The sum of first 46 positive and odd numbers is 2116
Solution:
Given that we have to find the sum of first 46 positive and odd numbers
The sum of first "n" natural odd numbers which are positive is given as:
[tex]Sum = n^2[/tex]
Here, n = 46
Therefore,
sum of first 46 positive and odd numbers = [tex]46^2[/tex]
sum of first 46 positive and odd numbers = [tex]46 \times 46 = 2116[/tex]
Thus the sum of first 46 positive and odd numbers is 2116
There are 32 girls and 36 boys that will form soccer teams. Each team will have 9 players. Extra players will be substitutes. How many teams can be formed? How many players will be a substitute?
The number of 9-players team formed = 7 teams.
The number of players for substitute = 5 substitute players.
Step-by-step explanation:
step 1: The total number of soccer players = 32 girls + 36 boys = 68 players.
step 2: Each team should have 9 players.
step 3:The number of 9-player teams that can be formed = 68/9 = 7 and Remainder is 5.
step 4: Therefore, The number of 9-players team formed = 7 teams.
The number of players for substitute = 5 substitute players.
what is 4th grade distributive property
the Distributive Property uses two operations: multiplication and addition. It is an essential key to success in algebra. The Distributive Property allows you to "distribute" a number to each of the addends within parentheses. It offers another way of solving a problem.
Answer:
A math property.
Step-by-step explanation:
Say you have a two big number and you don't know the answer on top of your head. You use distributive property to break it apart.
How many sides does a cube have
a cube has 6 sides reeeeeeeeeeeeeeeeee
a cube has 6 sides
1 in the front
1 in the back
1 on top = 6 sides
1 below
1 to one side
1 to another side
Your local Pizza restaurant offers free delivery with an expected 15% tip for the delivery person. Your pizza will cost 15.95 + 7% sales tax. What is your total cost?
The total cost which includes tip, food cost without tax and sales tax for the considered situation is 19.63 bucks approximately.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we're specified that:
Pizza cost = 15.95 +7% of tax on 15.95 bucks
Tip = 15% of pizza cost
Total cost = Pizza cost + tip
7% of 15.95 is: [tex]\dfrac{15.95}{100} \times 7 = 1.1165[/tex] bucks
Thus, pizza cost = The (15.95 + 1.1165) = 17.0665
Tip price = 15% of 17.0665 = [tex]\dfrac{17.0665}{100} \times 15 \approx 2.56[/tex] bucks.
Thus, total cost ≈ 17.0665 + 2.56 ≈ 19.63 bucks
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1/3x = 6 what is the letter x
Answer:
18
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
18
Step-by-step explanation:
1/3x=6
x=6/(1/3)
x=(6/1)(3/1)
x=18/1
x=18
[tex]If 180º\ \textless \ a\ \textless \ 270º[/tex] and [tex]cos a= -8/17[/tex] what is sin(−α)?
Enter your answer as a fraction in simplest form, like this: 3/14
Answer:
[tex]\frac{15}{17}[/tex]
Step-by-step explanation:
Look at the photo below for the details.
:)
2 Independent Practic
CA CC 8.EE.7, 8.EE.7b
Members of the Wide Waters Club pay
$105 per summer season, plus $9.50 each
time they rent a boat. Nonmembers must
pay $14.75 each time they rent a boat.
How many times would a member and a
non-member have to rent a boat in order
to pay the same amount?
Answer:
20
Step-by-step explanation:
Let x represent the number of rentals. Then the cost will be the same when ...
105 +9.50x = 14.75x
105 = 5.25x
105/5.25 = x = 20
Each would have to rent a boat 20 times in order to pay the same amount.
Under a dilation centered at the origin, the point (-4 , 3) has image at (8 , -6) The dilation is _____
Answer:
2
Step-by-step explanation:
see the image for the explanation
What value of x makes f(x) = -2 if f(x) = 3.4x - 7.1
A. -13.9 B. -1.5
C. 1.5 D. 2.8
Option C
For x = 1.5 we get f(x) = -2
Solution:
Given function is:
[tex]f(x) = 3.4x - 7.1[/tex]
We have to find the value of "x" so that f(x) = -2
Substitute f(x) = -2 in given function
[tex]-2 = 3.4x - 7.1[/tex]
Solve for "x" by moving the constants to one side and variables to other side
[tex]3.4x = -2 + 7.1\\\\3.4x = 5.1\\\\ \text{Divide both the sides of equation by 3.4 }\\\\x = \frac{5.1}{3.4}\\\\x = 1.5[/tex]
For x = 1.5 we get f(x) = -2
We can verify by substituting x = 1.5 in given function
[tex]f(1.5) = 3.4(1.5) - 7.1\\\\f(1.5) =5.1-7.1\\\\f(1.5) = -2[/tex]
Thus for x = 1.5 we get f(x) = -2
18 is what percentage of 25
Answer:
Step-by-step explanation:
72%
Answer: 72%
Step by Step Explanation:
1. We assume, that the number 25 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 25, so we can write it down as 100%=25.
