Answers
[tex] \frac{5a+5h}{a+h-1} - \frac{5a}{a-1} [/tex]
make the denominators the same and simplify:
[tex] \frac{(5a+5h)(a-1)}{(a+h-1)(a-1)} - \frac{5a(a+h-1)}{(a+h-1)(a-1)} [/tex]
expand: [tex] \frac{5a^2-5a+5ah-5h-(5a^2+5ah-5a)}{(a+h-1)(a-1)} [/tex]
simplify: [tex] \frac{-5h}{(a+h-1)(a-1)} [/tex]
now divide it by h, you have: [tex] \frac{-5}{(a+h-1)(a-1)} [/tex]
[tex]\bf \cfrac{\frac{\underline{5a^2+5ah-5a}-5h~~\underline{-5a^2-5ah+5a}}{(a+h-1)(a-1)}}{h}\implies \cfrac{\frac{-5h}{(a+h-1)(a-1)}}{h} \\\\\\ \cfrac{\frac{-5h}{(a+h-1)(a-1)}}{\frac{h}{1}}\implies \cfrac{-5h}{(a+h-1)(a-1)}\cdot \cfrac{1}{h} \\\\\\ \cfrac{-5\underline{h}}{\underline{h}(a+h-1)(a-1)}\implies \cfrac{-5}{(a+h-1)(a-1)}[/tex]
Related Questions
−2 is less than or equal to w , and 8 is greater than or equal to w Use w only once in your inequality.
Answers
A pond at a hotel 4,290 gallons of water. The groundskeeper drains the pond at a rate of 78 gallons of water per hour. How long will it take to drain the pond?
Answers
divide total gallons by rate:
4290 / 78 = 55 hours
A TV has a listed price of $607.95 before tax. If the sales tax rate is 8.75% , find the total cost of the TV with sales tax included.
Answers
Answer:
$661.15
Step-by-step explanation:
The addition of tax causes the price to be multiplied by (1+0.0875), so the final price is ...
$607.95×1.0875 ≈ $661.15
Jane can pack 48 shirts into each box. round to the nearest compatible numbers to estimate how many boxes she will need to box 1,453 shirts
Answers
Answer: There are 30 boxes for 1453 shirts.
Step-by-step explanation:
Since we have given that
Number of shirts = 48
Number of box for 48 shirts = 1
We need to adjust number of boxes she will need to box 1453 shirts.
So, number of boxes would be
[tex]\dfrac{1453}{48}\\\\=30.27\\\\\approx 30[/tex]
Hence, there are 30 boxes for 1453 shirts.
write the quotient in standard form:
8-7i/1-2i
Answers
22/5+(9/5)i
To get rid of i in the denominator, use the difference-of-two-squares formula: (a+b)(a-b) = a²-b²
The denominator of your fraction is 1-2i. If we were to multiply the denominator by (1+2i), we would get (1-2i)(1+2i) = 1-(-4) = 5.
Of course, if we are going to multiply the denominator by (1+2i), we must also multiply the numerator by (1+2i). So your numerator becomes:
(8-7i) * (1+2i) = 8 + 16i - 7i +14 = 22+9i
Thus,
(8-7i) / (1-2i) = (22+9i) / 5
But standard form requires that we complete the division. So:
(8-7i) / (1-2i) = 22/5 + (9/5)i
The answer, then, is 22/5 + (9/5)i
The quotient in standard form for (8 - 7i) / (1 - 2i) is (22 + 9i) / 5. In this form, the numerator has real and imaginary components, while the denominator is a real number.
The division is simplified, providing a representation of the complex number in a standard format.
To write the quotient result of division in standard form,
Get rid of the imaginary unit 'i' from the denominator.
To do that, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of 1 - 2i is 1 + 2i.
