Answer:
D) 12%
Step-by-step explanation:
The merchant marks his wares 40% more than the real price.
The merchant also allows 20% discount.
Let the real price = 100
After a 40% mark up, the price becomes
(40 /100) * 100
= 40
So we have 100 +40= 140
Discount of 20% = (20/100)* 140
= 28
The price is 140 - 28 = 112
Profit = 112 -100
= 12%
Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to collect. How much money does Rachel plan to collect for the shelter? Show your work.
Answer:
The money Rachael plan to collect for the shelter is $350.
Step-by-step explanation:
Given:
Rachel is collecting donations for the local animal shelter.
So far she has collected $245, which is 70% of what she hopes to collect.
Now, to find the money Rachael plan to collect for the shelter.
Let the total amount Rachael plan to collect be [tex]x[/tex].
Amount she collected = $245.
Percentage of amount she collected = 70%.
Now, to get the amount Rachael plan to collect we put an equation:
[tex]70\%\ of\ x=\$245.[/tex]
⇒ [tex]\frac{70}{100} \times x=245[/tex]
⇒ [tex]0.70\times x=245[/tex]
⇒ [tex]0.70x=245[/tex]
Dividing both sides by 0.70 we get:
⇒ [tex]x=\$350.[/tex]
Therefore, the money Rachael plan to collect for the shelter is $350.
What is the perimeter of a regular pentagon with a
side whose length is x +4?
1 x2 +16
2 4x + 16
3 5x + 4
4 5x + 20
Answer:the perimeter of the regular pentagon is 5x + 20
Step-by-step explanation:
The perimeter of a plane figure is the distance around the plane figure. The pentagon is a plane figure. It has 5 sides. Since it is a regular Pentagon, it means that all the sides are equal.
From the information given, the length of each side of the regular Pentagon is x + 4
The perimeter of the regular Pentagon would be 5 times the length of each side. It becomes
5(x + 4) = 5x + 20
The value of 528 would change by how much if 6 replaced 2
Answer: The value of 528 would change by 40 if 6 replaced 2
Step-by-step explanation:
The given number is 528. If we replace 2 by 6, the new number becomes 568. This is greater than the previous number. The difference between the new number and the previous number would be
568 - 528 = 40
Write an algebraic expression for the verbal expression, "17 less than k and 12"
Answer:
k-5
Step-by-step explanation:
"k and 12" : (k + 12)
"17 less than k and 12" : (k + 12) - 17
simplifying:
(k + 12) - 17
= k + 12 - 17
= k-5
In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?A. 0.9B. 0.7C. 0.45D. 0.3E. 0.25
Answer:
Option B is right
Step-by-step explanation:
Given that in the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.
Males Females
48% 52%
25 or more
age 40% 20%
One student in the class is randomly selected,
to find the probability that he or she will be less than 25 years old
= Prob (male and less than 25 years old)+Prob (female and less than 25 years old)
(since mutually exclusive and exhaustive)
= [tex]0.48(1-0.4) + 0.52(1-0.20)\\= 0.288+ 0.416\\= 0.704\\[/tex]
After rounding off to 1 one decimal
we get 0.7
Option B is right
Nicole's job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. On Monday, she earned a total of $63.75. What were her total sales?
Answer:her total sales is 25
Step-by-step explanation:
Let x represent her total sales.
Nicole's job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. This means that the amount that she receives for x total sales would be
60 + 15/100× x
= 60 + 0.15x
On Monday, she earned a total of $63.75. This means that
63.75 = 60 + 0.15x
63.75 - 60 = 0.15x
0.15x = 3.75
x = 3.75/0.15 = 25
PLEASE HELP ME
Using homeowners insurance of $1012 per year, property taxes 1.1% per year, and the annual 1% of the home's purchase price for maintenance, what is the true cost of a $96,000 home with a 30 year mortgage payment of $545.08 per month?
A. $301,012.43
B. $225,907.80
C. $287,068.80
D. $299,007.45
When considering mortgage payments, homeowners insurance, property tax and maintenance costs over 30 years, the true cost of the $96,000 home is $287,068.80.
Explanation:The true cost of a home not only includes the original purchase price but also takes into account annual homeowners insurance, property taxes, and maintenance costs. In this case, the purchase price is $96,000, homeowners insurance costs $1012 per year, property taxes are 1.1% of the home price each year, and annual home maintenance is 1% of the home price.
First, calculate the total mortgage payments made over 30 years. The monthly payment is $545.08, so the total mortgage payments are:
30 years * 12 months/year * $545.08/month = $196,228.80
Next, calculate the total cost of homeowners insurance over 30 years:
30 years * $1012/year = $30,360
Then, calculate the total property taxes over 30 years:
30 years * 1.1% of $96,000/year = $31,680
Lastly, calculate the total home maintenance over 30 years:
30 years * 1% of $96,000/year = $28,800
Adding all of these costs together gives the total cost of the home:
$196,228.80 + $30,360 + $31,680 + $28,800 = $287,068.80
So, the correct answer is option C: $287,068.80.
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Patrician saves $ 1.20 everyday while her sister Nicole saves $ 2.80 daily. The two girls saved $ 150.00 together. How much of this amount was saved by Nicole?
Amount saved by Nicole is $ 105
Solution:
Given that Patrician saves $ 1.20 everyday and Nicole saves $ 2.80 daily
The two girls saved $ 150.00 together
To find: Amount saved by Nicole
Let "x" be the number of days for which Patrician and Nicole saved money
Given that they both saved $ 150.00 together
So we can frame a equation as:
[tex]\text{(amount saved by patrician + amount saved by nicole) } \times x = 150.00[/tex]
[tex](1.20 + 2.80) \times x = 150\\\\4x = 150\\\\x = 37.5[/tex]
Therefore amount saved by nicole:
Nicole has saved $ 2.80 daily for "x" days
[tex]\text{ Amount saved by Nicole } = x \times 2.80\\\\\text{ Amount saved by Nicole } = 37.5 \times 2.80 = 105[/tex]
Thus amount saved by Nicole is $ 105
If A, B, and C are integers between 1 and 10 (inclusive), how many different combinations of A, B, and C exist such that A
[tex]\fontsize{18}{10}{\textup{\textbf{The number of different combinations is 120.}}}[/tex]
Step-by-step explanation:
A, B and C are integers between 1 and 10 such that A<B<C.
The value of A can be minimum 1 and maximum 8.
If A = 1, B = 2, then C can be one of 3, 4, 5, 6, 7, 8, 9, 10 (8 options).
If A = 1, B = 3, then C has 7 options (4, 5, 6, 7, 8, 9, 10).
If A = 1, B = 4, then C has 6 options (5, 6, 7, 8, 9, 10).
If A = 1, B = 5, then C has 5 options (6, 7, 8, 10).
If A = 1, B = 6, then C has 4 options (7, 8, 9, 10).
If A = 1, B = 7, then C has 3 options (8, 9, 10).
If A = 1, B = 8, then C has 2 options (9, 10).
If A = 1, B = 9, then C has 1 option (10).
So, if A = 1, then the number of combinations is
[tex]n_1=1+2+3+4+5+6+7+8=\dfrac{8(8+1)}{2}=36.[/tex]
Similarly, if A = 2, then the number of combinations is
[tex]n_2=1+2+3+4+5+6+7=\dfrac{7(7+1)}{2}=28.[/tex]
If A = 3, then the number of combinations is
[tex]n_3=1+2+3+4+5+6=\dfrac{6(6+1)}{2}=21.[/tex]
If A = 4, then the number of combinations is
[tex]n_4=1+2+3+4+5=\dfrac{5(5+1)}{2}=15.[/tex]
If A = 5, then the number of combinations is
[tex]n_5=1+2+3+4=\dfrac{4(4+1)}{2}=10.[/tex]
If A = 6, then the number of combinations is
[tex]n_6=1+2+3=\dfrac{3(3+1)}{2}=6.[/tex]
If A = 7, then the number of combinations is
[tex]n_7=1+2=\dfrac{2(2+1)}{2}=3.[/tex]
If A = 3, then the number of combinations is
[tex]n_8=1.[/tex]
Therefore, the total number of combinations is
[tex]n\\\\=n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8\\\\=36+28+21+15+10+6+3+1\\\\=120.[/tex]
Thus, the required number of different combinations is 120.
