Answer:
the 66th term is 1095
Which ordered pairs are in the solution set of the system of linear inequalities y > -1/3x +2 y < 2x + 3
The ordered pairs in the solution set of the system of linear inequalities y ≥ -1/3x +2 and y < 2x + 3 are (2, 2), (3, 1), and (4, 2).
What is the system of inequalities?One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.Given linear inequalities represented in the graph are:
y ≥ -1/3x +2
y < 2x + 3
In the graph, the shaded region above the solid line denotes the inequality,
y ≥ -1/3x +2
The shaded area on the right side of the dotted line denotes the inequality's solution set,
y < 2x + 3
And the common area of these inequalities will denote the solution set of the system of linear inequalities.
Ordered pairs are (2, 2), (3, 1), and (4, 2) and will therefore be located in the shared shaded area.
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HELP PLEASE!!
Use the point and the slope to graph each line. Write the equation of the line
Answer:
y = x in the slope intercept form
y - 2 = 1(x -2) in the point-slope form of a line
Step-by-step explanation:
Perpendicular slopes are opposite reciprocals of each other. So the perpendicular slope would be 1.
We could write this in the point slope form of a line and the answer would be:
y - 2 = 1(x -2) This would be the point slope form of a line.
If you want your answer in the slope intercept form
y -2 = 1(x-2)
y - 2 = x - 2 Add two to both sides
y = x
WHAT DO WE KNOW ABOUT PERPENDICULAR LINES ?
IS THAT WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE A PRODUCT OF -1.
TO FIND THE GRADIENT OF THE LINE PERPENDICULAR TO THE LINE WITH SLOPE/GRADIENT -1 WE CAN SAY
[tex]m1 \times m2 = - 1 \\ - 1 \times m2 = - 1 \\ m2 = 1[/tex]
THIS MEANS THAT THE GRADIENT OF THE NEW LINE IS 1
the general equation of the straight line is y=mx+c
[tex] - 2 = 1(2) + c \\ - 2 = 2 + c \\ c = - 2 - 2 \\ c = - 4[/tex]
This means that
[tex]y = 1x - 4 \\ simply \\ y = x - 4[/tex]
is 89.396668... a rational number
Answer: yes it is rational
Step-by-step explanation:
Answer: 89.396668... is a rational number
Step-by-step explanation:
Cedar just graduated from college. he accepted a position with a firm at an annual salary of 45,000. using the department of housing and urban development guidelines, what is the maximum amount cedar should pay for rent on a monthly basis?
The maximum amount Cedar should pay for monthly rent is 13,500.
We need to know the maximum amount of monthly rent cost to solve this problem. In this country, the department of housing and urban development has ruled that the maximum monthly rent cost is 30% of gross profit.
Max cost = 30% Gross
From the question above, the given parameter is
Gross profit = 45,000
By substituting the given parameter, the maximum monthly rent cost is
Max cost = 30% Gross
Max cost = 30% x 45,000
Max cost = 13,500
Hence, the monthly rent cost should have a maximum amount of 13,500.
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Please help me find the equation of the parallel line.
Given: 5x-2y=10, (3,-5)
I know that the formula is y-y1=m(x-x1) but what do I do with the 2y?
Thank you!
Answer:
mperpendicular = −2/5
Step-by-step explanation:
Use the given information to prove that DE=FD
The condition for the figure to be similar is that; DE = FD
What are similar figures?Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
In the problem, the ratio should be CD/DE = GD/DF
We can also write the ratios of the corresponding sides as:
CD/DE = GD/DF
Therefore, CE and GF are similar
Thus, the condition for the figure to be similar is that;
DE = FD
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Explain why the equation 4|x| + 30 = 2 has no solution.
Answer:
the answer will be a negative answer
Step-by-step explanation:
Esimate the value of 13 squared, between which two whole numbers
Answer:
168 and 170
Step-by-step explanation:
What’s the answer to this question
The recursive formula of the arithmetic sequence is:
xₙ = n*4 + 13
With that we can see that x₁₁ = 57
How to write the arithmetic sequence?Here we know that the first elements of the sequence are:
17, 21, 25, 29, ...
To find the common difference, d, we take the difference between any two consecutive elements, so we have:
c = 21 - 17 = 4
Then the recursive formula for the n-th term is:
xₙ = n*4 + d
The first element x₁ is 17, so we will have:
17 = 1*4 + d
17 - 4 = d = 13
The recursive formula is:
xₙ = n*4 + 13
b) the eleventh term of the sequence is given by replacing n in the above formula by 11.
x₁₁ = 4*11 + 13 = 44 + 13 = 57
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A scale drawing of a car is presented in the following three scales. Order thescale drawings from smallest to largest. Explain your reasoning. (There areabout 1.1 yards in a meter, and 2.54 cm in an inch.)A. 1 in to 1 ftB. 1 in to 1 mC. 1 in to 1 yd?
