Answer:
3
Step-by-step explanation:
Let's find the first term in terms of p.
So an arithmetic sequence is a linear relation.
That means it will have the same slope no matter the pair of points used. We are given the slope, the common difference, is 2. We are going to use point (9, 3+3p) and (1, t(1)) along with m=2 to find t(1).
[t(1)-(3+3p)]/[1-9]=2
Simplify denominator
[t(1)-(3+3p)]/[-8]=2
Multiply both sides by -8
t(1)-(3+3p)=-16
Add (3+3p) on both sides
t(1)=-16+3+3p
Combine like terms
t(1)=-13+3p
This means we can find the next term by adding 2 this.
t(2)=-11+3p
Let's find the next term by adding 2 this.
t(3)=-9+3p
Finally we can find the 4th term by adding 2 to this
t(4)=-7+3p
We are given the sum of the first 4 terms is 2p-10. So we can write:
-13+3p+-11+3p+-9+3p+-7+3p=2p-10
Combine like terms on left
12p-40=2p-10
Subtract 2p on both sides
10p-40=-10
Add 40 on both sides
10p=30
Divide both sides by 10
p=3.
-----------------
Checking:
t(1)=-13+3p=-13+3(3)=-13+9=-4
t(2)=-11+3p=-11+3(3)=-11+9=-2
t(3)=-9+3p=-9+3(3)=-9+9=0
t(4)=-7+3p=-7+3(3)=-7+9=2
----sum of the first 4 is -4
And 2p-10 at p=3 gives 2(3)-10=6-10=-4
So this part checks out
In general, the pattern that those 4 terms I wrote out follow t(n)=(-13-2)+2n+3p. I know this because the 0th term would have been (-13-2)+3p and this part goes up by 2 each time. The plus 3p part doesn't change.
Anyways t(9)=(-13-2)+2(9)+3p=-15+18+3p=3+3p. And this part looks good too.
HELP PLEASE! THIS IS MY LAST QUESTION ILL GIVE BRAINLIEST, NO LINKS. <3
Which of the following sets shows all the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20?
A) {1, 2, 3}
B) {2, 3, 4,}
C) {3, 4}
D) {4}
Answer: C {3, 4}
Step-by-step explanation:
Solve the inequality:
7x + 6 > 20
7x > 20 - 6
7x > 14
x > 2
Only 3 and 4 are greater than 2.
Someone please help me with this algebra problem
Step-by-step explanation:
8.4 is the ans
4x+8y=40
4x + 6.4=40
4x=40-6.4
4x=33.6
x=33.6÷4
x=8.4
Answer:
4x+8y=40
4x+(8+0.8)=40
4x+6.4=40
4x+6.4-6.4 =40-6.4
4x=33.6
4x÷4=33.6÷4
X=8.4
suppose a triangle has 2 sides of lengths 32 and 35 and that the angle between these 2 sides is 120 what is the length of the 3rd side of the triangle
Let the Vertices of the Δ be A , B , and C
We will follow the Usual Notation for Δ A B C , e.g., the side
opposite to the Vertex A will be denoted by a , m ∠ A = A , etc.
In this notation, let us assume that,
a = 32 , b = 35 , & , C = 120 ° & we have to find c
Using Cosine-Rule for Δ A B C , we have,
c²= a²+b² - 2 ab cos C = 32 ²+35² - 2 x 32 x 35 x cos 120° =
1024 + 1225 − 2240 cos ( 180 °− 60 °) = 2249 - 2240(-cos 60°)
2249+ 2240 (1/2)= 2249 + 1120= 3369
Answer: C= √3369 is about 58.04
Answer: 58.043087 (approximate)
===================================================
Explanation:
Refer to the diagram below. We can use the law of cosines to solve for c
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 32^2 + 35^2 - 2*32*35*cos(120)
c^2 = 3369
c = sqrt(3369)
c = 58.043087 which is approximate
Round this value however you need to.
how many 20p coins in £4
Answer two 20p coins make 40p
Step-by-step explanation:
Answer:
20 number of 20p makes £4.
Step-by-step explanation:
Let the number of 20p be x
Therefore,
[tex]x \times 0.20 = 4\\\\x = \frac{4}{0.20} = \frac{4 \times 100}{ 20} = 4 \times 5 = 20[/tex]
Randy walks his dog each morning. he walks 7/12 of a mile in 7 minutes how many miles does he walks in 1 minutes
Answer:
1/12 mile
Step-by-step explanation:
We can use a ratio to solve
7/12 miles x miles
---------------- = ---------------
7 minutes 1 minute
Using cross products
7 /12 * 1 = 7x
Divide each side by 7
7/12 * 1/7 = x
1/2 = x
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
⠀Randy walks his dog each morning. he walks 7/12 of a mile in 7 minutes ⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀how many miles does he walks in 1 minutes⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
⠀
Randy walks 7/12 miles in 7 minutes
Sooo
He walks in one minutes is
7/12 miles in 7 minutes one minutes is [tex]\sf{\dfrac{\dfrac{7}{12}}{7} }[/tex] one minute =[tex]\sf{\dfrac{7}{12}×\dfrac{1}{7} }[/tex] one minute=[tex]\sf{\dfrac{1}{12} }[/tex][tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
Hence,
he walks in 1 minutes is 1/12 miles.
Answer this please:
I attached a file for you to see
Answer:
C Infinitely many solutions
Step-by-step explanation:
i think! Good luck!!
a bag contains three red marbles five blue marbles and seven green marbles.what is the ratio of blue marbles to the total number of marbles
Answer:
5:15 simplified as 1:3
Step-by-step explanation:
GIVING BRAINLIEST!! Which of the following ordered pairs lies on the graph of y = tanx?
(5 pi, 0)
(-9pi/4, 1) <---- this is wrong
(-5pi, -1)
(pi/6, √3)
Answer:
[tex](5\pi ,0)[/tex]
identify the equation of the line graphed below
Given f(x)= 2^x and g(x)=x^2 answer the questions that follow
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
PLEASE HELP
Answer:
a. Yes it's correct, reasons;
I) let x=1, f(1)=2^1=2, g(x)=1^2=1 this proves that when a higher number is used the value of f(x) will be higher than g(x).
ii) As x approaches zero f(x) approaches 1, but g(x) approaches 0. Which will make the rate at which the graph of f(x) increase be faster than g(x)
b. f(x) has an infinite degree but g(x) has a finite degree of 2.
Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart(x) ∨ (x = x)
Answer:
b; ∀x P(x) ∨ ¬P(x)
Step-by-step explanation:
Suppose that we have a proposition p
Such that p can be true or false.
We can define the negation of p as:
¬p
Such that, if p is false, then ¬p is true
if p is true, then ¬p is false.
Also remember that a proposition like:
p ∨ q
is true when, at least one, p or q, is true.
Then if we write:
p ∨ ¬p
Always one of these will be true (and the other false)
Then the statement is true.
And if the statement depends on some variable, then we will have that:
p(x) ∨ ¬p(x)
is true for all the allowed values of x.
from this, we can conclude that the statement that is always true is:
b; ∀x P(x) ∨ ¬P(x)
Where here we have:
For all the values of x, P(x) ∨ ¬P(x)
What is the value of x?
oh my god you are such a god level hut
Answer:
A.36°
Step-by-step explanation:
65°+79°+X=180°
144+X=180°
X=180°-144°
X=36°
HELP ASAP PLEASE!!!!!!!
Answer:
the answer is 2
Step-by-step explanation:
it doesn't match the other but is 2
helppppppppppppppppppppp plzzzzz
Answer:
B. 16/3
Step-by-step explanation:
f(2) = 1/3 · 4²
f(2) = 1/3 · 16
f(2) = 16/3
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
Solution given:
Relationship base and hypotenuse is given by Cos angle
Now
Cos 60°=adjacent/hypotenuse=x/12
1/2=x/12
x=12/2
x=6
the value of x is 6.
2m^2-5m-3=0 by factorization
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
the length of each side of a nonagon is 3.25cm the perimeter of the nonagon is?
a,12.25
b,29.25m
c,29.25
d,none
Answer:
,29.25m
Step-by-step explanation:
maybe answer is correct
Answer: B. 29.25 cm
Step-by-step explanation:
Given
The prefix nona- came from Latin meaning "nineth"
Thus, nonagon has 9 sides
Solve
1 side = 3.25 cm
9 sides = 3.25 × 9 = 29.25 cm
Hope this helps!! :)
Please let me know if you have any question
Round the $40435.29 to the nearest thousand dollar
Answer:
$40000
Step-by-step explanation:
The nearest thousand dollar is rounding the thousand value from its hundred value, which in this case is 4. Since 4 is less than half of 10, the thousand value must round down to $40000.
Answer:
$40000.00
Step-by-step explanation:
Report this answer if its incorrect ^_^
What is the range of this set of heights in centimeters? {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178} 38 41 46 50
Answer:
50
Step-by-step explanation:
Given:
140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178
Arranging in ascending order (from the lowest to the highest)
= 132, 140, 142, 147, 149, 152, 158, 163, 165, 166, 168, 171, 173, 177, 178, 180, 180 181, 182
Range = highest number - lowest number
= 182 - 132
= 50
Answer:
50
Step-by-step explanation:
None
Find the angle marked with the ? mark
Answer:
53 degrees
Step-by-step explanation:
Angle N = angle E
because angle made by joining end points of same chord on circumference are always equal.
so angle E = 37
Angle D = 90 ( because angle made by diameter on circumference is 90 degrees)
Now in Triangle DEC. Sum if all the angles of triangle us 180
Angle D + angle E + ? = 180
37 + 90 + ? = 180
127 + ? = 180
? = 180 - 127
? = 53 degrees
What is the soution of (Image below)
Answer:
A
Step-by-step explanation:
Starting with the original equation:
[tex]\sqrt{1-3x} =x+3[/tex]
Squaring both sides to remove the root, and expanding the right side:
[tex]1-3x=(x+3)(x+3)[/tex]
Multiplying the right side:
[tex]1-3x=x^{2} +6x+9[/tex]
Combine like terms:
[tex]x^{2} +9x+8[/tex]
Factor:
(x+8)(x+1)
If x+8=0, then x= -8
If x+1=0, then x=-1
a^2×c^2/c^2×d^2+bc/ad reduce the algebraic
Answer:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Required
Simplify
We have:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Cancel out [tex]c^2[/tex]
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^2}{d^2}+\frac{bc}{ad}[/tex]
Take LCM
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Help! What is the equation of the line shown in the graph?
Answer:
y = -x -2
Step-by-step explanation:
Slope = -1
y intercept is -2
Slope = [tex]\frac{-4-1}{2-(-3) }[/tex] = [tex]\frac{-5}{5}[/tex] = -1
Tickets to a football final are selling well. On Thursday, 47 of the tickets are sold. On Friday, 14 of the tickets are sold. What fraction of tickets are available to sell on Saturday?
The question seems incomplete ; as the total number of tickets to be sold isn't given.
Answer:
61 / X
Step-by-step explanation:
Let's take the total Number of tickets to be sold as : X
Number of tickets sold on Thursday = 47
Number sold on Friday = 14
Fraction of tickets available for sale on Saturday :
(Total number of tickets already sold) / Total number of tickets to be sold
(Thursday + Friday sales) / total number of tickets to be sold
Fraction available for sale on Saturday = (47+14) / X
Fraction available for sale on Saturday = 61 / X
Kindly put value of x = total number of tickets available for sale to get the exact fraction.
Which of the following is the explicit rule for a geometric sequence defined by
a recursive formula of a, - 138-1 for which the first term is 7?
Answer:
C
Step-by-step explanation:
What you wrote is not the same thing as what the question is, or at least I don't think so. I'll answer the printed question.
First of all, the 13 is what separates each of the terms. In other words 7 is the first term. 13 must be raised to the n - 1 power.
It is written like this
an = 7 * 13^(n - 1)
you want a1 to be 7. The only way that can happen is if 13^0 which gives you 1.
So the correct answer is C
Find the perimeter of ΔJKL. Round your answer to the nearest tenth if necessary
Answer:
Step-by-step explanation:
as angles of two triangles are equal, so they are similar.
x/17 =35/14=40/16
x/17=35/14
x=35/14×17=85/2=42.5
perimeter of ΔJKL=40+35+42.5=117.5
what's this problem please
Answer:
Option A : 135°Step-by-step explanation:
If the table and ground are to be parallel then,
45° + x = 180° [Co-interior angles]
=> x = 180 - 45
=> x = 135° (Ans) (Option A)
what is the smiplest ratio for 75cm:1m:250 mm
Answer:
You need to convert all the units to one unit
**Does anybody knows how to do it***
instructions: state what additional information is required in order to know that the triangle are congruent for the given reason.
Given: ASA
With ASA, we need two angles and an included side. An included side is one that is between the two angles.
But, we need to make sure the sides match up. So, triangle KJI is congruent to triangle ZYX.
Therefore, we need to know that side JI is congruent to YX.
Hope this helps!
Barbara, a school superintendent, asks the local school board for permission to hire an additional teacher whenever the student enrollment at a certain grade level within a school increases by 35 students beyond capacity. This is an example of which type of decision
Answer:
Programmed
Step-by-step explanation:
Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.
