The given sequence160,80,40,20 is the geometric sequence.
In an Arithmetic sequence, the difference between the two consecutive terms is equal.
In a Geometric sequence, the common ratio of the two consecutive terms is equal.
The given sequence is 160, 80, 40, 20
Now,
[tex]T_{1} = 160\\T_{2} = 80\\T_{3} = 40\\T_{4} =20[/tex]
Subtracting the consecutive terms to calculate the common difference,
[tex]d = T_{2} -T_{1} = 80 -160 = -80[/tex]
[tex]T_{3} -T_{4} = 40 -80 = -40[/tex]
So, [tex]T_{2} -T_{1} \neq T_{3} -T_{4}[/tex]
So, the given sequence is not an arithmetic sequence.
Now, Calculating the common ratios,
[tex]r = \frac{T_{2} }{T_{1} } = \frac{80}{160} = \frac{1}{2}[/tex]
and, [tex]r =\frac{T_{3} }{T_{2} } = \frac{40}{80} = \frac{1}{2}[/tex]
Hence, the ratio is the same for consecutive terms.
So, the given sequence is the geometric sequence.
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An ostrich farmer wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the
rectangle (see the figure below). There are 700 feet of fencing available to complete the job. What is the largest possible total
area of the three pens?
The largest possible total area of the three pens is 15312.5sq.units.
What is a rectangular area?
The quantity of space occupied by a flat surface with a specific shape is referred to as the area.
Area of a Rectangle = (Length × Breadth) square units.
Here,
We let x be the length and y be the breadth of a rectangle area.
Given equation : 2y + 4x = 700
y + 2x = 350
y = 350 - 2x .......(1)
Area of rectangular field (A)= xy
A = x(350 - 2x)
A = 350x - 2x²
Differentiating w.r.t x we get,
A' = 350 - 4x
Again, differentiating w.r.t x we get,
A" = -4
Let A' = 0
350 - 4x = 0
4x = 350
x = 87.5
A is maximum at 87.5feets.
Hence, the largest possible total area of the three pens = XY = 87.5×175 = 15312.5 sq. units.
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Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.
(1,5) , (3,−2)
The required equation is y = - 3.5x + 8.5 (in slope-intercept form) of the line passing through the points with the given coordinates.
What is the slope of the line?The slope of a line is defined as the gradient of the line.
Given that the line that passes through two points (1,5), and (3,−2)
Let the required equation of the line will be as :
y - 5 = [(-2 - 5)/(3-1)](x - 1)
y - 5 = (-7/2)(x - 1)
y - 5 = - 3.5(x - 1)
y - 5 = - 3.5x + 3.5
y = - 3.5x + 3.5 + 5
y = - 3.5x + 8.5
Thus, the required equation is y = - 3.5x + 8.5 (in slope-intercept form) of the line passing through the points with the given coordinates.
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25% of 0÷4 = 0÷1 True or False?
Answer:
false
Step-by-step explanation:
25% is equivalent to 0.25
Make x the subject of m=n+x/p
The value of x is x=p(m-n).
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Given expression: m=n+(x/p)
To find: Make x the subject.
To make x the subject we have to separate the x to one side.
Expression m=n+(x/p)
Take n to another side,
(x/p)=m-n
Cross multiply,
x=p(m-n)
Therefore, the value of x is x=p(m-n).
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Try It
Solving Equations with Rational Numbers
Solve this equation: -7x+12 - 2x = 23 + 13x
Step 1: Simplify by combining like terms that are on the
same side of the equation. Which terms can be
combined?
Check
-7x+12-2x = 23+13x
Answer:
-6/11
Step-by-step explanation:
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Which expression is equivalent to 1/3(x+6)−4
The expression that must be equivalent to the one give must be 1/3x - 2
Equivalent ExpressionEquivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In this problem, we just need to simply the expression to get the answer to this.
1/3(x + 6) - 4
Step 1 : Expand or open the bracket
1/3x + 2 - 4
Step 2: Simplify the expression.
1/3x + 2 - 4 = 1/3x - 2
The equivalent expression must be 1/3x - 2
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Find the equation of a parabola with a focus at (–2,–3) and a directrix at y = –5.
A)
y = 1∕4(x + 2)2 – 4
B)
y = –1∕16(x + 2)2 – 4
C)
y = 1∕4(x – 2)2 – 4
D)
y = 1∕4(x + 2)2 – 8
The vertex form of Parabola is y= 1/4(x + 2)² -4 .
What is Vertex form of Equation?The general equation of a parabola is given by y = a(x – h)² + k or
x = a(y – k)² +h. Here (h, k) is vertex.
Given:
focus at (–2,–3) and a directrix at y = –5.
We know, the standard form is (x - h)² = 4p (y - k),
where the focus is (h, k + p) and the directrix is y = k - p
So, (h, k + p) = (-2, -3)
h = -2, k + p = -3
Directrix is y = k - p:
k - p = -5
k + p = -3
so, 2k = -8
k = -4
and, p = -3+ 4 = 1
Thus, the vertex is at (-2, -4) and p = 1, the equation is:
(x + 2)² = 4(y+ 4)
1/4(x + 2)² = y+4
y= 1/4(x + 2)² -4
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A doctor prescribes 100 milligrams of a therapeutic drug that decays by about 15% each hour. To the nearest hour, what is the half-life of the drug?
The drug administered to the patient by the doctor has a half-life of 5 hours
Half-LifeHalf-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.
The formula is given as;
T1/2 = ln2 / λ
Where;
λ = disintegration constant.But λ = 15% = 0.15/hr
t1/2 = ln2 / 0.15
T1/2 = 0.693/0.15
T1/2 = 4.62 = 5 hours.
The drug has an half-life of approximately 5 hours
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Determine an nth degree polynomial that satisfies the aforementioned conditions.
The polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
Given that,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-3 is a multiplicity 1 zero of p.
-4 is a zero, with multiplicity 1, of p.
3 is a root, with multiplicity 1, of p.
p(-2)=-40
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -3,-4 and 3.
a be the coefficient.
p(x)=a(x+3)(x+4)(x-3)
p(x)=a(x²-3²)(x+4)
p(x)=a(x²-9)(x+4)
p(x)=a(x³+4x²-9x-36)
Now, take x=-2
p(-2)=a((-2)³+4(-2)²-(-2)-36)
-40=a(-8+16+2-36)
-40=a(-26)
a=-40/-26
a=40/26
a=20/13
We get,
p(x)=20/13((x+3)(x+4)(x-3))
p(x)=20/13(x³+4x²-9x-36)
Therefore, the polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
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Jaclyn bought new shoes priced at $98 and sales tax is 8%. What is the total cost of the shoes after-tax?
The total cost of the shoes after tax is 105.84 dollars.
How to solve sales tax?Sales tax is a tax on goods and services purchased and is normally a percentage added to the buyer's cost.
Jaclyn bought new shoes priced at $98 and sales tax is 8%. The total cost of the shoes after tax can be calculated as follows;
Therefore, the cost after tax is the sum of the cost and the sales tax.
Hence,
sales tax = 8% of 98
sale tax = 8 / 100 × 98
sales tax = 784 / 100
sales tax = $7.84
Hence,
total cost after tax = 7.84 + 98 = 105.84 dollars
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can anyone help? thanks!
Answer: 175
Step-by-step explanation:
7 x 1 x 5^2
7 x 1 x 25
7 x 25
175
Answer:
175
Step-by-step explanation:
Since we have 7ca^2 and since we know a = 5 and c = 1, we can just plug in these values for a and c and follow the order of operations:
[tex]7ca^2\\7(1)(5)^2\\7(1)(25)\\7*25=175[/tex]
Limit x approaches 0 (tan^2x-sin) divide by x4
[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \stackrel{\textit{\Large L'Hopital's rule}}{\lim_{\theta \to 0}\cfrac{\frac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]}{\frac{d}{d\theta }[\theta 4]}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]\implies \cfrac{d}{d\theta }[[\tan(\theta )]^2-\sin(\theta )]\implies \stackrel{chain~rule}{2\tan(\theta )\cdot \sec^2(\theta )} ~~ -\cos(\theta ) \\\\\\ 2\tan(\theta )\cdot \cfrac{1}{\cos^2(\theta )}-\cos(\theta )\implies \cfrac{~~ \frac{2\sin(\theta) }{\cos(\theta) } ~~}{\cos^2(\theta )}~~ -\cos(\theta ) \\\\\\ \cfrac{2\sin(\theta) }{\cos^3(\theta) }~~ -\cos(\theta )\implies \cfrac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{d}{d\theta}[4\theta]\implies 4 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \lim_{\theta \to 0}\cfrac{ ~~ \frac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} ~~ }{4}\implies \lim_{\theta \to 0}\cfrac{2\sin(\theta)-\cos^4(\theta)}{4\cos^3(\theta)} \\\\\\ \displaystyle \lim_{\theta \to 0}\cfrac{2\sin(0)-\cos^4(0)}{4\cos^3(0)}\implies \lim_{\theta \to 0}\cfrac{2(0)-1^4}{4(1^3)}\implies {\Large \begin{array}{llll} -\cfrac{1}{4} \end{array}}[/tex]
50 POINTS!!
One Thursday night, Joel the delivery boy earned $43 in tips plus his usual $12/hr. He made $85. Write an equation for this situation.
