the specific formula for the sequence. [−3,1,5,9,13,...]
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x+4 is the specific formula for sequence [−3,1,5,9,13,...]
What is Sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is
−3,1,5,9,13,...
-3+4=1
1+4=5
5+4=9
9+4=13
As we can see above, to get from one number to the next it is simply adding 4. So the formula for sequence is x + 4.
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How to solve more complex problems involving angles the backwards Method
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What is a security deposit
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Which inequality will have a shaded area above its graph?
a
x − 9y ≤ 1
b
4x + 3y < 6
c
2x − y ≥ 4
d
x − 3y > 4
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Because If you solve the equation y will be greater than ...
x − 9y ≤ 1
Solve for y...
Subtract x from both sides...
- 9y ≤ - x + 1
Divide both sides by -9
REMEMBER WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER FLIP THE INEQUALITY SIGN....
y ≥ x/9 - 1/9
If the coefficient of y is negative, you’ll have to flip the inequality sign around in the process of isolating y. Which of those options have negative coefficients for y, and how would flipping the inequality sign effect them? Try to find the one option where the inequality ends up facing the y.
Solve 4(c + 2) < 4c + 10.
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4c + 8 < 4c + 10
4c - 4c < 10 - 8
0 < 2...no variables
this inequality has no solution
[tex]4c+8\ \textless \ 4c+10 [/tex]
[tex]8\ \textless \ 10 [/tex] [tex]\text{Cancel 4c on both sides}[/tex]
[tex]\text{Since}[/tex] [tex]8\ \textless \ 10 [/tex] [tex]\text{is always true, there are infinitely many solutions}[/tex]
Determine the axis of symmetry the vertex and the x-and y intercepts f(x)=x2+2x-3
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The x- and y intercepts is: x- intercept: (1,0),(-3,0)
y intercept: (0,-3)
Hope this helps!:)
The x- and y intercepts is: x- intercept: (1,0),(-3,0)
y intercept: (0,-3)
If 15% of x is 42, what is x?
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[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 42&15 \end{array}\implies \cfrac{x}{42}=\cfrac{100}{15}\implies x=\cfrac{42\cdot 100}{15}[/tex]
3/20x=42
x= 42* 20/3 (reciprocal)
x=14*20
x=406
Constructed Response 1: A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7. The student then adds 3.6 and 2.7 and gets 5.13 because 3 + 2 = 5 and 6 + 7 = 13. Identify the mistake in the student’s procedure and explain why this procedure won’t always work.
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So 3.6 + 2.7 = 5 units + 1 unit + 3 tenths = 6 units + 3 tenths = 6.3
If you write 5.13 that is 5 units and 13 hundreeths which is wrong.
The procedure used by the student wont work when the addtion of the two digits is 10 or greater than 10. In those cases, you must pass the left digit to the next place and sum it to the other digits that are in that place since the beginning.
Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35kg. Write an equation to determine the weight, w ww, of each of Carl's checked bags. Find the weight of each of his checked bags.
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2+4b=35
35-2=33
33/4=8.25kgs
Answer:
15.5 kg (each)
Step-by-step explanation:
Let [tex]w[/tex] be the weight of each checked bag (there are 2). Thus, we can write, from the information given:
[tex]w+w+4=35\\2w+4=35[/tex]
Now we solve this equation for [tex]w[/tex] to find weight of each checked bag:
[tex]2w+4=35\\2w=35-4\\2w=31\\w=\frac{31}{2}\\w=15.5[/tex]
So, the weight of each of his checked bags is 15.5 kg.
Help
simply. this math problem
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- 4 1/5 = -21/5 = -42/10
-13 1/10 = -131/10
-42/10 - -131/10=
-42/10 + 131/10 = 89/10 = 8 9/10
answer is A
Simplify 2y^2-7y-15/3y^2-8y-2 9y^2-1/4y^2-9 / y^2+3y-10/2y^2-9y+9
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Please help asap!!! I will mark brainliest!
Estimate 27.89 • 10.3 divided by 4.37 using compatible numbers
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if you round your answer= 66.0
hope this help!
Two lines that do not intersect are parallel.alwayssometimesnever
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Deshawn has several dimes and quarters that total $2.05. he has 3 fewer quarters than dimes. how many of each doe he have
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x = the number of dimes
y = the number of quarters
The total sum is $2.05, therefore
0.10x + 0.25y = 2.05
Divide through by 0.05 to obtain
2x + 5y = 41 (1)
There are 3 fewer quarters than dimes, therefore
y = x - 3 (2)
Substitute (2) into (1).
2x + 5(x - 3) = 41
2x + 5x - 15 = 41
7x = 56
x = 8
y = x - 3 = 5
Answer: 8 dimes, 5 quarters
The three interior angle measures of this triangle are x = °, y = °, and z = °.
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z = 180 - 100 = 80
y = 180 - (30+80) = 180 - 110 = 70
Answer:
30-70-80
Step-by-step explanation:
Markus receives dollar bills from his grandfather for one week on the first day he received $1 on the second day he received $2 on the third day he received $4 and on the fourth day he received $8 if this continues how much money will Marcos have by the end of the week
Answers
Answer:
127
Step-by-step explanation:
It gas geometric sequence,
We has a sequence: 1, 2, 4, 8, 16, 32, 64.
