Answers
Answer:
The rope is worth 13.
The shoe is worth 5.
The clock is worth 3.
Step-by-step explanation:
We know that the weights are 8 so we will use 8 for the weights.
Let s = show
Let r = rope
Let c = clock
We have three unknowns so we need three equations.
8 + s = r c + s = 8 s= c +2
There are a number of ways that we can approach this. Let's substitute
c + 2 for s in the first 2 equations.
8 + s = r
8 + c + 2 = r
10 + c = r
c + s = 8
c + c + 2 = 8
2c + 2 = 8
2c = 6
c = 3 we found the value of the clock.
Now, let's substitute 3 in for 3 in the bold equation above.
10 + c = r
10 + 3 = r
13 = r we found the value of the rope.
We can use any of the equations to find the shoe.
s= c + 2
s = 3 + 2
s = 5
This is tricky. It takes a lot of practice. Don't give up!
Shoe= 5
Rope= 13
Clock= 3
We can start by giving each item a variable. Shoe= s, rope= r, clock= c. The weight is 8, so we don't need to give it a variable. Our equations are now:
8+s= r
c+s= 8
s= c+2
Now, we can isolate a variable to solve for it using the substitution method. Let's start with s.
c+s=8
-c -c
s= 8-c
Now, we'll take another equation and plug s in.
8-c=c+2
+c +c
8= 2c+2
-2 -2
6=2c
c=3
Now we know that the clock is 3. Put 3 into the last equation, and add 3+2 to get 5 for the shoe. 5 in the first equation for the shoe plus 8 as the weight means the rope is 13.
hope this helped!
Related Questions
If y° and 48° are a pair of complementary angles then find y°
Answers
Answer:
y = 42 and/or x = 36
Step-by-step explanation:
y + 48 = 90
y = 42 (subtracted 48 from 90)
3x + 2x = 180 (angles are linear pairs)
5x = 180 (combine like terms)
x = 36 (divided by 5 on both sides)
I didn't know which question you needed help with, I hope this makes sense :)
❄ Hi there,
the sum of complementary angles is always 90°.
If we know one of these angles, we can set up an equation –
[tex]\triangleright\sf{y+48=90}[/tex]
and then solve for y...
[tex]\triangleright \ \sf{y=42}[/tex]
That's it!
❄
The list 76, 56, 93, 24, 45, 88, 13, 7, 37 is sorted using bucket sort with 4 buckets. which bucket will contain 45?
Answers
The bucket number 2 will contain 45 after sorting the data.
According to the statement
we have given that the a data list which is sorted into 4 buckets then we have to find he in which the umber 45 is sorted.
So, For this purpose,
The given data list is:
76, 56, 93, 24, 45, 88, 13, 7, 37
And the data is sorted into the buckets so,it is sorted in 4 buckets. and the data contain numbers from 0 to 100.
So, let the sorting.
We know that the 100 numbers are sorted in 4 buckets then it means each bucket contain 25 numbers.
So, let us consider a
BUCKET 1 : 0 to 25
it contains the data number 7, 13,24.
Now,
BUCKET 2 : 25 to 50
it contains the data number 37,45.
Now,
BUCKET 3 : 50 to 75
it contains the data number 56.
Now,
BUCKET 4 : 75 to 100
it contains the data number 76, 88, 93.
From sorting the 45 number sort in the bucket 2.
So,The bucket number 2 will contain 45 after sorting the data.
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Number
8.6134
5.5218
...to the nearest tenth ...to the nearest hundredth
..to the nearest thousandth
Concepts and Applicati
Answers
The following numbers are rounded up as follows:
8.6134
nearest tenth = 8.6nearest hundredth = 8.61nearest thousandth = 8.6135.5218
nearest tenth = 5.5nearest hundredth = 5.52nearest thousandth = 5.522How to round up?Rounding up a number means to round a number to the smallest integer that is not less than it, or to some other greater value.
Thousandth, hundredth and tenth are used after the decimal point.
nearest tenth means one number after the decimal pointnearest hundredth means two numbers after the decimal pointnearest thousandth means three numbers after the decimal point8.6134
nearest tenth = 8.6nearest hundredth = 8.61nearest thousandth = 8.6135.5218
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What is the average rate of change of f over the interval -4≤x≤5
Answers
The average rate of change over the interval is 2/9
How to determine the average rate of change?The interval is given as:
-4 ≤ x ≤ 5
From the table, we have:
f(5) = 4
f(-4) = 2
The average rate of change is then calculated as:
[tex]m = \frac{f(5) - f(-4)}{5 --4}[/tex]
This gives
[tex]m = \frac{4 - 2}{5 +4}[/tex]
Evaluate
[tex]m = \frac{2}{9}[/tex]
Hence, the average rate of change over the interval is 2/9
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If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0. 5, what is the probability that out of 8 newly hired people?
Answers
The probability that out of 8 newly hired people is 3.2.
According to the statement
we have given that the some conditions and based on these conditions we have to find the probability that out of 8 newly hired people.
So, For this purpose,
we have given that the
new employee in a fast-food chain still being with the company at the end of the year is 0.5
Now, we See that is probability of remaining with the company.
There is only one is 0.5.
According to the probability law
P + Q = 1
and this become
Q = 1 - 0.60.
And the probability of one people hired is Q.
Then
Q = 0.4
And probability that out of 8 newly hired people is
8Q = 0.4 * 8
it become 3.2.
So, The probability that out of 8 newly hired people is 3.2.
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Use the laplace transform to solve the given initial-value problem. y' − 2y = (t − 4), y(0) = 0
Answers
Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' − 2y = (t − 4),
y(0) = 0
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (0+ e^-s)/s + 1
⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}
⇒y(t) = 0 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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Find the missing length indicated.
Answers
The value of the missing length in the image shown using the Pythagoras theorem is x = 65
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.
Let h represent the missing red line. Using Pythagoras:
x² = h² + 25²
h² = x² - 25²
Also:
r² = h² + 144²
r² = x² - 25² + 144²
And:
(144 + 25)² = r² + x²
(144 + 25)² = (x² - 25² + 144²) + x²
x = 65
The value of the missing length in the image shown using the Pythagoras theorem is x = 65
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In step 2, the
property of equality was applied.
In step 4, the
property of equality was applied.
Answers
In step 2, the property of equality applied was addition property of equality.
In step 4, the property of equality applied was multiplication property of equality.
What is the Addition Property of Equality?The addition property of equality states that, to move a negative number over to the other side of an equation, add the number to both sides of the equation. For example, given the equation: a - c = b, to move c over to the other side of the equation, add c to both sides of the equation. we will have:
a - c + c = b + c
a = b + c.
What is the Multiplication Property of Equality?According to the multiplication property of equality, if we have, a/c = b, to isolate a, we would multiply both sides of the equation by c. Thus:
a/c × c = b × c
a = bc
In the table given, in step 2, 6 was added to both sides of the equation. This means the property of equality that was applied was: addition property of equality.
In step 4, both sides of the equation was multiplied by -2. Thus, the property of equality that was applied was: multiplication property of equality.
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Answer: step 2 - addition property
step 4 - multiplication property
Step-by-step explanation:
WILL GIVE BRAINLEST!!!
Kerry wants to know whether or not people will be voting in the upcoming presidential election. She posts signs giving the website for her survey. Which sampling method is described?
A. Unbiased Systematic Random Sample
B. Biased Convenience Sample
C. Unbiased Simple Random Sample
D. Biased Voluntary Response Sample
Answers
The purpose of statistical inference is to make estimates or draw conclusions about a.
Answers
The purpose of statistical inference population based upon information obtained from the sample.
What is statistical inference?statistical inference uses sample data to make estimates of or draw conclusions about one or more characteristics of a population.
The purpose of statistical inference is to estimate this sample to sample variation or uncertainty. Understanding how much our results may differ if we did the study again, or how uncertain our findings are, allows us to take this uncertainty into account when drawing conclusions. It allows us to provide a plausible range of values for the true value of something in the population, such as the mean, or size of an effect, and it allows us to make statements about whether our study provides evidence to reject a hypothesis.
We have four ideas for using the statistical inference.
1. Estimating uncertainty.
2. Confidence intervals.
3. Hypothesis tests.
4. Connections with other material.
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The given question is not complete.
The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.
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Id like some help!!!
Answers
Answer:
50.24 ft^2.
Step-by-step explanation:
Area = pi r^2
Here the radius r = 4
Therefore the area of the circle
= pi * 4^2
= 16 pi
= 16 *3.14
= 50.24 ft^2.
Simplify.
√75
OA. 3√5
OB. 15√5
OC. 25√3
OD. 5√3
Answers
Answer:
Option D
Step-by-step explanation:
Using the surd law :
[tex]\sqrt{ab} = \sqrt{a}\sqrt{b}[/tex]
We can find the largest square number that goes into 75 :
Let's write the multiples of 75 :
1 , 75
3 , 25
5 , 15
The only square number is 25
So using the law mentioned above we split √75 into :
√25√3
The square root of 25 is 5
Now we have our final answer of 5√3
Hope this helped and have a good day
The simplified form of expression √75 is 5√3.
Option D is the correct answer.
We have,
To simplify √75, we can factor it into its prime factors and then take the square root:
√75 = √(3 * 5 * 5)
= √(3 x 5²)
Take out the perfect square factor from under the square root:
= √3 x √5²
= √3 x 5
= 5√3
Thus,
The simplified form of expression √75 is 5√3 which is option D.
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A computer store decides to increase the prices of all the items it sells by 15%. the store manager uses matrices to prepare the new price list. matrix a contains the unit price of each product in each category. matrix b contains the revised price of each item in each category. how can the manager obtain the entries for matrix b? a. by adding 15 to each entry of matrix a b. by multiplying each entry of matrix a by 15 c. by multiplying each entry of matrix a by 1.15 d. by multiplying each entry of matrix a by 0.15
Answers
The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The manager could achieve scalar multiplication on Matrix A, utilizing the scalar 1.15.
What is the matrix?The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix. Matrices contain wide applications in engineering, physics, economics, and statistics as well as in different branches of mathematics.
Increasing the price by 15% would mean we exist taking 100% of the value + another 15%
100 + 15 = 115%
115% = 115/100 = 1.15.
Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.
Therefore, the correct answer is option c. by multiplying each entry of matrix a by 1.15.
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Answer:
C - by multiplying each entry by 1.15
Step-by-step explanation:
Edmentum.
HELP ASAP!!!! PLEASEEE!!!
Answers
Answer:
2
-2
Step-by-step explanation:
Use the second equation for x = -4.
f(-4) = 2
Use the third equation for x = 3.
f(x) = -x + 1 = -3 + 1 = -2
A retailer allowed 4% discount on his goods to make 20% profit and sold a refrigerator for Rs 10,848 with 13% VAT. By how much is the discount to be increased so that he can gain only 15%?
Answers
The discount to be increased so that he can gain only 15% is 8%.
What is a discount? Discounts are given when a reduction in the price is permitted to promote more purchases or timely payments. Discounts are divided into Trade reduction: The discount granted when substantial purchases are made is referred to as a trade discount.Discounts are given when a reduction in the price is permitted to promote more purchases or timely payments. Discounts are divided into Trade reduction: The discount granted when substantial purchases are made is referred to as a trade discount.Since sales discounts lower the cost of a product, they are not considered costs. These monetary discounts provided to consumers do, however, have an impact on a company's financial statements. Thus they must be reported as a decrease in revenue under the accounts receivable line item.How much is the discount to be increased so that he can gain only 15%:
The cost price of the goods - y.
The selling price of the goods - x.
The selling price is
1.2y (100% + 20% = 120%).
The refrigerator was sold at 13% VAT at Rs. 10848:
=> 1.2y + 13%(1.2y) = 10848
=> 1.2y + 0.156y = 10848
=> 1.356y = 10848
=> y = 8000
Thus, the cp is Rs 8000.
The selling price is:
=> 0.96x = 1.2y
=> 0.96x = 1.2(8000)
=> x = 10000
The selling price is Rs. 10000
For a profit of 15%, that is 1.15(8000) = 9200, the discount is:
(1 - discount)10000 = 9200
1 - discount = 0.92
Discount = 1 - 0.92 = 0.08 or 8%
How much is the discount to be increased so that he can gain only 15%: Discount=8%
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Give the equation for a circle with the given center and radius. center at (-1, 3), radius = 4
Answers
Answer:
(x + 1)² + (y - 3)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 3 ) and r = 4 , then
(x - (- 1) )² + (y - 3)² = 4² , that is
(x + 1)² + (y - 3)² = 16
Answer:
(x+1)^2 + (y-3)^2 = 16
Step-by-step explanation:
The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2 = (x+1)^2 + (y-3)^2 = 16.
1. If R = 32 - 11 (OC+2y). then find R when: x=2 and y=4
Answers
The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.
How to solve for the equation belowWe have this
R = 32 - 11 (X+2y)
we have the following values for x and y as 2 and 4 respectively.
What we have to do would be to find the value of R after we have put in these values in the equation.
To do this, we would then have:
R = 32 - 11(2 + 2*4)
R = 32 -11(2+8)
R = 32 - 11 * 10
R = 32 - 110
This would give us the value that says
R = -78
Hence the value of R is given as -78
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Annabella wants to make the most economical decision so she chose the 3-year car loan so that after the loan is paid off to be able to invest in a structured saving account if Anabella put $200 into a saving account each month with an annual interest rate of 3.2% interest compounded monthly how much money would she have in her account after 2 years
Answers
Answer:
Annabella will save $4950.11 after 2 years.
Step-by-step explanation:
GivenPeriodic payment P = $200,Period t = 2 years,Number of compounds, monthly n = 12,Interest rate, r = 3.2% = 0.032.To findFuture value of saving, FSolutionUse periodic compound formula:
[tex]F=P\cfrac{(1+r/n)^{nt}-1}{r/n}[/tex]
Substitute the values and calculate:
[tex]F=200\cfrac{(1+0.032/12)^{12*2}-1}{0.032/12} =4950.12[/tex] rounded
Step-by-step explanation:
Given P = $200, t = 2 years, n = 12,[tex] \sf \: r = 3.2\% = \frac{3.2}{100} = 0.032[/tex]To findFuture value of savingSolutionUse periodic compound formula:
[tex] \sf \: F=P\cfrac{(1+ \frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]
Substitute the values and calculate:
[tex]\sf \: F=200\cfrac{(1+ \frac{0.032}{12})^{12 \times 2}-1}{\frac{0.032}{12}}[/tex]
[tex]\sf \: F=200\cfrac{( \frac{ 12 + 0.032}{12})^{24}-1}{\frac{0.032}{12}}[/tex]
[tex]\sf \: F=200\cfrac{( {11.002 }{})^{24}-1}{0.002} [/tex]
[tex]\sf \: F=200 \times 24.7506[/tex]
[tex]\sf \: F=4950.12rounded[/tex]
Identify tanX as a fraction and as a decimal rounded to the nearest hundredth.
The figure shows right triangle X Y Z with right angle Y. The length of leg Z Y is equal to 7 point 2 units. The length of leg Y X is equal to 6 point 4 units. The length of hypotenuse X Z is equal to 9 point 6 units.
Answers
The value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13
How to determine the tangent trigonometry ratio?The complete question is added as an attachment
From the question, the given parameters are as follows:
Hypotenuse = XZ
Hypotenuse XZ = 9.6
Leg ZY = 7.2
Leg YX = 6.4
The tangent of X is then calculated as:
tan(X) = ZY/YX
Substitute the known values in the above equation
tan(X) = 7.2/6.4
Evaluate the above quotient
tan(X) = 1.125
Approximate the above result
tan(X) = 1.13
Hence, the value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13
So, the complete parameters are:
Hypotenuse = XZ
Hypotenuse XZ = 9.6
Leg ZY = 7.2
Leg YX = 6.4
tan(X) = 7.2/6.4
tan(X) = 1.13
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Which statement describes independent events?
A. You write the numbers 1 through 10 on
index cards. You randomly draw two
cards without replacement: a 6 and an 8.
C. You randomly draw a blue marble from a
bag, return the marble, and then
randomly draw a yellow marble.
B. A President and Vice President are
randomly selected from a group of 24
students.
D. You randomly draw four cards from a
standard deck of cards without
replacement. You draw a King, then a
Queen, then a Jack, and then an Ace.
Answers
The statement that describes independent events is:
C. You randomly draw a blue marble from a bag, return the marble, and then randomly draw a yellow marble.
How to determine the statement describes independent eventsIn this case, the events of drawing a blue marble and drawing a yellow marble are independent because the first draw does not affect the probability or outcome of the second draw.
Returning the marble to the bag ensures that each draw is independent of the previous one.
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Write the first five terms of the sequence with the given nth term. an = cos n 2
Answers
The first five terms of the sequence with the given n-th term [tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
For given question,
We have been given the n-th term of the sequence [tex]a_n = cos(\frac{n\pi}{2} )[/tex]
We need to find the first five terms of the sequence.
For n = 1
[tex]\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0[/tex]
For n = 2,
[tex]\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1[/tex]
For n = 3,
[tex]\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0[/tex]
For n = 4,
[tex]\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1[/tex]
For n = 5,
[tex]\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0[/tex]
Therefore, the first five terms of the sequence with the given n-th term[tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
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Use the drawing tools to form the correct answer on the graph.
Given the table of values, plot the corresponding points for the inverse of the function.
X
-1
0
1
2
f(x)
1
2
3
4
Answers
The inverse maps (x,y) onto (y,x).
Are the two triangles similar?
Answers
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
What are the values of sin a and tan a, if a is an acute angle in a right triangle:
cosa=15/17
Answers
Given that a is an acute angle in a right triangle, cos a = [tex]\frac{15}{17}[/tex]. The trigonometric ratio sin a = [tex]\frac{8}{17}[/tex] and tan a = [tex]\frac{8}{15}[/tex].
The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.
In any question,
cos a = [tex]\frac{base}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]
hypotenuse = side opposite of the right angle = 17
base = side adjacent to the acute angled marked = 15
[tex]hypotenuse^{2} = perpendicular ^2+base^2\\\\perpendicular = \sqrt{hypotenuse^2-base^2}[/tex]
perpendicular = [tex]\sqrt{17^2- 15^2} = 8[/tex]
sin a = [tex]\frac{perpendicular}{hypotenuse} = \frac{8}{17}[/tex]
tan a = [tex]\frac{perpendicular}{base} = \frac{8}{15}[/tex]
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need some help with this
Answers
Answer:XDDXXDXD
DXDXXDXDDXDXDXDXXDDXDEDXXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-XDDXDXDXstep explanation:
seria tu cacá XDXDXDXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Find the area of this triangle. Round to the nearest tenth.
Answers
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
What is the area of the triangle?
Given the data in the diagram;
Angle B = 133°Side a = 7Side c = 13Side b = ?Angle C = ?First we find the dimension of side b.
From the rule of cosines.
b = √[ a² + c² - 2acCosB ]
We substitute into the formula.
b = √[ 7² + 13² - ( 2 × 7 × 13 × cos( 133° ) ]
b = √[ 49 + 169 - ( 182 × cos( 133° ) ) ]
b = √[ 218 - 182×cos( 133° ) ]
b = √[ 342.1237 ]
b = 18.5
Next, we find angle C.
From rule of cosines.
cosC = [ b² + a² - c² ] / 2ba
cosC = [ 18.5² + 7² - 13² ] / [ 2 × 18.5 × 7 ]
cosC = [ 342.25 + 49 - 169 ] / [ 259 ]
cosC = [ 222.25 ] / [ 259 ]
cosC = [ 0.8581 ]
C = cos⁻¹[ 0.8581 ]
C = 30.9°
Now, we can find the area of the triangle.
