Answer:
The explicit formula is Tn = 34 + 3n
Step-by-step explanation:
The nth term of an arithmetic sequence can be represented using the formula
Tn = a + (n-1)d
where a is the first term , n is the number of terms and d is the common difference
For the 12 term(a12), n = 12
70 = a + (12-1)d
70 = a + 11d •••••••(i)
For the 30th term, n = 30
124 = a + (30-1)d
124 = a + 29d •••••••(ii)
Now, directly subtract equation i from ii, we have;
124-70 = (a-a) + (29d-11d)
54 = 18d
d = 54/18
d = 3
To get a , we substitute the value of d in any of the equations
let’s use the first
70 = a + 11d
substituting d = 3
70 = a + 11(3)
70 = a + 33
a = 70-33
a = 37
Thus the explicit formula for the nth term will be
Tn = a + (n-1)d
where a = 37 and d = 3
Tn = 37 + (n-1)3
Tn = 37 + 3n -3
Tn = 34 + 3n
Let ∠A, ∠B, and ∠C be acute angles. Use a calculator to approximate the measures of ∠A, ∠B, and ∠C to the nearest tenth of a degree.
cos A = 0.31, sin B = 0.89, tan C = 0.52
Answer:
1. ∠A = 71.9°
2. ∠B = 62.9°
3. ∠C = 27.5°
Step-by-step explanation:
By using a calculator, we have;
cos A = 0.31
sin B = 0.89
tan C = 0.52
1. Therefore, ∠A = cos⁻¹(0.31), inputting the digits in the calculator and looking for the inverse sign, we have;
∠A = cos⁻¹(0.31) = 71.94° = 71.9° to the nearest tenth of a degree.
2. For sin B = 0.89, we have;
∠B = sin⁻¹0.89 = 62.873° ≈ 62.9° with the answer rounded to the nearest tenth of a degree.
3. Similarly, for tan C = 0.52, inputting the values in the calculator and pressing the tan⁻¹ button, we have;
∠C = tan⁻¹(0.52) = 27.474°, which is 27.5° rounded to the nearest tenth of a degree.
Find the cosine of angle A (written as a fraction)
Answer: 0.92
Step-by-step explanation: cos a = side adj / hypotenuse
Cos a = 12/13 ~ 0.92307
Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each minute.
Graph the relationship between Mr. Mole's elevation relative to the ground (in meters) and time (in minutes).
Answer is that Mr mole goes 3 each minute for each minute add on those 3 as you add on those 3 write it down counting how many then you know the time and the meters hes been digging
what is s+53=g so g=68 so how old is sweet age add
Answer:
s = 15
Step-by-step explanation:
Using the given information to solve for s, the work would look something like this:
s + 53 =g, g=68
s + 53 = 68 (Subtract 53 from both sides to get s by itself)
53 - 53 = 0, 68 - 53 = 15
s = 15
Therefore, s is equal to 15
Hope this helps! Have a good rest of your day!
Answer:
15
Step-by-step explanation:
This is very simple, first we write the equation, s+53=g, and plug 68 into "g", so now we have s+53=68. Subtract both sides, s+53-53=68-53, and this equals 15 years of age
if butter the dog jumps two times and falls one time then how many times has he jumped?
Answer:1 or 3
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Jackson has 48 trading cards. His sister gives J him 12 more cards. Then he puts all of his trading cards in 6 equal stacks. How many cards, c, are in each stack
Answer:
there are 10 cards in each stack.
Step-by-step explanation:
if you add 48 (Jacksons cards) and 12 (his sisters cards) you will get 60 (all cards in total). and 60 (total number of cards) divided by 6 (number of piles) is 10. there will be 10 cards in each stack!
A roof on a castle tower is shaped like a cone with a diameter of 12 feet and has a slant height of 13 feet one bundle of Shingles covers 32 ft.² how many bundles should you buy to cover the roof? What is the surface area of the roof ?
Answer:
Step-by-step explanation:
d = diameter = 12ft
r = d/2 = 12/2 = 6ft
Slant height = 13ft
Surface area of cone = π r 2 + π L r
Where L is the slant height of the cone π = 22/7
SA = 22/7×6×6+22/7×13×6
SA = 113.14+245.142
SA = 358.28ft^2
If one bundle of shingle covers 32 ft.²
Hence,358.28ft^2 = 358.28ft^2/32 ft.²
= 11.196
= 11.2 bundles
Chantel is running for a rally race she ran 2,000 feet every day for six days how many yards did Chanel run
Answer:
4,000 yards
Step-by-step explanation:
2,000 ft * 6 days = 12,000 feet ran in total
Conversion: 3 feet = 1 yard
12,000 ft = 4000 yards
Write nine minus the quotient of two and a number x as a expression variable
Answer:
9-(2/x)
Step-by-step explanation:
2D+8=24
My question how do I solve for d
Answer:
2 x 8 = 16
2x8+8 = 24
Step-by-step explanation:
The table gives the mass of liquids with a volume of 5 cm3. A 2-column table with 4 rows. Column 1 is labeled liquid with entries water, glycerin, milk, olive oil. Column 2 is labeled Mass (grams) with entries 5, 6.3, 5.15, 4.9. Density is the ratio of mass to volume. Density = mass volume What is the density of milk? Use the drop-down menu to complete the statement. The density of milk is StartFraction grams Over centimeters cubed EndFraction.
The answer would be 1.03! hopes this helps!
Answer:
1.03
Step-by-step explanation:
i did the assignment on edg 2020/2021
. If they set up their camera 322 meters from the base of the mountain and the mountain is 597 meters high, what angle should he point his camera from the horizantal.
Answer:
the angle required for them to point their camera to the horizontal should be at 61.66°
Step-by-step explanation:
Given that the base of the camera is 322 meters from the horizontal and the height is 597 meters.
We can use the tangent of the trigonometric equation.
tan θ = opposite / adjacent
tan θ = 597/322
tan θ = 1.854
θ = tan⁻¹ (1.854)
θ = 61.66°
Hence, the angle required for them to point their camera to the horizontal should be at 61.66°
Answer:
Step-by-step explanation:
The position of the camera forms a right angle triangle. The horizontal distance from the base of the mountain represents the opposite side of the triangle while the height of the mountain represents the adjacent side of the triangle. To determine the angle, # that he should point his camera from the horizontal, we would apply the tangent trigonometric ratio which is expressed as
Tan # = opposite side/adjacent side
Tan# = 597/322 = 1.85
# = Tan^-1(1.85)
# = 61.61°
Ethan is responsible to write the minutes for the meeting. During the meeting, he finished writing of the minutes. Before getting off work, he finished another of the minutes. How much of the minutes does Ethan still need to work on?
How many non-congruent triangles can you draw with the given properties? a. Sides measuring 7 inches, 8 inches, and 16 inches b. Sides measuring 4 inches, 4 inches, and 6 inches c. Angles measuring 30°, 60°, and 90° d. Three angles measuring 120° e. Two angles measuring 45° and one side length measuring 10 inches
Answer:
The answers are;
a. None
b. None
c. Infinite
d. None
e. None
Step-by-step explanation:
The number of non congruent triangles that can be drawn depends on the uniqueness of the triangle
The parameters of a unique triangle are;
Knowing the Side Side Side (SSS)
Knowing the Side Angle Side (SAS)
Knowing the Angle Side Angle (ASA)
Knowing the Angle Angle Side (AAS)
However, knowing only the Side Side Angle it is possible to draw two non-congruent triangles
Therefore, considering each of the triangles gives;
a. Sides 7 inches, 8 in., and 16 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided properties
b. Similarly, the given triangle parameters are 4 in., 4 in., and 6 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided information
c. The parameters of the triangle given here are angles 30°, 60°, and 90° which is of the form Angle Angle Angle, or AAA for which the sides can be scaled to form an infinite number of non-congruent triangles
d. The parameters given are three angles measuring 120° which does not form a triangle as the sum of triangles in a triangle = 180°
Hence the number of non-congruent triangles that can be drawn in this case = 0
e. The parameters given are two angles measuring 45° and one side length of 10 in., hence the parameter is of the forms AAS or ASA hence the triangle is unique and it is not possible to draw two non-congruent triangle with the provided properties.
Samuel has a bell box that contains
4 door bells, 3 office bells, and 7 big
bells. Without looking, Samuel
Chooses a bell from the box, what is the
relative frequency probability the
when he selects a doorbell?
Answer:
4 out of 14
Step-by-step explanation:
there is only 4 door bells and 14 bells in total
At a furniture store there is a sale on kitchen tables and chairs. Single chairs sell $80 each. If a customer a set of 4 chairs, the total price would. be $250. What is the percent savings on the 4-chair set? Round to the nearest whole percent.
Answer:
4%
Step-by-step explanation:
1% of 250 is $2.50. Times 4 is $10. The difference between 240 and 250 is 10.
Answer:
235
Step-by-step explanation:
In a tiny house, an empty hot water heater requires 40 gallons of water. It takes 18 minutes to fill the hot water heater. Assuming a constant rate of flow, find the rate at which water flows into the tank. Express your answer to the nearest tenth of a gallon per minute.
ITS URGENT
Joshua just bought a new fish tank. The tank is 14 inches tall and has a radius of 4 inches. How much water can Joshua put in the tank? Use 3.14 for pi. *
A. 703.36 cubic inches
B. 56 cubic inches
C. 224 cubic inches
D. 175.84 cubic inches
Answer:
V = 703.36 in³ (This matches answer option A.)
Step-by-step explanation:
This fish tank has a cylindrical shape. The formula for the volume of a cylinder of radius r and height h is
V = (pi)(r²)(h).
We are told that h = 14 in and r = 4 in. Using 3.14 for pi:
V = (3.14)(4 in)²(14 in) =
V = 703.36 in³ (This matches answer option A.)
Find the Area of the Triangle. A = 1/2 (b x h)
Answer:
A=1/2(b×h)
divide a half by 12=6
6×4,since 4 is the height=24
Answer:
30 um²
Step-by-step explanation:
BC = √5² - 4²
= √25 - 16
= √9
= 3 um
AC = 12 + 3 = 15 um
A = AC×BD/2
= 15×4/2
= 15×2
= 30 um²
Use the graph of the function y = (x + 3)(x - 2) to find the
solutions of the quadratic equation 0 = (x + 3)(x - 2).
The solutions of the quadratic equation 0 = (x + 3)(x - 2) are
-6 and 0.
4 and 3.
-3 and 2
-2 and 1.
Answer:
Third option (-3 and 2)
Step-by-step explanation:
You do not need graphs for this necessarily. you just have to build two equations:
0=x+3
0=x-2
if you solve them, the results are:
-3 = x
2 = x
Answer:
option 3 is correct that is (-3,2) is the solution.
Step-by-step explanation:
1. f(x)=0.5x-1.5x +1I 4x<-1-1sx53 x>3
Answer:
sorry dont know
Step-by-step explanation:
good luck tho
\
f(x) = 0.5x-1.5x+1
4x<-1
-1 ≤ x ≤ 3
x < 3
Simplify.
(-9 - 8i) - (3 + 2i)
Answer:
-12-10i
Step-by-step explanation:
(-9 - 8i) - (3 + 2i)
First, remove parantheses.
-9-8i-3-2i
Combine like terms
-9-3-8i-2i
Solve it!
-12-10i
The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation I (d B) = 10 log left-bracket StartFraction I Over I Subscript 0 Baseline EndFraction Right-bracket, where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when I = 10 Superscript 32 Baseline (I Subscript 0)?
Answer:
The intensity in decibel is 320 decibelStep-by-step explanation:
Given the intensity, or loudness, of a sound measured in decibels (dB), according to the equation [tex]I (dB)= 10log(\frac{I}{Io} )[/tex] where;
I is the intensity of a given sound and
[tex]Io[/tex] is the threshold of hearing intensity
To get I(dB) when [tex]I=10^{32} Io[/tex]
We will substitute the value of I = [tex]I=10^{32} Io[/tex] into the equation above to have;
[tex]I (dB)= 10log(\frac{10^{32}Io }{Io} )\\I(dB)=10log10^{32}\\ I(dB)=32*10log10\\[/tex]
Since log10 = 1;
[tex]I(dB)=32*10(1)\\I(dB)=320[/tex]
The intensity in decibel is 320 decibel
Answer:
Its D or 80
Step-by-step explanation:
I=10^8 (I subscript 0) can be written as I/I subscript 0, and you can plug that right into the log to get 80.
How can individual attitudes and lack of response to injustice harm society as a whole? (this was meant to be in history)
x2 +8x+16=0 in factoring algorithm
Answer:
(x+4)^2 =0
Step-by-step explanation:
x2 +8x+16=0
What 2 numbers multiply to 16 and add to 8
4*4 = 16
4+4 =8
(x+4) (x+4) =0
(x+4)^2 =0
√g+5=3d-2
Solve for g
Answer: [tex]g=(3d-2)^2-5[/tex]
Step-by-step explanation:
[tex]\sqrt{g+5}=3d-2[/tex]
To get rid of the square root, we can square both sides of the equation.
[tex](\sqrt{g+5})^2=(3d-2)^2[/tex]
[tex]g+5=(3d-2)^2[/tex]
Subtract 5
[tex]g+5-5=(3d-2)^2-5\\g=(3d-2)^2-5[/tex]
Consider circle C with angle ACB measuring StartFraction 3 pi Over 4 EndFraction radians.
Circle C is shown. Line segments A C and B C are radii. Angle A C B is StartFraction 3 pi Over 4 EndFraction radians.
If minor arc AB measures 9 inches, what is the length of the radius of circle C? If necessary, round your answer to the nearest inch.
6 inches
12 inches
18 inches
24 inches
Answer:
12 inches
Step-by-step explanation:
I just took the unit test review on edge
Since the minor arc AB measures 9π inches, the length of the radius of circle C is equal to: B. 12 inches.
Given the following data:
Arc length = 9π inches.Central angle = 3π/4 radians.How to calculate the length of the arc?Mathematically, the length of an arc formed by a circle is calculated by using this formula:
Arc length = rθ
Where:
r is the radius of a circle.is the angle measured in radians.Substituting the given parameters into the formula, we have:
9π = r × 3π/4
36π = 3πr
36 = 3r
r = 36/3
Radius, r = 12 inches.
Read more on arc length here: https://brainly.com/question/20594692
#SPJ2
Solve using substitution! Please help!
I hope this helps you
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x –
10? Select two options.
Oy = x2 + 5x + 10
Oy + 5x = x2 + 10 + 4x – 10
0 0 = x2 - 9x
0 0 = x2 - 9x + 20
One x-value of a solution to the system is 4.
Answer:
0 = x2 - 9x + 20
Step-by-step explanation:
y + 5x = x² + 10 Simplify this equation
- 5x - 5x
y = x² - 5x + 10
Set both equations equal to each other since they both equal y
x² - 5x + 10 = 4x - 10
-4x - 4x
x² - 9x + 10 = -10
+ 10 + 10
x² - 9x + 20 = 0
If this answer is correct, please make me Brainliest!
which quadrilateral always has diagonals that are congruent but not necessarily perpendicular?
a) parallelogram
b) rectangle
c) rhombus
d) square
Answer:its a rectangle
Step-by-step explanation:
