Answer:
It is not arithmetic, so therefore there is no common difference
Step-by-step explanation:
An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. There is no constant term in the above pattern.
Answer:
not an arithmetic sequence
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers that have a common difference. That is, the difference between any term and the previous term is constant for the sequence. Other kinds of sequences have other relationships between the differences.
DifferencesThe "first" differences of this sequence are ...
10-4 = 619-10 = 931 -19 = 12The first differences are not constant. However, we notice the "second" differences are constant. These are the differences of successive first differences.
9 -6 = 312 -9 = 3 . . . . . . constant 2nd differencesSequence typeThe first differences are not constant, so this sequence is not an arithmetic sequence.
For polynomial sequences, the level of constant difference tell you the degree of the polynomial describing the sequence. This sequence has constant 2nd-level differences, so can be described by a 2nd degree (quadratic) polynomial:
f(n) = 1.5n² +1.5n +1 . . . . . a quadratic sequence
__
Additional comment
Sequences that are exponential have differences that have a common ratio. That ratio is the same at every level. It is the base of the exponential function.
express 3256 as the product of power of 10
Answer:
3.256*10³2
Step-by-step explanation:3.256 * 1000 = 3256 1000 =10³
Select the correct answer.
Which value of x makes this equation true?
-12x2(x + 9) = 5(x + 4)
O A.
OB.
O C.
O D.
Answer:
B. -2
Step-by-step explanation:
-12x -2(x+9) = 5(x+4)
*ALWAYS REMEMBER YOUR BODMAS*
-12x -2x - 18 = 5x + 20
*group the like terms*
-14x - 5x = 20 + 18
-19x = 38
x = -2
The value of x that makes the equation true is: x = -2.
B. -2.
Here, we have to find the value of x that makes the equation true, we need to solve for x.
Let's solve the equation step by step:
-12x - 2(x + 9) = 5(x + 4)
Distribute the -2 and 5 on the right side of the equation:
-12x - 2x - 18 = 5x + 20
Combine like terms on both sides:
-14x - 18 = 5x + 20
Move the variable terms (5x) to one side of the equation and the constant terms to the other side.
Let's subtract 5x from both sides:
-14x - 5x - 18 = 5x - 5x + 20
-19x - 18 = 20
Move the constant term (-18) to the other side of the equation.
Let's add 18 to both sides:
-19x - 18 + 18 = 20 + 18
-19x = 38
Finally, divide both sides by -19 to isolate x:
x = 38 / -19
x = -2
So, the value of x that makes the equation true is: x = -2.
B. -2.
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What is the solution to the equation below? (Round your answer to two
decimal places.)
7•Inx=2.4
A. x=99.48
B. x = 18.48
C. x=1.41
D. x= 1.9
Answer:
C
Step-by-step explanation:
7 × ln(x) = 2.4
ln(x) = 2.4/7 = 0.342857143...
x = e^0.342857143... = 1.408967466... ≈ 1.41
The table shows some information about the lifetimes,
t
, in hours, of some lightbulbs.
Lifetime Frequency
25 <
t
≤ 50 70
50 <
t
≤ 100 76
100 <
t
≤ 150 29
150 <
t
≤ 200 91
200 <
t
≤ 250 0
250 <
t
≤ 300 15
300 <
t
≤ 350 23
Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP.
Answer:
25 < t < 350
Step-by-step explanation:
The mean lifetime of a bulb ranges from 25 to 350 hrs but the question is unclear.
Pleaseee hurry and answer
What is the vertex of the graph of the function below?
y=x² + 4x-6
A. (2,0)
B. (-2,6)
C. (-2,-10)
D. (2,6)
All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? m e = startfraction z times s over startroot n endroot endfraction.
Use the distance formula to find the perimeter of the triangle below. Round you answer to the nearest hundredth.
jAlright, let's take this problem step-by-step:
What is the perimeter:
⇒ all the side-lengths added up
⇒ need to find side-length using distance formula
[tex]Distance_._. Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
- (x₁,y₁): first point
- (x₂,y₂): second point
Let's solve:
Find length of AC⇒ first point: (5,7)
⇒ second point: (3,3)
[tex]Distance =\sqrt{(3-5)^2+(3-7)^2} =\sqrt{4+16} =\sqrt{20} =4.472[/tex]
Find length of AB⇒ first point: (5,7)
⇒ second point:(8,6)
[tex]Distance=\sqrt{(8-5)^2+(6-7)^2} =\sqrt{9+1} =\sqrt{10}=3.162[/tex]
Find length of BC⇒ first point: (8,6)
⇒ second point: (3,3)
[tex]Distance = \sqrt{(3-8)^2+(3-6)^2} =\sqrt{25+9} =\sqrt{34}=5.831[/tex]
Now let's solve for the perimeter:
[tex]Perimeter = 4.472+ 3.126+ 5.831=13.429[/tex]
Answer: 13.43 (rounded to the nearest hundredth)
Hope that helps!
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The vertices of an isosceles triangle are A(-4, 0), B(-10, -2) and C(-6, -6).
What is the equation of the triangle's line of symmetry?
y = - x - 4
y = x - 4
y = x + 4
y = - x + 4
Solve the equation 7(w +13) = 35.
) What is the value of w?
Answer: -8
Step-by-step explanation:
7(w+13)=35 [given]w+13=5 [divide both sides by 7]w = -8 [subtract 13 from both sides]Answer:
7(w+13)=35
7w + 91 =35
7w=35-91
7w= -56
7w/7 = -56/7
w=-8
Find the value of z
[tex]\textsf {Finding y :}[/tex]
[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]
[tex]\implies \mathsf {y^{2} = 8}[/tex]
[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]
[tex]\textsf {Finding z :}[/tex]
[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]
[tex]\implies \mathsf {z^{2} = 72}[/tex]
[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]
Answer:
z =8.49 or 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]
Length of hypotenuse = 8+1=9
length of one side = 3
so, a²+3²=9²
a²+3²=9²
a²=81-9
a²=72
a=√72=8.49 or 6[tex]\sqrt{2}[/tex]
9. Classify the shapes shown below. Write the letter of each shape in the category that
describes it. Shapes may fall into more than one category, and not all shapes will be
used.
At least 1 right angle = A, C and E
At least 2 sides of equal length = B and E
At least 1 pair of parallel sides= B and E
What is a Parallel line?Parallel lines are those lines that are apart and they never meet till infinity.
Example of shapes that have sides with parallel line are the rectangle and parallelograms.
The shape B and E are rectangles and parallelograms respectively.
The shape that has angle 90° are right angle triangles and trapezium.
Therefore, the shapes that has right angles are A which is a trapezoid and E which is a rectangle.
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how to figure out pythagoras theorem?
Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
What is the Pythagoras Theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In △ABD and △ACB,
∠A = ∠A (common)
∠ADB = ∠ABC (both are right angles)
Thus, △ABD ∼ △ACB (by AA similarity criterion)
Similarly, we can prove △BCD ∼ △ACB.
Thus △ABD ∼ △ACB,
Therefore, AD/AB = AB/AC.
We can say that AD × AC = AB².
Similarly, △BCD ∼ △ACB.
Therefore,
CD/BC = BC/AC.
We can also say that
CD × AC = BC².
Adding these 2 equations, we get
AB² + BC² = (AD × AC) + (CD × AC)
AB² + BC² =AC(AD +DC)
AB² + BC² = AC²
Hence proved
Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
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Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....
Note: the first term should be b(1).
b(n) =
Answer:
b(n) = -11 + (n-1)*8
Step-by-step explanation:
Let n be the sequence number, with n=1 the first number b(1) -11
The sequence changes by +8 each step.
b(1) -11 + 8 = -3
b(2) -3 + 8 = 5
b(3) 5 + 8 = 13
b(4) 13
b(1) = -11
b(2) = -3. or b(1) + 1*8
b(3) = 5, or b(1) + 2*8
b(4) = 13, or b(1) + 3*8
We note that each step adds a multiple of 8 to the initial value of -11. This can be stated as (n-1)*8
The formula for this sequence would be b(n) = b(1) + (n-1)*8
b(n) = -11 + (n-1)*8
Check: Does n=3 return the value of 5?
b(n) = -11 + (n-1)*8
b(3) = -11 + ((3)-1)*8
b(3) = -11 + (2)*8
b(3) = -11 + 16
b(3) = 5 YES
Which are two possible reasons for the change within the frog population?
–3.2, 4.8, –7.2, 10.8, …
The given sequence;–3.2, 4.8, –7.2, 10.8, is a geometric progression common ratio of -1.5.
What is a geometric series?When all the terms of a geometric sequence are added, then that expression is called geometric series.
The given sequence ;
–3.2, 4.8, –7.2, 10.8, …
The common ratio
= -4.8/ 3.2
= - 1.5
The terms having a common ratio of -1.5 best describe the relationship between the successive terms in the sequence of the terms.
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what is 5xy-x^2t+2xy+3x^2t
Answer:
x • (2xt + 7y)
Step-by-step explanation:
1. ((5xy-((x2)•t))+2xy)+(3x2•t)
2. Pull out like factors :
2x2t + 7xy = x • (2xt + 7y)
Final result
x • (2xt + 7y)
Answer:
[tex]7xy + {x}^{2} t[/tex]
Step-by-step explanation:
[tex](5xy + 2xy) + ( - 2 {x}^{2} t + 3 {x}^{2}t) [/tex]
what is the measure of easy interior angle of a regular octagon?
The sum of the interior angle is 1080 and each angle measure is 135 degrees.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have an octagon
In an octagon the number of sides = 8
The sum of the angles in the octagon is given by:
= (n - 2)×180
n = 8
= (8 - 2)180
= 6×180
The sum of the interior angle = 1080
Each angle = 1080/8 = 135 degree
Thus, the sum of the interior angle is 1080 and each angle measure is 135 degrees.
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The diagram below shows a square inside a regular octagon. The apothem of the octagon is 15.69 units. To the nearest square unit, what is the area of the shaded region? 13 U 13 U Apothem length: 15.69 O A. 1463 square units B. 816 square units C. 647 square units OD. 764 square units
perimeter of octagon
8(13)104unitsNow area
perimeter×apothem /2104(15.69)/252(15.69)815.88units²Area of square
13²169units²Area of shaded region
815.88-169646.88units²647units²Answer:
C. 647 square units
Step-by-step explanation:
To find the shaded area, subtract the area of the unshaded square from the area of the octagon.
Area of the octagon
[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]
where:
n = number of sidesl = length of one sidea = apothemGiven:
n = 8l = 13a = 15.69Substitute the given values into the formula and solve for A:
[tex]\implies \textsf{Area}=\sf \dfrac{8 \cdot 13 \cdot 15.69}{2}[/tex]
[tex]\implies \textsf{Area}=\sf \dfrac{1631.76}{2}[/tex]
[tex]\implies \textsf{Area}=\sf 815.88\:\:square \:units[/tex]
Area of the square
[tex]\implies \textsf{Area}=\sf 13^2=169 \:\:square \:units[/tex]
Area of the shaded region
= area of the octagon - area of the square
= 815.88 - 169
= 646.88
= 647 square units (nearest square unit)
Josh has a big backyard. He loves Red Pine trees because they can grow as tall as 50m (200 feet).
Josh is 31.2 metres away from the Red Pine tree. The angle of elevation from Josh to the top of tree is 48º. His friend Jake also has a Red Pine tree in his backyard. It is half as tall as Josh's tree. Calculate the height of Jake's tree, rounded to two decimal places
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of Jake's tree is 17.325 trees.
What is a Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given Josh is 31.2 meters away from the Red Pine tree. The angle of elevation from Josh to the top of the tree is 48º. Therefore, the height of the Josh tree will be,
Tan(48°) = Height of the tree/ Distance between Josh and tree
Height of the tree = Tan(48°) × 31.2 meter = 34.65 meters
Now, Jake's tree is half as tall as Josh's tree. Therefore, the height of Jake's tree is,
Height of Jake's tree = 34.65 meters = 17.325 meters
Hence, the height of Jake's tree is 17.325 trees.
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If one pair of opposite sides of a quadrilateral is both congruent and____ then the quadrilateral is a parallelogram then the
Answer:
parallel
a quadrilateral can be a parallelogram only and only if pair of opposite sides are equal and parallel.
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
1 0 -1 -3
0 1 5
00 1
a.
X=-3
y--9
z-1
b. x-2
y=-9
N
I
T
C. X=-2
y--9
2-1
d. x-3
y=-9
2-1
The question is incomplete. Below you will find the missing content.
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
The correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
A matrix is in row echelon form when the first non-zero number from the left i.e. leading coefficient is always to right of the first non-zero number in the row above and rows consisting of all zeros are at bottom of the matrix.
The row echelon form of the matrix is given in the question.
from row-echelon form of the matrix, we can write the equation as,
x-5z=-3
y-4z=-5
Let's assume z=t, where t is the real number
now we can find x and y by putting z=t in the equation
x-5t=-3
⇒x=-3+5t
y-4t=-5
y=-5+4t
Now we get the solution of x,y,z in terms of t
x=5t-3
y=4t-5
z=t
where t is the real number.
So the correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
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The total marks obtained in a mathematics test was 384 if the mean was 24 how many children took the test
Please help me with my math
The value of z is 119° and the value of y is 28°.
What is corresponding angles?When two parallel lines meet any other line, comparable angles are generated in matching corners or corresponding corners with the transversal, these angles are called corresponding angles.
If the given diagram is modified a bit it will look as shown below, the two angles will be 61° because the two angles are corresponding angles.
Now, since 61° and x lie on the same side of the line, therefore, the sum of the two angles will be,
61° + x = 180°
x = 119°
Also, the angles measured at 61° and (3y-23)° lie on the same side of the transversal, therefore, these two angles are corresponding angles. Thus,
61° = (3y-23)°
61 = 3y - 23
y = 28
Hence, the value of z is 119° and the value of y is 28°.
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Ann reads 15 pages in 30 minutes. how many pages she can read in 2 hours
Answer:
60
Step-by-step explanation:
2hrs = 120
120/30= 4
4×15=60
Answer:
60 pages :)
Step-by-step explanation:
First we turn the hours into minutes to make it easier :)
1 hr = 60 minutes
2 hrs = 120 minutes
Now that we have done that, we divide :)
120/30 =4
And now we multiply 1 more time :)
4 x 15 = 60
Have an amazing day!!
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3 erasers cost $4.41. Write a proportion that would solve for the cost of 4 erasers.
Answer:
$5.88
Step-by-step explanation:
3 erasers ⇒ $4,41
4 erasers ⇒ $A
A = 4 erasers * $4.41 / 3 erasers
A = $ 5.88
Answer:
see below
Step-by-step explanation:
Proportion:
4.41 is to 3 erasers as 'x' is to 4 erasers:
4.41 /3 = x / 4 <======this is your proportion
or rearrange
4 * 4.41/3 = x
(this results in x = $ 5.88 for 4 erasers )
Solve for x..........
[tex]5x - x - 8 = 15 + 3x[/tex]
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 23 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 5x - x - 8 = 15 + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 8 = 15 + 3x[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 3x = 15 + 8[/tex]
[tex]\qquad \tt \rightarrow \: x = 23[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
x = 23
Explanation:
⇒ 5x - x - 8 = 15 + 3x
collect like terms
⇒ 5x - x - 3x = 15 + 8
add or subtract like terms
⇒ x = 23
Checking:
5(23) - 23 - 8 = 15 + 3(23)
115 - 23 - 8 = 15 + 69
84 = 84
In the year 2008, a person bought a new car for $23500. For each consecutive year after that, the value of the car depreciated by 10%. How much would the car be worth in the year 2011, to the nearest hundred dollars?
Answer:
$17131.50
Step-by-step explanation:
23500 decrease 10% =
23500 × (1 - 10%) = 23500 × (1 - 0.1) = 21150
21150 decrease 10% =
21150 × (1 - 10%) = 21150 × (1 - 0.1) = 19035
19035 decrease 10% =
19035 × (1 - 10%) = 19035 × (1 - 0.1) = 17131.5
Girl runs across Across a rectangle field diagonal covering a distance of 120m if the length of the field is 100m calculate the width of the field to the nearest metre
Answer:
66m
Step-by-step explanation:
Answer:
66 m
Step-by-step explanation:
ok so if you think about it, when she runs diagonal she's creating a triangle where she is running along the hypotenuse. we can now use the Pythagorean Theorem a^2 + b^2 = c^2 to solve for the other side with two of them being known.
plug values in
100^2 + w^2 = 120^2
square known values
10,000 = w^2 = 14,400
subtract 10,000 from both sides
w^2 = 4400
take the square root
w = 66 (rounded to the nearest whole number)
Given that sine of theta = 21/29, what is the value of cosine of theta, for 0° < theta < 90°?
If the value of θ is 46.4°. Then the value of the cosine of θ will be 20/29.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The value of sine of θ is 21/29.
Then the value of θ will be
sin θ = 21/29
θ = sin⁻¹(21 / 29)
θ = 46.4°
Then the value of the cosine of θ will be
cos θ = cos 46.4°
cos θ = 20/29
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what does ([tex](x^{2}+4x)(x)[/tex] equal
the first definition of an element was made by
