Answer:
[tex]Arrival\ Time = 5:30\ pm[/tex]
Step-by-step explanation:
Given
[tex]Current\ Time = 4pm[/tex]
[tex]Speed = 70mph[/tex]
[tex]Distance = 105miles[/tex]
Required
Determine the arrival time
First, we calculate the time taken from Belfast to Dublin using:
[tex]Speed = \frac{Distance}{Time}[/tex]
Substitute values to the expression.
[tex]70 = \frac{105}{Time}[/tex]
Cross Multiply
[tex]70 * Time = 105[/tex]
[tex]Time = \frac{105}{70}[/tex]
[tex]Time = 1.5\ hour[/tex]
Arrival time is then calculated as:
[tex]Arrival\ Time = Current\ Time + Time\ Taken[/tex]
[tex]Arrival\ Time = 4pm + 1.5\ hour[/tex]
[tex]Arrival\ Time = 5:30\ pm[/tex]
Combine Like Terms
22+15x=34-17x
Step-by-step explanation:
22+15x=34-17x
So now, the 34 will join the 22 and the 15x will join the -17x
22-34=-17x-15x
-12=-2x
So now, we divide both sides by -2x
and the negative will cancel negative so
x=6
Please Answer
Determine whether the triangles are similar. If similar, state how (AA, SSS, or SAS), and write a similarity statement.
Answer: The triangles are not similar.
===============================================
Explanation:
Create a 3x3 table. It has 3 rows and 3 columns.
Above the top row, we'll have the side lengths of triangle VUW
Along the left side of the table, we'll have the lengths of triangle LNM
Refer to the diagram below to see what I mean. I used a spreadsheet program to create the table.
Once you have those table headers set up, you'll divide each possible pair of side lengths between the two triangles. For example, VU/LN = 35/20 = 1.75 which is represented as the green cell in the upper left corner (row1,column1). The other 8 green table cells are filled out the same way. This table is a handy way to keep track of all the terms since it's easy to lose track. Again, refer to the diagram below.
After the table is filled out, we need to ask ourselves: "Does a certain value show up 3 times in the green cells?". If so, then we could have similar triangles assuming this value shows up in every row and every column in some fashion.
Unfortunately, we don't have a value show up 3 times in the green cells. The values 1.4 and 1.75 come close by showing up twice, but not three times.
Since we don't have a value show up 3 times, this means that the sides are not proportional to one another. Therefore, the triangles are not similar.
Quadratic Equation
The sum of the ages of two friends is 13 years and the product
of their ages is 42. Find their ages.
Step-by-step explanation:
The sum of ages of two friends is 13 years.
The product of their ages is 42.
Let the age of 1st friend and 2nd friend is x, y respectively.
1 st condition= The sum of ages of two friends is 13 yrs.
i.e x+y = 13........ (I)
2nd condition= The product of their ages is 42.
i.e X*y = 42........(ii)
From equation (I)
X+y = 13
or, X = 13-y........ (iii)
Putting the equation (iii) in equation (ii).
X*y= 42
(13-y) * y = 42
13y - y^2 = 42
[tex] {y}^{2} - 13y + 42 = 0[/tex]
[tex] {y}^{2} - (7 + 6)y + 42= 0[/tex]
[tex] {y}^{2} - 7y - 6y + 42 = 0[/tex]
[tex]y(y - 7) - 6(y - 7) = 0[/tex]
[tex](y - 6) (y - 7) = 0[/tex]
Either; y-6 = 0
y = 6
Or;
y-7=0
y = 7
Keeping the value of y as "7" in equation (ii)
x*y = 42
7x = 42
X = 42/7
Therefore, the value of X is 6.
Therefore, either 1st friend is 6 years and 2nd is 7 years.
Hope it helps...
Choose all of the equations for which x = 2 is a solution.
A. x + 3 = 5
B. +2 = 8
C. X+1=1
D. x - 2 = 4
EX - 7= -5
A tile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a total of $3,000 for 10,000 tiles. The equation y – 3,000 = 0.25(x – 10,000) models the revenue of the tile factory, where x is the number of tiles and y is the total cost to the customer.
Which function describes the revenue of the tile factory in terms of tiles sold?
What is the flat fee for delivery?
$
Answer:
1. f(x)=0.25x+500
2.500
Step-by-step explanation:
well, it was right, and to be honest I don't know how I got it right cause I guessed
USLI5
3) Graph the quadratic function given in factored form and identify the key features. Include at least 5 points on your
graph.
y=(- 3)(x + 1)
Zeros:
Axis of Symmetry:
Vertex:
Y-intercept:
Domain:
Range:
U3LT4
4) Write the quadratic equation of the following in vertex form: vertex (-1,3) and passes through (1, -5)
3. Graph the given quadratic function in the factored form as shown below.
4. The quadratic equation in vertex form, given the vertex (-1,3) and passes through (1, -5), is y = -2(x + 1)² + 3.
The given quadratic function in factored form is y = (x - 3)(x + 1).
Graph of the given quadratic function in the factored form as shown below.
Zeros: The zeros of the function occur when y = 0.
So the zeros of the function are x = 3 and x = -1.
Axis of Symmetry:
The axis of symmetry is x = (3 + (-1)) / 2 = 1.
Vertex:
The vertex is (1, -4).
Y-intercept:
The y-intercept is (0, -3).
Domain: The domain of a quadratic function is all real numbers, so the domain is (-∞, ∞).
Range: Since the coefficient of the x² term is positive, the parabola opens upward. Therefore, the range is y ≥ -4.
Write the quadratic equation of the following in vertex form: vertex (-1,3) and passes through (1, -5)
Using the given information, the vertex form equation can be written as:
[tex]y = a(x - (-1))^2 + 3[/tex]
To find the value of 'a,' we can substitute the coordinates (1, -5) into the equation:
-5 = a(1 - (-1))² + 3
-5 = a(2)² + 3
-5 = 4a + 3
-8 = 4a
a = -2
Plugging the value of 'a' back into the equation, we get the quadratic equation in vertex form:
y = -2(x + 1)² + 3
Therefore, the quadratic equation in vertex form, given the vertex (-1,3) and passes through (1, -5), is y = -2(x + 1)² + 3.
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Suppose x, y and z are integers. Prove that, if 3x−y + 5z is even, then at least one of x, y or z is even.
Given:
x, y and z are integers.
To prove:
If [tex]3x-y+5z[/tex] is even, then at least one of x, y or z is even.
Solution:
We know that,
Product of two odd integers is always odd. ...(i)
Difference of two odd integers is always even. ...(ii)
Sum of an even integer and an odd integer is odd. ...(iii)
Let as assume x, y and z all are odd, then [tex]3x-y+5z[/tex] is even.
[tex]3x[/tex] is always odd. [Using (i)]
[tex]5z[/tex] is always odd. [Using (i)]
[tex]3x-y[/tex] is always even. [Using (ii)]
[tex](3x-y)+5z[/tex] is always odd. [Using (iii)]
[tex]3x-y+5z[/tex] is always odd.
So, out assumption is incorrect.
Thus, at least one of x, y or z is even.
Hence proved.
Could someone create Equations & Explanations based on this question, because I need to solve using substitution and later modify it to create a system of inequalities.
Answer:
3 hours
Step-by-step explanation:
If both the cars are moving in the same direction,
Speed of orange sports car = 60 miles per hour
Since, this car has already moved for 1 hour,
Distance covered by the sports car = speed × time
= 60 × 1
= 60 miles
Speed of the green van = 30 miles per hour
Since, green van has already moved for the duration = 3 hours
Distance covered by the green van = speed × time
= 40 × 3
= 120 miles
Therefore, distance between sports car and green van = 120 - 60
= 60 miles
Relative speed of orange sports car with respect to green van = Speed of sports car - speed of green van
= 60 - 40
= 20 miles per hour
Time taken by the orange sports car to cover 60 miles (Distance between sports car and green van) = [tex]\frac{\text{Distance between the car and van}}{\text{Relative speed of the sports car}}[/tex]
= [tex]\frac{60}{20}[/tex]
= 3 hours
Therefore, orange sports car will take 3 hours to pass the green mini green van.
enlist education system found in Nepal
Answer:
Education in Nepal was long based on home-schooling and gurukulas.[citation needed] The first formal school (Durbar School), established by Jung Bahadur Rana in 1853, was intended for the elite. The birth of Nepalese democracy in 1951 opened its classrooms to a more diverse population.[citation needed] Education in Nepal from the primary school to the university level has been modeled from the very inception on the Indian system, which is in turn the legacy of the old British Raj.[1]
Step-by-step explanation:
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What is the product of 3.06 and 4.1 rounded to the nearest hundredth?