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Question : ow many types of zygotic combinations are possible between a cross AaBBCcDd × AAbbCcDD?
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What is 0.12¯¯¯¯ expressed as a fraction in simplest form? Enter your answer in the box. $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$$x\frac{ }{ }$$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Answer:
4/33
Step-by-step explanation:
x=0.121212...
100x=12.1212...
100 x-x=12
99 x=12
x=12/99=4/33
Given a decimal number 0.12, we have that its expression as a fraction in its simplest form is mathematically given as x=4/33
What is a Fraction?A fraction is simply a numerical quantity or use of integers in a form that is not in a whole number form.
Question Parameter(s):
X=0.121212...
Generally, the equation for the statement is mathematically given as
x=0.121212
Therefore
100x=12.1212...
100 x-x=12
99 x=12
x=12/99
x=4/33
In conclusion, X=0.121212 as a fraction is x=4/33.
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x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Answer:
y + b > 15
Step-by-step explanation:
given data
positive integers = x, y, a, b
x divided by y then remainder = 6
a divided by b then remainder = 9
to find out
possible value for y + b
solution
we know that here when x divided by y then remainder is 6
its mean y is greater than 6 and when a divided by b then remainder is 9
so its mean b is greater than 9
and we know remainder is less than divisor
so here y + b must be greater than = 6 + 9
y + b > 15
please help! thanks!
Answer:
D
Step-by-step explanation:
Remember how absolute values turn everything inside of it into a positive number? Like |-4|=4 and |4|=4 as well.
Well, it works the same for equations.
When you have an absolute value equation like this, you have to split it into two parts.
The positive version
| d-3.5 | ≤ 1.5
and the negative version
|-(d-3.5)| ≤ 1.5
solve for the value of d in both equation.
Remember that you have to flip the inequality sign when dividing or multiplying by a negative number
I assume you know how to graph the inequality once you get the value for d.
d≤5 and d≥2
so
2 ≤ d ≤ 5
meaning d is between 2 and 5.
A ribbon 56 cm long is cut into two pieces. One of the pieces is three times longer than the other. Find the length, in centimeters, of both pieces of ribbons
Answer:one piece is 42 centimeters and the other piece is 14 centimeters
Step-by-step explanation:
Let x represent the length, in centimeters, of one piece of the ribbon.
Let y represent the length, in centimeters, of the other piece of the ribbon.
The ribbon, 56 cm long is cut into two pieces. This means that
x + y = 56 - - - - -- - - - -1
One of the pieces is three times longer than the other. This means that
x = 3y
Substituting x = 3y into equation 1, it becomes
3y + y = 56
4y = 56
y = 56/4 = 14 centimeters
x = 3y = 2×14 = 42 centimeters
A container is 1/10 full of grain. If 21 additional gallons of grain are added, the container is 4/5 full. What is the volume of the container, in gallons?
Answer:
30 gallons
Step-by-step explanation:
let x represent the full container, then
[tex]\frac{1}{10}[/tex] x + 21 = [tex]\frac{4}{5}[/tex] x
Multiply through by 10 to clear the fractions
x + 210 = 8x ( subtract x from both sides )
210 = 7x ( divide both sides by 7 )
30 = x
The volume of the container is 30 gallons
Answer: the volume of the container is 30 gallons
Step-by-step explanation:
Let V represent the volume of the container, in gallons.
The initial volume of grains in the container is 1/0 × V = V/10
If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore
4/5 × V = 21 + V/10
4V/5 = 21 + V/10
4V/5 - V/10 = 21
7V/10 = 21
Multiplying the left hand side and right hand side of the equation by 10, it becomes
7V/10 × 5 = 21 × 10 = 210
7V = 210
V = 210/7 = 30
Which two types of decisions should remain centralized even in a decentralized decision-making environment?
Answer: Infrequent decisions and long lasting decisions
Step-by-step explanation:
Infrequent: decisions made infrequently, they are not urgent, and deeper consideration is appropriate (ex., product strategy, international expansion).
Long-lasting: Once made, these decisions are unlikely to change not immediately but at least in the short term (e.g., commitment to a standard technology platform, commitment to organizational realignment around Value Streams)
Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard deviation of 18 minutes. What is the probability that a tune-up will take more than 2hrs? Under 66 minutes?
Answer:
Step-by-step explanation:
Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = points scored by students
u = mean time
s = standard deviation
From the information given,
u = 102 minutes
s = 18 minutes
1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as
P(x > 120 minutes) = 1 - P(x ≤ 120)
For x = 120
z = (120 - 102)/18 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.8413
P(x > 120) = 1 - 0.8413 = 0.1587
2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as
P(x < 66 minutes)
For x = 66
z = (66 - 102)/18 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.02275
P(x < 66 minutes) = 0.02275
An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hour over 35. One week's paycheck (before deduction) was for $308.00. How many hours did the employee work
Answer: the employee worked for 41 hours
Step-by-step explanation:
Let x represent the total number of hours that the employee worked. An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hour over 35. Let y represent the amount earned for x hours. Therefore
y = 7×35 + 10.5(x - 35)
y = 245 + 10.5x - 367.5
One week's paycheck (before deduction) was for $308.00. This means that y = $308.00. Therefore,
308 =245 + 10.5x - 367.5
308 = 10.5x - 122.5
10.5x = 308 + 122.5 = 430.5
x = 430.5/10.5
x = 41
If you draw 2 cards from a shuffled 52 card deck, what is the probability that you'll have a pair?
Answer:
78/2,652, or 0.0294, or 2.94%.
Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
a) 1/3x
b) 3x/x-3
c) x-3/3x
d) x/x-3
e) x-3/x
Answer:
[tex]\frac{x-3}{3x}[/tex]
Step-by-step explanation:
Lindsay can paint 1/x of a certain room in 20 minutes.
1 hour = 3 times 20 minutes
rate of work by Lindsay in 20 minutes is [tex]\frac{3}{x}[/tex]
Let 't' be the work done by Joseph
rate of work by Joseph in 20 minutes is [tex]\frac{3}{t}[/tex]
Both completed the work in 1 hour
[tex]\frac{3}{x} +\frac{3}{t} =1[/tex]
solve the equation for 't'
Subtract 3/x on both sides
[tex]\frac{3}{t} =1-\frac{3}{x}[/tex]
[tex]\frac{3}{t} =\frac{x-3}{x}[/tex]
cross multiply it
[tex]3x=t(x-3)[/tex]
Divide both sides by x-3
[tex]\frac{3x}{x-3} =t[/tex]
Work done together is
[tex]\frac{x-3}{3x}[/tex]
Chrissie likes to tip a server in a restaurant a minimum of 25%. She and her friend have a lunch bill that is $13.78. Chrissie says the tip will be $3.00. Her friend says that is not a minimum of 25%. Tell who is correct, then complete the explanation.
Answer:
Step-by-step explanation:
Chrissie likes to tip a server in a restaurant a minimum of 25% of her lunch bill. She and her friend have a lunch bill that is $13.78. This means that the amount of tip that she would give to the server would be
25/100 × 13.78 = 0.25 × 13.78 = $3.445
If Chrissie says the tip will be $3.00, he is incorrect because the tip is $3.445 which is higher than $3
If her friend says that the amount is not a minimum of 25% he is correct because a minimum if 25% is $3.445 which is higher than $3
What is the value of secant theta given the diagram below? A unit circle is shown. A ray intersects point (negative 3, 6) in quadrant 2. Theta is the angle formed by the ray and the x-axis in quadrant 1. Negative StartRoot 5 EndRoot Negative StartFraction StartRoot 5 EndRoot Over 2 EndFraction StartFraction StartRoot 5 EndRoot Over 2 EndFraction StartRoot 5 EndRoot
Answer:
- √5
Step-by-step explanation:
Given that, a ray intersects point (negative 3, 6) in quadrant 2 and we are told to find the value of secant theta.
