Find the coordinates of point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
Answers
I'd like to point out, is 1:5 from R to T, since that matters, that way we know the ratio from RS is the 1 and the ratio ST is the 5.
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ R(-14,-1)\qquad T(4,-13)\qquad \qquad 1:5 \\\\\\ \cfrac{RS}{ST} = \cfrac{1}{5}\implies \cfrac{R}{T} = \cfrac{1}{5}\implies 5R=1T \implies 5(-14,-1)=1(4,-13)\\\\ -------------------------------\\\\[/tex]
[tex]\bf { S=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------\\\\ S=\left(\cfrac{(5\cdot -14)+(1\cdot 4)}{1+5}\quad ,\quad \cfrac{(5\cdot -1)+(1\cdot -13)}{1+5}\right)[/tex]
Answer: The required co-ordinates of the point S are (-11, -6).
Step-by-step explanation: We are given to find the co-ordinates of the point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
We know that
the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) in the ratio m : n is given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
According to the given information, we have
(a, b) = (-14, -1), (c, d) = (4, -13) and m : n = 1 : 5.
Therefore, the co-ordinates of the point S are given by
[tex]\left(\dfrac{1\times4+5\times(-14)}{1+5},\dfrac{1\times(-13)+5\times(-1)}{}\right)\\\\\\=\left(\dfrac{4-70}{6},\dfrac{-13-5}{6}\right)\\\\\\=\left(\dfrac{-66}{6},\dfrac{-18}{6}\right)\\\\=(-11,-3)[/tex]
Thus, the required co-ordinates of the point S are (-11, -6).
Related Questions
A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base, as shown below. Find an equation for the parabola if the vertex is put at the origin of the coordinate system
Answers
y - k = - a(x - h)^2
where (h,k) represents the vertex of the parabola and a represents the focus and tells you where the graph opens. If a is positive then it opens upward and if its is negative, it opens downward.
For this given situation, the vertex is at point (0,0) or at the origin so that h and k are zero.
y= - a(x)^2
To determine the value of a, we use the measurements given above. We make use of the maximum height and the span of the parabola. The point we will be using would be (18/2 , 96 ).
y= - a(x)^2
96= - a(9)^2
a = -32/27
So, the equation of the parabola would be
y= - (32/27)(x)^2
The equation of the parabola if the vertex is put at the origin of the coordinate system is y =-32/27x^2
The height of the arch is given s:
height = 96 ft
The width of the base is given as:
width = 18 ft
A point on the building would be
(x,y) = (width/2, height)
So, we have:
(x,y) = (18/2, 96)
Simplify
(x,y) = (9, 96)
A parabola is represented as:
y = -a(x - h)^2 + k
The vertex of the parabola is at the origin.
So, we have:
y = -ax^2
Substitute (x,y) = (9, 96)
96 = -a * 9^2
This gives
96 = -81a
Divide both sides by 81
a= -96/81
So, the equation of the parabola is
y =-96/81x^2
Simplify
y =-32/27x^2
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If a triangle has legs measuring 8 inches and 15 inches and has a hypotenuse measuring 17 inches, what is the ratio, in simplest form, of the shorter leg to the hypotenuse?
Answers
hope that helps
The measure of ______________ in a circle is half the measure of the intercepted arc.
A. a central angle
B. an interior angle
C. an inscribed angle
Answers
YES slay5 is correct the answer is : C. an inscribed angle
Answer: C. An inscribed angle
Step-by-step explanation:
Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.
Interior angle is an angle between two sides inside a polygon or a shape.
Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.
Two exterior angles of a triangle equal 100° and 150°. Find all the interior angles
Answers
180°-150°= 30° (angle 2)
180°-80°-30°= angle 3
angle 3 = 70°
∴ the interior angles are 80°, 30° and 70°
The angles of the triangle will be 70°, 30°, and 80°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
We know that the sum of the interior and the exterior angles is 180 degrees.
