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The equation of the line perpendicular to y = - (2 / 3) · x and the point (4, - 8) is y = (3 / 2) · x - 14.
How to determine the equation of a perpendicular line
Mathematically speaking, lines are represented by equations of the form y = m · x + b, where m and b are the slope and the intercept of the line. Additionally, two lines are perpendicular to each if the product of their slopes is equal to - 1.
First, we determine the slope of the perpendicular line:
m' = - 1 / m
m' = - 1 / (- 2 / 3)
m' = 3 / 2
Second, the intercept of the perpendicular line is:
b = y - m · x
b = - 8 - (3 / 2) · 4
b = - 8 - 6
b = - 14
Then, the equation of the perpendicular line is y = (3 / 2) · x - 14.
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Related Questions
HELP PLSSSSSSSSSSSSS
Answers
Answer:
the volume of the toy house is 66cm3
If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 4 times x plus 8 end quantity which of the following could accurately represent f and g?
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The representation of the composite functions f(x) and g(x) are f(x) =√x and g(x) = 4x + 8
How to determine the possible equations of the composite functions f(x) and g(x)From the question, we have the following parameters
(fg)(x) = h(x)
Such that
h(x) = √4x + 8
The given parameter implies that
(fg)(x) =√4x + 8
Let g(x) = 4x + 8
Substitute g(x) for 4x + 8 in the above equation (fg)(x) =√4x + 8
So, we have
(fg)(x) =√g(x)
Substitute g(x) for x in the above equation (fg)(x) =√g(x)
f(x) =√x
This means that
f(x) =√x and g(x) = 4x + 8
Hence, the possible equations are f(x) =√x and g(x) = 4x + 8
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Suppose a person's score on a personality test that is normally distributed with a mean of 50 and a standard deviation of 10. If you
were to pick a person completely at random, what is the probability that you would pick someone with a score on this test higher than 70?
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Answer:
2.28%
Step-by-step explanation:
P(X > 70) = 1 - Ф((70 - 50)/10) = 0.0228 = 2.28%
Which expressions can be used to find m∠ABC? Select two options.
cos−1(StartFraction 9.8 Over 6.3 EndFraction)
cos−1StartFraction 6.3 Over 9.8 EndFraction)
cos−1(StartFraction 7.5 Over 9.8 EndFraction)
sin−1(StartFraction 9.8 Over 7.5 EndFraction)
sin−1(StartFraction 7.5 Over 9.8 EndFraction)
]
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The expressions which can be used to find m∠ABC and from the task content are;
cos−¹(StartFraction 6.3 Over 9.8 EndFraction).sin−¹(StartFraction 7.5 Over 9.8 EndFraction).Which expressions can be used to find m∠ABC among the answers choices?It follows from the task content that the expressions which can be used to find m∠ABC are to be identified among the answer choices.
Since, it follows from trigonometric ratios that;
Sin theta = opposite/hypothenuse
Cos theta = adjacent/hypothenuse
It therefore follows that;
Cos(m∠ABC) = 6.3/9.8Sin(m∠ABC) = 7.5/9.8Therefore, the measure of angle ABC can be determined using any of the formulas above;
m∠ABC = cos-¹(6.3/9.8)m∠ABC = sin-¹(7.5/9.8)Therefore the two expressions which can be used to find m∠ABC are;
cos−¹(StartFraction 6.3 Over 9.8 EndFraction).sin−¹(StartFraction 7.5 Over 9.8 EndFraction).Read more on trigonometric ratios;
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Answer: the answer is B [tex]cos^{-1}(\frac{6.3}{9.8}) sin^{-1}(\frac{7.5}{9.8})[/tex]
Step-by-step explanation: it will be show below.
This is a Statistics question. Please Help
Answers
Considering the normally distributed variable, the proportion/percentage are given as follows:
a) Proportion of serves faster than 121 mph: 0.16.
b) Percentage of serves between 109 and 133 mph: 84%.
