[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
y is inversely proportional to [tex]\sf{x^2}[/tex].✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏
If y=2 when x=4, what is y when x=[tex]\frac{1}{2}[/tex] ?▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex] ✏
If y is inversely proportional to x^2, the equation looks as shown below:-
[tex]\sf{\longmapsto{y=\cfrac{k}{x^2}}[/tex], where k -- constant of proportionality
Plug in all values
[tex]\sf{\longmapsto{2=\cfrac{k}{4^2}}[/tex] , simplifying --
[tex]\sf{\longmapsto{2=k/16}[/tex]
multiply by 16 both sides
[tex]\sf{\longmapsto 2*16=k}}[/tex]
[tex]\sf{\longmapsto{32=k}}[/tex]
▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
Plug 32 into the second equation:-
[tex]\sf{\longmapsto y=\cfrac{32}{\bigg(\cfrac{1}{2}\bigg)^2}}[/tex]
simplify the complex fraction
[tex]\longmapsto\sf{y=\cfrac{32}{\cfrac{1}{4}}[/tex]
divide fractions
[tex]\sf{\longmapsto{y=\cfrac{32}{1}\div\cfrac{1}{4}}=\cfrac{32}{1}\cdot}\cfrac{4}{1}}=128}[/tex]
`hope that was helpful to u ~
You are investigating having business cards printed for your new game store. A local printing company charges $250 for the cardboard used and an hourly rate for labour of $40.
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost
of the cards, C.
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give
your answer to the nearest minute.
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you
get printed with your current budget?
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Answer:
See below.
Step-by-step explanation:
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.
C = $250 + ($40/hr)*h
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.
$1000 = $250 + ($40/hr)*h
($40/hr)*h = $750
h = 18.75 hours
(18.75 hours)(60 min/hr) = 1125 minutes
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?
(18.75 hr)*(1000 cards/hr) = 18,750 cards
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Photocopy Cost for the first 1000 single-sided cards is:
(1000 cards)*($0.15) = $150
Photocopy Cost for the final 17,750 single-sided cards is:
(17,750)*($0.10) = $1,775
Totoal photocopy cost for 18,750 single-sided cards is $1,925. [1775+150]
The cheapest option for 18,750 cards is printing: $1,000
Printing is (1,925 - 1000) $925 cheaper than photocopying.
if m = 2 and n = 5 then find the value of 6m+5n
Answer:
37
Step-by-step explanation:
6m+5n
plug in your given values
6(2) + 5(5)
12+25
=37
Answer:
37
Step-by-step explanation:
6m + 5n
6*2 + 5*5 = 12 + 25
= 37
Select the correct answer. which expression is equivalent to , if x > 0? a. b. c. d.
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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Complete question
Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0
3. You recently bought a rolled up poster at a convention and need to fit it in
your luggage. In order to pack it efficiently, we need to know the surface
area of the tube. If the radius measures out to be 0.4 inches and the height
is 25 inches, what is the full surface area? Use 3.14 for .
63.8 in²
1in²
62.8 in²
63.8 in3
Answer:
A. 63.8 in^2
Step-by-step explanation:
The surface area of a cylinder is given by:
A=2πrh+2πr^2
2πr^2 gives the area of the 2 ends, each with area πr^2.
2πrh gives the suface area of the outside of the cylinder.
r = 0.4 inches
h = 25 inches
Area = 63.8 in^2
Using the sine rule, calculate the length y. Give your answer to 2 s.f.
Answer:
y = 9.84 mm
Step-by-step explanation:
Sine rule:Law of sine:
[tex]\sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}[/tex]
a = y
A = 31°
b = 17 mm
B = 117°
[tex]\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\[/tex]
[tex]\sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\ y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm[/tex]
A certain university recently calculated the number of days that its students took to complete their master's degrees. It took 100 of the students 800 days. In contrast, it took 150 of the students 600 days. What is the average number of days that these students took to complete their master's degrees? a) 620 days b) 680 days c) 700 days d) 720 days?
Answer:
c) 700
Step-by-step explanation:
Add 800 and 600, and then divide by the number of number, or in this case, two. This should give you 700.
How do I do C?Someone please help asap.
You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.
Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.
The slope of the line is then
[tex]\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}[/tex]
which means that 1 in ≈ 2.5 cm.
So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)
[tex]64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}[/tex]
The difference between two integers is 8 and their product is 65. Assume that the larger of the two numbers is x. Write a quadratic equation in standard form that can be used to determine the value of x. Factor your equation from Part B and determine the possible solutions to your equation. Show your work. Write an expression for the second number.
A quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0.
The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5.