Two exterior angles of a triangle equal 100° and 150°.
The interior angle corresponding to the exterior angle of 100° will be
⇒ 180° - 100°
⇒ 80°
The interior angle corresponding to the exterior angle of 100° will be 80°.
The interior angle corresponding to the exterior angle of 150° will be
⇒ 180° - 150°
⇒ 30°
The interior angle corresponding to the exterior angle of 150° will be 30°.
Then the third angle of the triangle will be
⇒ 180° - 80° - 30°
⇒ 70°
The angles of the triangle will be 70°, 30°, and 80°.
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Express -2 in triganomic form
Answers
now, there are two possible angles for that tangent... however, let's look at our a,b components.
"a" is negative whilst "b" is positive, so is not 0 then, thus
[tex]\bf -2+0i\implies r[cos(\theta )+i~sin(\theta )]\implies 2[cos(\pi )+i~sin(\pi )][/tex]
Final answer:
To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.
Explanation:
The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.
In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.
For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.
Assume that all chickens have 4725 feathers. if it takes you 5.6 seconds to pluck 24.8 feathers, how many hours would it take you to defeather 7728 chickens? answer in units of hours.
Answers
So it takes 5.6 seconds to plucks 24.8 feathers. To find f/s we needs to find 24.8 divided by 5.6 which is 4.429f/s.
Now we need to find how long it will take to pluck one entire chicken. Since it takes us one second to pluck 4.429 feathers, we need to divide 4,725 by 4.429 to find how many seconds it will take us to pluck an entire chicken. This value is 1,066.832 seconds.
Since it takes us 1,066.832 seconds to pluck one chicken, it will take us
7,728 • 1,066.832 seconds to pluck 7,728 chickens. This value is 8,244,477.696 seconds.
To convert seconds to hours, we need to divide by 60 to get minutes and then divide by 60 again to reach our desired unit of measurement: hours
8,244,477.696 / 60 / 60 = 2,290.133 hours
It would take approximately 2284.722 hours to defeather 7728 chickens.
Explanation:To find out how many hours it would take to defeather 7728 chickens, we need to consider the time it takes to pluck a certain number of feathers. We are given that it takes 5.6 seconds to pluck 24.8 feathers. First, we find the time it takes to pluck one feather by dividing the time by the number of feathers: 5.6 seconds ÷ 24.8 feathers = 0.2258 seconds per feather.
Next, we find the total number of feathers on 7728 chickens by multiplying the feather count per chicken by the total number of chickens: 4725 feathers/chicken × 7728 chickens = 36,396,000 feathers.
Finally, we find the total time it would take to defeather all the chickens by multiplying the time per feather by the total number of feathers: 0.2258 seconds/feather × 36,396,000 feathers = 8,224,996.8 seconds. Converting this to hours, we divide by the number of seconds in an hour: 8,224,996.8 seconds ÷ 3600 seconds/hour ≈ 2284.722 hours.
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A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?
Answers
now, if we take 40 to be the 100%, how much is 8 off of it in percentage?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 40&100\\ 8&x \end{array}\implies \cfrac{40}{8}=\cfrac{100}{x}[/tex]
solve for "x".
How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.
Answers
Answer:
40,320.
Step-by-step explanation:
We are asked to find the number of ways in which 8 books could be arranged on a shelf.
The 1st could be arranged in 8 ways. Since one place is filled, so 2nd book could be arranged in 7 ways.
Similarly, the 3rd book could be arranged in 6 ways as first two places are already taken. This process will go on.
So the 8 books can be arranged in [tex]8\times 7 \times 6\times5\times4\times3\times2\times1=8![/tex]
[tex]8!=40,320[/tex]
Therefore, 8 books could be arranged in 40,320 ways.
The number of ways to arrange 8 books on a shelf is 40,320.
We have to determineHow many ways can 8 books be arranged on a shelf?
According to the questionThere is total number of books is 8.
Then,
The arranging the way of 8 books also be 8.
If one of the 8 books is placed in the first place, only 7 of them can be placed in 2nd place. In 3rd place, only 6 of them can be placed.
This continues all the way to 1.
A permutation is an arrangement of objects in a particular way.Then,
The number of ways to arrange 8 books on a shelf is,
[tex]= 8!\\ \\ = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\\ \\ =40,320 [/tex]
Hence, The number of ways to arrange 8 books on a shelf is 40,320.
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Are the traingles congruent? Why or why not?
Yes, A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
No, C is not congruent to any angle in DEF.
No, the congruent sides do not correspond.
Answers
Yes, A ≅ D and AB ≅ DE
Yes , A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
• Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
• Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
• A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
From the given data ,
AB ≅ DE
and , ∠BAC = 33°
∠EDF = 33°
Therefore by rules of congruent triangles
The two angles are the same and the corresponding sides are same
Hence , The two triangles ΔABC and ΔDEF are congruent
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Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property
Answers
1 acre = 43560 square feet
43560 = 484 * X
X=43560/484 = 90
the width = 90 feet
Answer:
90 feet
Step-by-step explanation:
Perform the following food service calculation. Size of juice can = 54 oz. Portions of juice served = 6 oz. Number of cases used = 2 Number of cans per case = 12 How many guests can be served? 54 216 1,944 7,776
Answers
24 cans x 54 oz per can = 1296 oz
1296 oz / 6 oz per serving = 216 guests served
Answer: 216 guests.
Step-by-step explanation: We are given total number of cases = 2 Number of cans.
Number of cans per case = 12 cans.
Total number of cans in 2 cases = 2 cases × 12 cans = 24 cans
Each can contain = 54 oz of juice.
24 cans would contain total = 24 cans × 54 oz per can = 1296 oz juice.
Number of oz per serving = 6 oz.
Total number of guests can be served = 1296 oz / 6 oz per serving = 216 guests.
Cannon took out a mortgage for $85,290 on his new house. If the interest rate is 8.5 percent and the loan is for 25 years, how much will he pay monthly if he must pay $8.05 per $1,000?
Answers
85,290÷1,000=85.29
Monthly payment is
85.29×8.05=686.58
Answer:
The answer is $686.584
Step-by-step explanation:
Given is, Cannon pays $8.05 per month for every $1,000, so we have a ratio: 8.05 / 1000
Now, we will find the second ratio which is an unknown payment per month over the price: x / 85290
Equaling them to solve for x :
[tex]\frac{8.05}{1000}=\frac{x}{85290}[/tex]
[tex]1000x=8.05*85290[/tex]
[tex]1000x = 686584.50[/tex]
So, x = 686.584
Hence, the answer is $686.584
If you have a $1 bill a 5 bill a 10 bill and a 20 bill how many different sums of money
Answers
ex : $1 + 10$ or 5$+10$
I takes for ever to list all the possibilities so you need to think about probabilities to chose a bill.
For each bill, you can add it to your sum or not; so it gives you 2 possibilities; you do that for each bill and you multipliate each what gives you :
2 * 2 * 2 * 2 = 16 different sums
(20 points) You are writing a research paper on plant cells. You got 48,600,000 results on the online search. How do you write 48,600,000 in scientific notation?
Answers
the system of equations graphed below has how many solutions?
Answers
The solution would be where the lines intersect
Answer:
answer is C. 0
Step-by-step explanation:
How do I find the terms?
Answers
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=4\\ a_1=-2\end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=-2+(2-1)4\\ 3&a_3=-2+(3-1)4\\ 4&a_4=-2+(4-1)4\\ 5&a_5=-2+(5-1)4 \end{array}[/tex]
----------------------------------------------------------------------------------------
A(n)= 1/4 * A(n) is just a way of saying, you get the next term by multiplying the current one by 1/4, and A(1) = 8, simply means the first term's value is 8.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=\frac{1}{4}\\ a_1=8 \end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=8\left( \frac{1}{4} \right)^{2-1}\\\\ 3&a_3=8\left( \frac{1}{4} \right)^{3-1}\\\\ 4&a_4=8\left( \frac{1}{4} \right)^{4-1}\\\\ 5&a_5=8\left( \frac{1}{4} \right)^{5-1}\\ \end{array}[/tex]
Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half hour. how many bacteria will the colony contain at the end of 24
Answers
so
[tex]a_0[/tex] is the number of bacteria after 0/2 = 0 hours
[tex]a_1[/tex] is the number of bacteria after 1/2 hours
[tex]a_2[/tex] is the number of bacteria after 2/2 = 1 hours and so on
so if we list a few terms of this sequence, we have:
[tex]a_0=1[/tex]
[tex]a_1=1*2[/tex]
[tex]a_2=1*2*2[/tex]
[tex]a_3=1*2*2*2[/tex]
[tex]a_4=1*2*2*2*2[/tex]
so clearly, [tex]a_n[/tex], the number of bacteria after [tex] \frac{n}{2} [/tex] hours, is equal to [tex] 2^{n} [/tex].
[tex]a_4_8[/tex] is the number of bacteria after
[tex]\frac{n}{2}=\frac{48}{2}= 24[/tex] hours.
Thus, we calculate [tex]a_4_8[/tex], which is [tex] 2^{48} [/tex].
Answer: the number of bacteria after 24 hours is [tex] 2^{48} [/tex].
A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.
Explanation:The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.
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Confused. Please help thank you!
Answers
#6 is using using ratios:
7/2x+4 = 4/x+3 =
8x+16 =7x+21 =
8x=7x+5 =
x=5
AC = 2(5)+4= 14 + 5+3=8, 14+8 =22
#7
ratio of known sides 9/4 =2.25 now multiply other 2 sides by 2.25
7*2.25 = 15.75
9*2.25=20.25
perimeter = 9 +15.75+20.25 = 45
A cyclist rides her bike at a speed of 10 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answers
Final answer:
The speed of the cyclist is 16 km/h and she will travel a distance of 32 kilometers in 2 hours.
Explanation:
To convert the speed from miles per hour (mph) to kilometers per hour (km/h), we can use the conversion factor of 1 mile = 1.6 kilometers. So, if a cyclist rides her bike at a speed of 10 mph, we can multiply 10 by 1.6 to find the speed in km/h. Therefore, the speed of the cyclist is 16 km/h.
To calculate the distance traveled in 2 hours, we can use the formula: distance = speed × time. Since the speed of the cyclist is 16 km/h and the time traveled is 2 hours, we can multiply 16 by 2 to find the total distance. Therefore, the cyclist will travel 32 kilometers in 2 hours
Final answer:
To convert the speed from miles per hour (mph) to kilometers per hour (km/h), multiply the speed by the conversion factor. The cyclist will travel 32 kilometers in 2 hours.
Explanation:
To convert the speed from miles per hour (mph) to kilometers per hour (km/h), we can use the conversion factor of 1 mile = 1.6 kilometers. Thus, if the cyclist rides at a speed of 10 mph, we can find the speed in km/h by multiplying it by the conversion factor:
Speed (km/h) = Speed (mph) x Conversion factor
Speed (km/h) = 10 mph x 1.6 km/mi = 16 km/h
Next, to calculate the distance the cyclist will travel in 2 hours, we can use the formula:
Distance = Speed x Time
Distance = 16 km/h x 2 hours = 32 kilometers
Simplify.
6m+7n+5m−3n
15mn
11m + 10n
m + 10n
11m + 4n
Answers
to simplify combine all like terms
6m +5m = 11m
7n-3n = 4n
so it would be 11m+4n
To which part of the prism are the arrows pointing
Answers
Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?
A.The horse hair is 2 times as thick as the human hair.
B.The horse hair is 5 times as thick as the human hair
C.The human hair is 2 times as thick as the horse hair
D.The human hair is 5 times as thick as the horse hair
Answers
A.The horse hair is 2 times as thick as the human hair.
Answer:
A.The horse hair is 2 times as thick as the human hair.
Step-by-step explanation:
We have been given that Mateo is studying a human hair with a diameter of [tex]6.5\times 10^{-4}[/tex] inches and a horse hair with a diameter of [tex]1.3\times 10^{-3}[/tex] inches.
Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.
[tex]\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}[/tex]
Now we will quotient rule of exponents to simplify our given problem.
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=2\times \text{Diameter of human hair}[/tex]
We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.
You give your friend a head start of 20 feet in a race. A linear equation representing your friend’s progress (in feet) after x seconds is y = 9x + 20. A linear equation representing your progress (in feet) after x seconds is y = 9x. Will you catch up to your friend? Explain.
Answers
By looking at the equation : The two lines does not have an intersection point .
To catch up to your friend or not in a race explained with equations and steps.
The question is: Will you catch up to your friend? Explain.
Step-by-step explanation:
Friend's progress equation: y = 9x + 20
Your progress equation: y = 9x
To catch up, set the equations equal: 9x + 20 = 9x
Solve for x: 20 = 0 (This equation has no solution)
You will not catch up to your friend.
Alicia drove 265 miles in 5 hours What is the average rate that she traveled 49 miles per hour 51 miles per hour 53 miles per hour 55 miles per hour
Answers
Grade 12 data!!
18% of a population eats yogurt daily. What is the probability that, in a group of 10 people, 4 of them eat yogurt daily?
0.0032 0.072 0.067 0.00032
Answers
Answer:
The probability that, in a group of 10 people, 4 of them eat yogurt daily is 0.067
Step-by-step explanation:
In this case we can apply a Binomial distribution in which there are n events and every event have a probability p to get a success. Then, the probability of x is:
[tex]P(x)=nCx*p^{x}*(1-p)^{n-x}[/tex]
Where x is the number of people who eat yogurt daily, n is the total number of people and p is the probability of eats yogurt daily.
Additionally nCx is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, for the question we know that:
n=10
p=0.18
x=4
Replacing this values on the equation, we get:
[tex]P(4)=10C4*0.18^{4}*(1-0.18)^{10-4}[/tex]
P(4)=0.067
Finally, the probability that, in a group of 10 people, 4 of them eat yogurt daily is 0.067
Melanie is flying from washington,
d.c., to seattle. her flight leaves at 10
a.m. when her plane lands, the pilot announces that it is 2 p.m. in seattle. how long did her flight take
Answers
Write x2 - 12x + 8 = 0 in vertex form.
Answers
you first add the three to the other side, then add 16 on both sides, make the left side x-4 squared, and lastly you subtract 19 from both sides.
n/a. It cannot be written in vertex form because it is not a conic section.
But if you are referring to x^2 - 12x + 8, the answer is: Y = (x - 6)² - 28 (i think)
THIS IS TIMED AND I NEED HELP!!!
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)
Answers
y = x - 1
x^2 + 2x - 3 = x - 1
x^2 + 2x - x - 3 + 1 = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0
x + 2 = 0 y = x - 1
x = -2 y = -2 - 1
y = -3
x - 1 = 0 y = x - 1
x = 1 y = 1 - 1
y = 0
ur solutions are : (-2,-3) and (1,0)
If you put down 20% on a $7000 car and pay monthly payments of $109.40 for 60 months, what is the total price of the car?
Answers
$109.40 x 60 = $6564
$1400 + $6564 = $7964
Answer:
7964
Step-by-step explanation:
ms johnson and ms smith were folding report cards to send home to parents. the ratio of the number of report cards ms johnson folded to the number of report cards ms smith folded is 2:3. At the end of the day , ms Johnson and ms smith folded at total of 300 report cards. How many did each person fold?