Answer:
a₂₁ = 188Step-by-step explanation:
The n-th term of an arithmetic sequence: [tex]a_n=a_1+d(n-1)[/tex]
so:
[tex]a_5=a_1+d(5-1)\\a_5=a_1+4d\\a_1=a_5-4d\\a_1=44-4d\\\\a_{10}=a_1+d(10-1)\\ a_{10}=a_1+9d\\89=44-4d+9d\\45=5d\\d=9\\\\a_1=44-4\cdot9 = 8\\\\a_{21}=a_1+ 20d=8+20\cdot9=188[/tex]
Can I get help with this
Answer:
The correct option is;
B) -6
Step-by-step explanation:
The given parameters are;
The line of symmetry of f(x) = The line of the reflection of g(x) over the y-axis
f(x) = 3·x² + b·x + c
From the given graph of g(x), we have;
The vertex point of g(x) = (-1, 8)
The line of symmetry is the line x = -1
The image of the reflection of (x, y) over the y-axis is (-x, y)
The image of the vertex of g(x) following a reflection across the y-axis is (1, 8)
Therefore;
The line of symmetry of the image of g(x) following a reflection over the x-axis is the line x = 1
The line (axis) of symmetry of a quadratic function is the line x = -b/(2·a), which is a line that always go through the vertex of the parabola
Where;
a = The coefficient of x²
b = The coefficient of 'x'
For f(x) = 3·x² + b·x + c, a = 3, and b = b
Given that f(x) and the image of g(x) have the same line of symmetry, we have;
The line of symmetry of f(x) is x = 1
Therefore, from the formula for the line of symmetry, we have;
x = -b/(2·a)
x = 1
By substitution, we have;
1 = -b/(2·a)
∴ -2·a = b
Given that a = 3, we get;
-2 × 3 = -6 = b
b = -6
An engineer needs to determine the distance across a river without swimming to the other side. The engineer notices a tree on the other side of the river and suddenly has an idea.
Describe how she will sketch her idea to be able to determine the distance. Make a sketch and support you figure by number use meter as unit.
Answer:
Step-by-step explanation:
The engineer can use a clinometer to measure the angle of elevation of the top of the tree. Let the height of the tree be represented by x, the she could determine the distance across the river, d, by applying the trigonometric function.
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{x}{d}[/tex]
the the distance, d = x ÷ Tan θ
Assume the angle of elevation of the top of the tree is [tex]30^{o}[/tex], and the height of the tree is 10 m, then the distance, d, across the river would be;
d = [tex]\frac{10}{0.5774}[/tex]
= 17.3190
d = 17.32 m
The sketch to the explanation is attached to this answer for more clarification.
The diameter of a circle is 75, find the circumference of the circle. Round your answer to
the nearest hundredth. (Two numbers after the decimal point).
Answer:
C ≈ 236
Step-by-step explanation:
Formula
Using the formulas
C=2πr
d=2r
Solve
Solving for C
C = πd = π· 75 ≈ 235.61945
C ≈ 235.62
To the nearest hundredth.
C ≈ 236
Jamal will cut a piece of wood that is 3 1/2 feet long into 1/4 foot sections. How many sections will result? plz help
Answer:
14 sections
Step-by-step explanation:
I think I'm correct but if I'm wrong tell me right away I'll try again.
pls help me ill give u candy
Answer:
8.9
Step-by-step explanation:
8^2+ s^2=12^2
64+s^2=144
s^2=80
s=square root of 80
s=8.9
what is the value of x? 6x−1=4x−5
Answer:
x = -2
Step-by-step explanation:
6x - 1 = 4x - 5
Bring like terms together
6x - 4x = 1 - 5
2x = -4
-4 / 2 = -2
What value(s) for n will make this equation true?
Answer:
B
Step-by-step explanation:
It the only one that make sense
What is the volume of the cylinder when the radius is 10 and the height is 15
Answer:
V = π r^2 h = π · 10^2 · 15 ≈ 4712.38898
Solve for x and y by using elimination. 4x - 3y = 12 x + 2y = 14
Answer:
8x + 5y = 14
Step-by-step explanation:
a mug in the shape of a cylinder has a base of with a radius of 4 cm. how many milliliters of liquid does it hold if filled to a height of 9cm?
(1 cm3 holds 1mL)
Answer:
v= 452.2 cm^3 or 452.2 mL
Step-by-step explanation:
v= pi(r)^2h
v=pi(4)^2(9)
v=452.2 cm^3
Complete the problem
5/10 +8/100
Answer:
0.58
Step-by-step explanation:
If a tank leaks 10 mL of fluid each hour, how long will it take to fill up a one-litre jar?
10 hours
1,000 hours
1 hour
100 hours
Answer:
100 hours
Step-by-step explanation:
To find the amount of liters in one hour, you divide 10 by 1000, which gives 0.01 liters each hour. From here, the 1 is in the hundredths place, so if you multiply by 100 hours, if will be at 1 liter.
