PLEASE HELP ILL MARK BRAINLIEST !!!
The following tables describe arithmetic sequences
(a) what is the common difference of the sequence xn?
(b) what is x8? what is x12?
(c) what is the common difference of the sequence am?
(d) what is a12? what is a15?
Answers
Answer:
a) the common difference is 20
b) [tex]x_8=115 , x_{12}=195[/tex]
c) the common difference is -13
d) [tex]a_{12}=52, a_{15}=13[/tex]
Step-by-step explanation:
a) what is the common difference of the sequence xn
Looking at the table, we get x_3=16, x_4=36 and x_5= 56
Deterring the common difference by subtracting x_4 from x_3 we get
36-16 =20
So, the common difference is 20
b) what is x_8? what is x_12
The formula used is: [tex]x_n=x_1+(n-1)d[/tex]
We know common difference d= 20, we need to find [tex]x_1[/tex]
Using [tex]x_3=16[/tex] we can find [tex]x_1[/tex]
[tex]x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25[/tex]
So, We have [tex]x_1 = -25[/tex]
Now finding [tex]x_8[/tex]
[tex]x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115[/tex]
So, [tex]\mathbf{x_8=115}[/tex]
Now finding [tex]x_{12}[/tex]
[tex]x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195[/tex]
So, [tex]\mathbf{x_{12}=195}[/tex]
c) what is the common difference of the sequence [tex]a_m[/tex]
Looking at the table, we get a_7=104, a_8=91 and a_9= 78
Deterring the common difference by subtracting a_7 from a_8 we get
91-104 =-13
So, the common difference is -13
d) what is a_12? what is a_15?
The formula used is: [tex]a_n=a_1+(n-1)d[/tex]
We know common difference d= -13, we need to find [tex]a_1[/tex]
Using [tex]a_7=104[/tex] we can find [tex]x_1[/tex]
[tex]a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195[/tex]
So, We have [tex]a_1 = 195[/tex]
Now finding [tex]a_{12}[/tex] , put n=12
[tex]a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52[/tex]
So, [tex]\mathbf{a_{12}=52}[/tex]
Now finding [tex]a_{15}[/tex] , put n=15
[tex]a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13[/tex]
So, [tex]\mathbf{a_{15}=13}[/tex]
Related Questions
Write an equation in point-slope form and slope-intercept form for each line.
the line passes through (1, -1) and (2, 0)
Answers
Answer:
Step-by-step explanation:
Answer:
I think its the one w -1= -1
Step-by-step explanation:
becuase 2 minus 1 is -1 nd -1 minus 0 is -1 i could be wrong
Harper simplemente encendió una vela nueva y luego la dejó arder hasta la nada. La longitud de la vela que permanece sin quemar, en pulgadas, se puede modelar mediante la ecuación L = 15-1.5t, L = 15−1.5t, donde tt representa el número de horas desde que se encendió la vela. ¿Cuál es la pendiente de la ecuación y cuál es su interpretación en el contexto del problema?
Answers
Answer:
La pendiente de la ecuación es -1.5 y su interpretación en el contexto del problema es que en este caso este valor indica que la longitud L de la vela luego de t horas desde que se encendió la decrece en 1.5 unidades por cada hora.
Step-by-step explanation:
La función lineal se define por la ecuación
f(x) = mx + b
o
y = mx + b
donde m es la pendiente de la recta y b es la ordenada al origen.
La gráfica de una función lineal es siempre una recta.
Como se mencionó, la m es la pendiente de la recta. La pendiente es la inclinación con respecto al eje x, que es el eje de abscisas.
La pendiente m significa que si aumentamos la x en una unidad, la y aumenta en m unidades. Si m es positiva (m > 0), entonces la función es creciente. En cambio, si la m es negativa (m < 0), entonces la función es decreciente.
En este caso, siendo L=1.5 - 1.5t y comparando con la expresión y=mx + b, podes observar que el valor de la pendiente m es -1.5. Como m es un número negativo, entonces se trata de una función decreciente. En este caso este valor de pendiente indica entonces que la longitud L de la vela luego de t horas desde que se encendió la decrece en 1.5 unidades por cada hora.
La pendiente de la ecuación es -1.5 y su interpretación en el contexto del problema es que en este caso este valor indica que la longitud L de la vela luego de t horas desde que se encendió la decrece en 1.5 unidades por cada hora.
How many solutions does 5(2x-3)=5 have
Answers
Answer:
1
Step-by-step explanation:
because it is a linear equation
Given g(x)=-x-4, solve for x when g(x)=10
Answers
Answer:
x= -14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
g(x)=x-4
g(x)=10 = g(x)=x-4 /+4
g(x)=14
Write the equation of the line that passes through the points (2,5) and (2, -6). Put
your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
Help Asap will mark brainliest! Prove polygon ABCDEF and polygon A′B′C′D′E′F′ are congruent or not congruent.
Answers
Answer:
They are congruent im just not sure how to prove it... maybe by showing the transformations that got it to that point?
Step-by-step explanation:
sorry ):
Answer:
They are congruent because they are the same size and shape.
Step-by-step explanation:
For f(x) = -3x + 19. what is the value of x for which f(x) = 4?
X=-5
X = -1
X=5
X=6
Answers
f(x) = -3(5) + 19
f(x)= -15 + 19
f(x) = 4
1) find the missing side of each triangle
A) 5 km
C) 10 km
B) 13 km
D) 12 km
Answers
Answer:
c
S1tep-by-step explanation:
8x8=64
6x6=36
64+36=100
10x10=100
x=10
Once you add 8^2 +6^2 you get 100=c^2
To get C on its own you need to get rid of the square so you do to opposite of squaring which is square rooting. The the square root of 100 is 10
Find f. Write your answer as a whole number or a decimal. DO NOT ROUND
Answers
Answer:
f = 8 feet
Step-by-step explanation:
In Δ EBC
∵ DF ⊥ BE
∵ CB ⊥ BE
∴ DF // CB
∵ D is the mid-point of CE
∵ DF // CB
∴ F is the mid-point of EB
∵ DF joining the mid-points of EB and EC
∴ DF = [tex]\frac{1}{2}[/tex] CB
∵ CB = f and DF = 4 ft
∴ 4 = [tex]\frac{1}{2}[/tex] f
→ Multiply both sides by 2
∴ 8 = f
∴ The value of f is 8 ft
simplify 4 ^ 9 x 4 ^ 3
Answers
1. 4 ^ 9 x 4 ^ 3
2. 4^9+3
answer: 4^12
Good luck!
What is the surface area of a cube with a side length of 5 inches?
O 25 square inches
O 100 square inches
O 125 square inches
O 150 square inches
Answers
Answer:
for lazy people is D. >w<
Step-by-step explanation:
In a class election, 30 students voted for Emerald and 15 students voted for Beau. What percent of students voted for Beau?
Answers
Answer:
1/3
Step-by-step explanation:
The total amount of students is 45. 1/3 of 45 is 15
Answer:
About 33.3% of students voted for Beau.
Josiah is in the business of manufacturing phones. He pays a cost of $150 per phone produced for materials and labor and also must pay a daily fixed cost of $300 to rent the building and equipment. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
Answer: C=150p+300
Step-by-step explanation:
Find the m∠ULE in the triangle below.
please
Answers
Answer:
m∠ULE = 60°
Step-by-step explanation:
To find the measure of ∠ULE we will use the property of exterior angle of a triangle.
Since, measure of an exterior angle of a triangle is equal to the sum of two opposite interior angles.
m∠LUR = m∠LEU + m∠ULE
109° = 49° + m∠ULE
m∠ULE = 109 - 49
= 60°
Therefore, measure of angle ULE is 60°.
Write 2x+y=17 in slope-intercept form.
Solve for y?
Answers
Answer: y=2x+17
Step-by-step explanation:
What is the binary number for 4
Answers
Step-by-step explanation:
[tex]4=2^2=\bold1\cdot2^2+\bold0\cdot2^1+\bold0\cdot2^0\\\\4_{10}=\bold{100}_2=0100_2[/tex]
Can someone explain factoring expressions to me
Answers
Answer:
Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.
Hope it helps. have a wonderful thanksgiving day! :)
pls help me with this.
Answers
==========================================================
Explanation:
Focus on triangle HKL. This is a right triangle with the horizontal leg KL = 2. The vertical leg is the unknown side HK. The hypotenuse is HL shown by the single tickmark.
Triangle HKJ is also a right triangle. It shares the leg HK and the hypotenuse JH is congruent to HL as indicated by the single tickmark.
By the hypotenuse leg theorem, we can show that triangle HKL is congruent to triangle HKJ
From there, the corresponding pieces JK and KL must be the same length. So we can say JK = 2 because KL = 2.
-------------------------------
Now use the segment addition postulate
GK = GJ + JK
GK = 7 + 2
GK = 9
Focus now on triangle GKH and triangle MKH. We can prove these are congruent triangles using the hypotenuse leg theorem. Here HK = HK as mentioned before; also, GH = HM due to the double tickmarks.
As you can probably guess by now, the hypotenuse leg theorem only applies to right triangles.
Since triangle GKH is congruent to triangle MKH, we know that
GK = KM
Since GK = 9, this makes KM = 9.
---------------------------------
Therefore,
GM = GK + KM
GM = 9 + 9
GM = 18
Find the slope and the y-intercept of the graph of the linear equation.
--5x = 8-y
Answers
Answer:
Slope: -5
Y-intercept: (0,8)
Step-by-step explanation:
Plz mark brainliest.
An object's speed decreases by 5% for each minute that it is slowing down. Which of the
following is closest to the percent that its speed will decrease over half-an hour?
Answers
Answer: 79%
Step-by-step explanation:
min —> 30 mins because half an hour is 30 mins.
(1 - 0.5)^30 = .214638..
1 - .214638 = .78536
round that to the closest percent equals 79%
Which side lengths form a right triangle?
Choose all answers that apply:
Answers
Answer:
C
Step-by-step explanation:
What is the slope?
WILL MARK AS BRAINLIEST!! !
(picture included ^^^^)
Answers
Answer:
12
Step-by-step explanation:
I NEED HELP PLEASE QUICKLY FOR MY TEST I BEG YOU GUYS PLEASE!!
Square RSTU is shown below with a line AB drawn through its center. If the square is dilated using a scale factor of 4 and a line is drawn through the center of the new dilated figure, what relationship will that line have with line AB in the drawing below? (10 points)
Answers
Answer:
the line will remain in the same place
Step-by-step explanation:
Answer:
Give the other person brainliest :)
Step-by-step explanation:
Just trying to help
30% × 750 =
(30 ÷ 100) × 750 =
(30 × 750) ÷ 100 =
22,500 ÷ 100 =
225;
Answers
Answer:
1.250
2.225
3.225
4.225
how to expand 2(x+7)
Answers
Answer:
(2x + 2 x 7)
Step-by-step explanation:
what is the answer for this -4(x-1)+6x=2(17-x)
Answers
Answer:
15/2 or 7.5
Step-by-step explanation:
-4(x-1)+6x=2(17-x) PEDMAS
-4x+4+6x=34-2x combine terms
2x+4=34-2x subtract 4 and add 2x
4x=30 divide by 4
x=15/2
Answer:
Step-by-step explanation:
-4x + 4 + 6x = 34 - 2x
Solving like terms
2x + 4 = 34 - 2x
Bringing like terms on one side
2x + 2x = 34 - 4
4x = 30
x = 30/4
x = 15/2
When x = 1, y= 2, z = 3, then find the value of the sum of 5x square , -2x cube y and 3y to the power 4
Answers
5 - 4 + 48= 49
The answer is 49
Answer:
1305
Step-by-step explanation:
Equation = [tex]( 5x )^{2} + ( -2x ^{3} )y + ( 3y )^{4}[/tex]
= (5×1)² + {(-2×1)³}×2 + (3×2)⁴
= (5)² + {-2}³×2 + (6)⁴
= 25 + (-8)×2 + 1296
= 25 + (-16) + 1296
= 25 - 16 + 1296
= 9 + 1296
= 1305
22. In the diagram below WXZ is a right angle. If the measure of WXV is 11 more than there times the measure of WXY and the measure of YXV = 139, find the measure of YXZ
Answers
Answer:
9(331)-123=1
Step-by-step explanation:
2. In the diagram below WXZ is a right angle. If the measure of WXV is 11 more than there times the measure of WXY and the measure of YXV = 139, find the measure of YXZ
A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n?
5 < n < 15
5 < n < 20
15 < n < 20
15 < n < 25
Answers
Answer: 15 < n < 25
Step-by-step explanation: this was the answer on edge
Answer: Option 4 or D. 15 < n < 25
Step-by-step explanation: Trust Me!
If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.
If you found any of my answers helpful please like and choose my answer as Brainliest. I would appreciate it! Good luck everyone! :)
In the figure below, m angle WXZ=113°, and m angle2 is 3° more then m angle1 Find m angle1
Answers
Answer:
m∠1 = 55° ; m∠2 = 58°
Step-by-step explanation:
Let m∠1 = x° , then m∠2 = x° + 3°
m∠1 + m∠2 = 113°
x° + x° + 3° = 113°
2x + 3 = 113
2x = 110
x = 55°
m∠1 = 55° and m∠2 = 58°
The value of m∠[tex]1[/tex] is [tex]55[/tex]° and m∠[tex]2[/tex] is [tex]58[/tex]°
In the given figure m∠WXZ = [tex]113[/tex]° and m∠[tex]2[/tex] is [tex]3[/tex]° more than m∠[tex]1[/tex].
What is angle?
An angle is formed when two rays are joined together at a common point.
Now,
Let m∠[tex]1[/tex] = x° and m∠[tex]2[/tex] = x° + 3°
According to given figure;
m∠[tex]1[/tex] + m∠[tex]2[/tex] = 113°
x° + x° + 3° = 113°
2x° + 3° = 113°
2x° = 110°
x° = 55°
Hence, the value of m∠[tex]1[/tex] = x° = 55° and m∠[tex]2[/tex] = 55° + 3° = 58°
Learn more about the Angle visit:
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