Answer:
3.1 A) 49; 64; and 81
B) 343; 512; and 729
C) 28; 36; and 45
3.2 A) 1²; 2²; 3²...
B) 1³; 2³; 3³...
C) 1; 1+2; 1+2+3; ...
3.3 A) aₙ = n²
B) aₙ = n³
C) aₙ = n·(n + 1)/2
3.4 A) 10,000
B) 1,000,000
C) 5,050
Step-by-step explanation:
The given sequences are;
A 1; 4; 9; 16; 25; 36...
B 1; 8; 27; 64; 125; 216...
C 1; 3; 6; 10; 15; 21;...
3.1 A) The terms, aₙ, of sequence 'A' are given as follows;
aₙ = n², where, n = 1, 2, 3,...
The next three terms of sequence 'A' are therefore;
a₇ = 7³ = 49, a₈ = 8² = 64, and a₉ = 9² = 81
The next three terms of sequence 'A' are ; 49; 64; and 81
B) The terms, aₙ, of sequence 'B' are given as follows;
aₙ = n³, where, n = 1, 2, 3,...
The next three terms of sequence 'B' are therefore;
a₇ = 7³ = 343, a₈ = 8³ = 512, and a₉ = 9³ = 729
The next three terms of sequence 'B' are; 343; 512; and 729
C) The terms, aₙ, of sequence 'C' are given as follows;
aₙ = n·(n + 1)/2, where, n = 1, 2, 3,...
The next three terms of sequence 'A' are therefore;
a₇ = 7×(7 + 1)/2 = 28, a₈ = 8×(8 + 1)/2 = 36, and a₉ = 36 + 9×(9 + 1)/2 = 45
The next three terms of sequence 'A' are ; 28; 36; and 45
3.2 A) The pattern of the numbers in sequence 'A', consists of squaring (raising to the power of 2) each number in the sequence of natural numbers
B) The pattern of the numbers in sequence 'B', consists of raising to the power of 3 each number in the sequence of natural numbers
C) The pattern is the triangular number sequence and consists of finding half the number dots that are present in a n by (n + 1) rectangle, which is given by finding the sum of the natural numbers up to the given term in the sequence
3.3 A) The formula for the general term of sequence, A, is aₙ = n²
B) The formula for the general term of sequence, B, is aₙ = n³
C) The formula for the general term of sequence, C, is aₙ = n·(n + 1)/2
3.4 A) The 100th term of sequence 'A', a₁₀₀ = 100² = 10,000
B) The 100th term of sequence 'B', a₁₀₀ = 100³ = 1,000,000
C) The 100th term of sequence 'C', a₁₀₀ = 100 × (100 + 1)/2 = 5,050.
Help me with this please
The solution to the quadratic equation x² - 4x + 1 = 0 is x = ( 4 ±√12 ) / 2
What is the solution to the quadratic equation?A quadratic equation in its standard form is expressed as;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the quadratic equation in the question;
x² - 4x + 1 = 0
a = 1b = -4c = 1We substitute this values into the quadratic formula above and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -(-4) ±√( (-4)² - ( 4 × 1 × 1)) / (2 × 1)
x = ( 4 ±√( 16 - 4) ) / (2)
x = ( 4 ±√12 ) / 2
Therefore, ( 4 ±√12 ) / 2 is the solution to the equation.
Option C) ( 4 ±√12 ) / 2 is the correct answer.
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boy i suck at geometry fr can someone help me
Answer:
The measure of Angle G is 41
Step-by-step explanation:
We know that in a parallelogram, opposite angles are congruent, therefore let's solve for x-value first;
3x + 11 = 5x - 9
11 = 5x - 3x - 9
11 = 2x - 9
11 + 9 = 2x
20 = 2x
20/2 = x
10 = x
Now that we have x-value, we can substitute it in the equation for Angle G to find it's angle measure;
5(10) - 9 = ∠G
50 - 9 = ∠G
41 = ∠G
So the final answer = The measure of Angle G is 41
Hope this helps!
Oscar is buying soil for his plants. He needs to fill one pot with 8 cups of soil and another pot
with 3 gallons of soil. If the price of soil is $2.50 per quart, how much, in dollars, will he pay in
all? You may use the conversions to help you answer the question.
Answer:
10
Step-by-step explanation:
2.50 4 times
Answer: 10
Step-by-step explanation:
.Answer only the second question and show steps
Answer:
Step-by-step explanation:
Perimeter is found by adding all the sides of a figure together. We have 2 lengths that are 10.5 long, and 2 widths that are 8.75 wide. Adding these together:
10.5 + 10.5 + 8.75 + 8.75 = 38.5 cm
this answer for # 2 question
Which numbers make a true statement when placed in the box? 7.902 > Select each correct answer.
a-7.912
b- 7.097
c- 7.920
d- 7.898
7.898 and 7.097 numbers make a true statement when placed in the box
What is number system ?A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, multiplication and division.
Numbers make a true statement when placed in the box
7.902 > ?
7.902 < 7.912
7.902 > 7.097
7.902 < 7.920
7.902 >7.898
Hence, the answer is 7.898 and 7.097
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A car depreciates by 5% in a year. If the initial value was $10,000, what is its value after a year?
Answer: $9,500
Step-by-step explanation:
If the value of the car depreciates by 5% in a year it means that the value of the car reduced by 5%.
First find the 5%:
= 5% * 10,000
= $500
Subtract this from the initial value to find the value after a year:
= 10,000 - 500
= $9,500
Answer:
$ 9500
Step-by-step explanation:
From the question given above, the following data were obtained:
Initial value = $ 10000
Depreciation rate = 5%
Value after one year =?
Next, we shall determine the depreciation value. This can be obtained as follow:
Initial value = $ 10000
Depreciation rate = 5%
Depreciation value =?
Depreciation value = Initial value × rate
Depreciation value = 10000 × 5%
Depreciation value = 10000 × 5/100
Depreciation value = $ 500
Finally, we shall determine the value of the car after one year. This can be obtained as follow:
Initial value = $ 10000
Depreciation value = $ 500
Value after one year =?
Value after one year = Initial value – Depreciation value
Value after one year = 10000 – 500
Value after one year = $ 9500
Therefore, the value of the car after one year is $ 9500
find the value of X. Round to the nearest tenth. Show or explain your answer.Please I need this answered ASAP.
Answer:
c=21.6
Step-by-step explanation:
First, find the last angle of the triangle.
The sum of all the angles in a triangle is 180 degrees.
A+90+37=180
A=53
Now find x
The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.
cos(B)=adj/hyp
rewrite as
c=a/cos(B)
c=17.3/cos(37)
c=21.66194688
Can you help me find this answer its due in a few minutes?
Answer:
D. 3.2 in^2
Step-by-step explanation:
48 divide 15 = 48/15 = 3.2
What is the range of the function graphed below?
Answer:
C.
[tex] - \infty < y < \infty [/tex]
Can someone please help me with my hw.
Answer:
The answer is 1,440
Step-by-step explanation:
Answer:
1, 440Step-by-step explanation:
god bless
from philippines
At a lunch shop, a hamburger costs $2.99 and a hot dog costs $2.50.
How much more does a hamburger cost than a hot dog?
To find the difference subtract the price of the hot dog from the price of the hamburger:
2.99 - 2.50 = 0.49
The hamburger cost $0.49 more than the hot dog.
To find the surface area of the pyramid, in square inches, Vikram wrote (33.2) (34.2) + 4 (one-half (34.2) (28.4)). What error did Vikram make? He used the same expression for the area of all four lateral faces. He used the wrong expression to represent the area of the base of the pyramid. He used the wrong value as the height when he found the area of the lateral faces. He used an expression for surface area that only finds the total area of three faces.
Answer:
B. He used the wrong expression to represent the area of the base of the pyramid.
Step-by-step explanation:
Given
See attachment for pyramid
[tex]Area = (33.2)(34.2) + 4 * \frac{1}{2} * 34.4 * 28.4[/tex]
Required
Vikram's error
The surface area of a square pyramid is:
[tex]Area = Base\ Area + 4 * Area \triangle[/tex]
Where
[tex]Base\ Area = Length * Length[/tex]
[tex]Base\ Area = 34.2 * 34.2[/tex]
[tex]4 * Area \triangle = 4 * \frac{1}{2} * Base * Height[/tex]
[tex]4 * Area \triangle = 4 * \frac{1}{2} * 34.2 * 28.4[/tex]
So:
[tex]Area = Base\ Area + 4 * Area \triangle[/tex]
[tex]Area = 34.2 * 34.2 + 4 * \frac{1}{2} * 34.2 * 28.4[/tex]
By comparing the calculated expression with
[tex]Area = (33.2)(34.2) + 4 * \frac{1}{2} * 34.4 * 28.4[/tex]
Option (b) is correct
Imani is a scientist working with a cylindrical beaker. The base of the right cylinder has a diameter of 19 cm. She fills the
beaker with 2256.254 Cms of an acid. Approximately how high did the acid fill up the beaker?
Answer:
7.96 cm
Step-by-step explanation:
radius of bottom: 19/2 = 9.5
area of bottom = pi * r^2 = 283.53
height * base area = volume
Poor jocelyn! She was running a race and at the 9 1/4 marker, she stumbled and twisted her ankle. If she was only 3/8 of the way, how long was the race?
Answer: 24 2/3
Step-by-step explanation:
Let the total distance of the race be represented by x.
Therefore, based on the information given, we can form an equation which will be:
3/8 of x = 9 1/4
3/8x = 9 1/4
0.375x = 9.25
x = 9.25/0.375
x = 24.67
The distance of the race is 24 2/3
The international cricket team is going to stadium to play the T20 cricket game. A coordinate grid is superimposed on a highway map of the city. The team hotel is at point (3, 4) and the stadium is at point (7, 1). The map shows a rest stop halfway between the hotel and the stadium. What are the coordinates of the rest stop? What is the approximate distance between the hotel and the stadium? (One unit is approximately equal to 6.4 miles.)
Answer:
The coordinate of the rest stop is: [tex](5,2.5)[/tex]
The distance between the hotel and the stadium is 32 miles
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,4)[/tex] --- Team hotel
[tex](x_2,y_2) = (7,1)[/tex] --- Stadium
Solving (a): The coordinates of the rest stop
The rest stop is at half way;
So, the coordinate is:
[tex](x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]
This gives:
[tex](x,y) = \frac{1}{2}(3+7,4+1)[/tex]
[tex](x,y) = \frac{1}{2}(10,5)[/tex]
Open bracket
[tex](x,y) = (5,2.5)[/tex]
Solving (b): Distance between the hotel and the stadium
We have:
[tex](x_1,y_1) = (3,4)[/tex] --- Team hotel
[tex](x_2,y_2) = (7,1)[/tex] --- Stadium
The distance (d) is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(3 - 7)^2 + (4 - 1)^2}[/tex]
[tex]d = \sqrt{(-4)^2 + 3^2}[/tex]
[tex]d = \sqrt{16 + 9}[/tex]
[tex]d = \sqrt{25}[/tex]
[tex]d =5[/tex]
From the question, we have:
[tex]1\ unit = 6.4\ miles[/tex]
So:
[tex]d =5 * 6.4\ miles[/tex]
[tex]d =32\ miles[/tex]
Parallelogram
15 in
18 in
Area:
Answer:
270
Step-by-step explanation:
brianliest?
The side lengths of a 45-45-90 triangle are in the ratio 1 : 1: V2. What is tan 45°?
A. V2/2
B. 1/2
C. V2
D. 1
Answer:
B. 1/2
Step-by-step explanation:
divide/
The value of measure of tan 45 is B. 1/2
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given that side lengths of a 45-45-90 triangle are in the ratio 1 : 1: √2
A 45-45-90 triangle is a special case of a right triangle in which both legs we have the same value and the hypothenuse is h.
By the Pythagorean Theorem:
Tan 45 = pythagoras/ base
Tan 45 = 1/2
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Find (a) the circumference and (b) the area of the circle. Use $3.14$ or $\frac{22}{7}$
for $\pi$ . Round your answer to the nearest hundredth, if necessary.
A circle with radius of 1 meter.
(a) circumference: about
m
(b) area: about
m²
Answer:
[tex]circumference = 2 \pi r = 2 \times 3.14 \ times 1 = 6.28m\\\\Area = \pi r^2 = 3.14 \times 1 \times 1 = 3.14m^2[/tex]
The circumference of the circle is, 6.28 meter.
And, The area of circle is, 3.14 meters²
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A circle with radius of 1 meter.
Now, We know that;
The circumference of the circle = 2πr
Hence, We get;
The circumference of the circle is,
⇒ 2 × 3.14 × 1
⇒ 6.28 meter
And, The area of circle is,
⇒ Area = πr²
⇒ Area = 3.14 × 1²
⇒ Area = 3.14 meters²
Thus, The circumference of the circle is, 6.28 meter.
And, The area of circle is, 3.14 meters²
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i give u brainliest if u answer
Answer: B & D
Step-by-step explanation:
how is 2/5 + 3/5 = 1
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer.....
= 2/5 + 3/5 = 5/5 = 1(When you simplify both numbers, you get 1)
Hope it helps!
Brainliest pls!
Follow me! :)
Imagine cutting up a pizza into 5 slices
If you take 2 slices, then you take 2 out of the 5, so the fractional amount you took is 2/5 of the full pizza.
If your friend takes 3 slices, then she or he takes 3/5 of the full pizza
Adding the two fractional amounts should get us back to 1 full pizza, which is why 2/5+3/5 = 1.
-----------
We could say this:
2/5 + 3/5 = (2+3)/5 = 5/5 = 1
Dividing any number over itself, as long it's not zero, always leads to 1.
So that's why 5/5 = 1.
PLEASE I NEEED HELP!!! YOU DONT HAVE TO AWNSER NUMBER 6
Answer:
6942-8.7 or 26/3-3.5 or -7/2HURRY WILL GIVE BRAINLIEST (if correct)
How many edges does the figure have?
A. 3
B. 4
C. 5
D. 6
Answer:
I think 6 I don't see it being anything other than that I can't even think right now that's crazy
Answer:
4
One at the ap-ex, and 3 on the side. A regular triangle has 3 sides, and since this is a third dimension shape, there is one at the top.
Factorize completely 3ac+6ab-15a
Answer:
3a(c + 2b - 5)
Step-by-step explanation:
Step-by-step explanation: The greatest common factor for the 3 terms here is 3a so factor out a 3a and what we're left with inside the parentheses is each of the terms in the original polynomial divided by 3a.
So we have 3a(c + 2b - 5) which is our final answer.
Pls show your work to answer the question.
Answer:
∠ EDC = 55°
Step-by-step explanation:
Since Δ ADE is isosceles then the 2 base angles are congruent , then
∠ EDA = [tex]\frac{180-20}{2}[/tex] = [tex]\frac{160}{2}[/tex] = 80°
Similarly for Δ BCD
∠ CDB = [tex]\frac{180-90}{2}[/tex] = [tex]\frac{90}{2}[/tex] = 45°
The 3 angles on AB sum to 180° , that is
80° + ∠ EDC + 45° = 180°
∠ EDC + 125° = 180° ( subtract 125° from both sides )
∠ EDC = 55°
This is kind of far fetched but does anyone have an idea of how to find elevation using cos tan and sin ?
Answer:
Step-by-step explanation:
Use right triangle trig and SohCahToa. Elevation could either mean the height of something or it could refer to an angle of elevation. Either way, these ratios can help you. Do you have an actual question?
(free point) hey guys i have everything caught up but in science i have a 96 but a missing project. projects a worth 80 percent of your grade will i still pass? today’s the last day
Answer:
Just do it to your best ability
Step-by-step explanation:
You should just do it because it could still make your grade look poor so it should be good for future you as youll be looked upon as a better student
What is 5.88 divided by -4
Answer:
-1.47
Step-by-step explanation:
5.88/-4= -1.47
In triangle ABC, a=31 , b=22 , c=18. Identify m∠A rounded to the nearest degree.
Answer:
101
Step-by-step explanation:
According to the Law of Cosines, for any △ABC with side lengths a, b, and c, a2=b2+c2−2bccosA; b2=a2+c2−2accosB; and c2=a2+b2−2abcosC
.
The Law of Cosines can be used because all three side lentghs are known.
Set up the equation for the Law of Cosines:
a2=b2+c2−2bccosA
Substitute the known values into the Law of Cosines:
312=222+182−2(22)(18)cosA
Square the values and multiply:
961=484+324−792cosA
Add:
961=808−792cosA
Subtract 808
from both sides:
153=−792cosA
Divide both sides by −792
:
153−792=cosA
According to this equation m∠A
is equal to the inverse cosine function of −153792
. Write this:
m∠A=cos−1(−153792)
Calculate the value of the inverse cosine −153792
on a calculator:
m∠A≈101°
Therefore, m∠A≈101°
.
Answer:
101
Step-by-step explanation:
calculate using the law of cosines
hope that helps!
if 9x × 3x+1 = 2187, what is the value of x
Answer:
1093/6
Step-by-step explanation:
9x + 3x + 1 = 2187
12x + 1 = 2187
12x = 2187 - 1 = 2186
12x = 2186
x = 2186/12 = 1093/6
Hope u understand
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ASAP NEED HELP PLEASE
Answer:
B
line n has slope equal to zero