Suppose that z varies jointly with x and y. When x=5 and y=4, z=12.
a) Write an equation that models the relationship.
b) Find z when x=15 and y=2.
For z varies jointly with x and y. When x=5 and y=4, z=12.
a. Equation that models the relationship is z=(3/5)xy.
b. When x=15 and y=2 then z=18.
As given,
a. Equation that models relationship z varies jointly with x and y is:
z is directly proportional to product of x and y
⇒z∝ xy
⇒z=k xy
where k is symbol of proportionality.
When x=5 and y=4, z=12
12=k(5× 4)
⇒k=12/(5× 4)
⇒k=3 /5
Hence, z=(3/5)xy
b. When x=15 and y=2
z=(3/5)×15×2
=18
Therefore, for z varies jointly with x and y, when x=5 and y=4, z=12.
a. Equation that models relationship is z=(3/5)xy.
b. When x=15 and y=2 then z=18.
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Zara and Chester are building fences.
Zara uses fence panels that are each 6 feet long and Chester uses fence panels that are each 4 feet long.
If both of their fences are the same length, what is the shortest possible length that Zara's fence could be ? Give your answer in feet
The shortest possible length that Zara's fence could be is 12 feet long.
The fence panels Zara uses are 6 feet long each and the fence panels that Chester uses is each 4 feet long.
The multiple of the number 6: 6, 12, 18, 24
The multiple of the number 4: 4, 8, 12, 16, 20, 24
The numbers 6 and 4 have the same multiple 12, 24. The least common multiple of them is 12.
So Zara's fence has the shortest length is 12 feet, because Zara and Chester have the same length fence as Zara uses fence panels that are each 6 feet long. Chester uses are 4 feet long.
The shortest length of Zara's fence is 12 feet.
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21Select all the correct answers.Which of the following transformations always creates congruent figures?translationsrotationsdilationsreflectionsResetSubmit
Rigid transformations, are transformations of the plane that preserves length. Reflections, translations, rotations, and combinations of these three transformations are rigid transformations. In a rigid transformation the pre-image and image are always congruent
Therefore, the answer is:
translations
rotations
reflections
The total cost (in dollars) to bowl n games is represented by C(n)=4.5n+2.5 . The shoe rental price increases 0.50. The new total cost is represented by T(n)=C(n)+0.5 . Describe the transformation from the graph of C to the graph of T .
In graphical representation it will get displaced by 0.5 units in x-axis.
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
various Transformations are :
The answer choices would ask us to consider some combination of the following transformations:
reflection across the y-axis: (x, y) ⇒ (-x, y)
reflection across the x-axis: (x, y) ⇒ (x, -y)
reflection across the line y=x: (x, y) ⇒ (y, x)
clockwise rotation 90°: (x, y) ⇒ (y, -x)
positive rotation 270°: (x, y) ⇒ (y, -x) . . . same as 90° CW
translation by (h, k): (x, y) ⇒ (x+h, y+k) . . . h units right, k units up
Here, The shoe rental price increases 0.50 that is the new total cost is represented by T(n)=C(n)+0.5, which is 0.5 greater then old price equation that is C(n)=4.5n+2.5 :
Now, In graphical representation it will get displaced by 0.5 units in x-axis.
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Use two conditional statements to draw a conclusion using the law of syllogisms
if a quadrilateral is a square, then it has four right angles, then it is a rectangle.
a. if a quadrilateral has four right angles, then then it is a square
b. if a quadrilateral is a square, then it has four right angles
c. if a quadrilateral is a square, then it is a rectangle
Using the law of syllogism, the conclusion is given as follows:
c. if a quadrilateral is a square, then it is a rectangle.
Law of SyllogismThe Law of Syllogism is a logic axiom which states that if the conditional statements p -> q and q -> r are true, the conditional statement p -> r is also true, basically applying the transitive property.
In the context of this problem, the statements are given as follows:
Statement p: Quadrilateral is a square.Statement q: Quadrilateral has four right angles.Statement r: Quadrilateral is a rectangle.Hence the conclusion is:
p -> r
Read as:
If p then r.
Replacing the statements, we have that:
If a quadrilateral is a square, then it is a rectangle.
Which means that option c is correct.
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3. Rhombus KLMN with vertices K(-3, 2), L(1, 4),
and N(-5, -2): (x,y) → (x, y-5)
M(-1,0)
The coordinates of KLMN after reflection along the y-axis is K'(3,2); L'(-1,4); M'(1,0); and N'(5,-2).
What is reflection?A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane, also known as the axis or plane of reflection. The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.So, the coordinates of KLMN when reflected across the y-axis:
When reflected along the y-axis, the image of (x, y) is (-x,y).
