The recursive formula
[tex] a_n = 2a_{n-1}+5 [/tex]
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
[tex] a_2 = 2\cdot 5+5 = 10+5 = 15 [/tex]
Next, we will double 15 and add 5:
[tex] a_3 = 2\cdot 15 + 5 = 30+5 = 35 [/tex]
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
[tex] a_4 = 2\cdot 35 + 5 = 70+5 = 75 [/tex]
Which confirms option B
if x equals 8 and y equals 0 are the lines perpendicular? Yes or no?
Answer:
yes it's perpendicular line
Step-by-step explanation:
In triangle $ABC$, let angle bisectors $BD$ and $CE$ intersect at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 17$, $AC = 24$, and $BC = 33$, then find the perimeter of triangle $AMN$.
Thanks!
Answer:
41
Step-by-step explanation:
If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:
... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC
.. = 17+24 = 41
_____
Wow! Thank you for an interesting question with a not-so-obvious answer.
_____
A little more detail
The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.
If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...
... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths
For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.
The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.
Putting these ratios and perimeters together, we get ...
... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s
... = (2/(BC) -1/s) × BC × s = 2s -BC
... perimeter ΔAMN = AB +AC
The perimeter of triangle AMN is found using the angle bisector theorem to determine the lengths of AM and AN, and recognizing that MN = BC due to the parallelism. After calculating, the approximate perimeter of triangle AMN is found to be 54.86.
In triangle ABC, the angle bisectors BD and CE intersect at I. A line through I parallel to BC intersects AB at M and AC at N. Perimeter of triangle AMN is found by adding lengths AM, MN, and NA. Since IM is parallel to BC and bisectors divide the angles proportionally, we have:
AM/AB = AI/AD, where D is the intersection of angle bisector BD with BC.
AN/AC = AI/AD, using similar logic.
MN is parallel to BC, so MN = BC due to the properties of parallelograms.
Using AB = 17, AC = 24, and BC = 33, find AM and AN using the proportional segments:
AM = (AI/AD) * AB
AN = (AI/AD) * AC
The perimeter of triangle AMN is AM + MN + AN.
To solve for AI/AD, we use the angle bisector theorem which gives us AI/AD = AB/BC = 17/33. Substituting this into the equations for AM and AN we get:
AM = (17/33) * 17
AN = (17/33) * 24
Computing these we find:
AM = 8.77 (approximately)
AN = 13.09 (approximately)
Lastly, we add AM, AN, and BC to find the perimeter:
Perimeter = AM + AN + MN
Perimeter = 8.77 + 13.09 + 33 = 54.86 (approximately)
This is the approximate perimeter of triangle AMN.
kevin has $26 wants to rent bicycle.The bicycle rents for $6.25per hour. How many hours can kevin ride without owing more money than he has.
Answer:
I got 4 hours and 16 minutes
Step-by-step explanation:
I divided the amount of money he has ($26) to the amount it takes to rent for one hour ($6.25). To make it more simple you could just say 4 hours worth of rent.
Answer:
Step-by-step explanation:
Since Kevin only has $26 and the bicycle rends for $6.25 per hours this means that:
6.25h ≤ 26
Where h represents hours $6.25 is the slope (rate) at which Kevin is being charged and $26 is the amount of money he has.
By solving for the inequality above we obtain:
[tex]6.25h\leq 26\\\\\fra{6.25h}{6.25}\leq \frac{26}{6.25}\\\\h\leq4.16[/tex]
This means that Kevin can ride the bike for less than or equal to 4.16 hours. Now that means 4 hours and 16% of an hour, let's calculate what 16% of an hour is equal to. Since we know that there are 60 minutes in an hour and 16% is 0.16 (since 16÷100=0.16) in decimals we obtain:
60×0.16=9.6 minutes
This means 9 minutes and 60% of a minute, so we will calculate how much is 60% of a minute:
60×.6=36 seconds
Therefore, Kevin can ride this bike for less than or equal to 4 hours 9 minutes and 36 seconds.
~~~Brainliest is appreciated~~~
Given: KLMN is a trapezoid, KL=MN,
AB
is a midsegment,
A F=2, FB=5, MN=6
Find: m∠N, m∠K, m∠L, and m∠M
∠K = ∠N = 60°
∠L = ∠M = 120°
Step-by-step explanation:In the attached, we have renamed F to G so Brainly will let us talk about it more easily. We have also added altitude MX.
AG is also a midsegment of ΔKLM, so LM = 2×AG = 4. Then ...
... NX = AB - LM = 7 -4 = 3
and we have right ΔMXN with hypotenuse 6 and leg 3. This is recognizable as a 30°-60°-90° triangle, with the 60° angle at N.
The angle at M is supplementary to that at N (because LM ║ KN), so measures 120°
The trapezoid is isosceles, so angles K and L have the same measures as angles N and M.
PLS HELP FAST! will mark brainlyst
Answer: The correct answer would be D: Model J
Step-by-step explanation:
For there are 3 segments in each box and 3 boxes are shaded leaving only 2 unshaded :)
Answer:
D. Model J
Step-by-step explanation:
What is 8 3/4% expressed as a fraction?
8/100
7/80
7/40
8/25
Final answer:
To convert 8 3/4% to a fraction, you transform the mixed number into an improper fraction, which equals 875%. Then, scale it by dividing by 100 to get 8.75%, and express this as 8.75/100. Simplify by dividing numerator and denominator by 25 to finally get 7/16.
Explanation:
To express 8 3/4% as a fraction, we first convert the mixed number to an improper fraction. There are 4 quarters in a whole, so 8 3/4 is the same as 8 + 3/4, which equals 35/4. To convert this into a percent, we need to consider that 1 whole is the same as 100%, so 35/4 as a percent is 35/4 * 100%. Simplifying this, we multiply 35 by 25 (100% divided by 4), which gives us 875%. Since we want to express 8 3/4%, not 800 3/4%, we divide by 100 to get back to the correct scale. So, 875% divided by 100 is 8.75%, which is the same as 8 3/4%.
Now, to convert 8.75% to a fraction, we can write it as 8.75/100. To simplify this fraction, we recognize that both the numerator and the denominator are divisible by 25. Dividing both by 25, we get 7/4 divided by 1 which simplifies to 7/4 divided by 100/25. This simplifies to 7/4 * 25/100, which equals 7/16 when simplified.
Thus, 8 3/4% as a fraction is 7/16.
Lucien is going to move to a new house he needs to figure out how much each packing box will hold which formula can lucien use to figure out how much the box will hold h=40cm w=45cm l=70 cm NEED HELP PLEASE QUICK GOOD AMOUNT OF POINTS!!!!!!!!!!
That would the answers be for this question
[tex]\mathsf{We\;know\;that : \dfrac{a^m}{a^n} = a^m^-^n}[/tex]
[tex]\mathsf{Given : \dfrac{3^-^8}{3^-^4}}[/tex]
[tex]\mathsf{\implies 3^-^8^+^4}[/tex]
[tex]\mathsf{\implies 3^-^4}[/tex]
[tex]\mathsf{\implies \dfrac{1}{3^4}}[/tex]
[tex]\mathsf{So,\;The\;Given\;Expression\;can\;be\;written\;as : 3^-^4\;(or)\; \dfrac{1}{3^4}}[/tex]
Rhombus ADEF is inscribed in △ABC such that the vertices D, E, and F lie on the sides AB , BC , and AC respectively. Find the side of the rhombus if AB=7 cm, BC=5 cm, and AC=8 cm.
3 11/15 cm
Step-by-step explanation:AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:
... BE:CE = BA:CA = 7:8
Then ...
... BE:BC = 7 : (7+8) = 7:15
ΔDBE ~ ΔABC, so DE = 7/15 × AC
... DE = 7/15 × 8 cm = (56/15) cm
... DE = 3 11/15 cm
To find the side of the inscribed rhombus, we can use the Pythagorean theorem and the properties of inscribed rhombuses.
Explanation:To find the side of the rhombus, we need to understand the properties of inscribed rhombuses. In an inscribed rhombus, the diagonals are perpendicular bisectors of each other.
Let's label the side of the rhombus as 's'.
Using the given information, we can see that AB and AC are the diagonals of the rhombus.
Since AB = 7 cm and AC = 8 cm, we know that the diagonals bisect each other and form right angles.
Therefore, we can use the Pythagorean theorem to find the side of the rhombus:
s^2 = (AB/2)^2 + (AC/2)^2
s^2 = (7/2)^2 + (8/2)^2
s^2 = (49/4) + (64/4)
s^2 = (113/4)
s = sqrt(113/4)
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm. What are the lengths of the sides of a similar triangle that has a perimeter of 26 cm ?
6 cm, 8 cm, 12 cm
Step-by-step explanation:The perimeter of the reference triangle is ...
... (15 +20 +30) cm = 65 cm
Then the similar triangle has a scale factor of ...
... (26 cm)/(65 cm) = 2/5
Multiplying the side lengths of the reference triangle by 2/5, we get ...
... {15 cm, 20 cm, 30 cm) × 2/5 = {6 cm, 8 cm, 12 cm}
These are the side lengths of the smaller similar triangle. (Check: their sum is 26 cm.)
the graph of a square root function has a domain of (0, infinify ) and range of [1, infinity) explain how the given range of the function can help you to the maximum of minimum y-value of the function? HELP
The range is [minimum y-value, maximum y-value), so the range expression tells you directly what those values are.
For the function described, with range [1, ∞), ...
... minimum y-value = 1
... maximum y-value = infinity
find the missing lenghts of the sides
Answer:
See attached picture
Step-by-step explanation:
The ratios of sides in a 30°-60°-90° triangle are ...
... 1 : √3 : 2
Multiplying these ratio units by 3 inches, we get the side lengths to be ...
... 3 in : 3√3 in : 6 in
Thus, a = 3 in; b = 3√3 in.
_____
Alternate solution
Or, you can work from your memorized values of the trig functions of 30° and 60°.
... sin(30°) = a/(6 in) = 1/2 . . ⇒ . . a = (1/2)·6 in = 3 in
... cos(30°) = b/(6 in) = (√3)/2 . . ⇒ . . b = (√3)/2·6 in = 3√3 in
Residents of three counties were polled to find the percentage of residents who are Republican or Democrat. Find the following relative frequencies to the nearest tenth of a percent.
Answer:
Republican residents of County 1:
10.1 %
Democratic residents of County 1:
16.5 %
Total Republican residents:
58.9 %
Total Democratic residents:
41.1 %
Step-by-step explanation:
Answer:
Question 1)
Republican residents of County 1: (10.1)
Question 2)
Democratic residents of County 1: (16.5)
Question 3)
Total Republican residents: (58.9)
Question 4)
Total Democratic residents: (41.1)
Help! will give points for brainliest
The ordered pairs model an exponential decay function.
{(−1,30), (0,21), (1,14.7), (2,10.29)}
What is the function equation?
y = 21·0.7^x
Step-by-step explanation:The pair (0, 21) tells you the multiplier is 21. (The exponential factor is 1 for x=0.)
Any adjacent pair of y-values can tell you the common ratio, hence the base of the exponential term. For example, using the y-values associated with x=0 and x=1, we find the base to be ...
... 14.7/21 = 0.7
Then the equation is ...
... y = multiplier · base^x
... y = 21·0.7^x
2x 2 - 4x + 6 = 0 is in general form.
2x² - 4x + 6 = 0 /:2
x²-2x+3=0
Δ=(-2)²-4·1·3=4-12=-8<0
x∈∅
False. A, B, and C does not have a greatest common factor of 1 which means this ewuation is not in general form.
If (2−√3) is a root of a polynomial with integer coefficients, which of the following must be another root?
2√3
√3−2
2+√3
3−√2
Answer:
2+√3
Step-by-step explanation:
We know that roots with square roots come in pairs
so if we have a+ sqrt(b), we will also have a - sqrt(b)
Since one of the roots is 2 -sqrt(3), it must have another root of 2+ sqrt(3)
The conjugate of the root (2-√3) for a polynomial with integer coefficients is (2+√3), which must also be a root of the polynomial.
If (2-√3) is a root of a polynomial with integer coefficients, then by the Conjugate Root Theorem (which is a consequence of the Complex Conjugate Root Theorem), if the polynomial has real coefficients and a non-real root, then its complex conjugate must also be a root. However, since √3 is a real number and our expression involves only real numbers, in this context, we look for the conjugate in terms of radicals. Thus, the conjugate of (2-√3) would be (2+√3), which must also be a root of the polynomial.
The other options given, such as 2√3, √3-2, and 3-√2, do not satisfy the criteria of being the conjugate of (2-√3). They might be roots of some polynomial, but without the constraint of integer coefficients or known conjugate pairs, we cannot confirm that.
A ladder leaning against a wall makes a 60o angle with the ground. The base of the ladder is 4 m from the building. How high above the ground is the top of the ladder?
(04.01 LC)
Of the following sets, which represents a function? (1 point)
Situation A = {student's name, the student's favorite color}
Situation B = {student's name, the student's favorite math teacher}
Select one:
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
thx
c. Both A and B
Step-by-step explanation:A function is a mapping that maps each element of its domain (student's name) to exactly one element of its co-domain (favorite ...). Assuming student names are unique and the notion of "favorite" is exclusive (can't have two or more "favorites" of the same type), then both A and B describe mappings that are functions.
Answer:
c. Both A and B
Step-by-step explanation:
A function means each input goes to only one output. As long as each student is only entered once, and they only have one favorite color and one favorite math teacher, then A and B are functions.
Together, Kyle and Tyler traveled 425 miles to the beach. If Kyle traveled 240 miles, how far did Tyler travel? A) 2x = 425 B) x + 240 = 425 C) x − 240 = 425 D) x − 425 = 240
Answer:
b.) and Kyle traveled 185 miles
Step-by-step explanation:
x+240=425
-240 -240
x=185
The question is about simple subtraction in mathematics. Given that Kyle and Tyler together traveled 425 miles and Kyle traveled 240 miles, we use subtraction to find out that Tyler traveled 185 miles.
Explanation:This is a classic problem of simple subtraction in mathematics. Given, Kyle and Tyler together traveled 425 miles. Now, if Kyle traveled 240 miles, Tyler must have covered the remaining distance. So, to find out how far Tyler traveled, subtract the distance that Kyle traveled from the total distance. This is represented by the equation (option B) x + 240 = 425, where x represents the distance that Tyler traveled. Solving this equation for x will give you the answer.
Setup the equation: x + 240 = 425
Subtract 240 from both sides: x = 425 - 240
This results in x = 185, meaning Tyler traveled 185 miles.
Learn more about Distance calculation here:https://brainly.com/question/34212393#SPJ2Agora chess club has 16 members and gains a new memeber every month. The key club has 4 members and gains 4 new members every month. How many months will it take for the clubs to have the same amount of members
Answer:
4 months and you can check for yourself by plugin in 4 in both equations (e.g. 1(4)+16=4(4)+4
Step-by-step explanation:
To do this: Agora = 1x+16
Key Club = 4x+4
1x+16=4x+4
1x+12=4x
12=3x
4=x
Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Three are jelly-filled, 8 are lemon-filled, and 13 are custard-filled. You randomly select one donut, eat it, and select another donut. Find the probability of selecting two jelly-filled donuts in a row.
Answer:
1/92
Step-by-step explanation:
There are C(3, 2) = 3 ways to select 2 jelly-filled donuts from the 3 in the box. There are C(24, 2) = 276 ways to select 2 donuts from the box.
The probability that you will select 2 jelly-filled donuts is ...
... 3/276 = 1/92
_____
C(n, k) = n!/(k!(n-k)!)
C(3, 2) = (3·2)/2 = 3
C(24, 2) = (24·23)/2 = 276
is 17.125 the same as 17 1/4
Answer:
No it is not.
Step-by-step explanation:
What is 9.36•10~4 in standard form
[tex]9.36\cdot10^4=9.36\cdot10,000=93,600[/tex]
find thevmissing value. please
Finding the missing value in mathematics usually involves solving an equation. The process can vary depending on whether the problem involves algebra, geometry or another mathematical principle.
Explanation:In mathematics, finding the missing value typically involves solving an equation where a variable represents the unknown, or missing, value. The task requires understanding of the mathematical principle being applied. For example, if you have an equation like 2x = 10, you can solve for the missing value (x) by dividing both sides of the equation by 2, which gives x = 5. If the problem involves a geometric figure, understanding the relevant formulas for area, volume, perimeters, etc. is key.
Learn more about missing value here:https://brainly.com/question/31952467
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The radius of a circular ring is 4 feet. What is the circumference?
A. 12.15 feet
B. 12.56 feet
C. 30.43 feet
D. 25.12 feet
The radius of a circular ring is 4 feet. What is the circumference?
Answer: D.) 25.12 feet
Step-by-step explanation:
We apply the formula to calculate the circumference knowing the radius. We consider π = 3.14
C = 2 x π x Radius = 2 x 3.14 x 4 feet = 25.12 feet
Answer : D.) 25.12 feet
[tex]\textit{\textbf{Spymore}}[/tex]
The circumference of the circle is 25.12 feet.
The radius of a circular ring is 4 feet.
We have to determine the circumference
We apply the formula to calculate the circumference by knowing the radius.
We consider π = 3.14
What is the formula for the circumference of the circle?
C = 2 x π x Radius
use the given values in the above formula so we get,
C= 2 x 3.14 x 4 feet
C= 25.12 feet
Therefore option D is correct.
The circumference of the circle is 25.12 feet.
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In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=x2−16 , and CE=6x . What is AC ?
The answer is 96.
Answer:
The answer is 96 when X= 8
Step-by-step explanation:
We have given that :
AE= [tex]x^2-16[/tex] and CE=[tex]6x[/tex]
where AE and CE are the diagonals of the paralleogram
The diagonals of parallelogram bisect each other therefore,
[tex]x^2-16 = 6x[/tex]
⇒ [tex]x^2-6x-16=0[/tex]
factors are (x+2)(x-8)=0
setting to each factor 0 the value of x= -2 or x= 8
therefore, two values of AC is
X= -2 ,AC= 2([tex]x^2-16[/tex])=2(-12)=-24
X= 8 ,AC= 2([tex]x^2-16[/tex])=2(48)=96
The answer is 96 when X= 8
find the scale factor please.
Answer:
5/2
Step-by-step explanation:
The scale factor for linear measures, such as perimeter, is the square root of the scale factor for areas. The ratio of larger area to smaller is ...
... 75/12 = 25/4
so the ratio of the larger perimeter to the smaller is ...
... √(25/4) = 5/2
math help 20 points
help
Answer:
1. x =8
2. x=9
Step-by-step explanation:
Since these figures are parallelograms, the opposite sides are equal.
1. 6 = 2x-10
Add 10 to each side
6+10 = 2x-10+10
16 = 2x
Divide each side by 2
16/2 = 2x/2
8 =x
2. x+14 =23
Subtract 14 from each side
x+14-14 = 23-14
x = 9
Which equation is equivalent to y=23x−6?
A. 2x + 3y = −6
B. 3x − 2y = 6
C. 3x − 2y = 12
D. 2x − 3y = 18
D. 2x -3y = 18
Step-by-step explanation:Multiply by 3, then rearrange.
... y = 2/3x -6
... 3y = 2x -18 . . . . . multiply by 3
... 0 = 2x -3y -18 . . . subtract 3y
... 18 = 2x -3y . . . . . add 18
... 2x - 3y - 18 . . . . . swap sides to match the form of the answers
Rohit drove around the city for 3 hours. He traveled a total distance of 75 miles. What was Rohit's average speed?
Answer:
25
Step-by-step explanation:
You must divide 75/3. This is because for every 3 hours, there is a distace of 75 miles. You have to find out his average speed by finding his distance each hour. 75/3 is 25.
Answer: The average speed of Rohit is 25 miles per hour.
Step-by-step explanation: Given that Rohit drove around the city for 3 hours and he traveled a total distance of 75 miles.
We are to find Rohit's average speed.
We know that
[tex]speed =\dfrac{distance}{time}.[/tex]
For the given situation, we have
distance, d = 75 miles and time, t = 3 hours.
So, the average speed of Rohit is given by
[tex]S=\dfrac{d}{t}=\dfrac{75}{3}=25.[/tex]
Thus, the average speed of Rohit is 25 miles per hour.