Answer:
Step-by-step explanation:
This is a simple linear equation.
Y=12x + 43
The 12x represents the money he makes hourly, as x represents each hour he works
+43 represents the amount of money in tips he made since this was added on top of the hourly pay he was making.
Answer:
your welcome
Step-by-step explanation:
42+43=85$
to get the 42 you have to do 83-43 and that leaves you with 42
A parallelogram has been found to have diagonals which are NOT congruent and slopes which are negative reciprocals.
What kind of quadrilateral is it?
It is a rhombus kind of quadrilateral.
What is quadrilateral?
A quadrilateral has four sides, is two-dimensional (flat), closed (the lines join up), and has straight sides.
A rhombus is a four-sided quadrilateral with all of the features of a parallelogram.
A rhombus has three more characteristics: consecutive sides that are congruent; diagonals that bisect pairs of opposite angles; and diagonals that are perpendicular to one another.
Moving clockwise, beginning at point A in the top left corner of a hypothetical rhombus ABCD, you can see that side AB is congruent to side BC and side CD is congruent to side DA.
Additionally, you can see that diagonals AC and DB are perpendicular to one another and that the rhombus' diagonals split pairs of opposing angles.
Hence, It is a rhombus kind of quadrilateral.
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The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For a month in which the executive's cellular phone bill was $87.80, how many minutes did the executive use the phone?
The number of minutes that the executive use the phone is 131 minutes.
How to calculate the number of minutes?From the information, the cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use.
Let the number of minutes be m.
This will be illustrated as:
35 + 0.40m = 87.80
Collect like terms
0.40m = 87.80 - 35
0.40m = 52.80
Divide
m = 52.40 / 0.40
m = 131
The number of minute is 131 minutes.
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HURRY PLS!! TEST!!!!
consider the line y=5x-5
find the equation of the line that is parallel to this line and passes through the point (3,4)
find the equation of the line that is perpendicular to this line and passes through the point (3,4)
Answer:
y=-5x+19
Step-by-step explanation:
yeah -ya...... right?
What is 2(5+777x60 ÷6[8-9]
Answer:
-15530
Step-by-step explanation:
plug it in to a calculator
why so random numbers
Answer:
Step-by-step explanation:
2(5+777x60/6x(-1))
2(5-7770)
2x(-7765)
-15530
What can be concluded about line that passes through the points (1,-2) and (4,-2)? Check all that apply.
The slope is 0.
The y-intercept is -2.
The line is vertical.
O The line is horizontal.
The line has no y-intercept.
The equation of the line is Y--2
All that apply are:
The slope is 0.
The y-intercept is -2
The line is horizontal.
The equation of the line is Y = -2.
Given points:
(1,-2) and (4,-2)
slope m = -2-(-2) / 4 - 1
= -2+2/3
= 0
so slope is 0
y = mx + c
(1,-2) passes
-2 = 0*1 + c
c = -2
y = 0*x + -2
y = -2
so the line is horizontal and equation of the line is y = -2.
The y-intercept is -2.
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the line segment from (0,0) to (6,18) is revolved about the x-axis to form a cone. what is the volume of this cone?
Answer:
Step-by-step explanation:
do you happen to know the formula for finding the area of a cone?
V=π*[tex]r^{2}[/tex]*h/3
does that formula look familiar?
we know the radius , r, is 18 and the height, h is 6 :) can you figure this out now? just plug those into the formula above :)
Solve for x. Round to the nearest tenth, if necessary.
Value of x rounded to nearest tenth is 25.5 units.
Given in question,
Right angled triangle CDE
θ = 20°
CD = perpendicular = 24 units
CE = Hypotenuse = x
Therefore,
cosθ = Perpendicular/Hypotenuse
cos 20 = 24/x
0.9397 = 24/x
x = 24/0.9397
= 25.54
Hence, value of x rounded to nearest tenth is 25.5 units.
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Value=x-y=3 questions is y-x
The value of (y-x) when (x-y) = 3 is -3.
According to the question,
We have the following equation:
x-y = 3
Now, we have to find the value of (y-x). We can easily do this by multiplying both sides of this equation by -1.
We know that the multiplication of two negative integers always gives us the positive results and the multiplication of one negative and one positive integer give us the negative results.
So, we will have the following expression:
-x+y = -3
It can rewritten as follows:
y-x = -3
Hence, the value of (y-x) when (x-y) = 3 is -3.
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Texas Roadhouse Corporate has decided to increase the price of
fried pickles by 15%. What will be the new price of the pickles?
The pickles are $3.99
Answer: The pickles are $3.99
Step-by-step explanation:For percents,this is always done by simply dividing the percent (in this case 15%) by 100%. So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number. 0.15 x $152.00=$3.99
Write the equation of a line in
y = mx + b form that passes
through (5,-5) and (-5, -3)
The equation of a line in y = mx + b form that passes through (5,-5) and (-5, -3) is y = (-1/5)x - 4.
The formula to calculate the slope between two points is equal to
[tex]m = y2-y1/(x2-x1)[/tex]
Find the slope of Line a
We have the points
(5,-5) and (-5, -3)
Substituting the value in the formula
[tex]m = -3 - (-5)/(-5-5)\\m = (-3 + 5)/(-10)\\m = 2/-10\\m = -1/5[/tex]
The slope is -1/5.
Finding the y-intercept from the below-given equation:
y = mx + b ...... (1)
Putting value of y = - 5, x = 5, m = -1/5
-5 = (-1/5) x (5) + b
-5 = - 1 + b
=> b = - 4
Putting the value of b = - 4 and m = -1/5 in equation (1). We get,
y = (-1/5)x - 4
Hence, the equation of the line is y = (-1/5)x - 4.
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Graph the equation below
Y=1/3x-1
Answer:
Step-by-step explanation:
You move left 1 unit and right 8 units. You end at (5, 5). Where did you start?
The coordinates of the starting point is (12, 5)
What are ordered pairs?Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)
The rule to move ordered pair one unit left 1 will be subtracted in the x coordinates
(5, 5) → one unit left → ( 5 - 1, 5 ) = (4, 5)
The rule to move ordered pair 8 units left, 8 will be added in the x coordinates
(4, 5) → one unit left → ( 4 + 8, 5 ) = (12, 5)
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what is the volume of the recycling box shown in the diagram , 20cm, 40cm, 60cm
Answer:
48000
Step-by-step explanation:
I multiplied the length times width time height (20x40x60) to get 48000.
A solve the first question
Answer:
A or C
Step-by-step explanation:
Evaluate the expression 23.5 − 6.8x when x = 3.
Answer:
3.1
Step-by-step explanation:
23.5-6.8x
x=3
first put 3 in for x
23.5-6.8(3)
now solve the expression
23.5-20.4
3.1
You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each? Explain your answer. a. 4 times 5 + 3 = 23 b. 4 times 5 = 20 c. 4 times 5 times 3 = 60 d. 4 + 5 + 3 = 12 Please select the best answer from the choices provided A B C D
There are total 4*5*3 = 60 ways of wearing one each.
What is Fundamental Counting Principle?
A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle.
Solution:
Let,
for three events A, B, and C, number of outcomes be a,b, and c respectively.
So, the total number of outcomes is given by the product of outcomes of all the events i.e. by using Fundamental Counting Principle.
In the question mentioned,
a = 4
b = 5
c = 3
So, total outcomes = 4*5*3 = 60 ways
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[tex]\frac{5x^{6}5x^{-2}125x2x^{4}2x^{-5} }{2x^{5}5x^{-3}2x^{6\\} }[/tex]
[tex]\cfrac{5x^6 5x^{-2}125x 2x^4 2x^{-5}}{2x^5 5x^{-3} 2x^6}\implies \cfrac{5\cdot 5\cdot 125\cdot 2\cdot 2}{2\cdot 5\cdot 2}\cdot \cfrac{x^6 x^{-2}x x^4 x^{-5}}{x^5 x^{-3} x^6} \\\\\\ \cfrac{ 5\cdot 125}{1}\cdot \cfrac{x^{6-2+1+4-5}}{x^{5-3+6}}\implies 125\cdot \cfrac{x^4}{x^8}\implies 125\cdot \cfrac{1}{x^8 x^{-4}}\implies \cfrac{125}{x^{8-4}}\implies {\Large \begin{array}{llll} \cfrac{125}{x^4} \end{array}}[/tex]