The table shows the amount of money in your savings account over a period of 6 weeks. You plan to keep saving at the same rate until you have $825 in the account. Which equation could you use to find the number of weeks,n, it would take to reach your goal?
A 55⋅n=825
B 55⋅n+100=825
C 100−n=825
D 100⋅n+55=825
Answers
Answer:
Choice B
Step-by-step explanation:
Looks like interest isn't being used, so that makes it simple.
Every week the same amount is added, that means we can use a linear equation, which is what it is asking us to pick between so it all works out, awesome.
Now, we need two things to make an equation. the slope and two points. Definitely have points so we need the slope.
The slope is found by taking any two points and finding the difference of their y values and dividing that by the distance of their x values. so find two points (x1, y1) and (x2, y2) and then use the formula(y2-y1)/(x2-x1) Also, we will say number of weeks is the x and the amount of money is y
No matter which point you use you will get the slope is 55
From there we find the function with the formula y - y1 = m(x - x1)
We know m and I reccomend using (0, 100) as our x1 y1 because 0 will usually make things easier.
y - y1 = m(x - x1)
y - 100 = 55(x-0)
y = 55x + 100
you could have used any point again, 0 just means it goes away if you add 0 or subtract 0. Of course your problem uses n so just replace x with n. and y is the value we want to end at, which is 825
825 = 55n + 100, or arranging it so it's the same as the option, 55*n + 100 = 825, so that's choice B
The equation that calculates the weeks it would take to reach the target is : 55n = 825.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the table shows the amount of money in your savings account over a period of 6 weeks and you plan to keep saving at the same rate until you have $825 in the account.
Assume that it would take [n] weeks to reach the target. The unit rate from the given table can be calculated as -
m = (155 - 100)/(1 - 0)
m = 55
So, we can write the equation as -
55n = 825
Therefore, the equation that calculates the weeks it would take to reach the target is : 55n = 825.
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Related Questions
Which graph represents the solution set of the system of inequalities? How do you know?
{x+y<1 2y≥x−4
Answers
Answer:
Step-by-step explanation:
It is the fourth one
Hope this helps
Mark me as brainiest
Please Help me!!!!!! Thank you so much
Answers
Answer:x1 = 1, x2 = - 1, x3 = 3
Step-by-step explanation:
x1 + 2x2 - x3 = - 4 - - - - - - - - - -1
x1 + 2x2 + x3 = 2 - - - - - - - - - -2
- x1 - x2 + 2x3 = 6 - - - - - - - - - -3
Let us eliminate x1 and x2. Subtracting equation 2 from equation 1, it becomes
-2x3 = - 6
x3 = -6/-2
x3 = 3
Adding equation 2 to equation 3, it becomes
x2 + 3x3 = 8 - - - - - - - - - - - 4
Substituting x3 = 3 into equation 4, it becomes
x2 + 3 × 3 = 8
x2 + 9 = 8
x2 = 8 - 9 = -1
Substituting x2 = -1 and x3 = 3 into equation 2, it becomes
x1 + 2 × -1 + 3 = 2
x1 - 2 + 3 = 2
x1 + 1 = 2
x1 = 2 - 1 = 1
Let us check by substituting x1 = 1, x2 = -1 and x3 = 3 into equation 1. It becomes
1 + 2 × - 1 - 3 = - 4
1 - 2 - 3 = - 4
-1 - 3 = - 4
-4 = - 4
Graph the linear equation.
x = - 9
help in any way u can please
Answers
This is a vertical line that goes through all points with an x-coordinate of -9.
To graph it, I can give you a couple of points this line goes through so you can draw it more easily.
Points that are on line: (-9,0) and (-9,1)
Suppose the size of a population of mustard plants is 6,000. According to genetic drift theory, what is the probability that a newly-arisen mutation will become fixed in this population?