To get the answer to the question,
The first step is to find the hypotenuse, we have to use the Pythagoras theorem where, Hypotenuse = opposite raise to power two + adjacent raise to power.
(I.e. h= O² + A²)
H = 6² + (-3)2
H = 36 + 9
H = 45
We then convert the answer to surds form.
H = 3√5
The next step is to find the value of secant theta.
To get the value of secant theta we will have to divide the hypotenuse by adjacent with a negative sign because of the negative sign in the second quadrant
We have
Sec ø = - (hypotenuse/adjacent)
Sec ø = - (3√5/ 3)
Sec ø = - √5
Answer:
-√5
Step-by-step explanation:
The length of a string is L inches. Samantha cuts it into two unequal pieces such that the length of the small piece is 35% of L.
If the length of the big piece is 24 inches longer than the length of the small piece, what is the ratio of the length of the small piece to the length of the big piece as a fraction in its lowest terms?
Answer:
The shorter piece x = 8.4 in
The longer one y = 15.6 in
Step-by-step explanation:
If we cut a string length L in to unequal pieces we get two pieces
first one with length x and the other one with length y
Let call x the smaller piece, then y = L - x will be the longer one
If x = 35 % then
x = 0,35* L and
y = L - x = L - 0,35*L ⇒ y = 0,65 L ⇒ y = 0.65*24
Now if L = 24 in
x = 0,35*24 ⇒ x = 8.4 in
and
L - x = 0.65*L ⇒ L - x = 0.65*24 y = L - x = 15.6 in
as way of verification you can add the length of the two pieces and find:
8.4 + 15.6 = 24 in
Final answer:
The ratio of the length of the small piece to the big piece is found to be 7/13 after calculating the lengths of each piece, with the small piece being 28 inches and the big piece being 52 inches.
Explanation:
Given that the length of the small piece is 35% of the total length L, we can denote the length of the small piece as 0.35L. The big piece is 24 inches longer than the small piece, so the length of the big piece is 0.35L + 24 inches. Since the string is cut into only two pieces, the total length L is the sum of the lengths of the two pieces, which means L = 0.35L + (0.35L + 24).
Simplifying, we have L = 0.7L + 24. Subtracting 0.7L from both sides gives 0.3L = 24 inches. Therefore, the total length of the string is L = 24 / 0.3 = 80 inches. So the small piece is 0.35L = 0.35 * 80 = 28 inches, and the big piece is 28 + 24 = 52 inches.
To find the ratio of the lengths of the small piece to the big piece, we divide the length of the small piece by the length of the big piece: 28/52. Simplifying this ratio by dividing both the numerator and denominator by 4 gives us 7/13. Therefore, the ratio of the length of the small piece to the big piece in its lowest terms is 7/13.
Lucy works at an electronics store as a salesperson. Lucy earns a 6% commission on the total dollar amount of all phone sales she makes, and earns a 2% commission on all computer sales. How much money would Lucy earn in commission on a day that she sold $1100 worth of phones and $1900 worth of computers? How much money would Lucy earn in commission on a day that she sold $xx worth of phones and $yy worth of computers?
Lacy would earn a commission of $104.
Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.
Step-by-step explanation:
Given,
Commission earned on phones sales = 6% = [tex]\frac{6}{100}=0.06[/tex]
Commission earned on computer sales = 2% = [tex]\frac{2}{100}=0.02[/tex]
Worth of phones sold = $1100
Commission amount = 0.06*1100 = $66
Worth of computers sold = $1900
Commission amount = 0.02*1900 = $38
Total commission amount = 66+38 = $104
Lacy would earn a commission of $104.
