DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027
DY^2 = 170 * 169^2 / (135^2 + 50 -
In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.
D
/ \
/ \
/ \
E-------F
Given that XF = 10, YF = 5, and EF = 13, we need to find DY.
We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:
EF / ED = EY / EJ (where J is the intersection of XY and DF)
EF / DF = EJ / EY
Substituting the given values, we get:
13 / ED = EY / EJ
13 / DF = EJ / (13 - EY)
Multiplying the above two equations, we get:
13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)
169 / (ED * DF) = EY / (13 - EY)
Substituting the values of XF = 10 and YF = 5, we get:
169 / (ED * DF) = 5 / 8
ED / DF = 135 / 169
Using the Pythagorean theorem on triangles DEX and DFY, we get:
ED^2 = EX^2 + DX^2
DF^2 = FY^2 + DY^2
Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:
ED^2 = EX^2 + (13 - EX)^2
ED^2 = 2EX^2 - 26EX + 170
Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:
DF^2 = FY^2 + DY^2
DF^2 = 170 - 26EY + EY^2 + DY^2
Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:
(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170
DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)
DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX) (Substituting XF = 10)
Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:
FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) (Substituting YF = 5)
DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2
Substituting the given values, we get:
DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027
DY^2 = 170 * 169^2 / (135^2 + 50 -
To learn more about equations visit:
https://brainly.com/question/11950137
#SPJ11
There is 13 of a gallon of water in a small fish tank. To clean the tank, Ray pours the water into two smaller bowls. How many gallons of water does Ray pour into each bowl?
Answer:
6.5 gallons
Step-by-step explanation:
if u see we have to divided 13 by 2 to see how much each bowl will have
13/2= 6.5 gallons
Write the equation of the line perpendicular y=5/2x+4 to
that passes through the point (-1,2)
The equation of a line is 2x + 5y = 8.
The given equation is :
y = 5/2x + 4
Here we have to find the equation of a line perpendicular to the given line passing through the point (-1,2).
The slope of a line is 5/2.i.e., \(m_{1}\) = 5/2
To find the slope of a line perpendicular to the line we have a formula:
\(m_{1}\)×\(m_{2}\) = -1
\(m_{2}\) = -1 /\(m_{1}\)
\(m_{2}\)= -1 × 2/5
=-2/5
The equation of a line is:
y = mx + c
The slope is -2/5 and the point is (-1,2)
c = y-intercept
So by putting the value we have:
2 = -2/5 × (-1) + c
c = 8/5
y = -2/5x + 8/55
y = -2x + 82x + 5y = 8
Therefore the equation of a line is 2x + 5y = 8.
To know more about the equation of a line refer to the link given below:
https://brainly.com/question/18831322
#SPJ1
can someone help me with algebra
i am very confused in addition algebra
and subtraction algebra, multiplication algebra,division algebra/please explain step by step !!!!
I understand that algebraic operations can be confusing at first, but I'll do my best to explain them step by step. Let's start with addition and subtraction in algebra, and then move on to multiplication and division.
Addition in Algebra:
Start with two or more algebraic expressions or terms that you need to add together.
Identify like terms, which are terms that have the same variables raised to the same powers. For example, 3x and 5x are like terms because they both have the variable x raised to the power of 1.
Combine the coefficients (the numbers in front of the variables) of the like terms. For example, if you have 3x + 5x, you add the coefficients 3 and 5 to get 8.
Write the sum of the coefficients next to the common variable. In this case, it would be 8x.
If there are any remaining terms without a like term, simply write them as they are. For example, if you have 8x + 2y, you cannot combine them because x and y are different variables.
Subtraction in Algebra:
Subtraction is similar to addition, but instead of adding terms, we subtract them.
Start with two algebraic expressions or terms.
Identify like terms, as we did in addition.
Instead of adding the coefficients, subtract the coefficients of the like terms.
Write the difference of the coefficients next to the common variable.
