Answer: [tex]45\ mph[/tex], [tex]5\ mph[/tex]
Step-by-step explanation:
Given
A motorboat takes 5 hours to travel 200 miles upstream and 4 hours to go downstream
Suppose the speed of motorboat in still water and rate of current be x and y respectively.
during upstream
[tex]\Rightarrow 5=\dfrac{200}{x-y}\\\\\Rightarrow x-y=40\quad \ldots(i)[/tex]
During downstream
[tex]\Rightarrow 4=\dfrac{200}{x+y}\\\\\Rightarrow x+y=50\quad \ldots(ii)[/tex]
Add (i) and (ii) we get
[tex]\Rightarrow 2x=90\\\Rightarrow x=45\ mph[/tex]
[tex]\therefore y=5\ mph[/tex]
Thus, the speed of boat in still water is [tex]45\ mph[/tex] and rate of current is [tex]5\ mph[/tex]
The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?
(−9, −2)
(−17, −2)
(−2, −17)
(−2, −9)
Answer:
D) [tex](-2,-9)[/tex]
Step-by-step explanation:
Vertex Form of a Vertical Parabola:
[tex]y=a(x-h)^2+k[/tex]
Vertex -> [tex](h,k)[/tex]
Axis of Symmetry -> [tex]x=h[/tex]
Vertical Scale Factor -> [tex]a[/tex]
To turn [tex]f(x)=x^2+4x-5[/tex] into vertex form, we need to complete the square on the right sideTherefore, if [tex]f(x)=0[/tex], then [tex]0+9=x^2+4x-5+9[/tex] completes the square on the right side This becomes [tex]9=(x+2)^2[/tex]This means that our function in vertex form is [tex]f(x)=(x+2)^2-9[/tex]Therefore, the vertex of the graph is [tex](h,k)=(-2,-9)[/tex].
The coordinates of the vertex of the graph is (-2, -9).
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
x² + 4x - 5
Given that axis of symmetry of the function is x = -2.
So the x coordinate of the vertex = -2.
y coordinates = f(-2) = 4 - 8 - 5 = -9
Hence the vertex is (-2, -9).
Learn more about Vertex form here :
https://brainly.com/question/13921516
#SPJ5
For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?
In the summer term sal wlks to school starting soon after 7 am when the hour hand is at angle of 110 degrees to the minute hand. She arrives at school before 8 am when
Answer:
She walked for 46 minutes
Step-by-step explanation:
Given
When she leaves home
[tex]h = 7am[/tex]
[tex]\theta_1 = 110^o[/tex]
When she arrives at school
[tex]H = 8am[/tex]
[tex]\theta_2 = 110^o[/tex]
Required
Time to walk to school
First, we convert [tex]\theta_1 = 110^o[/tex] to minutes:
[tex]\theta_1 = \frac{110}{6}[/tex]
[tex]\theta_1 = 18.33[/tex]
[tex]\theta_1 = 18[/tex] --- approximated
From the question, we understand that she left home past 7.
This means that the difference between the hour hand (at 7) and the minutes hand is 18 minutes.
Also, the minute hand is between 0 and 30 minutes
Subtract 18 minutes from 30 minutes;
[tex]Mins = 30-18=12[/tex]
She left home at 7:12am
Similarly;
[tex]\theta_2 = \theta_1 = 18\ mins[/tex]
From the question, we understand that she arrived before 8.
This means that the difference between the hour hand (at 8) and the minutes hand is 18 minutes
Also, the minute hand is between 30 and 60 minutes mark.
At the 8hour hand, the minutes is 40
Add 18 minutes from 40 minutes;
[tex]Mins = 40 + 18 = 58[/tex]
She arrived at 7:58am
The difference (d) is:
[tex]d =7:58am - 7:12am[/tex]
[tex]d =46[/tex]
The nation of Finlandia has 120,000 people. Of these, 20,000 are children under 16, 72,000 have jobs, 8,000 don't have jobs but are looking for work, and 20,000 are retired. With this info, calculate the labor force participation rate and the unemployment rate.
Answer: labor force participation rate =60%
unemployment rate = 6.67%
Step-by-step explanation:
The labor force participation rate is computed as
[tex]\text{labor force participation rate}=\dfrac{\text{Total employed persons}}{\text{Total population}}[/tex]
i.e. [tex]\text{labor force participation rate}= \dfrac{72000}{120000}[/tex]
[tex]= 0.6\ or\ 60 \%[/tex]
The unemployment rate is computed as:
[tex]\text{unemployment rate}=\dfrac{\text{Number of personsdon't have jobs }}{\text{Total population}}\\\\\text{unemployment rate}=\dfrac{8000}{120000}\\\\\text{unemployment rate}=0.0667\ or\ 6.67\%[/tex]
Hence, labor force participation rate =60%
unemployment rate = 6.67%
Solve for y.
-24 = -8y
Simply your answer as much as possible.
Answer:
Y=3
Step-by-step explanation:
-8 times 3 equals -24
Answer:
y = -3
Step-by-step explanation:
-24 = 8y
Divide both side by 8
-24/8 = 8y/8
-24/8 = y
divide -24 by 8 to get -3
-3 = y
rewrite ..( optional )
y = -3
How much should be added to 58.4 to makes 400?
Answer:
341.6
Step-by-step explanation:
400-58.4=341.6
Solve using suitable property and name the property applied. 3/5 x 35/24 + 15/6 x 3/5
What is the solution to the linear equation?
2.8y + 6 + 0.2y = 5y – 14
Answer:
2y +3x
Step-by-step explanation:
sjsjdjdsndnjssje
Find the square root of 362.1409 by division method
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The scale factor of the enlarged image of a bug is 1:0.125. The diagram measures 16mm, what is the actual length
Answer:
it is 2mm long
Step-by-step explanation:
16x0.125=2 so it is 2mm long
Pls help quicky! I will also give a brainliest!!!!!
Answer:
A) 7.12
Step-by-step explanation:
Simply, subtract 10.52 by 3.4 to get your answer or plug in each answer until you get 10.52
Hope this helps, good luck! :)
Awnser this for brainliest
Answer:
Missing number is 1
Step-by-step explanation:
3(2x+1)
Using distributive property,
=>3(2x)+2(1)
=>6x+2
someone help me please. this is annoying. which ones are right?
9514 1404 393
Answer:
B, C, D, E
Step-by-step explanation:
A square has all side equal, opposite sides parallel, and all angles equal (90°). Because all sides are equal, so are adjacent sides. All but the first and last descriptions apply to a square.
The first description is that of a trapezoid, which has exactly one pair or parallel sides. The last description is that of an isosceles (right) triangle, which has sides that are referred to as "legs."
Please help...*puppy eyes*
(Will pick brainliest)
Step-by-step explanation:
Note that the denominators in the expression are perfect squares:
[tex] {x}^{2} - 5xy + 6 {y}^{2} = (x - 2y)(x - 3y)[/tex]
[tex] {x}^{2} - 4xy + 3 {y}^{2} = (x - y)(x - 3y)[/tex]
[tex] {x}^{2} - 3xy + 2 {y}^{2} = (x - y)(x - 2y)[/tex]
We can then write the given expression as
[tex] \frac{1}{ {x}^{2} - 5xy + 6 {y}^{2} } + \frac{a}{{x}^{2} - 4xy + 3{y}^{2} } + \frac{1}{{x}^{2} - 3xy + 2{y}^{2}}[/tex]
[tex] \frac{1}{ {x}^{2} - 5xy + 6 {y}^{2} } + \frac{a}{{x}^{2} - 4xy + 3{y}^{2} } + \frac{1}{{x}^{2} - 3xy + 2{y}^{2}}[/tex]
[tex] = \frac{1}{(x - 2y)(x - 3y)} + \frac{a}{(x - y)(x - 3y)} + \frac{1}{(x - y)(x - 2y)}[/tex]
[tex] = \frac{(x - y)(x - 2y) {(x -3y)}^{2} + a {(x - y)}^{2} (x - 2y)(x - 3y) + (x - y){(x - 2y)}^{2}(x - 3y) }{ {(x - y)}^{2} {(x - 2y)}^{2} {(x - 3y)}^{2} } [/tex]
1/2h + 9 = 17 solve for h
Answer:
1/2h+9=17
We move all terms to the left:
1/2h+9-(17)=0
Domain of the equation: 2h!=0
h!=0/2
h!=0
h∈R
We add all the numbers together, and all the variables
1/2h-8=0
We multiply all the terms by the denominator
-8*2h+1=0
Wy multiply elements
-16h+1=0
We move all terms containing h to the left, all other terms to the right
-16h=-1
h=-1/-16
h=1/16
Anyone can help :(((:)
Answer:
Below
Step-by-step explanation:
The area of a circle is given by A=πr². Since we know the radius, we can sub r with 11.
This gives A=11²π, which by solving the square gives A=121π.
From there, you would solve with a calculator by typing 121×π, giving a final area of 380.132711084.
**This content involves using the circle area formula, which you may wish to revise. I'm always happy to help!
According to the table below, which of these is a possible taxable income for
a taxpayer filing with the Single filing status in the 25% federal income tax
bracket?
Single
Taxable
But not
income is
Bracket
over
over
$0
8.350
10%
8.650
33.950
15%
33,950
82 250
25%
82,250
171,550
28%
171,550
372,950
33%
372,950
35%
Based on the table, a possible taxable income for a taxpayer filing with the Single filing status is $50,000.
What is taxation?Taxation can be defined as the involuntary (compulsory) fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public institutions and activities.
Based on the table, the range of income for a married couple that is filing singly in the 25% federal income tax bracket is $33,950 to $82,250.
This ultimately implies that, a possible taxable income for a taxpayer filing with the Single filing status is $50,000.
Read more on tax here: https://brainly.com/question/25783927
Answer:
$137,050
Step-by-step explanation:
That is the correct answer on the test.
Can someone help me with this question please
Is pi over 2 rational or irrational
Answer:
rational
Step-by-step explanation:
Answer:
Step-by-step explanation:
Explanation: It is an irrational number. A number is rational if it can be expressed as a quotient of 2 integer numbers. Number π2 cannot be expressed as a quotient of integers, so it is an irrational number.
What is the surface area?
5 ft
4 ft
5 ft
6 ft
5 ft
square feet
Answer:250 ft
Step-by-step explanation:
5 ft x 4 ft = 20
5 ft x 6 ft = 30
20 + 30 = 50
50 x 5 ft = 250 ft
I hope this helps and if its wrong im sorry
Find each difference. (10 Points!)
Answer:
1. -6y^4 +4y^2 -12
2. x - 19
Step-by-step explanation:
1.
(6y^4+3y^2-7) - (12y^4-y^2+5)
= -6y^4+ 4y^2- 12
2. 3(x-5) - (3x+4)
= (3x-15) - (3x+4)
= x-19
A boat heading out to sea starts out at Point AA, at a horizontal distance of 804 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 12^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 2^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Answer:
672 feets
Step-by-step explanation:
Using the solution diagram attached, the vertical height, h of the lighthouse ;
Using trigonometry :
Tanθ = opposite / Adjacent
Tan 2 = h / 804
h = tan 2 * 804
h = 28.076 feets
Using h, we can obtain the distance CB :
Tan θ = opposite / Adjacent
Tan 2 = 28.076 / CB
CB = 28.076 / Tan 12°
CB = 132.08860 feets
Distance between A and B
804 - 132.08860
= 671.9 feets
A bakery offers a sale price of $2.75 for 3 muffins. What is the price per dozen
Answer:
4 muffins is $2.75
4*3=12
1 dozen is 12
2.75 * 3 =$ 8.25
Step-by-step explanation:
Does this graph represent a function? Why or why not?
Answer:
B yes
Step-by-step explanation:
As long as a verticle line intercepts the graph at no more than one point it is a function
Answer:
B. Yes, because it passes the vertical line test
Step-by-step explanation:
no x values are repeated
What is the slope of the linear function of (6 , 2) (9 , 8)
Answer:
1/2
Step-by-step explanation:
The formula for slope is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
9-6=3
8-2=6
3/6=1/2
How do you find the equations of the vertical and horizontal asymptotes for a graph when you only have the graph and no function?
Answer:
See below for answer and explanations (as well as an attached graph)
Step-by-step explanation:
Pay attention to the behavior of the asymptotes. If the asymptotes are approaching a certain x-value or y-value, then that value is undefined for the function.
Take for example [tex]y=\frac{1}{x}[/tex]:
As x approaches ∞ and -∞, then y approaches 0, which is our horizontal asymptoteAs y approaches ∞ and -∞, then x approaches 0, which is our vertical asymptoteSee the graph for a visual.
Which of the quotients are equivalent to -(48/17)
Answer:
oiie4546
Step-by-step explanation:
This is just for people to get points!! Whats 10 x 10?
Answer:
is equls to 100 Brainliest 6
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
The answer is -20.
Step-by-step explanation:
To evaluate the expression, plug x= -3 and y= -5 into the expression. By plugging in the information given from the problem, the expression will look like 4(-3) + 3(-5) + 7.
Next, solve the expression, and the answer will be -20.
Which statement is true? A.|-2.5|>|-3|
B: |-2.5|<|-3| C: |-2.5|=|-3|
Answer:
b.
Step-by-step explanation:
|-2.5|<|-3|
l -2.5 l = 2.5
l -3 l = 3
2.5 < 3