Vertex K(-3,2image )'s after reflection along the y-axis is K' (3,2)After reflection along the y-axis, the image of vertex L(1,4) is L' (-1,4)Vertex M(-1,0image )'s after reflection along the y-axis is M' (1,0)Vertex N(-5,2image )'s after reflection along the y-axis is N' (5,-2)Therefore, the coordinates of KLMN after reflection along the y-axis is K'(3,2); L'(-1,4); M'(1,0); and N'(5,-2).
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The correct question is given below:
Given a rhombus KLMN with vertices K(-3,2), L(1,4), M(-1,0), and N(-5,-2). What would the coordinates of its image be when reflected across the y-axis?
At a middle school 2 out of 5 students Participate in the science fair if they’re are 800 students how many students will be excepted to participate at the fair
anyone knows this??
Answer:
the answer is B 40 because∆ABC is a triangle
After multiplying, a calculator screen displays the answer shown below. How would you write this number in standard form?
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey. How many graduates from University A had an income under $20,000?
Income University A University B
Under $20,000 35 40
$20,000 to $39,999 90 63
$40,000 and over 35 37
Group of answer choices
a.35
b.90
c.160
d.75
The percentage of graduates from University A having income under $20,000 is 22%.
Percentage may be defined as the fraction which we get after dividing an entity from total number multiplied by 100. We have the total number of students in university A as 160. Now, we divide 35 that is the number of students who have an income under $20,000 in university A by 160 that is the total number of students in university A. We get the percentage as
P = (35/160) × 100
P = 0.218 × 100
P = 21.9 %
rounding off to nearest we get percentage as 22 %.
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Sarah leaves her house at 6:25 a.m. to walk to school, which is 4.5 miles away. she meets ur friend at 6:45 a.m. a mile away from her home. if she continues to walk with her friend without increasin speed, what time will she make it to school?
Sarah will take 90 minutes to reach her school from her house if she continues to walk with her friend without increasing speed.
According to the question,
We have the following details:
Sarah leaves her house at 6:25 a.m.
She meets her friend at 6:45 a.m.
So, we have:
The time taken by Sarah to meet her friend after 1 mile = (6:45 - 6:25) minutes
The time take by Sarah to meet her friend after 1 mile = 20 minutes
Now, we can find Sarah's speed.
We know that the formula of speed is as follows:
Speed = distance/time
Speed = 1/20 mile/min
Now, the distance of her school from her house is 4.5 mile.
So, we have:
Time taken = distance/speed
Time taken = 4.5/(1/20) min
Time taken = 4.5*20 min
Time taken = 90 minutes
Hence, the time taken by Sarah to reach her school from her house is 90 minutes.
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The measure of an angle is 136.8° more than the measure of a supplementary angle. What is the measure of each angle?
If the measure of an angle is 136.8 degrees more than the measure of a supplementary angle, then the measure of each angles are 21.6 degrees and 158.4 degrees
The supplementary angles are the angles whose measure add up to 180 degrees.
If x and y are supplementary angles
x + y = 180 degrees
Here the measure of an angle is 136.8 degrees more than the measure of supplementary angle.
So one angle will be x and other angle will be x+136.8
Then the equation will be
x + x+136.8 = 180
2x+136.8 = 180
2x = 43.2
x = 43.2/2
x = 21.6 degrees
Other angle is
21.6+136.8 = 158.4 degrees
Hence, if the measure of an angle is 136.8 degrees more than the measure of a supplementary angle, then the measure of each angles are 21.6 degrees and 158.4 degrees
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Solve the triangle.
a= 10.0 ft, b= 11.0 ft, c = 13.0 ft
What is the measure of angle A?
A=⁰
(Round to two decimal places as needed.)
What is the measure of angle B?
B =°
(Round to two decimal places as needed.)
What is the measure of angle C?
c=°
(Round to two decimal places as needed.)
...
Answer:
Below in bold.
Step-by-step explanation:
Using the Cosine Rule:
a^2 = b^2 + c^2 - 2bc cos A
10^2= 11^2 + 13^2 -2.11.13 cos A
cos A = (11^2 + 13^2 - 10^2) / (2*11*13)
= 0.66434
m < A = 48.368 degrees
= 48.37 degrees to 2 D. P's.
By the Sine Rule:
a / sin A = b / sin B
10 / sin 48.368 = 11 / sin B
sin B = 11 * sin 48.368 / 10
= 0.82217
m < B = 55.303
= 55.30 degrees to 2 D,P's
So, m < C = 180 - 48.37 - 55.30
= 76.33 degrees
3x-2y=109x+4y=-50Solve each system of equations by graphing. Clearly identify your solution.
Plot two points of each equation
Equation 1 Equation 2
3x - 2y = 10 9x + 4y = - 50
x y x y
0 -5 0 12.5
10/3 0 -50/9 0
Graph
A meteorologist was monitoring the temperature outside in degrees Fahrenheit (°F) and wrote the expression 78+(-6) -5. Which statement best describes this expression?
A
The temperature started at 78°F and decreased by 6°F. Then the temperature decreased by 5°F.
B
The temperature started at 78°F and increased by 6°F. Then the temperature decreased by 5°F.
C
The temperature started at 78°F and increased by 6°F. Then the temperature increased by 5°F.
D
The temperature started at 78°F and decreased by 6°F. Then the temperature increased by 5°F.
Correct option is A, The temperature started at 78°F and decreased by 6°F. Then the temperature decreased by 5°F.
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.
An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign, One such equation is 3x - 2 = 5 + x.
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A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
coordinate plane with points at negative 14 comma 1 labeled Woozy Wheel, negative 6 comma 2 labeled Bumper Boats, negative 2 comma negative 4 labeled Roller Rail, negative 2 comma negative 6 labeled Trolley Train, 2 comma negative 3 labeled Silly Slide, and 6 comma 11 labeled Parachute Plunge
Determine the distance between the Bumper Boats and the Parachute Plunge.
15 units
225 units
8 units
63 units
help pls i dont have lot of time!
The distance between the Bumper Boats and the Parachute Plunge is given by:
15 units.
What is the distance between two points?Suppose that we have two points with coordinates given yb [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following rule:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse representing the distance between them.
In the context of this problem, the coordinates of the Bumper Boats and of the Parachute Plunge are given as follows:
Bumber Boats: (-6, 2).Parachute Plunge: (6, 11).Hence the distance between these two points is given as follows:
[tex]D = \sqrt{(6 - (-6))^2+(11 - 2)^2}[/tex]
D = sqrt(12² + 9²)
D = 15 units.
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Answer: its 225
Step-by-step explanation: you should try it and find out. / I did
Arno buys a student ticket for $43.68 .
This is a saving of 16% on the full price of a ticket.
Calculate the full price of a ticket.
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, the full price of the ticket is 293.75.
What is Percentage?Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.
The cost of the ticket Arno buys is $43.68.
The discount she got for the original cost of ticket is 16%.
We need to find the original cost of the ticket.
We need to convert the percentage to a decimal number.
by dividing 16 with 100 we get the decimal value.
16%=16/100=0.16
Now, to find the original or full price of ticket, we need to multiply zero point one six with x equal to forty three point six eight.
0.16×x=43.68
Divide both sides by 0.16
x=293.75
Hence the full price of the ticket is 293.75.
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the 175 workers at a factory together produce 21,175 items per day what is the unit rate of items per worker
Answer: 121 im pretty sure
Step-by-step explanation: 21175 divided by 175
sncidc dslkjfdmqw;vkjjiofrceasZXsdZdcweiaubbciqeu
Can you help me with 8
Answer:
3= 95
a= 85
b=85
4=85
Step-by-step explanation:
Angles on a line add up to 180°
Corresponding angles are equal.
A line has a slope of 0 and passes through the point (-13, -11). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y= - 11
Step-by-step explanation:
A line with a slope of 0 is a horizontal line, parallel to the x- axis with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 13, - 11 ) with y- coordinate - 11, then
y = - 11 ← equation of line
Answer:
y = -11
Step-by-step explanation:
A line with slope as 0, is a horizontal line ( In other words parallel to x-axis).
There is no rise, only run.
Equation of the line is y = c.
y = -11
Read the following description of a data set.
Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any.
Rod noted the age of each person he spoke with, x, and the number of songs each could name, y.
The least squares regression line of this data set is:
y = 0.441x- 12.918
Complete the following sentence:
The least squares regression line predicts that if a person is one year older, they will able to name how many more songs.
the person is able to name .441 more songs
John runs each lap in 7 minutes. He will run at most 35 minutes today. What are the possible numbers of laps he will run today?Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.
Answer: At most 5 laps.
Step-by-step explanation:
N= # of laps
7mins times the number of laps= 7N
35 mins= at most
[tex]7n\leq 35\\\\\frac{7n}{7} \leq \frac{35}{7} \\\ \ \ \ n\ \leq \ 5[/tex]
Given f(x) = 3x³ + x + k, and x + 1 is a factor of f(x), then what is the value of
k?
Answer: k=-2
Step-by-step explanation:
[tex]\displaystyle\\3 x^2+x+k=\\\\3x^2+3x-2x+k=\\\\3x(x+1)-2(x-\frac{k}{2}) \\\\Hence,\\\\x-\frac{k}{2} =x+1\\\\-\frac{k}{2} =1\\[/tex]
Multiply both parts of the equation by -2:
[tex]\displaystyle\\-\frac{k}{2}(-2) =1(-2)\\\\k=-2[/tex]
the table shows information about the population of a city, what is the population in 2021
Is this sentence a fact or an opinion
Many Hindus celebrate a holiday called Diwali by lighting candles and exchanging gifts
Answer:fact
Step-by-step explanation:Opiians have a persianal veiw sush as "the cows should sleep in the shed" while facts are absolute "the cows sleep in the shed"
Determine another point on the line given two points on the line.
(0, 4), (2, 5)
The coordinates of another point are (4, 6).
We are given the coordinates of two points. The two points are (0, 4) and (2, 5). A straight line passes through the two given points.
We will find the equation of the straight line using the formula given below :
(y - y1) = [(y2 - y1)/(x2 - x1)](x - x1)
(y - 4) = [(5 - 4)/(2 - 0)](x - 0)
(y - 4) = (1/2)x
y = (1/2)x + 4
We have to find another point on the line. Let us choose a value for the x-coordinate equal to 4. The y-coordinate can be calculated as given below :
y = (1/2)4 + 4
y = 2 + 4
y = 6
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. (10 points) place these functions in order from slowest asymptotic growth to fastest asymptotic growth. justify the claimed order for each pair of consecutive functions that appear in your ordered list. for instance, if you claim that ????????(????)<????????(????) in growth rate for some choice of the functions ????????(????) and ????????(????), show that the limit test yields lim????→[infinity]????????(????)/????????(????)
Placing these functions from slowest asymptotic growth to fastest asymptotic growth. f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).The exponents we got.
Given that,
Placing these functions from slowest asymptotic growth to fastest asymptotic growth,
Come to question,
f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).
(ln ln ln n) < (ln n + 2021) < ([tex]n^{lg n}[/tex] ) < ((n/lg n)⁸) < (n⁸ - n⁶ + n⁴ - n² + 1) < (n²⁰²¹) < ([tex]32^{n/5}[/tex]) < (3³ⁿ) < ([tex]16^{lgn}[/tex]) < ( 2021 ∛n)
Let's understand, lg n < n < exponential. on the basis of it,
f₇(n) comes first, it will be smaller than f₄(n), because ln n is > ln ln ln n.
f₄(n) comes second, it will be smaller than f₀(n), because O(n) functions are larger than O(log n).
f₀(n) comes third, it will be smaller than f₃(n), because O(n⁸) functions are larger than O([tex]n^{log n}[/tex]).
f₃(n) comes fourth, it will be smaller than f₅(n), because (n⁸ - n⁶ + n⁴ - n² + 1) will give more larger value than ((n/lg n)⁸), these both functions are O(n⁸).
f₅(n) comes fifth, it will be smaller than f₉(n), because n⁸< n²⁰²¹.
f₉(n) comes sixth, it will be smaller than f₂(n), because n²⁰²¹ is O(n), whereas [tex]32^{n/5}[/tex] = 2n is exponential, and exponential are larger than O(n).
f₂(n) comes seventh, it will be smaller than f₆(n), because 2n < 3³ⁿ, both are exponential (2 < 3).
f₆(n) comes eight, it will be smaller than f₁(n), because 3³ⁿ < [tex]16^{logn}[/tex], both are exponential (3 < 16).
f₁(n) comes ninth, it will be smaller than f₈(n), because [tex]16^{logn}[/tex] < 2021 ∛n, both are exponential (16 < 2021).
Complete question: Place these functions in order from slowest asymptotic growth to fastest asymptotic
growth. Justify the claimed order for each pair of consecutive functions that appear in your ordered
list. For instance, if you claim that
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Dolores runs 2.2km north and 1.5km west. What is the shortest distance she must run back to the starting point, to the nearest tenth of a metre
Please show your work
I think this has something to do with the Pythagorean Theorem but I don't know what
The shortest distance to reach the starting point by Dolores is 2.7 kilometres.
The shortest distance will be the line directly connecting the two points. This will form the right angled triangle and hence can directly be calculated. We will be calculating hypotenuse from Pythagoras theorem.
Distance² = 2.2² + 1.5²
Taking square on Right Hand Side
Distance² = 4.84 + 2.25
Performing addition on Right Hand Side of the equation
Distance² = 7.09
Taking square root on Right Hand Side
Distance = ✓7.09
Distance = 2.7 kilometres
Thus, the shortest distance back to the starting point is 2.7 kilometres.
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Which of the following could be a real-world description of the quantity three times x end quantity divided by 8?
A. The cost of a pizza split by 8 people plus a $3 tip
B.The cost of a pizza plus a $3 tip divided by 8 people
C. The cost per pizza for 3 pizzas divided by 8 people
D. The cost per pizza for 8 pizzas divided by 3 people
Answer:
C. The cost per pizza for 3 pizzas divided by 8 people
Step-by-step explanation:
This is the only answer where you are multiplying by 3 and dividing by 8