4. We know, that x% equals 18 of the output value, so we can write it down as x%=18.
5. Now we have two simple equations:
1) 100%=25
2) x%=18
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=25/18
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 18 is what percent of 25
100%/x%=25/18
(100/x)*x=(25/18)*x - we multiply both sides of the equation by x
100=1.38888888889*x - we divide both sides of the equation by (1.38888888889) to get x
100/1.38888888889=x
72=x
x=72
now we have:
18 is 72% of 25
if 8 and 15 are sides to a right triangle, whats the missing side?
Answer:
17
Step-by-step explanation:
a[2]+b[2]=c[2]
8*8+15*15=hypotenuse.
64+225=289
[tex]\sqrt{x} 289[/tex]
hypotenuse=17
Pam bought several cartons of Giggle Fruit Drinks to sell during the track meet. She paid 50 cents per carton. She sold all but 15 of the cartons for $1 each. At the end of the day, her profit was $22.50. How many cartons of Giggle did she buy?
Good evening
Answer:
75Step-by-step
let c be the total number of cartoons
Cost of purchase = 50c
total sale price = 100(c-15)
profit = total sale price - cost of purchase
= 100(c-15) - 50c = 2250 cents
Then (100c-50c) - 1500 = 2250
then 50c = 3750
Then c = 3750/50 = 75
:)
Provide the missing reasons for the proof of part of the triangle midsegment theorem. Given: K is the midpoint of . L is the midpoint of . Prove: Answer: Statement Reason 1. K is the midpoint of . L is the midpoint of . 1. 2. and 2. 3. and 3. 4. and 4. 5. and 5. Substitution Property of Equality 6. 6. Division Property of Equality 7. 7. 8. ∆JMN≅∆JKL 8. 9. 9. 10. 10. 11. 11.
To prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
K is the midpoint of MJ.
L is the midpoint of NJ.
It is required to prove: MN = 2KL
From the diagram and table given in the picture:
1. K is MJ's midway. L is where NJ splits in half. ~ Given
2. MK, KJ, and NL, LJ: Midpoint Definition
3. Segment Congruence Postulate: MK=KJ and NL=LJ
4. Segment Addition Postulate: MJ = MK + KJ and NJ = NL + LJ
5. Substitution Property of Equality: MJ = 2KJ, NJ = 2LJ
6. The Division Property of Equality: MJ/KJ = NJ/LJ = 2
7. The Reflexive Property of J
8. The SAS Similarity Theorem, JMN, and JKL
9. Corresponding parts of identical triangles have a proportional relationship (MN/KL = MJ/KJ).
10. Substitution: MN/KL = 2
11. The Multiplication Property of Equality: MN = 2KL
Thus, to prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.
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(sum of interior angles = 10 (n-2) where n is the number of sides of the polygon)
1. what is the sum of the interior angles of a pentagon?
2. if the sum of the interior angles of a polygon equals 1080, then determine the sides of the polygon.
3. what is a polygon called if the sim of its interior angles equals 6840?
4. what is the sum of the interior angles of an octagon?
Answer:
Step-by-step explanation:
1) pentagon; n= 5
Sum of interior angles = 180*(n -2) = 180* (5-2) = 180 * 3 = 540
2) Sum of interior angles of a polygon = 1080
180*(n-2) = 1080
n - 2 = 1080/180
n -2 = 6
n = 6+2
n = 8
Polygon has 8 sides
3) Sum of interior angles of a polygon = 6840
180*(n-2) = 6840
n - 2 =6840/180
n -2 = 38
n = 38 + 2
n = 40
Polygon has 40sides
4)Sum of interior angles of an octagon = 180*(n-2) = 180* (8-2) = 180 - 6 = 1080
The sum of the interior angles of the 10-sided polygon on the left is 1440 °.
The answer is : 1440
A 12 ft. ladder is being placed against a 10 ft.
wall. At what angle of elevation should the
ladder be placed so that the top of the ladder
touches the top of the wall?
Answer:
Step-by-step explanation:
Height of wall = 10ft
Length of ladder = 12ft
Angle of elevation be x
Sin x = opp/hyp
Sin x = wall height/length of ladder
Sin x = 10/12
Sin x = 0.83
X = Sin-¹ (0.83)
X = 56.44°
Miguel drove 737 miles in 11 hours.
