Answers
Answer:
The function is exponential
Its equation is [tex]y = \frac{7}{3} \cdot(\frac{1}{3} )^x[/tex]
Step-by-step explanation:
We can see that, as x increases by a constant y increases by a factor of [tex]\frac{1}{3}[/tex]
So the table represents an exponential equation
The form of the equation is [tex]a\cdot(\frac{1}{3})^{x}[/tex]
All we have to do is determine a
Take the entry for x = 0
At x = 0, the equation becomes y = [tex]a\cdot(\frac{1}{3}) ^ 0[/tex]
Any number raised to the power 0 is 1
So at [tex]x = 0, y = a\cdot1 = a[/tex]
But we know the y value at x = 0 is [tex]\frac{7}{3}[/tex]
So [tex]a = \frac{7}{3}[/tex]
The equation of the function is
[tex]y = \frac{7}{3} \cdot(\frac{1}{3} )^x[/tex]
We can verify by plugging in a few values for x into the above equation and seeing if the corresponding calculated values concur with the one in the table
For [tex]x = - 1, y = \frac{7}{3}\cdot (\frac{1}{3})^{-1} = \frac{7}{3}\cdot 3 = 7[/tex]
You can try the other x values and see that computed and given y values concur
Related Questions
How do I solve this?
Answers
Which of these statements is true?
Answers
Answer: WX, ZY and WX and AB.
The 2nd one is correct.
in order to construct the perpendicular bisector of ab which statement describes the compass settings and the number of arc intersections needed
Answers
Answer:
The compass is placed at point a and point b, then two arcs are drawn respectively.
A line is drawn from the arcs passing through element being bisected.
[tex]{}[/tex]
I need help 3(1+3)*x(4+3)
Answers
A cement mixture calls for 3 pounds of cement for 3 gallons of water. What is the ratio of water to cement? Enter only the missing number.
Answers
Based on the calculations, the ratio of water to cement (W:C) is equal to 1:1.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Given the following data:
Quantity of cement = 3 pounds.Quantity of water = 3 gallons.Substituting the given parameters into the formula, we have;
Therefore, the ratio of water to cement is given by:
Ratio of water to cement, W:C = 3:3
Ratio of water to cement, W:C = 1:1.
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18. Callie's cat lost 4 1/2pounds before having
surgery. Two weeks after having surgery, her cat gained 2 7/8pounds. What was the total
change in weight of Callie's cat?
Answers
The total change in the weight of Callie's cat will be 1 5/8 pounds.
How to calculate the fraction?It should be noted that weight is a measurement of the force an acceleration field, particularly the gravitational field of the Earth near the surface, exerts on a particle or object.
From the information that was given, it should be noted that Callie's cat lost 4 1/2 pounds before having surgery and two weeks after having surgery, her cat gained 2 7/8 pounds.
Therefore, based on the information that was illustrated, it should be noted that the change in weight will be the difference between the weights given.
The change in weight will be:
= 4 1/2 pounds - 2 7/8 pounds
= 4 4/8 - 2 7/8 pounds.
= 1 5/8 pounds
Therefore, the change in weight of Callie's cat will be 1 5/8 pounds.
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36 hundredths divided by 9 tenths
Answers
Answer: The answer would be 0.4 or 4/10
Step-by-step explanation:
please answer this question
Answers
let x be the real part of z
let y be the imaginary part of z
[tex]arg(x +i y - 1) = arg(x + iy + 3i) \\ arg(x - 1 + iy) = arg(x + (y + 3)i) \\ arctan( \frac{y}{x - 1} ) = arctan( \frac{y + 3}{x} ) \\ arctan( \frac{ (\frac{y}{x - 1} ) - ( \frac{y + 3}{x}) }{1 +( \frac{y}{x - 1} )( \frac{y + 3}{x} )} ) = 0 \\ arctan( \frac{ \frac{xy - (x - 1)(y + 3)}{x(x - 1)} }{ \frac{x(x - 1) + y(y + 3)}{x(x - 1)} } ) = 0[/tex]
[tex]arctan( \frac{xy - xy - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y } ) = 0 \\ \frac{ - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y} = tan(0) = 0 \\ - 3x + y + 3 = 0 \\ y = 3x - 3[/tex]
[tex] \frac{x - 1}{y} = \frac{x - 1}{3x - 3} = \frac{x - 1}{3(x - 1)} = \frac{1}{3} \\ [/tex]
Answer:
[tex]\dfrac{x-1}{y}=\dfrac{1}{3}[/tex]
Step-by-step explanation:
Sums of real and imaginary numbers are known as complex numbers:
[tex]\large\boxed{z = x + iy}[/tex]
(where x is the real number and iy is the imaginary number).
Complex numbers can be represented on an Argand diagram.
The x-axis is the real axis.The y-axis is the imaginary axis.z = x + iy is represented on the diagram by the point P(x, y).
[tex]\textsf{Argument of a complex number $= \boxed{\arg z}$}[/tex]
It is the angle between the positive real axis and the line joining that number to the origin on an Argand diagram, measured in an anticlockwise direction.
[tex]\textsf{For \;$z = x + iy$, \;the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x}$.}[/tex]
[tex]\textsf{Given: \quad $\arg (z-1)=\arg(z+3i)$}[/tex]
[tex]\textsf{If $z$ is a complex number then $z = x + iy$}.[/tex]
[tex]\textsf{Substitute this into the given equation}:[/tex]
[tex]\begin{aligned} \arg(z-1)&=\arg(z+3i)\\\implies \arg(x + iy - 1) &= \arg(x + iy + 3i)\\\implies \arg((x - 1) + iy) &= \arg(x + i(y + 3))\end{aligned}[/tex]
[tex]\textsf{If the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x} \implies \theta=\tan^{-1}\left(\dfrac{y}{x}\right)$}:[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)=\tan^{-1}\left(\dfrac{y+3}{x}\right)[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)-\tan^{-1}\left(\dfrac{y+3}{x}\right)=0[/tex]
[tex]\boxed{\begin{minipage}{6.2cm}\underline{Trigonometric identity}\\\\ $\tan^{-1}(a)-\tan^{-1}(b)=\tan^{-1}\left(\dfrac{a-b}{1+ab}\right)$\\ \end{minipage}}[/tex]
Use the arctan identity:
[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{y}{x-1}-\dfrac{y+3}{x}}{1+\left(\dfrac{y}{x-1}\right)\left(\dfrac{y+3}{x}\right)} \right)=0[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{1+\dfrac{y(y+3)}{x(x-1)}} \right)=0[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{\dfrac{x(x-1)+y(y+3)}{x(x-1)}} \right)=0[/tex]
[tex]\implies \tan^{-1}\left({\dfrac{xy-(y+3)(x-1)}{x(x-1)+y(y+3)} \right)=0[/tex]
[tex]\implies \tan^{-1}\left({\dfrac{xy-xy+y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]
[tex]\implies \tan^{-1}\left({\dfrac{y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]
[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=\tan(0)[/tex]
[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=0[/tex]
[tex]\implies y-3x+3=0[/tex]
[tex]\implies y=3x-3[/tex]
[tex]\textsf{Substitute\;\; $y=3x-3$ \;\;into \;\;$\dfrac{x-1}{y}$}:[/tex]
[tex]\begin{aligned}\implies \dfrac{x-1}{y}& =\dfrac{x-1}{3x-3}\\\\ & =\dfrac{x-1}{3(x-1)}\\\\ & =\dfrac{1}{3}\end{aligned}[/tex]
[tex]\textsf{Therefore, the value of\; $\dfrac{x-1}{y}$\; is\; $\dfrac{1}{3}$}.[/tex]
A number is divided by four, and then the quotient is added to seventeen. The result is 25. Find the number. Write and solve the equation
Answers
Answer:
32
Step-by-step explanation:
32 divided by 4 is 8
8 + 17 = 25
There's your answer!
Answer:16
Step-by-step explanation:First you would have to subtract 17 from 25 and you'd get 8. Then you multiply 8 by 4 and you'll get 16 as your answer.
WHICH ONE IS IT
60PTS
Answers
Answer:
B. {-4, -2, 0, 2, 4}
Step-by-step explanation:
A definition for the word domain is the "input" of a function, also called the x values.
A definition for the word range is the "output" of a function, also called the y values.
With this knowledge, looking at the question, it is asking for the range of the relation, which means we are looking at the y values.
A is incorrect because it shows all values from -4 to 4, however some are not in the relation shown.
B is correct because it is showing all of the y values given in the table and no others.
C is incorrect because it is just showing the bounds of the relation, but not all values between.
D is incorrect because it is the domain of the function, or the x values.
Therefore, you were correct, and your answer is B.
Answer: B? Although its supposed to be {4, 2, 0, -2, -4}
a travel agent arranges a payment plan for a client it required a down payment of 250 and 15 monthly payment of 582 what was the the total cost if the plan
Answers
Answer:
Step-by-step explanation:
it is Payment: Uniform Payment Series: (F/P, i, ∞) = ∞. (A/F, i, ∞) = 0.
5. Writing Write and solve a two-step
word problem that can be solved using
multiplication as one step.
Answers
Answer:
50!!
Step-by-step explanation:
The teacher buys enough pencils for 10 of her students. She gives each student 5 pencils. How many pencils did she give away altogether?
