The sequence 4, 20, 36, 52, Required 6th term is 84.
What is sequence?A sequence is an enumerated group of objects in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of elements (possibly infinite). In contrast to a set, the same elements can appear more than once in a sequence at various positions, and unlike a set, the order is important. The formal definition of a sequence is a function from natural numbers to the elements in each position. An indexed family, which is a function from any index set, can be thought of as a generalisation of the idea of a sequence.
For instance, the letters (M, A, R, Y) are arranged with M coming first and Y coming last.
Given, sequence is an arithematic sequence with common difference 16 and first term 4.
So,
6th term = first term + 5 * common difference
= 4 + 5 * 16
= 84
Hence, the required 6th term is 84.
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Find the compound amount and interest if Php. 400,000 is invested at 8 %, compounded quarterly for 5 years and 6 months?
Answer:
618 391 .87
Step-by-step explanation:
5 years 6 months = 22 quarters
8% = .08 .08/4 = .02 interest per period
400 000 ( 1 + .02)^22 = 618 391.87
Does anyone know the answer? Please and Thank you!
Answer:
By multiplying both side with the inverse of the coefficient of x
Step-by-step explanation:
coefficient of x = -6/4
inverse of coeefficient =-4/6.
multiply both sides.
x = 12(-4/6) = -8
Two pirates were playing with golden coins. During game, the first pirate lost half of his coins to the second pirate, then the second pirate lost half of his coins to the first pirate, then again the first lost half of his coins to the second. At the end of the game, the first pirate had 21 coins, and the second had 45 coins. How many coins did the first pirate have initially?
A rectangle has a length of k cm (where k is an integer) and width of k +3cm. the perimeter of this rectangle is less than 24cm.
form and solve an inequality and find the largest possible value of k.
Answer:
So our unknown width is X and the unknown length is X + 3. We know the perimeter is 2 times the length plus 2 times the width so let's set up that equation:
2 X + 2 (X+3) = 24
Now solve for X
2 X + 2 X + 6 = 24
4 X + 6 = 24
4 X = 18
X = 4.5 - this is the width
X + 3 = 4.5 + 3 = 7.5 - this is the length
Step-by-step explanation:
Pls help me and show work! Thank you <3
Answer: 6
Step-by-step explanation:
If the lines are parallel, then this means that by the corresponding angles theorem, the two angles marked in the image are congruent.
If we consider the right triangle, then by the exterior angle theorem, [tex]4x+90=11x-8 \longrightarrow x=14[/tex].
So, if [tex]x=14[/tex], then the indicated angle measures [tex]56^{\circ}[/tex], and since vertical angles are congruent, [tex]9y+2=56 \longrightarrow \boxed{y=6}[/tex]
What is the area, measured in square centimeters, of the green shape
pictured below? Do not include units in your answer.
Icm
1 cm
Answer here
Step-by-step explanation:
we can easily count this, as the diagonal lines are squares truly in half. so, 2 such cut squares are in total 1 full square.
there is one central rectangle of 4×6 squares = 24.
then in the upper left corner there is a small 2×2 square = 4.
and then we have in the bottom left 2 and the bottom right also 2 small triangles (4 in total) with each having 1 full square and 2 half-squares (2 squares in total) as area.
so, 4×2 = 8 squares.
so, the whole area is
24 + 4 + 8 = 36
Prove the identity 2csc2x=csc^2xtanz
Step-by-step explanation:
Consider the LHS, after the 5th step, consider the RHS
[tex]2 \csc(2x) = \csc {}^{2} (x) \tan(x) [/tex]
[tex]2 \frac{1}{ \sin(2x) } = \csc {}^{2} (x) \tan(x) [/tex]
[tex]2 \times \frac{1}{2 \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]
[tex] \frac{1}{ \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]
[tex] \csc(x) \sec(x) = \csc {}^{2} (x) \tan(x) [/tex]
Consider the RHS
[tex] \csc(x) \sec(x) =( 1 + \cot {}^{2} (x) ( \tan(x)) [/tex]
[tex] \csc(x) \sec(x) = \tan(x) + \cot(x) [/tex]
[tex] \csc(x) \sec(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } [/tex]
[tex] \csc(x) \sec(x) = \frac{1}{ \sin(x) \cos(x) } [/tex]
[tex] \csc(x) \sec(x) = \csc(x) \sec(x) [/tex]
What is the measure of the unknown angle?
Image of a full circle divided into two angles. One angle is fifty degrees and the other is unknown
Group of answer choices
300°
The measure of the unknown angle in the full circle is calculated as: 310 degrees.
What is the Measure of a Full Circle?The angle measure of a full circle equals 360 degrees.
The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.
The unknown angle = 360 - 50 = 310 degrees.
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1. Jessica and her family are driving to see friends who live 750 miles away. They dri for 12.5 hours before they arrive. What is their rate of change?
1. 60 miles per hour
2. 50 miles per hour
3. 75 miles per hour
4. 55 miles per hour
Answer:
60 miles per hour.
Step-by-step explanation:
speed = distance / time
= 750 / 12.5
= 60 miles per hour.
Does this graph show a function? Explain how you know.
5
O A. No; the graph fails the vertical line test.
B. Yes, there are no y-values that have more than one x-value.
C. Yes; the graph passes the vertical line test.
D. No; there are y-values that have more than one x-value.
Answer: A. No; the graph fails the vertical line test.
The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.
For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.
Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.
Will give brainliest!! One x-intercept of y = x2 – 6x + c is 3.
How you can find the value of c?
What is the value of c?
What is true about the x-intercepts of this function?
Answer:
9.
Step-by-step explanation:
1) the condition 'One x-intercept of y = x2 – 6x + c is 3' means, that x=3 and y=0;
2) it is possible to substitute the values x=3 and y=0 into the given equation and to calculate 'c':
0=9-18+c; ⇒ c=9.
Records show that Oliver is typically 10-30 minutes late
for his shift at work. The distribution for the minutes he is
late forms a consistent pattern, which can be graphed as
the given uniform density curve.
Oliver will get a written warning if he is more than 16
minutes late for work. What percentage of the time will
Oliver get a written warning?
30%
46.7%
70%
100%
The percentage of the time will Oliver get a written warning when he is more than 16 minutes late for his shift at work is 46.7%.
What is a density curve?The density curve is a type or way of representation of numbered distribution data over a graph. Here, the outcomes are continues. The density curve can not be below the x-axis or horizontal line of the graph.
In a density curve,
The mean of a density curve is indicated by μ (mu).The standard deviation of a density curve is indicated by Sx.Records show that Oliver is typically 10-30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.
Oliver will get a written warning if he is more than 16 minutes late for work. The time remain after the 16 minutes is,
t=30-16
t=14 min
Thus, the percentage of the time will Oliver get a written warning is,
p=(14/30)*100
p=46.7 %
Thus, the percentage of the time will Oliver get a written warning when he is more than 16 minutes late for his shift at work is 46.7%.
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Answer:
46.7%
Step-by-step explanation:
Consider the function g, domain R, defined by f(x)=2x^2+4x-1.
What is the codomain of the g function?
A: ]-∞,-3]
B: [-1,+∞[
C: [-3,+∞[
D: ]-∞,-1]
So, the answer to this question is option C, but I don't know why. Can anyone explain it to me?
Answer:
see explanation
Step-by-step explanation:
the codomain are the values of f(x) from the y- coordinate of the vertex upwards.
given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = 2x² + 4x - 1 ← is in standard form
with a = 2 and b = 4 , then
[tex]x_{V}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1
substitute x = - 1 into f(x) for y- coordinate of vertex
f(- 1) = 2(- 1)² + 4(- 1) - 1 = 2 - 4 - 1 = - 3
vertex = (- 1, - 3 )
since the coefficient of the x² term > 0 then the graph opens up U
then codomain is [ - 3, ∞ )
The measure of angle w is 130 degrees. What is the measure of angle b? You can use the equations you just wrote to help. W=y. C+b=90. Y+c=180
Answer:
b = 40
Step-by-step explanation:
Solve system of equations.
1) w = y
2) c + b = 90
3) y + c = 180
Since we want to solve for b, second equation would be a good starting point.
c + b = 90
b = 90 - c
But what is c?
Let's make c the subject in 3rd equation.
y + c = 180
c = 180 - y
Insert c back in second equation.
b = 90 - c
b = 90 - (180 - y)
b = 90 - 180 + y
b = -90 + y
All we need now is y. Notice that in the first equation w equals y and w is 130°, which means y is also 130°. Substitute again.
b = -90 + y
b = -90 + w
b = -90 + 130
b = 40
---
This is how it looks like if you solve it in one go (same procedure as above but in one place).
c + b = 90
b = 90 - c
b = 90 - (180 - y)
b = -90 + y
b = -90 + w
b = -90 + 130
b = 40
An ice cream truck began its daily route with 84 gallons of ice cream. The truck driver sold 74% of the ice cream. How many gallons of ice cream were sold?
gallons of ice cream were sold
nearest gallon)
Answer:
We need to find 74% of 84 (that's the amount that was sold// If you would have been asked for the amount left, it would be (100%-74%), but here it's easier since it's already given to us)
Now, let's write the percentage as a fraction
74/100 of 84
**Trick, for percentages, anytime you see a "of" replace it with a multiplication symbol
74/100 x 84
Now, it's just a simple multiplication
(74x84)/100
*You can use a calculator and find your answer
It would give you 62.16 and you will need to round it to a whole number, so 62 gallons
*If you can't use a calculator, simplify the fraction as much as you can and try to approximate
Step-by-step explanation:
~62
Solve using the quadratic formula
x^2 - 8x - 84 = 0
Show all work
Answer:
x²-8x-84
Using quadratic Formular -b±√b²-4ac/2a
--8±/8²-4×1×-84 /2×1
8±/64+336/2
8±/400/2
8±20/2
8+20/2, 8-20/2
28/2, -12/2
14,-6
64,000 ÷ 110
Estimate :
Quotient :
Remainder:
Answer:
640; 581 R 90; 90
Step-by-step explanation:
you can round 110 to 100
64000/100 is simply 640
then you do the real math
the quotient is 581 r 90
this means the remainder is 90
When you pay with a debit or ATM card, you are not borrowing money. You are
spending your own money. When you pay with a credit card, you are always
borrowing money.
True.
False.
Pls help me and show work! Thank you <3
Answer: 70
Step-by-step explanation:
By the corresponding angles theorem, [tex]4x-50=2x+30 \longrightarrow x=40[/tex]
This means that [tex]2x+30=110[/tex].
Now, if we notice the linear pair, this means that [tex]y=\boxed{70}[/tex]
Interest rate. Multiple choice
Answer:
A. 9.9%
Step-by-step explanation:
[tex] {e}^{14r} = 4[/tex]
[tex] ln(4) = 14r[/tex]
[tex]r = \frac{ ln(4) }{14} = .099 = 9.9\%[/tex]
NO LINKS!! Please help me with this translation: 2 units right and 5 units up
Answer:
g(x) = 5|(x - 2) - 2| - 2
Step-by-step explanation:
To shift 5 units right :
⇒ f(x) = 5|(x - 2) - 2| - 7
⇒ Applied rule : a units right → f(x) = (x - a)
To shift 5 units up :
⇒ g(x) = 5|(x - 2) - 2| - 7 + 5
⇒ g(x) = 5|(x - 2) - 2| - 2
Answer:
[tex]g(x)=5|x-4|-2[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=5|x-2|-7[/tex]
Translate 2 units right:
[tex]\begin{aligned}\implies f(x-2)& =5|x-2-2|-7\\ & =5|x-4|-7 \end{aligned}[/tex]
Then translate 5 units up:
[tex]\begin{aligned}\implies f(x-2)+5& =5|x-4|-7+5\\ & =5|x-4|-2 \end{aligned}[/tex]
Therefore:
[tex]\implies g(x)=5|x-4|-2[/tex]
2(6n+8)
Explain please
Answer:
12n + 16
Step-by-step explanation:
2 (6n + 8)
= (2*6n) + (2*8) [distributive property]
= 12n + 16
Hope it helps ⚜
Answer:
12n + 16
Step-by-step explanation:
Distributive Property
a(b + c) = ab + acDistributing the terms
2(6n + 8)2(6n) + 2(8)12n + 16Which is correct???????
Answer:
Bias compare results implement treatments
Step-by-step explanation:
Please solve with explanation (high points)
By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.
How to find angles by trigonometric relationships
As planes ABCD and BCLK are perpendicular to each other, the triangles AKL and AKC are right angled. The required angles can be found by using the following trigonometric relationships:
[tex]\angle AKL = 90^{\circ}[/tex] (As line segments AK and KL are perpendicular to each other)
[tex]\angle AKC = \tan^{-1} \left(\frac{AC}{KC} \right) = \tan^{-1} \left(\frac{\sqrt{2}\cdot a}{\sqrt{5} \cdot a} \right) = \tan^{-1} \sqrt{\frac{2}{5} }[/tex] (as line segments AC and KC are perpendicular to each other)
[tex]\angle AKC \approx 32.312^{\circ}[/tex]
By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.
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Find a formula for the nth term in this
arithmetic sequence:
a₁ = -7, a2 = -1, a3 = 5, a4 = 11,
-7+(n-1)6
-7 is the starting term
n is the term that you are looking for
6 is the common difference
The formula for the nth term in the arithmetic sequence is:
a(n) = 6n - 13
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
We are given the first four terms of an arithmetic sequence:
a₁ = -7, a₂ = -1, a₃ = 5, a₄ = 11
To find the formula for the nth term, we need to find the common difference (d) first.
We can do this by subtracting any two consecutive terms:
d = a₂ - a₁ = (-1) - (-7) = 6
Now we can use the formula for the nth term of an arithmetic sequence:
a(n) = a₁ + (n - 1)d
Substituting the values we found:
a(n) = (-7) + (n - 1)(6)
Simplifying:
a(n) = -7 + 6n - 6
a(n) = 6n - 13
Therefore,
The formula for the nth term in the arithmetic sequence is:
a(n) = 6n - 13
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Write the equation for the line in slope-intercept form.
Answer:
y = -3x - 3
Step-by-step explanation:
The line intercepts the y-axis at -3, and moves down 3 on the y for moving to the right 1 along the x-axis
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. Find the value of X in the rhombus
X=____
Answer:
x = 2
Answer is explained in image itself.
An airplane takes off from an airport. When the
airplane reaches a height of 16,500 feet (ft), the
airplane has travelled a horizontal distance of 6,000 ft,
as shown in the diagram below.
The angle of elevation is = 70° and the distance the airplane travelled in the air is = 17,557ft
Calculation of the distance travelledTo calculate the angle of elevation of the airplanetan x° = opposite/adjacent
where opposite = 16,500 feet
adjacent = 6,000 ft
tan x° = 16,500 / 6,000
tan x° = 2.75
X = arctan ( 2.75)
X = 70°
To calculate the distance the airplane travelled in the air Pythagorean Theorem is used.C² = a² + b²
C² = 16,500² + 6,000²
C² = 272250000 + 36000000
C² = 308250000
C= √308250000
C= 17,557ft
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volume of the house?
Answer:
Step-by-step explanation:
1.5 x 4.5 x 4.5 = 30.375
30.375 ÷ 3 = 10.125
10.125= volume of the triangle
3 x 4.5 x 4.5 = 60.75
60.75 = volume of rectangle
60.75 + 10.125 = 70.875
70.875 = total volume
what is the value of c so that 9x^2 + 15x + c = 0 has one rational solution
Answer:
c=-9x^2-15x
Step-by-step explanation:
Answer:
c = 6.25
Step-by-step explanation:
For this to occur, the discriminant of the quadratic formula must = 0
b^2 - 4ac = 0
15^2 - 4(9)(c) = 0
36c = 225
c = 6.25