Normal DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure represented by X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.As stated in the problem, the mean and the standard deviation of the serve speeds are given as follows:
[tex]\mu = 115, \sigma = 6[/tex]
The proportion of serves faster than 121 mph is one subtracted by the p-value of Z when X = 121, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (121 - 115)/6
Z = 1
Z = 1 has a p-value of 0.8413.
1 - 0.8413 = 0.1587, which is the desired proportion.
The proportion of serve speeds between 109 and 133 mph is the p-value of Z when X = 133 subtracted by the p-value of Z when X = 109, hence:
X = 133:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (133 - 115)/6
Z = 3
Z = 3 has a p-value of 0.9987.
X = 109:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (109 - 115)/6
Z = -1
Z = -1 has a p-value of 0.1587.
0.9987 - 0.1587 = 0.84, hence the percentage is of 84%.
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Suzanne's salary grew from $40,000 in 2000 to $56,000 in 2021. during the same time period, Mike's salary grew form $38,000 to $53,000. Whose salary grew more in absolute change? In percentage change?
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Absolute change (AC) refers to the simple difference in the indicator over two periods. that is
[tex]\begin{gathered} \text{AC (Suzanne)=56000-40000} \\ \text{AC (Suzanne)=16000} \end{gathered}[/tex]and, for Mike:
[tex]\begin{gathered} \text{AC (Mike)=53000-3}8000 \\ \text{AC (Mike)=1}5000 \end{gathered}[/tex]Whose salary grew more in absolute change? Suzanne's salary.
The relative change (RC) express the absolute change as a pencentage of the value of the indicator in the earlier period:
[tex]RC=\frac{value\text{ 2nd period - value 1st period}}{\text{value 1st period}}\times100[/tex]For Suzanne, we have
[tex]\begin{gathered} RC(\text{Suzzane)}=\frac{56000-40000}{56000}\cdot100 \\ RC(\text{Suzzane)}=\frac{16000}{56000}\cdot100 \\ RC(\text{Suzzane)}=0.286\cdot100 \\ RC(\text{Suzzane)}=28.6 \end{gathered}[/tex]and for Mike, we have
[tex]\begin{gathered} RC(\text{Mike)}=\frac{53000-28000}{53000}\cdot100 \\ RC(\text{Mike)}=\frac{15000}{53000}\cdot100 \\ RC(\text{Mike)}=0.283\cdot100 \\ RC(\text{Mike)}=28.3 \end{gathered}[/tex]In percentage change? For Suzanne is 28.6% and for Mike 28.3%
Answer: Mike's salary grew from $ 38,000 to $ 53,000.
Step-by-step explanation:
URGENT Please help!!!!!!
Divide 6.1 x 1020 by 3.2 x 105. Express your answer in scientific notation.
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The value of the division of the expression will be; 19.52 x 10^{25}.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10.
Scientific notations have some of the profits; Better readability due to compact representation that value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
Given the expression as 6.1 x [tex]10^{20}[/tex] by 3.2 x 10⁵
We have to divide the expression
( 6.1 x [tex]10^{20}[/tex] ) / (3.2 x 10⁵)
= 19.52 x [tex]10^{20 + 5}[/tex]
= 19.52 x [tex]10^{25}[/tex]
Therefore, the value of the division of the expression will be; 19.52 x [tex]10^{25}[/tex].
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Write a cosine function that has an amplitude of 3, a midline of 5 and a period of 3/4. .
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A cosine function is said to have an amplitude of 3, a midline of 5, and a period of 3/4.
It is required to write the cosine function.
Recall that the standard form of a cosine function is:
[tex]y=a\cos(bx+c)+d[/tex]Where a is the amplitude, 2π/b is the period, c is the horizontal shift, and d is the midline or vertical shift.