Bryce took a quiz that consisted of true-or-false questions and multiple-choice questions. The true-or-false questions were worth 1 point each, and the multiple-choice questions were worth 2 points each. Bryce only knows that he answered 8 questions correctly and earned a total of 14 points. To determine the number of each type of question that he answered correctly, he wrote the system of linear equations x + y = 8 and x + 2 y = 14.
Which ordered pair is a solution to this system of linear equations, and what does the ordered pair represent?
(0, 8); Bryce answered 0 true-or-false questions correctly and 8 multiple-choice questions correctly.
(2, 6); Bryce answered 2 true-or-false questions correctly and 6 multiple-choice questions correctly.
(6, 2); Bryce answered 6 true-or-false questions correctly and 2 multiple-choice questions correctly.
(8, 0); Bryce answered 8 true-or-false questions correctly and 0 multiple-choice questions correctly.
Step-by-step explanation:
he answered seven of the multiple choice questions and answered one of the true or false questions that is;
7×2+1=14
The ordered pair is a solution is (2, 6).
Bryce answered 2 true-or-false questions correctly and 6 multiple-choice questions correctly.
The correct option is (B).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x + 2y = 14............(1)
x + y = 8
x = 8 - y.................(2)
Solving equation (1) and (2), we get
8 - y + 2y = 14
y + 8 = 14
y = 14 - 8
y = 6
and, x + y = 8
x + 6 = 8
x = 8 - 6
x = 2
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Ethan has partially filled the prism with 8 unit cubes.
A rectangular prism with length, height, and width of 3.
How many more cubes does he need to fill the prism completely?
10
15
19
21
Answer: is it c?
Step-by-step explanation:
Answer:
I think C is your answer.
Step-by-step explanation:
Lance's math quz has eight true faise questions. How many different choices for giving answers to the eight
questions are possible?
Answer:
2^8 = 256 choices
Step-by-step explanation:
Using the exponential growth function for the U. S. population from 1970 through 2003:
A = 205.1e^0.011t
with the U.S. population being 205.1 million in 1970,
when would the U. S. population reach 350 million?
A.
2028
B.
2048
C.
2018
D.
2038
Answer:
Step-by-step explanation:
Using the exponential growth function for the U. S. population from 1970 through 2003:
A = 205.1e^0.011t
with the U.S. population being 205.1 million in 1970, when would the U. S. population reach 350 million?
A.
2028
B.
2048
C.
2018
D.
2038
We have the expression
A = 205.1e^0.011t
We are asked to find when would the U. S. population reach 350 million
A = 350
350 = 205.1e^0.011t
We divide both sides by 205.1
Divide both sides by 205.1
350/205.1 = 205.1e^0.011t/205.1
1.7064846416 = e^0.011t
We take the log of both sides
log 1.7064846416 = log e^0.011t
log 1.7064846416 = t log 0.011
t = log 1.7064846416/ log 0.011
t = 0.1185057826
Colten bought a leash for his dog that was 1 meter 40 cm long. How long was the leash in millimeters?
Answer:
400 millimeters is the answer.
Answer:
1400 millimeters.
Step-by-step explanation:
Find the number of ways you can arrange (a) all of the letters and (b) two is the letters in the word ROCK. a. The number of ways you can arrange all of the letters in the word is __. b. The number of ways you can arrange two of the letters in the word is __.
Answer:
a) 24
b) 12
Step-by-step explanation:
a) For the 4 letters of the word ROCK
Selecting any first letter, we have 4 options
for the second, we have 3 options
for the third we have 2 options
for the fourth, we have only one option
So the number of ways will be ;
4 * 3 * 2 * 1 = 24 ways
b) 2 out of 4
For the first letter, we have 4 options, for the second, we have 3 options
so the number of options is 4 * 3 = 12 options
Solve the system of equations 3x = 84 - 2y 9x = 8y - 24
Answer:
[tex]3x = 84 - 2y - - - (i) \\ 9x = 8y - 24 - - - - (ii) \\ from \: (ii) \\ 3(3x) = 8y - 24 \\ but \: from \: (i) \: \: 3x = 84 - 2y \\ hence \: put \: (i) \: in \: (ii) \\ 3(84 - 2y) = 8y - 24 \\ 252 - 6y = 8y - 24 \\ 276 = 14y \\ y = \frac{138}{7} \\ x = \frac{104}{7} [/tex]
Jonathan has 25 coins in his pockets and they are all either nickels or quarters. If he has a total of
$3.25, how many of the coins are nickels and how many are quarters. Give me two equations and the answer in nickels and quarters
Answer:
The answer is 10 quarters and 15 nickels
Step-by-step explanation:
Lets say x equals the number of quarters and y quals the number of nickels. Since there is a total of 25 coins that means that x+y=25. But, the quarter costs 0.25, and the nickel costs 0.05. That means that we have to multiply the number of each coin with their cost. Which leads us to: (x*0.25)+(y*0.05)=3.25. By solving these two equations you'll see that x=10 and y=15.
Pierre was plotting the quadratic function f(x) = - x ^ 2 + 8x for an exit ticket His work is shown below .
Answer:
(a) The table
[tex]\begin{array}{cc}x & {f(x)} & {0} & {0} & {1} & {7}& {2} & {12} & {3} & {15} & {4} & {16} & {5} &{15} & {6} & {12} & {7} &{7} & {8} & {0}\ \end{array}[/tex]
(b) See attachment for graph
(c) He swapped the values of the x and y coordinates for one another
Step-by-step explanation:
Given
See attachment for complete question
Solving (a): Complete the table
[tex]f(x) = -x^2 + 8x[/tex]
[tex]x = 0[/tex]: [tex]f(0) = -0^2 + 8*0 = 0 + 0 = 0[/tex]
[tex]x = 1[/tex]: [tex]f(1) = -1^2 + 8*1 = -1 + 9 = 7[/tex]
[tex]x = 2[/tex]: [tex]f(2) = -2^2 + 8 *2 = -4 + 16 = 12[/tex]
[tex]x = 3[/tex]: [tex]f(3) = -3^2 + 8 *3 = -9 + 24 = 15[/tex]
[tex]x = 4[/tex]: [tex]f(4) = -4^2 + 8 *4 = -16 + 32 = 16[/tex]
[tex]x = 5[/tex]: [tex]f(5) = -5^2 + 8 *5 = -25 + 40 = 15[/tex]
[tex]x = 6[/tex]: [tex]f(6) = -6^2 + 8 *6 = -36 + 48 = 12[/tex]
[tex]x= 7[/tex]: [tex]f(7) = -7^2 + 8 *7 = -49 + 56 = 7[/tex]
[tex]x = 8[/tex]: [tex]f(8) = -8^2 + 8 *8 = -64 + 64 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cc}x & {f(x)} & {0} & {0} & {1} & {7}& {2} & {12} & {3} & {15} & {4} & {16} & {5} &{15} & {6} & {12} & {7} &{7} & {8} & {0}\ \end{array}[/tex]
Solving (b): Plot the graph
See attachment 2 for graph
Solving (c): Why he was marked as incorrect
By comparing the new attached graph (in b) and the graph of the original question, one will notice that the values of the x and y coordinates are switched.
This is why he was marked as incorrect.
PI QUESTION PLEASE HELP DUE TODAY HURRY DON'T GO PAST AND ONLY ANSWER IF YOU KNOW THE ANSWER!!!!! CORRECT ANSWER = BRAINLIEST!!!!!!!!!
Answer:
Area of Shaded Region; 6.25π square inches
Good luck <3
Answer: 19.625in
Step-by-step explanation:
Patrick rosses a penny and a number cube, with faces numbered 1 through 6, at the
same time,
A. Are the events dependent or independent Explain your thinking,
The events are independent because the outcome of one does not affect the outcome of the other one.
Which are examples of unit rates? Check all that apply.
1. $45 per ticket
2. 5 shows every 3 weeks
3. 30 seats for every row
4. $100 for 5 tickets
Which image below is an acute triangle?
Carrie often asks friends to play Among Us at lunch. Of the 5 games they play, Carrie wins 2 games. Consider this data:
If she keeps playing in 35 games, how many games should you expect Carrie not to win
Answer:
She'll lose 21 games out of 35. But she'll win 14 lol
All I did was see how many fives go into 35, and that's 7. So 3 (how many games she loses per 5 games) times 7 is 21.
Calculate the surface area of the figure:
54ft
198ft
21ft
108ft
Answer:
108
Step-by-step explanation:
malayalam note class 8 chapter 1
Answer:
pt2 hope it helps
Step-by-step explanation:
Hiii, I would love it if you can help me with this! I tried my best but it's really hard and I don't understand this.
Answer:
A
Step-by-step explanation:
82 inches! 6 feet is 72 inches. 12*6
A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. How many customers are on payment plan B? customers How many of the customers on plan B text? customers What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
Answer:
a=23 b=12 c=12/23
Step-by-step explanation:
I just did it on EDG, got it wrong so i could give you the answer XD
The likelihood that a randomly chosen consumer on plan B would text on the phone the most frequently is 13/23.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
According to the given data,
Number of customers on plan B = 13 + 10 = 23
Number of customers on plan B who text = 13
P(text|plan B) = P(text and plan B) / P(plan B),
where P(text and plan B) is the probability of a customer being on plan B and texting, and P(plan B) is the probability of a customer being on plan B, can be used to calculate the likelihood that a randomly chosen customer on plan B will text the most.
So,
P(text|plan B) = 13/23
Therefore, the probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
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