Answer:
x = -3/2
Step-by-step explanation:
x + 3 + d = 2x + 1 First term plus common difference = 2nd term
x -2 = d
x + 3 + 2d = 5x+2 First term + 2 d = third term re-arrange:
4x-1 = 2d sub in the definition of d from above
4x -1 = 2 (x-2)
4x-1 = 2x-4
2x = -3
x = -3/2
If x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The sequence in which consecutive terms will have common difference is called as Arithmetic sequence.
x+3, 2x+1, and 5x+2
The common difference between first term and second term
d=2x+1-x-3
d=x-2
The common difference between second term and third term
5x+2-2x-1=d
3x+1=d
Now plug in d value
3x+1=x-2
Subtract x from both sides
3x-x=-3
2x=-3
Divide both sides by 2
x=-3/2
Hence, if x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.
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Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. f(x)= x+a b g(x)=cx−d Part 2. Show your work to prove that the inverse of f(x) is g(x). Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph. Task 2 Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model: a√x+b+c=d Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation. Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous. Part 3. Explain why the first equation has an extraneous solution and the second does not.A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.” Use the graph below to justify the lead executive’s statement. Determine the approximate year that the two ad revenues were equal. See Text Version Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0: Year number Western Beach width (in feet) Dunes Beach width (in feet) 0 100 20 5 90 45 10 80 70 11 78 75 12 76 80 15 70 95 Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table. Between which years will the beaches have approximately the same width? Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
Answer: 5+10-15=30
5=35
=7
х=49
5√49+10-15=30
30=30
+1+7=4
=-4
it is no solution
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
A or 2
Step-by-step explanation:
Reason:
The 5's cancel out leaving the 2 behind as the final answer.
Another way to look at it is that the 5*2 up top multiplies to 10, then we divide that by the 5 in the denominator to end up with 10/5 = 2
If you are a visual learner, then draw a circle and divide it into 5 equal slices. Do this a total of five times. Each pizza having 2 slices, and 5 pizzas total, gives 2*5 = 10 slices overall. These ten slices can be rearranged into making 2 full pizzas.
See below.
simplify square root of 10,000,000 using powers of ten
using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]
Meaning of IndicesIndices in mathematics can be defined as a value that takes up in index form but still retain its magnitude.
It is writing big or complicated values in a simpler and smaller way.
Indices is so important for simplicity purposes.
in conclusion, using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]
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Please help me!!!!!! Thanks!!!!!!!!!!
Answer:
See below ~
Step-by-step explanation:
Question 4
Finding the lateral area :
⇒ Lateral area = 2πrh
⇒ Lateral area = 2π(8)(20)
⇒ Lateral area = 320π cm²
===============================================================
Finding the surface area :
⇒ Surface area = Lateral area + 2 × area of the circle
⇒ Surface area = 320π + 2 × π(8)²
⇒ Surface area = 320π + 128π
⇒ Surface area = 448π cm²
=============================================================
Question 5
⇒ In this scenario, the part that is painted is the lateral area
⇒ Area painted = 6 × 4 × 170
⇒ Area painted = 24 x 170
⇒ Area painted = 4,080 mm³
What is the ratio of the area of sector abc to the area of sector dbe?
The ratio of the area of sector abc to the area of sector dbe is 4:3
Area of a sectorThe formula for calculating the area of a sector is expressed as:
A = r²Ф
where:
r is the radiusФ is the subtended angleFor the sector ABC
A1 = (2r)²β
A1 = 4r²β
For the sector DBE
A2 = (r)²3β
A2 = 3r²β
Take the ratios
Ratio= A1/A2
Ratio = 4r²β/3r²β
Ratio = 4/3
Hence the ratio of the area of sector abc to the area of sector dbe is 4:3
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PLEASE HELP ASAP!!
Describe the transformations from the parent function, and define the function of the following graph.
Answer: Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B
Step-by-step explanation:
* Lets revise the vertical and horizontal stretch with reflection
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
- If k should be negative, the vertical stretch is followed by a reflection
across the x-axis
- A horizontal stretching is the stretching of the graph away from
the y-axis
- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally
stretched by dividing each of its x-coordinates by k.
- If k should be negative, the horizontal stretch or shrink is followed
by a reflection in the y-axis
* Lets solve the problem
∵ G(x) = sin x
∵ F(x) = -5.8 sin x
∴ F(x) = -5.8 G(x)
- From the rule above
∴ G(x) is stretched vertically by scale factor -5.8
∵ The scale factor is negative
∴ The vertical stretch is followed by a reflection across the x-axis
* The transformation is:
Vertical stretch by a factor of 5.8 , reflection across x-axis
i need help can u guys help ;-;
Answer:
The answer for x and y will be x = Y + 7 and Y = 6x + 7Step-by-step explanation:
Y=6x - 7
6x - 7 = Y
6x = Y + 7
6x/6 = Y + 7/6
X = Y + 7
Find out if the lengths form a right triangle
Answer:
The triangle is a right triangle.