Answers
Answer:
1/12,000
Step-by-step explanation:
Data provided in the question:
Size of a population of mustard plants = 6,000
Now,
According to genetic drift theory
The probability that a newly-arisen mutation will become fixed is given using the formula
⇒ 1 ÷ [ 2 × Size of a population of mustard plants ]
⇒ 1 ÷ [ 2 ×6,000 ]
⇒ [ 1 ÷ 12,000 ]
Hence,
probability that a newly-arisen mutation will become fixed in this population is 1/12,000
What is the simple interest earned on $3,672 at 4.5% for three years?
$459.72
$594.86
$518.36
$495.72
Answers
Answer: interest at the end of 3 years is $495.72
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 3 years
P = $3,672
R = 4.5%
Therefore
I = (3672 × 4.5 × 3)/100
I = 49572/100
I = 495.72
The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min. t (min) 0 0.5 1 1.5 2 2.5 3 r (l/min) 44 40 37 34 30 27 23
Answers
Answer:
100.75 liters
Step-by-step explanation:
Data provided in the question:
t (min) 0 0.5 1 1.5 2 2.5 3
r (l/min) 44 40 37 34 30 27 23
Now,
left endpoint approximation
= 0.5 × ( 44 + 40 + 37 + 34 + 30 + 27 )
= 0.5 × 212
= 106
Right endpoint approximation
= 0.5 × ( 40 + 37 + 34 + 30 + 27 + 23 )
= 0.5 × 191
= 95.5
Therefore,
the average of the left- and right-endpoint approximations
= [ 106 + 95.5 ] ÷ 2
= 100.75 liters
The total amount of water drained during the first 3 min is: 100.75 liters/min.
Total amount of waterLeft endpoint approximation
r = 1/2 ( 44 + 40 + 37 + 34 + 30 + 27 )
r= 1/2 × 212
r= 106 L/m
Right endpoint approximation
r= 1/2 × ( 40 + 37 + 34 + 30 + 27 + 23 )
r= 1/2 × 191
r= 95.5 L/min
Average of the left- and right-endpoint approximations
Average= [ 106 + 95.5 ] ÷ 2
Average=201.5÷2
Average= 100.75 liters/min
Inconclusion the total amount of water drained during the first 3 min is: 100.75 liters/min.
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Find the indicated term of the geometric sequence. a8 for 4, -12, 36, ...
Answers
Answer:
76
Step-by-step explanation:
Answer:
The 8th term of geometric sequence is -8748
ie., [tex]a_{8}=-8748[/tex]
Step-by-step explanation:
Given geometric sequence is 4,-12,36,...
Geometric sequence can be written as
[tex]a_{1},a_{2},a_{3},..,[/tex]
[tex]a_{1}=4=a[/tex]
[tex]a_{2}=-12=ar[/tex]
[tex]a_{3}=36=ar^2[/tex]
and so on.
common ratio is [tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]r=\frac{-12}{4}[/tex]
[tex]r=-3[/tex]
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]r=\frac{36}{-12}[/tex]
[tex]r=-3[/tex]
Therefore [tex]r=-3[/tex]
Geometric sequence of nth term is [tex]a_{n}=ar^{n-1}[/tex]
To find the 8th term:
[tex]a_{8}=ar^{8-1}[/tex]
[tex]a_{8}=ar^{7}[/tex]
here a=4 and r=-3
[tex]a_{8}=ar^{7}[/tex]
[tex]=4\times (-3)^7[/tex]
[tex]=4\times (-2187) [/tex]
[tex]=-8748[/tex]
[tex]a_{8}=-8748[/tex]
Therefore the 8th term of geometric sequence is -8748
PLEASE HELP IM TERRIBLE AT MATH!!!! WILL GIVE BRAINLIEST!!!
Divide 3x^2 + 4x − 4 by x + 2.
