The first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The quadratic sequence:
2, 12, 28, 50
a + b + c = 2
10, 16, 22 (first difference)
3a + b = 10
6, 6 (second difference)
2a = 6
a = 3
b = 1
c = -2
Tterm:
T(n) = 3n² + n - 2 = 688 (given)
After solving the quadratic equation:
n = 15, n = -46/3(n cannot be nagatve)
n = 15
n - 1 = 14
T(14) = 600
T(n) - T(n-1) = 688 - 600 = 88
Thus, the first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50
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Isaiah sketches a model of a skateboard ramp. The model has two surfaces on which to skate, represented by sides AB and AD in the diagram.
Triangle A B D is shown. A perpendicular bisector cuts angle B A D to form triangle A B C. Triangle A B C has angle measures 45, 45, and 90 degrees. Triangle A C D has angle measures 60, 30, and 90 degrees.
The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?
2 StartRoot 2 EndRoot in.
2 StartRoot 3 EndRoot in.
4 StartRoot 2 EndRoot in.
4 StartRoot 3 EndRoot in.
The length of the other skating surface AD of the ramp is 4√2 inches
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule shows the relationship between the sides and angles of a triangle.
Using sine rule:
AB / sinD = AD / sinB
4/sin(30) = AD / sin(45)
AD = 4√2 inches
The length of the other skating surface AD of the ramp is 4√2 inches
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(C.) 4√2
________
I got it wrong, the correct answer was revealed <3
HELP please, last question!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Fig. D is correct[tex]\textsf{ \underline{\underline{Explanation } }:}[/tex]
" when rays parallel to optical axis/ principal axis fall on a concave mirror it passes through focus of mirror after reflection "
[tex] \qquad \large \sf {Conclusion} : [/tex]
Fig. D is correctHaving trouble question is in attachment
Answer:
[tex]x=\frac{35}{9} .[/tex]
Step-by-step explanation:
[tex](3\sqrt{3})^{-x+1} =\frac{1}{3}*27^{x-5}\\( \sqrt{3^2*3}) ^{1-x}=\frac{1}{3} *((3)^3)^{x-5}\\(\sqrt{27} )^{1-x}=\frac{1}{3}*3^{3*(x-5)}\\ (\sqrt{3^3})^{1-x} =\frac{1}{3}*3^{3x-15}\\ 3^{\frac{3 }{2}*(1-x)}=\frac{1}{3}*3^{3x-15}\ |*3\\ 3*3^{\frac{3}{2}-\frac{3}{2}x}=3^{3x-15}\\ 3^{1+1,5-1,5}=3^{3x-15}\\ 3^{2,5-1,5x}=3^{3x-15}\ \ \ \ \Rightarrow\\2,5-1,5x=3x-15\\4,5x =17,5\ |*2\\9x=35\ |:9\\x=\frac{35}{9}.[/tex]
Determine the intercepts of the line.
Do not round your answers.
-4x + 7y = 3
The x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively
How to determine the intercepts of a lineThe y-intercept is the point where the value of x is zero while the x-intercept is the point where the value of y is zero
Given the function below;
-4x + 7y = 3
For the x-intercept
-4x = 3
x = -3/4
The x-intercept is (-3/4, 0)
For the y-intercept
7y = 3
y = 3/7
The y-intercept is (0, 7/3)
Hence the x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively
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Devin Gallagher purchased home entertainment equipment for $4,020.19 using the store's credit plan. He made
a 20% down payment.
Answer:
The answer will be $3216.152
Step-by-step explanation:
If you do the 20% of $4020.19 then the answer will came $804.038 and then subtract the result from $4020.19 then it will came $3216.152 and it is the result only.
here is the histogram of a data distribution. all class widths are 1. which of the following is the closest to the median of this distribution
The value of the median of the distribution is closest to 5.
What is the median?
A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The median is the number at the center of a dataset when the dataset is arranged in either ascending or descending order.
The numbers arranged in ascending order is : 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9
Median = 5
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Answer:
Step-by-step explanation:
A quarter of farmland is too rought to use if two fifth is kept for poultry farms and this leaves 221 areas for planting cash crop.what is the area of farm too rough to use
The area of the farm that is too rough to use is 157.86
What is the area?An object's area is how much space it takes up in two dimensions. In other terms, it's the measurement of the number of unit squares that are completely around the surface of a closed shape.
Let the total area of the farm be x.