Area = [ ab × sinC ] / 2
Area = [ 7 × 18.5 × sin( 30.9 ) ] / 2
Area = [ 129.5 × 0.51354 ] / 2
Area = 66.5 / 2
Area = 33.3 in²
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
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During the season, the Rangers played 25 games. They won 14 of the games.
What fraction and percent of the games did they lose? Show your work in the
space below. Remember to check your solution.
Answers
Answer:
See below
Step-by-step explanation:
Out of 25 games, they won 14
Fraction won = won / total = 14 / 25
Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %
To find the number of games lost
25-14 = 11
Fraction won = won / total = 11 / 25
Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %
To check your work, the percent total should be 100
56+44 = 100
Quadrilateral ABCD has vertices at A(0,0), B(0,3), C(5,3), and D(5,0). Find the vertices of the quadrilateral after a dilation with scale factor 2.5.
PLS ANSWER ASAP
Answers
The vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)
How to determine the vertices of the quadrilateral after a dilation with scale factor 2.5?The coordinates of the quadrilateral ABCD are given as:
A(0,0), B(0,3), C(5,3), and D(5,0)
When dilated by a scale factor of 2.5, we have the following equation
A' = A * 2.5
So, we have:
A' = (0,0) * 2.5
A' = (0, 0)
B' = (0,3) * 2.5
B' = (0, 7.5)
C' = (5,3) * 2.5
C' = (12.5, 7.5)
D' = (5,0) * 2.5
D' = (12.5, 0)
Hence, the vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)
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pls help me solve these
Answers
The conversion of 9.204 to a mixed number will be 9 51/250.
How to illustrate the information?It should be noted that converting decimal to mixed numbers simply means changing them to whole numbers and fractions.
Therefore, 9.204 will be:
= 9 204/1000
= 9 51/250
The percentage equivalent of 3 7/8 will be:
= (3 × 100) + (7/8 × 100)
= 300 + 87.5
= 387.5%
Dividing 72 in the ratio 2:3:4 will be:
= 2/9 × 72 = 16
= 3/9 × 72 = 24
= 4/9 × 72 = 32
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Solve the given differential equation by undetermined coefficients. y'' − y' − 12y = e4x
Answers
The general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]
For given question,
We have been given a differential equation y'' − y' − 12y = e^(4x)
We need to solve the given differential equation by undetermined coefficients.
We can write given differential equation as [tex](D^2-D-12)y=e^{4x}[/tex] where [tex]D=\frac{d}{dx}[/tex]
First solve the corresponding homogeneous differential equation:
y'' - y' - 12y = 0
The characteristic equation is:
m² - m - 12 =0
Let's find the roots of above quadratic equation by factorization.
⇒ m² - m - 12 = 0
⇒ (m - 4)(m + 3) = 0
⇒ m - 4 = 0 OR m + 3 = 0
⇒ m = 4 OR m = -3
Hence the complementary solution is,
[tex]y_c=C_1e^{4x}+C_2e^{-3x}[/tex]
Let the general solution of a second order homogeneous differential equation be [tex]y(x)=C_1(x)e^{4x}+C_2(x)e^{-3x}[/tex]
The unknown functions C1(x) and C2(x) can be determined from the system of two equations:
[tex]C'_1e^{4x}+C'_2e^{-3x}=0~~~~~~~............(1)\\\\C'_1(4e^{4x})+C'_2(-3e^{-3x})=e^{4x}~~~~~~~...................(2)[/tex]
from (1),
[tex]C'_2e^{-3x}=-C'_1e^{4x}[/tex]
Substitute this value in equation (2)
[tex]4C'_1e^{4x}+3C'_1e^{4x}=e^{4x}[/tex]
[tex]\Rightarrow C'_1=\frac{1}{7}[/tex] and [tex]C'_2=-\frac{1}{7}e^{7x}[/tex]
[tex]\Rightarrow C_1=\frac{1}{7} x+c_3[/tex] and [tex]C_2=\frac{1}{49}e^{7x}+c_2[/tex]
Therefore, the general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]
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