Anil completes the 72km journey between Bristol and Cardiff in 48 minutes. He then drives 69km from Cardiff to Swansea at an average speed of 60km/h
Work out Anil's average speed (in km/h) for his total journey from Bristol to Swansea.
(with working out pls)
Answers
Answer:
75 km/h
Step-by-step explanation:
48 minutes = 48/60
(48 : 12)/(60:12)
4/5
0.8 hours
average speed between Bristol and Cardiff = 72/0.8 = 90 km/h
average speed of the journey = (60 + 90)/2 = 150/2 = 75 km/h
Related Questions
Domain: -4
BOOKMARK
Determine the domain and range for the following graph.
Answers
The domain and range for the following graph, is written below:
Domain (interval notation) : [-4,4)
Range (interval notation): [1,4)
Domain (inequality notation): -4 ≤ x < 4
Range (inequality notation): 1 ≤ x < 4
What is domain and range?The collection of values that can be put into a function's domain are called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of values that a function can take on is known as its range. Following the putting of the x value, the function outputs this sequence of values.
Utilizing graphs is a useful tool for determining the scope and range of functions. A graph's domain is the entire set of input values shown on the x-axis since the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.
Domain (interval notation) : [-4,4)
Range (interval notation): [1,4)
Domain (inequality notation): -4 ≤ x < 4
Range (inequality notation): 1 ≤ x < 4
As we know,
Domain is the x-values of a function
Range is the y values of a function
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Write the equation of the line that goes through the point (4, -7) and is perpendicular
to the line y + 6 = -:
⅔ (x - 1). Use the table to show your work, if needed, to determine
each form, and then give each form.
Point-Slope Form
Slope-Intercept Form
Answers
The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.
What is line equation?
In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
The slope of line perpendicular to the line y +6=-2/5(x-1)
m1=5/2
point=(4,-7)
y-y1=m(x-x1)
y+7=5/2(x-4)
2y+14=5x-20
5x-2y=34
The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.
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Here is a scale drawing.
The tree has a height of 22 m
Work out the height of the building.
Answers
The height of the building is 44 meters
How to determine the height of the building?From the question, we have the following parameters that can be used in our computation:
Height of the tree = 22 m
From the question, we understand that
Scale of the diagram = 2
This means that
Height of the building = Height of the tree * Scale of the diagram
Substitute the known values in the above equation, so, we have the following representation
Height of the building = 22 m * 2
Evaluate
Height of the building = 44 m
Hence, the height is 44 m
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What is the length of the mid-segment of a trapezoid whose vertices are I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)?
Answers
The length of the mid-segment of the given trapezoid will be 8.5.
What is quadrilateral?A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.
In other meaning, a quadrilateral is a kind of polygon in which four sides for example rectangle, square, and parallelogram are quadrilateral.
As per the given vertices,
I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)
The trapezoid has been plotted below.
The length of LK = 3 - (-3) = 6 units.
Length IJ = 8 - (-3) = 11 units
The length of midsegment x = (11 + 6)/2 = 17/2 = 8.5
Hence "The supplied trapezoid's mid-segment will be 8.5 inches long.".
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need help asap! 100 points
also the option for "This interpretation ___ in the context of the problem."
is "Makes sense" and "Does Not Make sense"
and for "Based on the observations above, it is clear that an appropriate domain for the function is ______"
is: all real numbers
non negative real numbers
real numbers in a a
whole numbers (0,1,2,....)
positive integers (0,1,2,3,....)
integers in a
Answers
What is the function?
The function in this problem is defined as follows:
f(x) = 6x - 1.
Giving how many points a player is awarded when a dice of x is rolled.
The possible values at which the dice can land is up:
1,2,3,4,5,6.
Then the numeric values of the function are calculated replacing x by their values.
The only inputs that make sense are 1,2,3,4,5,6, as they are the values at which the dice can land. For example, a dice cannot land on neither 5.5 nor 10.
Missing Information
The function in this problem is defined as follows:
f(x) = 6x - 1.
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Two stores have the same item for the same price. • Store A offers successive discounts of 5% one week, 10% the next week, and 10% the third week. • Store B offers one discount of 25% the third week. Which offer results in the greater discount? Justify your answer. Show your work.
Answers
Answer:
Below
Step-by-step explanation:
10 % OFF means you pay 90% of price
x = original price
Store A : 5% off means price is .95x
then another 10% off would mean .9 * (.95x)
then another 10% off would mean .9 * ( .9 *(.95x)
this equals .7695 x
Store B 25% off means you pay 75%
price is then .75x
price of .75x at store B is < than .7695 x at store A
so B has greater discount
Answer:
Step-by-step explanation: To compare the discounts offered by Store A and Store B, we need to calculate the final price of the item after all discounts have been applied.
For Store A, the successive discounts of 5%, 10%, and 10% can be applied as follows:
The initial price of the item is reduced by 5%, resulting in a price of 0.95 * Price.
The price from step 1 is reduced by an additional 10%, resulting in a price of 0.9 * (0.95 * Price) = 0.855 * Price.
The price from step 2 is reduced by an additional 10%, resulting in a price of 0.9 * (0.855 * Price) = 0.7695 * Price.
For Store B, the single discount of 25% can be applied as follows:
The initial price of the item is reduced by 25%, resulting in a price of 0.75 * Price.
Comparing the final prices of the item at Store A and Store B, we can see that Store B offers a greater discount. The final price of the item at Store A is 0.7695 * Price, while the final price at Store B is 0.75 * Price. Since 0.75 is less than 0.7695, the final price at Store B is lower.
Therefore, Store B offers a greater discount on the item.
V-(j+y)=61y+82
solve for y
Answers
The value of expression in terms of y is y = (v-j-82)/62
What is expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given that an expression v-(j+y)=61y+82
Solving for y,
v-(j+y)=61y+82
v-j-y = 61y+82
v-j-82 = 61y+y
v-j=92 = 62y
y = (v-j-82)/62
Hence, The value of expression in terms of y is y = (v-j-82)/62
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a conditional probability p(b|a) is equal to its marginal probability p(b) if
Answers
A conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.
The likelihood that any two events will occur is equal to the sum of the probabilities of each event separately, less the probability that the two occurrences will meet. However, if two occurrences are incompatible with one another, then there is a zero probability of the two events intersecting, therefore the likelihood that either one or the other will occur is equal to the sum of the two individual probabilities.
To calculate conditional probability, use the following formula:
p( b | a ) = p( a ∩ b )/ p(a)
It is known that if two events A and B are independent, then p(a ∩ b) = p (a) . p(b)
So, p(b | a) = [p (a) . p(b)]/p(a) = p(b)
Thus, it is concluded that a conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.
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WILL GIVE BRAINLIST AND EXTRA POINTS TO BEST ANSWER PLEASE HLEP
7. Melanie bought some pizza for $2.50 per pound and hot dogs for $1.50 per pound. She spent a total of $30. Use the graph below to sketch all the possible combinations of pizza, p, and hot dogs, h, Melanie could have bought?
Answers
The solutions for the number of pizzas p and hot dogs h is
a) A ( p , h ) = A ( 0 , 20 )
b) B ( p , h ) = B ( 3 , 15 )
c) C ( p , h ) = C ( 6 , 10 )
d) D ( p , h ) = D ( 9 , 5 )
e) E ( p, h ) = E ( 12 , 0 )
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of pizza be = p
Let the number of hot dog = h
The cost of one pizza be = $ 2.50
The cost of one hot dog = $ 1.50
Now , the total amount with Melanie = $ 30
So , the equation will be
2.50p + 1.50h = 30
On simplifying the equation , we get
2.5p + 1.5h = 30 be equation (1)
Multiply equation (1) by 10 , we get
25p + 15h = 300
Now , the values of p and h which will satisfy the equation is
a)
Let p = 0 , h = 20
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 0 ) + 15 ( 20 ) = 300
300 = 300
So , the point A ( 0 , 20 ) satisfies the equation
b)
Let p = 3 , h = 15
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 3 ) + 15 ( 15 ) = 300
75 + 225 = 300
300 = 300
So , the point B ( 3 , 15 ) satisfies the equation
c)
Let p = 6 , h = 10
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 6 ) + 15 ( 10 ) = 300
150 + 150 = 300
300 = 300
So , the point C ( 6 , 15 ) satisfies the equation
d)
Let p = 9 , h = 5
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 9 ) + 15 ( 5 ) = 300
225 + 75 = 300
300 = 300
So , the point D ( 9 , 5 ) satisfies the equation
e)
Let p = 12 , h = 0
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 12 ) + 15 ( 0 ) = 300
300 = 300
So , the point E ( 12 , 0 ) satisfies the equation
Hence , The solutions for the number of pizzas p and hot dogs h is
a) A ( p , h ) = A ( 0 , 20 )
b) B ( p , h ) = B ( 3 , 15 )
c) C ( p , h ) = C ( 6 , 10 )
d) D ( p , h ) = D ( 9 , 5 )
e) E ( p, h ) = E ( 12 , 0 )
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For which function i the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the ame interval for the function g(x) = 1. 8x2?
Answers
Option D is correct the answer. The average rate of change over the interval 1 < x < 5 is greater than the average rate of change over the same interval for the function g(x) = 1. 8x2 is k(x) = 2x^2
The average rate of change:
Given a function y, the average rate of change S of y=f(x) in an interval (xs,xf) will be given by the following equation:
[tex]S=\frac{f(xf)-f(xo)}{xf-xo}[/tex]
In this problem, we have that:
Interval (1,5), so xf=5,xo=1
Then
[tex]S=\frac{f(5)-f(1)}{4}[/tex]
All options are compared to g(x).
[tex]g(x)=1.8x^{2}[/tex]
g(5) = 1.8*(5)^2 = 45
g(1) = 1.8*(1)^2 = 1.8
[tex]S=\frac{45-1.8}{4} =10.8[/tex]
A.=f(x) = x^2
f(5) = 5^2 = 25
f(1) = 1^2 = 1
[tex]S=\frac{25-1}{4} =6.25[/tex]
Smaller than 10.8, so this is not the answer.
B.=g(x) = 1.2x^2
g(5) = 1.2*(5)^2 = 30
g(1) = 1.2*(1)^2 = 1.2
[tex]S=\frac{30-1.2}{4} =7.2[/tex]
Smaller than 10.8, so this is not the answer.
C.=h(x) = 1.5x^2
h(5) = 1.5*(5)^2 = 37.5
h(1) = 1.5*(1)^2 = 1.5
[tex]S=\frac{37.5-1.5}{4}= 9[/tex]
Smaller than 10.8, so this is not the answer.
D.=k(x) = 2x^2
k(5) = 2*(5)^2 = 50
k(1) = 2*(1)^2 = 2
[tex]S=\frac{50-2}{4} =12[/tex]
Greater than 10.8, this is the answer.
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Reggie picked 32 apples in 4 minutes. What is the unit rate?
Answers
Answer:
8
Step-by-step explanation:
Based on the given conditions, formulate: 32 / 4 Cross out the common factor
I'LL GIVE BRAINLIEST!!
Jessica is building a fence around her garden. For every 3 feet of fencing, the cost is $27. Complete the table below showing the length of the fence and the cost.
Answers
Answer:
1, 54, 9, 90
Step-by-step explanation:
3ft=27$, so 1ft=9$. The constant of proportionality is 9 from feet to money so multiply the rest by 9 to get 54, divide backwards to get 9, and then multiply 10 by 9 to get 90.
Answer:
Length : 6 9 10
Cost ($) :54 81 90
Step-by-step explanation:
First, divide 27 by 3 to find the cost of 1 feet fence.
We get the answer 9
Then, to find the length, divide the cost by 9
And to find the cost, multiply the length of fence with 9.
Simple!
(btw I came here for the brainliest especially, so I hope you keep your word:) And hope this helped!)
Sam types a constant number of words per minute.
He takes 8 minutes to type a report of 416 words.
How long does it take him to type an essay of 1534 words?
Give your answer in minutes and seconds?
Answers
Answer:
It would take Sam 29 minutes and 30 seconds
In the figure, △EBA ≅ △EDC.
Triangles E B A and E D C are connected at point E. Angles A B E and E C D are right angles. Angle A E B and D E C are congruent. Sides B E and E D are congruent.
Because CPCTC, which relationships are true?
Check all that apply.
AE ≅ CE
∠BAE ≅ ∠DCE
∠CDE ≅ ∠BAE
AB ≅ BE
AC ≅ BD
Answers
Answer:
1. works
2. works
3. does not work
4. does not work
5. does not work because it does not exist
Step-by-step explanation:
if you have room on your paper, drawing a diagram would be super helpful.
I don't know if I'm 100% right so check with other people before submitting
Answer:The answers are A and B (AE =CE, BAE=CDE)
Step-by-step explanation:
Which of these points is closest to the point (7,1)?
A
(4,1)
B
(7,-1)
C.
(7,4)
D
(11,1)
Answers
Answer:
B (7,-1)
Step-by-step explanation:
(7,-1) is 2 points away from (7,1).
(4,1) and (7,4) are both 3 points away. (11,1) is 4 points away.
That makes B (7,-1) the closest to (7,1)
Parallel and perpendicular through points
Answers
The equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5 is 5y + x = -14.
What is a line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
Point (6,-4),
2x - y = 5,
Calculate the slope as the line is perpendicular to line 2x - y = 5
m = 2
The slope of the line perpendicular, m = - 1 / 5
Calculate the equation of the line as shown below,
[tex]y - (-4) = - 1 / 5 (x - 6)[/tex]
5 (y + 4) = -x + 6
5y + 20 = -x + 6
5y + x = -14
Therefore, the equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5 is 5y + x = -14.
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The complete question is:
What is an equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5?
The coordinates of points a and b are a(2, 16) and b(22, 4). what are the coordinates of the point that is 34 of the way from a to b?
Answers
The coordinates of the point is (17, 7)
How to determine the coordinates of the point?From the question, we have the following parameters that can be used in our computation:
Point A = (2, 16)
Point B = (22, 4)
Ratio = 3/4
The ratio can be expressed as
m : n = 3 : 1
The coordinates of the point can be calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
Substitute the known values in the above equation, so, we have the following representation
Point = 1/(3 + 1) * (3 * 22 + 1 * 2, 3 * 4 + 1 * 16)
So, we have
Point = 1/4* (68, 28)
So, we have
Point = (17, 7)
Hence, the point is (17, 7)
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1/2(40x-16)=32
What is the solution for x
Answers
Answer: x=2
Step-by-step explanation:
1/2(40x-16)=32
20x - 8 = 32
Add 8 on both sides
20x = 40
Divided both sides by 20
x = 2
what is 2+(-8) reinforce
Answers
Answer:
-6
Step-by-step explanation:
2+(-8)=-6
Rationalise the denominator 1/5-root 2
Answers
Answer:
the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).
Step-by-step explanation:
Correctly me if im wrong. To rationalize the denominator of the fraction 1/(5^(1/2)-2), we can use the conjugate of the denominator. The conjugate of a+b is a-b, so the conjugate of 5^(1/2)-2 is 5^(1/2)+2. We can then multiply the numerator and denominator of the fraction by the conjugate to obtain:
1/(5^(1/2)-2) * (5^(1/2)+2)/(5^(1/2)+2)
= (1*(5^(1/2)+2)) / ((5^(1/2)-2)*(5^(1/2)+2))
= (5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)
Notice that we can further simplify this expression by substituting 5^(1/2) with x and expanding the denominator:
(5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)
= (x+2) / (x^2 - 2x - 4)
= (x+2) / (x-2)(x+2)
The denominator of this expression can be further simplified by factoring out x-2, which gives us:
(x+2) / (x-2)(x+2)
= (x+2) / (x-2)(x-2 + 4)
= (x+2) / (x-2)(x^2 - 2x + 4 - 4)
= (x+2) / (x-2)(x^2 - 2x)
= (x+2) / (x-2)((x-1)(x+1))
Finally, we can use the fact that x-1 and x+1 are factors of x^2-2x, which means that we can factor out x-1 and x+1 from the denominator to obtain the fully simplified expression:
(x+2) / (x-2)(x^2 - 2x)
= (x+2) / (x-2)(x-1)(x+1)
= (x+2) / ((x-2)(x-1)(x+1))
Therefore, the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).
How to figure out the unit rate of 4/5 cup of lime juice for every 2 cups of yogurt what is the rate in cups of lime juice per cup of yogurt
Answers
Answer:
i think the answer is 2/5
Step-by-step explanation:
Can someone please help me with this assignment? I will mark your answer brainliest! :)
Answers
3(2x+1)=4x+6
6x+3=4x+6
6x-4x=6-3
2x=3
X=3/2
Are the following compound statements are logically equivalent P ∧ Q ∨ Q and P ∨ Q?
Answers
Answer:
Step-by-step explanation:
This has some significance in logic because if two propositions have the same truth table they are in a logical sense equal to each other – and we say that they are logically equivalent. So: ¬p∨(p∧q)≡p→q, or "Not p or (p and q) is equivalent to if p then q."
...
Logically Equivalent Statements.
p q p→q
F F T
Multiply. Write your answer as a fraction in simplest form.6x5/9
Answers
Answer:
10/3
Step-by-step explanation:
6 × 5 ÷ 9 = 30/9
However, you will realize that the numerator (30) and denominator (9) both are multiples of 3. That means we can divide the numerator and denominator by 3 to get an equivalent fraction:
(30 ÷ 3)/(9 ÷ 3) = 10/3
Therefore, the answer is 10/3
3x+8 = 3x+ does it have one solution no solution or infinite solutions? help needed extremely
Answers
Answer:
No solution
Step-by-step explanation:
There is no real value of [tex]x[/tex] you can substitute into this equation to make it true.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3,-5) and (5,0)
Answers
What is the absolute value of the integer -(-22)?(It is -(-22), not -22).
Answers
Answer:
22
Step-by-step explanation:
Knowledge Needed
| | (absolute value) = Makes anything inside positive after solving.
A negative number multiplied or divided by another negative number is positive.
Question
Set up the equation
| -(-22) |
| 22 |
Stays positive.
22
Two whole number A and B atify the following condition. Find A and B. A and B =44
Answers
After solving the equation, the value of A will be equal to 16 and the value of B will be equal to 28.
What is an arithmetic operation?
The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
As per the provided data in the question,
The given equation is,
A + B = 44
Given ratio A:B = 4:7
Let the value of A = 4x and value of B = 7x
4x + 7x = 44
11x = 44
x = 4
A = 4x
A = 4(4) = 16
B = 7x
B = 7(4) = 28.
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Find the measure of <1
A. 30 degree
B. 122 degree
C. 92 degree
D. 58 degree
Help!!!
(Picture is provided)
Answers
Answer: D. 58 degree
Step-by-step explanation:
A triangle has a total of 180 degrees
92 + 30 = 122 degree
180 - 122 = 58 degree
So, the answer is D. 58 degree
An airplane can level 1,500 miles in 4.5 hours at a constant speed how long will it take the airplane to travel 200 miles
Answers
Answer: 0.6 hours
Step-by-step explanation:
We will set up a proportion to help us solve.
[tex]\displaystyle \frac{1,500\; \;miles}{4.5\;\;hours} =\frac{200\;\;miles}{x\;\;hours}[/tex]
Next, we will cross-multiply and solve by multiplying and using inverse operations.
1,500 * x = 200 * 4.5
1,500x = 900
x = 0.6 hours