Answers
The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.
The exponential function is a type of mathematical equation that can be used to determine if anything is increasing or decreasing exponentially, such as population, money, or price.
The general form of an exponential function is given by
f(x) = abˣ or y = abˣ
Where 'x' is a variable and a and b are constants
Here we have
The graph shows the number of games system sold since 2005.
As we know an exponential function is represented as:
=> y = abˣ
From the given graph x = 0 and y = 30.5
=> 30.5 = ab⁰
=> 30.5 = a(1)
=> a = 30.5
When x = 1, y = 21.35
=> 21.35 = (30.5)(b¹)
=> b = 0.7
So the required exponential function can be written as
=> y = (30.5)(0.7)ˣ
Therefore,
The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.
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Related Questions
2
1²/
3
in all did Jane study for the two tests?
Last weekend Jane studied 4
x
x
3
A 8-2-201
8-hours
7
3
8- hours
4
B 8
C 911212
с
hours
11
D
8 hours
12
1 of 5
08:14
1
hours for her history final and 4
hours for her math exam. How many hours
4
Ne
Answers
The total number of hours that Jane studied for her two tests were 8 ¹¹ / ₁₂ hours
How to find the number of hours ?To find the number of hours that Jane studied, you first need to convert the hours studied for history and math, from mixed fractions to improper fractions.
4 ² / ₃ hours :
= ( 4 x 3 + 2 ) / 3
= 14 / 3 hours
4 ¹ / ₄ hours :
= ( 4 x 4 + 1 ) / 4
= 17 / 4 hours
Add up both hours by using a common denominator of 12 :
= ( ( ( 12 / 4 ) x 17 ) + ( ( 12 / 3 ) x 14 ) ) / 12
= ( 51 + 56 ) / 12
= 8 ¹¹ / ₁₂ hours
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The full question is:
Last weekend Jane studied 4 2 3 hours for her history final and 4 1 4 hours for her math exam. How many hours in all did Jane study for the two tests?
Find a function rule for the line that passes through the origin (0,0) and the point ( -6 - 12,).
Answers
The function rule for the line that passes through the origin and (-6,-12) is y = 2x.
In mathematics, a function is a rule that assigns to each element in a set a unique output value.
To find a function rule for the line that passes through the origin (0,0) and the point (-6,-12), we first need to determine the slope of the line. The slope of a line represents the rate of change between the x and y coordinates. We can find the slope using the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
where (x₁, y₁) represents the coordinates of the first point, and (x₂, y₂) represents the coordinates of the second point.
Using the given points, we can substitute in the values:
slope = (-12 - 0)/(-6 - 0)
slope = -12/-6
slope = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the function rule:
y - y₁ = m(x - x₁)
where m is the slope, and (x₁, y₁) represents the coordinates of a point on the line.
Substituting in the values we have so far, we get:
y - 0 = 2(x - 0)
y = 2x
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Fill in the blank. When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _____ . When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a ____.
Answers
When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.
In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ
where, μ--> population mean,
σ --> population standard deviation and
x --> the raw-score.
Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.
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a hospital director is told that 55% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is less than the expected percentage. a sample of 230 patients found that 115 were insured. determine the p-value of the test statistic. round your answer to four decimal places.
Answers
The p-value of the test statistic is 0.0401, which is less than the commonly used significance level of 0.05.
In statistical analysis, hypothesis testing is an essential method used to make inferences about population parameters using sample data. In this case, a hospital director wants to test a claim that the percentage of insured patients is less than the expected percentage.
The alternative hypothesis is that the percentage of insured patients is less than the expected percentage. To test this hypothesis, the director will use a one-tailed z-test for proportions. The test statistic is calculated as:
z = (p - P) / √(P(1-P) / n)
where p is the sample proportion, P is the expected proportion under the null hypothesis, and n is the sample size.
In this case, the sample proportion is 115/230 = 0.5, and the expected proportion is not specified. However, since the null hypothesis is that the percentage of insured patients is equal to the expected percentage, we can use the observed percentage of 55% as a reasonable estimate of the expected percentage. Thus, P = 0.55.
Plugging in these values, we get:
z = (0.5 - 0.55) / √(0.55 * 0.45 / 230) = -1.74
p-value = -1.74/0.069 = 0.0401
Trough this one we have identified that the test statistic's p-value is 0.0401, indicating that it is below the widely accepted significance level of 0.05.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.
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Plot the z intercepts y-intercept, vertex and axis of symmetry of the function h(x)=(x+1)^2-4
Answers
The axis of symmetry of the function is x=-1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is h(x)=(x+1)²-4.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (-1,-4)
Focus: (-1,-15/4)
Axis of Symmetry: x=-1
Directrix: y= -17/4
Plot the points (-3, 0), (-2, -3), (-1, -4), (0, -3) and (1, 0)
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (1,0),(-3,0)
y-intercept(s): (0,-3)
Therefore, the axis of symmetry of the function is x=-1.
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5. A typical car salesman receives 25% of the profit made from selling a car as commission. A salesperson has earned $4,300 in commission this month. How much profit did the dealership make on the cars that he sold? (1) $107,500 (3) $10,750 (2) $17,200 (4) $1,075
Answers
Answer: (2) $17,200
Step-by-step explanation:
We know the commission = 4,300. So we need to find a number (Let's x) times 25% (equal to 0.25) equal to 4,300
Put all that into an equation: x times 0.25 = 0.25x
0.25x=4,300
Now, all we need to do is solve for x.
Divide both sides by 0.25 to get 17200
1. What is the area of triangle ABC? * 12 60° 60° A A. 6/3 square units B. 18 V3 square units A B C. 36 /3 square units D. 72 /3 square units
Answers
Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice
What is a formula of area of triangle?
To calculate the area of a triangle, use the formula area = 1/2 * base * height.
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
where the base and height are the dimensions of the triangle that form a right angle.
In this case, we don't have the dimensions of the triangle that form a right angle, but we know that the triangle has two angles that are 60 degrees each. This tells us that the triangle is an equilateral triangle, and all three sides are equal.
Let's call the length of each side "s". Then, we can use the formula for the area of an equilateral triangle:
[tex]Area = (\sqrt(3)/4) * s^2[/tex]
Plugging in the given value of 12 for s, we get:
[tex]Area = (\sqrt{(3)/4) * 12^2}\\\\ Area \ = (\sqrt{(3)/4) * 144} \\\\Area = 36\sqrt{(3)}[/tex]
Therefore, the area of triangle ABC is [tex]36\sqrt(3)[/tex] square units.
Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice.
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Fill in the gap in the equation below by completing the square. x² + 12x +44 = (x + 6)² +
Answers
Answer:
[tex]8[/tex]
Step-by-step explanation:
[tex]x^2+12x+44=(x^2+12x+36)+8=(x+6)^2+8[/tex]
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
-x+6y=9
-4x+24y=48
Answers
Answer:
no solution
Step-by-step explanation:
- x + 6y = 9 → (1)
- 4x + 24y = 48 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x and y
4x - 24y = - 36 → (3)
add (2) and (3) term by term
0 + 0 = 12
0 = 12 ← false statement
this false statement indicates the system has no solution
Fully reduce the radical question using prime factorization technique:
[tex]\sqrt250h^4k^5[/tex]
THANK YOU SO MUCH I APPRECIATE IT
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{250 {h}^{4} {k}^{5} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(2 \times 5 \times 5 \times 5) \times (h \times h \times h \times h )\times (k \times k \times k \times k \times k} )[/tex]
[ take out one of the pair ~ ]
[tex]\qquad \sf \dashrightarrow \: 5 \times h \times h \times k \times k \sqrt{2 \times 5 \times k} [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 {h}^{2} {k}^{2} \sqrt{10k} [/tex]
That's our simplified answer ~
Answer:
<--> V 250h4k5
√(2 × 5 × 5 × 5) × (h×h×h×
[ take out one of the pair ~]
5 xhxhxkx k√2 × 5 × k
--> 5h2k2✓10k
Part 4: Fill in the blank. cos (56°) = sin(°)
Answers
The complete expression in the blank is cos (56°) = sin(34°)
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
cos (56°) = sin(°)
The blank expression can be calculated as
When x + y = 90;
sin(x) = cos(y)
Using the above as a guide, we have the following:
Blank + 56 = 90
Evakuate the like terms
Blank = 34
So, we have
cos (56°) = sin(34°)
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A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 112 million kilometers. Its orbital eccentricity is 0.3. Find the planet’s orbital period and its nearest and farthest orbital distances from its star.