The value for the second number is 5
Word Problem Leading To Quadratic Equation.The general formula for quadratic equation in a in standard form is
a[tex]x^{2}[/tex] + bx + c = 0
Given that the difference between two integers is 8
Let the two integers = x and y,
and their product is 65. If the larger of the two numbers is x. Then,
x - y = 8 and xy = 65
Since we are looking for the value of x, make y the subject of formula in the first equation.
y = x - 8
Substitute y in the second equation.
x(x - 8) = 65
[tex]x^{2}[/tex] - 8x - 65 = 0
[tex]x^{2}[/tex] - 13x + 5x - 65 = 0
(x - 13)(x + 5) = 0
x = 13 or -5
We will ignore -5 since x is the larger number.
To get y Substitute x in the second equation.
xy = 65
13y = 65
y = 65/13
y = 5
Therefore, a quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5
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If you can please explain how you got your answer so I can understand, Thank you!
Answer:
3 2/5
Step-by-step explanation:
Each slash/mark on the number line is 1/5, meaning that 6 marks away is 3 2/5.
To further explain how I know each mark is 1/5, each question had a denominator of 5, and if you count each mark from 2 1/5 (2 2/5, 2 3/5, 2 4/5, 3, etc) you will eventually land on 4 evenly.
Chemotherapy in adult highgrade glioma: a systematic review and metaanalysis of individual patient data from 12 randomized trials
Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.
What is Systemic chemotherapy?Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).
Some Key features of systemic chemotherapy are-
Background: In order to evaluate the effects of such treatment on survival and recurrence, we conducted a systematic review and meta-analysis.Methods: From 12 randomised controlled studies, information on 3004 patients was incorporated (11 published and one unpublished).Findings: Overall, the findings indicated a significant survival extension associated with chemotherapy, with a hazard ratio of 0.85 (95 percent confidence interval [CI] 0.78–0.91, p0.0001) or a relative reduction in mortality risk of 15%. There was no proof that a patient's age, gender, histology, performance status, or degree of resection affected how chemotherapy worked in any particular way.Interpretation: Further research into pharmacological treatment for malignant tumors is encouraged by this modest but noticeable improvement in survival from chemotherapy.To know more about Chemotherapy, here
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Find the missing values
Answer:
5
Step-by-step explanation:
5×(-4)=20
5×3=15
5×0.5=2.5
5×5=25
5×0=0
5×(-2)=-10
What is the equation of the line parallel to the given line with an x-intercept of 4? y = x
In the biblical account, adam lived to be how old?
a. 99
b. 122
c. 545
d. 930
Putting the other player's king in check is always a good move. true or false subject: chess
Putting the other player's king in check is always a good move. true
What is chess?The policies of chess allow a king to take an opponent's piece whilst in check, so long as that piece isn't always being defended. At the equal time, a king in the test is usually forced to move.The standard regulations of chess, a participant may not make any pass that places or leaves their king in the test. A player may additionally pass the king, seize the threatening piece, or block the check with some other piece. A king cannot look at the opposing king, considering this will vicinity the first king in check as well.
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Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]
Step-by-step explanation:
By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].
Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.
PLEASE ASAP NEEDED SO BADLY PLEASEE PLEASE
Answer:
[tex]6x^{2} -24x-10[/tex] with remainder -5
Answer:
[tex]6^2-24x-10-\frac{5}{x+4}[/tex]
In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder
Step-by-step explanation:
I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]
Please if anyone no math I really need help
Answer:
c
Step-by-step explanation:
option a (x-4) translates the graph 4 units right, not down
option b (x)-4 translates the graph 4 units down, not left
option c (x)+4 translates the graph 4 units up, so it is correct
option d (x+4) translates the graph 4 units left, not right
if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down
if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left
a set of data has the values 11,14,23 and 16
The number to add to the set of data is 26
How to determine the new number?The set of data is given as:
11,14,23 and 16
Let the new number be x
So that
Mean = 18
Mean is calculated as:
Mean = Sum/Count
So, we have:
(11 + 14 + 23 + 16 + x)/5 = 18
Multiply by 5
11 + 14 + 23 + 16 + x = 90
Evaluate the like terms
x = 26
Hence, the number to add is 26
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Complete question
A set of data already has the values 11, 14, 23, and 16. What value would have to be added to the set for the mean of the five numbers to be 18?
A landscaping company is covering this trapezoid-shaped yard with grass seed. A trapezoid with base lengths of 6 meters and 7 meters, and height 4 meters. How much area will they need to cover with grass seed
Area covered with grass seed = 10.4[tex]m^{2}[/tex].
What is trapezoid geometry?
A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.
Area of the trapezoid ={ (a+b)/2} +h
where a and b is base and h is height of the trapezoid geometry.
In the question,
a=6m , b=7m and h=4m.
According to the formula { (a+b)/2} +h.
Area covered with grass seed = {(6+7)/2} + 4
= 10.4[tex]m^{2}[/tex].
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Answer:
26
Step-by-step explanation:
GOT IT RIGHT`
Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside.
How high does the center of the frame need to be?
The height of the frame is 15 feet.
How to calculate the height?From the information given, the following can be depicted:
b - 10/a = 2/5
2a = 5b - 50
2a - 5b = -50
Also, slope of AC:
= (b - 10(/(a - 5) = 2/5
2a - 50 = -5b + 50
2a + 5b = 100
Both equations will be solved
The height of the frame will be:
= 5 + 10
= 15 feet
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Homer mowed 5 lawns in his first month and increased the number he mows by two for each month following. Which of the following is the correct interpretation of the rate of change and the initial value?
The equation which represent the interpretation of the scenario is 5 + 2x
AlgebraNumber of lawns Homer mowed = 5Additional laws mowed each month = 2Number of months = xTotal laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)
= 5 + (2 × x)
= 5 + 2x
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line segment connecting the vertices of a hyperbola is called the ________ ________, and the midpoint of the line segment is the ________ of the hyperbola.
line segment connecting the vertices of a hyperbola is called the transverse axis and the midpoint of the line segment is the center of the hyperbola.
What is transverse axis and center of hyperbola ?
The transverse axis is a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci lie on the line that contains the transverse axis. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints.
And The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect. Every hyperbola also has two asymptotes that pass through its center. As a hyperbola recedes from the center, its branches approach these asymptotes.
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The equation represents an ellipse. which points are the vertices of the ellipse? (7, 1) and (7, −5) (7, −10) and (7, 6) (10, −2) and (4, −2) (15, −2) and (−1, −2)
The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).
Which points among the answer choices represents the vertices of the ellipse whose equation is given?The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.
Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;
(x-h)²/a² +(y-k)²/b² = 1.
Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.
Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).
The vertices in this scenario are therefore;
(7+8, -2) and (7-8, -2).
= (15, -2) and (-1, -2).
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C
The graph of f(x) is shown.
O-4,0,2
For what values of x does f(x) = 0?
O-2.0.4
O-5.0.17
45
O-17.0.5
40
Answer: -4, 0, 2
Step-by-step explanation:
The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].
60% of UCLA is girls. What perrcentage are boys
.
Answer:
40%
Step-by-step explanation:
Percent must be equal to 100, so if 60 are girls, then 40% must be boys.
True or
False?
A binary predictor variable is tested for significance using a different test statistic than used for a quantitative predictor variable.
Answer:
it is False
Step-by-step explanation:
A square metal sheet has the side length of 1 cm. À circular hole of radius 2/5 cm is drilled in the middle of the sheet.
How far the hole is from the edge of the sheet?
Step-by-step explanation:
PLEASE I NEED HELP ASAP
The question is :
Danielle reflects shape S in the line x = - 1 , and then reflects the new shape in the line y = 2
Zachary reflects shape S in the line y = 2 , and then reflects the new shape in the line x = - 1
Work out the coordinates of the vertex that A maps to after
a) Danielle's two reflections.
b) Zachary's two reflections.
.
The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)
How to determine the coordinates of the vertex that A maps to after the two reflections?From the given figure, the coordinate of the vertex A is represented as:
A = (-5, 2)
The coordinates of the vertex that A maps to after Daniel's reflections
The rule of reflection across the line x = -1 is
(x, y) ⇒ (-x - 2, y)
So, we have:
A' = (5 - 2, 2)
Evaluate the difference
A' = (3, 2)
The rule of reflection across the line y = 2 is
(x, y) ⇒ (x, -y + 4)
So, we have:
A'' = (3, -2 + 4)
Evaluate the difference
A'' = (3, 4)
Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)
The coordinates of the vertex that A maps to after Zachary's reflections
The rule of reflection across the line y = 2 is
(x, y) ⇒ (x, -y + 4)
So, we have:
A' = (-5, -2 + 4)
Evaluate the difference
A' = (-5, 2)
The rule of reflection across the line x = -1 is
(x, y) ⇒ (-x - 2, y)
So, we have:
A'' = (5 - 2, 2)
Evaluate the difference
A'' = (3, 2)
Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)
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i need the answer to number 9
Answer:
502.5
Step-by-step explanation:
C = 24(12) + 5.50(39)
C = 288 + 214.5
C = $502.5
The taxi fare for the first two miles is $5 and for each additional mile the fare increases by $ 2. What is the taxi fare for a journey of n miles in dollars?
The taxi fare for a journey of n miles in dollars is 1 + 2n
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the equation of the system?The given parameters about the taxi fares are given as
First two miles = $5
Additional mile = Increment of $2
Let the number of miles be n
So, we have:
2 miles = $5
Additional miles = (n - 2) * 2
Add the above expressions
5 + (n - 2)* 2
Represent the value with f(n)
So, we have:
f(n) = 5 + (n - 2)* 2
Expand the bracket
f(n) = 5 + 2n - 4
Collect the like terms
f(n) = 5 - 4+ 2n
Evaluate the like terns
f(n) = 1 + 2n
Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n
So, the complete parameters are:
First two miles = $5
Additional mile = Increment of $2
n miles 1 + 2n
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