The smallest drawing will be the one that has the smallest drawing unit with respect to the the actual unit.
We have:
A. 1 in to 1 ft
B. 1 in to 1 m
C. 1 in to 1 yd
If we put them all in meters, we have:
A. 1 in to 0.3048 m
B. 1 in to 1 m
C. 1 in to 1/1.1 = 0.90... meters
Then, the small drawing will be B, as 1 meter is the largest actual unit.
Second, will be B, that has 1 in by approximately 0.9 meters.
Third and last, option A, which drawing has an scale of 1 in in 0.3048 meters.
We can calculate the scale as a ratio between the drawing units and actual units, expressed in the same units.
For example, for A, we have:
[tex]\frac{1\text{ in}}{1\text{ ft}}\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{12}[/tex]So the scale is 1:12.
NOTE: look that we have cancelled all the units with this operation.
For B, we have:
[tex]\frac{1\text{ in}}{1\text{ m}}\cdot(\frac{2.54\text{ cm}}{1\text{ in}})\cdot(\frac{1\text{ m}}{100\text{ cm}})=\frac{2.54}{100}=\frac{254}{10000}[/tex]For C, we have:
[tex]\frac{1\text{ in}}{1\text{ yd}}\cdot(\frac{1\text{ yd}}{3\text{ ft}})\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{36}[/tex]You can verify that B has the smallest scale (0.0254)
A landscape architect accrued $7,834.54 in credit card debt. If the architect makes a monthly payment of $500 (and makes no additional charges on the account), how many months will it take to repay the debt if the annual interest rate on the credit card is 18.6%? (Round your answer up to the nearest month.)
The $7,834.54 borrowed at 18.6% annual interest rate with the landscape architect's monthly payment of $500, gives the number of months it will take to repay the debt as approximately 19 months
What is a monthly payment?Monthly payment on a loan, is the amount the person who takes the loan, pays each month in order to settle the loan in a given time period.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot \left( \frac{r}{12} \right) \cdot \left( 1 + \frac{r}{12} \right)^{n} }{\left( 1 + \frac{r}{12} \right)^{n} - 1} }[/tex]
Where;
M = The amount the landscape architect paid monthly = $500
P = The amount loaned or borrowed = $7,834.54
r = The interest per annum = 18.6%
n = The number of monthly payment made
Therefore;
[tex] \displaystyle{500 = \frac{7834.54 \cdot \left( \frac{0.186}{12} \right) \cdot \left( 1 + \frac{0.186}{12} \right)^{n} }{\left( 1 + \frac{0.186}{12} \right)^{n} - 1} }[/tex]
Evaluating the above equation gives;
[tex] \displaystyle{500 = \frac{121.43537.1 \cdot 1.0155^{n} }{1.0155^{n} - 1} }[/tex]
[tex] \displaystyle{500 \times (1.0155^{n} - 1) = 121.43537.1 \cdot 1.0155^{n} }[/tex]
[tex] \displaystyle{500 \times 1.0155^{n} - 121.43537.1 \cdot 1.0155^{n} ) = 500 }[/tex]
Which by taking natural logarithms of both sides gives;
n•ln(1.0155) = ln(1.32077843609)
n = ln(1.32077843609) ÷ ln(1.0155) ≈ 18.09
Rounding up to the nearest month gives;
The number of months it will take the architect to pay the debt is approximately 19 months
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O skaters are racing toward the finish
race. The first skater has a 40 meter
d and is traveling at a rate of 12 meters
second. The second skater is travelin
ate of 14 meters
per
second. How long
it take for the second skater to pass
st skater?
The first skater has a 40 meter d and is traveling at a rate of 12 meters second, second skater is traveling rate of 14 meters per second. it will take 20 seconds for second skater to pass the first skater.
What is the definition of time?Time is continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in conscious experience. Time is often referred to as fourth dimension, along with three spatial dimensions.
Time has long been an important subject of study in religion, philosophy, and science, but defining it in manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and performing arts all incorporate some notion of time into their respective measuring systems.
12x+40=14x
40=2x
x=20
it will take 20 seconds for second skater to pass the first skater.
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Please Answer Fast!
There is a line that includes the point (-8, -8) and has a slope of. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{1}{4}[/tex] x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 8, - 8 ) into the partial equation
- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6
y = [tex]\frac{1}{4}[/tex] x - 6 ← equation of line
HELP FAST! Write an inequality for each of the phrases or word problems. Solve for the missing variable and
graph the solution set on the number line.
a. The value of number plus 17 is less than 12.
b. A number times negative three is at least 12.
c. The difference between a number and three is more than 10.
d. There were at most b bananas on your banana bunch. You have eaten at least one and have 8
left. How many were on the bunch?
e. Susanna purchased a shirt for $5, pants for $10, and a jacket for $25. She wants to buy at least
one purse for the outfit, but she wants to have something left of her original $65. How much
money might she spend on the purse?
f. An lift holds no more than 1200 pounds. If you are rolling a cart that weighs 760 pounds, how
much more can the elevator hold?
quick question thx!!
What is the slope of the line that passes through the points (7, -4) and (11,−4)?
The slope of the linear equation is 0, so this is a horizontal line.
What is the slope of the line?
A linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we have the points (7, -4) and (11,−4), then the slope is:
a = (-4 + 4)/(11 - 7) = 0
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David is a nurse, he wants to buy an apartment near his sister. Apartments in her neighborhood cost around $120,000. The bank has approved him for a loan with an interest rate of 3.95%. David is a recent graduate and needs his monthly payment to be low, he can afford to pay about $550 a month. David plans to sell the apartment or refinance the loan within five years when he knows he will be earning more money. PLEASE HELP
Answer:
Describe how anthropology challenges more commonly held notions of progress
Step-by-step explanation:
Please help what is the answer???
The babysitter charges $8 per hour plus $4 for gas to come to the house. If the babysitter earned $36, how many hours did the sitter work?
Answer: 8x + 3, where x is the number of hours
3) Two rooms in a house need to be painted.
Each room can be painted either white or
yellow.
Answer:
Paint them white as it looks better
Step-by-step explanation:
Yellow is a very bad choice to paint a room
please answer number 5 by finding the length indicated
What is the expression in radical form?
(5ab) =
○ √√25a²b²
O√√5a²b²
O √5a³b3
O √125a³b3
The radical form of the expression (5ab)[tex]^\frac{3}{2}[/tex] is √(125 a³b³).
What does radical form mean?Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.
What in mathematics is radical form?The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions.
According to the given data:Radical equation = b[tex]\frac{m}{n}[/tex]
= [tex]\sqrt[n]{b^m}[/tex]
So,
(5ab)[tex]^\frac{3}{2}[/tex] = [tex]\sqrt[2]{5^3}[/tex]
[tex]\sqrt[2]{5^3}[/tex] a³ b³
5³ = 125
√(125 a³b³)
The radical form of the expression (5ab)[tex]^\frac{3}{2}[/tex] is √(125 a³b³).
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ASAP I have a couple more minutes, please help! This lesson is called "The Pythagorean Theorem"
Answer: Number 5. is B-7CM
Number 8. is y=2/x
Step-by-step explanation:math
What equation is graphed in this figure?
A y+2=−32(x−2)
B y−4=−23(x+2)
C y+1=−23(x−3)
D y−3=32(x+1)
The equation of the line that passes through the graph is y + 2 = -3/2(x - 2)
How to determine the equation of the line?The graph represents the given parameter
From the graph, the points are given as
(0, 1) and (2, -2)
Calculate the slope of the points using
Slope = (y₂ - y₁)/(x₂ - x₁)
Rewrite as
m = (y₂ - y₁)/(x₂ - x₁)
This means that
Slope = m
So, we have the following representation
m = (-2 - 1)/(2 - 0)
Evaluate
m = -3/2
The equation of the line is then calculated as
y = m(x - x₁) + y₁
Where
(x₁, y₁) = (2, -2)
m = -3/2
So, we have
y = -3/2(x - 2) - 2
Add 2 to both sides
y + 2 = -3/2(x - 2)
Hence, the equation of the line is y + 2 = -3/2(x - 2)
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Jasim works in a restaurant.
The table shown gives his rates of pay.
Day
Mon to Fri
Weekend
Jasim worked for a total of 30 hours last week.
He worked 12 of these hours at the weekend.
Work out Jasim's pay for last week.
Rate of pay
£8.70 per hour
£10.80 per hour
Answer:
Step-by-step explanation:
The option that is most suitable for tabular data will be provided by-
Jasim's last week's total pay was £286.2.
Describe tabular data.Tabular data is data presented in the form of rows and columns.
Here,
Total time for which Jasim works last week = 30 hours
Time for which Jasim works at the weekend = 12 hours
Time for which Jasim works at the weekdays = (30 - 12) hours
= 18 hours
Jasim's pay during weekdays = £8.70
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £8.70 [tex]\times[/tex] 18
= £156.6
Jasim's pay during weekends = £10.80
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £10.80 [tex]\times[/tex] 12
= £129.6
Total pay of Jasim for last week = £(156.6 + 129.6)
= £286.2
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Can you help me with this math question
Answer:
40
Step-by-step explanation:
[tex]m \angle 2=20^{\circ}[/tex] (angle sum of triangle)
[tex]m\angle 1=40^{\circ}[/tex] (angle sum of triangle)
a sector with angle 120 degrees has a radius of r+4cm and its area is the same as the area of a circle with radius r cm.
By forming an equation in terms of 'r', show that r²-4r-8=0
Answer:
If area of sector = area of circle
1/3π(r+4)^2= πr^2
r^2-4r-8 =0
what is a sector?A sector is a cut out section of a circle. It is of two radii and an arc .
The area of a sector is angle substended/ 360 x area of a circle
area of a circle is πr^2
if area of circle is equal to the area of sector
120/360×π(r+4)^2=πr^2
divide both side by π
1/3(r+4)^2=r^2
multiply both sides by 3
(r+4)^2=3r^2
opening the bracket
(r+4)(r+4)=3r^2
r^2+ 8r +16=3r^2
3r^2-r^2- 8r -16=0
2r^2- 8r -16=0
divide all by 2
r^2- 4r -8=0
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A trapezium of area 140cm square has parallel sides 10cm apart and one of these 16m long. Find the length of the other parallel side
The length of the other parallel side = 7.5 cm
what is trapezium?
Trapezium is the quadrilateral whose only one pair of side is parallel.
as we know ;
AREA OF TRAPEZIUM=1/2*(sum of parallel side)*(height)
given:- one parallel side = 10 cm
height = 16 cm
Area= 140 cm
Assume:-
other parallel side =x cm
so,
140=1/2*(10+x)*16
140*2/16=10+x
280/16=10+x
35/2=10+x
17.5-10=x
x= 7.5cm
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If the length of a room is 4.02m, the width of a room is 3.37m, and the height of a room is 2.35m, what is the volume of the room m^3? after figuring out the volume, then find out the mass of the air kg in the room.
The value for the volume of the room is 31. 84 cubic centimeters(cm³)
The mass of the air in the room is 41. 39 kg
How to determine the volume of the roomThe formula for calculating the volume of the room is expressed as;
Volume = l × w × h
Where;
l is the length of the roomw is the width of the roomh is the height of the roomFrom the information given, we have to substitute the values of the measurements of the room into the formula.
We have;
Volume, v = 4. 02 × 3. 37 × 2. 35
Volume, v = 31. 84 cubic centimeters(cm³)
To determine the mass of the air in the room, we use the formula for mass which is expressed as;
Mass = Density × volume
Given that;
Density of air = 1. 3kg/m³Volume of the room = 31. 84 cubic centimeters(cm³)Substitute the values
Mass = 1. 3 × 31. 84
Mass = 41. 39 kg
Hence, the volume is 31. 84 cubic centimeters(cm³)
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write the equation of the line that is parallel to the given line and goes through the point (-8 2)
The equation for the line that is parallel to the given line and goes through the point (-8 2), is y = 3x + 26. See the explanation below.
What is the explanation for the above?Recall that the equation for the line is always given as:
y = mx + b
Where m is the slope.
Assuming that you have a line y = 3x + 2
The line parallel to this line but intersecting the point (-8,2) is found by using y = mx + b and solving for b
m = 3; x = -8; and y = 2
b = y - mx
b = (2) - (3) (-8)
b = 26
Hence the equation for the line that is parallel to the given line going through point (-8, 2) is
y = 3x + 26
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Full Question:
Find the equation in slope-intercept form of the line y= 3x + 2 that passes through the point (-8,2) and is parallel to the line.
Estimate the answer to 783 + 329 by rounding each number to the nearest hundred
Answer:
1100
Step-by-step explanation:
783 rounded to the nearest hundred is 800
329 rounded to the nearest hundred is 300
800+300=1100
The estimation of 783 + 329 = 1100.
What is Rounding off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
783 + 329
Now rounding off nearest hundred
783 rounded off to 800
and, 329 rounded off to 300.
So, 800+ 300 = 1100
Hence, the estimation is 1100.
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