The Recursive formula for an Arithmetic Sequence is a1 = -3, an = an-1 + 6.
What is Arithmetic sequence ?An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
Given:
an = -3 + 6(n – 1)
a1= -3
a2= 3
a3 = 9
Here the common difference is 6 and first term is -3
Hence, the recursive formula is a1 = -3, an = an-1 + 6.
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If an employer reduces the working week from 40 hours to 35 hours, with no
loss of weedy pay, calculate the percentage increase in the hourly rate of pay.
Answer:
14.285714285714 %
Step-by-step explanation:
suppose the weekly payment is of x dollars
Then
Previous payment : $(x/40) per hour
New payment : $(x/35) per hour
Then
The percentage increase in the hourly rate of pay is :
[tex]=\frac{\frac{x}{35} -\frac{x}{40} }{\frac{x}{40} } \times100[/tex]
[tex]=\frac{\frac{5x}{1400} }{\frac{x}{40} } \times100[/tex]
[tex]=\frac{5x}{1400} \times \frac{40}{x} \times100[/tex]
[tex]=\frac{200}{1400} \times100[/tex]
[tex]=\frac{1}{7} \times100[/tex]
[tex]=14.285714285714[/tex]
Find the values of a and b 3 * 2 = a + b if
value of a = 3
value of b = 2
a + b = 3 + 2 = 5 .
Add the following two numbers in scientific notation.
Answer:
3.31 x 10^4
Step-by-step explanation:
3.111 x 10^4 is 31110
2 x 10^3 is 2000
31110 + 2000 = 33100 or 3.31 x 10^4
Answer:
b) 3.31 × 10⁴
Explanation:
[tex]\sf \rightarrow \left(3.11\cdot 10^4\right)+ \left(2\cdot 10^3\right)[/tex]
remove parenthesis
[tex]\rightarrow \sf 3.11\cdot \:10^4+2\cdot \:10^3[/tex]
simplify
[tex]\rightarrow \sf 31100+2000[/tex]
add the numbers
[tex]\sf \rightarrow 33100[/tex]
convert to scientific form
[tex]\sf \rightarrow 3.31 \ x \ 10^4[/tex]
180 is equivalent to π/2 radians
true
false
Answer:
[tex]\fbox {False}[/tex]
Step-by-step explanation:
To convert a degree measure to radian measure, multiply with π/180.
⇒ 180 × π/180
⇒ π radians
false is the answers
please mark me as brainlest
Pls answer this asap
Answer:
The correct answer is A
Step-by-step explanation:
2 is exactly 7 units away from -5.
Use finite differences to identify the degree of the polynomial that best describes the data. 9 10 11 12 13 14
The forward differences for this data is 1, 1, 1, 1, 1, 1 (since 10 - 9 = 1, 11 - 10 = 1, etc). Since we only need one iteration of differences, a linear polynomial will fit the data exactly.
write the equation of the line that contains (-4, -3) and is parallel to the line x+2y=-10
Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you with this problem. We can solve this problem in 2 steps, respectively Theory and Solving.
I'll go ahead and start with the Theory.
TheoryBefore we attempt to solve the problem mathematically, we must first figure out how we're going to solve this problem.
We know that we have a line and a point, we can start by graphing the equation and point that we've received.
SolvingNow that we have our points plotted and our equations graphed, we can start to see that something odd is happening, the given point is on the line itself.
We can check this by inputting the points into our equation:
[tex](-4)+2(-3)=-10?\\(-4)+(-6)=-10?\\-10=-10[/tex]
This proves that our point is on the line that we were given.
According to the basic rules of Euclidean Geometry, we know that parallel lines can never intersect each other and due to this there cannot be any solution to this problem.
Any other line using this point would intersect the given line, and due to this, this problem has no real solutions.
* The only line that can use these points and graph is the line provided, and that cannot work due to the lines intersecting at an infinite number of points.
Cheers,
Galaxy.
Logarithm of x to the root 2 + logarithm (x-1) to the root 2 = 1
By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.
How to solve a logarithmic functions
In this question we need to solve a logarithmic equation by means of algebraic procedures and logarithm properties:
[tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex]
[tex]\log \sqrt{x\cdot (x-1)} = 1[/tex]
[tex]\log \sqrt{x^{2}-x} = 1[/tex]
[tex]\frac{1}{2}\cdot \log (x^{2}-x) = 1[/tex]
[tex]\log (x^{2}-x) = 2[/tex]
[tex]x^{2}-x = 2[/tex]
[tex]x \cdot (x-1) = 2[/tex]
[tex]x - 1 = \frac{2}{x}[/tex]
[tex]x - \frac{2}{x} = 1[/tex]
[tex]\frac{x^{2}-2}{x} = 1[/tex]
[tex]x^{2} - 2 = x[/tex]
[tex]x^{2}-x-2 = 0[/tex]
[tex](x-2)\cdot (x + 1) = 0[/tex]
[tex]x = 2 \,\lor \,x= -1[/tex]
By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.
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Find the values of the variables indicated below
M=
K=
Answer:
m=120
k=60
Step-by-step explanation:
a trapezoid has 360 degrees. subtract 120 degrees to get 240 degrees. we know that m=2k. 240=2k+2k which is 4k. 240 is 4k. k=60. m=2k, so mulitply 60 by 2 to get m=120
Gene has a gasoline budget of $300 per month. He uses an average of $6 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?
Answer:
300-6x
Step-by-step explanation:
Trust me
9^2 times 9^-6 exponential form
The result of the expression in exponential form is 9^-4
Product of exponentsGiven the expression below
[tex]9^2 \times 9^{-6}[/tex]
According the product law, since the base are equal, we will add the exponent to have:
[tex]9^2 \times 9^{-6}=9^{-6+2}\\9^2 \times 9^{-6} = 9^{-4}[/tex]
Hence the result of the expression in exponential form is 9^-4
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2 inches tall on week 4 3 inches tall on week 6 4 inches tall on
week 8
The linear relation of the height as a function of the number of weeks is:
y = 0.5*x
How to find the linear relation?A general linear relation is written as:
y = a*x + b
Where a is the slope.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we have the points of the form (week, height).
(4, 2)
(6, 3)
(8, 4)
If we use any two of these we can get the slope, so using the first two:
a = (3 - 2)(6 - 4) = 1/2 = 0.5
y = 0.5*x + b
To get the value of b, we can use the first point, it says that when x = 4, we have y = 2, then:
2 = 0.5*4 + b
2 = 2 + b
0 = b
Then the linear relation of the height as a function of the number of weeks is:
y = 0.5*x
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r=
help me please thank u
Answer:
[tex]\fbox {r = 34}[/tex]
Step-by-step explanation:
Finding IQ and RJ by tangent rule :
⇒ IQ = QK = 10
⇒ KR = RJ = 8
Finding PJ :
⇒ PJ = 32 - 8
⇒ PJ = 24
∴ But PJ = PI (by tangent rule)
⇒ PI = 24
Finding r :
⇒ PI + IQ
⇒ 24 + 10
⇒ r = 34
Solve this system of equations by
using the elimination method.
2x - 3y = 25
5x + 3y = 10
The ordered pair of solutions
is written in the format (x, y).
([?], [])
Enter
Answer:
(5,-5)
x=5
y=-5
Step-by-step explanation:
How to solve using elimination method.
First, add the two equations.
2x - 3y = 25
+ 5x + 3y = 10
7x=35
The y values got eliminated.
Next, divide 7 from both sides.
7x/7=35/7
x=5
Next, plug-in x=5 into one of the equations.
2(5) - 3y = 25
10-3y=25
Subtract 10 from both sides.
-3y=15
Divide -3 from both sides.
y=-5
Remember a positive divided by a negative is a negative.
Hope this helps!
If not, I am sorry.
solve for y in 1/8^2-3y=2^y-2
The value of y is 2.33924.
What is equation?
An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.
Given:
(1/8)²-3y = [tex]2^{y}[/tex]-2
1/64 - 3y = [tex]2^{y}[/tex]-2
1/64+ 2 = [tex]2^{y}[/tex]+3y
129/2 = [tex]2^{y}[/tex]+3y
Taking log on both side
log 129 - log 2 = y log 2 + 3 log y
2.11 - 0.301 = 0.301 y + 3 log y
1.809 = 0.301 y + 3 log y
1.809/3= 0.1 y + log y
0.603 = 0.1 y + log y
y = [tex]10^{\frac{603-100y}{1000}}[/tex]
y= 2.33924
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Examine the following dot plot.
A dot plot with 1 dot above 5, 1 dot above 10, 1 dot above 20, 2 dots above 30, 5 dots above 40, and 6 dots above 50.
© 2018 StrongMind. Created using GeoGebra.
Which answer correctly describes the shape of the data in the dot plot?
right-skewed
left-skewed
symmetrical
uniform
The data in the plot is Right skewed.
Therefore , Option A is the right answer
What is a Right skewed ?A right skewed distribution means most of the data lies to the right side of the graph's peak.
A dot plot is given and observing the data it can be seen that peak is towards the right side of the graph.
Thus the data in the plot is Right skewed.
Therefore , Option A is the right answer.
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Write an equation for a polynomial with all the following features:
a. The degree is 5. b. The polynomial has 4 terms.
c. The graph of the polynomial crosses the vertical axis at y = 12.
2. Identify the approximate input values of any relative maximums and minimums of
this 5th degree polynomial.
Please help!!
Construct the circle that circumscribes image DEF.
Answer:
See below
Step-by-step explanation:
General outlineConstruct the perpendicular bisectors of DE, EF, and DF.Identify the circumcenter. Draw the circumcircle.Circles & CircumcirclesTo construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.
Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle. The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.
Constructing perpendicular bisectorsTo construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).
So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.
Finding a point that is equidistant from two given points
Set the compass to any radius that is larger than half the distance between the two endpoints. If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.
Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice. If uncertain, draw the entire circle. Keeping the radius saved.
With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times. If it doesn't intersect two times, the radius chosen at the beginning was too small. Start the entire process over with a larger radius.
These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.
Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.
ProcessSteps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):
Set compass radius to length DEDraw circle, centered at D, through E. Keep radius set.Draw circle, centered at E, through D.Identify points of intersection of the circles from steps 2 & 3, M & NDraw line MNSet compass radius to length EFDraw circle, centered at E, through F. Keep radius set.Draw circle, centered at F, through E.Identify points of intersection of the circles from steps 7 & 8, Q & RDraw line QRSet compass radius to length DFDraw circle, centered at D, through F. Keep radius set.Draw circle, centered at F, through D.Identify points of intersection of the circles from steps 12 & 13, S & TDraw line STIdentify point of concurrency of line MN, line QR, and line ST; label it point PSet compass radius to length DP (or EP, or FP)Draw circle, centered at P, through points D, E, and F.Note: Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three. So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.
(a - b)(2x-3)+(6x+7)(a+b)
Factorise
Answer:
2(4ax+2bx+2a+5b)
Step-by-step explanation:
Find the equation of the parabola that has zeros of x = - 6 and x = 6 and a yintercept of (0, 4) .
-3(2x-5)<5(2-x)
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.
The given inequality is -3(2x-5)<5(2-x).
What is inequality?Inequality is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
At first simplify each side
LHS of inequality -3(2x - 5) = -3(2x) + -3(-5) [∵(-)(-) = (+)]
⇒ -3(2x - 5) = - 6x + 15
Now, RHS of the inequality 5(2 - x) = 5(2) + 5(-x) [∵(+)(-) = (-)]
⇒ 5(2 - x) = 10 - 5x
Now, - 6x + 15 < 10 - 5x
Subtract 15 from both sides
That is, - 6x < -5 - 5x
Add 5x to both sides
That is, - x < - 5
Remember the coefficient of x is negative, and then when you divide both sides by it you must reverse the sign of inequality.
Now, the coefficient of x is -1
So, divide both sides by -1
Then, x > 5.
Hence, the correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.
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Solve by elimination
show your work
y = 3x + 10
y = 2x - 8
im giving brainlyest
Answer:
[tex]x=-18, y=-44[/tex]
Step-by-step explanation:
[tex]y=3x+10\\y=2x-8\\\\3x+10=y\\2x-8=y\\3x-y=-10\\2x-y=8\\\\-2(3x-y=-10)\\3(2x-y=8)\\\\-6x+2y=20\\6x-3y=24\\-y=44\\y=-44\\-44=3x+10\\-54=3x\\x=\frac{-54}{3} \\x=-18\\\\x=-18, y=-44\\[/tex]
CHECK
[tex]-44=3(-18)+10\\-44=-54+10\\-44=-44\\\\-44=2(-18)-8\\-44=-36-8\\-44=-44[/tex]
please please help ME!!!
Answer:
720 Course Schedules
Step-by-step explanation:
When you choose the first course, there are 6 to choose from. When you scoose the second, there are only 5. This keeps going until the 6th course where there is only 1 choice.
You multiply these choices together. You should get 6×5×4×3×2×1
6×5=30
30×4=120
120×3=360
360×2=720
720×1=720
You then end up with 720 course schedules.
Jack goes to a restaurant in a state with a 7.25% sales tax. He buys a
meal and tips 20% before tax. Select the meal cost that would allow his
total bill, including tip and tax, to have a total cost equal to $15.
The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the meal cost, hence:
Total cost = x + 0.2x + 0.0725x
15 = 1.2725x
x = 11.79
The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.
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If two angles have the same angle measure, then they are said to be____.
A. Complementary
B.adjacent
C.congruent
Answer:
C
Step-by-step explanation:
2 equal angles are said to be congruent
Which function is increasing at the highest rate? A. B. A linear function on a coordinate plane passes through (minus 1, 3), and (2, minus 3) which intercepts axis at (0.5, 0), and (0, 1) C. A linear function, f, with an x-intercept of 8 and a y-intercept of -4. D. x 1 2 3 4 5 g(x) -5 -4 -3 -2 -1
The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.
The options are given in the image attached with the answer
What is a Function ?A function is a law that relates a dependent variable and an independent variable.
It is asked among the options given , which is increasing at the highest rate.
To increase at a rate , the value of the slope , m should be > 0
For the Option 1
for a straight line function , the slope is given by
m = ( y₂ -y₁)/(x₂-x₁)
m = ( -3 -3)/(2- (-1)) = -6 /3 = -2
Therefore the function is decreasing
For Option 2
12x - 6y = -24
-6y = -12x -24
y = 2x +4
m = 2 (increasing)
For option 3
m = (-4 + 5)/(2-1) = 1
For Option 4
(8,0) (0,-4)
m = (-4 -0) /(0-8) = 4/8 = 1/2
The highest rate on increasing is of 12x -6y = -24
Therefore Option B is the correct answer.
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What is the inverse of the function f(x) = 2x +1?
Answer:
y=0.5(x−1)
Step-by-step explanation:
Explanation: To find the inverse of a function, you have to substitute y for x in the equation and simplify to get a normal equation again. In this case, f(x) is y.
y=2x+1
x=2y+1
2y+1=x
2y=x−1
y=0.5(x−1)
Answer
[tex]y=\frac{x-1}{2}[/tex]
Step-by-step explanation:
To find the inverse of a function [tex]f(x)=2x+1[/tex] , we substitute x and y for each other and then solve for y to get a new function.
We rewrite the original function as:
[tex]x=2y+1[/tex]
And then we solve for y:
[tex]x-1=2y[/tex]
[tex]y=\frac{x-1}{2}[/tex]
This is our answer.
What is the equation of the line that passes through (-3, 4) and (3, -2)?
y = - x - 1
y = x + 7
y = x - 1
y = - x + 1
Answer:
y = -x +1
Step-by-step explanation:
p1 (-3,4)
p2 ( 3, -2)
line equation y = mx + b
The slope m equals
[tex] \frac{y2 - 21}{x2 - x1} [/tex]
[tex] \frac{ - 2 - 4}{3 - - 3} = \frac{ - 6}{6} = - 1[/tex]
y = - x + b
from any point
-2 = -3 + b
b = 1
line equation = y = -x +1
Question Progress
Find the following, giving your answers
to 1 decimal place.
10 cm/
Homework Progress
17/21 Marks
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.
Vol = ²
Curved
surface area
Answer:
[tex]\pi \times radius \times hieght[/tex]
It Sami anual Compound interest is applied interest, what instead of anual compound will be the profit of an investor It Sami anual Compound interest is applied interest , what instead of anual compound will be the profit of an investor.
Answer:
it's helps with learning the difference of thr compound