Area of the farm, too rough to use=x/4
Area of farm kept for poultry farms=2x/5
Remaining Area=221
Thus,
[tex]x-(\frac{x}{4}+\frac{2}{5}x)=221[/tex]
[tex]\\ x-\frac{13}{20}x=221\\[/tex]
[tex]\frac{7}{20}x=221\\[/tex]
x=631.43
Area of the farm too rough to use= 631.43/4
=157.86
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x =x=x, equals
^\circ
∘
degrees
Step-by-step explanation:
x = 145°
we don't even need the upper parallel line with the 35° angle.
it is simply based on the fact that the angles on both sides of 2 intersecting lines have to be the same (just left-right mirrored).
What type of reaction is HCl + AgNO3?
Answer:
Double-displacement reaction
Step-by-step explanation:
In double-displacement reaction, aka. double-replacement reaction, the cation of one compound is swapped with the cation of another. They have the general structure:
AB + CD ---> AD + CB
In this case, the silver cation (Ag⁺) from AgNO₃ is swapped with the hydrogen cation (H⁺) of HCl.
The complete balanced equation is:
HCl + AgNO₃ ---> AgCl + HNO₃
y ( x + w ) = c ( x + z )
The formula for x in terms of other terms in the equation is; x = (cz-yw)/(y-c).
What is the formular for x in term of other terms in the equation?According to the task content, it follows that the variable X is to be made the subject of the formula;
Hence, it follows that;
y ( x + w ) = c ( x + z )
yx +yw = cx +cz
x(y-c) = (cz-yw)
x = (cz-yw)/(y-c)
Remarks: The complete question requires that x be made the subject of the formula.
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Paladin furnishings generated $4 million in sales during 2021, and its year end total assets were $3.2 million. also, at year end 2021 current liabilities were $500,000, consisting of $200,000 of notes payable, $200,000 of accounts payable, and $100,000 of accrued liabilities. looking ahead to 2022 the company estimates taht its assets must increase by $.80 for every $1.00 increase in sales. paladin's profit margin is 3% and its retention ratio is 50%. how large of a sales increase can the company achieve without having to raise funds externally?
Without having to raise funds externally sales could increase by $84,507.04.
Given that $4 million sales in 2021 and in end of the year total assets are $3.2, current liabilities are $500,000, payable notes are $200,000, accounts payable is $200,000 and accrued liabilities are $100,000 and in 2022 assets must increase by $.80 for every $1.00 increase in sales.
The amount of sales increase that the company can achieve without having to raise funds externally is calculated by multiplying the current year sales with the self-supporting growth rate.
Current Year Sales = $4,000,000
Profit Margin = 3.00%
Dividend Payout Ratio = 50%
Therefore, the Retention Ratio = 50%
Total Spontaneous Liabilities is, $200,000 + $100,000=$300,000
Last Year Total Assets = $3,200,000
Therefore, the Self-supporting Growth Rate=Addition to Retained Earnings÷[Total Assets–Total Spontaneous Liabilities-Addition to Retained Earnings]
= [Last year sales×Profit Margin×(1-Dividend Payout Ratio)]÷[Total Assets-Total Spontaneous Liabilities-Addition to Retained Earnings]
= [$4,000,000×0.03×(1–0.50)]÷[$3,200,000-$300,000–{[$4,000,000×0.04×(1–0.050)}]
= $60,000÷[$3,200,000-$300,000-$60,000]
= $80,000÷$2,840,000
= 0.02112676 or 2.112676%
Therefore, the increase in sales that the company can achieve without having to raise funds externally = Last Year Sales×Self-supporting Growth Rate
= $4,000,000×2.112676%
= $84,507.04
Hence, the Increase in Sales so the company achieve without having to raise funds externally $84,507.04”
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Please help! Which of the following is a solution to the system of two equations y = 3x - 7 and 4x - 5y = -20?
a.) (5,8)
b.) (10,12)
c.) 2,-1)
d.) 9,20)
Answer:
a
Step-by-step explanation:
y = 3x - 7 → (1)
4x - 5y = - 20 → (2)
substitute y = 3x - 7 into (2)
4x - 5(3x - 7) = - 20
4x - 15x + 35 = - 20
- 11x + 35 = - 20 ( subtract 35 from both sides )
- 11x = - 55 ( divide both sides by - 11 )
x = 5
substitute x = 5 into (1)
y = 3(5) - 7 = 15 - 7 = 8
solution is (5, 8 )
Please help ill give whoever answers the best the brainliest answer :0
Answer:
The bottom graph
Step-by-step explanation:
It shows that the kid starts 4 meters away and slowly decreases the distance for 8 seconds, pauses for 3, and moves back for 4.
Answer:
the 4th answer option
Step-by-step explanation:
the first one is looking good too, but the difference is to start at 4 meters away.
and the first graph starts at 9 meets away.
so, it is the 4th graph :
starting 4 meters away the person is coming slowly closer and closer for 8 seconds, then stands still for 3 seconds, and then walks away quickly for 4 seconds.
remember, the passing time is on the x-axis moving to the right (bigger and bigger numbers).
while the distance to the person is on the y-axis. and that value can get bigger and smaller.
A cat gave birth to 11 calico kittens and 16 non-calico kittens. What is the ratio of calico kittens to non-calico kittens?
Answer:
11:16
Step-by-step explanation:
Type the equation for the graph below
Answer:
y = sin3x
Step-by-step explanation:
the equation is of the form y = sinbx
the period of the sine wave is
period = [tex]\frac{2\pi }{b}[/tex] ( b is the coefficient of x )
here period = [tex]\frac{\pi }{3}[/tex] × 2 = [tex]\frac{2\pi }{3}[/tex] , then
[tex]\frac{2\pi }{3}[/tex] = [tex]\frac{2\pi }{b}[/tex] ⇒ b = 3
y = sin3x ← equation of graph
Graph the equation y=−x 2 −8x−7 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
The graph of the given quadratic function is shown below
Graph of Quadratic equationsFrom the question, we are to graph the given quadratic function.
The given quadratic equation is
y = −x² −8x −7
The graph of the given quadratic function is shown below
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The final exam test scores were: 62, 66, 71, 75, 75, 78, 81, 83, 84, 85, 85, 87, 89, 89, 91, 92, 93, 94, 95, 99. Find the percentile rank for a score of 85 on this test.
Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.
What is the percentile of a measure?When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.
In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:
p = 10/20 = 0.5 x 100% = 50th percentile.
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Joy read 1/3 of the book in the morning and she reads some more at night by the end of the day she still had 2/5 of the book to read how much of the book did joy read at night?
Answer:
4/15
Step-by-step explanation:
Lets find a common denominator in order to find the total amount. There is a common denominator of 15 among 3 and 5. Therefore we will convert the fraction so they have the same denominator.
1/3 > 5/15
2/5 > 6/15
If Joy had read 5/15 of the book before reading at night, she already had the progress of being at 10/15 way through the book. At the end of the day, Joy had only 6/15 left of the book. To find the remainder, we subtract 10-6=4. This helps find the answer that Joy only read 4/15 of the book towards the end of the day.
In the diagram below, AB and TC are tangent to 0. Which equation could be solved to find x, the measure of AC?
A.1/2(238+58)=x
B.1/2(238-58)=x
C.1/2(238+x)=58
D.1/2(238-x)=58
The equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
Circle theoremThe given diagram shows two intersecting lines tangential to a circle at points A and C.
Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.
Mathematically;
<B = 1/2(arcADC - arcAC)
58 = 1/2(238 -x)
Hence the equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
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You enter a room. 2 dogs, 4 horses, 1 giraffe and a duck lie on the bed. 3 hens fly over a chair. How many legs are there on the floor
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
Two sides of a 90 degree triangle measure 6cm and 8cm, what is the length of the
hypotenuse?
10cm
3.7cm
100cm
14cm
24cm
please help!!!!!
Answer:
10 cm
Step-by-step explanation:
Hyp = [tex]\sqrt{6^{2}+8^{2} } =\sqrt{36+64} =\sqrt{100} =10[/tex]
Hope this helps
A school survey asked students which candidate they supported for class president. The survey data are shown in the relative frequency table. What percentage of females polled supported Martinez?
A:30%
B:58%
C: about 56%
D:about 54%
Answer:
About 56%
Step-by-step explanation:
Jane wants to buys some lollipops. If she buys 2 lollipops, she will have 3 dollars left. If she wants to buy 3 lollipops, she will need 2 more dollars. Jane has ___ dollars.
Since Jane wants to buys some lollipops, Jane has $13 dollars.
To answer the question, we need to solve simultaneous equations
What are simultaneous equations?Simultaneous equations are pairs of equations that contain two unknowns
How to calculate how much Jane has using simultaneous equationsLet
x = price per lollipop and y = total amount Jane hasWe know that If she buys 2 lollipops, she will have 3 dollars left, so we have that
y - 2x = 3 (1)
Also, If she wants to buy 3 lollipops, she will need 2 more dollars. So, we have that
y + 2 = 3x (2)
The required simultaneous equationsSo, the required simultaneous equations are
y - 2x = 3 (1)
y + 2 = 3x (2)
From (1), x = (y - 3)/2
Substituting x into (2), we have
y + 2 = 3x (2)
y + 2 = 3(y - 3)/2
2(y + 2) = 3(y - 3)
2y + 4 = 3y - 9
2y - 3y = -9 - 4
-y = -13
y = -13/-1
y = 13
So, Jane has $13 dollars.
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Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)
Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)
The loan amount is given as $76521
We first have to calculate the total amount of tuition
6970 x 4 + 11320 x 4
= 73160
a. How to solve for the new loan amount[tex]73160 (1+\frac{\frac{4.5}{100} }{12} )^1^2[/tex]
= 73160 x (1 + 0.00375)¹²
= 76520.95
Hence the new loan amount after agrace period of 1 year = $76521
b. PV = $76521
i = [tex]\frac{4.5/100}{12}[/tex]
= 0.00375
t = 10 years
[tex]PMT[\frac{1-(1+0.00375)^-^1^2^0}{0.0375} ]= 76521[/tex]
pmt = 793. 05
The monthly payment is $793. 05.
In ten years the total payment is 793.05 x 10 x 12
= 95166
Difference = 95166 - 76521
= $18645
In ten years her ,monthly payment on the loan would be $18645.
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end behavior of f(x)= 10/x^2-7x-30
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
What is the end behavior of a rational function
The end behavior of a rational functions is the horizontal asymptote of the rational function when x tends to ± ∞. Then, we find the end behavior by applying limits:
[tex]\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}[/tex]
[tex]\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}[/tex]
[tex]\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}[/tex]
[tex]\lim_{x \to \pm \infty} 0[/tex]
0
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
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KM=
What is the measure of KM?
Help please
Fill in the blank. Someone who works 40 hours per week for 50 weeks per year, with two weeks off, would work around __________________hours per year.
Answer:
about 1920
step by step explanation:
40×50weeks=2000hours per year.
40×2weeks(the weeks off) = 80
2000-80= 1920hours per year
A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems. Students are not expected to complete all of the questions, but are graded on the number they are able to get correct in the time limit. What component of mathematics fluency is most likely the goal of this type of assessment
The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
GIven,
A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems.
The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
The school district is assessing the rate because they are seeing how many questions students can answer in a given time frame.
Hence, The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
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Let theta be an angle in quadrant 2 such that cos theta =-3/4. Find the exact values of csc theta and cot theta.
Step-by-step explanation:
Since [tex]cos(\theta) = -\frac{3}{4}[/tex] we can get some information from this. First of all [tex]cos(\theta)[/tex] is defined as [tex]\frac{adjacent}{hypotenuse}[/tex]. So the adjacent side is 3 and the hypotenuse is 4. Using this we can find the opposite side to find [tex]sin(\theta)[/tex] to calculate csc and cot of theta. So using the Pythagorean Theorem we can solve for the missing side. Also I forget to mention we have to calculate the sign of the adjacent side and the hypotenuse. Since you're given that the angle is in quadrant 2, that means the x-value is going to be negative, and the y-value is going to be negative. And the x really represents the adjacent side and the y represents the opposite. So the adjacent side is what's negative. and the opposite is positive
Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
[tex](-3)^2 + b^2 = 4^2[/tex]
[tex]9 + b^2 = 16[/tex]
[tex]b^2 = 7[/tex]
[tex]b = \sqrt{7}[/tex]
So now we can calculate [tex]sin(\theta)[/tex].
[tex]sin(\theta) = \frac{\sqrt{7}}{4}[/tex]
Now to calculate the exact value of csc you simply take the inverse. This gives you [tex]csc(\theta)=\frac{4}{\sqrt{7}}[/tex]. Multiplying both sides by sqrt(7) to rational the denominator gives you [tex]\frac{4\sqrt7}{7}[/tex].
Now to calculate cot(theta) you find the inverse of tan. Tan is defined as [tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]. So all you do is take the inverse which is [tex]cot(\theta) = \frac{cos(\theta)}{sin(\theta)}[/tex].
Plug values in
[tex]cot(\theta) = \frac{-\frac{3}{4}}{\frac{4\sqrt{7}}{7}}[/tex]
Keep, change, flip
[tex]-\frac{3}{4} * \frac{7}{4\sqrt7}[/tex]
Multiply:
[tex]-\frac{21}{16\sqrt7}[/tex]
Multiply both sides by sqrt(7)
[tex]-\frac{21\sqrt7}{112}[/tex]
This is the value of cot(theta)
Geometric probability
Answer:
71.4%
Step-by-step explanation:
7+3+8+3=21 total fish
7+8=15 healthy fish
15÷21=0.7142=71.4%