Equate the given period to 2π/b and solve for b:
[tex]\begin{gathered} \frac{2\pi}{b}=\frac{3}{4} \\ \Rightarrow3b=8\pi \\ \Rightarrow\frac{3b}{3}=\frac{8\pi}{3} \\ \Rightarrow b=\frac{8\pi}{3} \end{gathered}[/tex]Hence, substitute a=3, b=8π/3, and d=5 into the standard form of the cosine function:
[tex]y=3\cos(\frac{8\pi}{3}x+c)+5[/tex]Since it is not given that the cosine function has a horizontal shift, substitute c=0 to get the required function:
[tex]y=3\cos(\frac{8\pi}{3}x)+5[/tex]The function is y=3cos((8π/3) x)+5.
A pizza is taken out of an oven and placed on a counter. The temperature, T, in degrees Fahrenheit, of the pizza after m minutes is modeled by the function Which graph represents the model?
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The graph of the exponential function that represents the temperature of the pizza after m minutes is given at the end of the answer.
Which model represents the temperature of the pizza?The model that represents the temperature of the pizza m minutes after it is taken out of the oven and placed on the counter is given by:
[tex]T(m) = 72 + 200e^{-0.0445m}[/tex]
The number e is the Euler number, and the function is the exponential function translated 72 units up, hence the minimum value that the pizza obtains is of 72 degrees Fahrenheit.
Due to the negative exponent, the temperature is decaying over time, but it never gets less than 72 ºF.
The time cannot be negative, hence the domain of the graph is given as follows:
m ≥ 0.
Then, considering this, the graph of the function is given at the end of the answer.
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Answer:
Step-by-step explanation:
a
5
6
Z
1
23
4.
75°
7
y
13 16
14 15
9 12
11
10
x
w
What is mZ2?
What is m1?
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Answer: [tex]m\angle 2=75^{\circ}, m\angle 1=105^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem, [tex]m\angle 2=75^{\circ}[/tex].
Using linear pairs, [tex]m\angle 1=105^{\circ}[/tex].
contains (1,1) and has a shape of f(x)=2x^2 vertex is on the y axis
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ANSWER
| x=0
Step-by-step explanation:
f(x) = 2x²
Rewrite the function by completing the
square
f(x)
= 2x²
Find the symmetry
X = 0
112Calculate and simplify as much as possible theperimeter and area of the largest figure. All four-sided figures are rectangles.9Perimeter =рArea =
Answers
SOLUTION:
Step 1:
In this question, we are meant to solve the following:
Step 2:
The perimeter of the largest figure is:
[tex]\begin{gathered} Length\text{ + Width + Length + Width} \\ =\text{ ( 12 + p ) + q + ( 12 + p ) + q} \\ =\text{ 24 + 2p + 2q} \\ =\text{ 24 + 2 ( p + q)} \end{gathered}[/tex]On the other hand, the area of the largest figure is:
[tex]\begin{gathered} \text{Length x Width} \\ =\text{ ( 12 + p ) x q} \\ =\text{ ( 12 + p )q} \end{gathered}[/tex]How do I write this in function notation part b
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
Total rice bought is 75kg
Each week, he used 4.5kg, this means in w weeks, he will use:
[tex]4.5\times w=4.5w[/tex]STEP 2: Get the remaining kilograms of rice after w weeks
This will be gotten by using the function below:
[tex]75-4.5w[/tex]Hence, the function will be gotten as:
[tex]r(w)=75-4.5w[/tex]Social Security is 6.2% of the first $97,500. Medicare is 1.45% of all income.
The state tax is 2% of gross pay, and the local tax is 1.5% of gross pay.
7.) Orville Staples is a painter who earns $30,000.00 a year. He is single and claims 3 allowances. Weekly deductions include $34.50 for medical insurance and union dues of $15.00.
Please calculate Federal Income Tax, Social Security Tax, Medicare Tax, State Tax & Local tax. Please show work.
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The deductions for the taxes are given as follows:
Federal Income Tax: $4,626.27.Social Security Tax: $1,860.Medicare Tax: $435.State Tax: $600.Local Tax: $450.What are his deductions?To calculate the taxes, we have to consider his gross pay, which is given in the text as follows:
Gross pay = $30,000.
