[SQA Advanced Higher 2019 Q17c(i) Edited]
The first three terms of a sequence are given by
5x+8, 2x + 1, x - 4
-
The sequence is geometric for x = 11. There is a second value for x that also gives a geometric sequence.
For this second sequence, show that x²+bx+c = 0 for b and c which are integers to be found.
For the given equations 5x+8, 2x + 1, x - 4 does not form the geometric sequence as the common ratio is not equal.
What is defined as the geometric sequence?A geometric sequence is a type of sequence in which the ratio of every two consecutive terms is constant. This ratio is referred to as a geometric sequence common ratio. In other words, each term in a geometric sequence is multiplied by a constant, yielding the next term. So a geometric sequence has the form a, ar, ar²..., where 'a' is the initial term and 'r' is the sequence's common ratio. The common ratio may be both positive and negative.For the given sequence;
The first three terms of a sequence are given by;
a = 5x+8,
ar = 2x + 1,
ar² = x - 4
Put the value of x = 11 to check if the sequence forms and GP.
a = 5x11+8 = 63
ar = 2x11 + 1 = 23
ar² = 11 - 4 = 7
Find the common ratio;
ar/ a = ar²/ar
23/ 63 = 7/ 23
But 23/ 63 ≠ 7/ 23
As, the common ratio is not same, it will not form as geometric sequence.
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Just another problem I dont have time for Can someone halp? I will mark brainliest if correct. Theres some decent points as well.
The definition for the linear piecewise function is given as follows:
B.
2x + 2, x ≤ 0.-4/3x + 4, x > 0.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For x to the left of 0, we have a line with intercept of 2, hence:
y = mx + 2.
When x increases by 1, y increases by 2, hence the slope is of m = 2 and:
y = 2x + 2, x ≤ 0.
For x to the right of 0, we have a line with intercept of 4, hence:
y = mx + 4.
When x increases by 3, y decreases by 4, hence the slope is of m = -4/3 and:
y = -4/3x + 4, x > 0.
Hence the definition of the function is given by:
B.
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Solve each equation.
x²-13 x-30=0
After solving, the factors of the equation x²-13x-30=0 are:
(x-15) and (x+2)What exactly is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value for the variable x as x = 7.So,
Given equation: x²-13x-30=0
Then,
x²-13x-30x²-x( - )-30x²-x( 15 - 2 )-30x²-15x+2x-30x(x-15)+2(x-15)Factors are: (x-15) and (x+2)
Therefore, after solving, the factors of the equation x²-13x-30=0 are:
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Use a calculator to find each value. Round your answers to the nearest thousandth.
sec 2.5
A savings account pays 4.62% annual interest, compounded continuously. After approximately how many years will a principal of $ 500 double?
After approximately 16 years, the principal amount of $500 double.
What do we mean by compound interest?Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate multiplied by the number of compound periods multiplied by one. The total initial loan amount is then deducted from the resulting value. The amount of interest added in each compounding period is determined by the interest rate, compounding period, and account balance. The basic formula is as follows: added interest = (interest rate for one period) × (balance at the beginning of the period).So, to find out how many years will a principal of $ 500 double:
Let x be the principal amount.The formula for calculating compound interest is as follows:
A = P(1 + r)^tThe value of r is 0.0462. In the equation, substitute this and x:
2x = x(1 + 0.0462)^t2 = (1.0462)^t (1.0462)^16 = (1.0462)^t t = 16Therefore, after approximately 16 years, the principal amount of $500 double.
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Expand each binomial.
(x²+2 y³)⁶
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x + y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ.
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (x² + 2y³)⁶
By using binomial expansion theorem, we get
(x² + 2y³)⁶ = x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸
(x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸
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Help me, anyone? I'll give brainliest to the most helpful answer
Check the picture below.
now, let's get their length of TZ and TX and thus we'll get their ratio as TX/TZ or TX : TZ
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad X(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TX=\sqrt{(~~4 - (-8)~~)^2 + (~~-1 - (-5)~~)^2} \implies TX=\sqrt{(4 +8)^2 + (-1 +5)^2} \\\\\\ TX=\sqrt{( 12 )^2 + ( 4 )^2} \implies TX=\sqrt{ 144 + 16 } \implies TX=\sqrt{ 160 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad Z(\stackrel{x_2}{7}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TZ=\sqrt{(~~7 - (-8)~~)^2 + (~~0 - (-5)~~)^2} \implies TZ=\sqrt{(7 +8)^2 + (0 +5)^2} \\\\\\ TZ=\sqrt{( 15 )^2 + ( 5 )^2} \implies TZ=\sqrt{ 225 + 25 } \implies TZ=\sqrt{ 250 }[/tex]
[tex]~\dotfill\\\\ TX~~ : ~~TZ\implies \cfrac{TX}{TZ}\implies \cfrac{\stackrel{TX}{\sqrt{160}}}{\underset{TZ}{\sqrt{250}}}\implies \cfrac{\sqrt{4^2\cdot 10}}{\sqrt{5^2\cdot 10}}\implies \cfrac{4~~\begin{matrix} \sqrt{10} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5~~\begin{matrix} \sqrt{10} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies {\LARGE \begin{array}{llll} \cfrac{4}{5} \end{array}}[/tex]
(x-2)²=9 in stanrard form
Answer:
Step-by-step explanation:
Your answer is going to be x²+4x-5=0
Describe a situation that could be represented by |x-4|=10
HELP ASAP!!!111
f(x)= |x|
g(x)=|x| + 1
We can think of gas a translated (shifted) version of f.
Complete the description of the transformation.
Use nonnegative numbers.
To get the function g, shift f ____ by __ units.
From the rules of transformation;
To get the function g, shift f upwards by 1 unit.
What is the transformation of the function?
Transformations simply takes the basic function and transforms it to another function.
The rules of transformation are;
f(x) transformed to f(x) + a means that the function will be moved 'a' units upwards.f(x) transformed to f(x) - a means that the function will be moved 'a' units downwards.f(x) transformed to f(x + a) means that the function will be moved 'a' units to the left.f(x) transformed to f(x - a) means that the function will be moved 'a' units to the rightNow, we want to transform f(x) = |x| into g(x) = |x| + 1
This means from the rules of transformation above, we can say that;
To get the function g, shift f upwards by 1 unit.
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Decide whether the following statements are always, sometimes, or never true.If a and b are rational numbers, then the product of (a+√b) and its conjugate is a rational number.
If a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.
The conjugate of ( a + [tex]\sqrt{b}[/tex] ) is ( a - [tex]\sqrt{b}[/tex] ) .
Product of ( a + [tex]\sqrt{b}[/tex] ) and ( a - [tex]\sqrt{b}[/tex] ) = ( a + [tex]\sqrt{b}[/tex] ) * ( a - [tex]\sqrt{b}[/tex] )
= ( [tex]a^{2}[/tex] ) - a[tex]\sqrt{b}[/tex] + a[tex]\sqrt{b}[/tex] - [ [tex]\sqrt{b} ^{2}[/tex] ]
= ( [tex]a^{2}[/tex]) - b .
The expression ( [tex]a^{2}[/tex]) - b is rational .
Hence , if a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.
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What is the solution of each exponential equation? Check your answer.
b. 5.2³x=400
Solution of exponential equation is , x = 10
What is exponential equation ?In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a is the base of function
x defines expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponential :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^{-x} = \frac{1}{a^x}[/tex]According to given statement,
5.2³ x =400
=> 5.8 x =400
=> 40x = 400
=> x =10
Thus solution for this equation is x =10.
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The complete question is :
What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
b. 5.2³x=400
If the ratios comparing two quantities are not equivalent, the two quantities are nonproportional.
True
False
please help me the question is in the picture
Answer: C, 21
Step-by-step explanation:
Which pair of words make this sentence FALSE?
The product of two (I) ___ numbers is always a (n) (II) number.
(A) (I) complex; (II) complex(C) (I) rational; (II) real B. (I) real; (II) complex(D) (I) imaginary; (II) imaginary
The product of two (I) rational numbers is always a (II) real number.