At the same rate, how long would it take him to drive 469 miles?
Final answer:
To find how long it takes Miguel to drive 469 miles at the same rate he drove 737 miles, simply divide the distance by his speed. In this case, it would take him 7 hours.
Explanation:
To find the time it would take Miguel to drive 469 miles at the same rate:
Calculate Miguel's speed: 737 miles / 11 hours = 67 miles per hour.Divide the distance to be traveled (469 miles) by Miguel's speed: 469 miles / 67 miles per hour = 7 hours.Therefore, it would take Miguel 7 hours to drive 469 miles at the same rate.
What is 4 divided by 230 long division
Answer:
0.0173913043
Step-by-step explanation:
I used a calculator
How to graph Y greater than or equal to 2
Answer:
Check the image as well as the explanation.Step-by-step explanation:
In order to graph [tex]y\geq 2[/tex], we first need to graph y = 2.
y = 2 is a straight line which will be parallel to the x-axis.
We need to graph [tex]y \geq 2[/tex].
3, 4, 5......> 2. That is, all these values satisfies [tex]y \geq 2[/tex].
Hence, the will be the area towards the points y = 3 / 4 / 5 / ......
A shopping mall parking garage charges $2 for the first half hour and $1.20 for each additional half hour (even if it is under 30 minutes). Write and solve and inequality to find how many hours you can park in the garage if you have $8 in cash
You can park in the garage for 5 hours 30 minutes
Solution:
Given that, shopping mall parking garage charges $2 for the first half hour and $1.20 for each additional half hour (even if it is under 30 minutes)
Therefore,
Cost for first half an hour = $ 2
Cost for each additional half an hour = $ 1.20
Let "x" be the number of each additional half hour
Therefore, total cost to pay is given as:
Total cost = Cost for first half an hour + (Cost for each additional half an hour)(number of each additional half hour)
Total cost = 2 + 1.20x
Given you have $ 8 in cash
[tex]8 = 2 + 1.20x\\\\1.20x = 8 - 2\\\\1.20x = 6\\\\x = \frac{6}{1.20}\\\\x = 5[/tex]
Total hours parked = first half an hour + 5
Thus you can park in the garage for 5 hours 30 minutes
I need help on this question ASAP
Answer:
15: 1
Step-by-step explanation:
Please see attached picture for full solution.
Train A traveled 173 miles in five hours. For Train B, y = 31.35x represents its rate of speed over the same five hours. Analyze the date to determine which train traveled at a faster rate and by what factor? (round to nearest tenth)
Answer:
D.Train A by a factor of 1.1
Step-by-step explanation:
At a video rental store, 434 movies were returned in less than two days. That number of movies is 62% of the total number of movies rented last week.
Answer:
700
Step-by-step explanation:
Hope this helps!
The problem is a mathematical exercise in determining the total number of movies rented from the provided percentage of those returned. By setting up an equation and solving it, we find that the total number of movies rented was 700.
Explanation:The student's question is on a mathematical concept related to percentages and determining the whole from a percentage portion. From the information provided, 434 movies, which represent 62% of the total number of movies rented last week, were returned. To calculate the total number of movies rented, we can let the total be x. With this, the equation representing the scenario is 0.62x = 434.
By solving for x, we get x = 434 / 0.62. After the calculation, we find that the total number of movies rented last week was 700. Therefore, the store originally rented out 700 movies.
Remember that when dealing with percentages, the percentage value (in this case, 62%) must be converted into decimal form before performing any calculation. This is done by dividing the percentage by 100, thus 62% becomes 0.62. For clarity, here's the step-by-step procedure:
Convert the percentage (62%) to a decimal (divide by 100): 0.62.Set up the equation where 62% of total movies rented (x) equals the number of movies returned (434).Solve for x by dividing the number of returned movies by the decimal percentage: x = 434 / 0.62.Conclude that 700 is the total number of movies rented out.
Stefan sells Jin a bicycle for $124 and a helmet for $19. The total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer: he spent $100.10 and gained $42.90
Step-by-step explanation:
A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).
A. 2/3
B. 3/2
C. 5/8
D. 3/4
Answer:
I think its B. because if you put 6/4and reduce it it would be 3/2
Step-by-step explanation:
Answer:
C. 5/8
Step-by-step explanation:
P(red) = 6/16
p(blue) = 4/16
p(red or blue) = P(red) + p(blue) = (6+4)/16 = 10/16 = 5/8
Choose the system of equations which matches the following graph:
a- x + 2y = −10
3x − y = 12
b- x − 2y = −10
3x − y = 12
c- x + 2y = −10
3x + y = 12
d- x − 2y = −10
3x + y = 12
Answer:
Option a
- x + 2y = −10
3x − y = 12
Step-by-step explanation:
step 1
Find the equation of the line with negative slope
we know that
The line with negative slope has a y-intercept at (0,-5) and passes through the point (2,-6)
Find the slope
[tex]m=(-6+5)/(2-0)=-\frac{1}{2}[/tex]
The equation in slope intercept form is
[tex]y=-\frac{1}{2}x-5[/tex]
Convert to standard form
Multiply by 2 both sides
[tex]2y=-x-10\\x+2y=-10[/tex]
step 2
Find the equation of the line with positive slope
The line with positive slope has a x-intercept at (4,0) and passes through the point (2,-6)
Find the slope
[tex]m=(-6-0)/(2-4)=3[/tex]
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3\\point\ (4,0)[/tex]
substitute
[tex]y-0=3(x-4)[/tex]
Convert to standard form
[tex]y=3x-12\\3x-y=12[/tex]
therefore
The system of equations is
- x + 2y = −10
3x − y = 12
At Joe's Print Shop, the amount of time it takes to complete a print job can be represented by t = 45 + 5p where t is
the time, in seconds, and p is the number of pages being printed. At Jerry's Print Shop, the amount of time it takes
to complete a print job can be represented by t = 30 + 6p where t is the time, in seconds, and p is the number of
pages being printed. What is the maximum number of pages for which the amount of time will be shorter to print
at Jerry's Print Shop than at Joe's Print Shop?
A. 11
B. 12
C. 13
D. 14
E. 15
The maximum number of pages for which the time to print at Jerry's Print Shop is less than at Joe's Print Shop is 14.
Explanation:This question deals with comparing two linear equations [tex]t1 = 45 + 5p[/tex] for Joe's Print Shop and t2 = 30 + 6p for Jerry's Print Shop. To determine the maximum number of pages (p) where Jerry's shop is quicker than Joe's, we need to find the value of p where t2 < t1.
Setting the two equations equal to each other, we get:
[tex]45 + 5p = 30 + 6p,[/tex]
Solving this equation, we find that p = 15.
However, p=15 is when the time at both shops is the same. Since we want the number of pages for which Jerry’s is less than Joe's, we should choose the next value lower, which is p=14.
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Suppose you know that ∠S and ∠Y are complementary and that m∠S = 5(m∠Y) − 180°. Find m∠Y.
Answer:
45°
Step-by-step explanation:
We know ∠ Y +∠ S = 90
and ∠ S= 5 ( ∠ Y)-180 so
leave S alone for both
90- ∠Y = 5 ( ∠Y) -180
270 = 6( ∠Y )
45= ∠ Y
∠S = 5( 45) -180
=225-180
=45
Final answer:
The measure of angle Y (m∠Y) is 45°, following the equation derived from the facts that angles S and Y are complementary and m∠S equals 5 times m∠Y minus 180°.
Explanation:
If ∠S and ∠Y are complementary angles, then the sum of their measures is 90°. According to the given information, m∠S = 5(m∠Y) − 180°. Since m∠S + m∠Y = 90°, we can set up the equation:
5(m∠Y) − 180° + m∠Y = 90°
Combining like terms to solve for m∠Y:
6(m∠Y) = 90° + 180°
6(m∠Y) = 270°
m∠Y = 270° / 6
m∠Y = 45°
The measure of angle Y, m∠Y, is 45°.
15. Find m∠DEC (the picture is not drawn to scale).
Answer:
m∠DEC = 123°
Step-by-step explanation:
First we need to solve for x the equation: x = (x - 45) + (x-12)
x = (x - 45) + (x-12) ⇔ x = 2x -57 ⇔ 0 = x - 57 ⇔ x = 57
since m∠DEC = 180 - x then m∠DEC = 180 - 57 = 123
How to solve 17=x+9 what is x
Answer:
x=8
Step-by-step explanation:
17=x+9
-9 -9
8=x
Answer:
x=8
Step-by-step explanation:
17-9=8
8+9=17
complete the steps to simplify (y^4/3•y^2/3)^-1/2. Apply the product of powers property to the expression inside the parentheses, then choose the equivalent expression.
A. (y^2)^-1/2
B. (y^8/3)^-1/2
C. (y^2/3)^-1/2
Option A
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Solution:
Given expression is:
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Product of powers property:
The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents
Which is represented as,
[tex]a^m.a^n = a^{m+n}[/tex]
Therefore, the given expression becomes,
[tex]\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Now add the exponents, we get
[tex]\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the above expression
[tex]\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the exponent of y, we get
[tex]\left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Thus Option A is correct
Answer:
The answer is A
Step-by-step explanation: