Answer:
The first term is 1
Step-by-step explanation:
The forward term to term rule is "multiply by 3 and add 1"
The backward rule is therefore
"subtract 1, then divide by three"
Apply the backward rule twice to go from 3rd to first term:
(13-1)/3 = 4
(4-1)/3 = 1
The first term is 1
Answer:
a_1 = 1
Step-by-step explanation:
your sequence is a_n = a_(n-1) * 3 + 1
if your 3rd one is 13 then:
a_3 = a_2 * 3 + 1 = (a_1 * 3 + 1) *3 + 1
13 = 9_a1 + 3 + 1
9 = 9*a_1
a_1 = 1 :)
Find the constant of proportionality (r) in the equation y = r x
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
help idk how to do these and its hard
Answer:
Hey there!
12^2+5^2=c^2
144+25=c^2
c=13
Let me know if this helps :)
Answer:
[tex]\Large \boxed{\mathrm{D) \ 13}}[/tex]
Step-by-step explanation:
[tex]\sf We \ can \ apply \ Pythagorean \ theorem.[/tex]
[tex]c=\sqrt{a^2 +b^2 }[/tex]
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex]c=\sqrt{5^2 +12^2 }[/tex]
[tex]\sf Evaluate.[/tex]
[tex]c=\sqrt{25+144}[/tex]
[tex]c=\sqrt{169}[/tex]
[tex]c=13[/tex]
Question 13 of 25
Which of the following is a correct name for a side of the given angle?
D
E
A. Point E
B. ED
C. DE
D. Point D
26.
What is the solution to. y - 9 > 4 + 2y?
HELP. answer if you can!
Answer:
y<−13
y−9>4+2y
Simplify both sides of the inequality
y−9>2y+4
Subtract 2y from both sides
y−9−2y>2y+4−2y
−y−9>4
Add 9 to both sides.
−y−9+9>4+9
−y>13
The divide both sides by -1
Answer:
[tex]\boxed{y < -13}[/tex]
Step-by-step explanation:
Hey there!
To solve for y we‘ll combine like terms and use the communicative property.
y - 9 > 4 + 2y
+9 to both sides
y > 13 + 2y
-2y to both sides
-y > 13
Divide -1 by both sides
y < -13
Hope this helps :)
Evaluate sin^-1 1/2 . Round your answer to the nearest hundredth.
Answer:
30.00Step-by-step explanation:
Given the expression [tex]sin^{-1} 1/2[/tex], the following steps must be taken to evaluate the expression.
[tex]Let\ y = sin^{-1}1/2[/tex]
[tex]y = sin^{-1} 0.5[/tex]
From the calculator, the value of y wil give;
[tex]y = 30\\\\y = 30.00 (to\ the \ nearest \ hundredth)[/tex]
Hence [tex]sin^{-1} 0.5 = 30.00[/tex].
Answer:
Step-by-step explanation:
The answer is 0.52
Hope that helped
Suppose that F(x) = x? and g(x) = -3x? Which statement best compares the
graph of G(x) with the graph of F(x)?
Answer:
flipped over the x-axis and stretched verticallyStep-by-step explanation:
Multiplying y by a value greater than 1 results in a vertical stretch. When the sign of it is negative there is a reflection over the x-axis. The appropriate choice is shown below.
__
The second attachment shows how the graph is flipped and stretched.
arav spent 1 3/4 hours in studies and 2 1/2 hours in playing cricket. how much time did he spent at all ??
Answer:
[tex] \boxed{4 \frac{1}{4} \: \: hours}[/tex]Step-by-step explanation:
Time spent in studies = [tex]1 \frac{3}{4} [/tex]
Time spent in playing cricket = [tex]2 \frac{1}{2} [/tex]
Now, let's find the hours that he spent at all:
[tex] \mathsf {1 \frac{3}{4} + 2 \frac{1}{2} }[/tex]
Convert mixed fraction into improper fraction
[tex] \mathsf{ = \frac{7}{4} + \frac{5}{2} }[/tex]
Take the LCM
[tex] \mathsf{ = \frac{7 + 5 \times 2}{4} }[/tex]
Multiply the numbers
[tex] \mathsf{ = \frac{7 + 10}{4} }[/tex]
Add the numbers
[tex] \mathsf{ = \frac{17}{4} }[/tex]
Convert the improper fraction into mixed fraction
[tex] \mathsf{ = 4 \frac{1}{4} }[/tex] hours
Hope I helped!
Best regards!
