Answers
The coordinates of the linear equation for (m, s) are; (0, 4), (2, 3), (-2, 5), (8, 0)
This is a one to one mapping and example of a function
How to solve linear equation problems?We are given the equation as;
2m + 4s = 16
Thus;
When m = 0, we have;
2(0) + 4s = 16
4s = 16
divide both sides by 4 to get;
s = 4
When s = 3;
2m + 4(3) = 16
2m + 12 = 16
2m = 16 - 12
Divide both sides by 2 to get;
m = 4/2
m = 2
When m = -2
we have;
2(-2) + 4s = 16
-4 + 4s = 16
4s = 20
divide both sides by 4 to get;
s = 5
When s = 0, we have;
2m + 4(0) = 16
2m + 0 = 16
2m = 16
Divide both sides by 2 to get;
m = 16/2
m = 8
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Related Questions
Question 3(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 6x +8=0 into the form (x-p)² =q?
[p and q are integers]
Answers
The correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
Vertex form of a quadratic equationThe vertex form of a quadratic equation is expressed as:
a(x-h)² + k
Given the quadratic equation
x^2 + 6x +8=0
Subtract 8 from both sides
x^2 + 6x +8 - 8 = 0 - 8
x^2 + 6x = -8
Complete the square
(x^2+6x+3^2) = -8 + 9
(x+3)² = -8 + 9
(x+3)² = 1
Hence the correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;
x^2 + 6x +8 +1 = 0 + 1
x^2 + 6x +8 +1 = 1
x^2 + 6x + 9 = 1
(x+3)² = 1
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The following contingency table gives the results of a sample survey of Sowetan male and female respondents regarding their preferred mobile phone service provider.
What is the probability of selecting a respondent who does not prefer Cell C?
a.
0.2250
b.
0.50
c.
0.3750
d.
0.65
e.
0.7750
Answers
The probability of selecting a respondent who does not prefer Cell C is 0.775
How to determine the probability?The complete question is in the attached image
From the attachment, we have
Prefer cell C = 90
Total = 400
So, the number of respondents that do not prefer cell C is
Do not = 400 - 90
Do not = 310
The probability is then calculated as:
P = 310/400
Evaluate
P = 0.775
Hence, the probability of selecting a respondent who does not prefer Cell C is 0.775
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Which function is graphed below?
Answers
The function that represents the given trigonometric graph is; f(x) = cos (x)
How to Interpret Trigonometric Graphs?From the given trigonometric Graph, we can see the following;
When x = 0, y = 1
When x = π/2, y = 0
When x = π, y = -1
When x = 2π, y = 1
Now, according to trigonometric functions in radians, we know that;
cos 0 = 1
cos π/2 = 0
cos π = -1
cos 2π = 1
These values correspond with what we have in the given trigonometric graph and as such we can say that the function that is graphed is;
f(x) = cos (x)
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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
Answers
When [tex]n=0[/tex], we have
[tex]5^{3^0} + 1 = 5^1 + 1 = 6[/tex]
[tex]3^{0 + 1} = 3^1 = 3[/tex]
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for [tex]n=k[/tex], that
[tex]3^{k + 1} \mid 5^{3^k} + 1[/tex]
Now for [tex]n=k+1[/tex], we have
[tex]5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)[/tex]
so we know the left side is at least divisible by [tex]3^{k+1}[/tex] by our assumption.
It remains to show that
[tex]3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1[/tex]
which is easily done with Fermat's little theorem. It says
[tex]a^p \equiv a \pmod p[/tex]
where [tex]p[/tex] is prime and [tex]a[/tex] is any integer. Then for any positive integer [tex]x[/tex],
[tex]5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3[/tex]
Furthermore,
[tex]5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3[/tex]
which goes all the way down to
[tex]5^{3^k} \equiv 5 \pmod 3[/tex]
So, we find that
[tex]\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3[/tex]
QED
what is the absolute value of -45/6. I need serious help
Answers
Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
The absolute value of a number is just its distance from zero. In other words, if it's negative, the absolute value would make the number positive. This makes the absolute value [tex]\frac{45}{6}[/tex]. Now, reduce to get[tex]\frac{15}{2}[/tex].
