Answer:
x = -5
Step-by-step explanation:
[tex]0.00005 = 5 \times {10}^{ - 5} \\ \\ \implies \: x = - 5[/tex]
Which expression is equivalent to (-36) - 128b ? *
Answer:
-36-128b
Step-by-step explanation:
Simply take -36 out of the parentheses to get -36-128b.
Calculate the volume of the figure.
5 ft
7 ft
A 48 cubic feet
B 63 cubic feet
99 cubic feet
D) 140 cubic feet
4 ft
Answer:
Step-by-step explanation:
Formula
Volume = L * w * h
Givens
L = 7 feet
w = 4 feet
h = 5 feet
Solution
V = L * w * h Substitute values into the formula
V = 7 * 4 * 5
V = 140 cubic feet.
Answer
140 ft^3
Answer:
D) 140 cubic feet
Step-by-step explanation:
The given information is,
→ Length (l) = 7 ft
→ Breadth (b) = 4 ft
→ Height (h) = 5 ft
Formula we use,
→ Volume of cuboid = l × b × h
Let's solve the problem,
→ l × b × h
→ 7 × 4 × 5
→ [ 140 ft³ ]
Hence, the volume is 140 ft³.
If 1/(a + b + c) = 1/a + 1/b + 1/c, show that 1/(a + b + c)^3 = 1/a^3 + 1/b^3 + 1/c^3
Expanding the cube, we have
[tex]\dfrac1{(a+b+c)^3} = \left(\dfrac1{a+b+c}\right)^3 \\\\ = \dfrac1{a^3} + \dfrac1{b^3} + \dfrac1{c^3} + 3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc}[/tex]
so it remains to be shown that
[tex]3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc} = 0[/tex]
Factorize the grouped sum on the left as
[tex]\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2} = \dfrac1{abc} \left(\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac\right)[/tex]
so that with simplification, it remains to be shown that
[tex]\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac + 2 = 0[/tex]
With a little more manipulation, we have
[tex]\dfrac ba + \dfrac ca = \dfrac{a+b+c}a - 1[/tex]
[tex]\dfrac cb + \dfrac ab = \dfrac{a+b+c}b - 1[/tex]
[tex]\dfrac bc + \dfrac ac = \dfrac{a+b+c}c - 1[/tex]
so that our equation simplifies to
[tex]\dfrac{a+b+c}a + \dfrac{a+b+c}b + \dfrac{a+b+c}c - 1 = 0[/tex]
which we can factorize as
[tex](a+b+c)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]
Finish up by using the hypothesis:
[tex]\left(\dfrac1{\frac1{a+b+c}}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]
[tex]\underbrace{\left(\dfrac1{\frac1a+\frac1b+\frac1c}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right)}_{=1} - 1 = 0[/tex]
and the conclusion follows.
Please help me I can’t get it right
=====================================================
Work Shown:
[tex]2\sqrt{b} + 5 = 11 - \sqrt{b}\\\\2x + 5 = 11 - x\\\\2x+x = 11 - 5\\\\3x = 6\\\\x = 6/3\\\\x = 2\\\\\sqrt{b} = 2\\\\b = 2^2\\\\b = 4\\\\[/tex]
What I did for a good portion of the early steps is replace [tex]\sqrt{b}[/tex] with x. Then I solved for x like with any normal equation. Once x is isolated, plug in [tex]x = \sqrt{b}[/tex] and isolate b itself.
------------
Let's check the answer:
[tex]2\sqrt{b} + 5 = 11 - \sqrt{b}\\\\2\sqrt{4} + 5 = 11 - \sqrt{4}\\\\2*2 + 5 = 11 - 2\\\\4 + 5 = 11 - 2\\\\9 = 9 \ \ \ \ \checkmark\\\\[/tex]
The answer of b = 4 is confirmed.
It's always a good idea to check the answer with any equation. This is especially true with square root equations because the solution might be extraneous (meaning that it works in some equations but not in the original starting equation).
Identify the center and radius of each equation (x-5)² + (y+7)² =64
Answer:
Radius: 8
Center: (5,-7)
Step-by-step explanation:
(x−a)2 + (y−b)2 = r2
To find the radius: find the square root of 64
To find the center, get the opposite of -5 and 7
opposites are: 5, -7
center is (5,-7)
9) work out 6 - 3x-2--10
Austin finished his English assignment ib 1/3 hours.then he completed his math assignment in 2/5 hours. What wS the total time hw sentence this two assignments
Answer:
11/15
Step-by-step explanation:
sum the two 1/3+2/5=11/15
Suppose you deposit $2500 in a savings account that pays you 5% interest per year. (Calculator)
(a) How many years will it take for you to double your money?
Answer:
14.20669 years
Roughly 14 years and 2.5 months.
Step-by-step explanation:
Assuming this is compound interest.
The formula is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=[/tex] Final Amount
[tex]P=[/tex] Principal Amount
[tex]r=[/tex] Interest Rate
[tex]n=[/tex] # of times interest is compounded per year
[tex]t=[/tex] Time in years
We are looking for the times in years to double the money so
[tex]2500*2=5000[/tex]
[tex]A=5000[/tex]
[tex]P=2500[/tex]
[tex]r=0.05[/tex]
[tex]n=1[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex] .
Step 1.
Plug in our numbers into the compound interest formula.
[tex]5000=2500(1+\frac{0.05}{1}) ^{1*t}[/tex]
Step 2.
Simplify the equation.
Evaluate [tex]1+\frac{0.05}{1}=1.05[/tex]
Evaluate [tex]1*t=t[/tex]
[tex]5000=2500(1.05) ^{t}[/tex]
Step 3.
Divide both sides of the equation by [tex]2500[/tex]
[tex]\frac{5000}{2500}=1.05 ^{t}[/tex]
Evaluate [tex]\frac{5000}{2500}=2[/tex]
[tex]2=1.05 ^{t}[/tex]
Step 4.
Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.
[tex]ln(2)=t*ln(1.05)[/tex]
Step 5.
Divide both sides of the equation by [tex]ln(1.05)[/tex]
[tex]\frac{ln(2)}{ln(1.05)}=t[/tex]
Step 6.
Evaluate
[tex]t=14.20669[/tex]
Roughly 14 years and 2.5 months.
BRAINLIEST!!!
A website requires users to set up an account that is password protected. If the password
format is four letters (A-Z) followed by a single digit number (0-9), and letters can be repeated, how
many different passwords are possible?
Answer:
4,569,760 different passwords
Step-by-step explanation:
[tex]26 \times 26 \times 26 \times 26 \times 10 = 4569760[/tex]
Digits can be repeated means repeatation is allowed
So
Total letters=26Total nos=10Total ways
26⁴×10456976×1045697601 fith of the sum of the 3 times a number and 9
Answer
3*9=27
27/ 1/5
5.25
Step-by-step explanation:
5.25=5 1/4
If f(x)= x^3 + 6x^2 - 9x + 14 and x-2 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answer
Write properties of function:
x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]
factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]
Explanation
Write properties of function: Write properties of function:
x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]
factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]
Answer: Write properties of function:
x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]
factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]
2. A more efficient packing of the discs is obtained by dividing the metal sheet into hexagons and cutting the circular lids and bases from the hexagons (see the last figure). Show that if this strategy is adopted, then
[tex] \frac{h}{r}=\frac{4 \sqrt{3}}{\pi} \approx 2.21 [/tex]
This exercise is about optimization and seeks to prove that if the new strategy of packing the discs is adopted, then h/r = [tex]\sqrt[4]{3}[/tex]/n ≈2.21.
What is the proof for the above strategy?We must determine the amount of metal consumed by each end, or the area of each hexagon.
The hexagon is divided into six congruent triangles, each of which has one side (s in the diagram) in common with the hexagon.
Step I
Next, let's derive the length of s = 2r tan π/6 = (2/([tex]\sqrt{3}[/tex])r². From this we can state that the area of each of the triangles are 1/2(sr) = (1/[tex]\sqrt{3}[/tex])r²
while the total area of the hexagon is 6 * (1/[tex]\sqrt{3}[/tex])r² = (2/[tex]\sqrt{3}[/tex])r².
From the above, we can state that the quantity we want to minimize is given as:
A = 2πrh + 2* (2/[tex]\sqrt{3}[/tex])r²
Step 2
Next, we substitute for h and differentiate. This gives us:
da/dr = - (2V/r²) + [tex]\sqrt[8]{3r}[/tex].
Let us equate the above to zero.
[tex]\sqrt[8]{3r} ^{3}[/tex] = 2V = 2πr²h ⇒ h/r =[tex]\sqrt[4]{3}[/tex]/n
The above is approximately 2.21
Because d²A/dr²=[tex]\sqrt[8]{3}[/tex] + 4V/r[tex]^{3}[/tex] > 0 the above minimizes A.
Learn more about Optimization at:
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Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer:
984
Step-by-step explanation:
Solve for the base: 14 x 10
Solve for the sides: 2(1/2(10 x 24))
Solve for the backside: 10 x 24
Solve for the slanted plane or front: 14 x 26
Answer:
the answer is in the picture
What is 10 to the 3 power
[tex]10^3 = 10 \times 10 \times 10 = 1000[/tex]
Teresa is maintaining a campfire.She has kept the fire steadily burning for 4 hours using 6 logs. The number of logs needed to keep the fire burning is proportional to the number of hours it burns. She wants to know how many logs she needs to keep the fire burning for 18 hours.
Select the equationis Teresa can use to determine the number of logs she needs, x, to maintain the fire for 18 hours.
A. x/6 = 4/18
B. x/6 = 18/4
C. x/18 = 6/4
D. x/4 = 18/6
E. 4/6 = 18/x
Answer:
E. 4/6 = 18/x
Step-by-step explanation:
4 hour using 6 logs
18 hours using x logs
The first to answer first will brainliest
Answer:
[tex]\sf \left(-\dfrac{1}{2},-\dfrac{1}{8}\right)[/tex]
See the graph below.
Equation: y = x³
Only (-0.5, -0.125) lies on the graph of the equation y = x³
option D is correct.Somebody help me to solve this problem.please help me.
Answer:
Tama po
Yan
Step-by-step explanation:
Enjoy po
Godbless
write equivalent fractions for 3\5 and 1\4 using 20 as the conman denominator
Answer:
12/20=3/5 5/20=1/4 so the answer would be 12/20 + 5/20
50 points each question (visit profile for more). Please help. How do I solve?
Answer:
Check the image of solution
the circumference of a circle is c centimeters. The diameter of thhe circle is 13 centimeters. which expression best represents the value of pi
Answer:
c/d
Step-by-step explanation:
The value of π is the ratio of the circumference of any circle to it's diameter, irrespective of it's size.
Samantha's age is 3 years more than half her uncle's age. If her uncle's age is z years, which of the following expressions best shows Samantha's age?
Answer:
See below
Step-by-step explanation:
z = uncle's age
1/2z +3 = Sam's age
Question 2 help meeee pleaseee
Thank you
3 cm/h easy peasy
Step-by-step explanation:
12 cm in 4 hrsFor 1 cm : 12/4 = 3 cmtwo coins are flipped then a card is drawn. there are how many total outcomes? deck is 52 and coins are fair.
Answer:
208
Step-by-step explanation:
A coin can have 2 total outcomes
A card deck can have 52 total outcomes
Im flipping 2 coins and then drawing a card
2 x 2 x 52 = 208
Use the diagram to write an equation that describes the position and the radius of ⊙P.
(x – 4)2 + (y + 2)2 = 16
(x + 4)2 + (y – 2)2 = 16
(x + 4)2 + (y – 2)2 = 4
(x – 4)2 + (y + 2)2 = 4
The equation of circle p with center at (-4, 2) and a radius of 4 units is (x + 4)² + (y - 2)² = 16
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The circle p has center at (-4, 2) with a radius of 4 units, hence, the equation is:
(x - (-4))² + (y - 2)² = 4²
(x + 4)² + (y - 2)² = 16
Find out more on equation at: https://brainly.com/question/2972832
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Answer asap and only if yk 100% its correct
Answer:
1.35 square miles I think
Step-by-step explanation:
Answer:
Julie travels 1.35 miles on the same path every day.
Area = 1.35 miles
Step-by-step explanation:
What we know so far:
- It takes 2.4 miles to walk from house to school.
- The distance from the park to school is 2.1 miles.
- It takes 1.5 miles to walk from your house to the park.
The area of a triangle is 0.5 or 1/2 x base x height.
As a result, 1.5 x 1.8 divided by two equals 1.35.
So, Julie walks 1.35 miles every day on the same route.
Area = 1.35 miles
Hope this helps! :D Brainliest?
what is 34x50^2+89-89 divided by 89
Answer:
(34×(50^2))+89-(89÷89)=8,5088
Step-by-step explanation:
hope this helps if not let me know have a great day
What is the total of all 3 tickets below. use the menu to solve
Answer:
$103.14
Step-by-step explanation:
The calculation of slips are amounted to a total of $103.14
write three addition problems that have a sum of -2
Answer:
1. -5+3
2. -6+4
3. -8+6
Step-by-step explanation:
they all will equal -2
Use the number line. How many 2-yard
long pieces of pipe can be cut from two
1-yard long pieces of pipe?
Answer:
Answer:
16 inches
Step-by-step explanation:
2 1/4 = 9/4 inches
Number of pieces = 36 / 9/4
= 36 + 4/9
= 16 inches
Unit Test
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