3.03 times 10^-3 in scientific nation
Answer:
3.03 • 10⁻³ is scientific notation
0.00303 is decimal form
11.Area of Triangle is 18 cm sq. and Sum of Base and Altitude is 12 cm. The Base and Altitude are:
(1 Point)
4 , 8 4 cm, 8 cm
8, 4 8cm, 4 cm
6 , 6 6 cm, 6 cm
10 , 2 10 cm, 2 cm
Answer:
base and altitude both are 6 cmand 6cm
Insert 2 sets of parentheses to make each sentence true: 2 x 14 – 9 – 17 – 14 = 7 (2 x 14) – 9 – (17 – 14) = 7 2 x (14 – 9) + (– 17 – 14) = 7 (2 x 14) – (9 – 17) – 14 = 7 2 x (14 – 9) – (17 – 14) = 7
Answer:
2 × (14 – 9) – (17 – 14) = 7
Step-by-step explanation:
Evaluate the choices to see which is true.
(2 x 14) – 9 – (17 – 14) = 7 ⇒ 28 -9 -3 ≠ 7
2 x (14 – 9) + (– 17 – 14) = 7 ⇒ 2(5) +(-31) ≠ 7
(2 x 14) – (9 – 17) – 14 = 7 ⇒ 28 -(-8) -14 ≠ 7
2 x (14 – 9) – (17 – 14) = 7 ⇒ 2(5)- 3 = 7 . . . . true
2. A curve has equation y = x2 – 2x - 3. A point moves along the curve in such a way that at P
the y coordinate is increasing at 4 units per second and the x coordinate is increasing at 6
units per second. Find the x coordinate of P.
[3]
Answer:
The x coordinate of P is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:
[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]
According to the statement of the problem, these variables are known:
[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]
Hence, the x coordinate of P is found by direct substitution:
[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]
[tex]4 = 12\cdot x -12[/tex]
[tex]x = \frac{4}{3}[/tex]
The x coordinate of P is [tex]\frac{4}{3}[/tex].
Dimitri and Jillian were trying to solve the equation:(x+1)(x+3)=12(x+1)(x+3)=12(x+1)(x+3)=12left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, plus, 3, right parenthesis, equals, 12Dimitri said, "The left-hand side is factored, so I'll use the zero product property."Jillian said, "I'll multiply (x+1)(x+3)(x+1)(x+3)(x+1)(x+3)left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, plus, 3, right parenthesis and rewrite the equation as x2+4x+3=12x^2+4x+3=12x2+4x+3=12x, squared, plus, 4, x, plus, 3, equals, 12. Then I'll solve using the quadratic formula with a=1a=1a=1a, equals, 1, b=4b=4b=4b, equals, 4, and c=3c=3c=3c, equals, 3.Whose solution strategy would work?Choose 1 answer:Choose 1 answer:(Choice A)AOnly Dimitri's(Choice B)BOnly Jillian's(Choice C)CBoth(Choice D)DNeither
Answer:
D. NeitherStep-by-step explanation:
The equation that Dimitri and Jillian were trying to solve is expressed as
(x+1)(x+3) = 12. They are both solving this equation to get the value of x.
Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;
Step 1: Multiply out the expression (x+1)(x+3)
= (x+1)(x+3)
= x(x)+ 3x+x+1(3)
= x² + 3x + x + 3
= x² + 4x + 3
He got x² + 4x + 3 on expansion
Step 2: He should have rewrote the equation as shown;
x² + 4x + 3 = 12
x² + 4x + 3 -12 = 0
x² + 4x -9 = 0
Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9
x = (-b±√b²-4ac)/2a
x = (-4±√(4)²-4(1)(-9))/2(1)
x = -4±√16+36/2
x = (-4±2√13)/2
x = (-4+2√13)/2 or (-4-2√13)/2
x = -2+√13 or -2-√13
Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.
earth is 93 million miles from the sun, while mars is 142 million miles from the sun. Theoretically, what is the closest distance mars could be to earth
Answer:
169.74
Step-by-step explanation:
this problem is like a triangle, the sun, mars, and earth are the three points, so you just use a^2 + b^2 = c^2 so basically
93^2 + 142^2 = c^2
8649 + 20164 = 28813
28813 square root = 169.74
Use the concept of slope to find t such that the three points are collinear. (-8,5) (0,t) (2,-1)
Answer:
t = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Since the points are collinear they lie on the same line.
Thus the slopes between any of the 3 points are equal.
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (2, - 1)
m = [tex]\frac{-1-5}{2+8}[/tex] = [tex]\frac{-6}{10}[/tex] = - [tex]\frac{3}{5}[/tex]
Repeat using
(x₁, y₁ ) = (- 8, 5 ) and (x₂, y₂ ) = (0, t) and equate to previous m
m = [tex]\frac{t-5}{0+8}[/tex] = [tex]\frac{t-5}{8}[/tex] = - [tex]\frac{3}{5}[/tex] ( cross- multiply )
5(t - 5) = - 24 , that is
5t - 25 = - 24 ( add 25 to both sides )
5t = 1 ( divide both sides by 5 )
t = [tex]\frac{1}{5}[/tex]
What is the recursive definition for 25,20,15,10?
Answer:
aₙ = 30 - 5n
Step-by-step explanation:
25,20,15,10, ...
We see from the given series that it is AP with:
First term = 25Common difference = -5 and it is decreasing seriesThen formula is:
aₙ= a₁ + (n-1)daₙ= 25 + (n-1)(-5) aₙ= 25 - 5n + 5aₙ = 30 - 5nWhich inequality represents the following situation ; times 5 less than a number is no more than 272
0
A 3(x - 5) = 27
B. {x-5527
C 3 (5 – ) 2 27
D.(x - 5) 27
Answer:
A.
Step-by-step explanation:
from what the question states im assuming it was 3 times 5 less than a number is no more than 272.
if we look at a it fits it perfectly.
3 times 5 less than a number is no more than 272 =
3(x-5) = 272.
Hope it helps <3
HELP HELP HELP Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. How
long will it take if they paint the room together? I’m not sure if it’s 1.4
Answer:
2 hrs, 24 min
Step-by-step explanation:
Sally: in one hour, she can paint 1/4 of the room.
Joe: in one our, he can paint 1/6 of the room
Hour one: 1/4+1/6=3/12+2/12=5/12
1÷5/12=1*12/5=12/5
12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes
Answer: 2.4 hours
Step-by-step explanation:
1/4 1/6
LCM
3/12+2/12=5/12 repricical 12/5 =2.4
10201 soldiers have queued up for an attack such that the number of queues is equal to number of the soldiers in each queue. Find number of soldiers in queue.
Answer:
101
Step-by-step explanation:
Given the following :
Number of soldiers = 10201
They are queued such that the number of queues = number of soldiers in each queue
Let number of queues = q
Therefore, if number of queues equals number of soldiers per Q,
Then ;
q × q = 10201
q^2 = 10201
Take the square root of both sides
q = √10201
q = 101
Number of soldiers per queues = 101
In the first quadrant you start at 5, 6 and move 4 units down. What point will you end up at? Thanks for your help! - Someone who's better at English than math
Answer:
(5, 2)
Step-by-step explanation:
(5, 6) go down 4 units means subtract 4 from the y
(5, 2)
The point to end up will be (5, 2).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the first quadrant you start at (5, 6 ) and move 4 units down.
Now,
Since, In the first quadrant you start at 5, 6 and move 4 units down.
Hence, The end up point = (5, 6 - 4)
= (5, 2)
Thus, The point to end up will be (5, 2).
Learn more about the coordinate visit:
https://brainly.com/question/18269861
#SPJ5
A car is traveling on a highway. The distance (in miles) from its destination and the time (in hours) is given by the equation d = 420 minus 65 t. What is the practical meaning of the d-intercept? a. Initially the car is 355 miles from its destination. b. Initially the car is 420 miles from its destination. c. Initially the car is 65 miles from its destination. d. Initially the car is 485 miles from its destination.
Answer:
the correct answer is b. Initially the car is 420 miles from its destination.
Step-by-step explanation:
1)A cylindrical container has a diameter of 14cm and a height of 20cm and is full of water. A student pours the water into another cylinder of diameter 20cm. How deep is the water in the second cylinder?
2)A cylindrical water tank is 70cm in diameter. To begin with, it is full of water. A leak starts at the bottom so that it loses 10l of water every hour. How long will it take for the water level to fall by 20cm?
3) A cylindrical storage vessel is 4m in diameter and 31/2m deep. How many kilolitres will it hold?
1) 9.8 cm
3) 194.68 kilo litters
Step By Step Explanation
Sister these questions are related to volume of cylinder.
You need to use this formula πr²h [ Where r is radius and h is height or depth]
_______________________________________
3)
Given:
Diameter = 4m
Therefore radius = 2m
Depth is 31/2 m
To Find:
How many kilo litters will it hold ?
Actually It's asking about Volume.
Solution:
You know, volume = πr²h
[tex] = \pi {(2 \: m)}^{2} \times ( \dfrac{31}{2})m[/tex]
[tex] = 3.14 \times 4 \: {m}^{2} \times \dfrac{31}{2} m[/tex]
[tex] = \: 62 \times 3.14 \times {m}^{3} \sf [\because \: {m}^{3} = kilolitters][/tex]
[tex] = \sf 194.68 \: \: kilolitters[/tex]
_______________________________________
1)
Given:
Diameter = 14 cm
[tex] \sf \therefore \: radius \: = 7 \: cm[/tex]
height = 20 cm
Diameter of other cylinder = 20 cm
[tex] \sf \therefore \: radius = 10 \: cm[/tex]
To Find:
Deep of water in other cylinder
Consider the depth of water be x
Solution:
Volume of water will remain constant in both
So,
[tex]V_1 = V_2[/tex]
[tex] \sf \: \pi {(r_1)}^{2} h_1 = \pi {( r_2 )}^{2} h_2[/tex]
[Eliminating π from both sides]
[tex] {(7)}^{2} \times 20= {(10)}^{2}x[/tex]
[tex]49 \times 20 = 100x [/tex]
[tex]x = \dfrac{49 \times 2}{10} [/tex]
[tex]x = \dfrac{98}{10} \implies \: 9.8[/tex]
Therefore the required value of x is 9.8 cm .
2c+17.6 =6 / 4 SOLVE give your answer as a decimal get brainly
Answer:
-8.05
Step-by-step explanation:
In order to solve for C you first have to subtract 17.6 from both sides.
2c=(6/4)-17.6
6/4 is 1.5
1.5-17.6=-16.1
2c=-16.1
c=-8.05
Answer:
1.5
Step-by-step explanation:
2c+17.6=6/4
2c+176/10=6/4
2c+88/5=6/4
2c=6/4-88/5
2c=30-352/20
2c=-322/20
2c=-161/10
c=-8.05
Proof:
2c+17.6=6/4
2(-8.05)+17.6=6/4
-16.1+17.6=6/4
1.5=1.5
Hope this helps ;) ❤❤❤
1/2x-(x-2/3a)+1/4a please help me im so confused!
The bottom of the swimming pool seem to be raised 3m above with water of refractive index 4/3. The depth of water is:
A. 12m
B. 29m
C. 4m
D. 6m
(will mark the brainliest with explanation)
3kg of rump steak costs £42 adel buys 4kg of rump steak work out how much adel pays
Answer:
The answer is £ 56Step-by-step explanation:
In order to find the amount Adel paid we use ratio and proportion
3kg of rump steak = £ 42
Therefore
4kg of rump steak = [tex] \frac{4 \times 42}{3} [/tex]
We have the final answer as
£ 56Hope this helps you
Answer:
£56
Step-by-step explanation:
since 3kg costs £42
1kg will be £42/3 which will be equal to £14
4kg will cost £14×4 which will be £56
Will Give Brainliest, answer ASAP x=
y=
Answer:
x = 21.25 , y = 5
Step-by-step explanation:
In a parallelogram
Consecutive angles are supplementary
Opposite angles are congruent, thus
125 + 4x - 30 = 180
4x + 95 = 180 ( subtract 95 from both sides )
4x = 85 ( divide both sides by 4 )
x = 21.25
8y² = 125 ( divide both sides by 5 )
y² = 25 ( take the square root of both sides )
y = [tex]\sqrt{25}[/tex] = 5
2) In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%. I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated. 3) If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastag
Answer:
Weight of wastage=179.775kg
weight of rice cultivated= 585.225 kg
percentage of rice cultivated=76.5%
Step-by-step explanation:
Area of land=100 square meters
Cultivated rice=765kg
Wastage=23.5%
1) Weight of the wastage=23.5% of 765kg
=23.5/100 × 765
=17977.5 / 100
=179.775 kg
2) Weight and percentage of rice cultivated.
weight of rice cultivated = 765 kg - 179. 775 kg
= 585.225 kg
percentage of rice cultivated = 100 - 23.5
= 76.5%
3) if area is increased 40 times in size
New area=1000 square meters × 40
=40,000 square meters
Cultivated rice= 765kg × 40
=30,600 kg
Cultivated rice excluding wastage=585.225 kg × 40
=23,409 kg
Plz help ASAP ill give brainliest What is 600 square
Answer:
360,000
Step-by-step explanation:
When you square something you multiply it by itself. With that in mind, 600 square or 600^2 would be 600x600 which equals 360,000. Please mark as brainliest.
Given the following angles, what ray is the common side of ZCFD and ZDFE?
D
E
0
Ray FD
Ray FE
Ray FC
Answer:
ray df or ray fd because both of these letters are consecutive in both of the angles.
Step-by-step explanation:
Answer:
Answer is Ray FD
Step-by-step explanation:
Given the following angles, what ray is the common side of ∠CFD and ∠DFE?
A. Ray FC
B. Ray FE
C. Ray FD
Work out the mean for the data set below: 3, 5, 4, 3, 5, 6 Give your answer as a fraction. answer
Answer:
4 1/3
Step-by-step explanation:
3 + 5 + 4 + 3 + 5 + 6 = 26
26/6 = 4 2/6 (4 1/3)
Answer:
13/3
Step-by-step explanation:
To find the mean, add up all the numbers and divide by the number of terms
( 3+5+4+3+5+6) /6
26/6
Divide top and bottom by 2 to simplify the fraction
13/3
