1. The first option is represented by a linear function, ∴ y = 50x + 150. The y intercept here is 150, as the first week is 200 dollars, not the 0th week. 200 - 50 = 150.
Given the domain here is 1 - 6 (6 weeks) we can plug in x as 1,2,3 etc and solve for y, completing the table.
Option A :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 250 | 300 | 350 | 400 | 450 |
And for option b we have an exponential function. 1 + 10% = 1 + 0.1 = 1.1. Therefore we have the function ∴ y = 200( 1.1 )^x-1 that models this situation. Remember that we have " x - 1 " as the exponent rather than x, as the first week begins with 200 dollars, not the 0th week.
That gives us the following table,
Option B :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 220 | 242 | 266.2 | 292.82 | 322.102 |
2. (a) We already calculated the " iterative rules " for each sequence in the first part. For your explanation on that behalf, just include the explanation above. Rule of Option A : y = 50x + 150. Rule of Option B : [tex]y = 200( 1.1 )^{x-1}[/tex].
(b) Let's take an example week and substitute into our equations to help clarify our friend's doubt. Say week 2...
y = 50(2) + 150 = 100 + 150 = 250 ✓
y = 200( 1.1 )^2-1 = 200( 1.1 )^1 = 200( 1.1 ) = 220 ✓
3. (a) A function is an equation that represents the relation between x and y, which is exactly the purpose of the rules y = 50x + 150, and y = 200( 1.1 )^x-1.
(b) I disagree with my friend. These particular examples do have y - intercepts, but just because a rule is a function, doesn't make it have a y - intercept. There are some exceptions, such as y = 1 / x.
(c) An input such as 18.5 is meaningless, as x represents the weeks. An employer doesn't provide the payments at half weeks.
4. Let's substitute 20 as x,
y = 50 * 20 + 150 = 1,000 + 150 = $1,150
y = 200( 1.1 )^x-1 = 200( 1.1 )^20-1 = 200( 1.1 )^19 = $1,223.1818
The first payment option will provide the greatest total income.
select all the equations where b=11 solution
Answer:
b + 18 = 7
77 = 7b
9 = b - 2
Noah has one dollar composed of dimes and nickles. He has twice as many 1 point
dimes as nickels, How many nickles does he have? *
Your answer
no❤️ ,,,,,,,,,,,,,,,,,,,
8 dimes 4 nickels
ur crazy bb why’d you even ask this question
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2 1/2. What is the value of x? PLEASE ANSWER ASAP!!
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Figure B = 2½ the size of figure A
One side of figure B is given as 5, therefore, 5 = 2½ of x in figure A.
Thus, [tex] 5 = 2\frac{1}{2}*x [/tex]
Solve for x
[tex] 5 = \frac{5}{2}*x [/tex]
[tex] 5*2 = \frac{5x}{2}*2 [/tex]
[tex] 10 = 5x [/tex]
[tex] \frac{10}{5} = \frac{5x}{5} [/tex]
[tex] 2 = x [/tex]
[tex] x = 2 [/tex]
Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°.
Answer:
La altura del globo con respecto al suelo es 449,6 metros.
Step-by-step explanation:
La afirmación está incompleta. El enunciado completo es: "Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?
El diagrama geométrico de la situación se encuentra descrita en el archivo adjunto. La altura aproximada del globo puede obtenerse con ayuda de las funciones trigonométricas, en este caso, se recomienda utilizar la función tangente de los ángulos de depresión:
Ciudad A
[tex]\tan 27^{\circ} = \frac{h}{1500\,m-x}[/tex]
[tex]0,510 = \frac{h}{1500\,m-x}[/tex]
Ciudad B
[tex]\tan 36^{\circ} = \frac{h}{x}[/tex]
[tex]0,727 = \frac{h}{x}[/tex]
Donde [tex]h[/tex] y [tex]x[/tex] son la altura con respecto al suelo y la distancia horizontal con respecto a la ciudad A.
A continuación, se elimina la altura de ambas ecuaciones por igualación y se determina la distancia horizontal del globo con respecto a la ciudad A:
[tex]0,727\cdot x = 0,510\cdot (1500\,m-x)[/tex]
[tex]1,237\cdot x = 765\,m[/tex]
[tex]x = 618,432\,m[/tex]
Finalmente, la altura del globo con respecto al suelo es:
[tex]h = 0,727\cdot x[/tex]
[tex]h = 0,727\cdot (618,432\,m)[/tex]
[tex]h = 449,600\,m[/tex]
La altura del globo con respecto al suelo es 449,6 metros.
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:
The SQ Root of 493
Step-by-step explanation:
Becaues this triangle is a right triangle, we can find the missing side usiing the pythagorean theorum.
The pythagorean theorun states A^2 + B^2 = C^2, so 18^2 + 13^2= 439
Then all you have to do is find the sq root of 439, but this question askes you not to.
Hope this helps :)
You toss a 6-sided number cube and
a coin at the same time. How many
possible outcomes are there?
A 2
B 6
C 8
D 12
Answer:
12
Step-by-step explanation:
There are 6 outcomes for the cube and 2 outcomes for the coin
6*2 = 12
There are 12 different outcomes total
-6 times (-6) times (-6)
Answer:
-216
Step-by-step explanation:
-6 x -6 =36
36 x -6 = -216
Answer:
-216
Step-by-step explanation:
Loryn,brian,and edna are donating book to the library.loryn donated 7 more books than brian.enda donated twice as many books as loryn. Together they donated a total of 53 books how many books did loryn donate
Answer:15
Step-by-step explanation: We know L+B+E=53 books
Loryn=L
Enda=2L
Brian=L-7
L+2L+L-7=53
Then solve for L
Leaving you with L=15
Check
15+2(15)+(15-7)
15+30+8=53
C is between B and D. BC=4x + 10 and CD=25. Find BD.
A: BD=105
B: BD=45
C: BD=17.5
D:BD=80
Answer:
A: =105
Step-by-step explanation:
Geometry CA Find measures
The measure of an angle is 2°. What is the measure of its supplementary angle?
Answer:
178
Step-by-step explanation:
Supplementary angles add to 180 degrees
Let x be the supplement to 2
2+x = 180
Subtract 2 from each side
2+x-2 = 180-2
x = 178
(Solve the following equation: 2 + 8x = 11x - 13 )
A. 5 B. -5 C. 15/19 D. - 15/19
Please help! I usally get these right but I'm completelly stumped! ( Please explain in detail )
Answer:
A. x = 5
Step-by-step explanation:
2 + 8x = 11x - 13 -------- subtract 2 from both sides
2 + 8x - 2 = 11x - 13 - 2
8x = 11x - 15 -------- subtract 11x from both sides
8x - 11x = 11x - 15 - 11x
-3x = -15
x = -15 / -3
x = 5
Answer:
x=5
Step-by-step explanation:
explain how a rational number and an irrational number and different
Answer:
Rational numbers: fractions with an integer numerator and a nonzero integer denominator.
Irrational numbers: numbers that are not rational such as π, root 3, and any non repeating, non ending decimal.
Which operation involving complex numbers requires the use of a conjugate to be carried out?
Answer:
Step-by-step explanation:
Rationalization.
2 + i
For example: " rationalize the denominator of --------- "
-3 + i
Please explain how you get the answer.
Convert decimals to fractions
10) 0.34
11) 0.252525....
12) 5.7777....
Answer:
0.34 ends in the hundredths place. so the fraction will be over one hundred
34/100 -- simplify this by dividing each side by 2: 17/50
0.252525... is a repeating decimal
set up an equation so the numbers to the right of the decimal place are the same
100x = 25.2525...
x = 0.2525...
subtract
99x = 25
divide
x = 25/99
5.7777... is also a repeating decimal
set up an equation so the numbers to the right of the decimal place are the same
10x = 57.777...
x = 5.777...
subtract
9x = 52
x = 52/9
1. Evaluate x2 + 10 if we let x= 3
Answer:
16
Step-by-step explanation:
[tex]x2 + 10 \\ = 3 \times 2 + 10 \\ = 6 + 10 \\ = 16[/tex]
Answer:
16
Step-by-step explanation:
You plug 3 in for x and then you have (3)2+10 and 3 times 2 is 6 plus ten is 16
Where is the answer to the expression 5 − 9 located on a horizontal number line? (1 point)
9 units to the left of 5
9 units to the right of 5
4 units to the right of 5
4 units to the left of 5
alex is traveling by train to a vacation spot that is 810 miles away. The train is traveling at 90 miles per hour, and it has already covered 180 miles. In exactly how many hours will alex reach his destination from his current position
Answer:
7 hours
Step-by-step explanation:
810 - 180 = 630
630/ 90 = 7
Answer:
x = 7 h
Explanation:
First, we write the data of the problem.
Alex travels 810 miles away
Train - 90 miles / h
Alex covers 180 miles.
How many hours does Alex walk in the distance?
1. Calculate the distance Alex still has to travel.
810 miles - 180 miles = 630 miles
2. We take into account the speed of the train to calculate how many hours Alex will cover the remaining distance.
90 miles .... 1 h
630 miles .... x h
x = 630 milesx1h / 90 miles
x = 7 h
How to do this question plz answer my question
Answer:
28 cm
Step-by-step explanation:
vertical side of each parallelogram is (y-6)/2 cm
perpendicular height of each parallelogram is 7 cm
Total area = 4sh
308 = 14(y-6)
y-6 = 22
y = 28 cm
BRAINLIEST PLS
What is the inverse of the function g(x)=-2(x-4)? g^-1(x)=___
Step-by-step explanation:
g(x) = y = 8 - 2x
(A) First transform the function in terms of x :
x = y - 8 / 2
(B) Replace x with y :
[tex] {g}^{ - 1} (x) = y = \frac{x}{2} - 4[/tex]
Someone please help me!!!!
Answer:
Below.
Step-by-step explanation:
Left side = 2 cos^2 ( π/4 - A/2) - 1
= 2 ( cos π/4 cos A/2 + sin π/4 sin A/2)^2 - 1
Now sin π/4 and cos π/4 = 1 /√2 so:
= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1
= 2 * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1
But cos^2 a/2 + sin^2 A/2 = 1 so we have:
2 * 1/2( 1 + 2sin A/2 cos A/2) - 1
= 1 + 2 sin A/2 cos A/2 - 1
= 2 sin A/2 cos A/2
Using the identity 2 sin A cos A = sin 2A
2 sin A/2 cos A/2 = sin A = right side.
So left side = right side and the identity is proved.
Answer: see proof below
Step-by-step explanation:
Use the Double Angle Identity: cos 2A = 2cos²A - 1
Use the Difference Identity: cos (A - B) = cosA · cosB + sinA · sinB
Use the Unit Circle to evaluate: cos (π/2) = 0 & sin (π/2) = 1
Proof LHS → RHS
[tex]\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A[/tex]
LHS = RHS: sin A = sin A [tex]\checkmark[/tex]
Joel took out a car loan for 12000 he paid 4800 in interest at a rate of 8% per year how many year will it take him to pay off the loan.
Answer:
5 years
Step-by-step explanation:
Simple interest on a loan of P for t years at rate r per year is ...
I = Prt
4800 = 12,000(0.08)(t)
4800/960 = t = 5
It will take Joel 5 years to pay off the loan.
ally and Anne went to the movies. They each purchased a drink. They also bought one popcorn and one veggie cup to share. Each woman’ total is modeled with this expression:
9 + 1.34 +
1
2
(3.50 +1.74)
How would you simplify the expression? Explain your steps.
Answer:
13.48
Step-by-step explanation:
A certain number is increased by 30 and the result is divided by two. The number obtained is three times the original number. Find the number.
Plss show working
Answer:
x = 6, PLEASE MARK AS BRAINLIEST
Step-by-step explanation:
Let this number be x:
1) Increase x by 30 = x + 30
2) Divide the result by 2 = [tex]\frac{x+30}{2}[/tex]
3) The number obtained is 3 times the original number =
[tex]\frac{x + 30}{2} = 3x[/tex]
[tex]{x + 30} = 6x[/tex]
[tex]30 = 5x[/tex]
[tex]x = \frac{30}{5}[/tex]
[tex]x = 6[/tex]
One card is to be drawn from a deck of 52 cards.The deck includes four types of cards.Red heart, red stars , black triangles , black circles .Each type has 13 cards numbered 1-13.What is the probability of drawing a red one a, black three , or a six of hearts.Give your answer in the simplify form .
Answer:
1/26 ; 1/26 ; 1/52
Step-by-step explanation:
Given the following :
A deck of 52 cards contains :
Red hearts, Red stars, black triangles, black circles
Each type of card is numbered from 1 - 13
Therefore,
Number of each type of card = 13, all numbered distinctly with digits between 1 - 13
Probability = (number of required outcomes / total number of possible outcomes)
If one card is drawn from the deck:
Probability of picking a red one :
This is either a red heart numbered 1 or a red red star numbered 1,
Therefore, Required outcomes = 2
Total possible outcomes = 52
P(a red one) = 2 / 52 = 1/26
B) A black three
This is either a black triangle numbered 1 or a black heart numbered 1,
Therefore, Required outcome = 2
Total possible outcomes = 52
P(a black three) = 2 / 52 = 1/26
C.) A six of hearts :
A hearts numbered six = 1
Therefore, Required outcome = 1
Total possible outcomes = 52
P(a black three) = 1 / 52 = 1/52
Solve this numerical problems
a Convert: 794mm into m and One day into sec.
To convert mm to m, divide by 1000:
794/1000 = 0.794 m
1 day = 24 hours
1 hour = 3600 seconds
24 x 3600 = 86,400 seconds in a day
Answer:
Step-by-step explanation:
To convert 794mm into m
1000mm = 1m
794mm = xm
m = 794/1000
m = 0.794m
One day to secs is
= 84,400secs
Is 2/3+4/5 a rational number
Answer:
Yes
Step-by-step explanation:
what is the midpoint of 2-3i and -4+6i
O2+31
-4-6i
0 -1+1.51
2-31
please help me on this
Answer: (1,-1/2)
Step-by-step explanation:
Point C on the coordinate plane has the coordinates (4,-2) after a dilation with a scale factor of 1/4 we will have to multiply the coordinates each by 1/4 to find the new coordinates.
So x = 4 * 1/4 = 1 Now the new x coordinate is 1
-2 * 1/4 = -2/4 = -1/2 Now the new coordinate for y is also -1/2
So we will now have the coordinates (1,-1/2)
Find the Slope of the line on the graph. write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
3
Step-by-step explanation:
3x-2y=6 and 5x-5y=5 Solve each system of equations
Answer:
x=4 and y=3
Step-by-step explanation: