Temperatures in °F can be converted in °C using the formula
C=5(F-32)/9
Make F the subject of the formula
Give your answer in the form aC+b/c where a,b and c are all positive integers
Answers
Answer:
Step-by-step explanation:
To make F the subject of the formula, you need to solve for F in the equation C = 5(F-32)/9.
You can do this by first multiplying both sides of the equation by 9 to get rid of the fraction:
C * 9 = 5(F-32)
Then, you can distribute the 5 on the right side of the equation:
C * 9 = 5F - 160
Then, you can add 160 to both sides of the equation to isolate the F term:
C * 9 + 160 = 5F
Finally, you can divide both sides of the equation by 5 to solve for F:
F = (C * 9 + 160)/5
This gives you the final form of the equation:
F = (9C + 160)/5
In this form, F is the subject of the formula. a = 9, b = 160, and c = 5 are all positive integers.
Answer:
[tex]F=\dfrac{9C+160}{5}[/tex]
Step-by-step explanation:
Given equation:
[tex]C=\dfrac{5(F-32)}{9}[/tex]
Multiply both sides by 9:
[tex]\implies 9C=5(F-32)[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{9C}{5}=F-32[/tex]
Add 32 to both sides:
[tex]\implies \dfrac{9C}{5}+32=F[/tex]
[tex]\implies F=\dfrac{9C}{5}+32[/tex]
Rewrite 32 as a fraction with denominator 5:
[tex]\implies F=\dfrac{9C}{5}+\dfrac{32 \cdot 5}{5}[/tex]
[tex]\implies F=\dfrac{9C}{5}+\dfrac{160}{5}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies F=\dfrac{9C+160}{5}[/tex]
Related Questions
Pls help on my math question and for part c it’s 48 since the teacher gave us answer only for tht part and show work pls :)
Answers
a) Equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0
b) Width of the rectangular rug be 3.5 feet
c) Diagonal of the rectangle is 12.5 feet
What is the area of the rectangle?
The area of a rectangle is the area occupied by the rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle. The perimeter of a rectangle is equal to the sum of all its four sides
It is given that area of a rectangular rug id 42 square feet. The rug is 8 feet longer than its wide
a) Let the width of the rectangular rug be x feet
Length of the rectangular rug = (x+8) feet
area of rectangular rug = Length × width = x × (x + 8) = [tex]x^{2}[/tex] + 8x
area of rectangular rug = 42
[tex]x^{2}[/tex] + 8x = 42
[tex]x^{2}[/tex] + 8x - 42 = 0
Therefore, equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0
b) If the length of the rectangle is 12 feet
Area of rectangle = 42 square feet
length × width = 42 square feet
12 × width = 42 square feet
width = 42/12 = 3.5
Therefore, width of the rectangular rug be 3.5 feet
c) Length of the diagonal of the rectangle = [tex]\sqrt{length^2+width^2}[/tex]
= [tex]\sqrt{12^2+3.5^2}=\sqrt{144+12.25}=\sqrt{156.25}= 12.5[/tex]
Therefore, diagonal of the rectangle is 12.5 feet
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please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
EP = GP
GP = HP
angle EFH = 45
Think these 3 are the right answers, hope it helps.
f(x) = 2x³x² - 29x
What is the greatest possible number of turning points?
Answers
Answer:
4
Step-by-step explanation:
First we need to get some definitions out of the way
Definition of a turning point
A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising). A polynomial of degree n will have at most n−1 turning points.Definition of degree of polynomial
The degree of a polynomial is the degree of the term having the highest degree.The given polynomial is[tex]f(x) = 2x^3x^2-29x[/tex]The highest degree of [tex]x[/tex] is the degree of the polynomial
We know that when we multiply same terms with different exponents, the exponents get added. Therefore
[tex]x^3x^2 = x^{3 + 2} = x^5[/tex]So the polynomial can be re-written as:
[tex]2x^5 -29x[/tex]The highest degree of [tex]x[/tex] is [tex]5[/tex] and this is the degree of the polynomial
So the maximum number of turning points [tex]= 5-1 = 4[/tex]
The perpendicular biector of ide AB of triangle ABC interect ide AB at point D and BC at point E. If angle CAB = 82 degree and angle C = 68 degree, what i angle CAE
Answers
The angle of CAE is 22
What is perpendicular bisector ?A line known as a perpendicular bisector cuts a specified line segment precisely in half, creating a 90° angle at the junction. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.
Perpendicular bisector of ABC's side AB crosses BC at point E and side AB at point D. Additionally, m CAB = 82 and m C = 68.
Adopt A E.
In ABC, the triangle's angle sum property is A+B+C=180°.
82°+∠B+68°=180°
∠B= 180°-150°
∠B=30°
AD=B DDE is a perpendicular bisector in A DE and B DE.
If ADE=BDE=90°
DE is common.
Δ A DE ≅ Δ E DB→→[S AS]
∠DEB=∠D A E→→[CPCT]----(1)
In Δ DBE
∠EDB + ∠DBE+∠BED=180°→→Angle sum property of Triangle.
90° +30°+∠BED=180°
∠BED=180°-120°
∠BED=60°
So, ∠BAE=∠BED=60°------[using (1)]
∠CAE=∠CAB - ∠BAE
= 82°-60°
= 22°
Therefore the angle CAE is 22
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I NEED HELP ASAP
FIRST TI ANSWER GET BRAINLEST
Answers
Answer:
4.
y = -1/6 * x - 7/3
Step-by-step explanation:
We can just check:
1.
y = -1/6 * x
this doesn't work for x = -2 and y = -2 (first point) because we get
-2 = -1/6 * -2 = 1/3
this is nonsense
2.
y = -6x - 3/7
this doesn't work for x = -2 and y = -2 (first point) because we get
-2 = -6 * -2 - 3/7 = 12 - 3/7 = 11 + 4/7
this is nonsense
3.
y = -6x
this doesn't work for x = -2 and y = -2 (first point) because we get
-2 = -6 * -2 = 12
this is nonsense
4.
y = -1/6 * x - 7/3
this works for x = -2 and y = -2 because
-2 = -1/6 * -2 - 7/3 = 2/6 - 7/3 = 1/3 - 7/3 = -6/3 = -2
it also works for x = 4 and y = -3 because
-3 = -1/6 * 4 - 7/3 = -4/6 - 7/3 = -2/3 - 7/3 = -9/3 = -3
Find the value of each variable
I’ve figured out Z, but need help with Y.
Answers
Answer: Y=112
Step-by-step explanation: Add all of the interior angles you have to get 248 and subtract 248 from 360.
67+80+101 = 248.
360-248 = 112
f(x) = 3x - 2 and g(x) = 2x
Find g(f(3))
Answers
Answer:
14
Step-by-step explanation:
To find g(f(3)), you will need to first find f(3) and then substitute that value into the function g(x).
To find f(3), substitute 3 for x in the equation for f(x):
f(3) = 3(3) - 2 = 9 - 2 = 7
Now substitute the value of f(3) into the equation for g(x):
g(f(3)) = g(7) = 2(7) = 14
Therefore, g(f(3)) = 14
Answer:
f(3)=7 g(3)=6
Step-by-step explanation:
f(x)=3x-2
f(3)=3(3)-2
f(3)=9-2
f(3)=7
g(x)=2x
g(3)=2(3)
g(3)=6
Simplify the expression |ab^3| if a>0 and b>0
Answers
The expression |ab^3| if a>0 and b>0 is even.
What is Parity Definition?
Even Function: A function is even if f(-x)=f(x) for all [tex]$x \in \mathbb{R}$[/tex] Odd Function: A function is odd if f(-x)=-f(x) for all [tex]$x \in \mathbb{R}$[/tex]
[tex]f(a): \quad|a|\left|b^3\right|[/tex]
[tex]f(-a): \quad|a|\left|b^3\right|[/tex]
[tex]-f(a):-|a|\left|b^3\right|[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
The expression |ab^3| if b>0
[tex]$$\begin{aligned}& f(a): \quad|a| b^3 \mid \\& f(-a): \quad|a|\left|b^3\right| \\& -f(a): \quad-|a| b^3 \mid\end{aligned}$$[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
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What is inverse of the function f(x) = 4(x - 3)?
