Solve each equation. Round to four decimal places.
e^x=8
Answer:
x ≈ 2.0794
Step-by-step explanation:
Given
[tex]e^{x}[/tex] = 8 ( take ln of both sides )
ln [tex]e^{x}[/tex] = ln 8
x lne = ln 8 [ lne = 1 ]
x = ln 8 ≈ 2.0794 ( to 4 dec. places )
Answer:
x ≈ 2.0794
Step-by-step explanation:
[tex] \small \sf \: e {}^{x} = 8[/tex]
Take the natural logarithm of both side of equation
[tex]\small \sf \: In ( e {}^{x} ) = In ( 8 )[/tex][tex] \small \sf \: Use \: In(e {}^{x} ) = x \: to \: simplify \: the \: expression.[/tex]
x = In( 8 )Write the number in exponential form.
x = In(2³)Use In(aⁿ) = n × In ( a ) to transform the expression.
x = 3In( 2 ) ≈ 2.07944Round to four decimal places = 2.0794
What is the simplified algebraic expression?
Question 17 (5 points)
Determine the value of x in the isosceles trapezoid.
2x
х
x = 60°
x= 65°
x= 180°
*= 90°
Question 4 of 10
Which describes the graph of y=-(x - 3)^2 + 2?
O A. Vertex at (-3,2)
O B. Vertex at (3,-2)
C. Vertex at (3,2)
O D. Vertex at (-3,-2)
Answer:Vertex at (3, -2)
Step-by-step explanation:
Pls help this set question
1: True
2: False
3: False
4: True
5: False
6: True
can someone do this step by step pls:)
Answer:
23
4* 4 = 16
cir = 2[tex]\pi[/tex]r = 2[tex]\pi[/tex](1.2) = 2.4[tex]\pi[/tex]
16 + 2.4[tex]\pi[/tex] = 23.53
Step-by-step explanation:
A rectangular tank 60 cm long and 50 cm wide is /5 full of water. When 24 liters of water are added, the water level rises to the brim of the tank. Find the height of the tank. (1 liter is 1000cm3 )
Answer:
The tank is 10cm high
Step-by-step explanation:
Given
[tex]L=60cm[/tex] -- length
[tex]W=60cm[/tex] -- width
[tex]x = \frac{1}{5}[/tex] --- water lever
[tex]Addition = 24L[/tex]
Required
The height of the tank
Let y represents the remaining fraction before water is added.
So:
[tex]y + x = 1[/tex]
Make y the subject
[tex]y = 1 - x[/tex]
[tex]y = 1 - \frac{1}{5}[/tex]
Solve
[tex]y = \frac{5 - 1}{5}[/tex]
[tex]y = \frac{4}{5}[/tex]
Represent the volume of the tank with v
So:
[tex]y * v = 24L[/tex]
Make v the subject
[tex]v = \frac{24L}{y}[/tex]
Substitute: [tex]y = \frac{4}{5}[/tex]
[tex]v = \frac{24L}{4/5}[/tex]
[tex]v = 30L[/tex]
Represent the height of the tank with h;
So, the volume of the tank is:
[tex]v = lwh[/tex]
Make h the subject
[tex]h = \frac{v}{lw}[/tex]
Substitute values for v, l and w
[tex]h = \frac{30L}{60cm * 50cm}[/tex]
Convert 30L to cm^3
[tex]h = \frac{30*1000cm^3}{60cm * 50cm}[/tex]
[tex]h = \frac{30000cm^3}{3000cm^2}[/tex]
[tex]h = 10cm[/tex]
does anyone know the answer to this question?
Answer:
(1,2)
Step-by-step explanation:
1. plug x into the equation:
[tex]2<\frac{2}{3}(1)+2[/tex]
2. simplify:
[tex]2<\frac{2}{3}+2[/tex]
[tex]2<\frac{2}{3}+\frac{6}{3}[/tex]
[tex]2<\frac{8}{3}[/tex]
since 8/3 is greather than 2, (1,2) is a solution
PLS HELP(algebra 1)
solve -7 + 18(17h + 19)
Answer:
335+306h
Step-by-step explanation:
solve the brackets first by distributing 18 to 17h and 19
-7+306h+342
then group the like terms
-7+342+306h
335+306h
10
What are the x- and y-coordinates of point E, which
partitions the directed line segment from A to B into a
ratio of 1:2?
B(-4,9)
9
8
X E
(
mn)(x2 – xı) + x
7-
6
5
4
mm. )(x2 - y) + y
3
-7 -6 -5 4 -3 -2 -14
2 3 4 5 6 7
0 (0, 1)
0 (-1,3)
O(-2,5)
(1,0)
X
-2.
3
A(2,-3)
19
Answer:
Step-by-step explanation:
The formulas to find the x and y coordinates of E are:
[tex]x=\frac{bx_1+ax_2}{a+b}[/tex] and [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where x1, x2, y1, and y2 are from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in to find x first:
[tex]x=\frac{2(2)+1(-4)}{1+2}=\frac{4-4}{3}=0[/tex] and now for y:
[tex]y=\frac{2(-3)+1(9)}{1+2}=\frac{-6+9}{3}=\frac{3}{3}=1[/tex]
The coordinates of E are (0, 1).
Given:
The points are A(2,-3) and B(-4,9).
The point E divides the segment AB in 1:2.
To find:
The coordinates of point E.
Solution:
Section formula: If a point divides a line segment in m:n, then the coordinates of the point is:
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using the section formula, the coordinates of point E are:
[tex]E=\left(\dfrac{1(-4)+2(2)}{1+2},\dfrac{1(9)+2(-3)}{1+2}\right)[/tex]
[tex]E=\left(\dfrac{-4+4)}{3},\dfrac{9-6}{3}\right)[/tex]
[tex]E=\left(\dfrac{0)}{3},\dfrac{3}{3}\right)[/tex]
[tex]E=\left(0,1\right)[/tex]
Therefore, the coordinates of the point E are (0,1).
The perimeter of a square is 80cm
state the length of one of its side
Answer:
20cm
Step-by-step explanation:
a square has 4 equally long sides.
when we know its perimeter, that means we know the sum of all 4 sides.
since all sides are equality long, we only need to divide the perimeter by 4 to get the length of an individual side.
80/4 = 20cm
Find angle m
A. 69
B. 23
C. 46
D. 167
Answer:
a
Step-by-step explanation:
∠DAF - ∠CFA=∠DFC
118-49 =69
Can someone help me with this math homework please!
At the time of her grandson's birth, a grandmother deposits $3000 in an account that pays 9.5% compounded monthly.
What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
Answer:
74820
Step-by-step explanation:
9.5% of 3000 is 285
there are 12 months in a year
so 12 times 21 equals 252
so 285 times 252 add 3000 equals 74820
Use the drop-down menus to identify the values of the parabola.
Vertex = ____
Domain = {x| ____ }
Range = {y| y ≤ ____ }
Answer:
Im guessing because their no chart.
Step-by-step explanation:
The answer is.
Vertex: 0,4.
Domain: X is a real number.
Range: 4.
i need help ASAP. PLEASE.
Answer:
1st one
Step-by-step explanation:
What is the length of each side of a square if its area is 121 ft??
11 feet
12 feet
10 feet
30 feet
Answer:
11 feet
Step-by-step explanation:
Given,
Area of square ( a^2 ) = 121 ft
To find : Length of each side ( a ) = ?
Formula : -
Area of square = a^2
a^2 = 121
a = √121
a = 11 feet
Answer:
11 ft = side length
Step-by-step explanation:
The area of a square is found by
A = s^2
121 = s^2
Taking the square root of each side
sqrt(121) = sqrt(s^2)
11 = s
13. For every 5 hours that he works, Andrew
is paid $60.20. How much is Andrew paid
in dollars per hour?
Fifth grade students from Garden City Elementary School left for a field trip at the time shown on the clock.(6:54am) They returned from the field trip at 10:24 p.M. How long were the students on this field trip?
Answer:
15 hour(s) and 30 minute(s).
Step-by-step explanation:
Answer:
krkrkrl4k3?8999kekek
Step-by-step explanation:
the UK. I have been a while. I have been a while. I have been a while. I have been a while 6e5 the UK. I have been a while. I have been a while. I have
. How do we have a look at the moment. The comments for the first time in the UK. I
Find the angle between u = (8,-3) and v = (-3,8). Round to the nearest tenth of a degree.
if f(1) = 2 – 2 anid 9(37)
and g(x) = x2 – 9, what is the domain of g(x) = f(x)?
Answer:
B
Step-by-step explanation:
Let divide g(x) by f(x)
[tex] \frac{ {x}^{2} - 9 }{2 - x {}^{ \frac{1}{2} } } [/tex]
The domain of a rational function cannot equal zero so let set the bottom function to zero.
[tex]2 - x {}^{ \frac{1}{2} } = 0[/tex]
[tex]x {}^{ \frac{1}{2} } = 2[/tex]
Square both sides
[tex]x = 4[/tex]
Also we can simplify the bottom denomiator into a square root function
[tex]2 - \sqrt{x} [/tex]
The domain of a square root function is all real number greater than or equal to zero because a square root of a negative number isn't graphable.
So we must find a answer that
Disincludes 4 from the intervalDoesnt range in the negative number or infinity)Range out in positve infinityThe answer to that is BQ14SIMPLIFY THE EXPRESSION 6ab of2adivided by12x12ab+14a-a
Answer:
25
Step-by-step explanation:
6ab of 2a ÷ 12 × 12ab + 14a - a
= 6ab * 2a ÷ 12 × 12ab + 14a - a
= 12a²b ÷ 144ab + 13a
= 12*a*a*b / 144*a*b + 13*a
= a/12 + 13*a
= 1/12 + 13
= 1/25
C-x:x is a two-digit natural number such that the sum of its digits is is 89
A survey asked people of different ages whether they get their news by
reading the paper. What is the probability that a person surveyed is 40 or
above, given that he or she gets the news by reading the paper? If necessary.
round your answer to the nearest percent.
Answer:
A) 60%
Step-by-step explanation:
24/40
= 0.6
0.6*100
= 60%
I really hope this is right and it helps.
the sherman family mad a down payment of $18,375 for a new house they mortaged the remaining cost of $129,625 the interest paid for 30 years was $273,116 what was the total cost of the house
Answer:
honestly this is a very poorly worded question...
it can be interpreted in several different ways....
the cost of the house (for them to purchase it) was
$129,625 + $18,375 = $148,000
The total amount that they paid for the house (money spent)
was
$129,625 + $18,375 + $273,116 = $421,116
all being said I think that the $148,000 is the answer that the question
is trying for you to figure out
Step-by-step explanation:
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x ≈ 52.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{KL}{LM}[/tex] = [tex]\frac{36}{28}[/tex] , then
x = [tex]tan^{-1}[/tex] ([tex]\frac{36}{28}[/tex] ) ≈ 52.1° () to the nearest tenth )
PLEASE HELP!!! Find the equation of the line passing through the point that (4,-1)that is parallel to the line 2x-3y=9
Answer:
y=2/3x-11/3
Step-by-step explanation:
line is parallel so the gradient will be the same ( m=2/3)
using the point (4,-1)
y=2/3x+c
-1=2/3*4+c
-1=8/3+c
c= -11/3
equation ---> y=2/3x-11/3
which points lie in the second quadrant? check all that apply.
Point F
Point E
These lie in the second quadrant.
Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form.
Answer:
12^(3/2)
Step-by-step explanation:
(2x6)^3/2
2x6=12
12^3/2= 41.5692193817
What are the zeroes of f(x) = x^2 + 5x + 6? (4 points)
A) x = -2, -3
B) x = 2,3
C) x= -2,3
D) x = 2, -3
Answer:
the answer is A, if you need explanation comment
Step-by-step explanation:
