Answer:
y = (3/4)x + 17/4
Step-by-step explanation:
since we know the slope is 3/4, we have y = 3/4x + b. next plug in the point given. 5= 3/4(1) + b, simplify the equation to get 17/4=b, and now we have our equation: y = 3/4x + 17/4
The nth term of a sequence is 3n2 - n + 10 where n is a positive integer. Which term in the sequence is equal to 54?
Answer:
4th term
Step-by-step explanation:
Equate the nth term formula to 54 and solve for n
3n² - n + 10 = 54 ( subtract 54 from both sides )
3n² - n - 44 = 0
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term.
product = 3 × - 44 = - 132 and sum = - 1
The factors are - 12 and + 11
Use these factors to split the n- term
3n² - 12n + 11n - 44 = 0 ( factor the first/second and third/fourth terms )
3n(n - 4) + 11(n - 4) = 0 ← factor out (n - 4) from each term
(n - 4)(3n + 11) = 0
Equate each factor to zero and solve for n
n - 4 = 0 ⇒ n = 4
3n + 11 = 0 ⇒ 3n = - 11 ⇒ n = - [tex]\frac{11}{3}[/tex]
Since n > 0 then n = 4
The 4th term of the sequence is 54.
What is a sequence ?A sequence is a set of numbers with a constant difference or a constant ratio or it have a certain relation with the next and previous term.
According to the given question the nth term of a sequence is 3n² - n + 10.
We have to determine which term is equal to 54 or the value of and it must be an integer.
So, 3n² - n + 10 = 54.
3n² - n - 44 = 0.
3n² - 12n + 11n - 44 = 0.
3n(n-4) +11(n-4) = 0.
(3n+11) = 0 OR (n-4) = 0.
n = - 11/3 OR n = 4. ( given the term no. is a positive integer ).
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Additional questions!!! Please help, due today!!!
Answer:
A.
Step-by-step explanation:
?
Graph 4x + 7y ≤ 28 in the first quadrant of the coordinate plane.
Answer:
StGraph the line using the slope and y-intercept, or two points.
Slope: −47
y-intercept: (0,−4)
x y
−7 0
0 −4
Step-by-step explanation:
plsefgrffghttgrewe helppppppppppppppppppppppppppppp
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The slope of the given line is its constant of proportionality ~
so, let's find the slope ~
[tex] \sf\dfrac{y_2 - y_1}{x_2 - x_1} [/tex][tex] \sf \dfrac{4 - 0}{1 - 0} [/tex][tex] \sf 4[/tex]The required value is ~ 4
Line FG passes through points (0, 2) and (3, 2). Line F′G′ is formed by dilating line FG by a factor of 2 about the origin. Which statement is true? Group of answer choices Line F′G′ is the original line. Line F′G′ passes through the origin. Lines FG and F′G′ are parallel to each other. Lines FG and F′G′ are perpendicular to each other.
Answer:
See the picture, it explains the correct choice is CStep-by-step explanation:
a) Line F′G′ is the original line. Falseb) Line F′G′ passes through the origin. Falsec) Lines FG and F′G′ are parallel to each other. TRUEd) Lines FG and F′G′ are perpendicular to each other. False8
-6
4
ल
-8-
What is the domain of function m?
co
-2
-8
6
- 4
x
HELPP
Answer:
( - ∞, ∞ )
Step-by-step explanation:
The domain of the function is all values of x , that is
- ∞ < x < ∞ , or in interval notation
(- ∞, ∞ )
Joseph is pouring concrete for his new patio. The area of the patio is 25.2 square feet
and the length is 7.2 feet. What is the width, w, of his patio?
Answer:
3.5ft
Step-by-step explanation:
A = L(W)
25.2 = 7.2(W)
3.5 = W
whats is 89 x 98789 =
please help me asap please
Answer:
8792221
Step-by-step explanation:
89 x 98789 = 8792221
8792221 is correct answer
(Hope this helps can I pls have brainlist (crown)☺️)
Suppose the graph of y = f(x) is translated left 2 units, and up 8 units, then stretched vertically by a
factor of 3.
The new graph will have equation y =
Answer: f(x)=3(x+4)+ 8
Step-by-step explanation:
Stretch vertically by a factor of 3: y = 3x
Then, translate two units leftward: y = 3(x+2)
Then, translate 8 units upward: y = 3(x+4)+ 8
A. Complete the table if y varies
directly as x or x2
B. Complete the table if y varies inversely as x.
Direct variation is represented by the equation y = k × x and inverse variation is represented by y = k/x
Table 1:
y = k × x
30 = k × 5
30 = 5k
k = 30/5
k = 6
So,
y = 30
y = 30 k = 6
y = 30 k = 6x = 5
y = 30 k = 6x = 5Equation: y = 6x
y = k × x
y = 10 × 8
y = 80
So,
y = 80
y = 80 k = 10
y = 80 k = 10x = 8
y = 80 k = 10x = 8Equation: y = 10x
y = 3x
18 = 3x
x = 18/3
x = 6
So,
y = 18
y = 18k = 3
y = 18k = 3x = 6
y = 18k = 3x = 6Equation: y = 3x
y = 2x²
72 = 2x²
x² = 72/2
x² = 36
x = √36
x = 6
So,
y = 72
y = 72k = 2
y = 72k = 2x = 6
y = 72k = 2x = 6Equation: y = 2x²
Table 2:
y = k/x
5 = k/6
5 × 6 = k
30 = k
So,
y = 5
y = 5k = 30
y = 5k = 30x = 6
y = 5k = 30x = 6Equation: y = 30/x
y = k/x
y = 36/4
y = 9
So,
y = 9
y = 9k = 36
y = 9k = 36x = 4
y = 9k = 36x = 4Equation: y = 36/x
y = 60/x
20 = 60/x
20x = 60
x = 60/20
x = 3
So,
y = 20
y = 20k = 60
y = 20k = 60x = 3
y = 20k = 60x = 3Equation: y = 60/x
y = 24/x
y = 24/12
y = 2
So,
y = 2
y = 2k = 24
y = 2k = 24x = 12
y = 2k = 24x = 12Equation: y = 24/x
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Please help. I need to get this right.
Answer:
∡SYZ = 34.2°
∡XYZ = 68.4°
Step-by-step explanation:
∡SYZ = 34.2° this must be true because this angle is congruent to ∡XYS
∡XYZ = 68.4° this must be true because ∡XYZ = ∡WYS + ∡SYZ
Hailey is putting up a fence in the shape of an isosceles triangle in her
backyard. The fence has side lengths as shown, where x represents the
number of feet in each fence section. The perimeter of the fence can be
covered using 8 total fence sections represented by the expression 8x. If
fencing costs $6.50 a foot, what would be the total cost of the fence?
(2x + 4) ft
(3x + 7) ft
.
(2x + 4) ft
Answer:
the total cost would be $ 780.00
Step-by-step explanation:
step by step explanation
Complete the missing factors
6a^2 + 11b - 35b^2 = ( 3a _______)(2a______)
please help me, thank you.
These tables of ordered pairs represent some points on the graphs of lines p and r.
Which system of equations is represented by lines p and r?
9x−4y=−92x+4y=15
3x−y=−127x+3y=21
2x−y=−82x+y=7
x−2y=−86x+5y=30
Line p
x y
−3 2
0 8
4 16
Line r
x y
−5 17
2 3
5 −3
Answer:
The answer above mine is correct and here is why.
Step-by-step explanation:
Please rate this answer choice 5 stars and leave a thanks, You do not need an acount to do this.g
Pat a
mber
4. In a hockey league, 87 players play on seven
different teams. Each team has at least 12
players. What is the maximum number of players
on any one team?
Answer:
15
Step-by-step explanation:
since there is 7 teams and 12 can be the minimum we can do 7 x 12=84
this means that 3 people could possibly be on one single team.
the maximum number is 12+3=15
Write 456 in expanded notation using powers of 10
Answer:
400+50+6
Step-by-step explanation:
456 means 400+50+6
Find the measures of angles 1 and 2.
Answer:
angle one:100 degrees
angle two:70 degrees
Step-by-step explanation: so angle two and the angle with 70 degrees are alternate angles, so they would be the same. at this point if you subtracted 70 from 180 because angle b is 180 degrees, you would get 110, so then you would have three angles, and it wouldn't be too hard to find the fourth, which is 100 degrees.
Find the length of side x to the nearest tenth.
309
X
60°
What is the average rate of change of the function f(x)=120(0. 1)x from x = 0 to x = 2? Enter your answer, as a decimal, in the box. Do not round your answer.
The average rate of change of the function is -59.4
The formula for calculating the rate of change of the function is expressed as:
[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Given the function
[tex]f(x)=120(0.1)^x\\f(0) = 120(0.1)^0\\f(0)=120\\[/tex]
Get the value of f(2)
[tex]f(2)=120(0.1)^2\\f(2) = 120(0.1)^2\\f(2)=1.2\\[/tex]
Substitute into the formula to have:
[tex]f'(x)=\frac{1.2-120}{2-0}\\f'(x)=\frac{118.8}{2} \\f'(x)= -59.4[/tex]
Hence the average rate of change of the function is -59.4
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Which expression is equivalent to x6 – 9?
(x3)2 – 33
(x3)2 – 32
(x3)3 – 32
This polynomial is an example of a .
Step-by-step explanation:
[tex] {x}^{6} - 9 = { ({x}^{3} })^{2} - {3}^{2} [/tex]
Answer:
(x^3)^2-3^2 , or b.
and its the diffrence of suqares.
Step-by-step explanation:
14. At a local fruit stand, Luisa spends $5.25 for 2 pounds of strawberries. At this rate, how much can she expect to pay for 3.5 pounds of strawberries? (round to the nearest hundredt
h) Proportion Answer
Use the graph to identify the following: end behavior. for a branlist
Answer:
the first option, increasing as x approaches infinity and decreasing as x approaches negative infinity
Step-by-step explanation:
Pls help I will put brainlist if u help me told nd thank u
Answer:
17+7=24
Step-by-step explanation:
I hope this help you
Answer
10
Step-by-step explanation:
Subtract 7 from both sides of the equation.
n=17−7
Subtract 7 from 17.
n=10
BRAINLIEST?
In two or more complete sentences describe how to determine if the function, f(x) =3cos(x) is even by looking at a graph
Answer:
You know that a cosine graph is a sine graph moved to the left by pi/2, therefore, like a linear equation, you need to make the cosine graph 3 times less width.
Step-by-step explanation:
20 points answer please
Answer:
just d
Step-by-step explanation:
Hope this helps!❆
By VCR Sales A dealer carries two models of VCRs. One sells for
$300 and the other sells for $225. The dealer sells 22 VCRs for a
total revenue of $5700. How many of each type did the dealer sell?
Answer:
2333
Step-by-step explanation:
100 points if you get this
Answer:
....
Step-by-step explanation:
Answer:
I AGREE
Step-by-step explanation:
euler formula find the number of edges of a polyhedron of 6 faces and 4 verticies
Euler's polyhedron formula, V − E + F = 2
[tex] = 4 - E + 6 = 2 \\ = E - 10 = 2 \\ = E = 2 + 10 \\ = E = 12[/tex]help im not good in math
Answer:
4
Step-by-step explanation:
yeah 4/8 is the answer. yeah-ya
A retirement account was opened with a $900 deposit. If the account earns 4.25% interest compounded continuously and has no other deposits or withdrawals, how long will it take the value to double?
It will take 16.66years long for the money to double
The formula for calculating the compound amount is expressed as:
A = P(1+r)^t
A is the amount after t years = 2(900) = $1800P is the amount invested = $900r is the rate in decimal = 4.25% = 0.0425Substitute into the formula to have:
1800 = 900(1+0.0425)^t
2 =(1+0.0425)^t
2 = 1.0425^t
ln2 = tln1.0425
t = ln2/ln1.0425
t = 0.6931/0.0416
t = 16.66years
This shows that it will take 16.66years long for the money to double
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