The Federal Income Tax for people in his income range is of $1,027.50 plus 12% of the amount over $10,275, hence:
Federal Income Tax = 1027.50 + 0.12 x (30000 - 10.275) = $4,626.27.
The Social Security tax is of 6.2% of his salary, hence:
Social Security Tax = 0.062 x 30000 = $1,860.
The Medicare tax is of 1.45% of his salary, hence:
Medicare Tax = 0.0145 x 30000 = $435.
The State Tax is of 2% os his salary, hence:
State Tax = 0.02 x 30000 = $600.
The Local Tax is of 1.5% of his salary, hence:
Local Tax = 0.015 x 30000 = $450.
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How many ounces of yogurt does the carton hold? (Hint: 1 ounce equals 1.805 in.³) round to the nearest tenth as needed
Answers
The carton holds 8.9 ounces of yoghurt
Explanation:The upper diameter, D = 2 in
R = D/2
R = 2/2
The upper radius, R = 1 inch
[tex]\begin{gathered} \text{The lower diameter, d= 2}\frac{7}{16}\text{ in = }2.4375 \\ \text{The lower radius, r = }\frac{d}{2}=\text{ }\frac{2.4375}{2}in\text{ = }1.22\text{ in} \end{gathered}[/tex]The height, h = 3 in
The volume of the cone frustrum is:
[tex]\begin{gathered} V=\frac{1}{3}\pi h(R^2+r^2+Rr) \\ V=\frac{1}{3}\times3.142\times3(1^2+1.22^2_{}+1.22(1)) \\ V=3.142(3.7084)) \\ V=11.65in^3 \end{gathered}[/tex]1.805 in.³ = 1 ounce
11.65in.³ = 11.65/1.805 ounce
11.65in.³ = 6.5 ounces
The carton holds 6.5 ounces of yoghurt
A client of Susan's has asked her to create a new wood floor for his living room. The design will be created by laying wood strips in different directions, as shown on the coordinate grid. Determine whether Quadrilateral can best be described as a trapezoid, a rhombus, a rectangle, or a square. Explain your reasoning.
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Answer: Where's the graph
Step-by-step explanation:
The area of a large plantation is eleven and seven hundredths kilometers. The length of the plantation is one tenth kilometers. How many kilometers is the width of the plantations?
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The width of the plantation is 110. 7 kilometers
How to determine the width of the plantationIt is important to note that the formula for calculating the area of a rectangle is expressed as;
Area, A = lw
Where;
A represents the area of the rectanglel is the length of the rectanglew is the width the rectangleGiven that;
The value of the area of the large plantation is eleven and seven hundredths kilometers.
This is expressed as;
Area = 11. 07 kilometers
The value of the length is one tenth kilometers.
This is expressed as;
Length = 1/10 kilometers = 0. 1 kilometers
Now, substitute the values into the formula to determine the width
11. 07 = 0. 1w
Divide both sides by the coefficient of w, w have;
11.07/0.1 = 0.1w/0.1
Find the quotient
w = 110. 7 kilometers
Hence, the value is 110. 7 kilometers
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All of the triangles below have a base to height ratio of 5:2. Label the missing dimensions
Answers
ANSWER:
1. b = 5
2. h = 6
3. b = 30
STEP-BY-STEP EXPLANATION:
We know the ratio between height and base.
By means of the following proportions we can determine the missing dimensions in each case:
[tex]\begin{gathered} \frac{5}{2}=\frac{b}{h} \\ \\ \text{ 1st triangle} \\ \\ \frac{5}{2}=\frac{b}{2}\rightarrow b=5 \\ \\ \text{ 2nd triangle} \\ \\ \frac{5}{2}=\frac{15}{h}\rightarrow h=\frac{15}{5}\cdot2\rightarrow h=6 \\ \\ \text{ 3rd triangle} \\ \\ \frac{5}{2}=\frac{b}{12}\rightarrow b=12\cdot\frac{5}{2}\rightarrow b=30 \end{gathered}[/tex]Can someone please help me with this (there is a part two)
Answers
Part A)
Let x be a number of horses that Sunshine Acre Farm can support. Since each horse needs 1.75 acres of pasture, and the farm has at most 35 acres of pasture available, then we can set the following inequality:
[tex]1.75x\le35.[/tex]Answer Part A)
[tex]1.75x\le35.[/tex]Finding a difference quotient for a linear or quadratic function
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Given the function
[tex]f(x)=-2x^2-3x+6[/tex]We are to look for the difference quotient:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Get f(x + h)
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-3(x+h)+6 \\ f(x+h)=-2(x^2+2xh+h^2)-3x-3h+6 \\ f(x+h)=-2x^2-4xh-2h^2-3x-3h+6 \\ \end{gathered}[/tex]Given f(x) expressed as:
[tex]f(x)=-2x^2-3x+6[/tex]Substitute both functions into the difference quotient;
[tex]\begin{gathered} \frac{-2x^2-4xh-2h^2-3x-3h+6-(-2x^2-3x+6)}{h} \\ \frac{-\cancel{2x^2}-4xh-2h^2-\cancel{3x}-3h+\cancel{6}+\cancel{2x^2}+\cancel{3x}-\cancel{6}}{h} \\ \frac{-4xh-2h^2-3h}{h} \end{gathered}[/tex]Factor out "h" from the result to have
[tex]\begin{gathered} \frac{\cancel{h}(-4x-2h-3)}{\cancel{h}} \\ -4x-2h-3 \end{gathered}[/tex]This shows that the simplified form of the expression is -4x - 2h - 3
Simplify −3(x+4)+5x Write your answer in factored form
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Answer:-3x - 12 + 5x
Step-by-step explanation:
jerry had 3409 pieces of marble he swallowed 1290 then is mom brought his 3456 more. How much does jerry have?
Answers
Answer: 5575 Marbles
Step-by-step explanation:
This can be solved simply by subtracting and adding.
3409-1290=2119
2119+3456=5575
I need help on what the question is asking. Can you help me solve it step by step?
Answers
Given:
The total number of tamiliies is N = 30.
The objective is to find the mean number of gallons of milk consumed by 30 families.
Explanation:
The total number of milk consumed consumed by 30 families can be calculated as,
[tex]\begin{gathered} T=(8\times3)+(9\times2)+(13\times5) \\ =24+18+65 \\ =107 \end{gathered}[/tex]To find mean:
The mean number of gallons of milk can be calculated as,
[tex]M=\frac{T}{N}[/tex]On plugging the obtained values in the above equation,
[tex]\begin{gathered} M=\frac{107}{30} \\ =3.56666\ldots\text{.} \\ =3.6 \end{gathered}[/tex]Hence, the mean number of milk consumed by 30 families is 3.6 gallons.
on the unit circle., in standard position an angle of which measure is coterminal with an angle that measures 3pi/5 radians
Answers
Coterminal angles are angles with the same terminal sides.
[tex]\theta\rightarrow\theta+2\pi\rightarrow\theta-2\pi[/tex]For the given angle, the coterminal angles are;
[tex]\begin{gathered} \theta=\frac{3\pi}{5} \\ \theta+2\pi=\frac{3\pi}{5}+2\pi=\frac{3\pi}{5}+\frac{10\pi}{5}=\frac{13\pi}{5} \\ \theta-2\pi=\frac{3\pi}{5}-2\pi=\frac{3\pi}{5}-\frac{10\pi}{5}=-\frac{7\pi}{5} \\ \theta+2(2\pi)=\frac{3\pi}{5}+4\pi=\frac{3\pi}{5}+\frac{20\pi}{5}=\frac{23\pi}{5} \end{gathered}[/tex]From the given answer choices, the coterminal angle is;
[tex]\frac{23\pi}{5}[/tex]help help help help help help help
Answers
The total capacity of her tank would be; 21 gallons.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Leslie makes a stop at a gas station. she put 14 gallons into her tank. if the tank is now 2/3 full.
Let c be the total capacity of the tank.
Then, we can find the capacity of her tank;
c x 2/3 = 14
Cross multiplication;
c = 14 x 3/2
c = 7 x 3
c =21
Hence, the total capacity of her tank would be; 21 gallons.
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if h(x, y) moves 12 units to the left and 4 units up. what is the rule that describes this translation .
Answers
Answer:
(x,y) -> (x-12, y+4)
Step-by-step explanation:
(x,y) -> (x-12, y+4)
Which equation shows the inverse property of multiplication?
Answers
Answer:
What are the outstanding traditional Chinese culture?
1. Drama is a general term for stage performing arts that achieve narrative purposes in the form of language, movement, dance, music and puppets.
2. Chinese painting, originated in the Han Dynasty, mainly refers to the scroll painting painted on silk, rice paper and silk and mounted.
3, Calligraphy, calligraphy is a unique form of artistic expression of the beauty of Chinese characters in China and the surrounding countries and regions that have been deeply influenced by Chinese culture.
4, Shadow Puppets, also known as "Shadow Puppets" or "lantern Puppets", is a kind of folk drama made of animal skins or cardboard silhouettes to perform stories.
5. Pingju, which is popular in northern China, is one of the traditional operas of the Han nationality and one of the most popular operas among the people. It ranks among the five kinds of operas in China.
Please Answer Fast
Write down the next two terms in these quadratic sequences:
9, 13, 19, 27, ___, ___
-5, 0, 9, 22, ___, ___
Answers
The next two terms of the first quadratic sequences are 37 and 49.
The next two terms of the second quadratic sequences are 39 and 60.
What are the next two terms?A quadratic sequence is a sequence in mathematics where the second difference between consecutive terms in the sequence is the same
The first step is to determine the relationship between the terms in the quadratic sequence.
The difference between 9 and 13 = 13 - 9 = 4
The difference between 19 and 13 = 19 - 13 = 6
The difference between 27 and 19 : 27 - 19 = 8
It can be seen that the first difference between the terms in the sequence quadratic sequence increases by 2.
The difference between the fourth term and the fifth term would be 8 + 2 = 10
Fifth term = 27 + 10 = 37
The difference between fifth term and the sixth term would be 10 + 2 = 12
37 + 12 =49
The first step is to determine the relationship between the terms in the quadratic sequence.
The difference between 0 and -5 : 0 - -5 = 5
The difference between 0 and 9 = 9 - 0 = 9
The difference between 9 and 22 = 22 - 9 = 13
Based on the first difference between the consecutive terms in the digit, it can be seen that the first difference increase by a value of 4.
The difference between the fourth term and the fifth term would be : 13 + 4 = 17
Fifth term = 22 + 17 = 39
The difference between fifth term and the sixth term would be 21 ( 17 + 4)
39 + 21 = 60
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many of these boxes do you need to buy?you need to buy 40 packsExample 2.At a restaurant one day. 60 sandwiches were sold in all, some on rye bread and 28 onwhite bread. The number of sandwiches sold on try bread was twice the number soldthe day before. How many sandwiches on rye bread were sold the day before"?
Answers
rye bread sandwiches + white bread sandwiches = total number of sandwiches
rye bread sandwiches + 28 = 60
rye bread sandwiches = 60 - 28
rye bread sandwiches = 32
This number, 32, is twice the day before, that is, the day before was half of 32 sandwiches, which is 32/2 = 16.
The day before, 16 sandwiches on rye bread were sold.
13) y = 4x - 3 -8x + 6y = 14
Answers
Replacing y in the second equation
[tex]\begin{gathered} -8x+6(4x-3)=14_{} \\ -8x+24x-18=14 \\ 16x=14+18 \\ 16x=32 \\ x=\frac{32}{16} \\ x=2 \end{gathered}[/tex]Then
[tex]\begin{gathered} y=4(2)-3 \\ y=8-3 \\ y=5 \end{gathered}[/tex]Just checking our answer
[tex]-8(2)+6(5)=-16+30=14[/tex]So the correct answer is x=2 and y=5