A. x − 2
B. x + 6
C. 3x − 2
D. 3x + 6
Answers
Answer:
It is C
Step-by-step explanation:
(3x-2)(x+2)
3x(x)+3x(2)-2(x)-2(2)
3x^2+6x-2x-4
3x^2+4x-4 <----------
(Im bad at explaining but that is right trust me :P)
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
Answers
If it's 4 o'clock, the hour hand will be on the 4 and the minute hand will be on the 12.
This takes 4 partitions/pieces of the clock, and there are 12 different partitions. That's 4/12, or 1/3 of the entire clock.
The total clock is a 360 degree angle.
360 * (1/3) = 120
1/3 of 360 degrees is 120 degrees.
Since the angle between the minute and hour hand takes up 1/3 of the clock, the angle is 120 degrees.
Let me know if you need any clarifications, thanks!
Solve for x. The triangles in each pair are similar.
Answers
Answer:
Step-by-step explanation:
Triangle TML is similar to triangle TVU. Side TV measures 36 and side TM meaures 9; side TV is 4 times longer than side TM. Same with sides VU and ML. VU is 4 times longer than ML. That means that side TU is 4 times longer than side TL. Side TL measures x - 4; side TU measures 24 + x - 4 which is x + 20. That means that x + 20 = 4(x - 4) and x + 20 = 4x - 16 and
3x = 36 so
x = 12
Ben drinks tea at an incredible rate. He drinks 3\dfrac123 2 1 3, start fraction, 1, divided by, 2, end fraction liters of tea every \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction of an hour. Ben drinks tea at a constant rate.
Answers
Answer:
[tex]5\frac{1}{4}[/tex] liters per hour.
Step-by-step explanation:
Consider the question: Ben drinks tea at an incredible rate. He drinks [tex]3\frac{1}{2}[/tex] liters of tea every [tex]\frac{2}{3}[/tex] of an hour. Ben drinks tea at a constant rate. How many liters of tea does he drink in one hour?
To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:
[tex]3\frac{1}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]
Convert mixed fraction into improper fraction:
[tex]\frac{7}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]
Convert division problem into multiplication problem by flipping the 2nd fraction:
[tex]\frac{7}{2}\text{ Liters}\times \frac{3}{2}\text{ hour}[/tex]
[tex]\frac{21}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]
[tex]5\frac{1}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]
Therefore, Ben drinks [tex]5\frac{1}{4}[/tex] liters per hour.
Answer:
He drinks 21/4, or 5 1/4, liters of tea in 1 hour
Step-by-step explanation:
The following question is missing: How much does he drink in one hour?
Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:
7/2 liters / x liters = 2/3 hour / 1 hour
x = (7/2)/(2/3) = 7/2 * 3/2
x = 21/4 = 5 1/4 liters
What is the area of a right triangle with the given vertices? A(3,1) , B(5,4) , C(6,−1)
Answers
Answer:
[tex]\frac{13}{2}[/tex] square units
Step-by-step explanation:
We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).
We have to find the area of triangle.
We know that area of triangle=[tex]\frac{1}{2}\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid [/tex]
[tex]x_1=3,x_2=5,x_3=6[/tex]
[tex]y_1=1,y_2=4,y_3=-1[/tex]
Substitute the values in the formula then we get
Area of right triangle =[tex]\frac{1}{2}\mid (3(4+1)+5(-1-1)+6(1-4))\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\mid (15-10-18)\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\times 13=\frac{13}{2}[/tex] square units
A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second random sample of 432 workers from another mid-sized city (city two) found 91 people who work at more than one job. Find a 99% confidence interval for the difference between the proportions of workers in the two cities who work at more than one job.Select one:a. (0.003, 0.159)b. (0.021, 0.141)c. (-0.159, 0.004)d. (0.031, 0.131)e. Sample sizes aren't large enough to justify using z-procedures
Answers
Answer:
99% confidence interval is:
(0.00278 < P1 - P2< 0.15921)
Step-by-step explanation:
For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:
[tex][(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }[/tex]
Where [tex]p_{1}[/tex] : proportion sample of individuals who worked
at more than one job in the city one
[tex]n_{1}[/tex]: Number of respondents in the city one
[tex]p_{1}[/tex] : proportion sample of individuals who worked
at more than one job in the city two
[tex]n_{1}[/tex]: Number of respondents in the city two
Then
α = 0.01 and α/2 = 0.005
and [tex]z_{\alpha/2} = 2.575[/tex]
[tex]p_{1} = \frac{112}{384} = 0.2916[/tex]
[tex]p_{2} = \frac{91}{432} = 0.2106[/tex]
[tex]n_{1}= 384[/tex] and [tex]n_{2}= 432[/tex]
The confidence interval is:
[tex][(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }[/tex]
(0.00278 < P1 - P2< 0.15921)
Molly is making Strawberry infused water for each ounce of strawberry juice she uses three times as many ounces of water she wants to make a total of 64 ounces of strawberry infused water
Answers
Answer:
The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.