A rational number is defined as any number which can be written in the form of p\q where p, q are whole numbers and co-prime.
A real number is any a number that can be indicated on the number line.
A complex number is an imaginary number which does not reside on the number line, rather can be placed in the complex plane.
The product of any two rational numbers produces a rational number and all rational numbers belong in the superset of Real numbers.
Let us consider the possibilities of the other options as given.
A) Let us consider two complex number 2+i and 2-i . When multiplied they produce 3 which is not a complex number.
B)Product of two real numbers can never produce a complex number.
D)Imaginary and complex are same kind of numbers hence they also follow the first option and is not true.
Hence the only correct option is C as we have surmised that the product of two rational numbers will always produce a real number.
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is table shows a proportional relationship.
*
10 points
Captionless Image
Based on the table given, we can infer that the table shows a proportional relationship.
What is a proportional relationship?A proportional relationship refers to when the value of x and y increase by the same ratio for all the values in the distribution.
In the given table, Pens is increasing by 3:
= 3, 6, 9, 12
Boxes keep increasing by 1:
= 1, 2, 3, 4
This shows that the table shows a proportional relationship because both pens and boxes are increasing by the same rate.
In conclusion, the table given shows a proportional relationship.
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A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 5 feet per second. The elevator for the miners descends 17 feet per second. One day, the equipment elevator begins to descend. After 31 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 12 seconds? At that time, which elevator is deeper?
After 12 seconds, the equipment elevator will be 204 feet under the ground while the miner's elevator will be 235 feet under the ground.
After 12 seconds, the miner's elevator is deeper.
What is speed?It is the ratio of distance and time.
We have,
Equipment elevator:
Speed = 5 feet per sec
Miner's elevator:
Speed = 17 feet per sec
Now,
The position (distance) of the equipment elevator after 31 seconds and 12 seconds:
Distance = speed x time
Distance = Distance after 31 sec + Distance after 12 sec
= (31 x 5) + (16 x 5)
= 155 + 80
= 235 feet
The position (distance) of the equipment elevator after 12 seconds:
= 17 x 12
= 204 feet
Therefore, after 12 seconds, the equipment elevator will be 204 feet under the ground while the miner's elevator will be 235 feet under the ground.
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Principal $960 interest rate 9% time in nine months what is the simple interest
keeping in mind that a year has 12 months, thus 9 months is really 9/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$960\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (960)(0.09)(\frac{3}{4}) \implies I=64.8[/tex]
b. What are the expressions ⁴√x³} and (⁵√y⁴) in exponential form?
Exponential Form
We've all heard the term "exponential." What does that word mean? Exponential means growing faster and faster. However, in mathematics, it represents a formula with one or more exponents. So, we know it as exponential form. I would say that things can grow exponentially as the items being talked about get bigger and faster and faster.
So, we use the following method to write the given expression in exponential.
Expression 1 = ⁴√x³
Expression 2 = ⁵√y⁴
Use n*sqrt{a}x=a^(x/n) to rewrite 4*sqrt{x}3 as x^ (3/4)
similarly, we can write the second equation as
Use n*sqrt{a}x=a^(x/n) to rewrite 5*sqrt{y}4 as y^ (4/5)
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please help me fast!!!
Answer:
94.6 m
Step-by-step explanation:
Just put in the number in the info to the formula
formula to find distance travelled, s= 1/2 (u + v) t
U = 0
V = 43
t = 4.4
s= ??
so ,
s = 1/2 (0+43) ×4.4
s = (43× 4.4) ÷ 2
s = 189.2 ÷ 2
s = 94.6 m
yay
Find 90% of 1,000 kilometers.
Answer:
900 kilometers
Step-by-step explanation:
Convert the percentage into a decimal.
90 ÷ 100 = 0.9
Multiply 1000 by 0.9
1000 * 0.9 = 900
What is the sum? seven-thirds plus negative three-eighths
Answer:
1/2 is the correct answer
Step-by-step explanation:
7/8 - 3/8 = 7 -3/8 = 4/8=1/2
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Integer -17 represents Rudy's score for 2 weeks.
