Answer:
g(n) = g(n-1) -15
g(1) = -65
Step-by-step explanation:
We can find the recursive formula from the explicit formula for this arithmetic sequence by substituting 1 and (n+1) for n in the explicit formula.
__
g(n+1) = -50 -15(n+1) = (-50 -15n) -15 . . . . . find g(n+1)
g(n+1) = g(n) -15
and ...
g(1) = -50 -15(1) = -65
Then the recursive formula can ge written as ...
g(n) = g(n-1) -15
g(1) = -65
_____
Additional comment
We found g(n+1) = g(n) -15. Substituting n-1 for n in this formula puts it in the form we need for answering the question:
g((n-1)+1) = g(n-1) -15
g(n) = g(n -1) -15
Either of these forms tells you how to get the next term from the previous one.
Answer:
g(n) = g(n-1) -15
g(1) = -65
Step-by-step explanation:
answer on khan
Suppose there are 20 equally-sized marbles in a bag. Six marbles are blue, seven red, three of them orange, three of them black, and one green. If you choose a red marble, you win nothing. Selecting a blue marble will win you 25 cents. Selecting an orange marble will win you 50 cents, selecting a black marble will cost you a dollar, and if you choose the green one, you win three dollars.
Answer:
i dont know what youre trying to answer but if your trying to answer how much money can you get if you get all of the marbles you get $9
just blue- $1.50
just orange- $1.50
just black- $3
just green- $3
red=$0
Solve log x = 4. plese help
Answer:
x = 10^4 = 10000
Step-by-step explanation:
log(x) = 4
x = 10^4
Find the value of x. (25 points!)
Answer:
22.5
Step-by-step explanation:
By the angle bisectors theorem,
30/32 = x/24
x=24(30/32) =22.5
Dersan went for a run to prepare for a long distance race coming up. From his house, he ran 6 miles directly north, and then 8 miles directly west. From there, he ran the diagnoal distance back to his house. How many total miles did Dersan run?
Answer:
24
Step-by-step explanation:
So, Dersan's path is a right triangle. You have to find the last side. You can use the triples or 6^2+8^2=c^2 but I'll use a triple.
3,4,5.
The last side is 10.
6+8+10=24
hope this helped!
Solve for x and y
7y - 5x = 45
x = 8 – 2y
Answer:
Hope the pictures will help you.
The solution to the system of equations is x = -2 and y = 5.
What is the solution to the system of equations?Given the parameters:
7y - 5x = 45
x = 8 - 2y
To solve the system of equations, substitute the expression for x from the second equation into the first equation.
7y - 5x = 45
Plug in x = 8 - 2y:
7y - 5( 8 - 2y) = 45
7y - 40 + 10y = 45
Collect and add like terms:
7y + 10y = 45 + 40
17y = 85
y = 85/17
y = 5
Plug the value of y into the second equation and solve for x:
x = 8 - 2y
Plug in y = 5:
x = 8 - 2( 5 )
x = 8 - 10
x = -2
Therefore, the value of x is -2 and y is 5.
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Find the perimeter of the composite figure
7+7+5+5=24
So therefore the permeter is 24
The surface area of a cylinder is 432 pi yd2. The height of the cylinder is five times the radius. What is the diameter of the cylinder?
Since the surface area of this cylinder is [tex]432\pi \;yd^2[/tex], its diameter is equal to 12 yards.
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Given the following data:
Surface area of cylinder = [tex]432\pi \;yd^2[/tex]Height = 5r.Substituting the given parameters into the formula, we have;
[tex]432\pi = 2\pi r(5r) + 2\pi r^2\\\\432\pi = 2\pi 5r^2 + 2\pi r^2\\\\216=5r^2+r^2\\\\216=6r^2\\\\r^2=36\\\\r=\sqrt{36}[/tex]
r = 6 yards.
For the diameter:
Diamter = 2 x radius
Diamter = 2 x 6
Diameter = 12 yards.
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Complete each sentence with minimum or maximum and the corresponding numeric values.
The
value of f(x) = –|x – 4| – 5 is
when x =
.
The
value of f(x) = x2 – 2x + 1 is
when x =
.
Answer:
First problem: max when x = 4
Second problem: min when x = 1
Step-by-step explanation:
The graph of f(x) = –|x – 4| – 5 is a translation of that of g(x) = -|x|. The vertex of the latter is (0, 0). First this must be translated 4 units to the right and then the resulting graph 5 units downward. The vertex of this translation is (4, -5). Since this graph opens downward, this (4, -5) is the maximum function value, that is, when x = 4.
The graph of f(x) = x2 – 2x + 1, or (better yet) f(x) = x^2 – 2x + 1, or
f(x) = (x - 1)^2 + 0, is that of a parabola that opens upward and has its minimum at x = 1, or (1, 0).
Help, please! It's all in the screenshot
Answer:
cube root of 9. the third option
Step-by-step explanation:
x^3 = 9
we take the cube root of both sides.
so x = cube root of 9
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 64 cm, find its length and width.
Answer:
Length: 24 cm
Width: 8 cm
Explanation:
Let Width be "w"
Then Length is "3w"
=================
Perimeter of rectangle = 2(length+width)
===================================
2(3w+w) = 64(4w) = 32w = 8So, width is 8 cm
Length: 3w ⇒ 3(8) ⇒ 24 cm
Answer:
Length = 24 cmWidth = 8 cmStep-by-step explanation:
Given
Length = 3 x Width Perimeter = 64 cmSolving
Perimeter = 2(Length) + 2(Width)Perimeter = 2(Length + Width)Perimeter = 2(3 x Width + Width)Perimeter = 2(4 x Width)Perimeter = 8 x Width64 = 8 x WidthWidth = 64/8 = 8 cmLength = Width x 3 = 8 x 3 = 24 cmWhat is the difference between renewable and non-renewable resources? (Select all that apply).
1. Non-renewable resources can replenish themselves, but renewable resources cannot.
2. Renewable resources can replenish themselves, but non-renewable resources cannot.
3. Non-renewable resources are in abundance, but renewable resources are limited.
4. Renewable resources are in abundance, but non-renewable resources are limited.
Answer:
non renewable you can't renew what you already bought and renewable you can renew what you bought
Answer:
yes
Step-by-step explanation:
Does 5, 7, and 9 make a right angle?
No
Step-by-step explanation:
For a triangle to have a right angle the square sums of the legs have to equal the square of the hypotenuse.
In this case 9 is the hypotenuse which is the longest side in a triangle. 5 and 7 are the two smaller sides which make them the legs.
Putting this set of numbers into the pythagorean theorem is the way to solve this.
5²+7² should equal 9² if the triangle is a right triangle.
Solve the squares: 25+49=81
This would add up to be 74 and that is not equal to 81, so by this statement we can conclude that 5, 7, and 9 do not make a right triangle.
Fiona is studying how income taxes impact various families and their finances .she creates a table with various amounts of taxes owed and estimates that this represents 9%of each familys gross income
Income tax is the tax that is imposed by the government on the income that is generated by individuals and businesses.
What is a tax?Your information is incomplete. Therefore, an overview of a tax will be given. It should be noted that a tax is a compulsory levy that is paid by individuals and businesses.
Also, income tax is the tax that is imposed by the government on the income that is generated by individuals and businesses. This is important to generate revenue for the government.
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A trigonometry student stands 25 meters from a building and measures the angle of elevation to the top of the building as 30â°. how accurate does her angle measurement have to be if she wants her propagated percentage error in estimating the height of the building to be no more than 5%?
Using the slope concept, it is found that the angle measurement has to be within 1.2º of 30º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, considering the horizontal distance and the actual angle, the following equation is applied to find the actual height:
[tex]\tan{30^\circ} = \frac{h}{25}[/tex]
[tex]h = 25\tan{30^\circ}[/tex]
h = 14.43.
For an error of 5%, the bounds of h are as follows:
[tex]h_{min} = 0.95 \times 14.43 = 13.71[/tex]
[tex]h_{max} = 1.05 \times 14.43 = 15.15[/tex]
Hence, the angles will be given by:
[tex]\tan^{\alpha} = \frac{13.71}{25}[/tex]
[tex]\alpha = \tan^{-1}{\left(\frac{13.71}{25}\right)}[/tex]
[tex]\alpha = 28.8[/tex]
[tex]\tan^{\alpha} = \frac{15.15}{25}[/tex]
[tex]\alpha = \tan^{-1}{\left(\frac{15.15}{25}\right)}[/tex]
[tex]\alpha = 31.2[/tex]
Hence the angle measurement has to be within 1.2º of 30º.
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Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are. N A B M
Answer:
Step-by-step explanation:
4. Find the value of x.
to
90°
Answer:
90
Step-by-step explanation:
Measure of one arc = 90°
-> Measure of other arc = 360°- 90° = 270°
x° = 1/2 (270° - 90°)
-> x° = 1/2 * 180°
-> x° = 90°
-> x° = 90°
-> x = 90
A summer camp had
440
campers register this year. This is a
10
%
increase over the number registered last year.
Part A
The equation below relates
440
and
c
,
the number of campers registered last year. Complete the equation by entering a number in the
□
.
Enter only a whole number or decimal.
c
=
440
Part B
Enter a number in the
□
to show how many campers,
c
,
were registered last year.
campers
The equation that relates the number of campers this year to the number of campers last year is c = 440 / 1.10
The number of campers last year is 400.
What are percentages?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are used to measure frequency.
How many campers attended last year?The number of campers last year = number of campers this year / (1 + percentage increase)
440 / 1.1 = 400
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What is the equation of this trend line?
Enter your answers by filling in the boxes.
please help me get into my dream school!
Answer:
Step-by-step explanation:
The line rises to the left so the slope is negative.
The slope m = -24/12 = -2.
Using the point-slope formula and taking the point (12, 0) on the line:
y - y1 = m(x - x1) where m = -1, x1 = 12 and y = 0:
y - 0 = -2(x - 12)
y = -2x + 24 <------- this is the required equation.
Answer:
Blank 1 : -2
Blank 2 : 24
Step-by-step explanation:
The first blank denotes the rate of change, or the slope of the graph.
Slope = y₂ - y₁ / x₂ - x₁
m = 16 - 24 / 4 - 0m = -8/4m = -2Blank 1 : -2The second blank denotes the value of variable K when the value of variable J is 0, or rather the y-intercept of the graph.
The y-intercept is clearly (0, 24)
Blank 2 : 24HELP ASAP
Linear equations
In Texas, the average number of tornadoes in May was about 154% of the average number of tornadoes in April. Write and solve a proportion to find the average number of tornadoes that occurred in April.
The table of the average number of tornadoes is an illustration of proportions
The average number of tornadoes in April is 28
How to determine the average number of tornadoes in April?From the table, we have:
Average number of tornadoes in May in Texas = 43
From the question, we have:
May = 154% * April
This gives
43 = 154% * April
Express as decimal
43 = 1.54 * April
Divide both sides by 1.54
April = 27.9
Approximate
April = 28
Hence, the average number of tornadoes in April is 28
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An angle measures 88° more than the measure of its complementary angle. What is the measure of each angle?
Could you guys help me with this?
Answer:
It might be a two degree angle! :)
Step-by-step explanation:
What is pi with 400 numbers.
the first 400 digits of pi
3.1415926535897932384626433832795028841971
6939937510582097494459230781640628620899
8628034825342117067982148086513282306647
0938446095505822317253594081284811174502
8410270193852110555964462294895493038196
4428810975665933446128475648233786783165
2712019091456485669234603486104543266482
1339360726024914127372458700660631558817
4881520920962829254091715364367892590360
0113305305488204665213841469519415116094
We did it! We made it to the end! thanks for helping everyone!
Answer:
12.058
Step-by-step explanation:
You steal one "count" from the 8, and move it to the 7 so you have 12.0587, instead of 12.0578. Then, you are able to take off the 7 from the back.
A T-shirt company wants to make at least $1,000 during a weekend and they sell $10 and $20 shirts. They want to sell at least 60 shirts. What are the vertices of the feasible region? Select all that apply.
Answer:
90 if I am wrong sorry I have a hard time with math
Please help with this problem. I don’t understand the answer for this equation. The answer for this equation is 7/2( a+ b) i’m just not understanding where the seven is coming from.
Answer:
7/2(a+b)
Step-by-step explanation:
To add fractions you need to find the LCM (least common multiplier) and then combine.
least common multiplier of a+b, 2(a+b) : 2(a + b)
Adjust fractions based of LCM
2/2(a + b) + 5/2(a +b)
2+5/2 (a + b) =
7/2 (a + b)
I hope this makes sense! :)
PLS HELP, EXPLANATION IS GREATLY APPRECIATED!!!!!
Answer:
a = alpha
(sin a)^2
Step-by-step explanation:
(tan a)^2=(sin a)^2/(cos a)^2
(sec a)^2 = 1/(cos a)^2
if we combine we get ((sin a)^2 * (cos a)^2)/(cos a)^2
simplafy
HOPE THIS HELPSSSS<3
Estimate the value of 96.8 x 9.74
Answer:
1000
Step-by-step explanation:
Let's round!
96.8 can be rounded to 100
9.74 can be rounded to 10
100*10=1000
Hope this helps!
The estimated value of the given product is 970. The given product is (96.8×9.74). This is obtained by using the rounding-off method.
What is estimation?Estimating means finding something close to the actual answer. In other words, it is approximating.Estimating decimal products involves many strategies.General strategy is rounding-off to the nearest value method.Estimating the given product:The given product is (96.8×9.74)
Here the first decimal number in the product is 96.8
Since the digit after the decimal point 8 is nearer to the value of 10, it is rounded to 97. I.e., 96.8≅97
And the second decimal number is 9.74
Since the digit after the decimal 7is nearer to the value of 10, it is rounded to 10. I.e., 9.74≅10
So, the product is 97×10=970
Thus, 96.8×9.74≅970 (approx.)
Therefore, the estimated value is 970.
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help me, Sofia practices swimming and has every day for three weeks. the first day she trains 15 minutes and each day she trains 5 minutes more than the day before She constructs the sequence for the first week of training and determines the elements of the sequence and the type.
Answer:
20
Step-by-step explanation:
you add 15 and 5
Evaluate 49x - 2 when x = 1
Answer:
47
Step-by-step explanation:
49x - 2
==> plug in x = 1
49(1) - 2
==> multiply 49 and 1
49 - 2
==> subtract 2 from 49
= 47
Answer:
47
Step-by-step explanation:
49x means 49×x
So substituting 1 into the equation gives us :
(49×1)-2
49-2
47
Therefore our answer is 47.
Fill in the blank to make the fractions equivalent. 10/16 and /8 ?
Answer:
5 or 5/8
Step-by-step explanation:
To go from 10/16 to a bottom number/denominator of 8, you have to divide by 2.
Whatever you do to the top, you also do to the bottom, so you would divide 10, the numberator, by 2 to find the missing value.
10/2 is 5.
There is your answer.
