The time (in hours) taken by the bus and the car to travel between the two towns in terms of x is 5 hours 20 minutes and 4 hours respectively and the equation in x formed is [tex]x^2 + 15x -2700=0[/tex]
Given that:-
Distance between towns A and B = 240 km
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at x km/h.
Let the speed of the bus be s km/hr and,
The time taken by the car to travel from A to B be t hours.
Hence,
(15+x)*t = (t + 80/60)*x
15t + xt = xt + 4x/3
15t = 4x/3
t = 4x/45 hours.
Hence,
(15 + x)*(4x/45) = 240
x(x + 15)/45 = 60
[tex](x^2 + 15x) = 60*45[/tex]
[tex](x^2 + 15x) = 2700\\x^2 + 15x -2700=0\\x^2-45x+60x-2700 = 0[/tex]
x(x-45) +60(x - 45) = 0
(x - 45)(x + 60) = 0
x = 45,-60
As the time cannot be negative,
x = 45 km/hr
t = (4*45)/45
t = 4 hours (time taken by car)
Time taken by bus = 4 hours + 80 minutes = 5 hours 20 minutes
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Identify the area of the rhombus.
Answer:
2160ft²Step-by-step explanation:
rhombus formed by 4 right triangles, 51ft hypotenuse and 45ft cathetus (90: 2 = 45). we use pythagoras to find the missing side so that we can find the area of a triangle and multiply it by 4
c = √(51²-45²)
c = √(2601 - 2025)
c = √576
c = 24ft
Area triangle= (½)×b×h
(½)45 * 24 =
(½)1080=
540ft²
multiply by 4
540 * 4 =
2160ft² (Area of the rhombus)
or
Rhombus Area Using Diagonals:
A = ½ × d1 × d2
A = ½ * 90 * 48
A = 2160ft² (Area of the rhombus)
Multiplying Rational Numbers -2/3 (-1/5)
Answer:
[tex]{ \rm{ - \frac{2}{3}( - \frac{1}{5} ) }} \\ \\ = { \rm{( - 1 \times - 1)( \frac{2}{3} \times \frac{1}{5} )}} \\ \\ = { \rm{( \frac{2 \times 1}{3 \times 5} )}} \\ \\ = { \rm{ \frac{2}{15} }}[/tex]
Answer: [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
1. Simplify the expression
[tex]-2/3(-1/5)[/tex]
2. Multiply the fractions
[tex]\frac{\left(-2\cdot -1\right)}{\left(3\cdot 5\right)}\\[/tex]
3. Simplify the arithmetic
[tex]\frac{2}{\left(3\cdot 5\right)}[/tex]
4. Simplify the arithmetic
[tex]\frac{2}{15}[/tex]
The cost of 2 rugby balls and 3 golf balls is £18.39.
The cost of 5 rugby balls and 7 golf balls is £45.10.
Work out the cost of
a) a rugby ball.
b) a golf ball.
The cost of a rugby ball is $6.57
The cost of a golf ball is $1.75
How to calculate the cost of a rugby and golf ball ?Let x represent the cost of a rugby ball and y represent the cost of a golf ball
2x + 3y= 18.39.........equation 1
5x + 7y= 45.10.........equation 2
multiply equation 1 by 5 and equation 2 by 2
10x + 15y= 91.95
-
10x + 14y= 90.2
y= 1.75
Substitute 1.75 for y in equation 2
5x + 7(1.75)= 45.10
5x + 12.25= 45.10
5x= 45.10-12.25
5x= 32.85
x= 32.85/5
x= 6.57
Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75
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Marisol is organizing a party for the student council with a $50 budget. the linear function 15x+2y=50 represents the number of pizzas x and the number of bottled drinks y she can buy. if marisol buys 2 pizzas, how many bottled drinks can she buy?
The number of bottled drinks bought by Marisol is 10 in the student council party.
What is defined as the liner equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 12x+8y = 3 but also -x+8y = 2 are two-variable linear equations.For the given linear equation;
The total budget of the party is $50.
The linear function function which represents the number of pizzas x and the number of bottled drinks y is;
15x + 2y = 50
Now, the number of pizza bought = 2.
To find the value of bottled drinks, put x = 2 in the linear function.
15×2 + 2y = 50
Simplify the equation;
30 + 2y = 50
2y = 50 - 30
2y = 20
y = 10
Thus, the total number of bottled drink bought by the Marisol is 10.
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Expand the following
8(p+ 4)
Answer:
8p+32
Step-by-step explanation:
Nora bought 8-½ pounds of potatoes for $27.63.
What is the price, in dollars, of 1 lb of potatoes?
Answer:
$3.25
Step-by-step explanation:
This question tests on the concept of conversion.
Given from the question,
8.5 pounds = $27.63
(8.5 ÷ 8.5) pounds = $27.63 ÷ 8.5
1 pound = $3.25 (Rounded off to 2 decimal places)
I'm not sure , hellp
In the given parallelogram,
∠W = 85°
∠WXV = 59°
Since, VW is parallel to XY,
So,
∠YVX = ∠WXV ............... (Alternate interior angles)
⇒ ∠YVX = 59°
Now,
∠W = ∠Y .................. (Opposite angles of a parallelogram are equal)
⇒ ∠Y = 85°
As we know that opposite sides of a parallelogram are equal,
Therefore,
VW = YX
⇒ 2x = 6
⇒ x = 6/2 = 3 units
What is a Parallelogram?A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides.In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it.The parallelepiped is a parallelogram's three-dimensional equivalent.Order 2 rotational symmetry (through 180°) is present in a parallelogram (or order 4 if a square). The shape must be either a rhombus or an oblong if it also possesses precisely two lines of reflectional symmetry (a non-square rectangle). A square object is one with four lines of reflectional symmetry.
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Fred says that the two equations below have the same solution:
Equation A: -3 (x+9)= 18
Equation B: x +9=-6
Describe the acceptable move that proves the two equations are equivalent.
Yes the acceptable move that proves the two equation are equivalent.
What is equivalent equation?
equivalent equation are algebraic equations that have identical solutions or roots. Adding or substracting the same number or expression to both side of an equation produce an equivalent equation. Systems of equations that have the same solutions are said to be equivalent equations. Finding and resolving equivalent equations is an important skill for everyday life as well as for algebra classes. Consider some illustrations of equivalent equations, how to solve them for one or more variables, and practical applications of this knowledge.
Sol-
By observing both equations
In equation A : -3(x+9)=18
Divide the equation A by -3
=> (x+9)=-6
And this result equals to equation B
Hence both equations are equivalent
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3. In the diagram below the grey shapes have the same area. Work out the value of x.
Answer:
x = 7 units
Step-by-step explanation:
Left area = (3x-1)(4)
Right area = 8*12 - (4 ( x -3)) and the areas are =
(3x-1)4 = 8*12 - ( 4(x-3)) expand both sides
12x - 4 = 96 - 4x + 12 solve for x = 7 units
Answer:
Area of big rectangle: 8 x 12 =96
Area of white part : 4(x-3)
96-(4(x-3))
96-(4x-12)
96-4x+12
Area of rectangular grey part: 108-4x
Area of other grey figure:
4(3x-1)
= 12x- 4
Finding x:
12x-4 = 108 -4x
-4-108 = -4x - 12x
112 = 16x
x= 7
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John is putting 10 books in a row on his bookshelf. He will put one of the books, Pride and Prejudice, in the first spot. He will put another of the books, Little Women, in the last spot. In how many ways can he put the books on the shelf?
John is putting 10 books in a row on his bookshelf. he would arrange it in
40,320 ways.
What is permutation?Generally, A permutation is a rearrangement of a set of elements. In other words, it is a way to arrange a set of items in a specific order. For example, the permutations of the set {1, 2, 3} are {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}. The number of possible permutations of a set of n elements is n!.
John is placing 8 books on the shelf in between Pride and Prejudice and Little Women.
The number of ways to arrange these 8 books is 8! (8 factorial).
since the order of the books in the first and last spots is predetermined,
The final answer is 8! = 40320ways
= 40,320 ways.
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a restaurant offers 4 appetizers, 2 main courses, and 3 desserts. carlos wants to order 3 appetizers, 0 main courses, and 3 desserts. how many different meals could carlos order?
ANSWER ASAP PLEASE TEST ALMOST DUE
Your boss is still trying to save money on car rentals. You compare Alpha Car Rental, which charges $72.00 per day with unlimited free mileage, and Amazing Car Rental, which charges $22.90 plus 30 cents per mile.
a. Some days you drive many miles, and some days you drive fewer miles. Determine the range of daily mileage for which each company is the less expensive choice.
b. Write a report to your boss that includes your recommendations about which car-rental company to use depending on the number of miles you plan to drive. Explain how you arrived at your recommendation. Use computations/written work, graphs, or tables to provide support for your conclusions.
Answer:
A)
If you are driving many miles a day, Alpha Car Rental is cheaper. If you are driving fewer miles a day, then Amazing Car Rental is cheaper.
B)
You can find this out by graphing the 2.
Alpha: y = 0x + 72.
Amazing: y = 0.30x +22.9
Where y is cost, and x is miles.
When you graph the 2, Alpha is a straight line because it has no mileage charge. The 2 linear functions meet at point (163.6, 72). Meaning if you drive more than 163 miles, it is cheaper to use Alpha Car Rental over Amazing Car rental.
Hope that helps
suppose you have 3 possible mutually exclusive initiating events (causes) and 4 possible outcome events (consequences) that are not mutually exclusive. how many scenarios do you have?
The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. The two events are mutually exclusive if they cannot occur at the same time.
What pairs of occurrences can never coexist?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously.
A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.
What are some examples of mutually exclusive events?
Several instances of occurrences that can never occur simultaneously include:
The outcomes of receiving head or tail while flipping a coin are mutually exclusive.
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HELP PLS I NEED THIS DONE BY TOMORROW!!
PLS BE 100% CORRECT
The answer to the following verbal expressions of inequality are:
A: x ≤ 69;
B: The option that shows the graph of the inequality d<2 is Option C.
C: The option that shows the graph of the inequality of x ≤ 5 is option B.
D: represents the graph of the inequality given in option C that is x > -8
E: The inequality that describes the situation is ≥ 49 (Option B)
What is inequality?In mathematics, inequality is defined as a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
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Which inequality is true when the value of z is -16
How do you solve this equation x²=36
You can see the following steps to know the solvation
x² = 36
x = √36
x = 6.
Jason was paid 10 cents for every golf ball he found and brought back to the shop.
Answer: C.
Step-by-step explanation:
X would represent the number of golf balls he brought back and .10 is the amount of money he makes for each of them.
Answer:
0.10x
Step-by-step explanation:
x stands for the amount of golf balls he brings back to the shop and 0.10 stands for the 10 cents he gets paid for each ball.
susanne checks the temp. at 11:00am she notices that if the temp. rises by 8 more degrees it will break the record high temp. for the day witch is 82 degreese
The current temperature based on the information given about Sussane is 74°.
What is temperature?It should be noted that temperature is used to illustrate the hotness and the coldness that's in a a particular body.
Let the current temperature be represented as x.
Since Susanne checks the temp. at 11:00am and she notices that if the temp. rises by 8 more degrees it will break the record high temp. for the day witch is 82 degrees, the current temperature will be:
x + 8 = 82
x = 82 - 8
x = 74°
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What is the next digit in the quotient?
5?
8)4184
-40
18
————
Answer: 2
Step-by-step explanation:
The greatest divisor of 8 that is less than 18 is 16, and 16 divided by 8 is 2.
The next digit of quotient is 16.
Here given that,
4184 is divisible by 8
since we know that,
Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.
4184 is divisible by 8 we get,
⇒ 4148/8
⇒ 516
So, the quotient is 516
Hence,
The next digit is 16.
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y is inversely proportional to x. when x=3 y=8. work out the value of y when x is 8
Answer:
y = 3
Step-by-step explanation:
given y is inversely proportional to x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
to find k use the condition x = 3, y = 8
8 = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )
24 = k
y = [tex]\frac{24}{x}[/tex] ← equation of proportion
when x = 8 , then
y = [tex]\frac{24}{8}[/tex] = 3
Answer
3
Step-by-step explanation:
when one is increasing the other one should decrease.since 3 has increased by 5 ,then y should decrease by 5.
Write a real-world problem
that is represented by the division problem 38 ÷ 5 = 7 R3 in which it makes sense to round the quotient up to 8.
Answer:
See below
Step-by-step explanation:
Comment
This is a good question. It makes you think about when you should round and maybe when you shouldn't.
You have a building side that is 38 square yards. You want to know how much paint to buy to cover the given side.
Let us say that each can of paint could cover 5 square yards. You cannot buy any can that might be smaller to take care of the 3 remaining square yards.
You have no choice. You have to round the answer from 7 R 3 to 8.
Two ships leave a port at the same time. the first ship sails on a bearing of 32 degrees at 16 knots and the second on a bearing of 122 degrees at 24 knots. how far apart are they after 2.5 hours?
The ships and the port form a right triangle and hence, their distance is 72.1 nautical miles
Knot is a velocity unit equals to nautical miles per hour.
The situation can be depicted in the attached picture.
The distance travelled by the 1st ship after 2.5 hours is:
s1 = 16 knots x 2.5 hours = 40 nautical miles.
The distance travelled by the 2nd ship id:
s2 = 24 knots x 2.5 hours = 60 nautical miles.
Since the angle difference between those 2 ships is 90⁰, the distance between the ships can be obtained using the Pythagorean Theorem.
Referring to the attached picture,
d² = 40² + 60²
d² = 1600 + 3600
d² = 40² + 60²
d² = 5200
d = 72.1 nautical miles
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The art department is planning a trip to a museum. The bus costs $100 plus $7 per student. A professor donated $40 to defray the costs. If the school charges students 10$ each, how many students need to go on the trip not to lose money?
Total 20 students should go to the trip to not to lose money.
Cost of bus = 100 dollars
For students the charge is 7 dollars per student.
Amount professor donated to defray the cost is 40 dollars.
School is charging 10 dollars per student for the trip.
Therefore, reduced cost = 100 - 40 = 60 dollars
Profit earned from each student is 10 - 7 = 3 dollars.
Hence, minimum students should go to the trip will be 60 ÷ 3 = 20.
Since, 20 × 3 = 60, the cost is covered and no money is lost.
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The perimeter of the rectangle below is 144 units. Find the length of side RS.
The numerical value of side RS of the rectangle with a perimeter of 144 units is 30 units.
What is the numerical length of RS in the given rectangle?A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
P = 2( l + w )
Given the data in the question;
Perimeter of the rectangle P = 144 unitsLength RQ = 4z + 2Width RS = 3zz = ?First we determine the value of the variable z, plug the given values into the perimeter formula and solve for z.
P = 2( l + w )
144 = 2( (4z + 2 ) + (3z) )
144 = 2( 4z + 2+ 3z )
144 = 2( 7z + 2 )
144 = 14z + 4
14z = 144 - 4
14z = 140
z = 140/14
z = 10
Now, find the numerical value of side RS.
Width RS = 3z
RS = 3( 10 )
RS = 30
Therefore, the length of side RS of the rectangle is 30 units.
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suppose that a poll finds that % of taxpayers who filed their tax return electronically self-prepared their taxes. if three tax returns submitted electronically are randomly selected, what is the probability that all three were self-prepared?
The probability that the three tax returns submitted were self-prepared is 0.0325.
What do we mean by probability?The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.Both the overall number of favorable outcomes and the likelihood of any specific event are interdependent.A typical definition of probability is the ratio of favorable outcomes to all other outcomes in the sample space.Probability of an Event P(E) = (Number of favorable outcomes) ÷ (Sample space).So, the formula for the binomial probability distribution of x successes in n tries:
[tex]P(X=x)={ }^n C_x p^x(1-p)^{n-x}[/tex]Where the probability of success is p, and n is the number of trials.
If three electronically filed tax returns are randomly chosen, the likelihood that all three were prepared by the taxpayer is given by:
P(X = 3) = ³ C₃ (0.319)³ (1 - 0.319)³⁻³= (1)(0.319)³(1)= 0.032461759 = 0.0325Therefore, the probability that the three tax returns submitted were self-prepared is 0.0325.
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The correct question is given below:
Suppose that a poll finds that 31.9% of taxpayers who filed their tax returns electronically self-prepared their taxes. If three tax returns submitted electronically are randomly selected, what is the probability that all three were self-prepared?
Which of these types of income is taxed? A federal tax refunds B interest on savings account C interest from municipal bonds
Answer:
the answer is A
Step-by-step explanation: the reason i said A is because the answer is litteraly in the question if you think about it
Anyone know the answer for this
Answer: x=17
Step-by-step explanation:
1.Identify relationship
Since both the angles are on the inside of both parallel lines and on the same side of the transversal you know that you have a same side interior relationship that makes them supplementary
2. set up equation
because they are supplementary you know that they are equal to 180 which gives the equation: 3x+6+123=180
3. solve the equation
3x+6+123=180
3x+129=180 | combine like terms
3x=51 | subtract 123 from both sides
x=17 | divide by 3 on both sides
3.
7 ft
8.7 ft
10 ft
566567889988766433678
A local charity raised $7,280 selling T-shirts. Each T-shirt cost $16
Answer:
most have 455 T-shirts
Step-by-step explanation:
if u do $7,280÷$16= 455
Answer:most have 455 T-shirts
Step-by-step explanation:if u do $7,280÷$16=
Charles buys 50 packs of pens.
There are 15 pens in each pack.
Each pack costs £4.20.
Charles sells each pen for 60p but he only manages to sell of the pens.
How much profit did he make?
By using the method of subtraction, the profit earned by charles is £4.8
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
There are 15 pens in each pack.
Each pack costs £4.20.
Charles sells each pen for 60p but he only manages to sell of the pens.
60p x 15 = 9
So, the profit earned by charles is 9- 4.20 = 4.8
Therefore, the profit earned by charles is £4.8
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