Answers
Answer:
1) 36
b) 5
c) 3.0
Step-by-step explanation:
1) The recursive formula that defines the given sequence is
[tex]a_1=12 \\ a_n=a_{n-1}+4.[/tex]
That means we keep adding 4 to the subsequent terms:
The sequence will be:
12,16,20,24,28,32,36,...
Therefore the seventh term is 36.
2) The sequence is recursively defined by;
[tex]a_1=20\\ a_n=a_{n-1} - 5[/tex]
This means, we have to keep subtracting 5 from the subsequent terms.
The sequence will be;
20,15,10,5,...
Therefore the fourth term is 5
3) The sequence is recursively defined by:
f(n+1)=f(n)+0.5
where f(1)=-1.5
This means that, the subsequent terms can be found by adding 0.5 to the previous terms.
The sequence will be:
-1.5,-1.0,-0.5,0,0.5,1,1.5,2.0,2.5,3.0,....
Therefore f(10)=3.0
Related Questions
Can someone help me with the question shown above. It is a 7th grade math problem
Answers
-
-
22*15 = 330
-
-
330-125 = 205.
Solve the quadratic:
2X^2-64=0
Answers
Answer:
do you mean x=7
Step-by-step explanation:
this aint a quadratic function a qaudratic function is ax^2+bx+c=c
Anusha needs to find a rectangular container large enough to hold a volume of 130 in.3. Which container should she use?
A. a container with the dimensions 2 by 5 by 10 inches
B. a container with the dimensions 3 by 4 by 10 inches
C. a container with the dimensions 3 by 5 by 10 inches
D. a container with the dimensions 4 by 2 by 10 inches
PLEASE HELP!!
Answers
Option C
Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Solution:
Anusha needs to find a rectangular container large enough to hold a volume of 130 cubic inches
The volume of rectangular container is:
[tex]volume = length \times width \times height[/tex]
Option A
Container with the dimensions 2 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 2 \times 5 \times 10 = 100[/tex]
Thus volume is 100 cubic inches
Option B
Container with the dimensions 3 by 4 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 4 \times 10 = 120[/tex]
Thus volume is 120 cubic inches
Option C
Container with the dimensions 3 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 5 \times 10 = 150[/tex]
Thus volume is 150 cubic inches
Option D
Container with the dimensions 4 by 2 by 10 inches
Therefore, volume is given as:
[tex]Volume= 4 \times 2 \times 10 = 80[/tex]
Thus volume is 80 cubic inches
Thus Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Answer:C. a container with the dimensions by 5 by 10 inches
If the radius of the smaller sphere is 3 inches and the radius of the larger sphere is 6 inches how many times greater is the volume of the larger sphere
Answers
Answer:
8
Step-by-step explanation:
The formula of volume is 4/3 × π × radius3.
volume of smaller sphere = 4/3 x 3.14 x 3*3*3
v = 113.04
volume of larger sphere = 4/3 x 3.14 x 6*6*6
v = 904.32
904.32 / 113.04 = 8
The Answer Is 8 times
Which equation represents a proportional relationship?
y=2x2
y = 4x - 2
y= 1/2x +3
y=5x
Answers
Answer:
D: y = 5x
Step-by-step explanation:
According to Google, a proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if: y=kx. for some constant k , called the constant of proportionality. So the only one in that form would be the y = kx.
The constant k = 5
5 1/2 of 2 1/3 is what number?
Answers
Answer:
19 1/4
Step-by-step explanation:
5 1/2 of 2 1/3
Change mixed fraction to improper fraction
11/2 of 7/2
Of means multiplication
11/2 x 7/2
77/4
19 1/4
Can u solve 7-12 and 14 please
Answers
Answer:
1. 19
Step-by-step explanation:
The figure on the right is made up of 5 squares.
Each side of the square is 7 cm.
What is the area of the figure?
Answers
Answer: [tex]245cm^{2}[/tex]
Step-by-step explanation:
The formula for calculating the area of a square is given by :
Area = [tex]l^{2}[/tex]
where [tex]l[/tex] is the length of a side .
Therefore , the area of one of the square given implies :
Area = [tex]7^{2}[/tex]
Area [tex]= 49[/tex]
And since there are 5 squares in all , the area will therefore be :
Area = [tex]5[/tex] x[tex]49[/tex]
Area = [tex]245cm^{2}[/tex]
Therefore: the area of the shape is [tex]245cm^{2}[/tex]
What is the slope of the line that contains the
coordinate points (8, -3) and (-2, 7)?