PLEASE IF ANYONE CAN HELP I HAVE 35 MINUTES LEFT 1-8 ANSWERS ONLY WILL DO THANK YOU
Answers
Answer:
1. x=2 2.
y=1
Step-by-step explanation:
Im sorry I TRIED :(
Please help me answer this question, 20 POINTS!
Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
Answers
It's 4 buns & 5 cakes
Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.
E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share. Thereafter, dividends are expected to growth at a constant rate of 6% per year. The discount rate for TYK is 10%. How much would you pay for one share in Company TYK?
Answers
14.11 is the price of one share in the company TYK.
How much would you pay for one share in Company TYK?Given:
Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share.Dividends are expected to grow at a constant rate of 6% per year.The discount rate for TYK is 10%.Find:
How much would you pay for one share in Company TYK?Solution:
The dividend is the amount paid to the shareholders for their investment in the company.
Dividend at end of 7th year = $1 per share (given)
dividend expected growth rate = 6% (given)
the dividend will be paid from the end of seven years.
So find the price of the share at the end of the 6th year.
price at the end of the 6th year
= Dividend at the 7th year/discount rate growth rate
= 1/(10%-6%) = 1/4% = 25
price of the share at the end of the 6th year is $25
discount price 10% (given)
current price share = 25/(1+10%)^6
= 25/(1.1)^6
= 25/1.77
= 14.11
The current price of the share is $ 14.11
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Jason’s utility and telephone bills for the month totaled $180. The utility bill was 3 times as much as the telephone bill. How much was each bill?
Answers
Answer:
telephone was $45, utility was $135
Step-by-step explanation:
Let the telephone bill be x, then the utility bill is 3x
3x+x = 180
4x = 180
x = 45
3x = 135
A = {1, 2, 6}
B = {x|x is an odd whole number less than 8}.
Find An B.
Answers
Answer:
A∩B = { 1 }
Step-by-step explanation:
Consider the sets :
A = {1, 2, 6}
B = {x ;where x is an odd whole number less than 8}
Suppose the numbers of B are natural numbers (not integers).
Then
B = {1 , 3 , 5 , 7}
We obtain :
A = {1, 2, 6} and B = {1 , 3 , 5 , 7}
The intersection of A and B or the set A∩B :
is the set of the common numbers of A and B.
Then
A∩B = { 1 }
The set A intersection B(or, A∩B) for the given set A and set B exists {1}.
What is A intersection B, (A∩B)?"The set A intersection B(or, A∩B) exists described as the set composed of all elements that belong to both A and B".
The intersection of a set A with a B exists the set of elements that exist in both sets A and B. The intersection exists represented as A∩B.
The intersection of two mathematical objects exists where they overlap. For geometric objects, the intersection exists as a point or group of points where the objects cross.
For numerical or non-numerical sets, the intersection exists every number or object the two sets contain in common.
Given: A = {1, 2, 6}
B = {x | x is an odd whole number less than 8}.
From the above information, we get
⇒ B = {1, 3, 5, 7}
If A = {1, 2, 6} and B = {1, 3, 5, 7}
then A∩B = {1, 2, 6} ∩ {1, 3, 5, 7}
A∩B = {1}
Therefore, the correct answer A∩B exists {1}.
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The coconut milk is in a can but he doesn’t know how much the can holds.
The can is 12 cm high and the diameter is 8 cm.
Using the formula V = π r2 h, work out how much coconut milk is in the can.
Use 3 as a value for π.
Give your answer using the correct units.
Answers
Super confused need help
Answers
(7)/(3) of it is 5 (5)/(6)
Answers
let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}[/tex]
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
all real values of x where x < -1
Step-by-step explanation:
See attached graph.
