[tex]\ln(5-x) = \ln 5 - \ln x\\\\\implies \ln(5-x) + \ln x = \ln 5\\\\\implies \ln[(5-x)x] =\ln 5\\\\\implies \ln(5x -x^2) = \ln 5\\\\\implies 5x -x^2 = 5\\\\\implies x^2 -5x +5 =0\\\\\implies x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 5}}{2(1)}\\\\\implies x = \dfrac{5 \pm \sqrt{5}}{2}\\\\\text{Hence} ~x = \dfrac 12\left(5 + \sqrt 5\right)=3.62~~ \text{and}~~ x =\dfrac 12 \left(5-\sqrt 5\right) =1.38[/tex]
Answer:
x1 = 3.618, x2 = 1.382
Step-by-step explanation:
ln(5-x) = ln5 - lnx
ln(5-x) + ln(x) = ln5
ln(5x-x^2) = ln5
5x-x^2=5
0=x^2-5x+5
x = -(-5)±√((-5)²-4(1)(5)) / 2(1)
x = 5±√(25-20) / 2
x = 5±√5 / 2
x1 = 3.618, x2 = 1.382
Please help me solve this problem, thank you.
Step-by-step explanation:
first you need to find the 17 and 8 triangles missing sides length so we do a squared plus b squared equals c square and since we have c which is 17 we subtract 8 squared or 64 from 17 square and we get 225. next the missing line from the next one is done the same way 225 minus 9 squared or 81 and we get 144 and the square root of that is 12 we do 12 squared 144 minus 6 squared because we already know that the side is six because it gives it to us and we get 10.392
For each computer Isabella sells, she earns a 5% commission. If she sells 3 computers for
$985.00 each, what is her commission?
$14.78
b. $49.25
$147.75
a.
C.
i need help i don’t understand this i’m a freshman in highschool doing a mi
2+2 THIS IS A LIFE OR DEATH QUESTION PLZZ
UMMM I THINK IT'S UH A CARROT, I'M SMART the real answer is 4 though lol
What is the value of the expression
4x+y when x = 2 and y = 4?
2y-1
Much help needed thanks!
Maybe Audrey waited 6 pounds 14 in ounces at birth convert her weight to ounces
Answer:
110 ounces :))
Step-by-step explanation:
PLEASE HURRY! WILL MARK BRAINLIEST IF CORRECT (Screenshot)
Answer:
The length of XY is 22.5
Step-by-step explanation:
Since you need to hurry I will not write an explanation
Hope this helps! :)
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Bruce walks 3/4 mile in 1/5 what is his spewd miles per hour
Answer: Bruce's speed is 3.75 mph(miles per hour).
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6830 and his stock in Company B was worth $2600. The stock in Company A has increased 20% since last year and the stock in Company B has increased 5%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Step-by-step explanation:
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6830 and his stock in Company B was worth $2600. The stock in Company A has increased 20% since last year and the stock in Company B has increased 5%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Molly tried to evaluate 93\times5193×5193, times, 51 using partial products. Her work is shown below.
\begin{array}{llrr} &&93 \\ &&\underline{{}\times51} \\ &\blueD{\text{Step 1}}&\blueD{3}& \blueD{1\times3\text{ ones}}\\ &\greenD{\text{Step 2}}&\greenD{90}& \greenD{1\times 9\text{ tens}}\\ &\maroonD{\text{Step 3}}&\maroonD{150}& \maroonD{50\times 3\text{ ones}}\\ &\goldE{\text{Step 4}}&\underline{{}+\goldE{ 4{,}500}}& \goldE{50\times 9\text{ tens}}\\ &\purpleD{\text{Step 5}}&\purpleD{4{,}743}& \end{array}
Step 1
Step 2
Step 3
Step 4
Step 5
93
×51
3
90
150
+4,500
4,743
1×3 ones
1×9 tens
50×3 ones
50×9 tens
Since molly's solution tally's with the given solution, hence Molly's solution is correct.