For $x of phones, we will multiply the given amount with commission rate;
Commission amount of $x phones = 0.06*x = 0.06x
For $y computers;
Commission amount of $y computers = 0.02*y = 0.02y
Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.
Keywords: percentage, addition
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in triangle abc shown below side ab is 6 and side ac is 4
which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Question is Incomplete, Complete question is given below:
In Triangle ABC shown below, side AB is 6 and side AC is 4.
Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer
Segment AD is 3 and segment AE is 2.
Segment AD is 3 and segment AE is 4.
Segment AD is 12 and segment AE is 4.
Segment AD is 12 and segment AE is 8.
Answer:
Segment AD is 3 and segment AE is 2.
Step-by-step explanation:
Given:
side AB = 6
side AC = 4
Now we need to prove that segment DE is parallel to segment BC and half its length.
Solution:
Now AD + DB = AB also AE + EC = AC
DB = AB - AD also EC = AC - AE
Now we take first option Segment AD is 3 and segment AE is 2.
Substituting we get;
DB = 6-3 = 3 also EC = 4-2 =2
From above we can say that;
AD = DB and EC = AE
So we can say that segment DE bisects Segment AB and AC equally.
Hence From Midpoint theorem which states that;
"The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side."
Hence Proved.
The sum of the circumference of two circles is 38π cm and the sum of their areas is 193π cm². Calculate the radii of the circles.
Answer:
The radii of the circles are 12 cm and 7cm.
Step-by-step explanation:
Let the radii of the circles be [tex]r_{1}\ and\ r_{2}[/tex]
Given:
Sum of circumference of two circles= 38π cm
Formula for circumference of a circle with radius r = 2πr
[tex]2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19[/tex]------------1
Sum of areas of two circles= 193π cm²
Area of circle with radius r = πr²
[tex]\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193[/tex]-------2
Substituting r2 = 19 - r1 in equation 2 we get:
[tex]r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7[/tex]
Then r2 = 19 - r1
[tex]r_{2}=12\ or\ 7[/tex]
One end point of a line segment is(-3,-6). The length of the line segment is 7 units. Find four points that could serve as the other end point of the given line segment.
Answer:
(-10, -6), (4, -6), (-3, -13), (-3, 1)
Step-by-step explanation:
The easiest points to find that have rational coordinates are the ones 7 units up or down, left or right from the given point. Those are listed above.
We used the distance formula to find four points that could serve as the other end of a line segment with one end at (-3, -6) and length of 7 units. The four points are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).
Finding the Other End Point of a Line Segment
To find four points that can serve as the other end point of a line segment with one end point at (-3, -6) and a length of 7 units, we use the distance formula. The distance formula is:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Given, (x₁, y₁) is (-3, -6) and the distance is 7, we need to find (x₂, y₂) such that:
√((x₂ + 3)² + (y₂ + 6)²) = 7
Squaring both sides: (x₂ + 3)² + (y₂ + 6)² = 49
Case 1: Let x₂ = 0(0 + 3)² + (y₂ + 6)² = 49
9 + (y₂ + 6)² = 49
(y₂ + 6)² = 40
y₂ + 6 = ±√40
y₂ = -6 ± √40
(x₂ + 3)² + (0 + 6)² = 49
(x₂ + 3)² + 36 = 49
(x₂ + 3)² = 13
x₂ + 3 = ±√13
x₂ = -3 ± √13
Thus, the four possible points for the other end point of the line segment are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).
Explain how the law of superposition was used to determine your findings.
Answer:sdxfrcgtvyhujikokjhgfdsasdfghjknbv 6yujhgtrfgb srry .\.
Find all roots x^3 + 7x^2 + 12x = 0
Answer:
Therefore the THREE roots are
[tex]x=0\ or\ x=-3\ or x=-4[/tex]
Step-by-step explanation:
Given:
[tex]x^{3}+7x^{2} +12x= 0[/tex]
To Find:
All the Roots = ?
Solution:
As the degree of the polynomial is THREE then the number of root are also THREE.
[tex]x^{3}+7x^{2} +12x= 0\\\\x(x^{2}+7x +12)= 0\\\\x=0\\or\\x^{2}+7x +12= 0\\[/tex]
Now one root is Zero For other we need to Factorize
So by Splitting the middle term
i.e Factor of 12 such that sum should be 7
i.e 3 × 4 = 12 and 3 + 4 = 7
∴ [tex]x^{2}+7x +12= 0\\x^{2}+3x+4x +12= 0\\x(x+3)+4(x+3)=0\\(x+3)(x+4)=0\\\\x+3=0\ or\ x+4 = 0\\\\\therefore x=-3\ or x=-4\ \textrm{Which are the roots}[/tex]
Therefore the THREE roots are
[tex]x=0\ or\ x=-3\ or x=-4[/tex]
the length of a rectangle increases at a rate of 0.5 cm/sec and the width decreases at a rate of 0.5 cm/sec at the time when the length is 10cm and the width is 7 cm what is the rate of change in the area of the rectangle?
Answer:
Step-by-step explanation:
let length=x
width=y
area A=xy
[tex]\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}\\ \frac{dx}{dt}=0.5 ~cm/sec\\\frac{dy}{dt}=-0.5~cm/sec\\\frac{dA}{dt}=10*(-0.5)+7(0.5)=-5+3.5=-1.5[/tex]
area is decreasing at the rate of 1.5 cm^2/sec
The rate of change in the area of the rectangle when the length is 10 cm and the width is 7 cm, with their rates of change being 0.5 cm/sec and -0.5 cm/sec respectively, is -1.5 cm²/sec.
Explanation:To determine the rate of change in the area of a rectangle where the length is increasing at 0.5 cm/sec and the width is decreasing at 0.5 cm/sec, we can use the concept of derivatives from calculus.
Let L be the length and W be the width of the rectangle. The area A of the rectangle is given by A = L * W. Given that the length is increasing at 0.5 cm/sec (dL/dt = 0.5 cm/sec) and the width is decreasing at 0.5 cm/sec (dW/dt = -0.5 cm/sec) the rate of change of the area with respect to time can be found using the product rule for derivatives: dA/dt = (dL/dt) * W + L * (dW/dt).
At the moment when the length L is 10 cm and the width W is 7 cm, we can plug these values into the formula: dA/dt = (0.5 cm/sec) * 7 cm + 10 cm * (-0.5 cm/sec). This simplifies to dA/dt = 3.5 cm2/sec - 5 cm2/sec, giving us the rate of change in the area as dA/dt = -1.5 cm2/sec.
Charlotte pays $24 for 3 yards of landscaping fabric and 6 yards of chicken wire. Kami pays $30 for 6 yards of landscaping fabric and 3 yards of chicken wire. What is the price of 1 yard of chicken wire?
Answer: the price of 1 yard of chicken wire is $2
Step-by-step explanation:
Let x represent the cost of one yard of landscaping fabric.
Let y represent the cost of one yard of chicken wire.
Charlotte pays $24 for 3 yards of landscaping fabric and 6 yards of chicken wire. This means that
3x + 6y = 24 - - - - - - - - - - 1
Kami pays $30 for 6 yards of landscaping fabric and 3 yards of chicken wire. This means that
6x + 3y = 30 - - - - - - - - -2
Multiplying equation 1 by 6 and equation 2 by 3, it becomes
18x + 36y = 144
18x + 9y = 90
Subtracting
27y = 54
y = 54/27 = 2
Substituting y = 2 into equation 1, it becomes
3x + 6×2 = 24
3x = 24 - 12 = 12
x = 12/3 = 4
Answer:
$2 per yard.
Step-by-step explanation:
Let the price per yard of landscaping fabric be f and the price of chicken wire per yard be c.
3f + 6c = 24 Multiply this equation by - 2:
-6f - 12c = -48 Also:
6f + 3c = 30
Adding the last 2 equations:
-9c = -18
c = 2.