Answers
The inverse of the function f(x) = 4(x - 3) is f⁻¹(x)=(x+12)/4.
What is meant by inverse function?A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) generates y, then y entered into f's inverse creates x. x . Invertible refers to a function that has an inverse, which is represented by the symbol f1.
Inverse functions are functions that "reverse" one another in the broadest sense. If f, for instance, goes from a to b, then its inverse, f 1 f -1 f 1f, start superscript, minus 1, end superscript, must go from b to a.
Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F has an inverse if there are no horizontal lines that cross the graph of f more than once.
Let f(x)=y
f(x)=4(x-3)
f(x)=y
y=4(x-3)
x=4(y-3)
x=4y-12
4y=x+12
y=(x+12)/4
Therefore, f⁻¹(x)=(x+12)/4
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in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
Answers
American adults believes in alien for the given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).
As given in the question,
Sample of American adults surveyed 'n' = 200
Percent of people believes in aliens are success 'p'= 72%
= 0.72
Percent of people who don't believes (failure) in aliens ' 1 - p' = 1 - 0.72
= 0.28
95% Confidence interval that represents Americans adults who believes in aliens
value of z - score for 95% confidence interval = ± 1.96
Margin of error 'MOE'= (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200
= 1.96 ( √0.2016 / 200)
= 1.96 ×√0.001008
= 0.063
Lower limit = p - MOE
= 0.72 - 0.063
= 0.66
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.78
Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).
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Segment AB has point A located at (8, 9). If the distance from A to B is 10 units, which of the following could be used to calculate the coordinates for point B
O 10 √(x+8)2+(y+9)²
O10-√√(x+9)²+(y+8)²
O10-√√(x-8)2+(y-9)²
O10-√(x-9)2+(y-8)²
Answers
Thus, we get that 10= sqrt((x-8)^2+(y-9)^2
The price of the shirt was $38. It was reduced by 20% and then again by 10%. What was the final price of the shirt?
Answers
Answer:
Step-by-step explanation:
$38, 20% off = $30.40
$30.40, 10% off = $27.36
$27.36 is the final price of the shirt
The surface area of this cylinder is 118.378 square yards. What is the height?
Use ≈ 3.14 and round your answer to the nearest hundredth.
r = 2.9 yd
Answers
The surface area of this cylinder is 118.378 square yards. 3.6 yard is the height.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. Square units are used to measure it at all times.
The terms "lateral surface area," "curved surface area," and "total surface area" refer to three different forms of surface area.
Surface area and volume are the cylinder's two main characteristics because it is a three-dimensional form. The area of the two circular bases combined with the cylinder's curved surface area equals the cylinder's overall surface area. Its volume is the three-dimensional area that a cylinder takes up.
Given that,
Surface area (A) of the cylinder = 118.378 square yards.
radius (r) = 2.9 yard
As we know, A = 2πrh + 2πr²
putting the values we get -
or, 118.378 = 2πr (h + r)
or, 118.378 = 2 × 3.14 ×2.9 × (h + 2.9)
or, 118.378 = 18.212 × (h + 2.9)
or, 6.5 = h + 2.9
or, h = 6.5 - 2.9
or, h = 3.6 yard
Thus, 3.6 yard is the height of the cylinder.
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HELP MEEEEE PLEASEEEEEE
Answers
The bus is covering a distance of 42 miles in 1 hour 30 minutes then the speed of the bus will be 28 mph.
What is Average speed?
The overall distance the object covers in a given amount of time is its average speed. The scalar quantity represents the average speed. It does not have direction; it is represented by magnitude.
As per the given data provided in the question,
Total distance traveled by bus = 42 miles
Total time is taken by the bus = 1 hour 30 minutes = 1.5 hours.
Then the average speed of the bus will be,
[tex]Average\ Speed(S) = Total\ Distance/Total\ Time[/tex]
S = 42/1.5
S = 28 mph.
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A new club sent out 250 coupons to boost sales for next year's memberships. They provided 4 times as many to potential members than to existing members. How many coupons did they send to existing members?
A.
4
B.
50
C.
5
D.
54
Answers
Answer: 50 existing members
The ribbon on a spool is 13 yards long. How many 4 inch pieces of ribbon can be cut from the spool?
Answers
Answer:
117
Step-by-step explanation:
13 yards = 468 inches
468 ÷ 4 = 117
Multiply (-8.328)(15.99)
Answers
Answer:
-133.16472
Step-by-step explanation:
N/A
Answer:
-133.16472
Step-by-step explanation:
How do you simplify 5+5x-3x+1
Answers
Answer:
6 + 2x
Step-by-step explanation:
5 + 5x - 3x + 1
add 5 + 1
6 + 5x - 3x
collect like terms 5x -3x
6 + 2x
Step-by-step explanation:
Please follow me the answer is 6+2x
or 2x+6
Ohdhhdhdhdgdueyehehehhegehehehgegr
Answers
Answer:
JSHKAKSBKSBAK?
Step-by-step explanation:
Line r has an equation of y=
6/7x+1. Line s includes the point (7,–7) and is perpendicular to line r. What is the equation of line s?
Answers
The equation of line s is y + 7 = -7/6(x - 7).
What is slope of a line?
A line's steepness and direction are measured by the line's slope. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, Δy, Δx respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx
Given equation of line r is y = 6/7x+1.
The slope of line r is m = 6/7
The slope of the line that is perpendicular to line r is -1/m = - 7/6.
The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m(x - x₁).
Putting m = - 7/6, x₁ = 7 and y₁ = -7 in y - y₁ = m(x - x₁):
y - (-7) = - 7/6(x - 7)
y + 7 = - 7/6(x - 7)
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A line with a lope of 1/6 pae through the point (0,-3) what i it equation in lope intercept form
Answers
An equation of line having slope 1/6 and passes through the point (0,-3) is y = 1/6x - 3
We know that the slope-point form of line is:
(y - y1) = m(x - x1)
Here, we need to find an equation of line having slope 1/6 and passes pae through the point (0,-3)
let (x1, y1) = (0, -3)
and m = 1/6
substitute values in above formula,
(y - (-3)) = 1/6 (x - 0)
y + 3 = 1/6 (x)
y = 1/6x - 3
which is slope-intercept form of line (y = mx + b)
Therefore, equation of line is y = 1/6x - 3
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Solve for x
Note drawn to scale
Geometry
Answers
Answer:
x=2
Step-by-step explanation:
1. Set the proportions equal: 5/2x-3 = 15/27
2. Butterfly method: 27x5 = 3x-3 x 15
3. Continue solving: 135 = 45x-45
4. Break it down: 45x = 90
5. Solution: 2 because 45 x 2 is equal to 90
Answer:
x=4
Step-by-step explanation:
[tex]\frac{3x-3}{5}=\frac{24+3x}{20}[/tex] Original equation. A proportion can be set up so that
you can find x. One proportion can be one side over the
other side of one of the smaller triangle set equal
to the total length of the larger triangle. 27 and -3 can
combine forming 24, which continues to be added to 3x.
15 and 5 can be combined to become 20.
20(3x-3)=5(24+3x) Now, cross multiply. This involves the distribution of one
term to the terms it's multiplied by. 20*3x=60x and
20*-3=-60. 5*24=120 and 5*3x=15x.
60x-60=120+15x Now, the goal is to get x alone on one side. You can do
this by combining like terms. Subtract 15x from both
sides and add 60 to both sides.
45x=180 Then, divide by 45 to get x by itself.
x=4 This is your answer.
1 A, B and C are points on a circle with centre O.
8 cm A-B
15 cm B-C
B
AOC is a diameter of the circle.
AB= 8 cm
BC= 15 cm
Angle ABC = 90°
Work out the total area of the regions shown shaded in the diagram.
Give your answer correct to 3 significant figures.
Diagram NOT
accurately drawn
Answers
The total area of the shaded region is solved to be 154.93 cm²
How to find the total area of the shaded regionThe diameter is solved using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let x be the required distance
x² = 8² + 15²
x² = 289
x = √289
x = 17
Work out the area of the triangle using the formula
= 1/2 * base * height
base = hypotenuse or diameter
height = radius = diameter/2
= 0.5 * 17 * 8.5
= 72.25 cm²
Area of the circle
= Π * radius²
= 22/7 * 8.5²
= 226.98 cm²
shaded portion
= Area of the circle - area of the triangle
= 226.98 - 72.25
= 154.93 cm²
the area of the shaded portion is 154.93 cm²
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The congruency theorem can be used to prove that △wut ≅ △vtu.
Answers
As per the congruency theorem, the two triangles are congruent.
Congruency theorem:
Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."
Given,
Here we need to prove that congruency theorem can be used to prove that △wut ≅ △vtu.
Let us consider triangles WUT and VTU.
And in these triangles:
=> WU≅VT
And in those one, ∠T≅∠U,
Therefore, m∠T = m∠U = 90°
Here the side TU is common.
Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.
Then the side TU is common leg and sides WU and VT are hypotenuses.
Therefore, the HL theorem states: if the hypotenuse (WU) and one leg (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.
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Answer: HL
Step-by-step explanation:
what value of k does the equation k + 4/x +3/x^2 =0. (I) two real and different roots. (Ii)coincident and real root. (iii) no roots
Answers
The value of k will be equal to 4/3 and there will be two real and different roots.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the equation is k + 4/x +3/x² =0. The value of k will be calculated as,
k + 4/x +3/x² =0.
kx² + 4x + 3 = 0
b² - 4ac =0
4² = 4 x k x 3
16 = 12k
k = 4/3
Therefore, the value of k will be equal to 4/3 and there will be two real and different roots.
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0.4x+6.1forx= -5
show work
Answers
0.4(-5) + 6.1 = 4.1
0.4(-5) + 6.1
-2 + 6.1 = 4.1
0.4x + 6.1 = 4.1
help me with this please !!!!
Answers
Answer: 2 times!
Step-by-step explanation:
(-1,0)
(4/3, 0)
Answer:
C.2
Step-by-step explanation:
See attached: the graph of your function
a project has the following projected outcomes in dollars: $210, $320, and $540. the probabilities of their outcomes are 25%, 55%, and 20% respectively. what is the expected value of these outcomes?
Answers
The expected value of these outcomes are $262.5, $496 and $648 respectively
How to calculate expected values?You should know that the expected value are the proportion of the values when valued with the percentages
The given values are $210, $320 and $540
The given percentages are 25%, 55% and 20%
The expected values are
0.25*210 = $52.5+210=$262.5
0.55*320=176+320=$496
0.20*540=108+540=$648
Therefore the projected values of the project are $262.5, $496 and $648 respectively
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A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?
(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)
Answers
If the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.
Given that, a full pond containing 625 gallons of water begins losing its water at a rate of 20% per week.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, number of gallons water being used for x weeks is
625-320=305 gallons
Now, number of gallons of water used in a week= 20% of 305
= 20/100 ×305
= 0.2 ×305
= 61 gallons
So, number of weeks = x=305/61
= 5
Therefore, if the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.
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Answer:
5
Step-by-step explanation:
Look that guys answer is better
What is the value of cosine (startfraction x over 2 endfraction) if tangent x = one-half and x is in quadrant iii? negative startstartroot startfraction 5 minus 2 startroot 5 endroot over 10 endfraction endendroot negative startstartroot startfraction 5 + 2 startroot 5 endroot over 10 endfraction endendroot startstartroot startfraction 5 minus 2 startroot 5 endroot over 10 endfraction endendroot startstartroot startfraction 5 + 2 startroot 5 endroot over 10 endfraction endendroot.
Answers
Given that x is in quadrant 3, its value for tan x=1/2 will be 206.565°, and its value for cos(206.565°) will be -0.894.
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.
Here,
Tan x=1/2
π<x<3π/2
x=tan⁻¹/²(1/2)
x=26.565°
As the x is in quadrant 3,
=180+26.565°
=206.565°
cos(206.565°)=-0.894
The value of x for tan x=1/2 will be 206.565° as x is in quadrant 3 and for the same value of x, cos(206.565°) will be -0.894.
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Answer:
-sqrt 5 - 2 sqrt 5/10
Step-by-step explanation:
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