Step-by-step explanation:
Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:
[tex]a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256[/tex]
Therefore, the triangle is right.
answer that for me xx
How many scalene triangles can be made?
Answer:
I think 24.
Step-by-step explanation:
Plsssss helpppppoooooooooopppppppppppppppppppppp
Answer:
4
Step-by-step explanation:
( I will give brainlist ) Help its A Math Problem !!! Determine if the following table is linear, exponential or quadratic. Then write the equation that represents the function.
Answer:
Linear
Step-by-step explanation:
X = X + 1
Y= Y *3
A table of data is linear if there is a constant average rate of change between all pairs of points
There is because X is being added one every time and Y is being multiplied by 3 every time.
Hope this helps!
help answer this pls
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter?
Answer:
17,964.9 cubic meters
Step-by-step explanation:
Hey there!
The formula for finding the area of a sphere is:
[tex]V=(4/3)\pi r^3[/tex]
Where V is volume, and r is radius
The question already tells us that the diameter is 32.5m
*Remember, the diameter isn't the radius. It is the radius times two*
Now, we have to divide 32.5 by 2 to get the radius
32.5/2 is 16.25
Now we can plug this into the formula
16.25 cubed is 4291 after being rounded to the nearest tenth
Now we multiply 4291 by 3.14 (pi)
4291 x 3.14 is 13473.7 after being rounded to the nearest tenth
Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere
13473.7 x 4/3 is 17964.93333333...
Since it is asking us to round to the nearest tenth of a cubic meter;
The volume of the sphere will be 17,964.9 cubic meters
[tex]\rule{300}{1}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
We are asked to find the volume of a sphere, which we can find using the following formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Where:-V=volumeπ=pi (3.14…)r=radiusProvided information:-diameter (d)=32.5 mWhat we need in order to find the volume:-radiusWhat we need in order to find the radius:-Since the radius is exactly one-half of the diameter, we divide the diameter by 2 in order to find the radius:-[tex]\bold{r=d\div2}[/tex]
Replace d with 32.5:-
[tex]\bold{r=32.5\div2}[/tex]
Therefore, the sphere's radius is as follows:-
[tex]\bold{r=16.25}[/tex] m
[tex]\rule{300}{1}[/tex]
Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Replace r with 16.25:-
[tex]\bold{V=\dfrac{4}{3} \pi (4291)}[/tex] Next, we replace π with 3.14:-
[tex]\bold{V=\dfrac{4}{3} \times3.14\times4291}[/tex]
On simplification,
[tex]\bold{V=\dfrac{4}{3} \times13,473.74}[/tex]
On further simplification,
[tex]\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
If cos x = −1/4 and csc x < 0, find cot x/2
The value of cot x/2 is √3/√5.
What is Trigonometry?Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations.
given:
cos x=-1/4
sin x= √15/4
cosec x= 4/√15
and, cot x= -1/√15
Now, cot x/2= cosec x+ cot x
= 4/√15-1/√15
= 3/√15
= √3/√5
Hence, the value of cot x/2 is √3/√5.
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A merchant bought 1000 electric bulbs at the rate of Rs.150 each. 50 of them were broken on the way and the remaining he sold at the profit of 5%.What was the selling price of each bulb?
Answer:
₹165.79
Step-by-step explanation:
Given:-
No. of electric bulbs = 1000
cost of each electric bulb = ₹ 150
No. of bulbs broken = 50
Selling price of each bulb = x
Profit percentage = 5%
To Find:-
The selling price of each bulb.
Solution:-
Cost price of 1000 electric bulbs,
= 1000 × ₹150
= ₹1,50,000
5% profit on the total cost price,
= {5}/{100}× ₹150000
= ₹7500
Total selling price = ₹157500
No. of bulbs remaining = 950
Therefore, selling price of each bulb,
= {₹157500}/{950}
= ₹165.79
Therefore,
Selling price of each bulb = ₹165.79
Round 418 to the nearest ten.
Answer:
The answer should be 420.
~
Step-by-step explanation:
1.1 solve for x, where 0°< x 90°. write your answer to one decimal place. 1.1.1 tanx=sin38° 1.1.2cosec( x+10°)=1.345
The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0
How to solve the trigonometry ratios?The equations are given as:
tan(x)=sin38°
cosec( x+10°)=1.345
In tan(x)=sin38°, we have:
tan(x)=0.6157
Take the arc tan of both sides
x = 31.6
Also, we have:
cosec(x+10°)=1.345
Take the inverse of both sides
sin(x+10°) = 0.7434
Take the arc sin of both sides
x+10 = 48.0
Subtract 10 from both sides
x = 38.0
Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0
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Which climate has moderate rainfall, nutrient rich soils, and has a relatively thick layer of topsoil?
A. Desert
B. Arctic
C. Tropical rainforest
D. Grassland
Determine the interquartile range for the following data 1,15,16,16,19,24,25
Answer:
IQR = 9
Step-by-step explanation:
Q3 = 24
Q1 = 15
24-15=9
Give brainliest, please!
Hope this helps :)
If the radius of the circle is 14 meters, find the length of arc RS
(brainliest given)
To find a certain part of the arc:
⇒ we find a fraction of the circumference
Based on the diagram and information given:
radius: 14 metersarc: RS⇒ which spans 116 degrees of the entire 360 degrees the whole
arc covers
Thus let's solve:
[tex]Length_.of_.arc = (\frac{116}{360})*(2*\pi *14)[/tex] ≈ [tex]28.34_.meters[/tex]
Answer: 28.34 meters
Hope that helps!
#76 will give brainliest! please help
Answer:
2nd option, (6x + 8)(x - 1) = 0
Step-by-step explanation:
Answer:
[tex](6x+8)(x-1)[/tex]
Step-by-step explanation:
We can separate the 2x into -6x + 8x. Then this will give us [tex]6x^2 - 6x + 8x - 8 = 0[/tex]. Now we can factor out a 6x and an 8 to give us [tex]6x(x-1) + 8(x-1) = (6x+8)(x-1)[/tex] by the distributive property.
Hope this helps! :)
If humans have infinity magnetite why cant we think of a another colur
What is the difference of the y coordinate (0,3) and the y coordinate (4,0)
Answer:
3
Step-by-step explanation:
The difference of the two y-coordinates is found by ...
a) identifying the y-coordinates
b) computing their difference.
__
Each ordered pair lists the y-coordinate second.
(0, 3) ⇒ y-coordinate = 3
(4, 0) ⇒ y-coordinate = 0
The difference of the y-coordinates is ...
3 -0 = 3
Layla walked a total of 12 kilometers by making 4 trips to school. After 5 trips to school, how many kilometers will Layla have walked in total? Assume the relationship is directly proportional.
Answer:
[tex]=15km[/tex]
Explanation:
[tex]12[/tex] [tex]km[/tex] ÷ [tex]4[/tex]
[tex]=3[/tex] [tex]km[/tex] per trip to school
Now that we know that Layla walks 3 km to walk to school, we multiply that by 10
[tex]3[/tex] [tex]km[/tex] × [tex]5[/tex] [tex]trips[/tex]
[tex]=15[/tex] [tex]km[/tex]
∴ Layla walked 15 km in total
In a hostel, 120 students had provisions of food for 60 days. After 20 days, some students were added to the hostel, the provision of food finished 10 days ago earlier. How many students were added?
Answer:
If I'm right, the answers should be 40.
HELP ME PLEASE IVE BEEN STRUGGLING WITH THIS FOR SO LONG
Answer:
m∠ACE = 90°Step-by-step explanation:
Figure Interpretation:
m∠CBA + m∠CDE = 180
m∠BCA = (180-m∠CBA)/2
m∠DCE = (180-m∠CDE)/2
=======================
Then
m∠BCA + m∠DCE = (180-m∠CBA)/2 + (180-m∠CDE)/2
= [360-(m∠CBA+m∠CDE)]/2
= [360 - 180]/2
= 90
finally,
m∠ACE= 180 - (m∠BCA + m∠DCE)
= 180 - 90
= 90
Jeremiah paid $5.76 for some pencils at the school store. if each pencil cost $0.18, how many pencils did jeremiah buy?
Answer:
They bought 32 pencils
Step-by-step explanation:
5.76 divided by 0.18 = 32
Geometry problem help, will reward brainly! both dont have to be solved, but id really appreciate it.
Answer:
height: 8 mslant height: 5 inStep-by-step explanation:
The parameter of interest can be found by putting the given values into the appropriate volume or area formula for a pyramid, then solving for the unknown. The relevant formulas are ...
V = 1/3s²h . . . . . s is the base length; h is the height
A = s(s +2h) . . . . s is the base length; h is the slant height
__
height given volumeUsing the given values for the volume and the length of the base, the formula becomes ...
V = 1/3s²h
96 m³ = 1/3(6 m)²h . . . . . . . . . . use the given values for V, s
(96 m³)/(12 m²) = 8 m = h . . . . . divide by the coefficient of h
The height of the pyramid is 8 meters.
__
slant height given areaUsing the given values for area and the length of the base, the formula becomes ...
A = s(s +2h)
47.25 in² = (3.5 in)(3.5 in + 2h) . . . . use the given values for A, s
13.5 in = 3.5 in + 2h . . . . . . . . . . . divide by 3.5 in
10 in = 2h . . . . . . . . . . . . . . . . . subtract 3.5 in
5 in = h . . . . . . . . . . . . . . . . divide by 2
The slant height of the pyramid is 5 inches.
22.
Round 203.497 to the nearest whole number
Answer:
≈ [tex]\sf 203[/tex]