220x219
Answers
Answer:
-1
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
= (7 - (-3))/(-2 - 8)
= (7+3)/(-10)
= 10/(-10) = -1
Write this decimal in number, thirty-nine thousandths
Answers
Answer:
0.039
Step-by-step explanation:
Joe tracked the height of his Dalmatian puppy from age 13 weeks to 25 weeks. He graphed the data and determined the line of best fit is y = 1.12x + 28.78 where x is the age in weeks and y is the height in centimeters. How old was the puppy when he was 54 centimeters tall? Round to the nearest tenth.
a. 22.5 weeks
b. 28.2
c. 73.9
d. 89.3
Answers
Answer:
22.5 weeks
Step-by-step explanation:
y = 1.12x + 28.78 represents the height of the puppy. Here that height is 54 cm:
Then 54 = y = 1.12x + 28.78
Combining the constants, we get 1.12x = 25.22. Dividing both sides by 1.12, x turns out to be 22.5 weeks.
Does Y+7=2x and
2y=4x-14 have a solution?
Answers
Answer: It has no exact solution
Over the past 6 days you’ve spent $8, $14, $12, $11, $5 and $13 dollars on food . On average, how much per day are you spending on food?
A)$10.50
B)$11
C)$11.5
D)$12
E)$11.25
Answers
Answer:
The answer is A)$10.50
Step-by-step explanation:
In order to solve the average amount, you have to add the total amount of money spent and divide it by the total number of times you spent money on food. The total sum of money spent was $63. If you divide that by how many times you ate (6 times) you'll get the dividend/answer of 10.5.
Hope this helps :)
You are spending, on average, A) $10.50 per day on food.
The correct answer is A) $10.50.
To find the average amount spent per day on food, you need to add up the total amount spent over the 6 days and then divide it by the number of days (6).
Total amount spent on food = $8 + $14 + $12 + $11 + $5 + $13
= $63
Average amount spent per day = Total amount spent / Number of days
= $63 / 6
= $10.50
So, you are spending, on average, $10.50 per day on food.
for such more question on average
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Simplify: (-7x^2y^4)(-2x^3y^4)
Answers
Answer: 14x^5y^8
Step-by-step explanation:
(-7x^2y^4)(-2x^3y^4)
-7x^2y^4*-2x^3y^4, next take out the constants
−(7×−2)x^2x^3y^4y^4, -(7*-2)=14, so now you just need to add the variables.
(x^2+x^3)+(y^4+y^4)=x^5y^8
14x^5y^8
Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)
- Cutiepatutie ☺❀❤
Which summation formula represents the series below? 1 + 2 + 6 + 24
Answers
Question:
Which summation formula represents the series below? 1 + 2 + 6 + 24
(a) [tex]\sum_{n=2}^{5}(n-1) ![/tex]
(b) [tex]\sum_{n=0}^{3} n ![/tex]
(c) [tex]\sum_{n=1}^{4}(n+1) ![/tex]
(d) [tex]\sum_{n=2}^{5} n ![/tex]
Answer:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex] is the correct answer.
Explanation:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](2-1) !+(3-1) !+(4-1) !+(5-1) ![/tex]
Subtracting, we have,
[tex]1 !+2!+3 !+4 ![/tex]
Expanding the factorial,
[tex]1+(2*1)+(3*2*1)+(4*3*2*1)[/tex]
Simplifying, we get,
[tex]1+2+6+24[/tex]
Thus, the summation [tex]\sum_{n=2}^{5}(n-1) ![/tex] represents the series [tex]1+2+6+24[/tex]
Hence, Option a is the correct answer.
Option b: [tex]\sum_{n=0}^{3} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]0!+1!+2!+3![/tex]
Expanding the factorial,
[tex]0+1+(2*1)+(3*2*1)[/tex]
Simplifying, we get,
[tex]0+1+2+6[/tex]
Thus, the summation [tex]\sum_{n=0}^{3} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option b is not the correct answer.
Option c: [tex]\sum_{n=1}^{4}(n+1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](1+1) !+(2+1) !+(3+1) !+(4+1) ![/tex]
Adding, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=1}^{4}(n+1) ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option c is not the correct answer.
Option d: [tex]\sum_{n=2}^{5} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=2}^{5} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option d is not the correct answer.
Hence, the correct answer is Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
Answer: A
Step-by-step explanation:
BRAINLIEST 60 POINTS!! PLEASE HELP ITS DUE TODAY
First image is for question 1, and second image is for question 2
1. Remember what we know about vertical angles and solve for x.
2. Use the figure to answer the questions.
(a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain.
Answers
Answer:
1.[tex]x^\circ= 7^\circ[/tex]
2.(a)Therefore , Side LJ =side CA
(b) BC = KL
Step-by-step explanation:
1.
we know that, vertically opposite angles are congruent .
[tex]\therefore (x+16)^\circ= (4x-5)^\circ[/tex]
[tex]\Leftrightarrow 4x^\circ-x^\circ= 5^\circ+16^\circ[/tex]
[tex]\Leftrightarrow 3x^\circ= 21^\circ[/tex]
[tex]\Leftrightarrow x^\circ= 7^\circ[/tex]
2.
(a)SAS = side,angle , side
Given ,side AB = side KJ
and ∠CAB= ∠LJK
All Pythagorean Triples are unique.
Since side AB = side KJ
Therefore , Side LJ =side CA
It satisfies SAS postulate ThereforeΔABC≅ΔKJL
(b)
HL Theorem: If hypotenuse and one leg of of a right triangle are congruent to the hypotenuse and one leg of of other right triangle , then the triangle congruent.
Since,
All Pythagorean Triples are unique.
Then hypotenuse of ΔABC=ΔLKJ ⇔BC = KL
find the value of x.
13,15,17,x,20,21; The median is 18.
Answers
Answer:
1
Step-by-step explanation:
13 15 17 x 20 21
Cross out all outer numbers
We are left with 17 and x
With double medians, you add those two together and then divide them by two.
With the median (total) being 18, we will first add 17+x then divide Y/2 = 18
The value of x is 1
A building has the shape of a pyramid within a square base. The mid segment parallel to the ground of each triangular face of the pyramid has a length of 58 feet. Find the length of the base the pyramid.
Answers
Answer:
The length of the base the pyramid is 116 feet.
Step-by-step explanation:
See the diagram attached to this answer.
Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.
Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.
Hence, [tex]\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}[/tex]
⇒ AB = 2 × 58 = 116 feet.
The length of the base the pyramid is 116 feet. (Answer)
Final answer:
The length of the base of the pyramid in question, referenced as the Great Pyramid of Cheops, is historically known to be 230 meters on each side.
Explanation:
The student's question relates to finding the length of the base of a pyramid with a known mid-segment length in one of the triangular faces.
Based on the information provided, which references the Great Pyramid of Cheops (or the Great Pyramid of Giza), the original square base length of the pyramid was 230 meters on each side.
This measurement is crucial for answering questions related to the geometry and scale of pyramids in mathematical problems.
Darius uses the shadow method to estimate the height of the flagpole. He finds that a 5-foot stick casts a 4-foot shadow. At the same time , he finds that the flagpole casts a 20-foot shadow . What is the height of the flagpole. Sketch a diagram.
Answers
Answer:
The height of the flagpole is 25 foot.
Step-by-step explanation:
Given:
Height of the stick = 5 foot
Shadow of the stick = 4 foot
Another one:
Height of the flagpole = 'x'
Shadow of the flagpole = 20 foot
Note:The shadows are formed at the same time of the day so the Sun makes an equal angle with both the situation.
Here from both ends it forms two similar triangles.
So,
We can say that:
⇒ [tex]\frac{Height\ of\ the\ flagpole}{Shadow\ of\ the\ flagpole}=\frac{Height\ of\ the\ stick}{Shadow\ of\ the\ stick}[/tex]
⇒ [tex]\frac{x}{20}=\frac{5}{4}[/tex]
⇒ [tex]\frac{x}{20}\times 20=\frac{5}{4}\times 20[/tex]
⇒ [tex]x=25[/tex] foot
So Darius estimated height of the flagpole = 25 foot.
If the total surface area of a cube is 302.46ft2 what best describes the length of the side of the cube?
Answers
Answer:
7.1ft
Step-by-step explanation:
The formula for calculating the total surface area of a cube is 2(L²+L²+L²)
=2(3L²)
= 6L²
Where L is the length of the cube
If the total surface area of a cube is 302.46ft², then
302.46 = 6L²
L² = 302.46/6
L² = 50.41
L =√50.41
L = 7.1ft
The length of the side of the cube is 7.1ft
The length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
To find the length of the side of a cube given its total surface area, we need to use the formula for the surface area of a cube.
The formula for the surface area of a cube is:
[tex]\[ \text{Surface Area} = 6s^2 \][/tex]
where s is the length of a side of the cube.
Given the total surface area is [tex]\( 302.46 \, \text{ft}^2 \)[/tex], we can set up the equation:
[tex]\[ 6s^2 = 302.46 \][/tex]
To solve for s we first divide both sides by 6:
[tex]\[ s^2 = \frac{302.46}{6} \][/tex]
[tex]\[ s^2 = 50.41 \][/tex]
Next, we take the square root of both sides to find s
[tex]\[ s = \sqrt{50.41} \][/tex]
[tex]\[ s \approx 7.1 \, \text{ft} \][/tex]
Thus, the length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
Find the measure of θ. (to the nearest tenth)
A) 16.2°
B) 16.8°
C) 17.1°
D) 17.9°
Answers
Answer: D
Step-by-step explanation:
On USA test prep the answer is D.
Answer:
They are incorrect. The answer is actually 36.9
Step-by-step explanation:
What is this (20+25)/3
Answers
Answer:
78 witch is 15%
Step-by-step explanation:
A rectangle has a height of 4cm and a width of 8cm what is the area
Answers
Answer: 32
Step-by-step explanation:
4cm × 8cm = 32cm
I need help please and thank you
Answers
Answer: [tex]Perimeter= 71.75[/tex]
The parameter of a 2-D figure is the total length of its boundaries.
Step-by-step explanation:
In the given figure a hexagon is given with the length of its sides given in mixed fraction.
A mixed fraction can be solved by [tex]p\frac{x}{y} =\frac{(p*y)+x}{y}[/tex]
So adding the given sides in the figure:
[tex]Perimeter=14\frac{3}{4}+ 4\frac{1}{2}+ 8\frac{1}{2}+10 \frac{2}{5}+10 \frac{2}{5}+12 \frac{4}{5}[/tex]
[tex]=\frac{(14*4)+3}{4} +\frac{(4*2)+1}{2} +\frac{(8*2)+1}{2} +\frac{(10*5)+2}{5}+ \frac{(10*5)+2}{5} +\frac{(12*5)+4}{5}[/tex]
[tex]=\frac{59}{4}+ \frac{9}{2}+ \frac{17}{2}+ \frac{52}{5}+ \frac{52}{5}+ \frac{64}{5}[/tex]
[tex]=14.75+4.5+8.5+10.4+10.4+12.8[/tex]
[tex]Perimeter= 71.75[/tex]
The perimeter of the given figure is 71.75
Claire is that in the first five years between 1977 in 1980 to the hospital about $12 per year are in the second five years between 1983 in 1888 the causal only by about two dollars a year show that Claire is correct
Answers
Answer:
Step-by-step explanation:
Which expression is equivalent to 4√147
A. 28√3
B. 12√7
C. 3√7
Answers
Answer:
A) 28*sqrt(3)
Step-by-step explanation:
Answer:
28√3 is your answer
Step-by-step explanation:
Solve the equation for 3y-4=6-2y
Answers
To solve the equation, you need to isolate/get "y" by itself in the equation:
3y - 4 = 6 - 2y Add 2y on both sides
3y + 2y - 4 = 6 - 2y + 2y
5y - 4 = 6 Add 4 on both sides
5y - 4 + 4 = 6 + 4
5y = 10 Divide 5 on both sides
[tex]\frac{5y}{5} =\frac{10}{5}[/tex]
y = 2
PROOF
3y - 4 = 6 - 2y Substitute/plug in 2 for y
3(2) - 4 = 6 - 2(2)
6 - 4 = 6 - 4
2 = 2
After Solving the equation for 3y-4=6-2y, we get y = 2. We must isolate the variable y on one side of the equation in order to get the solution to the equation 3y - 4 = 6 - 2y. Here's a step-by-step procedure:
Start by solving 3y - 4 = 6 - 2y, which is the provided problem.
Add 2y to both sides of similar phrases to combine them: 3y + 2y - 4 = 6 - 2y + 2y.
Simply put, this is: 5y - 4 = 6.
Add 4 to both sides of the variable word to isolate it: 5y - 4 + 4 = 6 + 4.
This may be summarised as 5y = 10.
To find y, multiply both sides of the equation by 5. (5y) / 5 = 10 / 5.
This may be condensed to: y = 2.
Consequently, y = 2 is the answer to the equation 3y - 4 = 6 - 2y.
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What's 0 divided by 0?
Answers
Answer:
Nothing
Step-by-step explanation:
You can't divide by zero
Answer:
ANYTHING DIVIDED BY 0 IS ALWAYS ZERO
Step-by-step explanation:
PLEASE MARK BRAINLIEST
Translate this phrase into an algebraic expression. 17 more than twice Craig's height. Use the variable c to represent craig's height
Answers
Answer:
C2+17
Step-by-step explanation:
Algebraic expression is 2c + 17
Given phrase;17 more than twice Craig's height
Find:Algebraic expression
Computation:We know that;
c = craig's height
So,
twice Craig's height
⇒ 2c
17 more than twice Craig's height
⇒ 2c + 17
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V=15.81 V, P = 500 mW, I=
Answers
Answer:
0.032 Amperes
Step-by-step explanation:
in this question We are given;
Voltage, V =15.81 VPower, P = 500 mW (Milli-watts)We are required to determine the current, I
We need to know that power, P is given by the product of current and voltage.
That is;
Power = VI
But; 1 mW = 0.001 Watts
Thus, 500 mW = 0.5 watts
Rearranging the formula;
I = Power ÷ V
= 0.5 watts ÷ 15.81 V
= 0.0316 Amperes
= 0.032 A
Thus, the current, I is 0.032 Amperes