Given the working on a partial product of 93 and 51 carried out by Molly as shown:
[tex]\begin{array}{llrr} &&93 \\ &&\underline{{}\times51} \\ &\blueD{\text{Step 1}}&\blueD{3}& \blueD{1\times3\text{ ones}}\\ &\greenD{\text{Step 2}}&\greenD{90}& \greenD{1\times 9\text{ tens}}\\ &\maroonD{\text{Step 3}}&\maroonD{150}& \maroonD{50\times 3\text{ ones}}\\ &\goldE{\text{Step 4}}&\underline{{}+\goldE{ 4{,}500}}& \goldE{50\times 9\text{ tens}}\\ &\purpleD{\text{Step 5}}&\purpleD{4{,}743}& \end{array}[/tex]
This partial product can also be solved as shown below:
[tex]93 \times 51 = (90+3)\times (50+1)[/tex]
Applying the distributive law:
[tex]93 \times 51 = 90(50) + 90(1) + 3(50) + 3(1)\\93 \times 51 =4500 + 90 + 150 + 3\\93 \times 51 =4500+240+3\\93 \times 51 =4740+3\\93 \times 51 =4743[/tex]
Since molly's solution tally's with the given solution, hence Molly solution is correct.
Learn more about partial product at: https://brainly.com/question/24716925
Find the coefficient of x in the polynomial ( 4y - 13 - 5z - 4x )
[tex]\large\huge\green{\sf{Answer:-}}[/tex]
the coefficient of x in the polynomial ( 4y - 13 - 5z - 4x ) is -4Answer:
[tex]\huge\boxed{\sf -4}[/tex]
Step-by-step explanation:
The given polynomial is:
4y - 13 - 5z - 4x
Coefficient:
The term/number (along with the sign) with that certain variable is called coefficient.
x has the coefficient of :
-4 (number along with x)
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Express as a single power.
a) 1
b) -5
c) [tex]\frac{6^3.6^5}{6^2.6^4} = \frac{6^{3+5} }{6^{2+4} } = \frac{6^8}{6^6} = 6^{8-6}=6^2[/tex]
What is log Subscript 5 Baseline (4 times 7) + log Subscript 5 Baseline 2 written as a single log?
log5(4*7)+log5(2)=log5(28)+log5(2)=log5(56)
Answer:
Its D
Step-by-step explanation:
just took the test
What is the area of a rectangle that has side lengths of 7 yard and yard?
10 square yard
18
20
square yard
15
24 square yard
8
square yard
My Progress
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is it like mutiplying and dividing
The area of the rectangle that has side lengths of 7 yards and 3 yards is 21 square yards.
What is the rectangular shape?Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.
To find the area of the rectangle that has side lengths of 7 yards and 3 yards, use the formula as described below,
the area of the rectangle = length x width of the rectangle.
Substituting the value of the side lengths to the formula,
The area of the rectangle = 7 x 3
The area of the rectangle = 21 square yards.
Therefore, the area is 21 square yards.
To learn more about the rectangular;
brainly.com/question/21416050
#SPJ7
put the following unit fractions in order from smallest to largest. 1/16 1/24 1/8 1/10 1/4 1/12 1/3 1/6 1/2
Answer:
1/24, 1/16, 1/12, 1/10, 1/8, 1/6, 1/4, 1/3, 1/2
Step-by-step explanation:
If you have this many fractions and they all have the same numerator, then the smallest number will have the biggest denominator and the biggest number will have the smallest.
So when you have all numbers with the same numerator and you're trying to put them in order from smallest to greatest, it's like putting the denominators in order from largest to smallest. (So, the 1/24 is the SMALLEST and the 1/2 is the BIGGEST.
James is observing the population of the fish he put into a pond. He built a pond and
populated it with 700 fish. The population of the fish doubles every year.
The exponential equation is given by y = 700(2)ˣ
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of fish after x hours.
Given that he starts with 700 fishes, hence
a = 700
The population of the fish doubles every year, hence:
b = 2
The exponential equation becomes:
y = 700(2)ˣ
Find out more at: https://brainly.com/question/12490064
Helppppppppppppppppppp
Answer:
<6
<4
Step-by-step explanation:
Remote interior angle is an interior angle that is not adjacent to the exterior angle of interest.
<6
<4
Multiply. −2(−5)(−3)
Answer: -30
Step-by-step explanation:
-2 X -5 = 10
10 X -3 = -30
Therefore, -2(-5)(-3) = -30
The multiplication of −2(−5)(−3) is -30
The multiplication of numbers in brackets with negative signs takes a method whereby the signs are taken into account when performing the arithmetic operation.
From the given question, we are to multiply:
= - 2 × (-5) × (-3)
= +10 × (-3)
= -30
Learn more about the multiplication of numbers here:
https://brainly.com/question/1755985
Eight people met in a public park for a nature walk. Before they set off to look for birds, they all introduce themselves and each person shook hands with each of the other people. How many handshake were exchanged?
Answer:
56 handshakes
Step-by-step explanation:
one person shakes seven hands
eight people shook seven hands each
8×7=56
Compound interest compounded quarterly is given every ______ months. *
1 point
1
3
6
Answer:
3 months
a quarter is a period of three months
Step-by-step explanation:
Two motorcyclists, who start their journeys at the same instance from two different cities,
travel with uniform speeds of 40 km/h and 50 km/h respectively towards each other. If they meet
each other after 1.5 hours after commencing their journeys, find the distance between the two
cities.
QUICK
Answer:
54
Step-by-step explanation:
a computer performs a calculation in 3.5 x 10^-5 seconds to solve a math problem. How long does the computer need to calculate the solutions to 5 x 10^4 math problems. Enter your answer in standard form
Step-by-step explanation:
let's do this in 2 steps :
1. go for 1×10⁴ math problems
2. multiply that result by 5 to fully cover 5×10⁴
1.
3.5×10^-5 × 1×10⁴ = 3.5×10^-1
2.
5 × 3.5×10^-1 = 16.5×10^-1 = 1.65×10⁰
so, the computer needs 1.65×10⁰ or simply 1.65 seconds.
An item is regularly priced at $29. It is on sale for 80% off the regular price.
X is y% of what number?
Answer:
42
Step-by-step explanation:
yeah-ya.......... right?
In developing an interval estimate of the population mean, if the population standard deviation is unknown _____.
Answer:
the sample standard deviation and t distribution can be used
Step-by-step explanation:
Find a unit vector in the direction of ⃗PQ if P = (4, -7) and Q = (2, -3)
Kevin will be taking six classes next semester (Algebra, World History, Psychology, Political Science, Chemistry, and Art Theory) and would like to know how many different ways he can order his class schedule given that his university offers six time slots for classes each day. Assuming there are no constraints and each class can be taken in any time slot, how many different ways can Kevin order his classes?
=========================================================
Explanation:
We have 6 slots to fill A,B,C,D,E,F
There are 6 choices for choice A, then 5 choices for slot B, 4 for C, and so on until we reach one choice for slot F. Count down by 1 each time a slot is filled.
Multiply out those values to get: 6*5*4*3*2*1 = 720
For more information, check out the concept of factorials.
---------
Another approach is to use the nPr permutation formula which is
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
where in this case n = 6 and r = 6.
Carter has a rope that is 6 meters long. He cuts the rope in half. Then he cuts one of the halves into pieces that are 1-third meter each.
He would have 4 pieces of rope
4.
(03.02)
Match each statement (term) with its value in relation to 0 (definition). (10 points)
1.
Oliver owes his sister $27.
2.
A building is 38 feet tall.
3.
Erica jumped 2.7 feet above ground.
4.
The scuba diver was 38 feet below sea level.
5.
The basement is 8.3 feet below ground.
a.
38
b.
-38
c.
-8.3
d.
-27
e.
2.7
Answer:
Below
Step-by-step explanation:
1.-d
2.-a
3.-e
4.-b
5.-c
Answer:
-8.3ithink so
Step-by-step explanation: