Answer:
The machine decreases in value by 20% each year.
After 1 year the machine is worth only .8 of its original value.
The machine will only decrease by .2 * (.8 A) in the second year not .2 * A where A is the original amount.
A1 = .8 A
A2 = .8 A1 = .64 A value of machine after 2 years
.8 is the value Barry needs when the machine is new
.8^n never goes to zero
After 10 years value = .8^10 A = .11 A of its original value
Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern lighthouse and N 21o E from the southern lighthouse, how much closer is the closest lighthouse to the boat than the lighthouse furthest away? The northern lighthouse is 51.3 miles closer than the southern lighthouse. The northern lighthouse is 24.4 miles closer than the southern lighthouse. The northern lighthouse is 79.9 miles closer than the southern lighthouse. The northern lighthouse is 17.0 miles closer than the southern lighthouse.
Answer:
The northern lighthouse is approximately [tex]24.4\; \rm mi[/tex] closer to the boat than the southern lighthouse.
Step-by-step explanation:
Refer to the diagram attached. Denote the northern lighthouse as [tex]\rm N[/tex], the southern lighthouse as [tex]\rm S[/tex], and the boat as [tex]\rm B[/tex]. These three points would form a triangle.
It is given that two of the angles of this triangle measure [tex]40^{\circ}[/tex] (northern lighthouse, [tex]\angle {\rm N}[/tex]) and [tex]21^{\circ}[/tex] (southern lighthouse [tex]\angle {\rm S}[/tex]), respectively. The three angles of any triangle add up to [tex]180^{\circ}[/tex]. Therefore, the third angle of this triangle would measure [tex]180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}[/tex] (boat [tex]\angle {\rm B}[/tex].)
It is also given that the length between the two lighthouses (length of [tex]\rm NS[/tex]) is [tex]75\; \rm mi[/tex].
By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, [tex]\angle {\rm B}[/tex] is opposite to side [tex]\rm NS[/tex], whereas [tex]\angle {\rm S}[/tex] is opposite to side [tex]{\rm NB}[/tex]. Therefore:
[tex]\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}[/tex].
Substitute in the known measurements:
[tex]\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}[/tex].
Rearrange and solve for the length of [tex]\rm NB[/tex]:
[tex]\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}[/tex].
(Round to at least one more decimal places than the values in the choices.)
Likewise, with [tex]\angle {\rm N}[/tex] is opposite to side [tex]{\rm SB}[/tex], the following would also hold:
[tex]\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}[/tex].
[tex]\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}[/tex].
[tex]\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}[/tex].
In other words, the distance between the northern lighthouse and the boat is approximately [tex]30.73\; \rm mi[/tex], whereas the distance between the southern lighthouse and the boat is approximately [tex]55.12\; \rm mi[/tex]. Hence the conclusion.
2 complementary angles are in the ratio 3:6. Find the angles
Answer:
The angles are 60°, and 30°
Step-by-step explanation:
Complementary angles add up to 90°
3 = 6 = 9
90/9 = 10
10 * 3 = 30
10 * 6 = 60
-Chetan K
Can someone pls help me
Pls get it right.
Using Pythagorean theorem
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto P^2=8^2-(4\sqrt{3})^2[/tex]
[tex]\\ \sf\longmapsto P^2=64-48[/tex]
[tex]\\ \sf\longmapsto P^2=16[/tex]
[tex]\\ \sf\longmapsto P=4[/tex]
________
[tex] \: [/tex]
a² = c² - b²
a² = 8² - (4√3)²
a² = 64 - 48
a² = 16
a = √16
a = 4
my head hurts help will ya?
Solution : 24 × [20 + (5 × 3)] ÷ 8
So, first let's solve the integers within perenthesis
24 × [20 + 15] ÷ 8 24 × 35 ÷ 8Now, we need to divide it first after which we'll multiply the rest
24 × 4.375 105The answer should be 105
You pay $80 for a game system. The monthly rental fee for games
is m dollars. Your cost for the year is $188. Using the equation
12m + 80 = 188, how much is your monthly fee?
Answer: 9
Step-by-step explanation:
12m + 80 = 188
-80 - 80
12m = 108
12m = 108
12 12
m = 9
can u hurry and help please
Answer:
18.84
Step-by-step explanation:
Hope this helps :)
Answer:
18.84
The equation for circumference is 2πr which means that you times 2 by pi and then the radius which is 6 divided by 2 so 3. Then you get 6π which is 18.84
Which statement about the function y = −14x − 2 is true?
Answer:
slope is -14
X int. X is at 1/7
y int. y is at -2
Step-by-step explanation:
If you graph it you will see.
Pls Help
Use slope-intercept form, y = mx + b, to find the value for the y-intercept (b) of a line that has a slope of 6 and passes through the point (3, –5).
b=
a. -23
b. -14
c. 21
d. 33
What is the new equation written in slope-intercept form?
a. y=6x-23
b. y=6x-14
c. y=6x+21
d. y=6x+33
Answer:
y-intercept: -23
y = 6x - 23
Step-by-step explanation:
Slope: 6
Point (3, -5)
y-intercept: -5 - (6)(3) = - 5 - 18 = - 23
PLEASE PLEASE HELP WILL GIVE BRAINIEST AND ALOT OF POINTS PLEASE SHOW WORK TOO
a rectangle has a width of 1.75x+6.8 and a length of -3.5y - 2.7, find the perimeter
Answer:
3.5x + 13.6 - 7y -5.4
Step-by-step explanation:
Perimeter is equal to 2 times the sum of the length and width
2(1.75x+6.8-3.5y-2.7) = 3.5x + 13.6 - 7y -5.4
A rental car agency charges $220 per week plus $0.15 per mile to rent a car. How many miles can you travel in one week for $340?
The number of miles you can travel in one week for $340 is ?.
Answer:
800 miles
Step-by-step explanation:
You would make the equation .15x+ $200 and put that equal to 340 to get the equation:
.15x+$200=340
-$200 (subtract the like term first)
.15x=120
.15x over 120
Your answer comes out to be x=800.
Clasifica los siguientes números en los conjuntos numéricos a los que pertenezcan. Si es posible
Exprésalos en forma de fracción.
a)
8
c) −43
e)
1,27
g)
1,01002000300004...
b) −0,81
d) numero PI
f) − 64
h) 6
Can someone please help me
The last option; intersecting, but not perpendicular
Which of the following is an even function?
Of(x) = (x - 1)2
O f(x) = 8x
Of(x) = x2 - x
O f(x) = 7
Answer:
f(x) = 7
Step-by-step explanation:
In an even function of x, all powers of x are even (2, 4, 6, etc.).
In this case we have f(x) = 7, or 7x^0, which is an even function because the power (0) of x is even.
The first one to answer gets brainy
Tìm giá trị nhỏ nhất của hàm số: y = cos 2x + 4cos x - 3
Answer:
upp7fpfpzfpufpufpufpufpu
Step-by-step explanation:
uxcicicovovovovovvNC coordinatorby McKnight
What is the time on this clock?
Answer:
11:53 ish.
Step-by-step explanation:
At 1 pm one day the temperature inside a freezer was -20°C
The freezer broke down.
The temperature inside the freezer went up by 4°C every hour after 1pm.
At what time did the temperature inside the freezer reach 0°C?
Answer:
6 p.m.
Step-by-step explanation:
HEEELP PLEASE
A company prepares a graph of its profit forecast. The annual budget predicts monthly income of at least $5000 more than expenditures.
What inequality models this situation?
Let x represent the expenditures in dollars for a given month and let y represent the income in dollars for the same month.
Express your answer as an inequality in slope-intercept form.
Answer:
that's he
ard
Step-by-step explanation:
sole it your seldf fast ⏩ fast food in advance of my head I can you e d f 3
BRAINLIEST ASAP!!!!!!!!!! Please someone help
2.07 divded by 0.9
what does that equal
Answer:
2.3
Step-by-step explanation:
whats x+10<6 as a inequality sign?
Answer:
x < -4
Step-by-step explanation:
x + 10 < 6
-10 < -10
x < -4
20 points!!!
What is the solution to the system
(1) x+y+z=-3
(2)3y-z=4
(3) 2x-y-2z=-5
Answer:
I'm sorry but which ones are the x, y, and z, like (x, z, y)?
Step-by-step explanation:
By the way I promise you respond back and answer just making sure I know which variables are what so I can answer with the correct answer.
joyce is y years old.she is 10 years older than peter . what will be the sum oftheir ages ij 5 years time?
What is the sample space for a spinner with four equal sections, numbered 1 to 4?
A. 1, 2, 3, 4
B. 4-1. 4-2. 4-3. 4-4
C. 1-1,1-2, 1-3, 1-4
D. 1, 2, 3, 4, 5
PLEASE HELP
Answer:
A. 1, 2, 3, 4
Step-by-step explanation:
I. When sample space means all possible case could happend.
In this case we have 4 equal sections numbered 1 to 4.
So from 1st section to 4th sections could happend fairly.
That makes 1, 2, 3, 4 is the right answer.
Hope that help :)
(calculus) please help! will mark brainliest!
Hello friend,
The answer to your question is attached in the image uploaded by me. Please refer them.
✍️ By Benjemin ☺️
Dave ran 10km in 40 minutes. He rested for 5 minutes then ran a further 8 km in 35 minutes.Work out his average speed for the whole journey. (Give your answer in km/h)
Answer:
27/2 km/hr
Step-by-step explanation:
I need these ASAP………..
Step-by-step explanation:
1) 3x - 4 = 86 + 24
→ 3x - 4 = 110
→ 3x = 110 + 4 = 114
→ x = 114/3 = 38
therefore, value of x is 38.
2) -10x = 30 + 90
→ -10x = 120
→ x = 120/10 = 12
→ x = 12
therefore, value of x is 12.
3) -8x + 23 + 51 = 130
→ -8x + 74 = 130
→ -8x = 130 - 74
→ -8x = 56
→ x = 56/8
→ x = 7
therefore, value of x is 7.
4) -9 + 2x = 59 + 90
→ -9 + 2x = 149
→ 2x = 149 + 9
→ 2x = 158
→ x = 158/2 = 79
→ x = 79
therefore, value of x is 79.
hope this answer helps you dear...take care !
A building is 240 feet tall. On a scale drawing, 1/4 inch = 10 feet. What is the height of the building in the scale drawing?
15 in
9 in
60 in
13 in
Help Pleaseee
Answer:
60 in = 240 ft
Step-by-step explanation:
240/4 = 60
—
15 x 4 = 60
9 x 4 = 36
60 x 4 = 240
13 x 4 = 52
plzzz help!!
Order the following from greatest to least.
Answer:
I think the answer is C
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
122%=122% 49/29=169% 26/15=173%, 1.98=198%
8/x = 2x+1 Solve this pls