[tex]y= f(x) = 3^x+1\\\\\text{Replace x with y and solve for y}\\ \\~~~~~~x=3^y+1\\\\\implies 3^y = x-1\\ \\\implies \ln(3^y) = \ln(x-1)\\\\\implies y \ln 3= \ln(x-1)\\\\\implies y= \dfrac{\ln(x-1)}{\ln 3}\\\\\implies f^{-1}(x) = \dfrac{\ln(x-1)}{\ln 3}[/tex]
image coordinate plane with points plotted at ordered pairs Q (-4, 4) R (2, 4) S (5,-3) T(2,-3) and U (-4, -3) first persin to get it in 30 min get brainlest
Answer:
I have graphed them on desmos and given you three options to choose from:
Step-by-step explanation:
1. with lines (complete shape)
2. with lines (incomplete shape)
3. without lines
Hope this helps!
Answer:
here
Step-by-step explanation:
Will the product of 2 2/5 x 1/6 be larger or smaller than 2 2/5
Answer:
Smaller
Step-by-step explanation:
2 2/5 * 1/6 = 2/
5
= 0.4
Conversion a mixed number 2 2/
5
to a improper fraction: 2 2/5 = 2 2/
5
= 2 · 5 + 2/
5
= 10 + 2/
5
= 12/
5
To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/
5
= 10/
5
b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
c) Write a previous answer (new numerator 12) over the denominator 5.
Two and two fifths is twelve fifths
Multiple: 12/
5
* 1/
6
= 12 · 1/
5 · 6
= 12/
30
= 2 · 6/
5 · 6
= 2/
5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 30) = 6. In the following intermediate step, cancel by a common factor of 6 gives 2/
5
.
In other words - twelve fifths multiplied by one sixth = two fifths.
Hello can u guys help me please
Answer:
[tex]\displaystyle \frac{1}{4}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle\frac{4^{6} }{4^{7}}[/tex]
Expand:
[tex]\displaystyle\frac{4*4*4*4*4*4 }{4*4*4*4*4*4*4}[/tex]
Simplify ones, in this case [tex]\frac{4}{4}[/tex]:
[tex]\displaystyle \frac{1}{4}[/tex]
If you raise 4 to the power of 6, to the power of 7, and then simplify the fraction, you will get the same result. This method is much quicker when you have numbers with the same bases (here the base is 4) so I used this way.
Maitri and Aabhas do a work in 12 hours.
Aabhas and Kavya do the work in 15 hours.
Kavya and Maitri do
work in 20 hours.
In how many hours will they finish it together and separately?
Pls help me
Answer:
See below ~
Step-by-step explanation:
Given
Maitri and Aabhas do a work in 12 hoursAabhas and Kavya do the work in 15 hoursKavya and Maitri do the work in 20 hoursSolving
Take Maitri, Aabhas, and Kavya to be x, y, z respectivelyx + y = 12 (1)y + z = 15 (2)x + z = 20 (3)Take Equation 1 and rewrite it so that it is equal to x.
x = 12 - yTake Equation 2 and rewrite it so that it is equal to z.
z = 15 - yNow, substitute these values in Equation 3.
x + z = 2012 - y + 15 - y = 20-2y + 27 = 202y = 7y = 7/2 = 3.5 hours [Aabhas]Substitute the value of y in Equation 1.
x + 3.5 = 12x = 8.5 hours [Maitri]Substitute the value of y in Equation 2.
3.5 + z = 15z = 11.5 hours [Kavya]Add the values of x, y, and z together.
x + y + z8.5 + 3.5 + 11.512 + 11.523.5 hours [together]NO LINKS!! Please help me with this problem
FGHIJ ≅ STUQR
Solve for HI
[tex]\sf \dfrac{HI}{GH} = \dfrac{UQ}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{HI}{56} = \dfrac{25}{35}[/tex]
[tex]\rightarrow \sf HI = 40[/tex]
Solve for QR
[tex]\sf \dfrac{IJ}{GH} = \dfrac{QR}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{72}{56} = \dfrac{QR}{35}[/tex]
[tex]\rightarrow \sf QR = 45[/tex]
Solve for ST
[tex]\sf \dfrac{FG}{GH} = \dfrac{ST}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{48}{56} = \dfrac{ST}{35}[/tex]
[tex]\rightarrow \sf ST =30[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{GH}{HI}=\dfrac{UT}{UQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{HI}=\dfrac{35}{25}=\dfrac{7}{5}[/tex]
[tex]\\ \rm\Rrightarrow HI=56(5)/7=8(5)=40[/tex]
#QR
[tex]\\ \rm\Rrightarrow \dfrac{GH}{JI}=\dfrac{UT}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{72}=\dfrac{35}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{7}{9}=\dfrac{35}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow RQ=35(9)/7=5(9)=45[/tex]
#ST
[tex]\\ \rm\Rrightarrow \dfrac{GH}{FG}=\dfrac{UT}{ST}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{48}=\dfrac{7}{6}=\dfrac{35}{ST}[/tex]
[tex]\\ \rm\Rrightarrow ST=6(35)/7=6(5)=30[/tex]
A
Select the correct answer from each drop-down menu.
The front, back left and right sides of the second floor of the house will be painted. The roof will not be painted. The total surface area to be
painted is 728 square feet. The windows shown each measure 3 feet by 2 feet. There are no other windows on the second floor.
Ich 4) to
hft
2017
25 ft
What is the value of 2
The front and back of the top section of the
The bottom section of the second floor can be modeled by a
second floor can be modeled by the bases of a
The value of hin feet is
Reset
Next
Answer: rectangular prism, triangular prism, 6
Step-by-step explanation:
The area of base of the triangular prism can be calculated by the half of the product of the height of the triangular base of prism and base of prism.
How to calculate the area of the base of a rectangular prism?The area of base of the rectangular prism can be calculated by the product of the length of the rectangular base of prism and the breadth of prism.
The area of the bottom section of the second floor = 2( area of the front part of the wall + area of the side of the wall)
= 2( 20*h + 25*h)
=90h
The front and back of top section of second floor = 2* area of the front wall=2*(1/2*20*(h+4))=20h+80
Total area of the second floor=total area of the window+total area to be painted
⇒Total area of the second floor= 728 + (2* area of the window)
⇒Total area of the second floor= 728 + (2*3*2)
⇒area of front and back of top section of second floor + The area of the bottom section of second floor = 728+12
⇒area of front and back of top section of second floor + The area of the bottom section of second floor = 740
⇒(20h+80)+90h=740
⇒110h+80=740
⇒110h=740-80
⇒110h=660
⇒h=660/110
⇒h=6 feet
Therefore the value of h is 6 feet.
Learn more about area of triangular Prism
here: https://brainly.com/question/17111476
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1 box of blue counters from which 25 counters have been removed and then the remaining number has been doubled
Expand 96•06 using powers
Answer:
Step-by-step explanation:
Use long multiplication to evaluate.
576
At a local school,940 students each wrote 40 letters to students in another country.How many letters were written in all?
Answer:
37,600
Step-by-step explanation:
940 X 40 = 37,600.
simple multiplication
Answer:
, 37,000
Step-by-step explanation:
940 x 40= 37,000
please help me thanks
Answer:
y = 3x
Step-by-step explanation:
i cant see any equations
but the equaiton would be..
The graph shows the function f(x) = 3* What is the value of f-1(x) at x = 3?
Answer:
1
I've attached a screenshot from my graphing calculator of [tex]f(x)[/tex] in blue and [tex]f^{-1}(x)[/tex] in red. Notice how the red line (inverse function) has (3, 1)
Step-by-step explanation:
[tex]f(x) = 3^x\\f^{-1}(x) =\ ?\\[/tex]
We must first figure out the inverse function of [tex]f(x)[/tex] which is [tex]f^{-1}(x)[/tex]
[tex]y = f(x) = 3^x\\y = 3^x\\log\ y = log\ 3^x\\log\ y = x \times log\ 3\\x = \frac{log\ y}{log\ 3}\\[/tex]
We say y = f(x) to begin with, but after find x = ...
we must 'swap' x and y
[tex]x = \frac{log\ y}{log\ 3}\\y = \frac{log\ x}{log\ 3}\\[/tex]
[tex]f^{-1}(x) = \frac{log\ x}{log\ 3}[/tex]
[tex]f^{-1}(3) = \frac{log\ 3}{log\ 3} = 1[/tex]
Calc I optimization problem, Please see attachment!
=======================================================
Explanation:
Let C be the corner point.
x = distance from P to C
That makes segment AP to be 70-x feet long
Focus on the right triangle PBC. Use the pythagorean theorem to find the hypotenuse PB.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\PB = \sqrt{(PC)^2 + (CB)^2}\\\\PB = \sqrt{x^2 + 90^2}\\\\PB = \sqrt{x^2 + 8100}\\\\[/tex]
If we knew what x was, then we could find a numeric value for PB.
---------------------
It costs $28 per foot to run cable along the ground. This is the portion from A to P. So it costs 28(70-x) dollars to run that portion of cable above ground. Simply multiply the cost per foot by the number of feet.
Similarly, the cost from P to B is [tex]53\sqrt{x^2+8100}[/tex] since it costs $53 per foot to have it run underground.
The total cost is therefore [tex]28(70-x) + 53\sqrt{x^2 + 8100}[/tex]
The derivative of this will help determine when the cost is minimized.
Type that function into GeoGebra and have it compute the derivative.
You should find that the x intercept of the derivative curve is exactly x = 56
If x = 56, then 70-x = 70-56 = 14
This means AP = 14 feet is the amount of cable to run along main street.
This also leads to [tex]PB = \sqrt{x^2 + 8100} = \sqrt{56^2 + 8100} = 106[/tex]
The total length of the wire is 14+106 = 120 feet
It costs $28 per foot along the 14 ft section, so 28*14 = 392 dollars is the cost for this section.
It costs $53 per foot along the 106 ft section, so 53*106 = 5618 dollars is the cost for this other section.
The total min cost is 392+5618 = 6010 dollars
------------------
Side note: You could do all this without a calculator to compute the derivative and use algebra to end up with x = 56. However, I think the use of technology is beneficial because it's fast/efficient. In real world settings, you won't be likely to pull out pencil/paper to get things done. The modern world relies on computers. It's refreshing to see that your teacher encourages the use of technology.
Let me know if you need me to go over the algebraic steps and I'll update my answer.
Helpppppp pleaseeeee ):
Answer:
Smily face=5 lightning=8
Step-by-step explanation:
5+5=10 8x3=24 24+10=34
8x5=40 5x8=40
7. A sector of a circle has are length 2cm and central angle 0.4 radians. Find its
radius and and area?
solve 1 + cos theta = 2 cos^2 theta
[tex]~~~~1+ \cos \theta = 2 \cos^2 \theta \\\\\implies 2\cos^2 \theta -\cos \theta -1 = 0\\\\\implies 2 \cos^2 \theta -2\cos \theta + \cos \theta -1 = 0\\\\\implies 2 \cos \theta( \cos \theta -1) +(\cos \theta -1)=0\\\\\implies (\cos \theta -1)(2 \cos \theta +1)=0\\\\\implies \cos \theta = 1, ~~\cos \theta = -\dfrac 12\\\\\implies \theta = 2n\pi,~~~ \theta = 2n\pi \pm \dfrac{2\pi}3[/tex]
Solve the inequality įx - 2 Ž. Which number line represents the graph of the solution?
7 8 9 10 11 12 13 14 15
th
-5-4-3-2-1 0 1 2 3 4 5
-1
3
4
niwa
1
4
0
H
8
-
7
9
0
-1
1
9
-
No
2 5 4 1 2
3 9939
Answer:
2 ND option
solve and write
A triangle has perimeter 38 cm.
Two sides of the shapes are put
together to make a pentagon
A square has perimeter 48 cm.
What is the perimeter
of the pentagon?
cm
Answer:
62cm
Step-by-step explanation:
You were told the perimeter of the triangle is 38
but two sides are added to make a Pentagon. and that Pentagon is made up of a triangle and a square.
so if we find the side of the square, we can equally get the other two sides of the triangle.
hint: (because it's a square, we would be getting an isosceles triangle, meaning two sides are equal)
because one side of the pentagon added to the other two sides of the triangles gives us the perimeter of the triangle.
we first find the sides of the square with all sides equal by diving by 2
[tex] \frac{48}{2} = 12[/tex]
the sides of the square making the perimeter of the square 12cm.
now we subtract 12 from the perimeter of the triangle 38
[tex]38 - 12 = 26[/tex]
now that we have gotten one side we can get the other two by dividing the result by 2
[tex] \frac{26}{2} = 13[/tex]
so the other two sides of the triangle are 13cm.
now since we have the sides of the square and the triangle, we can find the perimeter of the pentagon by adding.
all the sides of the triangle without the base which is also the top of the square.
so instead of adding 4 times of 12, we add 3 times of 12 and 2 times of 13.
3(12)+2(13) = 62
or
12 + 12 + 12 + 13 + 13 = 62cm
bianca's dad was taking everyone out to eat for her birthday. he spent $8 total on the adults and $9 total on the kids. how much did it cost for everyone?
Find the area of the shaded region
Answer:
20.52 cm²
Area of shaded region:area of semi-circle - area of triangle
[tex]\dashrightarrow \sf \dfrac{1}{2} \ \pi (radius)^2 \ - \ \sf \dfrac{1}{2} *base*height[/tex]
[tex]\rightarrow \sf \dfrac{1}{2} (3.14)(6)^2 - \dfrac{1}{2} *12*6[/tex]
[tex]\hookrightarrow \sf 56.52 \ - \ 36[/tex]
[tex]\hookrightarrow \sf 20.52 \ cm^2[/tex]
a sphere is inscribed in a cube with a volume of 125 cubic inches what is the volume of the sphere
Answer:
using [tex]\pi[/tex]: 65.45 in³ (nearest hundredth)
using [tex]\pi =3.14[/tex]: 65.42 in³ (nearest hundredth)
Step-by-step explanation:
The radius of the sphere is half the side length of the cube (see attached diagram). Therefore, the side length of the cube = 2r
Given:
volume of the cube = 125 in³side length of cube = 2r[tex]\textsf{Volume of a cube}=x^3\quad \textsf{(where}\:x\:\textsf{is the side length)}[/tex]
[tex]\implies 125=(2r)^3[/tex]
[tex]\implies \sqrt[3]{125}=2r[/tex]
[tex]\implies 5=2r[/tex]
[tex]\implies r=\dfrac52[/tex]
Substitute the found value of r into the volume of a sphere equation:
[tex]\begin{aligned}\textsf{Volume of a sphere} & =\dfrac43 \pi r^3\\\\ & =\dfrac43 \pi \left(\dfrac52\right)^3\\\\ & =\dfrac43 \pi \left(\dfrac{125}{8}\right)\\\\ & =\dfrac{500}{24} \pi\\\\ & =\dfrac{125}{6} \pi\\\\ & =65.45\:\sf in^3\:(nearest\:hundredth) \end{aligned}[/tex]
Find all solutions in the interval [0,2π)
Answer:
Its B
Step-by-step explanation:
Given x^2+y^2=r^2 and the figure of the right triangle with legs x and y and hypotenuse r, prove cos^2θ+sin^2θ=1.
I need assistance filling out the blanks on the attached document.
By definition of cosine and sine,
cos(θ) = x/r
sin(θ) = y/r
so that
cos²(θ) + sin²(θ) = (x/r)² + (y/r)²
… = x²/r² + y²/r²
… = (x² + y²)/r²
… = r²/r²
… = 1
To that end, I would say
• [blank1] = "Division property of equality"
That is, we divide both sides of an equation by the same number and equality still holds since r ≠ 0
• [blank2] = "Definition of cos"
• [blank3] = "cos²(θ) = x²/r²"
• [blank4] = "Defintion of sin"
• [blank5] = "sin²(θ) = y²/r²"
• [blank6] = "Simplify"
More specifically, x² + y² = r² is given, so
x²/r² + y²/r² = (x² + y²)/r² = r²/r² = 1
What is the difference between a regular and irregular quadrilateral?
Answer:
ir
Step-by-step explanation:
irregular
regular
what do you notice different?
the both have r, e, g, u, l, a, r, but one has ir at the beginning.
can someone please help? :((
if you want another 50 points or more you could maybe help with one of the previous unanswered questions on my profile
Just find the vertex and then compare with graph
#a
y=2x²-8y=2(x-0)²-8Parabola opening upwards
Vertex at (0,-8)Graph 3
#2
y=(x+3)²+0Vertex at (-3,0)
Graph IV
#3
y=-2(x-4)²+8Parabola opening downwards as a is -ve
Graph I
#4
One graph is left
Graph IiAnswer:
a) graph iii)
b) graph iv)
c) graph i)
d) graph ii)
Step-by-step explanation:
Vertex form of a quadratic equation: [tex]y = a(x - h)^2 + k[/tex]
where [tex](h, k)[/tex] is the vertex (turning point)
First, determine the vertices of the parabolas by inspection of the graphs:
Graph i) → vertex = (4, 8)Graph ii) → vertex = (3, -8)Graph iii) → vertex = (0, -8)Graph iv) → vertex = (-3, 0)Next, write each given equation in vertex form and compare to the vertices above.
[tex]\textsf{a)}\quad y=2x^2-8[/tex]
[tex]\textsf{Vertex form}: \quad y=2(x-0)^2-8[/tex]
⇒ Vertex = (0, -8)
Therefore, graph iii)
[tex]\textsf{b)} \quad y=(x+3)^2[/tex]
[tex]\textsf{Vertex form}: \quad y=(x+3)^2+0[/tex]
⇒ Vertex = (-3, 0)
Therefore, graph iv)
[tex]\textsf{c)} \quad y=-2|x-4|^2+8[/tex]
[tex]\textsf{Vertex form}: \quad y=-2|x-4|^2+8[/tex]
⇒ Vertex = (4, 8)
Therefore, graph i)
[tex]\textsf{d)} \quad y=(x-3)^2-8[/tex]
[tex]\textsf{Vertex form}: \quad y=(x-3)^2-8[/tex]
⇒ Vertex = (3, -8)
Therefore, graph ii)
For each of the following prisms,find (I) its volume (ii) its total surface area
A rectangular field is 30 yards in length and 81 feet in width.
What is the area of the field in square feet?
Answer:
7290in ^2
Step-by-step explanation:
covert 30yd to feet which equals too 90ft.
Then multiple 90 x 81 = 7290
cosx(tanx+cotx)=
Pls Help
Step-by-step explanation:
Tangent is equal to sine over cosine. Cotangent is equal to cosine over sine. Therefore:
[tex]cos(x)( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )[/tex]
Distribute the cos(x) into the sum to get:
[tex]sin(x) + \frac{ {cos(x)}^{2} }{sin(x)} [/tex]
Get a common denominator by multiplying the first term by sine over sine to get:
[tex] \frac{ {sin(x)}^{2} }{sin(x)} + \frac{ {cos(x)}^{2} }{sin(x)} [/tex]
The numerator adds to equal 1 due to a common trigonometric identity. Therefore the only remaining term is:
[tex] \frac{1}{sin(x)} [/tex]
PLEASE HELP!!!!!!!!!
Answer:
With Graph and Without Graph.
Step-by-step explanation:
Without graphing calculator, you plug in your x-values into the equation
y = 16 -x^2 to solve for y-values.
f(x) = 16 - x^2
f(-4) = 16 - (-4)^2 = 16 - 16 =0
...
f(4) = 16 - (4)^2 = 16 - 16 =0
With Graphing Calculator.
What key features do the functions f(x) = 12x and g of x equals the square root of x minus 12 end root have in common?
Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions have an x-intercept in common.
Both f(x) and g(x) include domain values of [12, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions increase over the interval (-6, 0).
Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞). Then the correct option is D.
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The functions are given below.
[tex]\rm f(x) = 12x \\\\g(x) = \sqrt{x - 12}[/tex]
Then the domain of f(x) is (-∞, ∞) and the domain of g(x) is (12, ∞). And both the functions increases in the interval of (12, ∞).
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ1
What solution value does not satisfy the compound inequality X - 7 < 17 or -6x >
36?
O A) x = -1
OB) x=0
O C) x= - 10
C
O D) x=25
Dx = 25
Inequalities are expressions not separated by an equal sign. The solution of the compound inequality will be -6 < x < 24
Compound inequalityInequalities are expressions not separated by an equal sign.
Given the compound inequalities
X - 7 < 17 or -6x >36
For the inequality
x - 7 < 17
x < 17 + 7
x < 24
Similarly for -6x >36
x < -36/6
x < -6
The solution of the compound inequality will be -6 < x < 24
Learn more on inequality here: https://brainly.com/question/11613554