Handle any remaining terms without a like term in the same way as in addition.
Multiplication in Algebra:
Multiply the coefficients of the terms together. For example, if you have 2x * 3y, multiply 2 by 3 to get 6.
Multiply the variables together. In this case, multiply x by y to get xy.
Write the product of the coefficients and variables together. So, 2x * 3y becomes 6xy.
Division in Algebra:
Divide the coefficients of the terms. For example, if you have 12x / 4, divide 12 by 4 to get 3.
Divide the variables. If you have x / y, you cannot simplify it further because x and y are different variables. So, you leave it as x / y.
Remember, these steps are general guidelines, and there might be additional rules and concepts specific to certain algebraic expressions.
It's important to practice and familiarize yourself with these operations to gain confidence and improve your understanding.
need help solving please
Answer:
d
Step-by-step explanation:
If x=5 and y=3 find the value of x+2y
Answer:
x=5
y=3
then ,
x+2y= 5+2 *3
= 5+6
= 10
Let's say that the value of a car over time is given by the equation:
y = 20,000 (.88)
Tell me the following two things:
a) Is this a growth or decay problem and why?
b) What is the percent amount that the value changes by each year?
Answer:
Step-by-step explanation:
So bascially decay means shrinks or shrivels. Growth means like growing, bigger, sort of like a happy plant :D.
To find if this is getting bigger or is shrinking, lets plug in something simple like 1 for the time(t). Sooo:
20,000*.88^1
Since its a 1 exponent it does nothing so:
20,000*.88
Now this is 17600 you can use calculator but if you do this in head like me all I did is multiply 88 by 2 which was simply since 8 times 2 is 16 so 160+16 is 176 then I added zeros:
y=17600
As we can see this is smaller than 20,000, so it is a decaying problem.
By what percent tho.
Well this is pretty easy to reconize once you understand where to find it.
When they talk about percentage, they mean how much it decreased by.
This is 100%-the multiplyied value.
In this case the multiplyed value is 0.88, sooo:
100%-88%=18%
So the percent amount that the value decreased by is 18%.
Hope this helps!
Find the solution to the boundary value problem
D2y/dt2 – 7 dy/dt + 10y = 0, y (0) = 10, y(t)= 9
The solution is____
The solution to the given boundary value problem is y(t) = 3e^2t + 6e^5t.
To solve the boundary value problem, we can first find the characteristic equation associated with the given second-order linear homogeneous differential equation:
r² - 7r + 10 = 0.
Factoring the quadratic equation, we have:
(r - 2)(r - 5) = 0.
This equation has two distinct roots, r = 2 and r = 5. Therefore, the general solution to the differential equation is:
y(t) = c₁e^(2t) + c₂e^(5t),
where c₁ and c₂ are constants.
Using the initial conditions, we can determine the specific values of the constants. Plugging in the first initial condition, y(0) = 10, we have:
10 = c₁e^(2*0) + c₂e^(5*0),
10 = c₁ + c₂.
Next, we use the second initial condition, y(t) = 9, to find the value of c₁ and c₂. Plugging in y(t) = 9 and solving for t = 0, we have:
9 = c₁e^(2t) + c₂e^(5t),
9 = c₁e^0 + c₂e^0,
9 = c₁ + c₂.
We now have a system of equations:
c₁ + c₂ = 10,
c₁ + c₂ = 9.
Solving this system, we find c₁ = 3 and c₂ = 6.
Therefore, the solution to the boundary value problem is y(t) = 3e^(2t) + 6e^(5t).
To know more about linear homogeneous , refer here:
https://brainly.com/question/31129559#
#SPJ11
If you have an independent group design and ordinal data, which test do you use?
The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test
Given: Independent group and ordinal data. To find which test to use.
What's the Kruskal Wallis test?
The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.
The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.
The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.
How to calculate the Kruskal Wallis test?
The computation of the Kruskal- Wallis statistic requires
Combine the individualities from all the separate samples and rank order the entire group.Regroup the individualities into the original samples and cipher the sum of the species( T) for each sample. A formula is used to cipher the Kruskal- Wallis statistic which is distributed as a ki-square statistic with degrees of freedom equal to the number of samples minus one. The attained value must be lesser than the critical value for ki- forecourt to reject H0 and conclude that there are significant differences among the treatments.Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.
Know Further about "statistical tests" then: https//brainly.com/question/14128303
#SPJ4
We can use the Kruskal Wallis test when we have an independent group design and ordinal data.
We are given an independent group design and ordinate data.
We need to tell which test to use on them.
The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.
The null hypothesis for the Kruskal- Wallis test tells us that:
There are no methodical or harmonious differences among the treatments being compared.
Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.
Learn more about Kruskal Wallis test here:
https://brainly.com/question/28329564
#SPJ4
What is the product of –12 and –4?
Answer:
48
Step-by-step explanation:
-12 x -4 = 48 (When we multiply two negetive numbers, the product becomes positive )
Answer:
48
Step-by-step explanation:
i did the quiz
help me please, brainliested ;)
Answer:
Literally. can't help. you dude.
Please help me PLEASE..Thank you
Answer:
1)=-18x^5+60x^4-50x^3
2)k=3m/2-12
3)6x^2(x+2)(x-2)
Step-by-step explanation:
Hope dis helps :)
could i have brainliest
Nicola used 25% of the milk she collected from her goats this morning to make cheese. If she has 8.4 quarts of milk left over, how many quarts of milk did she collect this morning?
Answer:
11.2
Step-by-step explanation:
The answer is 11.2
11.2*.25=2.8
11.2-2.8=8.4
5/2
Irrational
Rational
Answer:
Rational
Step-by-step explanation:
What x value solves the equation?
3x – 5 = 1
x=
Answer:
x = 2
Step-by-step explanation:
3x – 5 = 1
+ 5 +5
3x = 6
x = 6 ÷ 3
x = 2
Answer:
2
Step-by-step explanation:
Step 1:
3x - 5 = 1 Equation
Step 2:
3x = 6 Add 5 on both sides
Step 3:
x = 6 ÷ 3 Divide
Answer:
x = 2
Hope This Helps :)
Is this correct??? Or no correlation
given a fair 6 sided die equal probability of 1,2,3,4,5,6. if you roll it 5 times. proab that sum is divisible by 6
The probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.
To find the probability that the sum of the rolls is divisible by 6, we need to determine the favorable outcomes and the total number of possible outcomes.
First, let's identify the favorable outcomes. In this case, the sum of the rolls can be divisible by 6 if the sum is either 6 or 12.
1. For the sum of 6:
- One possible outcome is rolling a 6 on the first roll and rolling a 1 on the remaining four rolls.
- Another possible outcome is rolling a 5 on the first roll and rolling a 2 on the remaining four rolls.
- We can also have rolling a 4 on the first roll and rolling a 3 on the remaining four rolls.
- Similarly, rolling a 3 on the first roll and rolling a 4 on the remaining four rolls.
- Finally, rolling a 2 on the first roll and rolling a 5 on the remaining four rolls.
- This gives us a total of 5 favorable outcomes.
2. For the sum of 12:
- One possible outcome is rolling a 6 on all five rolls.
- This gives us a total of 1 favorable outcome.
Now let's determine the total number of possible outcomes. Since we are rolling a fair 6-sided die 5 times, the total number of possible outcomes is 6^5 (since each roll has 6 possible outcomes).
Therefore, the probability that the sum of the rolls is divisible by 6 is:
(total number of favorable outcomes) / (total number of possible outcomes)
= (5 + 1) / (6^5)
= 6 / 7776
= 1 / 1296
So, the probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.
To know more about probability visit:
https://brainly.com/question/31828911
#SPJ11
NEED HELLPPP ASAP
(Thank you)
Answer:
ask your teacher it would be good for you and also teachers give u good thing about that okay but i can't help you sorry.
Step-by-step explanation:
One tub of dried cranberries costs $4. How many tubs can you buy for $12?
Answer:
3
Step-by-step explanation:
girl honestly how does this question even come up
anyways you do 12 divided by 4 to get 3
wich answer choice below best represents the quotient 1,610=35?
10 / 243.16 pls help me
Answer: hope it helps!!
0.0411251850633
Desmos graphing calculator is very helpful for these types of problems...
Answer:
Step-by-step explanation:
Expand \(\frac{10}{243.16}\)
by multiplying both numerator and the denominator by 100.
\(\frac{1000}{24316}\)
Reduce the fraction
\(\frac{1000}{24316}\)
to lowest terms by extracting and canceling out 4.
\(\frac{250}{6079}\)
a study by the national center for education statistics found that 1 out of 5 students reported being bullied
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
what us the circumference of circular ground of diameter d m ? find it.
answer:
\(\pi d \: m\)
can you explain me how?
Here the diameter = dm
Formula of circumference for circle: 2πr or πd
where "d" is diameter and "r" is radius
diameter = 2(radius)For this question:
circumference:
π(d)π(dm)πdmBetween 2015 and 2021. Faimont Chateau Lake Louise has reduced water consurnption by 20,000 m3. To ensure our water quality, surface water quality samples are collected from Lake Louise and Louise Creek on an annual basis, as part of an ongoing water chemistry monitoring program. Based on the materials of the course, water quality concems involve analyzing the presence of trace minerals and__
a. vitamins b. oxygen c. nutrients d. nitrates
Water quality concerns, as part of the water chemistry monitoring program, involve analyzing the presence of trace minerals and nutrients in surface water samples collected from Lake Louise and Louise Creek. Correct option is C.
To ensure water quality, it is crucial to assess the presence of various substances in the water samples. While trace minerals are essential to understand the composition of the water and detect any potential contaminants or harmful elements, nutrients also play a significant role.
Nutrients in water refer to substances such as nitrogen and phosphorus, which are essential for the growth and survival of aquatic organisms. However, excessive nutrient levels can lead to water quality issues such as eutrophication, harmful algal blooms, and oxygen depletion. Monitoring and analyzing nutrient levels in surface water samples help identify any imbalances and potential ecological impacts.
The ongoing water chemistry monitoring program at Faimont Chateau Lake Louise collects annual surface water samples from Lake Louise and Louise Creek to ensure the continued evaluation of trace minerals and nutrients. This proactive approach allows for the early detection of any deviations from desired water quality standards, enabling appropriate actions to maintain the ecological health of the water resources.
Learn more about water resources here:
https://brainly.com/question/28161871
#SPJ11
For what value(s) of x is the instantaneous rate of change in f(x) = 2x positive?
The value(s) of x for which the instantaneous rate of change in f(x) = 2x positive is all set of real values
How to determine the values of x?The equation of the function is given as
f(x) = 2x
The above function is a linear function
Next, we differentiate the function to determine the rate of change
So, we have
f'(x) = 2
When the instantaneous rate of change in f(x) = 2x positive, we have
f'(x) > 0
So, we have
2 > 0
The above is true
Hence, the value(s) of x for which the instantaneous rate of change in f(x) = 2x positive is all set of real values
Read more about rate of change at
https://brainly.com/question/8728504
#SPJ1
Which fraction is represented by the blue portion of the picture
Answer:
B. 5/8
Step-by-step explanation:
because there are 8 boxes and 5 colored
I will give you 30 points
1. Three examples of situations where consistency is important:
HealthcareFinancial transactionsSports RulesHow do these portray consistency?Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.
Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.
Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.
2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.
learn more about consistent: https://brainly.com/question/14633769
#SPJ1
What is the probability that either event will occur?
15
A
17
B
2
P(A or B) = P(A) + P(B)
P(A or B) = [?]
The probability that either event will occur is 0.83
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 12
Other Events = 6
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 12 + 6
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 12/36
For either events, we have
P(A or B) = 30/36 = 0.83
Hence, the probability that either event will occur is 0.83
Read more about probability at
brainly.com/question/251701
#SPJ1
Binita is going to buy 450 envolopes
Buying from Value World would cost Binita £0.72 less (in pounds) than buying from Letters2go.
To compare the costs of envelopes from both shops, we need to calculate the price per envelope.
At Letters2go, the price per envelope is:
3.29 pounds / 25 envelopes = 0.1316 pounds per envelope
At Value World, the price per envelope is:
(1.95 pounds * 2 packs) / (10 envelopes * 2 packs + 1 free pack) = 0.1300 pounds per envelope
So the price per envelope at Value World is slightly less than the price per envelope at Letters2go.
To buy 450 envelopes, Binita would need to purchase:
18 packs of 25 envelopes at Letters2go (18 x 25 = 450 envelopes)
45 packs of 10 envelopes at Value World (45 x 10 = 450 envelopes)
At Letters2go, the cost of 18 packs of 25 envelopes would be:
18 packs x £3.29 per pack = £59.22
At Value World, the cost of 45 packs of 10 envelopes (with 15 packs being free) would be:
30 packs x £1.95 per pack = £58.50
Therefore, buying from Value World would cost Binita £59.22 - £58.50 = £0.72 less than buying from Letters2go.
Correct Question :
Binita is going to buy 450 envelopes.
Here is some information about the cost of envelopes in two shops,
Letters2go : Pack of 25 envelopes for £3.29
Value World : Pack of 10 envelopes for £1.95, Buy 2 packs get 1 pack free
How much less, in pounds (£), will it cost Binita to buy the envelopes from Value World.
To learn more about pounds here:
https://brainly.com/question/29180665
#SPJ1
If A= arcsin(-4/5) in Quadrant IV and B=arctan(5/12) in Quadrant III, what is the values of tan(arcsin(-4/5)+arctan(5/12))? ASAP please...
Answer:
-33/56
Step-by-step explanation:
suppose: A,B are the 2 angles of a triangle
we have: A = arcsin\(\frac{-4}{5}\)
B = arctan \(\frac{5}{12}\)
=> sin A = \(\frac{-4}{5}\) => cos A = \(\sqrt{1-\frac{(-4)^{2} }{5^{2} } } =\frac{3}{5}\) (because A is in quadrant IV)
tan B = \(\frac{5}{12}\)
have:
\(1+ cot^{2}B=\frac{1}{sin^{2}B } => 1+\frac{1}{tan^{2} B}=\frac{1}{sin^{2}B } \\=> 1+\frac{1}{\frac{5^{2} }{12^{2} } } =\frac{1}{sin^{2}B }\\ => sin^{2}B=\frac{25}{169}\)
because B is in quadrant III => \(sin B=-\sqrt{\frac{25}{169} }=\frac{-5}{13}=>cosB=-\sqrt{1-\frac{5^{2} }{13^{2} } }=\frac{-12}{13}\)
tan(arcsin(-4/5)+arctan(5/12)) = tan( A + B)
but A,B are the 2 angles of a triangle => tan(A + B) = \(\frac{sin(A+B)}{cos(A+B)}\)
have: sin(A+B) = sinA.cosB + cosA.sinB = \(\frac{-4}{5}.\frac{-12}{13} +\frac{3}{5}.\frac{-5}{13}=\frac{33}{65}\)
cos(A + B) = cosA.cosB - sinA.sinB =\(\frac{3}{5}.\frac{-12}{13}-\frac{-4}{5}.\frac{-5}{13}=\frac{-56}{65}\)
=> tan(A + B) = \(\frac{33}{65}:\frac{-56}{65}=\frac{-33}{56}\)
Answer:
pie/6
Explaniation:
just took the test on k12