Answer:
12.55
Step-by-step explanation:
The product of 3.06 and 4.1 rounded to the nearest hundredth is 12.55.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The given decimal numbers are 3.06 and 4.1.
Now, product =3.06×4.1
= 12.546
To the nearest hundredth is 12.55
Therefore, the product of 3.06 and 4.1 rounded to the nearest hundredth is 12.55.
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Explain it too and is it x method?
where does (3.5,1.75) go on a coordinate plane?
what are the intercepts of the equation
-2A+2y = -8
At the end of a football season a coach is adding up everyone's scores nathan has scored 11 more than harry harry has scored 10 more then jack. If the total of their scores is 91, how much did harry score
Answer:
Harry has a score of 30
Step-by-step explanation:
Let us represent their scores as:
Nathan = x
Harry = y
Jack = z
At the end of a football season a coach is adding up everyone's scores
Nathan has scored 11 more than harry
x = y + 11
Harry has scored 10 more then jack.
y = z + 10
z = y - 10
If the total of their scores is 91
x + y+ z = 91
y + 11 + y + y - 10 = 91
3y + 1 = 91
3y = 91 - 1
3y = 90
y = 90/3
y = 30
Since Harry's score is represented as y, Harry has a score of 30
Find the measure of the indicated side. Round to the nearest tenth.
Answer:
x=23.5
Step-by-step explanation:
[tex]cos59.3=\frac{12}{x}\\x(cos59.3)=12\\x=\frac{12}{cos59.3}\\x=23.5[/tex]
I NEED THIS QUICK PLEASE ILL MARK YOUR BRAINLY
The sum of 2 numbers is 96. The larger number is 9 less than 4 times the smaller. Find both numbers.
Answer:
75 & 21
Check:
75 + 21 = 96
21 * 4 - 9 = 75
Correct!
Answer:
the smaller number is 21 and the larger number is 75
Step-by-step explanation:
First make a simple equation where x = the smaller number and y = the larger number
ie: 96=x+y
Now make an equation to find the larger number.
ie: y=4x-9
Now substitute the y value in the first equation for the y value in the second equation
ie: 96=x+(4x-9)
Then solve for x
ie: x=21
Then plug in your new x value into the first or second equation to solve for y.
ie: 96=21+y
ie: y=75
Share $112 in the ratio 10:18 PLZ HELP
Answer:
$40 and $72, see below :)
Step-by-step explanation:
One way we can do this is to add the total ratios and then divide that from 112.
10x + 18x = 28x = 112
28x = 112
x = 4
That means, for every ratio, you just have to multiply the amount by 4.
so for example, 10 is just 10 * 4 = 40
So, your answer would be you share the money into $40 and $72
The regular price of a jacket is $62.00. If the discount rate is 15%, how much was the discount?
Discount amount = price x discount percentage as a decimal:
Discount amount = 62.00 x 0.15 = 9.30
Discount = $9.30
Answer:
$52.70
Step-by-step explanation:
The graph of a linear system is shown.
What is the solution to this linear system? Enter a value in each box to create an ordered pair.
( , )
Answer:
(1, 2)
Step-by-step explanation:
From the graph attached,
Two lines are representing linear system of equation.
Since, solution of any system of linear equations is a common point of the two lines.
In other words, point of intersection of these lines represent the solution of linear system of equations.
Solution of the linear system of equations → (1, 2)
Figure ABCD is a trapezoid. Find
the value of x.
Answer:
Step-by-step explanation:
because we have a kite,
AB=AD
4x=x+15
4x-x=15
3x=15
x=5
Im confused on this can someone help me out
please help me with this question
Answer:
B. 36
Step-by-step explanation:
Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6)?
Given:
Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).
To find:
The equation of hyperbola.
Solution:
We have, directrices at y = ±2 so this hyparabola is along the y-axis.
The standard form of hyperbola is
[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex] ...(i)
where, (h,k) is center, foci are [tex](h,k\pm c)[/tex] and directrix are [tex]y=k\pm \dfrac{a^2}{c}[/tex].
