Answer:
The given symbol for the nth triangular number = Tₙ
The given symbol for the nth square number = Qₙ
The given symbol for the nth pentagonal number = Pₙ
The mathematical formula for the nth triangular number, Tₙ = n·(n + 1)/2
The nth square number is given by Qₙ = n²
The nth pentagonal number is given by Pₙ = n·(3·n - 1)/2
(a) T₃.ₙ₋₁ = (3·n - 1)·(3·n - 1 + 1)/2 = (3·n - 1)·(3·n)/2 = 3·(3·n - 1)·(n)/2 = 3·Pₙ
Therefore;
T₍₃.ₙ ₋ ₁₎ = 3·Pₙ
(b) Pₙ - Qₙ = n·(3·n - 1)/2 - n²
Expanding the above equation gives;
n·(3·n - 1)/2 - n² = (3·n² - n - 2·n²)/2 = (n² - n)/2 = n·(n - 1)/2
T₍ₙ ₋ ₁₎ = ((n - 1)· ((n - 1) + 1))/2 = ((n - 1)· n)/2 = n·(n - 1)/2
∴ Pₙ - Qₙ = n·(3·n - 1)/2 - n² = n·(n - 1)/2 = T₍ₙ ₋ ₁₎
∴ Pₙ - Qₙ = T₍ₙ ₋ ₁₎
Therefore, we get;
P₃.ₙ - Q₃.ₙ = T₍₃.ₙ ₋ ₁₎
Where, T₍₃.ₙ ₋ ₁₎ = 3·Pₙ from (a) above, gives;
P₃.ₙ - Q₃.ₙ = 3·Pₙ
∴ P₃.ₙ - 3·Pₙ = Q₃.ₙ
Plugging in the values, gives;
P₃.ₙ = (3·n)·(3·(3·n) - 1)/2 = (3·n)·((9·n) - 1)/2
3·Pₙ = 3·n·(3·n - 1)/2
P₃.ₙ - 3·Pₙ = (3·n)·((9·n) - 1)/2 - 3·n·(3·n - 1)/2 = (3·n)·(((9·n) - 1) - (3·n - 1))/2
(3·n)·(((9·n) - 1) - (3·n - 1))/2 = (3·n)·(9·n - 1 - 3·n + 1)/2 = (3·n)·(6·n )/2 = 9·n²
Q₃.ₙ = (3·n)² = 9·n²
∴ P₃.ₙ - 3·Pₙ = P₃.ₙ - 3·Pₙ
Step-by-step explanation:
[tex]x^2-x-6=0[/tex]
Answer:
x = 3 or x = -2
Step-by-step explanation:
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
3.
The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.
A. quadratic; y = 91x2 + 0.77
B. exponential; y = 91 • 0.77x
C. linear; y = 0.77x + 91
D. quadratic; y = 0.77x2 + 91
Answer:
B. exponential; y = 91 • 0.77x
Step-by-step explanation:
I just substituted the x on all of them and only one got the correct y which is B.
...............................................................................................................................................
The Answer is B.
y=91*0.77^x
...............................................................................................................................................
Answer:
B. exponential; y = 91 • 0.77x
Step-by-step explanation:
Just is
7+3√5/3+√5 - 7-3√5/3-√5
Answer:
0
Step-by-step explanation:
We can write the equation in a simpler form so it doesn't look like a mess of numbers:
[tex]7+\frac{3\sqrt{5}}{3}+\sqrt{5} -7 -\frac{3\sqrt{5}}{3}-\sqrt{5}[/tex]
Because we are just adding three terms together and then subtracting those exact terms, we have the answer as 0.
The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Find the
i)value of x
ii) area
iii)cost of weeding the plot at GHc 0.24 per m²
Answer:
P.=2(2x+5)+2(x-10)=80cm
6x-10=80
x=90/6=15cm
Area= L*W= 35*5=175 squared cm= 0.0175 squared m
Cost= 0.24 * 0.0175 = GHc 0.0042
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The cost of weeding the rectangular plot is 0.0042 GHc.
What is a rectangle?That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
A.) The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Therefore, we can write,
Perimeter of the rectangel = 2(L+W)
80 = 2[(2x+5)+(x-10)]
80/2 = 2x+5+x-10
40 = 3x -5
40+5 = 3x
x = 15
Hence, the value of x is 15.
B.) The length of the rectangle = (2x+5) = 2(15)+5 = 35 cm = 0.35 m
The width of the rectangle = (x-10) = 15-10 = 5 cm = 0.05 m
Now, the area of the rectangle = L×B = 0.35m × 0.05m = 0.0175m²
C.) Given the cost of weeding 1m² is 0.24, therefore, the cost of weeding the rectangular plot is
Cost = 0.0175 × 0.24 = 0.0042 GHc
Hence, the cost of weeding the rectangular plot is 0.0042 GHc.
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Determine the value of x in the diagram
Which equation is equivalent to -2(2 − 2x) = 4 − 8(1 − x)?
Answer:
x = 0
Step-by-step explanation:
-2(2 − 2x) = 4 − 8(1 − x)
Apply the distributive property:
−2(2 − 2x) = 4 − 8(1 − x)
(−2)(2) + (−2)(−2x) = 4 + (−8)(1) + (−8)(−x)
−4 + 4x = 4 + (−8) + 8x
Combine like terms:
4x − 4 = (8x) + (4+−8)
4x − 4 = 8x + (−4)
4x − 4 = 8x − 4
Subtract 8x from both sides:
4x − 4 − 8x = 8x − 4 − 8x
−4x − 4 = −4
Add 4 to both sides:
−4x − 4 + 4= −4 + 4
−4x = 0
Divide both sides by -4:
-4x/-4 = 0/-4
x = 0
Answer: 0
Step-by-step explanation:
At 5:00 a.m., the temperature outside was 6°F below zero. By noon, it rose by 15°F.
At 7:00 p.m., the temperature dropped by 5°F. What was the evening temperature?
Answer:
The evening temperature is 4° F
Step-by-step explanation:
6° F below 0 = -6.
15° F. -6 + 15 is 9.
9° F. 5° F. 9 - 5 = 4
The Changs received a delivery of fuel oil totaling 35.00 gallons. The oil cost $3.05 per gallon. What did the Changs pay for the delivery
Answer:
$106.75
Step-by-step explanation:
Since the cost of a gallon of oil cost $3.05, we are going to have the equation y = 3.05x, where x represents the number of gallons of oil.
Since the Changs have 35 gallons of oil, the equation would be;
3.05(35) = 106.75
The Changs paid $106.75 for the delivery.
Help anyone can help me do the question,I will mark brainlest.
Step-by-step explanation:
h) p^2+b^2=h^2
5^2+x^2=8^2
25+x^2=64
x^2=64-25
x^2=39
x=√39
x=6.244998
We know that
p² + b² = h²
Part a
5² + x² = 8²
x² = 64 - 25
x = √39
Part B
4² + 6² = x²
16+36 = x²
√52 = x
√2×2×13 = x
x = 2√13
Must click thanks and mark brainliest
The cost,c(x), for a taxi ride is given by c(x)=3x+2.00, where x is the number of minutes. What does the slope mean for this situation
Answer:
for every minute it will cost 3 dollars
Step-by-step explanation:
c(x)=3x+2.00
The cost to get in the taxi is 2 dollars
The slope is 3
3x means that for every minute it will cost 3 dollars
How do radical expressions relate to everyday life , give atleast 3 examples !!!!!
15. The perimeter of the triangular field is 540m and its sides are in the ratio 25:12:5 find the area of the field.
Answer:
let the sides be 25x,12x and 5x ......then
25x+12x+5x=540
45x=540
x=25
sides are 25×12=300
12×12=144
5×12=60
we can find area by herons formula
On Monday a post office employee processed a batch of letters, on Tuesday she processed three times as many, and on Wednesday she processed 5,000 cards. In the 3 days she processed 15,000 letters. How many did she process on Tuesday
Let the number of letters processed on Monday = x
She processed 3 times letters on Tuesday.
Therefore, number of letters processed on Tuesday = 3x
Number of letters processed on Wednesday = 5000
Total number of cards processed in 3 days = 15000
Therefore, equation for the situation will be,
x + 3x + 5000 = 15000
4x = 15000 - 5000
4x = 10000
x = 2500
Since, number of letters processed on Tuesday = 3x
Therefore, number of letters processed on Tuesday = 3(2500)
= 7500
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please help! i have no idea
Answer:
θ = 51.7
SOH-CAH-TOA
CAH: COS = ADJ/HYP cos(θ) = 19.4/29.3
θ = 48.5
93.2 + 48.5 + x = 180
x = 38.3
90 + 38.3 + θ = 180
θ = 51.7
Step-by-step explanation:
what is the value of x
Answer: 24(option A) is the answer
exterior angle = 360/n
so, n = 15
then, 360/15 = 24
I need help to find the value of x. Round to the nearest tenth
Answer:
17.1
Step-by-step explanation:
tan(35)=12/x, x=17.1
Answer:
x ≈ 17.1
Step-by-step explanation:
The angle is 35 degrees, so we do tan(35)
Which equals the side divided by x.
tan(35) = 12 / x
So x ≈ 17.1
lf y 1/4 · when x=5, find y when x=7. given that y varies directly with x.
y=
Answer:
y= 0.35
Step-by-step explanation:
y 1/4
when x=5,
find y=? when x=7.
given that y varies directly with x.
y = kx
Where k is the constant of proportionality
k= y/x
k= (1/4)÷ 5
k= 0.05
y= kx
y= (0.05)(7)
y= 0.35
I Hope this will helpful...
Hawa is going to see a movie and is taking her 5 kids. Each movie ticket costs $15 and
there are an assortment of snacks available to purchase for $3 each. How much total
money would Hawa have to pay for her family if she were to buy 10 snacks for
everybody to share? How much would Hawa have to pay if she bought & snacks for
everybody to share?
Total cost with 10 snacks:
Total cost with x snacks:
Answer:
The snack s will cost 30$. But the movies would cost 75$
The amount of money that he pays for her family if she were to buy 10 snacks for everybody to share will be $30.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Hawa is going to see a movie and is taking her 5 kids. Each movie ticket costs $15 and there is an assortment of snacks available to purchase for $3 each.
The amount of money that he pays for her family if she were to buy 10 snacks for everybody to share will be given as,
⇒ 10 x $3
⇒ $30
More about the linear equation link is given below.
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Find the measure of one interior angle for the following regular polygon
Answer:
108 degrees
Step-by-step explanation:
The formula for the total sum of the angles in any REGULAR shape is
[tex](n-2) * 180[/tex], where n represents the number of sides.
The shape in the picture shown is a pentagon (5 sides).
[tex](5-2) * 180\\[/tex]
[tex]3 * 180[/tex]
= [tex]540[/tex]
So the angle sum is 540 degrees.
Again, we are told that it is a regular polygon, meaning all sides and angles in the shape are equal.
So to find one angle, just divide it by the number of sides.
[tex]540/5 = 108[/tex]
Answer: 108 degrees
Step-by-step explanation:
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
Q = (√x-5)² + (√x+4)-41
Answer:
. .
Step-by-step explanation:
x^2-9x√x-12
solve by using formula (a+b)^2 and open the brackets
Last year 160 new candidates submitted applications to work for an agency. This year, that number is on target to increase by 25%. There are 6 months left in the year. How many new applications has the agency received so far this year?
Answer:100
Step-by-step explanation:
Given
Last year 160 new candidates submitted to work for agency
It is expected to increase by 25% that is , increase in one year should be
[tex]\Rightarrow 160+160\times 25\%\\\Rightarrow 160(1+0.25)\\\Rightarrow 160\times 1.25\\\Rightarrow 200[/tex]
200 application in the upcoming year. So, in 6 months, agency must have accepted 100 applications.
Noah had to water 7 plants. Each plant needed 14 ounces of water. Noah multiplied to find out how much water he would need. Which equation shows the addition equation he could use to check his answer?
14 + 14 + 14 + 14 + 14 + 14 = 84
14 + 7 = 21
14 + 14 + 14 + 14 + 14 + 14 + 14 = 98
7 + 7 + 7 + 7 + 7 + 7 + 7 = 49
Answer:
n3 14 + 14 + 14 + 14 + 14 + 14 + 14 = 98
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
The diagram below represents which percent?
An area model with 4 shaded sections and 1 unshaded section.
Answer:
25%
Step-by-step explanation:
1 ÷ 4 = 0.25
0.25 x 100 = 25 = 25%
please help me !! :)
Answer: c
Step-by-step explanation:
c is the same and it is the correct answer
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. (Help ASAP)
Is it a, b, c or d?
Answer:
C.
Step-by-step explanation:
212/4 = 53, so 53/1, or 53 miles are driven every hour.
cherly gets paid $8 per hour at her job at the record store. she made a total of $96 last week .write a multiplication equation to show how many hours she worked last week
Answer:
8(h)=96
Step-by-step explanation:
Remember when you are writing a multiplication equation, it's a division backwards.
96/8=h
h×8=96
hope this helps you
goodluck
Answer: 8x=96
Step-by-step explanation:
8X = 96
X = 96/8
X = 12 hours
A dealer marks a T-shirt with a price 20 PERCENT more than the cost price. It he sells it at a discount of I5 PERCENT.. What will be his gain Or loss percent ? (Take cost price as Rs 100)
Answer:
Rs 2,or 2%profit
Step-by-step explanation:
the price he marked:
[tex]100 \times \frac{120}{100} = 120[/tex]
(20 percent more than cost price)
The discount he put: 15 percent
[tex]120 \times \frac{85}{100} [/tex]
Rs102
102 is 2 more than 100
and is 2%profit.
Brainliest please
What is the reciprocal of 7/9 it’s a fraction by the way
Answer:
9/7
Step-by-step explanation:
Reciprocal means 1 over the number
1 / (7/9)
1 * 9/7
9/7
Answer:
[tex] = \frac{9}{7} [/tex]
Step-by-step explanation:
Reciprocal means inverse:
[tex] {( \frac{7}{9} })^{ - 1} = (\frac{9}{7} ) {}^{1} \\ \\ = \frac{9}{7} [/tex]
Evaluate the expression when b= -6.
b^2-6b+4
Answer:
76
Step-by-step explanation:
when b = -6
b^2 - 6b + 4
(-6)^2 - 6(-6) + 4
36 + 36 + 4 = 76
(remember, a negative times a negative always equals a positive)
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