So, let's perform the multiplication:
(8 - 7i) / (1 - 2i) × (1 + 2i) / (1 + 2i)
Now, use FOIL (First, Outer, Inner, Last) method to expand the numerator:
Numerator = (8 - 7i)(1 + 2i)
= 8 + 16i - 7i - 14i² (remember that i² is -1)
= 8 + 9i - 14(-1)
= 8 + 9i + 14
= 22 + 9i
Now, let's expand the denominator:
Denominator = (1 - 2i)(1 + 2i)
= 1 + 2i - 2i - 4i²
= 1 - 4i²
= 1 - 4(-1)
= 1 + 4
= 5
Therefore, the quotient in standard form is (8 - 7i) / (1 - 2i) = (22 + 9i) / 5.
learn more about quotient here
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Log_2(log_5 x) =3 show steps
Answers
If Log(x) = y ; then b^y = x
[tex]Log_{2} (Log_{5} (x)) = 3 \\ \\ 2^{3} = Log_{5} (x) \\ \\ 8 = Log_{5} (x) \\ \\ x = 5^{8} \\ \\ x = 390,625[/tex]
Answer:
[tex]\large \textsf{Read below}[/tex]
Step-by-step explanation:
[tex]\large \text{$ \sf log_2\:(log_5\:x) = 3$}[/tex]
[tex]\large \text{$ \sf log_2\:(log_5\:x) = log_2\:8$}[/tex]
[tex]\large \text{$ \sf log_5\:x = 8$}[/tex]
[tex]\large \text{$ \sf log_5\:x = log_5\:390,625$}[/tex]
[tex]\large \boxed{\boxed{\text{$ \sf x= 390,625$}}}[/tex]
Three times a first number decreased by a second number is 1. the first number increased by twice the second number is 12. find the numbers.
Answers
Final answer:
The first number is 2 and the second number is 5.
Explanation:
Let's represent the first number as x and the second number as y.
According to the problem, we have the following equations:
3x - y = 1 (Equation 1)
x + 2y = 12 (Equation 2)
To solve this system of equations, we can use the method of substitution. We can rearrange Equation 2 to solve for x:
x = 12 - 2y
Now, we substitute this value of x into Equation 1:
3(12 - 2y) - y = 1
Expand and solve for y:
36 - 6y - y = 1
Combine like terms:
-7y = -35
Divide both sides by -7:
y = 5
Now, substitute this value of y back into Equation 2 to find x:
x + 2(5) = 12
x + 10 = 12
Subtract 10 from both sides:
x = 2
Therefore, the first number is 2 and the second number is 5.
When converted to speeds, which list is in order from slowest to fastest?
17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes
Answers
17 miles in 2 minutes ....17/2 = 8.5 miles per minute
26 miles in 4 minutes.....26/4 = 6.5 miles per minute
33 miles in 6 minutes.....33/6 = 5.5 miles per minute
60 miles in 8 minutes.....60/8 = 7.5 miles per minute
slowest to fastest :
(1) 33 miles in 6 minutes
(2) 26 miles in 4 minutes
(3) 60 miles in 8 minutes
(4) 17 miles in 2 minutes
I believe that is answer C
When converted to speeds, the list which is in order from slowest to fastest is:
1) 33 miles in 6 minutes
2) 26 miles in 4 minutes
3) 60 miles in 8 minutes
4) 17 miles in 2 minutes
Step-by-step explanation:We know that speed is defined as the ratio of distance and time.
Here we are given distance and time in each of the options and we will check the speed of each and arrange them in increasing order.
1)
33 miles in 6 minutes
The speed is:
[tex]\dfrac{33\ \text{miles}}{6\ \text{minutes}}=5.5\ \text{miles\ per\ minute}[/tex]
2)
26 miles in 4 minutes
The speed is:
[tex]\dfrac{26\ \text{miles}}{4\ \text{minutes}}=6.5\ \text{miles\ per\ minute}[/tex]
3)
60 miles in 8 minutes
The speed is:
[tex]\dfrac{60\ \text{miles}}{8\ \text{minutes}}=7.5\ \text{miles\ per\ minute}[/tex]
4)
17 miles in 2 minutes
The speed is:
[tex]\dfrac{17\ \text{miles}}{2\ \text{minutes}}=8.5\ \text{miles\ per\ minute}[/tex]
Since,
[tex]5.5\ \text{miles\ per\ minute}<6.5\ \text{miles\ per\ minute}<7.5\ \text{miles\ per\ minute}<8.5\ \text{miles\ per\ minute}[/tex]
Hence, the increasing order of speed is:
1→2→3→4
the slope of the line below is -5 which of the following is the point-slope form of the line (2,-8)
A. y - 8 = 5 (x + 2)
B. y + 8 = -5 (x - 2)
C. y - 8 = -5 (x + 2)
D. y + 8 = 5 (x - 2)
Answers
[tex] y - y_1 = m(x - x_1)[/tex]
m = slope = -5
[tex]y - y_1 = -5(x - x_1)[/tex]
(x,y) = (2,-8)
[tex]x_1 = 2[/tex]
[tex]y_1 = -8[/tex]
[tex]y - y_1 = -5(x - x_1)[/tex]
[tex] y - (-8) = -5(x - 2)[/tex]
[tex] y + 8 = -5(x - 2)[/tex] <------Answer
Use a surface integral to find the general formula for the surface area of a cone with height latex: h and base radius latex: a(excluding the base).
Answers
[tex]\mathbf s(u,v)=\left\langle u\cos v,u\sin v,\dfrac hau\right\rangle[/tex]
with [tex]0\le u\le a[/tex] and [tex]0\le v\le2\pi[/tex]. Then
[tex]\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv=\sqrt{1+\dfrac{h^2}{a^2}}u\,\mathrm du\,\mathrm dv[/tex]
The area of this surface (call it [tex]\mathcal S[/tex]) is then
[tex]\displaystyle\iint_{\mathcal S}\mathrm dS=\sqrt{1+\frac{h^2}{a^2}}\int_{v=0}^{v=2\pi}\int_{u=0}^{u=a}u\,\mathrm du\,\mathrm dv=a^2\sqrt{1+\frac{h^2}{a^2}}\pi=a\sqrt{a^2+h^2}\pi[/tex]
Final answer:
The surface area of a cone with height h and base radius a, excluding the base, is found using the lateral surface area formula A = π · a · l, where l is the slant height given by √(a² + h²).
Explanation:
To find the general formula for the surface area of a cone with height h and base radius a using a surface integral, excluding the base, we consider the lateral surface area of the cone. This is given by the integral along the slant height of the cone. To derive the formula, the slant height, l, can be found using the Pythagorean theorem, since the triangle formed by the slant height, radius of the base, and the height of the cone is a right triangle. The relationship is given by l = √(a² + h²).
The lateral surface area A can then be expressed as A = π · a · l. Substituting for the slant height, we get A = π · a · √(a² + h²), which is the desired formula.
This formula assumes that the cone is a right circular cone and the lateral surface is a smooth curve.
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes y= 1/2 x− 3/2
Answers
The x-intercept would be, (3,0). And the y-intercept would be, (0,-3/2).
circle P had a circumference of approximately 75 inches. what is the approximate of the radius ,r? use 3.14 for
Answers
2×3.14×r=75
6.28 r=75
r=75/6.28=11.943=12 inch (nearly)
Answer:
1) 12in
Step-by-step explanation:
The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.
Will Reward Brainliest!
Answers
So, I solved it for you but I couldn't type it here because they don't have everything I need :) . Please see the pictures below for the answer.
Best of luck!
If you need help in the future, just send me a message then I'll help you out :)
Garebear~
What number is the solution of the inequality of 10.6 < b
Answers
The photography club has 28 members .there are 12 boys in the club . What is the ratio of boys to girls in simplest form?
Answers
Write the ratio boys/girls as 12/16. Reduce this to 3/4.
How much does mike earn at fresh foods if he works 20 hours ? 40 hourss ? 60 hours ? when mike gets paid 10 per hour
Answers
1 hour = $20
20 hours = $ 20 x 20
= $400
40 hours = $20 x 40
= $800
60 hours = $20 x 60
= $1,200
Hope this helps :))
~Top
The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.
Which points did the manager label?
(0, 12) and (5, 0)
(0, 10) and (24, 0)
(0, 24) and (10, 0)
(0, 5) and (12, 0)
Answers
(0,10) and (24,0) is the final answer.
The average person lives for about 78 years. Does the average person live for at least 1,000,000 minutes? (Hint: There are 365 days in each year, 24 hours in each day, and 60 minutes in each hour.)
Answers
Answer:
cool kkdkdkkdkkfkkfkfkd
John spent $24 of his savings on a watch and 1/5 of the remainder on a shirt. He still had 2/3 of his savings left. How much were his savings at first?
Answers
how much is 1/5 of x? well is just (1/5)x or just x/5.
how much is 2/3 of x? well, is just (2/3)x or 2x/3.
we know those sum will add up to "x", let's check then.
[tex]\bf \stackrel{shirt}{\cfrac{x}{5}}+\stackrel{watch}{24}+\stackrel{leftover}{\cfrac{2x}{3}}=x\impliedby \begin{array}{llll} \textit{multiplying all by the \underline{LCD of 15}}\\\\ \textit{to get rid of the denominators} \end{array} \\\\\\ \boxed{15}\cdot \cfrac{x}{5}+\boxed{15}\cdot 24+\boxed{15}\cdot \cfrac{2x}{3}=\boxed{15}\cdot x\implies 3x+360+10x=15x \\\\\\ 13x+360=15x\implies 360=15x-13x\implies 360=2x \\\\\\ \cfrac{360}{2}=x \implies 180=x[/tex]
Final answer:
To find John's original savings, we set up an equation based on the information given and solved for the total savings, which was found to be approximately $154.29.
Explanation:
John spent $24 on a watch and then 1/5 of the remainder of his savings on a shirt. After these purchases, he had 2/3 of his savings left. To determine John's original savings, let's represent his total savings as S. After purchasing the watch, John had S - $24 remaining. He then spent 1/5 of this remainder on a shirt. After buying the shirt, 2/3 of his savings was left, which can be represented by the equation:
2/3 * S = (S - $24) - 1/5 * (S - $24)
Now, we can solve for S, by first distributing the 1/5 on the right-hand side of the equation:
2/3 * S = (S - $24) - 1/5 * S + 24/5
Then, we combine like terms:
(2/3 - 1/5) * S = $24 - 24/5
To combine the fractions, find a common denominator, which in this case is 15:
(10/15 - 3/15) * S = 96/5 - 24/5
(7/15) * S = 72/5
Finally, we multiply both sides of the equation by the reciprocal of 7/15 to solve for S:
S = (72/5) * (15/7)
S = (72*15)/(5*7)
S = $154.29
Therefore, John's original savings was approximately $154.29.
For a circle of radius 3 feet, find the arc lengths subtended by a central angle of 57 degrees.
Answers
Answer: The length of an arc is 2.98 feet.
Step-by-step explanation:
Since we have given that
Radius of a circle = 3 feet
Angle subtended at the centre = 57°
We need to find the length of an arc:
As we know the formula for "Length of an arc":
[tex]Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet[/tex]
Hence, the length of an arc is 2.98 feet.
at a school pep rally, the ratio of students who wore red to those who wore yellow is 7 to 3. There are 300 students at the pep rally, and each student wore either red or yellow. How many more students wore red?
Answers
30 x 7 = 210 - red
30 x 3 = 90 - yellow
210 - 90 = 120 more students
I hope this helps and have a wonderful day filled with joy!!
Rewrite the statement in mathematical notation. (Let n be the number of cases of Bangkok flu and t be time.) There are presently 450 cases of Bangkok flu, and the number is growing by 10 new cases every month.
dn/dt=
Answers
Final answer:
To represent the growth of Bangkok flu cases over time mathematically, the derivative dn/dt equals 10, indicating a constant increase of 10 cases per month.
Explanation:
To rewrite the statement in mathematical notation where n is the number of cases of Bangkok flu and t is time, we will express the changing number of cases as a function of time. Given that there are currently 450 cases and the number of cases is growing by 10 every month, we would write the instantaneous rate of change of the number of cases with respect to time as dn/dt = 10.
This is because the phrase 'growing by 10 new cases every month' implies a constant rate of growth over time, which is directly translated into a derivative in mathematical terms. In more complex scenarios, rates of growth could follow a pattern that might be represented by a function of t. However, in this case, the growth is linear and constant, which simplifies to the derivative being equal to the rate of growth: 10 cases per month.
Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)
Answers
From 1:20 to 1: 55 we have 35 minutes or 7 x 5 minutes or
7 x 30° = 210°
To convert degree into radian, we apply the following formula:
degree/180° = radian/π
210/180 = r/π or (cross multiplication) →Radian = (π x 210/180
→ Radian = 7π/6 (simplify by 30)
Answer:
Part 1:
In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.
What is the center of a circle whose equation is x^2+y^2-12x-2y+12=0
Answers
(x-H)² + (y-K)² = r² where (H, K) are the coordinates for the center of the circle and r is the radius. You can do this by completing the square for both x and y terms:
x² + y² - 12x - 2y + 12 = 0
x² + y² - 12x - 2y = -12
x² - 12x + y² - 2y = -12
To complete the square take half of the x-term and square it then add it to both sides of the equation. So take half of -12 which is -6, square it: -6² = 36 and add it to both sides.
x² - 12x + 36 + y² - 2y = -12 + 36
Do the same for y:
x² - 12x + 36 + y² -2y + 1 = -12 + 36 + 1
Now reduce each perfect square polynomial to squared form by remembering the FOIL rule for factoring:
(Ax + B)(Cx + D)
First + Outer + Inner + last
A²x² + ADx + BCx + D²
Now just work backwards and figure out what terms multiply to give you the trinomial you have. Let's start with the x :
x² - 12x + 36
Looks like 36 is perfect square of 6 and the negative sign in the middle term indicates subtract 6, so x - 6. Check it!
(x - 6)² = x² - 3x - 3x + 36 = x² - 6x + 36
Yes, it works! Now the y :
y² - 2y + 1
This looks good too since 1 is a perfect square:
(y - 1)² = y² - 1y - 1y + 1 = y² - 2y + 1
Perfect!
Now put it back into the equation:
x² - 12x + 36 + y² - 2y + 1 = -12 + 36 + 1
(x - 6)² + (y - 1)² = -12 + 36 + 1
Simplify the right:
(x - 6)² + (y - 1)² = 25
Beautiful! The equation of the circle! The center is (6,1) with radius 5. Now we can attack the parts in the question.
(a) First part asks us to find point B, knowing point A is (3,-3) and that AB is a diameter of the circle. Since we know the coordinates of the center and the fact that a diameter is just a line that goes through the center, we have 3 points on the line: A, B, and the center. We can just realize that the point B is equidistant and exactly opposite the point A with respect to the center. So let's find the difference between point A and the center, and move that distance to get to B:
center - A = (1 - -3) / (6 - 3) = (1 + 3) / (6 - 3) = 4 / 3
How are the rules for division of signed numbers similar to the rules for multiplication of signed numbers?
Answers
like the sign of the product or quotient will be positive. Multiply or divide, if the signs aredifferent unlike the sign of the product or quotient will be negative
Final answer:
The division and multiplication of signed numbers follow the same sign rules: two positive numbers yield a positive result, two negatives give a positive, and a pair of numbers with different signs results in a negative outcome.
Explanation:
The rules for the division of signed numbers are similar to the rules for multiplication of signed numbers. Both operations follow the same pattern concerning the signs of the numbers involved:
When two positive numbers are involved, the result is positive (e.g., [tex]\frac{2}{1} = 2[/tex] or 2 x 1 = 2).
When two negative numbers are involved, the result is also positive (e.g., [tex]\frac{-2}{-1} = 2[/tex] or (-4) x (-3) = 12).
When one positive and one negative number are involved, irrespective of the operation, the result is negative (e.g., [tex]\frac{-3}{1} = -3[/tex] or (-3) x 2 = -6).
Therefore, both division and multiplication of signed numbers primarily depend on the signs of the numbers to determine the sign of the answer.
3.1666666667 as a fraction
Answers
Then 3.166666666666 ... = 3 1/6 => 19/6 (as a fraction).
What are fissures and how are theu created by land subsidence?
Answers
as soil is pulled in to this location, it has to come from somewhere and it comes from the nearby land mass, whilst covering that sink-hole made by this one gap underneath, the land mass splits on other parts where the extra soil came from, causing the fissure.
so the fissure is made from the extra soil used to cover the sink-hole, whilst covering the sink-hole made by the underneath gap, making another gap on the surface above, and that is what the fissure ends up as.
in a sense, the gap underneath kinda tranferred to above at the surface.
One of the angles formed by two intersecting lines is 42°. What is the measure of the other three angles?
Answers
we know that those two angles must add to 180 degrees, so lets form an equation to figure out the other angle
42 + x = 180
subtract 42 from both sides
x = 138
so 138 degrees is the first AND the 3rd angle
the opposite angle from the 42 degree angle also happens to be 42 degrees
this is because there are two lines in total right?? if you draw out the 42 degree angle and the 138 degree angle, flip that upside down, the angles are the same!!
i hope this helps!!
Answer:
42, 138, 138
Step-by-step explanation:
Solving Equations with Variables on Both Sides
1. (g+4) - 3g = 1 + g
g = 1
g = 4
no solution
identity
2. -6a + 3 = -3(2a - 1)
a=5
a=10
no solution
identity
3. 0.5b + 4 = 2(b+2)
b=0
b=0.5
no solution
identity
4. 8 -(3 + b) = b - 9
7
8
no solution
identity
Answers
g+4-3g=1+g
subtracting g from both sides
4-3g=1
subtracting 4 from both sides
-3g=-3
g=1
2)
-6a+3=-3(2a-1)
extending the right side
-6a+3=-6a+3
adding 6a to both sides
3=3
which is an identity
3)
0.5b+4=2(b+2)
extending the right side
0.5b+4=2b+4
subtracting 0.5 b from both sides
4=1.5b+4
subtracting 4 from both sides
0=1.5b
b=0
4)
8-(3+b)=b-9
subtracting 8 from both sides
-(3+b)=b-17
extending the left side
-3-b=b-17
adding b to both sides
-3=2b-17
adding 17 to both sides
14=2b
b=7
G evaluate lim h → 0 (1 + h)9 − 1 h . hint: this limit represents the derivative of a function f at a given point
a. find f and a, and then evaluate the derivative.
Answers
Write [tex]1=1^9[/tex], and recall that for a differentiable function [tex]f(x)[/tex], the derivative at a point [tex]x=a[/tex] is given by
[tex]f'(a)=\displaystyle\lim_{h\to0}\frac{f(a+h)-f(a)}h[/tex]
which would suggest that for this limit, [tex]f(x)=x^9[/tex] and [tex]a=1[/tex]. We have [tex]f'(x)=9x^8[/tex], and so the value of the limit would be [tex]9(1)^8=9[/tex].