On comparing foci, we get
[tex](h,k\pm c)=(0,\pm 6)[/tex]
[tex]h=0,k=0,c=6[/tex]
On comparing directrix we get
[tex]k\pm \dfrac{a^2}{c}=\pm 2[/tex]
[tex]\dfrac{a^2}{c}=2[/tex]
[tex]\dfrac{a^2}{6}=2[/tex]
[tex]a^2=12[/tex]
Now,
[tex]a^2+b^2=c^2[/tex]
[tex]12+b^2=(6)^2[/tex]
[tex]b^2=36-12[/tex]
[tex]b^2=24[/tex]
Putting [tex]h=0,k=0,a^2=12,b^2=24[/tex], we get
[tex]\dfrac{(y-0)^2}{12}-\dfrac{(x-0)^2}{24}=1[/tex]
[tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex]
Therefore, the equation of hyperbola is [tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex].
Answer:
the person above has the right answer. I took the test.
Step-by-step explanation:
The person above is correct.
Solve for V in V= s^3, if s= 4.
V=
Answer:
64
Step-by-step explanation:
v = s^3
v = (4)^3 [4x4x4]
v = 64
x-2y=3
4x -8y = 12
Substitution
Answer:
Solution in photo
Step-by-step explanation:
Factor completely 3x^2+y
A.) x(3x+y)
B.) y(3x^2)
C.) xy(3x+1)
D.) prime
Answer:
Non of the above
Step-by-step explanation:
[tex]3 {x}^{2} + y \\ = x(3x + \frac{y}{x} ) \\ or \\ = y( \frac{ 3{x}^{2} }{y} + 1)[/tex]
Answer:
D. Prime
I just took the test
Step-by-step explanation:
The temperature on the moon can vary from -172°C to -126°C. Find the difference between the maximum and minimum temperature.
I really need step by step explaining please!! :D
Answer:
The range is 46
Step-by-step explanation:
-172 is the minimum
-126 is the maximum
subtract -126 by -172 and you get 46
Given f of x equals 5 times x minus 6 for x less than 3, equals x squared for x between 3 and 5 inclusive, and equals 2 times x plus 15 for x greater than 5 find f '(x) and give its domain.
Answer:
D. 5 for x less than or equal to 4, equals 2x for x between 4 and 6 including 6, and equals 4 for x greater than 6 Domain: All real numbers.
Step-by-step explanation:
Find the complete diagram attached
First we need to get the derivative of the functions
For the function f(x) = 5x - 6
Using the formula
If f(x) = axⁿ
f'(x) = naxⁿ⁻¹
For the function f(x) = 5x - 6
f'(x) = 1(5)x¹⁻¹
f'(x) = 5x⁰
f'(x) = 5
For the function f(x) =x²-2
f'(x) = 2x²⁻¹
f'(x) = 2x
For the function f(x) = 4x+10
f'(x) = 1(4)x¹⁻¹
f'(x) = 4x⁰
f'(x) = 4
Get the domain
The domain is the value of the input variable x for which the functions exists. For the functions given, the domain will be on all real numbers i.e the functions will exists for any value of x on the number line.
Hence Option D is correct
Answer:
Was the answer above correct????
Step-by-step explanation:
A ladder 12 m long is propped up against a building at an angle of 15°. How far up the wall does the ladder go?
The ladder can go as far as 3.1m
Application of SOH CAH TOAThe given set up is. a triangle with the following parameters
Angle of elevation = 15 degrees
Hypotenuse = 12m
Required
Height of the building
Using the expression
sin theta = opp/hyp
sin 15 = h/12
h = 12sin15
h = 3.1m
Hence the ladder can go as far as 3.1m
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-15x^2+801x-5900
Answer:
The widgets should be sold for $26.7 for the company to make the maximum profit.
Step-by-step explanation:
Given the quadratic equation
[tex]f\left(x\right)=-15x^2+801x-59000[/tex]
As the leading coefficient is (-3), so the graph would be a downward Parabola.
Thus, the maximum profit would be at the vertex.
The selling price 'x' can be determined by determining the x-coordinate of the vertex.
In order to calculate the x-coordinate of the vertex, we can find this by
x = -b/2a
where a = -15 and b = 801
x = -801 / 2(-15)
x = -801/-30
x = 801/30
x = 267/10
x = 26.7
Therefore, the widgets should be sold for $26.7 for the company to make the maximum profit.