Step-by-step explanation:
Let the amount of Strawberry juice in ounces be 'j'
Let the amount of water in ounce be 'w'
Given:
For each ounce of strawberry juice she uses three times as many ounces of water.
It means that amount of water in ounce is 3 times of amount of strawberry juice in ounce.
framing the equation we get;
[tex]w=3j[/tex]
Now we need how many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water.
We know that Total Strawberry infused water is equal to sum of amount of Strawberry juice in ounces and the amount of water in ounces
Framing in equation form we get;
[tex]j+w=64[/tex]
But we know [tex]w=3j[/tex]
hence,
[tex]j+3j= 64\\\\4j=64\\\\j=\frac{64}{4} = 16 \ ounces[/tex]
Hence amount of Strawberry juice = 16 ounces
Amount of water = [tex]3j = 3\times16 =48 \ ounces[/tex]
Hence The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.
The posterior lobe of the pituitary gland is NOT a true endocrine gland because ________. A it is unable to function as an endocrine tissue because it is actually part of the neural system due to its location B it is strictly a part of the neural system and has little or nothing to do with hormonal release C embryonically it was an endocrine tissue, but in the adult human it is no longer functional
Answers
Isn't this Anatomy and Physiology?
Find the LCM of 2, 10 and 6
Answers
Answer:
30
Plz click the thxs button or mark brainliest!
Yours Truly.
Answer:
30
Step-by-step explanation:
2 2 10 6
3 1 5 3
5 1 5 1
1 1 1
2*3*5 30
30% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
Answers
Answer:
30% companies will offer both wireless internet and free on-board snacks.
Step-by-step explanation:
Percentage of major companies who equip their planes with wireless internet access = 30%
Percentage of major airlines who offer passengers free on-board snacks = 70%
Therefore, from the given information, the maximum percentage of the companies who offer both wireless internet facility as well as on-board snacks may be 30% only.
For the given pentagon ABCDE the diagonal
EC
∥
AB
. I, G, F, H are midpoints of
BC
,
CD
,
DE
,
EA
respectively. The length of
FG
is 50% more than the length of AB. Find the area of the quadrilateral HFGI, if A△ADB = 16sq. in.
Answers
Answer:
28 in²
Step-by-step explanation:
Without constraining the problem unduly, we can make the assumption that AB = 2 inches. Then the altitude from AB to D is h in ...
Area ABD = (1/2)(AB)h
16 in² = (1/2)(2 in)(h)
16 in = h . . . . . . . . . . . divide by 1 in
__
The altitude D to AB is the sum of the heights from D to EC (h1) and from AB to EC (h2). That is ...
16 = h1 + h2
We also know that the height from FG to EC is 1/2 the height from D to EC, hence (1/2)h1. Likewise, the height to midsegment HI from either EC or AB is half the height from EC to AB, hence (1/2)h2. This means the total height of the quadrilateral HFGI is (1/2)h1 + (1/2)h2 = (1/2)(h1 +h2) = 8.