10 x 5 = 50
Answer:
write any one positive aspect of your religion
Simplify (34)−1. I need to know this plsssss
Answers
Answer:
Step-by-step explanation:
Neuer started a systematic investment program by buying $200.00 with of mutual funds on the first day of every month starting on February 1. When you purchase mutual funds, you purchase units in the fund. Neuer purchased as many units as he could with his $200.00, including fractions of units. Unit prices for the first six months were $10.00, $10.60, $11.25, $9.50, $9.20 and $12.15 respectively.
(a) What is the simple average of the unit prices?
(b) What is the total number of units purchased during the first six months (Correct to three decimals)?
(c) What is the average cost of the units purchased?
(d) What is the value of Neuer's mutual fund holdings on July 31 if the unit price on that date is $11.90?
Answers
a) The simple average of the unit prices is $10.45.
b) The total number of units purchased during the first six months is 115.898 units.
c) The average cost of the units purchased is $10.35.
d) The value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19.
What is an average?An average refers to the mean of a data set.
The average is computed as the total value divided by the number of values in the data set.
Data and Calculations:Month Unit Price Total Value Units
February $10.00 $200 20.000
March 10.60 200 18.868
April 11.25 200 17.778
May 9.50 200 21.052
June 9.20 200 21.739
July 12.15 200 16.461
Total prices $62.70 $1,200 115.898
Simple Average = $10.45 ($62.70/6)
The average cost of the purchased units = $10.354 ($1,200/115.898)
Thus, the value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19 (115.898 x $11.90).
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How far away is Akis house from the pizza place?
Answers
Leah wants to divide x by -5/12. What number should she multiply by x to find the answer?
Answers
Considering the algorithm to divide a number by a fraction, she must multiply x by -12/5 to find the answer of the division of x by -5/12.
What is the algorithm to divide a number by a fraction?To divide a number, or even another fraction, by a fraction, we need to multiply the numerator by the inverse of the denominator.
Taking the following division of fractions as an example, we have that:
(a/b)/(c/d).
The numerator is given by a/b.The denominator is given by c/d.The inverse of the denominator is d/c. (to find the inverse of a fraction, we exchange the numerator by the denominator).Hence the quotient is:
a/b x d/c.
For this problem, the division is:
x/(-5/12).
Hence:
The numerator is given by x.The denominator is given by -5/12.The inverse of the denominator is -12/5.Thus the quotient is given by:
-12x/5.
Meaning that she must multiply x by -12/5 to find the answer of the division of x by -5/12.
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which shows all the critical points for the inequality x^2-9x/x-5<0
Answers
The critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.
The critical point is a single value at which the function is not differentiable
The inequality is given as:
(x² - 9 x) / (x - 5) < 0.
Factorize the numerator
x (x - 9) / (x - 5) < 0.
Equate it to 0, we get that:
x (x - 9) = 0 or x - 5 = 0
x = 0 or x - 9 = 0 or x - 5 = 0
So, the critical points will be:
x = 0 or x = 9 or x = 5.
Therefore, the critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.
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if four out of every nine trick-or-treaters that came to your house last Halloween were dressed as Snow White, what proportion of trick-or-treaters were not dressed as Snow White?
Answers
The proportion of Trick-or-treaters not dressed as Snow white are 5/9.
A proportion may be defined as the way of representation of numbers or letters in the form of ratios which are made equal to each other. For example, if there are 1 mango and 2 bananas then the ratio is written as 1:2 that is for every 1 mango there are 2 bananas and there are 1/3 mangoes and 2/3 bananas.
Total number of Trick-or-treaters = 9
Total number of Trick-or-treaters dressed as Snow white = 4
Total number of Trick-or-treaters not dressed as Snow white = 9-4 = 5
Thus, Proportion of Trick-or-treaters not dressed as Snow white = 5/9
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You are working on a banner for Friday’s pep
rally. The length of the banner is 6 times the
width. The length is 18 feet.
l
GO WILDCATS! w
What is the width?
Answer in units of feet.
Answers
The width of the banner of the Friday’s pep rally is 3 feet.
How do you find the percentage of number?To calculate a percentage, divide the value by total value and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.
Calculating a percentage means determining a portion of a whole in terms of 100. A percentage can be calculated in two ways:
The unitary method is used.By changing the fraction's denominator to 100.For the given expression;
The length of the Friday’s pep rally banner is 18 feet.
Let the width be 'b'.
The given condition is;
The length of the banner is made 6 times the width.
Then,
6 time the width = length
6×w = 18
w = 18/6
w = 3
Therefore, the width of the banner is found as 3 feet.
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i only have one chance to get this right! please help.
Answers
Answer:
D. 2z^3/y
Step-by-step explanation:
xyz^2 = 2z^4
z(xyz) = z(2z^3)
xyz = 2z^3
xz = (2z^3)/y
Perforated for Easy
Between which two thousands
does 10,357 fall?
and
Use the number line below to
show how you would round 10,357
to the nearest thousand.
10,357 rounds to
Answers
Solve the following equation. 3x/7 -2 = 15Then place the correct number in the box provided.
Answers
Answer:
[tex]{ \tt{ \frac{3x}{7} - 2 = 15 }} \\ \\ { \tt{3x - (2 \times 7) = (15 \times 7)}} \\ { \tt{3x - 14 = 105}} \\ { \tt{3x = 119}} \\ { \tt{x = 39.67}} \\ { \tt{ 39\frac{2}{3}}}[/tex]
Answer:
[tex] \sf \large \: x = \frac{119}{3} [/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
3x/7−2=15
Step 1: Simplify both sides of the equation.
3x/7−2=15
3/7x+−2=15
3/7x−2=15
Step 2: Add 2 to both sides.
3/7x−2+2=15+2
3/7x=17
Step 3: Multiply both sides by 7/3.
(7/3)*(3/7x)=(7/3)*(17)
x=119/3
I need help to solve this! Thank you
Answers
Answer:
f(2) = 3
Step-by-step explanation:
You want the value of f(2), given the graph of f(x).
Function valueThe value of the function for a given argument is found by locating the point on the graph with an x-coordinate equal to the argument. The y-coordinate of that point is the function value.
See the attachment.
The y-coordinate associated with the point that has an x-value of 2 is 3.
f(2) = 3
Which classification of the real number system describes all of the following numbers listed below? 0.5, −13, 0.62, 3.14, 19%
Rational Numbers
Whole Numbers
Irrational Numbers
Integers
Answers
The numbers 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer
How to determine the classification of the real numbers?The numbers are given as:
0.5, −13, 0.62, 3.14, 19%
Numbers that can be represented as a fraction of two integers are rational numbers
The given numbers can be represented as a fraction of two integers
i.e.
0.5 = 5/10
0.62 = 62/100
3.14 = 314/100
19% = 19/100
This means that 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer (because it has no decimal point and it is negative)
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HELP ASAP
Write 8,350,000,000 in scientific notation.
8.35 × 10−9
8.35 × 109
835 × 10−7
835 × 107
Answers
[tex]8.35 \times {10}^{9} [/tex]
or
[tex]835 \times {10}^{7} [/tex]
What is the smallest possible common factor between 2 numbers? When would that number also be the GCF? When would the lesser of 2 numbers also be the GCF of those 2 numbers?
Answers
Answer:
1
Step-by-step explanation:
What is the smallest possible common factor between 2 numbers? When would that number also be the GCF? When would the lesser of 2 numbers also be the GCF of those 2 numbers?
The points Q, R, S and T all lie on the same line segment, in that order, such that the
ratio of QR RS: ST is equal to 6:3:1. If QT = 10, find RS.
Answers
The RS line segment will be 16 units long.
What exactly are collinear points?An axis is a line on which points are located, especially if that line is connected to a triangle or other geometric shape. Because a line is determined by two factors, two points are transparently collinear. If the points are in a straight line, they are collinear points.The collinear points are Q, R, S, and T.
The collinear's condition will then be determined:
QR + RS + ST = QTThe points Q, R, S, and T all lie on the same line segment in that order, so the QR:RS:ST ratio is 1:4:5. If QT = 40.
Let QR / 1 = RS / 4 = ST / 5 = xQR = xRS = 4xST = 5xThe value of the variable x will then be:
QR + RS + ST = QTx + 4x + 5x = 4010x = 40x = 4The length of the line segment RS will then become:
RS = 4xRS = 4 (4)RS = 16Therefore, the RS line segment will be 16 units long.
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The correct question is given below:
The points Q, R, S, and T all lie on the same line segment, in that order, such that the
ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.
dividing decimals
0.745/ 9.089
Answers
Answer:
0.745/9.089
Multiply numerator and denominator by 1000
=745/9089
Help asap! and don't answer for the points only if you know for sure it's right
Answers
Step by step
We know adult tickets are $20 each
We know a child’s ticket is 40% less, so a child’s ticket is 60% of $20 = $12
(100% - 40% less = 60%)
So 2 adult tickets x $20
+ 2 child tickets x $12
2($20) + 2($12) = total cost
$40 + $24 = $64 total cost
Answer:
Child ticket: 12 dollars
Total price: 64 dollars
Step-by-step explanation(Child ticket price):
[tex]T = X(1 - P\%)\\T = 20(1 - 40\%)\\T = 20(1 - 0.4)\\T = 20(0.6)\\T = 12[/tex]
-----------------------------------------------------------------------------------------------------------
Step-by-step explanation(Total price):
[tex]T(12) * 2 + (20.00 * 2) = \$64[/tex]
Hope this helps.
there are 25 boxes of paper, each box has 789 pieces of paper. how many pieces of paper are there in all?
Answers
25 times 789 is 19725
the answer:19,725