As seen in the diagram below, Shandra is building a walkway with a width of feet
to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the
pool and the walkway will be 168 square feet, how wide should the walkway be?
Answers
The walkway should be about 2.57feet.
What is the total surface area?
The total surface area of the building is the sum of the total faces of an object contains.
The formula is expressed as:
TSA = 2(lw + wh + lh)
where,
l is the length ,w is the width , h is the height
Calculation
Given the following parameters
TSA = 168 square feet
length = 8 feet and Height = 6 feet
Required
Width of the walkway, Substitute the given values in the formula
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
4w = 84 - 48
14w = 36
w = 2.57feet
The walkway should be about 2.57feet.
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Determine whether the relation represents y as a function x. x=y^2
Answers
It is false that x is a function of y
How to determine the true statement?The equation is given as:
x = y^2
Set y = 2
x = (2)^2
x = 4
Set y = -2
x = (-2)^2
x = 4
Different values of y give the same x value.
This means that x is not a function of y
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Exponentiation is the raising of one number to the power of another. This operation is performed using two asterisks **. Let's use exponentiation to solve a known problem. You are offered a choice of either $1.000.000 or $0.01 (one penny) doubled every day for 30 days (the resulting amount is doubled every day). Task: Write a program to calculate the amount that will result from the doubling to understand which choice results in a larger amount. Hint: Let's see how exponentiation can be useful to perform the calculation. For example, if we want to calculate how much money we will have on the 5th day, we can use this expression: 0.01*(2**5) = 0.32 dollars (multiply the penny by 2 raised to the power of 5).
Answers
In math, Exponentiation refers to the operation of raising one quantity to the power of another. See the program running the exponentiation below.
What is the required code?The code is given below:
number_of_days = 30
amount_after_30days = 0.01 * (2 ** number_of_days)
# print the amount
print(amount_after_30days)
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Is this Network a HAMILTONIAN Circuit? If so write the path.
Answers
The path of the given Hamiltonian diagram is A, E, B, C, D, F. See explanation below.
What is a Hamiltonian Path?A Hamiltonian path, also known as a traceable path, is one that visits each vertex of the graph precisely once.
A traceable graph is one that contains a Hamiltonian path.
Hence, the path is given as;
A, E, B, C, D, F
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2. Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives one A in three-credit class, one D in three-credit class, three B in three-credit class and two C in one-credit class, what is the student’s grade point average?
Answers
Based on the student's grades, and the credit hours, their grade point average is 2.60.
What does the student get as their GPA?First, find the grade points earned:
= (4 x 3) + (1 x 3) + (3 x 3) + (2 x 1)
= 12 + 3 + 9 + 2
= 26
The GPA is:
=Grade points earned / total number of credits
= 26 / (3 + 3 + 3 + 1)
= 26 / 10
= 2.6
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The population of a city is modeled by the equation P(t)=232012e0.23t where t is measure in years. If the city continues to grow at this rate, approximately how many years will it take for the population to reach one million? Round your answer to two decimal places
Answers
In around 6.35 years, the population will be 1 million.
how many years will it take for the population to reach one million?
The population is modeled by the exponential equation:
[tex]P(t) = 232,012*e^{0.23*t}[/tex]
Then we just need to solve the equation for t:
[tex]P(t) = 232,012*e^{0.23*t} = 1,000,000[/tex]
Let's solve that:
[tex]232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\[/tex]
If we apply the natural logarithm to both sides:
[tex]ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35[/tex]
So in around 6.35 years, the population will be 1 million.
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Find a12 given the geometric sequence 4, 8, 16, 32, ...
A. 32,768
OB. 8192
OC. 16,384
D. 4096
Reset Selection
Answers
The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)
How to find a determined element of a geometric sequence by exponential formulae
Sequences are series of elements generated according to at least one condition, usually equations. geometric sequences are generated according to a exponential formulas, whose form and characteristics are described below:
f(n) = a · bⁿ ⁻ ¹ (1)
Where:
a - First element of geometric sequenceb - Common ratio of the geometric sequencen - Element index within the geometric sequenceIf we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:
f(12) = 4 · 2¹² ⁻ ¹
f(12) = 4 · 2¹¹
f(12) = 4 · 2,048
f(12) = 4,096
The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)
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Teacher increases spatial awareness for children as they use position words and provide experience through mapping and manipulating shapes.
a. True
b. False
Answers
It is true teachers can increase spatial awareness as they use position words or implement mapping and shape manipulation.
Whatis spatial awareness?This refers to the ability to understand the position of one's body in relation to space and other objects as well as understanding how location and movement work.
How can spatial awareness be increased in children?In children spatial awareness can be increased through:
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Sharon is planting tulip
bulbs in her garden. In the
catalog she sees a disclaimer that there is a 1/15 probability that a bulb will not flower. If Sharon plants 90 bulbs, how many tulips can she expect to see in her garden?
Answers
Answer:
84 flowers.
Step-by-step explanation:
We must multiply 90 by 1/15 to get 6 bulbs that will not flower. 90-6 is 84.
Fill in the blank 57.59 - ___=1.29
Answers
Answer: 57.59- 56.3=1.29
Step-by-step explanation:
57.59-x = 1.29
-x= 1.29-57.59
(—) -x= - 56.3
x=56.3
What is the discount and sale price of a $300 item that has been discounted at 10%?
Answers
Answer:
Discount: $30 off
New Sale Price: $270
Step-by-step explanation:
$300*10% =
30
$300-30=
$270
or
$300*.1=
30
$300-30=
$270
What is the range of y = log Subscript 8 Baseline x?
Answers
The range of [tex]y =\log_8(x)[/tex] is the set of all real values
How to determine the range?The function is given as:
[tex]y =\log_8(x)[/tex]
The above function is a parent logarithmic function.
The parent logarithmic function have a range of the set of all real values
Hence, the range of [tex]y =\log_8(x)[/tex] is the set of all real values
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Answer:
D
Step-by-step explanation:
on edg
Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
Answers
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]The composite function is of the given functions f(x) and g(x) is:
[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
[tex]x + 3 \geq 0[/tex]
[tex]x \geq -3[/tex]
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
[tex]\sqrt{x + 3} - 3 \neq 0[/tex]
[tex]\sqrt{x + 3} \neq 3[/tex]
[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]
[tex]x + 3 \neq 9[/tex]
[tex]x \neq 6[/tex]
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
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The Apollo space program lasted from 1967 until 1972 and included 13 missions.The missions lasted from as little as Z hours to as long as 30ours.The duration of each flight is listed below. 9 195 241 295 142% 142% 147 a.Expain why the flight times b.Find Mean and the Median of flight times c.Find range and the standard deviation of flight times
Answers
The mean and the median based on the information given will be 166.08 and 195.
How to calculate the value?It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.
The median is simply the middle number. This will be 195.
The range will be:
= 301 - 7
= 294
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WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40
Answers
Answer:
20
Step-by-step explanation:
20+20=40
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.
g(x) = f(x − 3) + 4
A.
The graph of function f is shifted left 3 units and up 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted right 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and down 4 units.
Answers
The graph of function f is shifted right 3 units and up 4 units.
Let f(x) be the parent function
Now use the Rule : f(x)→f(x-b) to find the shifting of graph
The graph shifts right by b units
So, shift the graph by 3 unit
So, f(x)→f(x-3)
So, the graph shifted right by 3 units
2nd rule used is Rule : f(x)→f(x)+b to find the another shifting of graph
The graph shifts up by b units
Now shift the obtained graph up by 4 units
So, f(x-3)→f(x-3)+4
So, the graph shifts up by 4 units
Thus, The graph of function f is shifted right 3 units and up 4 units.
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