What are integers?A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts. The set of integers is frequently denoted by the Z in mathematical notation.Rudy's scores:
Week 1: 15Week 2: -32Then, add 15 and -32 as follows:
= 15 + (-32)= 15 - 32= - 17Therefore, integer -17 represents Rudy's score for 2 weeks.
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0.625(x+10) -10 =x SOLVE
42 less than x is -50 write the word as an equation then solve (HURRY DUE TOMMOROW!!!!)
Answer:
equation: x-42=50
answer: x=8
Step-by-step explanation:
lets write the equation. We have 42 less than x is -50. 42 less than x could translate to x-42 and if it is 50, then that is what x-42 equals.
So we would have x-42=50
Now you can carry over the -42 to start solving
x-42=50
+42 +42
(notice it is added on both sides. I add them to get rid of the -42 on the x side and whatever you do to one side you ALWAYS do to the other.)
x= 50-42
x= 8
i hope this helps :)
For a given calendar year, Mrs. Terry pays the first $2,500 of her medical expenses plus 20% of all medical expenses
over $2,500. In the equation shown, y represents the amount that she pays when x is the total dollar amount of her
medical expenses for the year.
V = 2,500 + 0.2 (x - 2,500)
for x ≥ 2,500
If y = $2,632 for this year, what is x, Mrs. Terry's total medical expenses?
The total expenses of Mrs Terry is given as $3160
How to solve for the total expensesWe have to form the equation as
2632 = 2500 + 20%(x - 2500)
We have to use the multiplicative distributive law here
Such that we would have
2632 = 2500 + 0.2x - 500
We have to rearrange the terms
2632 - 2500 + 500 = 0.2x
632 = 0.2x
Next we have to divide through by 0.2
632 / 0.2 = x
3160 = x
Hence the total expenses of Mrs Terry is given as $3160
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1.what is the question of f(x)
2. Height of the tunnel if the road is 14ft wide by 7 ft shoulders
Answer:
Question 1
f(x) = 19 sin(x [tex]\pi[/tex]/38)
Question 2
f( 7) = 10.39ft
f(24) = 17.4ft
Step-by-step explanation:
f(x) = a sin(x+s)
x = opening length
a = amplitude
s = shift
Question 1
using half of sine
x = opening = 38ft wide
s = 19
f(x) = 19 sin(x [tex]\pi[/tex]/38)
Question 2
road width = 7 + 17 + 7 = 31
height at x = 7 or at x = 7 + 17 = 24
f( 7) = 19 sin(7 π/38) = 10.39ft
f(24) = 19 sin(24 π/38) = 17.4ft
6. Steve can save 9 dollars every day while Maria can save 12 dollars every day. What is the least number of days it will take each person to save the same amount of money?
Answer:
Steve has to save for 4 days and Maria has to save for 3 days and they will save $36 each.
Step-by-step explanation:
S = 9 x 4 = 36
M = 12 x 3 = 36
Please help me! Brainliest to the person who answers this!
The area of the rectangular fenced area for dog run is given by:
A = 4x² + 34x + 18.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that:
The area is given by A = lw.The perimeter is given by P = 2(l + w).For this problem, the section enclosed by the fence is divided into two triangles, as follows:
One of dimensions 8 and 2x.Another with dimensions 6 + 2x and 2x + 3.Hence the total area is:
A = 8(2x) + (6 + 2x)(2x + 3)
A = 16x + 4x² + 18x + 18
A = 4x² + 34x + 18.
Hence the area of the rectangular fenced area for dog run is given by:
A = 4x² + 34x + 18.
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Find each value without using a calculator. If the expression is undefined, write undefined.
sec (-π)
The value of the expression sec (-π) is equal to -1 if the given expression is undefined.
As given in the question,
Given expression: sec (-π)
Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)
Hypotenuse = √ (-1)² + 0²
= 1
Value of the expression is given by
sec α = Hypotenuse / Base (x-coordinate)
⇒sec(-π) = 1 / -1
⇒sec(-π) = -1
Therefore, the value of the expression sec (-π) is equal to -1.
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