Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
A stained-glass window is shaped like a right triangle. The hypotenuse is 15feet. The length of one leg is three more than the other. Find the lengths of the legs.
let us build equation for unknown legs
If we keep the length pf one leg as x
the other leg would be x +3
so we can build a relationship using pythagoras theorem
x^2 + (x+3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x+ 9-225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0 dividing whole equation by 2
x^2 + 12x - 9x - 108 = 0
x ( x + 12 ) - 9 (x + 12) = 0
(x -9) ( x +12) = 0
solutions for x are
x = 9 or x = -12
as lengths cannot be negative
one side length is 9cm
and other which is( x + 3)
9 + 3
12cm
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:
Hypotenuse² = First Leg² + Second leg²
Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:
15² = x² + (x + 3)²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
x² + 3x - 108 = 0
x = - 12 or x = 9
Since the length cant the negative hence x= 9, x + 3 = 12
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Find out more at: https://brainly.com/question/10040532
what is the answer 2×3+4×100-50+10
Answer:
366
Step-by-step explanation:
2×3+4×100-50+10
PEMDAS says multiply and divide from left to right
6 + 400 - 50 +10
Then add and subtract
406-50+10
356+10
366
Answer:
[tex]\boxed{366}[/tex]
Step-by-step explanation:
[tex]2 \times 3+4 \times 100-50+10[/tex]
Multiplication is first.
[tex]6+400-50+10[/tex]
Add or subtract the numbers.
[tex]350+10+6[/tex]
[tex]366[/tex]
Solve for x 90°, 45°, and x°
Answer:
x= 45
Step-by-step explanation:
In this diagram, there is an angle that is split into 2 angles.
The angle is a 90 degree angle. We know this because of the little square in the corner that denotes a right angle.
Therefore, the 2 angles inside of the right angle must add to 90 degrees. The 2 angles that make up the right angle are x and 45.
x+45=90
We want to find x. We need to get x by itself. 45 is being added on to x. The inverse of addition is subtraction. Subtract 45 from both sides.
x+45-45=90-45
x= 90-45
x=45
The measure of angle x is 45 degrees.
A survey of 700 non-fatal car accidents showed that 183 involved faulty equipment. Find a point estimate for the population proportion of non-fatal car accidents that involved faulty equipment.
Answer:
Point of faulty equipment car = 0.2614 (Approx)
Step-by-step explanation:
Given:
Total number of car = 700
Faulty equipment car = 183
Find:
Point of faulty equipment car
Computation:
Point of faulty equipment car = Faulty equipment car / Total number of car
Point of faulty equipment car = 183 / 700
Point of faulty equipment car = 0.261428571
Point of faulty equipment car = 0.2614 (Approx)
Which best describes the meaning of the statement if A then B
Answer:
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
Step-by-step explanation:
You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as "negation of a" or " b" in mathematical terms is written like this
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
You can show that they are logically equivalent because they have the same truth table.
Math question, need help
In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.
Answer:
[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]
First answer is correct.
Step-by-step explanation:
we know that,
[tex] {x}^{a} = {x}^{b} [/tex]
[tex]a = b[/tex]
So, according to that,
[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]
Therefore,
[tex]2x - 1 = 5x - 14[/tex]
Amy and Bob decide to paint one wall of a building. Working alone, Amy takes 12 hours to paint the entire wall while Bob takes 18 hours for the same. Amy painted the wall for 4 hours and then Bob took over and completed the wall. How long did it take for them to paint the entire wall
Answer:
16 hours
Step-by-step explanation:
From the above question, we are given the following information
For one wall, working alone,
Amy can paint for 12 hours
Which means, in
1 hour , Amy would have painted = 1/12 of the wall
Bob can paint for 18 hours
Which means ,
in 1 hour, Bob would have painted = 1/18 of the wall.
We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.
Step 1
Find the portion of the wall Amy painted before Bob took over.
Amy painted the wall for 4 hours before Bob took over.
If:
1 hour = 1/12 of the wall for Amy
4 hours =
Cross multiply
4 × 1/12 ÷ 1
= 4/12 = 1/3
Amy painted one third(1/3) of the wall
Step 2
Find the number of hours left that Bob used in painting the remaining part of the wall
Let the entire wall = 1
If Amy painted 1/3 of the wall
Bob took over and painted = 1 - 1/3
= 2/3 of the wall
If,
Bob painted 1/18 of the wall = 1 hour
2/3 of the wall = ?? = Y
Cross multiply
2/3 × 1 = 1/18 × Y
Y = 2/3 ÷ 1/18
Y = 2/3 × 18/1
Y = 36/3
Y = 12 hours.
This means, the number of hours Bob worked when he took over from Amy = 12 hours.
Step 3
The third and final step is to calculate how many hours it took them to paint the wall
Number of hours painted by Amy + Number of hours painted by Bob
= 4 hours + 12 hours
= 16 hours
Therefore, it took them 16 hours to paint the entire wall.
CAN ANYONE HELP ME PLEASE? Two numbers total of 52 and have a difference of 30. Find the two numbers. The larger number is ? and the smaller number is ?
Answer:
41 and 11.
Step-by-step explanation:
Let's say the 2 numbers are x and y.
Since they add up to 52, x + y = 52.
Seeing as the difference is 30, x - y = 30 assuming x is the larger number.
We have left:
x + y = 52
x - y = 30
By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82
Therefore x = 41.
Since x + y = 52
41 + y = 52
Therefore y = 11
Therefore we have: the larger number is 41 and the smaller number is 11.
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g? X Y 2 2 3 5 4 9 5 13 A: (4,9) B:(-3.-5) C:(13,5) D:(-2,-2)
Answer:
D (13,5)
Step-by-step explanation:
X 2 3 4 5
Y 2 5 9 13
So the ordered pairs are (2,2),(3,5), (4,9), (5,13)
and the ordered pairs for the inverse are
(2,2),(5,3), (9,4), (13,5)
from which D (13,5) is found among the options.
Answer:
b
Step-by-step explanation:
PLZ HELP ITS 20 POINTS Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
The answer is (1,-5). (i.e x=1 and y=-5).
Hope it helps..
Answer:
(1,-5)
Step-by-step explanation:
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2 + y2 = (4x2 + 2y2 − x)2
(0, 0.5)
(cardioid)
Answer:
y = x + 0.5
Step-by-step explanation:
This is a very trivial exercise, follow the steps below:
Step 1: Perform the implicit differentiation of the given equation
[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]
[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]
Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:
[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]
Step 3: Find dy/dx at the point (0, 0.5)
[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]
Step 4: The equation of the tangent line to a curve at a given point is given by the equation:
[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]
In a game of rock-paper-scissors, you have a 1/3 chance of winning, a 1/3 chance of losing, and a 1/3 chance of tying in any given round. What is the probability that you will win at least twice in 3 rounds, given that there aren't any tied rounds in this particular match
Answer: 1/5
Step-by-step explanation:
given data;
chances of winning = 1/3
chances of losing = 1/3
chances of tying in a given round = 1/3
solution:
probability that you would win atleast 2 in any 3 matches without a tied match is
1/3 / ( 2 - 1/3 )
= 1/3 / 5/3
= 1/5
the probability of winning 2 of 3 games without a tie is 1/5
A young Greek by the name of Zeno is riding his horse to his friends house which is two miles away. He travels half the distance in one hour. But his horse gets tired, and only travels half the remaining distance the second hour, and, again, only half the remaining distance in the third hour. How many miles did Zeno travel in those three hours?
Answer:
1.75 miles
Step-by-step explanation:
Zeno's friend's house is two miles away. He travels half the distance in one hour.
0.5 × 2 = 1
The second hour, his horse travels half the remaining distance.
0.5 × 1 = 0.5
The third hour, his horse travels half the remaining distance.
0.5 × 0.5 = 0.25
1 + 0.5 + 0.25 = 1.75
Zeno travels 1.75 miles in three hours.
Hope this helps.
Use the given conditions to write an equation for the line in point-slope form
Passing through (7,3) and (4,4)
OA
1
1.
y-3 = - =(x-
5(x-4) or y-4 = - 3(x - 7)
B.
1
1
y-3= - 3(x-7) or y- 4= - 3(x - 4)
O C. y - 3 = 7(x + 7) or y-4= 4(x-3).
OD
1
1
y + 3 = - 3(x+7) or y+4= - 3(x+4)
Answer:
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
Steb by step explanation:
The condition for the line is (7,3) and (4,4).
Point slope form of equation is in this format below.
(Y-y1)= m(x-x1)
We have the given parameters in the above format except the m
M = gradient
Gradient= (y2-y1)/(x2-x1)
Gradient=(4-3)/(4-7)
Gradient= 1/-3
Gradient= -1/3
So
(Y-y1)= m(x-x1)
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces?
Answer:
P = 0.0714
Step-by-step explanation:
If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.
Additionally, from the 28 cubes painted only 4 have exactly two painted faces.
Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:
[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]
Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.
An investigation of a number of automobile accidents revealed the following information:
18 accidents involved alcohol and excessive speed.
26 involved alcohol.
12 accidents involved excessive speed but not alcohol.
21 accidents involved neither alcohol nor excessive speed.
How many accidents were investigated?
Answer:
59 accidents were investigated.
Step-by-step explanation:
The question above is a probability question that involves 2 elements: causes of accidents.
Let
A = Alcohol
E = Excessive speed
In the question, we are given the following information:
18 accidents involved Alcohol and Excessive speed =P(A ∩ E)
26 involved Alcohol = P(A)
12 accidents involved excessive speed but not alcohol = P( E ) Only
21 accidents involved neither alcohol nor excessive speed = neither A U B
We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)
P(A Only) = 26 - 18
= 8
So, only 8 accident involved Alcohol but not excessive speed.
The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)
= 8 + 12 + 18 + 21
= 59
Therefore, 59 accidents were investigated.
Graph y less than or equal to 3x
Answer:
See Image Below.
Step-by-step explanation:
The Shaded region is the area of numbers that this equation satisfies.
Answer:
Please see attached image
Step-by-step explanation:
In order to graph the inequality, start from plotting the boundary line defined by the equality;
y = 3 x
You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:
for x = 0 then y = 3 (0) = 0
for x = 1 then y = 3 (1) = 3
Then use the points (0, 0) and (1, 3) to plot the boundary line.
After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.
When you use it in the inequality, you get:
(0) [tex]\leq[/tex] 3 (3)
0 [tex]\leq[/tex] 9
which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.
Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.
how many pairs of matching surfaces does a cereal box have
Answer:
3 pairs
Step-by-step explanation:
Top and Bottom
Front and Back
Side and Side.
Cereal Boxes have 6 sides
20 points please help!!!
Answer:
a = 16
b = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).
That means these points lie on the graph of the function 'f' represented by,
f(x) = a(b)ˣ
For the point (0, 16),
f(0) = a(b)⁰
16 = a(1)
a = 16
For another point (1, 12),
f(1) = a(b)¹
12 = ab
12 = 16(b) [Since a = 16]
b = [tex]\frac{12}{16}[/tex]
b = [tex]\frac{3}{4}[/tex]
Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.
When 394 Beach Boys fans were surveyed, 113 said that California girls was their fav song. Find a point estimate for the true proportion of BB fans who favor that song??
1. 0.713
2. 113
3. 0.287
4. 0.95
5. None of the above
Answer: 3. 0.287
Step-by-step explanation:
Let p be the true proportion of BB fans who favor that song.
As per given, Sample size for survey of Beach Boys fans = 394
Number of Beach Boys fans said that California girls was their fav song = 113
Then, the sample proportion of BB fans who favor that song: [tex]\hat{p}=\dfrac{113}{394}[/tex]
[tex]=0.286802030457\approx0.287[/tex]
Since sample proportion is the best estimate for the true proportion.
Hence, a point estimate for the true proportion of BB fans who favor that song is 0.287.
So, the correct option is 3. 0.287 .
Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.)
1. dy/dt = 35t^4
2. dy/dx = 5x^(5/7)
Answer:
1. Y= 7t^5 +C
2. Y= 35/12x^(12/7)+C
Step-by-step explanation:
The general solution will be determined by integrating the equations as the integration is a simple integration.
For dy/dt = 35t^4
The general solution y
= integral (35t^4)dt
The general solution y
=( 35/(4+1))*t^(4+1)
= 35/5t^5
= 7t^5 +C
To prove by differentiating the above.
Y= 7t^5 +C
Dy/Dt= (5*7)t^(5-1) +0
Dy/Dt= 35t^4
For dy/dx = 5x^(5/7)
Y=integral 5x^(5/7)Dx
Y= 5/(5/7 +1)*x^(5/7+1)
Y= 5/(12/7) *x^(12/7)
Y= 35/12x^(12/7)+C
To prove by differentiating
Y= 35/12x^(12/7)+C
Dy/Dx= (35/12)*(12/7) x^(12/7-1) +0
Dy/Dx=(35/7)x^(5/7)
Dy/Dx= 5x^(5/7)
Which phrase best describes the graph of a proportional relationship?
A) a straight line passing
B) a straight line
C) a curve
D) not a straight line
Answer:
A. a straight line passing
Step-by-step explanation:
Answer:
a straight line passing
Step-by-step explanation:
Find a power series for the function, centered at c. f(x) = 1 9 − x , c = 4 f(x) = [infinity] n = 0 Incorrect: Your answer is incorrect. Determine the interval of convergence. (Enter your answer using interval notation.)
Looks like the given function is
[tex]f(x)=\dfrac1{9-x}[/tex]
Recall that for |x| < 1, we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :
[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]
Then
[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]
which converges for |(x - 4)/5| < 1, or -1 < x < 9.
Una masa de 16 libras viaja con una velocidad de 30 m/s . Cuál es su energía cinética?
Energía cinética = 1 / 2mv²
Donde m es la masa y v es la velocidad
De la pregunta
la masa es de 16 libras
la velocidad es de 30 m / s
16 libras es equivalente a 7.257 kg
Entonces la energía cinética es
1/2(7.257)(30)²
Que es 3265.65 juliosEspero que esto te ayude
find the area of the triangle shown
Answer
B. 27
firist divide 9÷2=4.5
the formula
=1/2×4.5×6
=13.5
cause there are 2 triangles. let's multiply 13.5 with 2
13.5×2= 27²
Find the value of y.
Answer:
[tex] \sqrt{55} [/tex]Step-by-step explanation:
∆ BCD ~ ∆ DCA
[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]
Plug the values:
[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]
[tex] \frac{5}{y} = \frac{ y}{11} [/tex]
Apply cross product property
[tex]y \times y = 11 \times 5[/tex]
Calculate the product
[tex] {y}^{2} = 55[/tex]
[tex]y = \sqrt{55} [/tex]
Hope this helps...
Good luck on your assignment..
Line AB and Line CD are parallel lines. Which translation of the plane can we use to prove angles x and y are congruent, and why?
Answer:
Option C.
Step-by-step explanation:
In the given figure we have two parallel lines AB and CD.
A transversal line FB intersect the parallel lines at point B and C.
We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.
[tex]\angle ABC=\anle ECF[/tex]
[tex]x=y[/tex]
To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.
Therefore, the correct option is C.
?? help out plssss ill do the thing wtv its called
Steps to solve:
1 = -4 + 3/8x
~Add 4 to both sides
1 + 4 = -4 + 4 + 3/8x
~Simplify
5 = 3/8x
~Multiply 8/3 to both sides
5 * 8/3 = 3/8x * 8/3
~Simplify
13 1/3 = x
As we look through the answer choices, we can see that none resembles any of the steps I did above but by looking at the answers for each one, the only logical answer is B since it has a final answer of x = 40/3 or 13 1/3.
Best of Luck!
Really need help on question 10.
Answer:
44 degrees
Step-by-step explanation:
4 multiplied by 7 is 28.
28 + 2 = 30
angle ABC = 30 degrees
3 multiplied by 7 is 21
21 - 7 = 14.
angle CBD = 14 degrees.
30 + 14 = 44.
The answer is ABD = 44 degrees
The volume of a cylinder varies jointly with the base (area) and the height. The volume is 40 inches^3 when the base (area) is 6 inches^2 and the height is 20 inches. Find the volume of the cylinder (after finding the variation constant) when the base (area) is 8 inches^2 and the height is 12 inches.
Answer: K = ¹/₃, V = 32in³
Step-by-step explanation:
Volume of s cylinder (V) = πr²h where πr² is the base area.
Now from the question,
V ∞ πr²h
V = kπr²h where k is the constant of proportionality which is also the variation constant.
40 = 6 x 20 x k
40 = 120k and
k = ⁴⁰/₁₂₀
= ¹/₃.
Now to find the volume when base area is 8in² and h is 12,
V = 8 x 12 x ¹/₃
V = 32in³