It can be solved by two method either sum these digits individually or use formula of sum of geometric sequence
We have formula: [tex]S_n=\frac{a_1(1-r^n)}{(1-r)}[/tex]
Here r = Common Ratio = 2 ÷ 1 = 4÷2 = 2
and a = First term = 1
⇒ [tex]S_n= \frac{1\times(1-2^7)}{(1-2)} \\\Rightarrow S_n=\frac{(1-128)}{-1}\\ \Rightarrow S_n=127[/tex]
Bill weighs 120 lbs and is gaining ten lbs each month. Phil weighs 150 lbs and is gaining four lbs each month. How many months will it take for bill to wiegh the same as phil?
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Bill: 120 + 10x
Phil: 150 + 4x
If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:
120+10x = 150 + 4x [starting equation]
-120 -4x -120 -4x [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]
6x = 30 [divide both sides by 5]
5 5
x=6. They will weigh the same in six months.
Algebraic equations are equations that contain variables that are unknown. These unknown variables are represented by any letters of the Alphabet.
it will take 5 months for Bill to weigh the same as Phil.
Let's represent the number of months they gain extra weight as: m
Step 1
Bill weighs 120 lbs and is gaining ten lbs each month. The algebraic equation for the above statement is :
120 ib + 10 ib x m
120 + 10m ........Equation 1
Phil weighs 150 lbs and is gaining four lbs each month. The algebraic equation for the above statement is :
150 ib + 4 ib x m
150 + 4m ........Equation 2
Step 2
We equate equations 1 and 2 to each other
Equation 1 = Equation 2
120 + 10m = 150 + 4m
Collect like terms
10m - 4m = 150 - 120
6m = 30
Divide both sides by 6
6m/6 = 30/6
m = 5
Therefore, it will take 5 months for Bill to weigh the same as Phil
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does velocity or mass impact momentum more and why
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Both mass and velocity equally affect momentum in classical physics. However, at relativistic speeds, velocity has a more significant effect on momentum due to relativistic mass increase.
Explanation:The impact of mass and velocity on momentum depends on the context of the object's motion. In classical physics, momentum is defined as the product of an object's mass and velocity, thus both mass and velocity equally influence momentum. However, for objects moving at relativistic speeds—approaching the speed of light—the effect of velocity on momentum is more pronounced due to the relativistic mass increase. To illustrate, a football player with greater mass has a larger impact due to having more momentum when moving at the same velocity as a player with less mass. In contrast, at relativistic speeds, an increase in velocity would result in an exponentially greater momentum, surpassing the effect of just increasing mass.
In triangle JKL, if line JK is equal to line JL, angle J equals 23x-4, angle K equals 4x-1, and angle L equals 9x-31, find x and the measure of each angle.
Answers
Equation: 4x - 1 = 9x - 31
Solved: x = 6
Angle measures: ∡J = 23(6) - 4 = 138 - 4= 134
∡K = ∡L = 23
m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° is the answer.
From the figure attached,
JK and JL are equal sides of the triangle.m(∠J) = 23x - 4m(∠K) = 4x - 1m(∠L) = 9x - 31Since, two sides JK and JL of ΔJKL are equal in measure,
Therefore, ΔJKL is an isosceles triangle.
By the property of an isosceles triangle, opposite angles of the equal sides are equal.
Therefore, m(∠K) = m(∠L)
4x - 1 = 9x - 31
9x - 4x = 31 - 1
5x = 30
x = 6
By substituting the value of 'x' in the measures of each angle,
m(∠J) = 23x - 4
= 23(6) - 4
= 138 - 4
= 134°
m(∠K) = 4x - 1
= 4(6) - 1
= 24 - 1
= 23°
m(∠L) = 9x - 31
= 9(6) - 31
= 23°
Therefore, m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° will be the answer.
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Sharon is twice as old as brian, and in 5 years the sum of their ages will be 25 years. find their present ages.
Answers
Answer:
sharon=10
Step-by-step explanation:
The present age of Sharon and Brain is 10 years old and 5 years old.
Given,
Sharon is twice as old as brian.
In 5 years the sum of their ages will be 25 years.
We need to find their present ages.
What are the important terms in solving age problems?Some of the terms are:
In x years - add x years to the present age
x years ago - Subtract x years with the present age
Before x years - subtract x years to the present age
After x years - add x years to the present age
Find the present age of Sharon and Brain.
Let the present age of:
Sharon - S
Brain - B
Now,
Sharon is twice as old as brian.
We can write this as:
S = 2B ____(1)
In 5 years the sum of their ages will be 25 years.
It can be written as:
(S + 5) + (B + 5) = 25
S + B + 10 = 25
S + B = 25 - 10
S + B = 15 _____(2)
From (1)
We get,
2B + B = 15
3B = 15
B = 5. ______(3)
Putting (3) in (2)
S + 5 = 15
S = 15 - 5
S = 10
We have,
B = 5 and S = 10
Thus the present age of Sharon and Brain is 10 years old and 5 years old.
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