The number of lines and triangles illustrates combination
36 lines can be drawn to join the nine points84 triangles can be drawn using the nine pointsThe number of lines that can be drawn
The given parameters are:
Total points, n = 9
Total points on each line, r = 2
The number of lines that can be drawn is then calculated using the following combination formula
Lines = nCr
This gives
Lines = 9C2
Evaluate the combination expression
Lines = 36
Hence, 36 lines can be drawn to join the nine points
The number of triangles that can be drawnThe given parameters are:
Total points, n = 9
Total points on each triangle, r = 3
The number of triangles that can be drawn is then calculated using the following combination formula
Triangles = nCr
This gives
Triangles = 9C3
Evaluate the combination expression
Triangles = 84
Hence, 84 triangles can be drawn using the nine points
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Question
The sum of the measures of the angles of a triangle is
180. The sum of the measures of the second and third angles is five
times the measure of the first angle. The third angle is 30 more than the second. Let T. y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
Provide your answer below:
Answer:
t = 30°y = 60°z = 90°Step-by-step explanation:
The given relations can be used to write three equations for the angle values.
Setupt + y + z = 180 . . . . . sum of all angle measures
y + z = 5t . . . . . . . . second and third total 5 times the first
y + 30 = z . . . . . . third angle is 30 more than the second.
__
SolutionUsing the third equation to substitute for z in the first two equations gives ...
t + y + (y +30) = 180 ⇒ t +2y +30 = 180
y + (y +30) = 5t ⇒ 2y +30 = 5t
Using the second of these equations to substitute for (2y+30) in the first, we have ...
t +5t = 180
t = 180/6 = 30 . . . . . . divide by the coefficient of t
Using this value in our equation for 5t gives ...
2y +30 = 5(30)
2y = 120
y = 60
Then the value of angle z is ...
y +30 = z = 60 +30
z = 90
The first, second, and third angles are 30°, 60°, and 90°, respectively.
three times the number of books that you have
Step-by-step explanation:
let b represent the number of books
b×b×b
b3
Sandra wrote p(x) = 30x + 5x2 in vertex form. Her work is below.
1. p(x) = 5x2 + 30x
2. p(x) = 5(x2 + 6x)
3. (six-halves) squared = 9;
4. p(x) = 5(x2 + 6x + 9) – 5(9)
5. p(x) = 5(x + 3)2 – 45
What is the vertex of this function? Is it a maximum or a minimum?
What is the axis of symmetry of this function?
Answer:
Step-by-step explanation:
hello :
p(x) = 5(x + 3)2 – 45
the vertex is the point : A(-3 ; -45)
minimum -45
the axis of symmetry is the line when an equation is : x = -3
Convert 6 2/3 % to a fraction lowest terms
Answer:
109/150
Step-by-step explanation:
Answer: 109/150
6% = 6/100
6/100 = 18/300 (Multiply Numerator and Denominator by 3)
2/3 = 200/300 (Multiply Numerator and Denominator by 100)
200/300 + 18/300 = 218/300
218/300 = 109/150 (Simplify by Dividing Numerator and Denominator by 2)
If y - 18 = 14, what is the value of 3(y + 5)?
Answer:
y-18=14
add 18 on both sides
y=32
plug that into the equation below
3(Y+5)
3(32+5)
add 32 and 5
3(37)
multiply
3
....
3 x 37 = 111
A man earns Rs.9600 and he saves Rs.2400 in a month.What percentage does he spends?
Given Information :-
⠀⠀
A man earns rs. 9600He saves Rs. 2400⠀
To Find :-
⠀
The percentage of amount he spends⠀
Solution :-
⠀
To find the percentage of expenditure, we must know how much amount does he really spend, thus :
⠀
➥ Expenditure = Earnings - Savings
➥ Expenditure = Rs. 9600 - Rs. 2400
➥ Expenditure = Rs. 7200
⠀
Now, we can find the percentage,
⠀
[tex] \sf \hookrightarrow Percentage_{expenditure} = \dfrac{Expenditure}{Earnings} \times 100 \\ \\ \\ \sf \hookrightarrow Percentage_{expenditure} = \frac{7200}{9600} \times 100 \qquad \: \: \: \: \\ \\ \\ \sf \hookrightarrow Percentage_{expenditure} = \frac{72 \cancel{00}}{96 \cancel{00}} \times 100 \qquad \quad \\ \\ \\ \sf \hookrightarrow Percentage_{expenditure} = \frac{ \cancel{72}}{ \cancel{96}} \times 100 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Percentage_{expenditure} = \cancel \frac{3}{4} \times 100 \qquad \qquad \: \: \\ \\ \\ \sf \hookrightarrow Percentage_{expenditure} = 0.75 \times 100 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Percentage_{expenditure} = \underline{ \boxed{ \orange {\frak{75\%}}}} \: \star \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the percentage of his expenditure is 75%.
