The time that both gongs will strike together again after striking simultaneously at 12 noon is 2 : 34 pm.
What time would the gongs strike together?The time the gongs will strike together again can be determined by calculating the least common multiple of 22 and 77. The multiple of a number is the product of a number and another number. For example, a multiple of 2 is 10. The least common multiple is the smallest multiple that is common to two or more numbers.
The least common multiple would be determined using the prime factorisation method.
Prime factors of 22 = 2 x 11
Prime factors of 77 = 7 x 11
The least common multiple = 2 x 7 x 11 = 154
The next time both gongs would strike at the same time is 154 minutes or 2 hours 34 minutes
12 noon + 2 hours + 34 minutes = 2 : 34 pm
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Question 12
REASONING Given: 2a²
a
= 72. Conjecture: a = 6. Write a counterexample.
A counterexample to show that 2a^2 = 72 where a = 6 is that a = -6 will still arrive at 72
What is counterexample?This is a term that counters a statement. we can therefore say that counterexample is one that proves a statement to be false.
How to write the counterexamplegiven data
2a² = 72
Conjecture: a = 6
The counterexample is a = -6
substituting a = -6 into the given equation
= 2a²
= 2 * ( -6 )^2
= 2 * ( 36 )
= 72
Since a = -6 gave same answer of 72 as a = 6 then a = -6 is the counterexample
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how do i multiply these ? (5x-6.9)(2x+12.2)
Answer:
10x^2 + 47.2x - 84.18
Step-by-step explanation:
You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible
PLEASE HURRYYYY
The segment contains points S(a, b) and T(c, d). Which formula should be used to find the midpoint of the segment?
is 12x17=6x34 true or is it flase i cant do it
John's commute to work is 20kmhr while Sheri's commute is 500mmin.
Who has the fastest commute to work in mihrif 1.61km=1mi?
By 6.2 miles per hour, Sheri commutes more quickly.
We are given that,
John travels to work = 20km/hr
Sheri travels to work = 500m/min converting this into km/hr we get ,
1.61km/hr or 1 mile
John travels to work at the following rate:
[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]
Sheri travels work at the following rate:
[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]
Computing the difference between the two,
18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr
thus, by 6.2 miles per hour, Sheri commutes more quickly.
What are conversions in maths?
An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.
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If g(x) = -x, for what value of x does
g(x) = -9?
Answer:
x = 9
Step-by-step explanation:
given g(x) = - x and g(x) = - 9 , the equate right sides
- x = - 9 ( multiply both sides by - 1 )
x = 9
In a Sports league each team has 36 players and 3 coaches. There are also a number of team assistants. The ratio of team assistants to players is 1/6. What is the ratio of coaches to assistants?
Answer:
1/2
Step-by-step explanation:
We know that each team has the following:
36Players + 3Coaches + ?Assistants = Sports League
We know that the ratio of assistants to players is 1/6, rewrite the equation accordingly:
36Players + 3Coaches + 6Assitants = Sports League
Now find the ratio of coaches to assistants:
3Coaches / 6Assistants = 1/2
PLEASE HELP I NEED THIS VERY VERY SOON!!!!
Tim and Jim leave Chicago traveling in opposite
directions. Jim travels 65 mph and Tim travels
63 mph. In how many hours will they be 1056
miles apart?
The formula for time, t = d/s which means time exists equivalent to distance divided by speed.
The times taken to travel 441 miles apart exists 8.25 hours
What is the time formula?Time can be defined as the dimension based on which the evolution of any system takes place. It can be measured in terms of seconds, minutes, hours, days, weeks, months, and years.
The formula for time, t = d/s which means time exists equivalent to distance divided by speed.
Given: Train running in the opposite direction
Speed of one train (S1) = 65 mph
Speed of one train (S2)= 63 mph
Distance to be covered = 1056 miles
Train exists running in the opposite direction, so their relative speed = (S1 + S2)
Relative speed = (65 + 63) = 128 mph
Now, time is taken to travel 1056 miles apart
Time = Distance / relative speed
Time = 1056/128 = 8.25 hours
Therefore, the times taken to travel 441 miles apart exists 8.25 hours
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Consider the matrices.
What matrix results from B + A?
Enter your answer by filling in the boxes.
Answer:
Step-by-step explanation:
[tex]\displaystyle\\A=\left[\begin{array}{ccc}-1&6\\-2&2\\4&9\\-5&-11\end{array}\right] \ \ \ \ \ \ \ \ \ B=\left[\begin{array}{ccc}-4&-1\\-8&8\\2&-7\\-6&5\end{array}\right] \\\\A+B=B+A\ (commutativity)\\\\\Rightarrow B+A=\left[\begin{array}{ccc}-4+(-1)&-1+6\\-8+(-2)&8+2\\2+4&-7+9\\-6+(-5)&5+(-11)\end{array}\right] \\\\\\ \Rightarrow B+A=\left[\begin{array}{ccc}-5&5\\-10&10\\6&2\\-11&-6\end{array}\right][/tex]
3.if the m∠1 is 57° , find the measure of ∠6.
Show your work
123°
180°-57°=<6=123°
Find the value of x
A. x = 20
b. x = 32
c. x = 24
d. x = 28
Using proportions, it is found that the value of x would be 28.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We have been given two triangle, we need to find the value of x.
Then using proportions;
12/(x-7) = 8 / 14
Cross multiplication;
12 (14/8) = x - 7
3 (14/2) = x - 7
21 = x - 7
x = 21 + 7
x = 28
Therefore, the value of x is 28.
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Which recursive sequence would sequence 5,-8,5
The recursive sequence that defines 5, -8, 5, is given by:
[tex]a_n = -a_{n-1} - 3[/tex]
In which the first term is of [tex]a_1 = 5[/tex].
What is a recursive sequence?A recursive sequence, in general terms, can be defined as follows:
[tex]a_n = f(a_{n - 1))[/tex]
In which the first term [tex]a_1[/tex] is given.
This rule means that the nth term of the sequence is a function depending on the previous term, the (n-1)th term of the function.
In the context of this problem, the sequence is given as follows:
5, -8, 5.
From the first to the second term, the number changed the signal and was subtracted by 3, and the same is true for the second to third term, as follows:
-5 - 3 = -8.-(-8) - 3 = 8 - 3 = 5.Then the recursive rule for the sequence is given as follows:
[tex]a_n = -a_{n-1} - 3[/tex]
With first term of [tex]a_1 = 5[/tex].
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Guys i need help is this right?
The range of the function in this situation as required in the task content is; Choice D; 0 ≤ y ≤ 3.
How to determine the range of a function?It follows from the task content that the range of the function described by the situation is to be determined.
The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.
It follows that since the distance he has remaining, y is a function of how long he has been riding the bike, x and it's said that; the boy lives 3 miles from the library; the range of the function described is; Choice D ; 0 ≤ y ≤ 3.
Please Note: The term, domain encompasses the set of all possible input values, otherwise termed the independent variable, x.
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What number does
2(x+3)²
3(x-1)²
represent WHEN x = 3?
Answer:
72 and 12
Step-by-step explanation:
substitute x = 3 into the expressions
2(x + 3)²
= 2(3 + 3)²
= 2(6)²
= 2 × 36
= 72
--------------------
3(x - 1)²
= 3(3 - 1)²
= 3(2)²
= 3 × 4
= 12
On your own sheet of paper, use long division to find the quotient of 5,550 ÷ 39. What is the remainder?
Answer: Quotient 142
Remainder 12
Step-by-step explanation:
The quotient is 142 and the remainder is 12.
The long division method is as follows :
[tex]142[/tex]
[tex]39\sqrt{5550}[/tex]
-39
165 (3rd 5 taken down )
-156
90 ( 0 taken down )
-78
12
step 1 : take the first two digits (55) of the divident , now multiply 39 with such a number that the product of those two must not go above 55 but should be closest to it.
step 2 : write the number on top and subtract the answer from 55.
step 3 : Now bring down the third 5 and write it after the answer of the subtraction. So the number becomes 165.
step 4 : Again multiply 39 with such a number that the product of those two must not go above 165 but should be closest to it.
step 5 : write that number on top after the previous number and subtract the answer from 165.
step 6 : Now bring down the 0 and write it after the answer of the subtraction. So the number becomes 90.
step 7 : Again multiply 39 with such a number that the product of those two must not go above 90 but should be closest to it.
step 8 : write that number on top after the previous number and subtract the answer from 90.
We have to repeat these steps until all the digits from the divident are used and the remainder comes out to less than the divisor.
Here all the digits of divident are used and the remainder (12) is also less than the divisor (39), so we stopped.
Hence the quotient is 142 and the remainder is 12.
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Pls answer the question on the image attatched.
Step-by-step explanation:
loga(x) calculates simply the exponent of a needed to get x as result.
so, 5 "to the power of the exponent of 5 needed to get 7" is 7 (we give 5 the exponent that it needs to create 7, so it creates 7).
the same thing with 2, where we give 2 the exponent it needs to create 1/49. so, it creates 1/49.
we get therefore
7 × 1/49 = 7/49 = 1/7
Help please i forgot about this
Whats the product of 3 plus 4
whats 5 times 8
The dash triangle is a dilation image of the solar triangle with a center at the origin. Is a dilation and enlargement or a reduction find the scale factor of the dilation.
Because the scaling factor is a whole number, which is 3, the enlargement of the dashed triangle is a dilatation.
Recall:
Dilation enlarges or shrinks a figure or shape.The original image prior to any reduction or expansion is the image of a dilatation.The new image created following any necessary reduction or enlargement is the scale copy.Any side length of the new image divided by the corresponding side length of the old image gives the scale factor.The dilation is a reduction if the scale factor is a fraction.The dilatation is an enlargement if the scale factor is a whole number.Thus:
For the dashed triangle, measure the separation between the points (2, -2) and (0, -2).
(2, -2) to (0, -2) is separated by 2 units.Using the coordinates (6, -6) and (0, -6) for the solid triangle, calculate the equivalent distance:
(6, -6) and (0, -6) are separated by 6 units.Scale factor = 6/2 = 3
The dilation is an enlargement because the scale factor is a whole number.
In conclusion, the enlarged dashed triangle indicates a dilatation because the scale factor, which is 3, is a whole number.
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Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.
Let x be the number of minutes water has been added.
(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = ____
Amount of water in the second pool (in liters) = ____
(b)
Write an equation to show when the two pools would have the same amount of water.
______________
Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.
Let x be the number of minutes water has been added.
(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = 23x + 728
Amount of water in the second pool (in liters) = 37x
(b)
Write an equation to show when the two pools would have the same amount of water.
this is when:
23x + 728 = 37x
subtract 23x from both sides:
23x + 728 - 23x = 37x - 23x
728 = 14x
divide both sides by 14:
728/14 = 14x/14
x = 52
So, pools are equal after 52 minutes.
What is the
Range??
Help me out plsss
Answer:
1≤x≤|R+
Step-by-step explanation:
since range is from the y axis
the starting point is 1 UpTo positive real numbers and it doesn't include 0
Evaluate the quantity of x cubed minus 2x squared plus 3x minus 7 end quantity divided by the quantity of x minus 1 end quantity period. x squared minus x plus 2 minus 5 divided by the quantity x minus 1 end quantity x squared minus 2x plus 2 minus 9 divided by the quantity x minus 1 end quantity x squared minus x plus 4 minus 9 divided by the quantity x minus 1 end quantity x cubed minus 2x plus 2 minus 5 divided by the quantity x minus 1 end quantity
Answer:
(x^3 + 3x^2 - 2x + 7)/x- 2
Expand the numerator in the above expression
(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)
Rearrange the terms of the numerator in the above expression
(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)
Factorize the numerator in the above expression
[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)
Factor out x^2 + 5x + 8
[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)
Split the fractions
(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)
Divide the common factors
(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome
Answer:
The answer is really option A. x^2 - x +2-5/x-1
Step-by-step explanation:
I just took the test and got it right :)
(X) 1.10.PS-7
Simplify the expression. Write the answer in scientific notation.
(7×10¯²) (9×10¯²)
(7×10¯²) (9×10¯²) = ¯
(Simplify your answer. Use scientific notation. Use the multiplication symbol in the r
Enter you
The scientific notation is 6.3 × [tex]10^{-3}[/tex]
The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])
Calculate the product or quotient
=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])
Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]
=63 × [tex]10^{-2-2}[/tex]
=63 ×[tex]10^{-4}[/tex]
= 6.3 × [tex]10^{-3}[/tex]
Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].
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[3^2 x (189 divided by 9] -30
Step-by-step explanation:
[tex]3 {}^{2} (189 \div 9) - 30 \\ 9 \times 189 \div 9 - 30 \\ 189 \div 1 - 30 \div 1 \\ 189 - 30 \div 1 \\ = 159[/tex]
according to bodmas
Answer:
159
Step-by-step explanation:
Using BODMAS - Bracket Of Division Multiplication Addition Subtraction
Step 1: Bracket
189/9=21
Hence [3^2 x (21)]-30
Step 2:
3^2= 9
Step 3: Calculate within parentheses [9* 21] : 189
9*21=189
Step 4: Open bracket
[189]-30=159
i give brainlest can somebdy pls help me
After evaluating the given fraction, the resultant answer is (C) 1¼.
What are fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, 8 ÷ 6⅖:
Now, evaluate as follows
8 ÷ 6⅖8 ÷ 30+2/58 ÷ 32/58/1 × 5/325/4Which can also be written as 1¼.
Therefore, after evaluating the given fraction, the resultant answer is (C) 1¼.
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35 = u/5 + 12 solve for u and simplify the answer as much as possible
Answer:
u = 115
Step-by-step explanation:
35 = u/5 + 12
35 - 12 = u/5
(35 - 12) * 5 = u
u = (35 - 12) * 5
u = 115
A college has 19 engineering students for every 81 students enrolled. if the college has 750 students, approximately how many are engineering students
The total number of engineering students is 176 approximately among the 750 students enrolled in the college by using the proportionate formula.
It is mentioned here that a college has 19 students of engineering for every 81 students who got enrolled.
Therefore the ratio of engineering students to total number of students is as follows:
No. of engineering students = 19
Total number of students = 81
Ratio = [tex]\frac{19}{81}[/tex]
Now if the total number of students that the college has is 750 then the number of engineering students can be found by using the proportionate formula as the ratio of the engineering to the total students will remain same.
Total number of students = 750
Let the number of engineering students be y
Ratio = [tex]\frac{y}{750}[/tex]
Comparing it with the above ratio and using the proportionate formula,
[tex]\frac{19}{81} = \frac{y}{750}[/tex]
⇒ y = [tex]\frac{19*750}{81}[/tex]
⇒ y = 175.925
So approximately 176 were the engineering students among 750 students enrolled.
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The table shows the percent of each type of movie in Brayden's collection. What is the ratio of Action movies to all of the movies in Brayden's collection?
Movie Type Percent of Collection
Comedy 20%
Action 40%
Drama 15%
Science Fiction 25%
Select all that apply.
A.
2 : 5
B.
3
20
C.
2
3
D.
2
5
E.
3 : 20
the ratio of action movies to all movies is 2: 5 .
In mathematics, a ratio illustrates how frequently one number appears in another. On a fruit tray, the ratio would be eight to six if there were eight oranges and six lemons.
Ratios can be lowered by dividing each quantity by the sum of all the common factors between the numbers (much like fractions are).When the ratio's numbers are the smallest practical integers, the fraction is said to be in its simplest form.The ratio's antecedent and consequent are frequently referred to as A and B, respectively.Let Brayden has x number of movies in total.
Total number of action movies in his collection = 40% of x = 0.4 x
Other movies = 1 - 0.4x = 0.6 x
Ratio of action movies to all movies = 0.4x : x = 2: 5
Therefore the ratio of action movies to all movies is 2: 5 .
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The difference between the total surface area and curved
surface area of a hemisphere is 154 cm2, find its volume.
If the difference between the total surface area and curved surface area of a hemisphere is 154 cm2, then its volume is 718.66 cm³
What is hemisphere?In general, the term "hemisphere" refers to the lower half of the earth, such as the northern or southern hemispheres. A hemisphere, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.
In everyday life, we encounter a variety of objects that have a hemisphere shape, such as a cherry that is shaped like a hemisphere when cut in half or a grapefruit that has a hemisphere shape when cut in half.
The difference between the total surface area and curved surface area of a hemisphere is 154cm.
Total Surface Area of Hemisphere = 3πr²
And Curved Surface Area of Hemisphere = 2πr²
It is Given that
Total Surface Area of Hemisphere - Curved Surface Area of Hemisphere. = 154.
Substituting the values, we get,
⇒ 3πr² - 2πr² = 154
⇒ πr² = 154
⇒ r² = 154/π
⇒ r² = 154 × (7/22)
⇒ r² = 7 × 7
⇒ r = 7.
Now, lets find the volume which is
Volume of Hemisphere = 2/3πr³
V = 2/3π(7)³
V = 2/3(22)(7)²
V = 2156/3
V = 718.66 cm³
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F(x)=3x^2-4x+8G(x)=2x-5 use the functions above to find the value of g(f(-2)) I don’t understand how to do this
Given,
[tex]f(x)=3x^2-4x+8,\text{g(x)=2x-5}[/tex]To find g(f(-2)). we first find the value of f(-2).
The value of f(-2) is,
[tex]\begin{gathered} f(-2)=3(-2)^2-4(-2)+8 \\ \text{ =3(4)+8+8} \\ \text{ =12+8+8} \\ \text{ =28} \end{gathered}[/tex]So now to find the value of g(f(-2)),
[tex]g(f(-2))=g(28)[/tex]So the value of g(28) is,
[tex]\begin{gathered} g(28)=2(28)-5 \\ \text{ =56-5} \\ \text{ =51} \end{gathered}[/tex]So the value of g(f(-2)) is 51.
Corinne made $60,400 last year. She received a 2% annual raise. What will her new salary be for the upcoming year?
Answer:
61608 i believe
Step-by-step explanation:
2% of 60400= 1208
60400+1208=61608