Step-by-step explanation:
For the 1st picture,
The 2nd option is the answer.
Let say we have
[tex] a_{3}[/tex]
Replace it into the recursive formula.
[tex] a_{3} = a_{3 - 2} + (a) _{3 - 1}[/tex]
We are given a,1 and a,2 so the 3rd terms has to be
[tex]2[/tex]
So the second option is the answer.
For the second picture, a geometric sequence is a group of terms that has the same ratio between each consecutively.
Infinite means going on forever
The fourth option is the answer.
Answer:
1,1,2,3,5
part #2 none are exactly correct... the terms go on forever, so 1 &2 are out...
the "difference" is definitely not the same, so three is out..
4 is the closest, but the ratio is not the same, there is a trend in the ratio..
this is the Fibonacci sequence, and the ratio trends toward the "golden ratio" ( φ -phi) but never is exactly φ because φ is irrational
Step-by-step explanation:
Need help on this activity!!
In this activity, you will rearrange and solve a rational equation and find and use the inverse of a rational equation.
As we’ve seen, for a circuit with two resistors arranged in parallel, we can calculate the total resistance in the circuit, , in ohms, with this equation.
Question 1
Part A
Question
Rewrite the equation to represent the resistance of resistor 2, , in terms of and .
Answer:
My best guess rn is the first option
Step-by-step explanation:
the last dude had it close but it was basically flipped as you can tell.
The answer is (C) [tex]R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
We need to make [tex]R_2[/tex] the subject of the formula [tex]R_T=\frac{R_1R_2}{R_1+R_2}[/tex]
First remove the denominator by multiplying both sides by the binomial [tex](R_1+R_2)[/tex]
[tex]R_T\times (R_1+R_2)=\frac{R_1R_2}{R_1+R_2}\times(R_1+R_2)\\\\R_TR_1+R_TR_2=R_1R_2[/tex]
Arrange all terms containing [tex]R_2[/tex] on one side
[tex]R_1R_2-R_TR_2=R_TR_1[/tex]
Factor out [tex]R_2[/tex] from the LHS
[tex]R_2(R_1-R_T)=R_TR_1[/tex]
Finally, divide both sides by the binomial [tex](R_1-R_T)[/tex] to leave [tex]R_2[/tex]
[tex]R_2(R_1-R_T)\times\frac{1}{(R_1-R_T)}=R_TR_1\times\frac{1}{(R_1-R_T)}\\\\R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
Learn more about change of subject of formula here: https://brainly.com/question/343660
looking for the equation, slope, and y-intercept of: (1,-3) and (0,-1)
Answer:
Equation: y = -2x - 1
Slope: -2
Y intercept: -1
Step-by-step explanation:
First, find the slope using rise over run, (y2 - y1) / (x2 - x1):
(y2 - y1) / (x2 - x1)
(-1 + 3) / (0 - 1)
2 / -1
= -2
So, the slope is -2. Plug this and a point into slope intercept form, y = mx + b, and solve for b:
y = mx + b
-1 = -2(0) + b
-1 = 0 + b
-1 = b
So, the y intercept is -1. Create the equation by plugging in the slope and b into y = mx + b:
y = mx + b
y = -2x - 1
The equation of the line is y = -2x - 1.
Answer: y=-2x-1. Slope is -2 and y int. is -1.
Step-by-step explanation:
First, you need to find the slope by using the slope formula y2-y1/x2-x1. Plug in the x and y coordinates, which simplifies as -1-(-3)/0-1, and furthermore to 2/-1, or -2. The y intercept can be found by the second point, (0,-1). Therefore, the y int. is -1.
If an = 2n - 8, then which one is not a term of the sequence? ( an means nth term)
a) 13
b) 16
c) 204
d) 198
Answer:
13 is answer
Step-by-step explanation:
hope it helps
Can someone plz help with this problem
Answer:
I think the answer is 2
Step-by-step explanation:
Between 30 and 60 is double b so just divide 4 by 2.
The function (1) describes the height, in feet, of an object at time, in seconds, when it is launched upward from the ground at an initial speed of 112 feet per second.
a. Find the domain.
b. What does the domain mean in this context?
Answer:
see below
Step-by-step explanation:
The domain is the values that the input takes
The values go from 0 to 7
0≤x≤7
This is the time from the initial launch until the object hits the ground
Rewrite
4/10 : 1/25 as a unit rate.
A: 10:1
B: 25:4
C: 2:125
D: 100:1
Answer:
4/10 : 1/25
4/10 / 1/25 = 4/10 x 25/1 = 100/10 = 10.
10 can also be written as 10:1, so A is correct.
Hope this helps!
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
the area of a trapezoid is 21 inches, one of its bases is 8 inches and its height is 3 inches. What is the length of the last base?
Answer:
6 inches
Step-by-step explanation:
A=b1+b2/2*h
Fill in the equation with what we know
21=8+x/2*3
Isolate x
Quick steps: 21/3=7*2=14-8=6
x=6
PLEASE HELP PLEASE!!!! AB←→||CD←→ . Find the measure of ∠BFG.
Answer:
BFG = 135
Step-by-step explanation:
The angles are alternate interior angles and alternate interior angles are equal when the lines are parallel
3x+15 = 5x-5
Subtract 3x from each side
3x+15-3x = 5x-5-3x
15 = 2x-5
Add 5 to each side
15+5 = 2x-5+5
20 = 2x
Divide by 2
20/2 = 2x/2
10 =x
We know that AFG + BFG = 180 since it forms a straight line
AFG + BFG = 180
3x+15 + BFG = 180
3(10) + 15 + BFG = 180
30+15 + BFG = 180
45 + BFG = 180
BFG = 180-45
BFG = 135
Answer:
<BFG = 135
Step-by-step explanation:
They are the same angle, so they will be equal to eachother.
3x + 15 = 5x - 5
-3x -3x
----------------------
15 = 2x - 5
+5 +5
-----------------------
20 = 2x
----- ----
2 2
10 = x
3(10) + 15
30 + 15
45
180-45 = 135
The answer is 135.
A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 7 miles. Find the probability of the following events: a. The car travels more than 69 miles per gallon. Proba
Answer:
0.28386
Step-by-step explanation:
Given that :
Mean, μ = 65 miles
Standard deviation, σ = 7 miles
Probability that car travels more than 69 miles per gallon :
Recall,
Z = (x - μ) / σ ; x = 69
Z = (69 - 65) / 7 = 0.5714
The probability :
P(Z > z) = P(Z > 0.5714) = 1 - P(Z < 0.5714)
P(Z > 0.5714) = 1 - P(Z < 0.5714) = 1 - 0.71614 = 0.28386
P(Z > 0.5714) = 0.28386
how many square metres of floor are there in a room of 6 metres
ig something like that
Answer:
36² metres
Step-by-step explanation:
I'm assuming you mean 6 metre wide/long floor. Area is L*W so 6*6
use the ratio of a 45-45-90 triangle to solve for the variables
Answer:
1:1:√ 2
Step-by-step explanation:
Answer:
u = 14
v = 14
Step-by-step explanation:
since both angles around the 90 degree angle are the same, also the sides need to be of equal length. v = u
so, we can use Pythagoras
(14×sqrt(2))² = u² + u² = 2u²
196×2 = 2u²
196 = u²
u = 14 = v
A hollow metal sphere has an external diameter of 12 cm and a thickness of 2 cm. (i) Given that the mass of 1 cm of the metal is 5.4 g, find the mass of the hollow sphere in kg. (ii) The hollow sphere is melted and recast to form a solid sphere. Find the radius of the solid sphere.
Answer:
(i) 3.438159 kg
(ii) 5.336803297 cm
Step-by-step explanation:
the external diameter = 12 cm, => the radius = 6 cm.
the internal diameter = 12 - 2×2 = 8 cm, radius = 4 cm.
I assume the mass of 1 cm³ (not cm) is 5.4 g (very, very light metal).
the material is in the volume of external sphere minus internal (empty) sphere.
the volume of a sphere is
4/3 × pi×r³
V-e = 4/3 × pi×6³ = 4/3 × pi×216 = 4×pi×72 = 904.7786842 cm³
V-i = 4/3 × pi×4³ = 4/3 × pi×64 = 268.0825731 cm³
V-e - V-i = 4/3 × pi×(216-64) = 4/3 × pi×152 = 636.6961111 cm³
1cm³ = 5.4g
636.6961111 cm³ = 5.4×636.6961111 = 3438.159g = 3.438159 kg
for (ii) we need to work with the volume of the material and calculate backwards to find the radius of the sphere with the full volume of that size.
636.6961111 = 4/3 × pi×r³ = 4/3 × pi×152
152 = r³
r = 5.336803297
The velocity of a particle moving along a straight line is given by v(t)=6t2+4t−5 cm/sec at time t seconds with initial position s(0)=3 cm. What is the position of the particle at t=2 seconds, in cm?
Answer:
s(2) = 17 cm
Step-by-step explanation:
We are told that the velocity function is;
v(t) = 6t² + 4t − 5 cm/sec
Integral of velocity gives distance.
Thus;
s(t) = ∫v(t) = ∫6t² + 4t − 5
s(t) = 2t³ + 2t² - 5t + c
We are told that s(0)=3 cm
Thus;
s(0) = 2(0)³ + 2(0)² - 5(0) + c = 3
Thus; c = 3
Thus;
s(t) = 2t³ + 2t² - 5t + 3
At t = 2 secs
s(2) = 2(2)³ + 2(2)² - 5(2) + 3
s(2) = 17 cm
Use what you know about sine, cosine, and tangent to calculate the height of the buildings in the diagram below.
Answer:
x = 32 feet
Step-by-step explanation:
By applying tangent rule in ΔACD,
tan(40°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{AB+AC}{CD}[/tex]
= [tex]\frac{x+BC}{87}[/tex]
x + BC = 73 -----(1)
By applying tangent rule in ΔBCD,
tan(25°) = [tex]\frac{BC}{CD}[/tex]
= [tex]\frac{BC}{87}[/tex]
BC = 40.57
By substituting the value of BC in equation (1),
x + 40.57 = 73
x = 32.43
x ≈ 32 feet
The area under the standard normal curve to the right of z = -0.51 is 0.6950. What is the area to the left of z = 0.51?
Answer:
0.305
Step-by-step explanation:
We are told that area under the standard normal curve to the right of z = -0.51 is 0.6950
Thus, to get the area to the left, we just subtract 0.6950 from 1.
Thus;
area to the left of z = 0.51 is;
P( z < 0.51) = 1 - 0.6950 = 0.305
x3 + (y +z) factorize
how many solutions does the equation below have? 3x-8=-2x+9/3
Answer:
1
Step-by-step explanation:
[tex]\\ \sf\longmapsto 3x-8=-2x+\dfrac{9}{3}[/tex]
[tex]\\ \sf\longmapsto 3x-8=-2x+3[/tex]
[tex]\\ \sf\longmapsto 3x+2x=3+8[/tex]
[tex]\\ \sf\longmapsto 5x=11[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{11}{5}[/tex]
Plz help........
1. -1114 ÷ ( - 117)
2. -212 ÷ ( -123)
3. - 512 ÷ 58
4. 27 ÷ ( -79)
Answer:
1. 1114/117 2. 212/123 3. -256/29 4. -27/79
Step-by-step explanation:
1. 1114/117
2. 212/123
3. -256/29
4. -27/79
In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. 2 and 4
C. 1, 2, and 3
D. none
Answer:
None
Step-by-step explanation:
No lines can be folded over to match up with the opposite side
Geometry, please answer question ASAP
Answer:
Triangle ACB =~ triangle DFE, by adding 6 units to each side of both triangles their relationship will not change. They are still similar.
Step-by-step explanation:
The answer isn't great in all honesty but it's been a long time since I took geometry and I don't 100% remember the proper way of stating it. Though I am 100% sure they stay similar.
Sorry couldn't be of more help but figured something was better then nothing
What is the median for the set of data? 6, 7, 10, 12, 12, 13
Answer choices:
6
7
10
12
12
13
Answer:
11
Step-by-step explanation:
If the set of numbers are not in least to greatest first set them up into their positions. But since this set is already in least to greatest we can go to the next step.
6, 7, 10, 12, 12, 13
Cross off all numbers until you get to the middle:
6, 7, 10, 12, 12, 13
Find the mean of the numbers in the middle:
10 + 12 = 22
22 / 2 = 11
The answer is 11
Hope this helped.
Answer:
11
Step-by-step explanation:
10+12=22
22÷2=11
median is equal to the middle number after being arranged in ascending order.
Algebra
factorize
a4 - 3a2b2 + b4
Answer:
The term a⁴-3a²b²+b⁴ can't be factorised
Write a verbal expression for (c-2)d
Answer:
the sum of c minus 2 multiplied by d ------> (c-2)d
Chi needs to simplify the expression below. (1.25 -0.4)-7+4x3 Which operation should she perform first?
I need an answer quickly
Answer:
She should first perform the operation in the parentheses, you can reference the order of the operations based on PEMDAS.
Step-by-step explanation:
1. parentheses operations
2. multiply 4 x 3
3. add the value you get from the parentheses with -7
4. with that value add it to the product of 4 and 3
Hope that helped! :)
Answer:
Subtraction
Explanation:-
[tex]( 1.25 -0.4) \div7+ 4 \times 3[/tex]
Using BODMAS Rule:-
BracketsOrdersDivisionMultiplicationAdditionSubtractionIn bracket, the operation subtraction should be performed first .
What's 672 divided by 32
Answer:
the answer is 21
Step-by-step explanation:
Look at the graph shown.
Which equation best represents the line? (4 points)
y = 1 over 3.x − 1
y = 3x − 1
y = −x + 1 over 3.
y = 3x + 1
Answer:
y=3x - 1
Step-by-step explanation:
we are going to base the answer off of the y=mx+b form where m represents slope and b represents the y-intercept.
we know that b must be -1 because the line hits the y-axis when y is -1
this now leaves us with either the first or second choice
we then choose two points to find the slope. I am using (0,-1) and (1,2). If you count the boxes, the y-value increases by 3 as the x-value increases by 1. So the slope is 3/1 or 3.
so then we know the answer is y=3x-1
hope this helps
Can I please get help with these 2 questions about polygons
Answer:
a)139°
Step-by-step explanation:
two co interior angles make one opposite exterior angle
49+90=139°
For the parabola y = (x+14)^2 -4, The value of the y coordinate of the vertex is?
Answer:
-4
Step-by-step explanation:
y = (x+14)^2 -4
The equation is in vertex form
y = a(x-h)^2 + k where (h,k) is the vertex
The y coordinate of the vertex is k = -4
Answer:
y - coordinate = - 4
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = (x + 14)² - 4 ← is in vertex form
with vertex = (- 14, - 4 )
The y- coordinate of the vertex = - 4
Find the slope of the line that contains (-1, 9) and (9, 9).
Step-by-step explanation:
using the slope formula, we can see that the slope is 0