Answers
T = 2 * pi * (a^3 / (G * M))^(1/2)
where T is the orbital period, a is the semi-major axis (average distance) of the orbit, G is the gravitational constant, and M is the mass of the star.
First, we'll convert the average distance from kilometers to meters:
a = 112 million km = 112 x 10^6 m
Next, we'll find the semi-minor axis using the formula:
b = a * sqrt(1 - e^2)
where e is the eccentricity.
b = 112 x 10^6 m * sqrt(1 - 0.3^2) = 112 x 10^6 m * sqrt(0.91) = 112 x 10^6 m * 0.954
Next, we'll find the semi-major axis:
a = 112 x 10^6 m
Finally, we'll substitute these values into the formula for the orbital period:
T = 2 * pi * (a^3 / (G * M))^(1/2)
T = 2 * pi * (112 x 10^6 m)^3 / (G * M)^(1/2)
Since M is the mass of the sun, we'll use the mass of the sun in kilograms:
M = 1.989 x 10^30 kg
G = 6.67430 x 10^-11 m^3 kg^-1 s^-2
T = 2 * pi * (112 x 10^6 m)^3 / (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 1.989 x 10^30 kg)^(1/2)
T = 2 * pi * (112 x 10^6 m)^3 / (6.67430 x 10^-11 * 1.989 x 10^30)^(1/2)
T = 2 * pi * (112 x 10^6 m)^3 / (1.327 x 10^-20)^(1/2)
T = 2 * pi * (112 x 10^6 m)^3 / (1.153 x 10^-10)
T = 2 * pi * (112 x 10^6 m)^3 / 1.153 x 10^-10
T = 2 * pi * (112 x 10^6 m)^3 / 1.153 x 10^-10
T = 2 * pi * (112 x 10^6 m)^3 / 1.153 x 10^-10
T = 5.201 x 10^7 s
So, the orbital period of the planet is approximately 5.201 x 10^7 seconds, or about 1.6 years.
The nearest and farthest orbital distances from the star are equal to the semi-minor and semi-major axes, respectively.
Nearest distance = b = 112 x 10^6 m * 0.954 = 106.6 x 10^6 m
Farthest distance = a = 112 x 10^6 m
You are 70% of the way through an 800 page novel. How many pages have you read?
Answers
Answer: You have read 560 pages.
Step-by-step explanation:
70 divided by 100 x 800 = 560.
Answer:
Step-by-step explanation:
800(.70)= 560 pages that have been read
Write 15+45 as a product of 2 factors using GCF and the distributive property
Answers
We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).
We are given the following expression-
15 + 45
Now, we can factorize 15 into prime factors as follows -
= 3 × 5 (15 × 1)
Similarly, we can factorize 45 into prime factors as follows -
= 3 × 3 × 5 (15 × 3)
Thus, the greatest common factor of 15 and 45 is 15, so we can
= 15 × 1 = 15 and 15 × 3 is 45
Hence, we can write (15 + 45) as 15(1 + 3).
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Jordan bought a $300,000 house, paying 10% down, and getting a 30 year loan with 3% interest for the remaining amount.
How much is the loan amount going to be?
What will her monthly payments be?
How much interest will she pay over the life of the loan?
Answers
Answer:
The down payment that Jordan made on the house was $300,000 x 10% = $30,000. So, he financed $300,000 - $30,000 = $270,000.
where
M = monthly payment
P = loan amount ($270,000)
r = monthly interest rate (3% / 12 months = 0.003)
n = number of payments (30 years x 12 months/year = 360)
This comes out to a monthly payment of approximately $1,173.38.
To simplify
The loan amount is- $270,000
Her monthly payment will be- $1,173.38
The amount of interest she will pay is- $8,100
Graph the points, connect them in orden, find the perimeter of the polygon (-1,-1),(-1,1),(1,1),(3,-3)
Answers
Answer: the perimeter of the polygon is 29cm
Step-by-step explanation:
LAST TIME I NEED HELP XD
Answers
Answer:
Step-by-step explanation:
no idea. i have a idea!
do it your self
The diagrams below show the portion of another class mural that Josephine was supposed to paint and how much she actually did paint. Use the pictures to answer the questions that follow.
Answers
Based on the information in the graph, it can be inferred that Josephine must have painted 1/4 of the painting.
How to find the amount (fraction) of the paint that Josephine should have painted?To find the amount (fraction) of the paint, Josephine should have painted the section marked on the image. To know how much that section is equivalent to, we must take as a reference that the entire painting would be 1.
So, if we divide the painting in half, it would be 1/2, that is, we paint 1 of 2 possible parts. However, in the case of Josephine there are 4 possible parts and she only painted one. From the above, what she should have painted was 1/4.
Note: This question is incomplete. Here is the complete information:
question:
Approximately what portion of the painting was Josephine supposed to paint?
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the tortoise and the hare are running a 1 km race. after running comfortably for 7 s, the hare is so far ahead that he decides to take a nap under a tree, 100 m away from the finish line. if the tortoise is moving constantly at a speed of 0.27 m/s, and the maximum speed of the hare is 15 m/s, how long can the hare afford to nap if he does not want to lose the race?
Answers
The hare can afford to nap for a maximum time of 3,690 seconds without losing the race if his speed is 15 m/s.
After running for 7 seconds, the hare has covered a distance of:
[tex]distance = speed \times time\\distance = 15 \times 7\\[/tex]
distance = 105m
The hare is now 895 m away from the starting line and 100 m away from the finish line.
The hare needs to cover a distance of 100 m to reach the finish line, while the tortoise needs to cover a distance of 895 m.
calculate the time it would take the tortoise to reach the finish line:
[tex]time = \frac{100}{0.27}[/tex] = 3704 seconds
The maximum speed of the hare is 15 m/s, which means the time it would take the hare to cover the distance is:
[tex]time = \frac{100}{15}[/tex] = 6.67 seconds
so, the time hare have to nap so that he does not lose race = 3704 - (7+6.67) ≅3690 seconds
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Here are the first four terms of a sequence.
7
12
17
22
Write an expression for the nth term of this sequence
Answers
Answer:
[tex]\mbox{\large a_n = 2 + 5n}[/tex]
Step-by-step explanation:
The sequence is 7 12 17 22
This is an arithmetic sequence where any two successive terms is a constant known as the common difference
The difference between any two successive terms is 5
The common difference is 5
The nth term can be found by the expression
[tex]a_n = a_1 + d(n-1)[/tex]
where
[tex]a_n \textrm{ is the $n^{th}$ term}[/tex]
[tex]\mathrm{a_1\;is\;the\;first\;term}[/tex]
[tex]\mathrm{d\;is\;the\;common\;difference}\\[/tex]
In this sequence
[tex]a_1 = 7\\d = 5\\[/tex]
[tex]a_n = 7 + 5(n-1)\\\\a_n = 7 + 5n - 5\\\\a_n = 2 + 5n[/tex]
We can verify that this is correct is to determine the 5th term of the sequence which should be 22 + 5 = 27
Applying the expression for 5th term
[tex]a_5 = 2 + 5(5)\\= 2 + 25\\= 27[/tex]
The theater sells two types of tickets: adult tickets for $13 and child tickets for $3. Last night, the theater sold a total of 220 tickets for a total of $1820. How many adult tickets did the theater sell last night? Show your work here Enter your answer
Answers
The required adult tickets and 104 child tickets, which gives a total revenue of $1820.
What is equation of variable?An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 = 10. "X" in this case is a variable.
According to question:Let x be the number of adult tickets sold and y be the number of child tickets sold.
We know that the total number of tickets sold is 220:
x + y = 220
We also know that the total revenue from ticket sales is $1820:
13x + 3y = 1820
We can use the first equation to solve for y in terms of x:
y = 220 - x
Substituting this into the second equation, we get:
13x + 3(220 - x) = 1820
Simplifying this equation:
10x + 660 = 1820
10x = 1160
x = 116
Therefore, the theater sold 116 adult tickets last night.
To check, we can substitute x = 116 into the equation for y:
y = 220 - x = 220 - 116 = 104
So, the theater sold 116 adult tickets and 104 child tickets, which gives a total revenue of $1820.
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What is 6,000,000 + 1,000,000? Answer ASAP!!! NEED HELP
Answers
Answer: 7,000,000
By the way: How do we have almost the same name?
Answer:
the answer is 7,000,000
Step-by-step explanation:
6,000,000+1,000,000=7,000,000
Which statements describe the graph of 2 8/9>x
There is an open circle on ²9.
21909.
The graph contains the point 0
,8
There is a closed circle on ²ğ.
The arrow points to the left.
The arrow points to the right.
2x on a number line? Select three options.
Answers
The inequality 26/9 > x represents a line with an open circle at 26/9 going toward positive infinity represented by an arrow.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality [tex]2\frac{8}{9} > x[/tex].
26/9 > x.
Now, As the inequality is strictly greater than 26/9 it would be represented by a line open circled at 26/9 and going towards +∞.
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a person in a lighthouse 22m above sea level sights a buoy in the water. if the angle of depression to the buoy is 25o, how far from the base of the lighthouse is the buoy?
Answers
If the angle of depression to the buoy is 250, then the buoy is approximately 47.2 meters from the base of the lighthouse.
What is angle of depression ?
The angle of depression is the angle between a horizontal line of sight and the line of sight from an observer to a point or object that is lower than the observer. It is commonly used in trigonometry and geometry problems that involve the height or depth of an object relative to an observer or the ground.
We can start by drawing a diagram to visualize the situation.
In the diagram, A represents the location of the lighthouse, B represents the location of the buoy, and x represents the distance from the base of the lighthouse to the buoy that we want to find.
Since the angle of depression from the lighthouse to the buoy is 25 degrees, we know that angle ABx is also 25 degrees. We also know that the height of the lighthouse above sea level is 22 meters.
We can use the tangent function to find the value of x:
tan(25°) = opposite / adjacent
tan(25°) = 22 / x
Solving for x, we get:
x = 22 / tan(25°)
x ≈ 47.2 meters
Therefore, the buoy is approximately 47.2 meters from the base of the lighthouse.
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A right triangle has side length 8 15 and 17 use these lengths to find Cos M Tan M and Sin M
Answers
Answer:
Cos A: [tex]\frac{15}{17}[/tex]
Tan A: [tex]\frac{8}{15}[/tex]
Sin C: [tex]\frac{8}{17}[/tex]
How I did it:
Cos A: [tex]\frac{Base}{Hypotenuse}[/tex] This is the basic " fraction "
Or in similar terms: = [tex]\frac{ab}{bc}[/tex]
Cos A = [tex]\frac{15}{17}[/tex]
Tan A = [tex]\frac{Perpendicular}{Base}[/tex]
Similar terms once again = [tex]\frac{ac}{ab}[/tex]
Tan A = [tex]\frac{8}{15}[/tex]
Sin A = [tex]\frac{Perpendicular}{Hypotnuse}[/tex]
Similar terms = [tex]\frac{ac}{bc}[/tex]
Since A = [tex]\frac{8}{17}[/tex]
Thus your answers are:
Cos A = [tex]\frac{15}{17}[/tex]
Tan A = [tex]\frac{8}{15}[/tex]
Sin A = [tex]\frac{8}{17}[/tex]
explain how to solve the equation and how to check the solution.
40 = 8y
plse help me
Answers
Answer:
y=5
divide 40 by 8
times 5 by 8 to check your solution
Answer:
see explanation
Step-by-step explanation:
40 = 8y ( isolate y by dividing both sides by 8 )
5 = y
As a check
substitute y into the right side of the equation and if both sides are equal then it is the solution.
right side = 8y = 8 × 5 = 40 = left side
since both sides are equal then y = 5 is the solution to the equation
PLEASE HELP DUE TOMORROW
Ok, so I know the answer is 1 but I just need some work to prove it.
Answers
Answer:
The sum of the digits in the mystery year is 9
Step-by-step explanation:
Let me try to help you
given the number of packages of hot dogs is d
given the number of packages of buns is b
so the total of hot dogs = total of buns
=> 8d = 6b or 4d = 3b
The number can be only integers like 1, 2, 3, 4, 5
So the smallest integer for d is 3 and b is 4
If you buy 3 packages of hot dogs, the number of hot dogs is 3 x 8 = 24
If you buy 4 packages of bun, the number of buns is 4 x 6 = 24
Divide #hot dogs by #packages of buns
So 24/4 = 6
Divide the result by 1/3
6 / (1/3) = 18
Sum of the digits
1 + 8 = 9
Hope this helps
Use substitution to solve the system. +3x5y = 7 y = +2x4
Answers
Answer: To solve the system of equations using substitution, we'll start by rearranging one of the equations so that one of the variables can be expressed in terms of the other. In this case, we'll rearrange the second equation to find y in terms of x.
y = 2x + 4
Next, we'll substitute this expression for y into the first equation:
+3x + 5(2x + 4) = 7
Expanding the right-hand side:
+3x + 10x + 20 = 7
Combining like terms:
13x + 20 = 7
Subtracting 20 from both sides:
13x = -13
Dividing both sides by 13:
x = -1
Finally, we'll use the expression we found for y in terms of x to find the corresponding value of y:
y = 2x + 4
y = 2(-1) + 4
y = -2 + 4
y = 2
So the solution to the system is (x, y) = (-1, 2).
Step-by-step explanation:
h(x)=−(x−2)
2
+16h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 2, right parenthesis, squared, plus, 16
What is the height of the ball at the time it is thrown?
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Answer:
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Which transformation maps △UVW to △EFG?
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Option D (x, y)→ (-2x, 2y) is the transformation that maps triangle UVW to triangle EFG.
What do you mean by Transformation?In mathematics, a transformation refers to a process of changing the position, size, or orientation of a geometric shape. It is a fundamental concept in geometry, algebra, and other branches of mathematics that studies the properties of objects and their relationship with space.
Transformations can be classified into two main types: rigid and non-rigid transformations. Rigid transformations preserve the size and shape of the object while changing its position and orientation. Common examples of rigid transformations are translations, rotations, and reflections. Non-rigid transformations, on the other hand, change the size and shape of the object as well as its position and orientation.
Transformations are used in various areas of mathematics and science, such as computer graphics, physics, and engineering. They are also important in real-world applications, such as in designing and modeling objects, analyzing data, and solving practical problems.
The transformation involves a reflection across the y-axis (multiplication by -1 on the x-coordinate) and a dilation by a factor of 2 in the y-direction (multiplication by 2 on the y-coordinate).
Applying this transformation to the coordinates of triangle UVW:
(0, -2) -> (0, -4)
(2, 0) -> (-4, 0)
(-2, 2) -> (4, 4)
These transformed coordinates match the coordinates of triangle EFG, so option D is the correct answer.
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