Answer:
8, 11, 14
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
[tex]a_{n}[/tex] = 8 + (n - 1)3 , then
a₁ = 8 and d = 3 , thus
a₂ = 8 + 3 = 11
a₃ = 11 + 3 = 14
The first 3 terms are 8, 11, 14
Answer:
8
11
14
THAT IS THE ANSWER TO THE QUESTION
46+9a=-5a+74 solve for a
Answer: a=2
Step-by-step explanation:
-14a=-28
divide both sides by -14
a=2
Subtract 2y²+5y +8 from 6y- 2y+3.
Answer:
The answer to this problem would be :
-2y^2-y-5
Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Statement Reason 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given 2. m∠H + m∠J + m∠K = 180° 2. ? 3. 30° + 50° + m∠K = 180° 3. substitution property 4. 80° + m∠K = 180° 4. addition 5. m∠K = 100° 5. subtraction property of equality 6. m∠J = m∠P; m∠K = m∠N 6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent 8. △HKJ ~ △LNP 8. AA similarity theorem Which reason is missing in step 2?
Answer:
[tex]2. m\angle H+m\angle J +m\angle K =180^{\circ}[/tex]
Reason: the sum of all interior angles of any triangle is equal to 180º.
Step-by-step explanation:
1) Organizing
Statement 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. Reason: given
2) Since the sum of all internal angles of any triangle is equal to 180º, just like the formula. N the number of sides of a triangle:
[tex]S_{i}=180^{\circ}(n-2)\rightarrow 180(3-2) \therefore S_{i}=180^{\circ}[/tex]
3) We can also say
[tex]m\angle K=180^{\circ}-(m\angle H+m\angle J)\\m\angle K=180^{\circ}-\left ( 30^{\circ}+50^{\circ} \right )\\m\angle K=100^{\circ}[/tex]
Similarly to the other triangle:
[tex]m\angle L=180^{\circ}-(m\angle N+m\angle P)\\m\angle L=180^{\circ}-\left ( 100^{\circ}+50^{\circ} \right )\\m\angle L=30^{\circ}[/tex]
4) Hence,
[tex]2. m\angle H+m\angle J +m\angle K =180[/tex]
Reason: The sum of interior angles is equal to 180º.
Answer:
B
Step-by-step explanation:
Martha has $10,000 saved and wants to attend a college with a current tuition of $10,000 a year. She will graduate from high school in five years. Roughly how much more will Martha need to save for one-year's tuition to account for an annual rate of inflation of 3%?
Answer:
$1,592.74
Martha will need to pay $1,592.74 more
Step-by-step explanation:
Using the compound interest/inflation formula;
A = P(1+r)^(t)
Where;
A = final value
P = initial value = $10,000
r = inflation rate = 3% = 0.03
t = time = 5 years
Substituting the values;
A = $10,000(1+0.03)^(5)
A = $11592.740743
A = $11,592.74
How much more will Martha need to save;
C = final value - initial value = A - P
C = $11,592.74 - $10,000
C = $1,592.74
Martha will need to pay $1,592.74 more
Answer:
1,590.00
Step-by-step explanation: I took the test
Bryan’s golf coach suggested he take some golf lessons. The pro at windy fairways charges $20.00 per month plus $10.00 per lesson. The pro at sunny sands charges $100.00 per month for unlimited classes. How many classes does he have to take for both pros be the same price?
Answer:
8
Step-by-step explanation:
(100 - 20) / 10 = 8
Answer: He has to take a class per month from the both pros
Step-by-step explanation:
Put the following temperatures in order from least to greatest (1 is the least and 5 is the greatest):
Group of answer choices
The temperature was 25 degrees below zero
The pool temperature was 78 degrees
Water freezes at 32 degrees
The low temperature in December is -3 degrees
The temperature in the refrigerator was 34 degrees.
Answer:
25 degrees below zero, -3, 32, 34, 78
Part 3
1. Be sure your work is shown and steps are in order.
2. List all the possible rational roots.
3. Use synthetic division to test the possible rational roots and factor possible.
4. Identify complex roots if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations.
3a. p(x)= 2x^5 - 9x^4 + 6x^3 + 22x^2 - 20x - 25
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
p(x) = (x +1)^2(2x -5)(x^2 -4x +5)
complex roots: 2±i
see the last attachment for a graph
Step-by-step explanation:
2. The leading coefficient of p(x) is 2, and the constant term is 25. The Rational Root Theorem tells you possible rational roots will be of the form ...
±(divisor of 25)/(divisor of 2)
That is, they are ...
±1/2, ±1, ±5/2, ±5, ±25/2, ±25
__
3. Before we get into synthetic division, we choose to see if we can reduce this list any. We note that p(0) = -25. The value of p(1) is the sum of the coefficients:
p(1) = 2 -9 +6 +22 -20 -25 = 30 -54 = -24
Similarly, the value of p(-1) is the same sum with odd-degree coefficients negated:
p(-1) = -2 -9 -6 +22 +20 -25 = 42 -42 = 0
So, we found our first root: -1. Using synthetic division, we can reduce the polynomial and start over. See the first attachment for this division.
__
The reduced polynomial is ...
p1(x) = 2x^4 -11x^3 +17x^2 +5x -25
We already know that +1 is not a of it. Checking -1, we have ...
p1(-1) = 2 +11 +17 -5 -25 = 0
So, we found our second root: -1. Using synthetic division, we can reduce the polynomial and start over. See the second attachment for this division.
__
The reduced polynomial is ...
p2(x) = 2x^3 -13x^2 +30x -25
The alternating signs tell us there are no more negative real roots. They also tell us there are 1 or 3 positive real roots. We know p2(0) = -25. Then ...
p2(1) = 2 -13 +30 -25 = 32 -38 = -6
The average rate of change between these points is (-6 -(-25))/(1 -0) = 19. At this rate, we expect a root between x=1 and x=2. Testing x=2 using synthetic division, we get a remainder of -1. (See the 3rd attachment.) Then the rate of change between x=1 and x=2 is (-1 -(-6))/(2-1) = 5, suggesting x=5/2 might be a worthwhile test value.
The synthetic division is shown in the 4th attachment. You will note that we divide the polynomial p2(x) by its leading coefficient, so the coefficients used for p2(x) in the synthetic division are 1, -13/2, 15, -25/2. The remainder of 0 tells us that (x -5/2) is a factor of p2(x)/2, or (2x -5) is a factor of p2(x).
__
The reduced polynomial is ...
p3(x) = x^2 -4x +5
This can be written in vertex form as ...
p3(x) = (x -2)^2 +1
The positive leading coefficient means the graph opens upward, and the vertex at (2, 1) means there are no real solutions.
The real solutions to p(x) are x = -1, -1, and 5/2.
__
4. The complex solutions will be the solutions to ...
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i . . . . complex roots of p(x)
__
5. The graph is shown in the last attachment. The odd degree and positive leading coefficient of p(x) means the overall shape will be from lower left to upper right (/). That is, the sign of the end value of p(x) will match the sign of x.
The graph will touch the x-axis from below at x = -1, and will cross at x = 2.5. There is no particular symmetry.
The final quadratic factor is graphed and its vertex shown. The vertex matches that of the vertex-form equation for p3(x), above.
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
real solutions to p(x) are x = -1, -1, and 5/2.
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i complex roots
What is the volume of the prism? 1080 cm 2700 cm 3240 cm 6480 cm
Answer:
Volume of prism = 3,240 cm³
Step-by-step explanation:
GIven.
Hexagonal prism.
Side of base(b) = 12cm
Height of prism = 9cm
Height of base (h)= 10cm
Find:
The volume of the prism.
Computation:
Area of base of hexagonal prism = n/2[bh]
Area of base of hexagonal prism = 6/2[(12)(10)]
Area of base of hexagonal prism = 360 cm²
The volume of prism = Area of base of hexagonal prism × Height of prism
The volume of prism = 360 × 9
Volume of prism = 3,240 cm³
what is the slope-intercept equation of the line below?
Answer:
4
Step-by-step example
Slop is the
Find a linear second-order differential equation F(x, y, y', y'') = 0 for which y = c1x + c2x4 is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c1 and c2. (Use yp for y' and ypp for y''.)
Answer:
[tex]4y+ y"x^2-4y'x = 0[/tex]
↓
[tex]F(x, y, y', y'') = 0[/tex]
Step-by-step explanation:
From the information given:
[tex]y = c_1x + c_2x^4 \\ \\ y^1'= c_1 + 4c_2x^3 \\ \\ c_1 =y' - 4c_2x^3 \\ \\[/tex]
So;
[tex]y = y'x -4c_2x^4+c_2x^4 \\ \\ y - y'x - 3c_2x^4 \\ \\ y'= y"x+y'- 12c_2x^3 \\ \\ c_2= \dfrac{y"x}{12x^3} \\ \\ c_2= \dfrac{y"}{12x^2}[/tex]
∴
[tex]y = y'x- \dfrac{3x^4*y'' }{12x^2} \\ \\ \\ y = y'x - \dfrac{y" x^2}{4} \\ \\ \\ 4y+ y"x^2-4y'x = 0[/tex]
↓
[tex]F(x, y, y', y'') = 0[/tex]
Carol is y years old and her daughter is 25 years younger.find carols present age if sum of ages in 6 years time is 75
solve 5kx+ 6=7kx for x
Answer:
A
x= 3/x
Step-by-step explanation:
5kx + 6 = 7kx
collect like term
5kx - 7kx = -6
-2kx = -6
minus cancel out
=> 2kx = 6
divide bothside by 2k
=> x = 6/2k
=> x = 3/k
Answer:
Step-by-step explanation:
its A just trust :)
answer.
The temperature decreased from
17° on Saturday to -7° on Sunday.
What was the total change in
temperature?
Answer:
Decreased 24 degrees
Step-by-step explanation:
subtract the 17 from Saturday which gets you to 0 but it ends up being -7 on Sunday so i did 17+7 and it gives 24 so that's how much it went down
Explain how to solve this problem by writing down the steps. The grass on the field erodes by -1 1/2% every year. If the total length of grass on the field was 220 feet long 3 years ago, how long is the length of grass on the field now?
Answer:
Step-by-step explanation:
Since the grass on the field erodes by -1 1/2% every year, it means that the rate of erosion is exponential. It is therefore eroding in geometric progression. We would apply the formula for determining the sum of n terms of a geometric sequence which is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of terms(number of years) in the sequence.
a represents the first term in the sequence(the length 3 years ago)
r represents the common ratio(rate of erosion)
From the information given,
a = 220 feet
r = - 1.5/100 = - 0.015
n = 3
Therefore, the length of the field after 3 years, S3(length of the field now) would be
Sn = a(1 - r^n)/(1 - r)
S3 = 220(1 - (- 0.015^3)/(1 - - 0.015)
S3 = 220.0007425/1.015
S3 = 216.7495 feet
C. Courtney got a remote control car for her birthday. It is a metallic
purple with chrome wheels that are 1 1/2 inches in diameter. She said to
her friend, Dylan, “My remote control car goes faster than my mom's
car on the freeway.” “No way,” said Dylan. Courtney said, “I will prove it to
you.” Courtney measured off a distance of 115 inches. Dylan said, “Okay, I
will time how long it takes your car to travel that distance. I have a stopwatch
feature on my watch.” Courtney raced her remote control car over the
115-inch distance. Dylan said, “Wow, that only took 3.21 seconds. That seems
really fast.” “See, I told you,” said Courtney. “But really how fast is it going?”
answered Dylan. Determine the speed of Courtney's remote control car and
compare its speed to that of a regular car traveling on the freeway. Explain
how you found your solution. Why might the manufacturer get away with
advertising that the remote control car Travels Faster Than Life?
please help!!!!
Answer: No. the remote control car traveled 2 miles per hour whereas a car typically travels between 30 miles per hour and 60 miles per hour.
Step-by-step explanation:
[tex]\dfrac{115\ inches}{3.21\ seconds}\times \dfrac{1\ foot}{12\ inches}\times \dfrac{1\ mile}{5280\ feet}\times \dfrac{60\ seconds}{1\ minute}\times \dfrac{60\ minutes}{1\ hour}\\ \\\\=\dfrac{414,000\ miles}{203,385.6\ hours}\\\\\\=\dfrac{2.0\ miles}{1\ hour}[/tex]
Speed of Courtney's remote control car is: 2 mph
Courtney's remote control car is slower than an average freeway car since averagely the speed of a car on the freeway is usually 60 mph.
Given that:
Distance covered by Courtney's car = 115 inches
Time taken to cover that distance = 3.21 seconds
Converting inches to miles and seconds to hours:
[tex]1 inch \approx 0.0000158 miles\\115 inches = 115 \times 0.000158 miles\\=\approx 0.00182 miles\\\\3.21 seconds = \dfrac{1}{3600} \times 3.21 \: hours\\= 0.00089 \: hours\\[/tex]
Thus speed of Courtney's car can be calculated as
[tex]Speed = \dfrac{distance}{time}\\\\= \dfrac{0.00182}{0.00089} mph\\\\= 2.089 mph \approx 2 mph[/tex]
Thus Speed of Courtney's car is approx 2 miles per hour whereas the average speed of a car on a freeway is about 60 miles per hour.
Learn more here:
https://brainly.com/question/11583742
40 points. Topic: Solving a word problem using a system of linear equations of the form y = mx + b A phone company offers two monthly plans. Plan A costs $8 plus an additional $0.17 for each minute of calls. Plan B costs $21 plus an additional $0.12 for each minute of calls. For what amount of calling do the two plans cost the same? ____minutes What is the cost when the two plans cost the same? $_____
Answer:
The plans will cost the same for $260 minutes of calling. These minutes will cost $52.20
Step-by-step explanation:
Plan A: $8 + ($0.17/min)t
Plan B: $21 + ($0.12/min)t
Equate these, obtaining $8 + ($0.17/min)t = $21 + ($0.12/min)t, or:
($0.17/min)t - ($0.12/min)t = $13, or
($0.05/min)t = $13 , so t = 260 minutes. The plans will cost the same for $260 minutes of calling.
Find the cost in this situation: It is $21 + ($0.12/min)(260 min), or $52.20
Can you please help me
Answer:
complementary angle: 63
supplementary angle: 153
Step-by-step explanation:
Complementary angles mean angles that add up to 90. Therefore 90-27=63
Supplementary angles are angles that add up to 180. Therefore 180-27=153
Is parallel to ? Explain. Yes, because both lines have a slope of . Yes, because both lines have a slope of . No, because the slopes of the lines are not equal. No, because the slopes of the lines are not opposite reciprocals of each other.
Answer:
I'd need to see the lines but basically, parallel lines have to be directly across from each other and they have to be the same size, I put a pic so you can see what I mean
Hope this helps you
Answer:
C) yes, because both lines have a slope of 2/3
Step-by-step explanation:
edg2020
Factor the trinomial by grouping.
9x^3 - 3x^2 -30x
Answer:
3x(3x+5)(x-2)
Step-by-step explanation:
[tex]9x^3-3x^2-30x= \\\\3x(3x^2-x-10)= \\\\3x(3x^2+5x-6x-10)= \\\\3x(x(3x+5)-2(3x+5))= \\\\3x(3x+5)(x-2)[/tex]
Hope this helps!
Use factoring to solve
2x^2-17x-35=0
Answer:
This does not factor
Step-by-step explanation:
2x^2-17x-35=0
Since the x^2 has a coefficient of 2
(2x ) ( x )
Looking at the factors of -35
-1 35 1, -35
-5 7 5, -7
We need to get to -17
You cannot factor this
-
. Alexandro, o professor de Física, avisou aos alunos que a média bimestral seria calculada conforme o seguinte critério: Adicionam-se as notas obtidas no projeto, na prova e no trabalho em grupo e divide-se o resultado obtido por três. Laura é uma das alunas do professor Alexandre. As notas de Laura: Projeto: 5,0 Prova: 6,5 trabalho em grupo: 9,5. A) Por que o resultado deve ser dividido por 3?
Answer:
É necessário dividir por 3 para calcular a média simples das 3 notas.
Média = 7.
Step-by-step explanation:
O resultado deve ser dividido por três porque três notas com pesos iguais (projeto, prova e trabalho em grupo) foram somadas, portanto para calcular a média bimestral de Laura, a soma das três notas deve ser dividida por 3. A média de Laura é:
[tex]M=\frac{5,0+6,5+9,5}{3}\\ M=7[/tex]
help pls tysm
What are two examples of financial institutions?
Answer:
The major categories of financial institutions include central banks, retail and commercial banks, internet banks, credit unions, savings, and loans associations, investment banks, investment companies, brokerage firms, insurance companies, and mortgage companies
Step-by-step explanation:
sorry i did not put 2 examples, i put too many examples lollll
Answer:
There are two primary types of financial institutions non-depository and depository.
Step-by-step explanation:
an insurance company would fall under the non-depository group, and a credit union would be defined as a depository institution.
Kate has a $75 gift card to a coffee shop. Each Friday, she purchases a latte for $5. She created a graph to represent the amount of money on her gift card each week. Does Kate's graph represent the situation? Why or why not? A. No, because the amount of money on her gift card should increase each week. B. Yes, because she starts with $5 on her gift card. C. No, because the graph should start at the origin D. Yes, because the amount of money on her gift card should decrease each week.
Answer:
D. Yes, because the amount of money on her gift card should decrease each week.
Step-by-step explanation:
The amount of money on the gift card decreases every Friday as it states in the problem.
Yes Kate's graph represent the situation, because the amount of money on her gift card should decrease each week. so option D is correct.
What is Graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
We can see that the graph shows that the slope is decreasing, if you got $75 and spend $5.00 each Friday, wouldn't that be decrease and Lastly, of course, they should not start at the origin as they started at $75.00.
The amount of money on the gift card decreases every Friday as it states in the given situation.
Learn more about finding the graphed function here:
https://brainly.com/question/27330212
#SPJ2
Find M a
A.
49
B.
35
C.
95
D.
275
Answer:
85
Step-by-step explanation:
The sum of the angles of a triangle are 180 degrees
A + B+ C = 180
A +72+ 23 = 180
Combine like terms
A + 95 = 180
Subtract 95 from each side
A +95-95 = 180-95
A =85
Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?
7th grade math I need some help
Answer:
Step-by-step explanation:
[tex](-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-14-1+\frac{3}{2}b-4b[/tex]
= ([tex]-15-\frac{5}{2}b[/tex])
[tex](5+2b)+(2b+\frac{3}{2})=(5+\frac{3}{2})+(2b+2b)[/tex]
= [tex](4b+\frac{13}{2})[/tex]
[tex](\frac{7}{2}b-3)-(8+6b)[/tex] = [tex](\frac{7}{2}b-6b)-(3+8)[/tex]
= ([tex]-\frac{5}{2}b-11[/tex])
[tex](-10+b)+(7b-5)=(-10-5)+(b+7b)[/tex]
= [tex](8b-15)[/tex]
Cristian, iris, and Morgan each get an equal share of 1/2 of a pizza. Which model represents the fraction of the pizza each person gets?
Answer:
Model B or 1/3 of the Pizza
Answer:
1/3
Step-by-step explanation:
model 1/3
If p(y) = y^3+3 y^2-5y-6, then p (-3) = ------------------
Answer:
9
Step-by-step explanation:
[tex]p(y)=y^3+3y^2-5y-6 \\\\p(-3)=(-3)^3+3(-3)^2-5(-3)-6= \\\\-27+27+15-6= \\\\9[/tex]
Hope this helps!
Answer:
p(-3)=9
Step-by-step explanation:
This question ask us to find p(-3), or what p(y) is when y is equal to -3.
We know that:
p(y)= y^3+3 y^2-5y-6
We want to find p(-3), so substitute -3 in for every y.
p(-3)= (-3^3)+3(-3^2)-5(-3)-6
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Solve the exponents first (-3^3 and -3^2)
-3^3=-3*-3*-3= -27
-3^2= -3* -3= 9
p(-3)= -27+ 3(9) -5(-3) -6
Next, multiply 3 and 9
p(-3)= -27+27-5(-3)-6
Then, multiply -5 and -3
p(-3)= -27+27+15-6
-27 and 27 equal 0, so they cancel each other out.
p(-3)=15-6
p(-3)= 9
Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Answer:
35/70*100 = 50 miles
Step-by-step explanation:
For the Black Panther Trip 420 students were scheduled to go. After collecting more parent surveys, 15% more students are going on the trip. Each admission ticket cost $22.75. What was the total amount paid for all the tickets purchased?
Answer: $ 10,988.25
Step-by-step explanation:
Hi, to answer this question, first we have to multiply the original number of students scheduled to go to the trip (420) by the added students’ percentage (15%) in decimal form (divided by 100)
420 x (15/100) = 420 x 0.15 = 63 students added
Adding the number of extra students to the original number:
420+63 = 483 students (total number of students)
Finally, we have to multiply the result by the cost of each admission ticket (22.75)
483 x 22.75 = $ 10,988.25