Answers
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \underset{\textit{we'll use this one}}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2.7e^x-5 ~~ = ~~33.6\implies 2.7e^x~~ = ~~38.6\implies e^x=\cfrac{38.6}{2.7} \\\\\\ \log_e(e^x)=\log_e\left( \cfrac{38.6}{2.7} \right)\implies x=\ln\left( \cfrac{38.6}{2.7} \right)\implies x\approx 2.66[/tex]
Related Questions
Samuel worked 1/4 of a day on Tuesday and 3/8 of a day on Wednesday. Which
of these represents the fraction of a day he spent working on both days?
Answers
Rewrite 1/4 to have 8 as the denominator: 1/4 = 2/8
Now add the two days together:
2/8 + 3/8 = 5/8
Answer: 5/8
f(x) = x² + 2x − 3
Find f (2)
f(2) is equal to type your answer...
Answers
Answer:
f(2) = 5
Step-by-step explanation:
Given: f(x) = x² + 2x - 3
We are asked to find the value of the function when x = 2.
In the function, substitute 2 as the value of x and simplify:
f(2) = (2)² + 2(2) - 3
f(2) = 4 + 4 - 3
f(2) = 8 - 3
f(2) = 5
When x is equal to 2, the value of the function is 5.
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4 divided by 5yards 1 foot
Answers
Mitch walks 30 meters in 20 seconds. How many meters does Mitch walk per second?
Answers
Speed= distance/time
So speed= 30/20 = 1.5 m/s
Answer:
1.5 meters per second
Step-by-step explanation:
30 ÷ 20 = 1.5
Please help! I need the right answer : (
A cone with the height h radius r has volume v=1/3 m2h. if the cone has a height of 6 in. And volume of v=8♊︎(pie)x+24m♊︎(pie), what is the radius r in terms of x? A. r=3x+2. B. r=4x^2+12x+9. C. r=2x+3 D. r= (2x+3) (2x-3)
Answers
Answer:9514 1404 393
Answer:
h = 3V/(πr²)
Step-by-step explanation:
The formula can be solved for h by multiplying both sides by the inverse of the coefficient of h.
_____
Additional comment
Whenever a variable has a coefficient you don't want, you can make that be 1 by multiplying the equation by the inverse of the coefficient. This is the same as dividing by the coefficient. This makes use of the fact that for any non-zero 'a', the ratio a/a has a value of 1. Anything multiplied by 1 is unchanged.
V = ah ⇒ V/a = (ah)/a = h(a/a) = h·1 = h
Note that we multiply the whole equation (both sides of the equal sign) by 1/a. The basic rule of equality is that you can do whatever you like to an equation, as long as you do it to both sides.
Step-by-step explanation:
Help. Please and thanks.
Answers
Answer:
D
Step-by-step explanation:
the other 3 options are all true.
the sum of all angles in a triangle is always 180°.
so, when T is 40°, that leaves 180-40 = 140° to the other 2 angles. in an isoceles triangle they must be equal to each other, so they are half of the remaining 140°, which is 70°.
and of course the 2 sides are equal (hence "isoceles").
a) Let A x B = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)} then, find A, B, n(A), n(B)
Answers
Step-by-step explanation:
A={1,2,3}
B={5,6}
n(a)=3
n(b)=2
2. What is the measure of angle A?
Answers
Answer:
the answer is 63 degrees
Step-by-step explanation:
3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then, they have been leaving Planet X at a rate of 120 residents per year.
The following equation describes this situation:
\quad -120\cdot 3 = -360−120⋅3=−360minus, 120, dot, 3, equals, minus, 360
What does -360−360minus, 360 tell us?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
A total of 360360360 residents left Planet XXX in the past three years.
(Choice B)
B
360360360 residents left Planet XXX each year.
(Choice C)
C
None of the above
Answers
Answer:
A total of 360 residents left Planet X in the past 3 years.
Step-by-step explanation:
120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.
Answers
A total of 360 residents left Planet X in the past 3 years.
Step-by-step explanation:
120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.A total of 360 residents left Planet X in the past 3 years.
A shirt on sale for 25%off. Sandy paid 7.50 for the shirt. What was the shirts regular price
Answers
£10
Step-by-step explanation:
firstly what you have to do is
since the percentage is decreased
we will say 100 - 25% = 75%
then we say 7.50/75% = 10
So we know that the original price was
£10 pounds
As 10- 25%= 7.5
The shirt's regular price is 10.
Given,
A shirt on sale for 25%off.
Sandy paid 7.50 for the shirt.
We need to find the regular price.
The regular price is the same as the selling price.
We have,
Regular price = Paid price + offer discount%
offer discount = 25%
Paid price = 7.50
If after 25% off Sandy paid 7.50 which means Sandy paid only 75% of the price.
The regular price is always 100%
= Paid price + offer discount%
= 75% + 25%
So we have,
75% = 7.5
Multiplying 25/75 on both sides.
25/75 x 75% = 7.5 x 25/75
25% = 2.5
We see that the offer discount is 2.5.
We have,
Regular price = Paid price + offer discount%
= 7.50 + 2.5
= 10
Thus the shirt's regular price is 10.
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Adelle keeps track of the time her bus arrives at her stop. Since she has been keeping track, her bus has arrived on time 16 days and has been late on 4 days. Based on her data, what percentage of the time should Adele expect the bus to be late?
Answers
Answer:
25%
Step-by-step explanation:
4 days of 16 days is 25% or 1/4
Hope this helps! ;-)
Consider the line y=-2/3x+9 . Find the equation of the line that is parallel to this line and passes through the point (-8,3) . Find the equation of the line that is perpendicular to this line and passes through the point (-8,3) .
Answers
The equation of line which is parallel to line is y = (-2x-7)/3.
What is Gradient?
Gradient is the ratio between change in y-axis to change in x-axis.
Here, Given Equation of line is y = [tex]\frac{-2}{3}x+9[/tex]
gradient of line m₁ = -2/3
Equation of line passing through point (-8, 3) and gradient -2/3 (parallel to given line) is
(y - y₁) = m₂(x - x₁)
( y - 3) = -2/3(x+8)
3y - 9 = -2x -16
3y = -2x -16 + 9
3y = -2x -7
y = (-2x-7)/3
Thus, the equation of line which is parallel to line is y = (-2x-7)/3
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Answer correctly for branliest!
Answers
Select ALL the expressions that have a value of 2² – 3³ + 29.
1. (78 ÷ 3) – 24
2. 83 – 14 × 62 – 2
3. –|–6|
4. |–6|
5. 72 – 3.1 – 19 × 2.1
Answers
There is no expression that is the same as the value of 2² – 3³ + 29 which is = 2.
Simplification of the given expressionTo simplify the expression 2² – 3³ + 29. is as follows:
2² – 3³ + 29 = 4- 9+29
= 29 -5
= 24
(78 ÷ 3) – 24. To simplify is = 78/3=26-24 = 2 (false)83 – 14 × 62 – 2. To simplify is = 69- 60 = 9 (false)–|–6|. To simplify is -(-6) = +6( false)-6( false)72 – 3.1 – 19 × 2.1: To simplify is = 49.9×2.1 = 104.79 (false)Therefore, there is no expression that is the same as the value of 2² – 3³ + 29. which is 2.
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Write a slope-intercept equation for a line that passes through (-2,3) and (2,-5)
The slope of the given line is m
(Simplify your answer. Type an integer or a simplified fraction.)
Answers
Answer:
y - 3 = -2 * (x+2)
Step-by-step explanation:
HELP PLEASE 100 POINTS!!!
Given that triangle PHT is a right triangle and Line HY is an altitude, what is the missing justification in the proof that (PH)^2 + (HT)^2 = (PT)^2?
Answers
Step-by-step explanation:
Given information: Triangle PHT is a right
triangle and Line HY is an altitude.
According to the reflexive property, a side or
an angle is congruent to itself.
If A is an angle of a triangle then using
reflexive property
LAN LA
¿PIT ~ LYT
(Both are right angles)
IT ~ LT
(Reflexive property)
APHT~ AHYT
(AA rule of similarity)
Other statements and reasons are present in
the table.
The missing reason is reflexive property.
Therefore the correct option is D.
The missing reason is reflexive property.
Therefore, the correct option is D.
What is a triangle?A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle.
Given that a triangle PHT is a right triangle and Line HY is an altitude.
According to the reflexive property, a side or an angle is congruent to itself.
If A is an angle of a triangle, then using reflexive property.
∠A ≅ ∠A
∠PHT ≅ ∠HYT (Both are right angles)
∠T ≅ ∠T (Reflexive property)
ΔPHT ~ ΔHYT (AA rule of similarity)
Other statements and reasons are already in the table.
Hence the correct option is D.
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5) Mary is taking a swimming lesson on a rectangular pool which is 9 meters wide and 12 meters long. Find the area of the swimming pool.
a. What is asked?
b. What are given?
c. What is/are the operation/s to be used?
d. What is the number sentence?
e. What is the answer?
Answers
a) The Area of the swimming pool.
b) 9 meters wide, 12 meters long.
c) 9, 12 & multiplication.
d) 9 • 12
e) 108
Stephanie is helping a midwife weigh new-born babies. The scales are in pounds but the sheet she has to complete is in kilogrammes. The baby weighs 8.06 lbs. When she converts this on a calculator the display reads 3.65595152. What is this in kilogrammes to 3 decimal places?
Answers
The weight of baby in kg is, 3.659 kg.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The baby weighs 8.06 lbs.
Now, We know that;
⇒ 1 pound = 0.454 kg
Hence, The weight of baby in kg is,
⇒ 8.06 pounds = 8.06 × 0.454 kg
= 3.659 kg
Thus, The weight of baby in kg is, 3.659 kg.
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47/6m+n- 7/2m-6/5n
Simplify
Answers
Answer:
[tex]\frac{13m}{3}-\frac{n}{5}[/tex]
Step-by-step explanation:
1) Simplify [tex]\frac{47}{6}m[/tex] to [tex]\frac{47m}{6}[/tex]
[tex]\frac{47m}{6}+n-\frac{7}{2}m-\frac{6}{5}n[/tex]
2) Simplify [tex]\frac{7}{2}m[/tex] to [tex]\frac{7m}{2}[/tex]
[tex]\frac{47m}{6}+n-\frac{7m}{2}-\frac{6}{5}n[/tex]
3) Simplify [tex]\frac{6}{5}n[/tex] to[tex]\frac{6n}{5}[/tex]
[tex]\frac{47m}{6}+n-\frac{7m}{2}-\frac{6n}{5}[/tex]
4) Collect like terms.
[tex](\frac{47m}{6}-\frac{7m}{2})+(n-\frac{6n}{5})[/tex]
5) Simplify.
[tex]\frac{13m}{3}-\frac{n}{5}[/tex]
5. A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously
rotated around a straight line to form an object whose volume is 150.
6
10
hich line could the rectangle be rotated around?
A. a long side
B. a short side
C. the vertical line of symmetry
D. the horizontal line of symmetry
Answers
TheThe line that the rectangle could be rotated around is: C. the vertical line of symmetry.
Vertical line of symmetryAnalysis
Volume=Base area×height
If the rectangle rotated around horizontal line of symmetry
V1=Ah=πr²h
=π×9×10
=90π
If the rectangle rotated around short line
V2=Ah=πr²h
=π×10²×6
=π×100×6
=600π
If the rectangle rotated around vertical line of symmetry
V3=Ah=πr²h
=π×5²×6
=π×25×6
=150π
Therefore the correct option is C.
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HELP ASAP PLEASE!!!!!!!
Answers
The circumference of a circular garden is 122.46 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer. feet
Answers
The radius of the circular garden whose circumference is 122.46 feet is: 19.5 feet.
What is the Circumference of a Circle?Circumference = 2πr, where r is the radius of the circle.
Given the following:
Circumference = 122.46 feetRadius (r) = ?π = 3.14122.46 = 2(3.14)(r)
122.46/2(3.14) = r
r = 19.5 feet.
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T
yler wants to determine if an individual's age affects whether or not they like jazz, rock, or country music. Which type of inference test should Tyler use?
Answers
The appropriate test is the chi-squared test for association/independence.
What is an inference test?A statistical inference involves hypothesis testing about a population using a sample.
In this case, Tyler wants to determine if an individual's age affects whether or not they like jazz, rock, or country music. The appropriate test is the chi-squared test for association/independence.
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Answer:
chi-squared test
Step-by-step explanation:
Got it right on the test.
i need help with this question
Answers
Answer:
Simulation --> An imitation
Sample --> The part of a population
Biased sample --> A sample that is not
Population --> A group
PLEASE I NEED HELP ASAP!!!!!!!!
Note: please add the answer next to the number its from so I can know which question was answered
Answers
Answer:
B, B
Step-by-step explanation:
< less than
> Greater Than
If it has a line under it it is equal too as well as greater or less.
The close dot means equal too and the open mean not equal to
The ratio of cats to dogs at the veterinarian is 21:39. What percent of the total animals are cats?
Answers
Answer:
35%
Step-by-step explanation:
Assuming that there are no other animals in the vet other than dogs and cats, that means the total amount of animals is 21 + 39, which is 60 animals. To find the percent of cats, simply place the number of cats based on the ratio (21) over the total number of animals (60) and multiply by a 100:
21/60 = 0.35
0.35 x 100 = 35%
Hope this helps!!
Answer:
35%.
Step-by-step explanation:
Fraction that are cats = 21 / (21+39)
= 21/60
= 100 * 21/60
= 35%.
13 - 6(2 − 6)² +8 evaluate
Answers
Step-by-step explanation:
______________________13 - 6 ( 2 - 6 )² + 8
= Solution
= 13 - 6 (- 4 ) ² + 8
Now...remove the negative number...because negative number raise to even powers are positive...
= 13 - 6 × 4² + 8
= 13 - 96 + 8
= 13 + 8 - 96
= 21 - 96
= - 75
Hence the answer is - 75....
[tex]..[/tex]
______________________
Two cars, A and B, are travelling along a straight road and in the same direction. Car B is 20 km
ahead of Car A. Car A is travelling at 60 km · while Car B at 50 km 1. They both start at 12:00
hours. At what time Car A will overtake Car B?
Answers
Answer:
2 o'clock
Step-by-step explanation:
Their 'closing speed' is 60 - 50 = 10 km/hr
they have 20 km between them
at closing speed this will take 20 km / 10 km/hr = 2 hours for the cars to meet....this would be at 14:00 or 2 oclock
answer for branliest!
Answers
Answer: 19.62 * 10^7 cm
Step-by-step explanation:
Let a and b be rectangle sides.Area = a * bPerimeter = a + b + a + b = (a + b) * 2a = 9.2 * 10^7 cm
Area = 5.612 * 10^14 cm^2
Find: Perimeter - ?
Area = a * bb = Area / ab = (5.612 * 10^14) / (9.2 * 10^7) = 0.61 * 10^7 cm
Perimeter = (a + b)*2Perimeter = (9.2 * 10^7 + 0.61 * 10^7) * 2 = (9.2 + 0.61) * 10^7 * 2 = 9.81 * 2 * 10^7 = 19.62 * 10^7 cm
use the information provided to write the equation of each circle. center: (3, -15) radius: 3
Answers
Equation of circle in general
(x-h)²+(y-k)²=r²For centre at (h,k)
So our equation is
(x-3)²+(y+15)²=3²(x-3)²+(y+15)²=9