Answer:
Step-by-step explanation:
I'll just write log for log base 10. The important rules about logarithms we need to know are:
[tex] a \log b = \log( b^a) [/tex]
[tex] \log a + \log b = \log( ab) [/tex]
and at the end we'll need something like
[tex]\log a = \log b \implies a=b[/tex]
Suitably armed we can begin,
[tex] \left( 1 + \dfrac{1}{2x} \right) \log 3 + \log 2 = \log (27 - 3^{1/x}) [/tex]
First rule,
[tex] \log 3^{ 1 + 1/2x} + \log 2 = \log (27 - 3^{1/x}) [/tex]
Second rule,
[tex] \log 2(3^{ 1 + 1/2x}) = \log (27 - 3^{1/x}) [/tex]
Third rule,
[tex] 2(3^{ 1 + 1/2x}) = 27 - 3^{1/x} [/tex]
We can rewrite this to be a quadratic equation in [tex]y=3^{1/2x}[/tex].
[tex] 6 (3^{1/2x}) = 27 - (3^{1/2x})^2 [/tex]
[tex]y^2 +6y - 27 =0[/tex]
[tex](y - 3)(y+9)=0[/tex]
[tex]y=3 \textrm{ or } y=-9[/tex]
First solution:
[tex]3^{1/2x} = 3 = 3^{1}[/tex]
[tex]1/2x = 1[/tex]
[tex]1=2x[/tex]
[tex]x = 1/2[/tex]
Second solution,
[tex]3^{1/2x} = -9[/tex]
No real powers of 3 will be negative, no solution here.
Answer: x=1/2
Check:
1 + 1/2x = 2 so the left side is log 2(3²) = log 18
Right side, log(27-3^2) = log 18 √
Find the greatest common factor of the
following monomials:
39n3 48n2
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Monomial means an algebraic expression that consists of using ONE term}[/tex]
[tex]\mathsf{39n^3: 1, 3, 13, 39, n, n, n}[/tex]
[tex]\mathsf{48n^2: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, n, n}[/tex]
[tex]\large\textsf{Like terms: 1, 2, 3, n, n}[/tex]
[tex]\boxed{\boxed{ \large\textsf{Answer: \bf The GCF (Greatest Common Factor): 3n}^2}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{aAmphitrite1040:)}[/tex]
A hiker is descending 152m every 8 minutes what will be hikers change in elevation in half an hour? what as an integers
Answer:
570 meters
Step-by-step explanation:
[tex]\frac{8}{152} :\frac{30}{y}[/tex]
y × 8 = 152 × 30
8y = 4560
8y ÷ 8 = 4560 ÷ 8
y = 570
What is the length of BC? Please include how you got it :)
Answer:
BC = 24
Step-by-step explanation:
We know that triangles CAB and CED are similar because all three of their angles are the same. Thus, we know that the side lengths of these triangles have to be proportional to each other. You would match side BC with side DC and sides AC with EC.
AC/EC = BC/DC
30/10 = (32-x)/x
3 = (32-x)/x
Then using algebraic properties, solve for x.
3x = 32 - x
4x = 32
x = 8.
Lastly, plug in 8 for the x in BC, 32 - 8, so the length of BC is 24
Answer:
B
Step-by-step explanation:
Δ CBA and Δ CDE are similar triangles, then the ratios of corresponding sides are equal, that is
[tex]\frac{CB}{CD}[/tex] = [tex]\frac{CA}{CE}[/tex] , substitute values
[tex]\frac{32-x}{x}[/tex] = [tex]\frac{30}{10}[/tex] = 3 ( multiply both sides by x )
32 - x = 3x ( add x to both sides )
32 = 4x ( divide both sides by 4 )
8 = x
Then
BC = 32 - x = 32 - 8 = 24 → B
What is the length of a diagonal of a rectangle 9m long and 5m wide?
PLEASE HELP ME! this is due TONIGHT!! thank you so much
explaining your answer = brainliest/ five stars
the area of the parallelogram is ___ square feet
Answer:
Step-by-step explanation:
here,
base=28 ft
height=24 ft
are of parallelogram=base*height
=28*24
=672 ft^2
Answer:
672 ft²
Step-by-step explanation:
Area of parallelogram is the same as the area of a rectangle.
28 × 24 = 672 ft²
what is the length of side x in the above right triangle
Answer:
4
Step-by-step explanation:
b² - a² is the formula
5² - 3²
16
√16
= 4
what is the value of 64 2/3?
Answer:
[tex] \frac{194}{3} [/tex]
Step-by-step explanation:
[tex]64 \frac{2}{3} [/tex]
[tex]64 + \frac{2}{3} [/tex]
[tex]64 \times \frac{3}{3} + \frac{2}{3} [/tex]
[tex] \frac{64 \times 3}{3} + \frac{2}{3} [/tex]
[tex] \frac{64 \times 3 + 2}{3} [/tex]
[tex] \frac{192 + 2}{3} [/tex]
[tex] \frac{194}{3} [/tex]
Hope it is helpful...Find the rest of the equation.
Answer:
D = 48 E= 90 F = 42 FE = 15
Step-by-step explanation:
Sorry, i dont know how to get DF and DE yet
Verify Expreimentally that if all sides and all angles of a quadrilateral are equal then it is the square
Answer:
Wikipedia says:
"In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles)."
https://en.wikipedia.org/wiki/Square
Step-by-step explanation:
Write the expression in complete factored form.
p(y+ 9) + u(y + 9) =
Answer:
(p+u)(y+9)
Step-by-step explanation:
p(y+9)+u(y+9)
Multiply them out
py+uy+9p+9u
y(p+u)+9(p+u)
=(p+u)(y+9)
Plot the points P (2, -3) & Q (-5, -3) whose ordinates are same. To which axis the line PQ is parallel.
Given :
The points P (2, -3) & Q (-5, -3) whose ordinates are same.
To Find :
To which axis the line PQ is parallel.
Solution :
In given points the ordinates are same.
Therefore, the line is parallel to the x- axis.
Hence, this is the required solution.
if sin A-cos B then A+B=
Answer:
sinA=sin(90-B)
sinA=90_B
now,A+B
=90
PLEASE HELP!
*multiple choice*
List the sides in order from shortest to longest.
Answer:
I think it's a
I'm not that sure tho
Pythagoras
1.if the radius of the smaller circle is 3, find it’s area
2. Find the area of the yellow ring
3. Find the area of the white ring
Answer:
1. [tex]Area = 28.26[/tex]
2 and 3: See explanation
Step-by-step explanation:
Solving (1)
[tex]r = 3[/tex] --- radius
The area is:
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14* 3^2[/tex]
[tex]Area = 28.26[/tex]
There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.
However, the following formula will be used to calculate the required areas.
[tex]Area = \pi r^2[/tex] --- same process as (1)
PLEASE HELP ME!!! THANK YOU i really need it
The radius of a circle is 6 inches. What is the area of a sector bounded by a 102° arc?
give exact answer in simplest form
explaining your answer = brainliest/ five stars
Answer:
10 1/5 pi
Step-by-step explanation:
First find the area of the circle
A = pi r^2 = pi *6^2 = 36 pi
Then find the fraction of the circle that is shaded
A circle is 360 degrees
102/360 =17/60
Multiply the fraction by the area
17/60 * 36 pi
51/5 pi
10 1/5 pi
Answer:
32.04
Step-by-step explanation:
firstly area of a sector is angle/360 multiplied by pi *r squared
so in this case it is going to be 102/360 *pi *6^2
6 squared is 36 all multiplied by pi and 106/360
it is advisable that you enter them all at once in your calculator
the final answer will be32.0444507
which is rounded to 32.04
Help plz
1) __ × 4 = -20
2) __-7 = - 2
3) __ × - 5= 20
4) __- 9 = - 2
5) __+ 17 = 20
Answer:
1) -5
2) 5
3) -4
4) 7
5) 3
Step-by-step explanation:
1) -20 divided by -4
2) -2 plus 7
3) 20 divided by 5
4) -2 plus 9
5) 20 minus 17
can anyone help me solve ...
Answer:
a) x= 34°
b) x = 51°
Step-by-step explanation:
Points to keep in mind when solving triangle problems.
An isosceles triangle has two equal sides and the angles opposite to those sides are also equal angles.
A triangle with all sides equal is called an equilateral triangle, which is also called equiangular triangle.
Jason wants to know the percentage of M & M's that are green. He chooses a sample of 30 M & M's from a bag, and 3 of them are green. What is the margin of error of his experiment (round to 4 decimal places)? .1074 .1074 .9845 .9845 .1235 .1235 .8824
Answer:
The margin of error of his experiment is of 0.1074.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
30 M & M's from a bag, and 3 of them are green.
This means that [tex]n = 30, \pi = \frac{3}{30} = 0.1[/tex]
Standard 95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.1*0.9}{30}}[/tex]
[tex]M = 0.1074[/tex]
The margin of error of his experiment is of 0.1074.
The height of a parallelogram is four times the base. The base measures 3.5 ft. Find the area of the parallelogram.
Answer:
49ft^2
Step-by-step explanation:
3.5ft X 4= 14ft
Area of parallelogram formula:
(perpendicular height)(base)= area
(14ft)(3.5ft)=49ft^2
A silo consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal. The diameter of the cylindrical base of the silo is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft. Calculate the surface area of the silo. Leave your answer in terms of π.
480π sq. ft.
276π sq. ft.
216π sq. ft.
204π sq. ft.
Answer:
216π sq ft
Step-by-step explanation:
given that :
d = 12 ft => r = 12/2 = 6ft
h(cyl) = 10 ft
h(cone) = 8 ft
the surface area = ?
the solution :
the slant of cone = √r²+h²
= √6²+8²= √100 = 10 ft
the surface area of silo =
the lateral area of cone + the lateral area of cylinder + the base area
= π×r×slant + 2×π×r×h(cyl) + π×r²
= π×6×10 + 2×π×6×10 + π×6²
= 60π + 120π + 36π
= 216π sq ft
The surface area of the silo will be 216π square feet. Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A silo consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal.
The surface area is the sum of the surface area of the cone and cylinder. Then we have
The diameter of the cylindrical base of the silo is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft.
Surface area = πrl + 2πrh + πr²
The length of the radius will be
r = d /2
r = 12 / 2
r = 6 ft
The length of slant height will be
l² = 6² + 8²
l² = 100
l = 10 ft
Then the surface area of the silo will be
SA = π × 6 × 10 + 2π × 6 × 10 + π6²
SA = 60π + 120π + 36π
SA = 216π square feet
The surface area of the silo will be 216π square feet.
Then the correct option is C.
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ2
Write the slop form of an equation of the line thet passes throughtl (4-3)and(2,1
Answer:
y+2x-5= 0
Step-by-step explanation:
Applying,
(y-y₁) = m(x-x₁)............... Equation 1
Where m = slope
But,
m = (y₂-y₁)/(x₂-x₁)
Given: y₁ = -3, y₂ = 1, x₁ = 4, x₂ = 2
m = (1+3)/(2-4)
m = 4/-2
m = -2
Substituting into equation 1
(y+3) = -2(x-4)
y+3 = -2x+8
y = -2x+8-3
y = -2x+5
y = 5-2x
y+2x-5 = 0
Please help me i'm struggling!
50 points. I am stuck on this question, Please help!
Line AB is the diameter of circle E. The measure of < CBD = 63 degrees and the measure of Arc CA is 36 degrees. Find angles ADB, angles ABD, angles BAD and arc BD.
Thank you
Step-by-step explanation:
arc CAD = 2×63= 126°
< ADB = ½×180 = 90°
arc AD = 126-36 = 90°
< ABD = ½×90° = 45°
< BAD = 180-90-45 = 45°
arc BD = 2×45 = 90°
Lee drove 635 miles and used 25 gallons of gasoline. How many miles did Lee's car travel per gallon of gasoline?
Pls help me with this
Answer:
5.85
Step-by-step explanation:
100%-> 6.50
100%-10% = 90 %
90%-> 6.50/100 x 90
=5.85
A scatter plot with a line is shown below.
Which statement is most likely correct about the line.
G(x) = 8x - 9 for g(x) = 23
Express 4x + 3y - 8 = 0 in slope and y-intercept form.
Step-by-step explanation:
Given equation :-
4x + 3y - 8 = 0Slope intercept form :-
y = mx + c→ 4x + 3y - 8 = 0
→ 3y = -4x + 8
→ y = (-4x + 8)/3
→ y = -4/3x + 8/3
Answer:
y = -4/3x + 8/3.
Step-by-step explanation:
4x + 3y - 8 = 0
3y - 8 = -4x
3y = -4x + 8
Divide through by 3:
y = -4/3x + 8/3.
CAN SOMEONE PLEASE HELP ME??!!
Answer:
RO = 17.9
Step-by-step explanation:
If they're similar, the fraction between their sides need to be equal, so do this:
NK/NM = RO/RQ
71.6/64 = RO/16
71.6•16/64 = RO
RO = 17.9
PLEASE HELP ASAP, giving brainlist t anyone who answers <3