__
We are given that FG is 50% longer than AB, so its length will be ...
FG = AB×(1 + .5) = (2 in)(1.5) = 3 in
Since FG is the mid-segment of triangle CDE, base EC is twice its length, or ...
EC = 2×FG = 2(3 in) = 6 in
__
Mid-segment HI is the average of the base lengths of trapezoid ABCE, so is ...
HI = (EC +AB)/2 = (6 + 2)/2 = 4
__
Now, we know the height and base lengths of trapezoid HFGI, so we can find its area as ...
A = (1/2)(b1 +b2)h = (1/2)(3 in + 4 in)(8 in) = 28 in²
The area of quadrilateral HFGI is 28 square inches.
_____
You can make any assumption you like about the dimension of AB, and the rest of the dimensions scale accordingly. The result is still the same.
There are three grades in the school. One grade has 1/3 of the students, one grade has 1/4 of the students. What fraction of students is in the remaining grade?
Answers
Answer:
Step-by-step explanation:
Let x represent the total number of stdents that has all grades in the school.
There are three grades in the school. One grade has 1/3 of the students, this means that number of students that belongs tho this grade is 1/3 × x = x/3
One grade has 1/4 of the students, this means that number of students that belongs to this grade is 1/4 × x = x/4
Total number of students in both grades would be x/3 +/x/4 = 7x/12
The number of students in the remaining grade would be
x - 7x/12 = 5x/12
fraction of students in the remaining grade would be
(5x/12)/x = 5/12
Answer:
2/4
Step-by-step explanation:
i dont want to think
Let R and S be partial orders on a nonempty set A prove that T = R intersection S is also a partial order on A.
Answers
Answer:
See proof below
Step-by-step explanation:
We denote (x,y)∈R as xRy, and we also use the similar notation xSy for (x,y)∈S. Remember that R and S are reflexive, antisymmetric and transitive relations (the definition of partial order).
To prove that R∩S⊆A is a partial order, we will prove that R∩S is reflexive, antisymmetric and transitive.
Reflexive: Let a∈A. R is reflexive thus aRa. S is also reflexive, then aSa. Then (a,a)∈R and (a,a)∈S which implies that (a,a)∈R∩S, that is, a(R∩S)a for all a∈A.Antisymmetric: Let a,b∈A and suppose that a(R∩S)b and b(R∩S)a hold. In particular, aRb and bRa. Since R is antisymmetric, a=b.Transitive: Let a,b,c∈A and suppose that a(R∩S)b and b(R∩S)c hold. Then aRb, bRc, aSb and bSc are true. The first two statements imply by the transitivity of R that aRc. Similarly, from the last two we have that aSc. Thus a(R∩S)c as we wanted to prove.What is the value of \dfrac{d}{dx}\left(\dfrac{2x+3}{3x^2-4}\right) dx d ( 3x 2 −4 2x+3 )start fraction, d, divided by, d, x, end fraction, (, start fraction, 2, x, plus, 3, divided by, 3, x, squared, minus, 4, end fraction, )at x=-1x=−1x, equals, minus, 1 ?
Answers
The question asks for the derivative of the function (2x+3)/(3x^2-4) at x=-1. Using the quotient rule, we find the derivative and then substitute x=-1 into it to get the required value.
Explanation:The question aims to find the derivative of the function f(x) = (2x + 3) / (3x^2 - 4) and then find its value at x = -1. To do this, we need to use the Quotient Rule which is (f(x)/g(x))' = (g(x)*f'(x) - f(x)*g'(x))/(g(x))^2.
Here f(x) = 2x + 3 and g(x) = 3x^2 - 4. So, the derivative of the function becomes f'(x) = ( (3x^2 - 4)*2 - (2x + 3)*6x ) / (3x^2 - 4)^2 which simplifies to (6x^2 - 8 - 12x^2 - 18x) / ( 9x^4 - 24x^2 + 16). Now, substitute x = -1 into f'(x) to get the desired value.
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Bryce has heard that gas appliances are cheaper to use and can lower utility costs. He is interested in purchasing a new gas stove for his kitchen to replace his electric stove. Assuming that the stove gets used one hour per day, use the following chart to determine how much Bryce will save each year in utility costs by purchasing the gas appliance.
Answers
Answer:
C. $29.20
Step-by-step explanation:
The difference between using an electric stove and a gas stove everyday is 13 cents - 5 cents= 8 cents.
Saving 8 cents everyday.
Therefore for a year, Bryce will save 8 cents × 365days = 2920 cents
Then 2920 cents = $(2920÷100)
=$29.20
Answer:
C. $29.20
Step-by-step explanation:
Ray hired sun and peter to help him move .Sun charged a $20 flat fee and $30 per hour.Peter charged $25 per hour. Write an expression for ray's total cost if sun and peter each work h hours.
Answers
Answer:
Step-by-step explanation:
Ray hired sun and peter to help him move.
Let h represent the number of hours that each of them worked.
Let y represent Ray's total cost for hiring Sun and Peter for h hours.
Sun charged a $20 flat fee and $30 per hour. The total amount that Sun charges would be
20 + 30h
Peter charged $25 per hour. The total amount that Peter charges would be
25h
An expression for Ray's total cost if Sun and Peter each work h hours would be
y = 20 + 30h + 25h
y = 20 + 55h
Answer:
[20+(30+25)]h or (20+55)h
Step-by-step explanation:
20 will not be changed.
Total cost per hour is 55
add $20
Hope this helps
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
Answers
The question is missing the figure. So, it is attached below.
Answer:
Area of the shaded sector is 144π units squared.
Step-by-step explanation:
Given:
Central angle of the sector is, [tex]\theta=\frac{8\pi}{9}\ rad[/tex]
Radius of the circle is, [tex]R=18\ units[/tex]
We know that, area of a sector of a circle of radius 'R' and central angle [tex]\theta[/tex] is given as:
[tex]A=\frac{1}{2}R^2\theta[/tex]
Plug in [tex]\theta=\frac{8\pi}{9},R=18[/tex]. This gives,
[tex]A=\frac{1}{2}\times (18)^2\times \frac{8\pi}{9}\\\\A=(\frac{324\times 4}{9})\pi\\\\A=(36\times 4)\pi\\\\A=144\pi\ units^2[/tex]
Therefore, the area of the shaded sector is 144π units squared.
Answer: 144Pi units squared
Step-by-step explanation:
A rug has an area of x2+x−20 square feet. Which expression represents the dimensions of the rug? A (x+4)(x−5) B (x+2)(x−10) C (x−4)(x+5) D (x−2)(x+10)
Answers
Answer: the correct option is
C (x−4)(x+5)
Step-by-step explanation:
The area of the rug in square feet is expressed as
x^2+x−20
The given equation is a quadratic equation and the roots of the equation represents the dimensions of the rug. To simplify the equation, we would apply the factorization method.
We will get two numbers such that, their difference will be x and their sum will be -20x^2. The numbers are 5x and 4x. Therefore
x^2+ 5x - 4x −20 = 0
x(x + 5) - 4(x +5)
The roots are (x - 4)(x + 5)
The area of the rug is represented by the quadratic expression[tex]x^2 + x - 20,[/tex] which factors to (x + 4)(x - 5). This matches option A, verifying that these are the dimensions of the rug.
The student has a quadratic expression representing the area of a rug, which is[tex]x^2 + x - 20[/tex] square feet. To find the dimensions of the rug, we need to factor this expression. Factoring quadratic expressions involves finding two binomials that multiply to give the original quadratic expression. In this case, the correct factorization is (x + 4)(x - 5).
We can verify this by using the FOIL method (First, Outer, Inner, Last) to expand the binomials: (x + 4)(x - 5) = [tex]x^2 - 5x + 4x - 20 = x^2 - x - 20[/tex], which matches our original expression.
Thus, option A is the correct choice.
Laneka owns a cake shop.She is currently preparing cakes for two anniversary parties. The first cake has 3 small tiers and 1 medium tier and will serve a total of 100 guests. The second one has 3 small tiers and 2 medium tiers and will serve a total of 140 guests represent the situation with a system of equations
Answers
Answer:
The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].
Step-by-step explanation:
Let 's' represents the number of guest small tier can serve.
Let 'm' represents the number of guest medium tier can serve.
Now Given:
For First cake:
Number of small tiers = 3
Number of medium tier = 1
Total serving guest = 100
Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.
Framing in equation form we get;
[tex]3s+m=100[/tex]
For Second cake:
Number of small tiers = 3
Number of medium tier = 2
Total serving guest = 140
Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.
Framing in equation form we get;
[tex]3s+2m=140[/tex]
Hence The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].
Which system of linear inequalities is represented by the graph?
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]x+5y\geq 5[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the solid line [tex]x+5y=5[/tex]
The slope of the solid line is negative
The y-intercept of the solid line is (0,1)
The x-intercept of the solid line is (5,0)
[tex]y\leq 2x+4[/tex] ----> inequality B
The solution of the inequality B is the shaded area below the solid line [tex]y= 2x+4[/tex]
The slope of the solid line is positive
The y-intercept of the solid line is (0,4)
The x-intercept of the solid line is (-2,0)
therefore
The graph in the attached figure
5+3r=5r-19(if there is no solution,type in ''no solution'')r= Answer
Answers
Answer: 12 = r
Step-by-step explanation: When we have this kind of a setup, we want to put our variables together on one side of the equation and our numbers together on the other side of the equation.
First, let's put our variables on the right side by subtracting 3r from both sides of the equation. That gives us 5 = 2r - 19.
Now we can move our numbers to the left by adding 19 to both sides of the equation and we get 24 = 2r.
Divide both sides by 2 and 12 = r
Note:
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper or digitally. It will really pay off for you down the line.
4n-12=12-4n(If there is no solution, type in "no solution") n= Answer
Answers
Answer:
n = 3
Step-by-step explanation:
+4n | +4n
8n-12=12
+12| +12
8n=24
24/8= 3
n=3
For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of the first 10 terms in the sequence, then T isA. Greater than 2B. Between 1 and 2C. Between 1/2 and 1D. Between 1/4 and 1/2E. Less than 1/4
Answers
Answer:
Option D. is the correct option.
Step-by-step explanation:
In this question expression that represents the kth term of a certain sequence is not written properly.
The expression is [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].
We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].
where k is from 1 to 10.
By the given expression sequence will be [tex]\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......[/tex]
In this sequence first term "a" = [tex]\frac{1}{2}[/tex]
and common ratio in each successive term to the previous term is 'r' = [tex]\frac{\frac{(-1)}{4}}{\frac{1}{2} }[/tex]
r = [tex]-\frac{1}{2}[/tex]
Since the sequence is infinite and the formula to calculate the sum is represented by
[tex]S=\frac{a}{1-r}[/tex] [Here r is less than 1]
[tex]S=\frac{\frac{1}{2} }{1+\frac{1}{2}}[/tex]
[tex]S=\frac{\frac{1}{2}}{\frac{3}{2} }[/tex]
S = [tex]\frac{1}{3}[/tex]
Now we are sure that the sum of infinite terms is [tex]\frac{1}{3}[/tex].
Therefore, sum of 10 terms will not exceed [tex]\frac{1}{3}[/tex]
Now sum of first two terms = [tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]
Now we are sure that sum of first 10 terms lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{3}[/tex]
Since [tex]\frac{1}{2}>\frac{1}{3}[/tex]
Therefore, Sum of first 10 terms will lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{2}[/tex].
Option D will be the answer.