⠀
[tex] \underline { \rule{227pt}{2pt}}[/tex]
⠀
Answer:
5%
Step-by-step explanation:
Earns= Rs 640
Spends= Rs 608
Saves= (Rs 640 - Rs 608) =Rs 32
therefore, 32/640x100
help for (40 points) this is a k 12 thing
Answer:
4240 in²
rectangle prism area: 2(wl+hl+hw)
=======
area:
2*(20*36+25*36+25*20)4240 in²You plan to go snowboarding. The resort charges $15 an hour in addition to $25 to rent a board. Write an equation that represents the cost to go snowboarding for the day. You have 100.00 to spend that day how many hours can you snowboard?
Answer:
6 Hours
Explanation:
Linear Equation: mx+b=y
x variable: Hour
Hourly Fee: $15(x)
(Initial) Rent Fee: $25
Balance: $100
Equation:
15x+25=100
15x+25-25=100-25 -- Separate the constant terms from the x by subtracting 25 from both sides.
15x=100
15x/15=100/15 -- Isolate the x variable by dividing 15 from both sides.
x=6.6.. -- Round down to 6 (not 7) because you can't afford to snowboard for 7 hours with less than $15.
x=6 Hours
answer: 6 hours
Step-by-step explanation:
I did this on a paper
If 65% of a number is 234 and 10% of the same number is 36, find 75% of that number
65%= 234
100%= 234÷65×100
100%= 360
75%= 360÷100×75
75%= 270
write equivalent expressions 3(x-6)
Answer:
3(x-6)=3x-18
Step-by-step explanation:
why do the leaves drop?
Why do the leaves drop:
Dropping them gives the plant a fresh start in the spring (naturally)environmental stress, diseaseHope that helps!
a. Use the appropriate formula to find the value of the annuity
b. Find the interest
Rate
Periodic Deposit
$6000 at the end of each year
15.5% compounded annually
Time
10 years
The value of the $6000 annuity given annual compounding is $124,836.12.
What is the value of the annuity?
The value of the annuity can be determining using this formula: amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
n = number of years r = interest rate$6000 x [(1.155^10) - 1/0.155] = $124,836.12
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It costs $5.25 to rent bowling shoes. Each game costs $3.00. You have $26.25. How many games can you bowl?
First lets write an equation to help us solve this.
26.25=3x+5.25
x=7
26.25 - 5.25 = 21.
21/3 = 7.
Answer:
You can bowl 7 games.
Step-by-step explanation:
To begin, you need shoes.
-$5.25
So, we would do $26.25 minus the amount for shoes $5.25
$26.25-$5.25 = $21
You now have $21 to spend on bowling the games. Since it is $3 each game, we can do the equation $21 = $3x. We can do this becuase you have $21 to spend and each game costs $3. So we can put x for how many games and 3 as the price of each game. Now, we simplify to get x alone. This will be how many games you can bowl.
21 = 3x
Divide by 3 on both sides
7 = x
So, you can bowl 7 games.
a computer screen is 22cm by 12cm. what is the perimeter of the screen
Answer:
The perimeter is 68 cm.
Step-by-step explanation:
Two sides of 22cm = 44cm
Two sides of 12 cm = 24 cm
44cm + 24cm = 68cm.
30 points
The length of the shorter leg of a 30-60-90 Special Right Triangle is 6 cm long. How long is the hypotenuse of the triangle?
Question 2 options:
12 cm
62–√ cm
63–√ cm
6 cm
Answer:
Your answer would be 12cm
Step-by-step explanation:
I just take a quiz and got it right.
Tickets for a movie cost $8 for evenings and $5 for matinees. They sold 440 tickets sold and collected $3130 in ticket sales.
Determine which system(s) you could use to calculate the number of matinee tickets sold.
a. x + y = 3130
5x + 8y = 440
b. x + y = 440
5x + 8y = 3130
c. x + y = 3130
8x + 5y = 440
d. x + y = 440
8x + 5y = 3130
d is the answer
let the number of tickets be x and y
then the prices are multiplied to the number of tickets.
Find the interest rate for a principal of $9442 and charged $30233 in interest for 18 years.
Which is the best example of an out-of-pocket cost?
A. A claim
B. A benefit
C. A deductible
D. A repair estimate
A best example of an out-of-pocket cost is: C. A deductible.
What is an Out-of-Pocket Cost?An out-of-pocket cost can be described as a cost you pay from your own personal reserve, which may include coinsurance, deductibles, copays, and some services covered by an individual's health plan.
Out-of-pocket cost may be reimbursed.
Thus, a best example of an out-of-pocket cost is: C. A deductible.
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Answer: C. A deductible
Step-by-step explanation:
Please help
(Also show work) and its volume not SA
Answer:
75 inches cubed
Step-by-step explanation:
V=lwh
2 1/2 = 2.5
4 = 4
7 1/2 = 7.5
2.5 x 4 x 7.5=75
75 cubic inches
What’s the circumference of circles
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's find the circumference of given circle ~
Circumference :
[tex]\qquad \tt\dashrightarrow \:c =2 \pi r[/tex]
where,
r = radius = 3 ydnow, let's calculate circumference ~
[tex]\qquad \tt \dashrightarrow \:c = 2 \times \pi \times 3[/tex]
[tex]\qquad \tt \dashrightarrow \:c = 6 \pi \: \: yd[/tex]
Now, let's plug in approximate value of pi :
[tex]\qquad \tt \dashrightarrow \:c = 6 \times 3.14 \: \: [/tex]
[tex]\qquad \tt \dashrightarrow \:c = 18.84 \: \: yd[/tex]
Jose has scored 330 points on his math tests so far This semester. To get an for the semester he must score at least 425 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests,n, to get an A.
Answer:
(425-330)/n=A
Step-by-step explanation:
in one year the water level of a lake change is b -3/8 in the water level of the lake continue to change at this rate for 7 years how many inches will the water level of the lake have changed
Answer:
-21/8 or -2 5/8
Step-by-step explanation:
The lake change is the same for all 7 years so you can subtract -3/8 seven times.
-3/8-3/8-3/8-3/8-3/8-3/8-3/8 = -21/8
as a mixed number it's -2 5/8
can please someone help me with more of these asap
Answer: 75.36
Step-by-step explanation: Lenght of arc=2nr
=2nx12in
=75.36
lenght of arc of sector=120/360x75.36
=25.12
At midnight the temperature
was -12°C. Twelve hours
later the temperature had risen
19°C. What was the midday
temperature?
Answer:
7C
Step-by-step explanation:
Help pls! I rlly need this
Answer:
799.04
Step-by-step explanation:
First take the area of the rectangle, which would be 50 × 20 = 1000.
Then find the area of the circle. The area of a circle is [tex]\pi r^{2}[/tex]. Since the question says to use 3.14 for pi, your area would be 3.14 × 8².
8² equals 8 × 8 which is 64 and 3.14 times 64 is 200.96.
Since the circle is not part of the shaded area, you subtract the area of the rectangle by the area of the circle. 1000 - 200.96 is 799.04
what is the slope of the line that passes through -14, 13 and 7, 0
Slope = change in y / change in x
slope = (0 - 13) / (7 - -14)
slope = -13/28
jack had m problems to complete during his vacation. (a) how many problems did jack solve per day? (b) suppose jack was solving 15 problems per day. (c) How many problems were assigned for homework
Jack's problems illustrates algebraic expressions
He solved m/5 problems everyday.75 questions were assigned in totalProblems solved per dayThe given parameter is:
Problems = m
From the complete question, we understand that all questions were solved in 5 days.
So, the number of questions solved per day is:
Daily = m/5
Number of problems in the assignmentWe have:
Daily = m/5
He solved 15 daily.
So, the equation becomes
m/5 = 15
Multiply both sides by 15
m = 75
Hence, 75 questions were assigned in total
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PLEASE HELP ASAP W EXPLANATION !!!
Based on the net shown below, what is the type of solid this represents and find the surface area of the solid to the nearest hundredth.
Answer:
326.6 cm²Step-by-step explanation:
The figure has 2 triangular and 3 rectangular faces.
This is a right triangular prism.
Find the area of each face and add up to get the total surface area.
Each triangle has base of 10 and height of:
[tex]h = \sqrt{10^2-5^2} =\sqrt{75} =8.66[/tex] cmTotal surface area is
[tex]A = 2(1/2*10*8.66) + 3(10*8) = 326.6[/tex]If a floor plan has a key for 1 graph paper line = 5 ft in real life, what is the area of a rectangular room in real life if the area on the floor plan is 44?
*HINT: the key is for a dimension, but your answer is an area.*
=======================================================
Explanation:
1 unit along the grid represents 5 feet in real life.
A 1 unit by 1 unit square on the graph paper represents a 5*5 = 25 square foot area in real life.
This means we multiply by 25 when going from the floor plan's area to the real world area.
44*25 = 1100 square meters is the area of the room in real life when the floor plan says the area is 44 sq units.
For which values of x is the expression undefined
Answer:
x = 7
Step-by-step explanation:
x - 7 = 0
x = 7