Lesson 3: Revisiting Proportional Relationships
what is the tangent ratio of angle x°
Answer:
tan x = 3/4
Step-by-step explanation:
The hypotenuse of the triangle is 10 ft.
For angle x, the opposite leg is 6 ft, and the adjacent leg is 8 ft.
tan A = opp/adj
tan x = 6 ft / 8 ft
tan x = 3/4
I need help please!!! My teacher doesn't teacher and she has asked us to do a problem I don't know how to do it. Can somebody explain or give the answer and show your work so I can understand that way? I will be giving away 20 points and brainliest. Thank You!
A patient is told to avoid caffeine for 8 to 12 hours before a blood test scheduled for 6 a.m. The blood test is reliable for up to 50 milligrams of caffeine in the bloodstream. The patient’s body metabolizes caffeine at a rate of 13% per hour.
a. At 10 p.m., the patient drinks a cup of coffee containing 150 milligrams of caffeine. Will the patient be ready for the blood test by 6 a.m.? Explain.
b. How many milligrams of caffeine could the patient have ingested at 7 p.m. and been ready for the blood test at 6 a.m.?
Using exponential functions, it is found that:
a) Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.
b) The patient could have ingest 231 milligrams of caffeine.
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
Caffeine metabolize at a rate of 13% per hour, hence [tex]r = 0.13[/tex].Then:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = A(0)(1 - 0.13)^t[/tex]
[tex]A(t) = A(0)(0.87)^t[/tex]
Item a:
The coffee cup contains 150 milligrams of caffeine, hence [tex]A(0) = 150[/tex].
At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).
[tex]A(t) = A(0)(0.87)^t[/tex]
[tex]A(8) = 150(0.87)^8[/tex]
[tex]A(8) = 49.2[/tex]
Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.
Item b:
This A(0), considering A(11) = 50, hence:
[tex]50 = A(0)(0.87)^{11}[/tex]
[tex]A(0) = \frac{50}{(0.87)^{11}}[/tex]
[tex]A(0) = 231[/tex]
The patient could have ingest 231 milligrams of caffeine.
A similar problem is given at https://brainly.com/question/25537936
A pump fills a pool at a constant rate. At the end of 4 minutes it has filled 36 gallons
of water. Which table represents the relationship between the number of minutes and
the number of gallons of water in the pool?
А
B
Time
Water
(minutes) (gallons)
Time Water
(minutes) (gallons)
4.
1
1
4
8
2
2
8
12
3
3
12
с
D
Time
Water
(minutes) (gallons)
Time Water
(minutes) (gallons)
1
9
9
1
2
18
18
2
3
27
27
3
Answer:
C
Step-by-step explanation:
36 gallons ÷ 4 minutes = 9 per minute
please help me asap..
ty :)
Answer:
x = 3, 0
y = 0, -4
Step-by-step explanation:
the students at Walden Middle school are selling tins of popcorn to raise money for new uniforms. they sold 42 tins in the first week. how much money did they make in the first weeks
Answer:
$388.50
Step-by-step explanation:
9.25 * 42 = $388.50
Seven tickets for a Broadway show cost $385. How much will only 4 tickets cost?
Answer:
That seems a little hard-
Step-by-step explanation:
Answer:
$220
Step-by-step explanation:
If seven tickets cost 385, then 1 ticket costs one-seventh of that amount, so we divide it by 7 to see how much one ticket costs.
385/7 = 55
One ticket is $55. To find out how much 4 tickets cost, multiply 55, the price of one ticket, by 4.
55 * 4 = 220
$ tickets cost $220
What is the remainder when 3 is
synthetically divided into the polynomial -2x2 + 7x - 9?
A. -6
B. -4
C. 2
D. 0
The remainder when 3 is synthetically divided into the given polynomial is; Choice A; -6.
What is the remainder when 3 is synthetically divided into the polynomial?It follows from the task content that the remainder when 3 is synthetically divided into the polynomial is to be determined.
On this note, it follows that the expression evaluation at x = 3 represents the required remainder.
Therefore, we have;
-2 (3)² + 7 (3) - 9
= -18 + 21 - 9
= -27 + 21
= -6
Ultimately, the required remainder when 3 is synthetically divided into the polynomial is; -6.
Therefore, the correct answer choice is; Choice A; -6.
Read more on synthetic division of Polynomials;
https://brainly.com/question/7066192
#SPJ1
Abigail must move a bucket of tomatoes from her garden to her kitchen, as represented on the grid below.
y
Kitchen
L(5, 1)
-1 0
2
Garden
-(-3, 4)
Answer:
Step-by-step explanation:
9.43
han earns $33,00 for babysitting 4 hours. at this rate, how much will he earn if he babysits for 7 hours?
Answer:
$57.75
Step-by-step explanation:
7×33/4
231/4
57.75
Basically find the circumcenter.
the map shows the three most highly populated location of a city, City officials want to build an emergency healthcare cent in a location that sis the same distance from each of the three locations. Find the coordinates of the location the city should use for the emergency healthcare center.
Coordinates:
A(2,14) B(12,14) C(5,0)
Answer:
(7 , 7.75)
Step-by-step explanation:
What is the solution for the system of equations?
y = -x +4
y = x- 2
• (3, 1)
• (1, - 2)
• (-2, 1)
• (1, 3)
Answer:
1, 3
Step-by-step explanation:
// Solve equation [2] for the variable y
[2] y = x - 2
// Plug this in for variable y in equation [1]
[1] (x -2) + x = 4
[1] 2x = 6
// Solve equation [1] for the variable x
[1] 2x = 6
[1] x = 3
// By now we know this much :
y = x-2
x = 3
// Use the x value to solve for y
y = (3)-2 = 1
d.One rectangle weighs what
Answer:
the answer is 2
Step-by-step explanation:
because 7 + 2 = 9 then 9+2=11
A car travels 270 kilometers in 6 hours. How far will it
travel in 9 hours at the same speed?
Pls pa help po
Answer:
405
Step-by-step explanation:
divide 270 by 6 the multiply what you got with 9
:)
HELP!!!
list the sides of ABC in order from shortest to longest!
HELP ME WITH THIS PLEASEEE !
Answer:
34 i think i got it really wrong but...
Step-by-step explanation:
can someone please tell me how to do 2470; 3030; 3320; 4030; 2900; 4120 in stem and leaf diagram?
Before you start, please make a title for your Stem & Leaf plot.
1) Make two columns; Stem and Leaf.
2) Under "Stem" list the following whole numbers: 0, 1, 2, 3, 4, 5, 6. Notice that each number will correspond to each number you gave us.
3) Under "Leaf":
Only the last digits of the numbers go into the Leaf. If I number, for example, starts with 0, the remaining digits go into the Leaf.
4) Create a Key, which allows whoever is reading your plot to understand what the plot means. For example 2|4=24, since 2 is the stem and 4 is the leaf. We usually read a stem and leaf plot as the remaining digits go after the stem but if otherwise a Key is a must have when creating a plot.
The Key can be any set of numbers you have in your Stem and Leaf plot.
Quick easy question
Answer:16
Step-by-step explanation:
144^0.5 = 12
400^0.5 = 20
a^2=b^2+c^2
20^2 = 12^2 +x^2
x^2 = 400-144= 256
x =16
Answer:
16
Step-by-step explanation:
Which list shows the numbers below in order from least to greatest? 5.78,-5.9,58%,-(23)/(4) A -5.9,-(23)/(4),5.78,58%, C -5.9,-(23)/(4),58%,5.78 B -(23)/(4),-5.9,58%,5.78, D 58%,-(23)/(4),5.78,-5.9
Answer:
D
Step-by-step explanation:
Find the value of x.
Answer:
x = 83°Step-by-step explanation:
[tex] {x}^{o} + {75}^{o} + {97}^{o} + {105}^{o} = {360}^{o} \\ {x}^{o} + {277}^{o} = {360}^{o} \\ {x}^{o} = {360}^{o} - {277}^{o} \\ {x}^{o} = {83}^{o} \\ [/tex]
What is a theme of the poem "Dream Variations" by Langston Hughes?
It is life's desire to live freely and expressively without boundaries.
People have the power within to make a fresh start in life.
One should spend less time living in the past and enjoy the present.
It is important to find balance between work and rest.
One theme of the poem Dream variations is the desire to live freely and expressively (option A).
In poems and other literary texts, themes are deep ideas about life that are indirectly expressed by the author. In the case of the poem "Dream variations", the author Langhtons Hughes refers to life and death.
About life, Hughes expresses the importance of living life at its fullest before death occurs. This desire to live freely and expressively is shown in verses such as:
"To fling my arms wideIn the face of the sun"
or in
"To whirl and to dance"
Learn more about poem in: https://brainly.com/question/9527212
Answer:
Step-by-step explanation:
I took the quiz :)
Select the correct answer.
Which equation best models the set of data shown in this table?
Х
0
2
4
6
00
8
10
12
14
16
18
11
19
у
27
35
37
40
44
45
48
52
OA. y = 11v– 0.3 + 4.3
OB.y = 1177 + 0.3 – 4.3
O c.
y = 23 + 17
OD. y = 2.3 – 17
Answer: I cannot tell what equations you are talking about.
Step-by-step explanation:
Please type in the equations instead of copying and pasting so we can know what the actual equation is. Thank you.
Answer: B
Step-by-step explanation:
Got it right
What is the value of the expression below?
(8+1/8) divided by (2.5+3/4)
2.5
4.875
11.375
26.4
Answer:
2.5
Step-by-step explanation:
(8+1/8) = 8.125
(2.5+3/4) = 2.5 + 0.75 = 3.25
8.125 / 3.25 = 2.5
What is the slope of the line through (6,0) and (7,1)
[tex]\huge \bf༆ Answer ༄[/tex]
Let's find the slope of line passing through given points ~
[tex] \sf \dfrac{y2 - y}{x2 - x1} [/tex][tex] \sf \dfrac{1 - 0}{7 - 6} [/tex][tex] \sf \dfrac{1}{1} [/tex][tex] \sf1[/tex]Hence, slope of the line will be 1.
Answer:
1
Step-by-step explanation:
slope = (change in y)/(change in x)
slope = (1 - 0)/(7 - 6)
slope = 1/1 = 1
Answer: 1
Five pipes can fill a tank in 80 minutes. At the same rate, how long will it take 8 pipes to fill the same tank?
Answer:
50 minutes
Step-by-step explanation:
it takes 80 minutes for 5 pipes
so for 1 pipe it will take 5x80=400min
and for 8 pipes it will take 400/8=50min
How do i Multiply and divide integers? please answer quick if possible ♀️
Answer
To multiply integers, simply multiply the unsigned numbers and place the sign on the product by repeating the above rules.
To divide unsigned integers, we divide the unsigned numeric values and put a minus sign on the result.
Latoya took a taxi home from her best
friends house. The taxi charged an initial
fee of $3 plus an additional $1.75 per mile.
write an expression that represents the
amount of money Latoya will spend on
the taxi after traveling x amount of
hours.
Answer:
y=1.75x+3
Step-by-step explanation:
Using slope-intercept form, we can use our initial value of 3, plus our 1.75 per mile, or x, since miles are calculated per hour
Answer:
y=1.75x+3
Step-by-step explanation:
Do you mean x amount of miles? if you do, you would add 3 because 3 is the amount of money that you have to pay no matter how far you go. You would get 1.75x because the number of miles you travel in the taxi, you would have to multiply that number by 1.75 to get the amount of money you would have to pay in addition to the 3 dollars that you would definitely have to pay.
What is the equation of the line that passes
through the points (0, -6) and (-2, -7)?
A forest covers 54,000 acres. A survey finds that 0.6% of the forest is old-growth trees. How many
acres of old-growth trees are there?
Answer:
324
Step-by-step explanation:
Please Help! I don't have much time to finish!
Answer:
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Step-by-step explanation:
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