Explanation:
The notation [tex]a_1 = 10[/tex] says that the first term is 10.
The notation [tex]a_n = a_{n-1}+3[/tex] is the recursive rule that says "to find the nth term, we add 3 to the previous term". So we add 3 to each term to get the next one.
first = 10second = first+3 = 10+3 = 13third = second+3 = 13+3 = 16fourth = third + 3 = 16+3 = 19This sequence is arithmetic due to the common difference d = 3.
Answer:
Step-by-step explanation:
a1=10
a_{n}=a_{n-1}+3
n=2
[tex]a_{2}=a_{1}+3=10+3=13\\n=3\\a_{3}=a_{2}+3=13+3=16\\n=4\\a_{4}=a_{3}+3=16+3=19\\first~four~terms~are\\10,13,16,19[/tex]
BRAINLIEST Which equation could be solved using this application of the quadratic formula?
A.
x2 + 1 = 2x − 3
B.
x2 – 2x − 1 = 3
C.
x2 + 2x − 1 = 3
D.
x2 + 2x − 1 = -3
The quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.
What is the quadratic formula?A standard quadratic equation of the form ax² + bx + c = 0, can be solved using the quadratic formula, which is given as:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
How to solve the question?In the question, we are asked for the quadratic equation, which could be solved using this application of the quadratic formula:
[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]
To find the quadratic equation for which we use the quadratic formula
[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]
we compare this equation with the standard quadratic formula,
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
to get a = 1, b = 2, and c = -4, to get the standard quadratic equation, ax² + bx + c = 0, as (1)x² + (2)x + (-4) = 0, or x² + 2x - 4 = 0.
Now, we convert the given options in the standard form to check for the correct choice:
A. x² + 1 = 2x - 3 ⇒ x² - 2x + 4 = 0, which is not the correct choice.B . x² - 2x - 1 = 3 ⇒ x² - 2x - 4 = 0, which is not the correct choice.C. x² + 2x - 1 = 3 ⇒ x² + 2x - 4 = 0, which is the correct choice.D. x² + 2x - 1 = -3 ⇒ x² + 2x + 2 = 0, which is not the correct choice.Thus, the quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.
Learn more about the quadratic formula at
https://brainly.com/question/1214333
#SPJ2
find the distance of gap d
Answer:
[tex]\displaystyle d \approx 15.8768[/tex]
Step-by-step explanation:
We want to find the distance of d or AB.
From the right triangle with a 35° angle, we know that:
[tex]\displaystyle \tan 35^\circ = \frac{50}{PB}[/tex]
And from the right triangle with a 42° angle, we know that:
[tex]\displaystyle \tan 42^\circ = \frac{50}{PA}[/tex]
AB is PA subtracted from PB. Thus:
[tex]\displaystyle d = AB = PB - PA[/tex]
From the first two equations, solve for PB and PA:
[tex]\displaystyle \frac{1}{\tan 35^\circ } = \frac{PB}{50} \Rightarrow PB = \frac{50}{\tan 35^\circ}[/tex]
And:
[tex]\displaystyle \frac{1}{\tan 42^\circ } = \frac{PA}{50} \Rightarrow PA = \frac{50}{\tan 42^\circ}[/tex]
Therefore:
[tex]\displaystyle d = AB = \frac{50}{\tan 35^\circ} - \frac{50}{\tan 42^\circ}[/tex]
Using a calculator:
[tex]\displaystyle d= AB \approx 15.8768[/tex]
The question is "find the lowest common multiple of 4 and 6"
with step by step explaination
Answer:
12
Step-by-step explanation:
4s multiples:
4,8,12,16,20,24
6s multiples:
6,12,18,24,30,36
lowest number that is a common multiple between both 4 and 6:
12
Answer: 2
Step-by-step explanation:
[tex]\frac{3}{2x}[/tex]-[tex]\frac{11}{5}[/tex]=[tex]\frac{7}{8}[/tex].[tex]\frac{64}{49}[/tex]
Answer:
x=35/78
Step-by-step explanation:
3/2x-11/5=(7/8)*(64/49)
3/2x-11/5=8/7
3/2x=8/7+11/5
3/2x=117/35
x=(35*3)/(2*117)
x=35/78
Please help me
A person starts walking from home and walks: 6 miles East 6 miles Southeast 3 miles South 5 miles Southwest 2 miles East This person has walked a total of 22Correct miles Find the total displacement vector for this walk: If this person walked straight home, they'd have to walk miles
Answer:
1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)
2) The number of miles they'd have to walk is approximately 13.856 miles
Step-by-step explanation:
1) The distance, direction, and location of the path of the walk the person takes, are listed as follows;
Start location, (0, 0)
6 miles East walk to location, (6, 0)
6 miles Southeast to location, (6 + 3·√2, -3·√2)
3 miles South to location, (6 + 3·√2, -3·√2 - 3)
5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)
2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)
(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)
Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)
The total displacement vector, [tex]\underset{d}{\rightarrow}[/tex] = ((16 + √2)/2, -(6+11·√2)/2)
d = (16 + √2)/2)·i - (6+11·√2)/2)·j
2) If the person walked straight home, the number of miles they'd have to walk, [tex]\left | \underset{d}{\rightarrow} \right |[/tex], is given as follows;
[tex]\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }[/tex]
Therefore;
If the person walked straight home, the number of miles they'd have to walk [tex]\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles[/tex]
Which pair of polygons is congruent?
Answer:
C
Step-by-step explanation:
Polygon 3 and 5 are congruent cause they have the same length of side
Rectangle ABCD is similar to rectangle JKLM. AB = 12, BC = 8, CD = 12, DA = 8, and JK = 15. What is the scale factor from JKLM to ABCD? Reduce all answers.
Answer:
4/5 or 0.8
Step-by-step explanation:
this problem description is not very precise. it leaves out the definition what corners or sides of JKLM correspond to corners and sides of ABCD.
I assume J and K correlate to A and B, and JK is a long side of JKLM.
so, we are going from JKLM to ABCD.
that means we are going from larger to smaller (as JK = 15 and therefore larger than AB = 12).
what is the scale factor to go from 15 to 12 ?
15 × x = 12
x = 12/15 = 4/5 or 0.8
For what values of k does the equation (2k + 1)x^2 + 2x = 10x – 6 have two
real and equal roots?
The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]
In this question, we use the concept of the solution of a quadratic equation to solve it, considering that a quadratic equation in the format:
[tex]ax^2 + bx + c = 0[/tex]
has two equal solutions if [tex]\Delta = b^2 - 4ac[/tex] is 0.
------------------------------------
In this question:
The equation is:
[tex](2k+1)x^2 + 2x = 10x - 6[/tex]
Placing in the correct format:
[tex](2k+1)x^2 + 2x - 10x + 6 = 0[/tex]
[tex](2k+1)x^2 - 8x + 6 = 0[/tex]
Thus, the coefficients are: [tex]a = 2k + 1, b = -8, c = 6[/tex]
------------------------------------
Delta:
We want it to be positive, so:
[tex]\Delta = b^2 - 4ac[/tex]
[tex]\Delta = 0[/tex]
[tex]b^2 - 4ac = 0[/tex]
[tex](-8)^2 - 4(2k+1)(6) = 0[/tex]
[tex]64 - 48k - 24 = 0[/tex]
[tex]-48k + 40 = 0[/tex]
[tex]-48k = -40[/tex]
[tex]48k = 40[/tex]
[tex]k = \frac{40}{48}[/tex]
[tex]k = \frac{5}{6}[/tex]
The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]
A similar question is found at https://brainly.com/question/12144265
If a translation of (x,y) (x+6,y-10) is applied to figure ABCD, what are the coordinates of D?
Image of figure ABCD is missing and so i have attached it.
Answer:
D_new = (-1, - 12)
Step-by-step explanation:
From the figure attached, the current coordinates of D are; (-5, -2)
Now, we are told the figure undergoes a translation of (x,y) (x+6,y-10)
Thus, this means we add 6 to the x value and subtract 10 from the y-value.
Thus, new coordinate of D is;
> (-5 + 6, -2 - 10)
> (-1, - 12)
Answer:
1, -12
Step-by-step explanation:
D = -5, -2
|
-5 + 6 = 1
|
-10 and -2 is -12
1, -12
did it on edge, got it right.
Two sides of a right triangle measure 5 inches and 6 nches, and the third side measures 61 inches.
The length of the third side is about
inches _ . The perimeter of the triangle is about
inches. __
Answer:
The length of the third side is 7.81 inches and the perimeter of the triangle is about 18.81 inches
Step-by-step explanation:
Evelyn earned a score of 86 on Exam A that had a mean of 71 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Evelyn score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
Answer:
580
Step-by-step explanation:
Assuming that the answer should be in terms of z scores, we can calculate the z score as
z = (observed value - mean)/(standard deviation)
For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is
z = (86-71)/20 = 0.75
Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have
0.75 = (observed score - 550)/40
multiply both sides by 40 to remove a denominator
0.75 * 40 = observed score - 550
add 550 to both sides to isolate the observed score
0.75 * 40 + 550 = observed score = 580
Last year, Mary opened an investment account with $5400. At the end of the year, the amount in the account
had decreased by 6%.
Write an equation of the graph (shown below) in slope intercept form.
Answer:
Step-by-step explanation:
Okay! so first, let's specify the components of a slope intercept form equation.
We got y=mx+b as a general formula, where m is slope and b is the y intercept.
The graph gives us two points on the line at (0, 5) and (-6, 7)
To find slope, we can use this slope equation. I suggest you memorize it-it helps a lot with future problems!
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
Plugging in the points into the equation, we get 2/-6, or -1/3
we really don't need to do much work anymore, since the choices are given. There is only one choice left with -1/3 as slope m, which is D.
The y intercept can be found at wherever the line intersects the y axis. In this line, it crosses 5, which means b=5.
y=mx+b
y=-1/3x+5
Writing equations in standard form:
(1,-6) and (-7,2)
How would I write this in standard form? I already tried but I keep getting x+y=7 and it says it’s wrong so could someone help?
Answer:
[tex]x + y = - 5[/tex]
Step-by-step explanation:
hopefully it is clear and makes sense
:)
what is the value of the smallest of five consecutive integers if the least minus twice the greates equals -3
A. -9
B. -5
C. -3
D. 5
Answer: (b)
Step-by-step explanation:
Given
There are five consecutive integers and the least minus twice the greatest equals to -3
Suppose [tex]x,x+1,x+2,x+3,x+4[/tex] are the five consecutive integers
According to the question
[tex]\Rightarrow x-2(x+4)=-3\\\Rightarrow x-2x-8=-3\\\Rightarrow -x=8-3\\\Rightarrow x=-5[/tex]
option (b) is correct.
here is another question i need help
**URGENT PLEASE HELP**
Find g(x), where g(x) is the translation 2 units right and 13 units down of f(x) = -2x + 5.
Answer:
g(x)=x+9
Step-by-step explanation:
When translating a graph, adding the number of units shifts the graph to the left and subtracting the number of units shifts it to the right. Since you need the graph translated 9 units to the left, you will need to add that many units to x
therefore, g(x)=x+9
Answer:
g(x)=x-8
Step-by-step explanation:
-2+2 = 0, so g(x) = x
5-13 = -8
Use the points slope formula..
Answer:
y = -5/14 -13/7
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
m = (1 - -4)/(-8 - 6)
= (1+4)/(-8-6)
= 5/-14
=-5/14
Point slope form is
y-y1 = m(x-x1)
y - -4 = -5/14(x-6)
y+4 = -5/14(x-6)
We want the equation in slope intercept form y = mx+b
Distribute
y+4 = -5/14x + 15/7
Subtract 4 from each side
y+4 -4= -5/14x + 15/7-4
y = -5/14x +15/7 - 28/7
y = -5/14 -13/7
Find the area of the triangle.
Answer:
B
Step-by-step explanation:
area=1/2×32×6.1=16×6.1=97.6 yd²
Answer:
Choice B. 97.6 yd^2
Step-by-step explanation:
B×W×.5= A
Find the volume of each figure. Round your answers to the nearest tenth, if necessary
Answer:
1.92 m³
hopefully this answer can help you to answer the next question.
Plz help me out with this ;)
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Data should be analyzed using each of the following except:
A. measures of central tendency
B. shape
C. population size
D. spread
Find the missing length the triangles are similar.
Answer:
Step-by-step explanation:
The missing length is 13 because,
Lets say the top triangle is A and the bottom triangle is B.
Triangle A gives us the side GF, and Triangle B gives us the sides TU and ST. Since the triangles are similar(as stated in the problem), we can pair 2 sides GF(A) and TU(B) which is 11:22.(one way I usually figure which sides are similar is by first- matching the hypotenuse, then checking which of the remaining two is longer.. if that made any sense). You can see that their relationship is x2 or /2 (In another word, from A to B is multiplication- ex: 11 * 2 is 22, and from B to A is division- ex 22/2 is 11.) Since the missing number is the hypotenuse of triangle A and you know the Hypotenuse of triangle B all you have to do is divide side TS by 2 to get side SF. So the missing side is 13.
Answer: 13
[tex]\sqrt{\\\frac{9+\sqrt{17} }{2}[/tex]
[tex]\huge\underline\pink{✏ANSWER}[/tex]
Hello and sorry but it's a Gatheted Question Can you fix it Can you?Sorry for answering a nonsense
#BrainliestBunch
What is 3x^2-5x-13=0
Answer:
D. 58
Step-by-step explanation:
Given, 3x+8x+4x=6x+63
⇒15x=6x+63
⇒9x=63
⇒x=7
Then 5x+23=5(7)+23
=35+23
=58
The temperature on a winter was -23 °F. The temerature rise by 5 °F when the sun came up. When the sun set again, the temperature dropped by. 7°F. Write and evaluate an exspression to find the temperature after the sun set.
Answer:
-25
Step-by-step explanation:
First, add 5 to -23 since the temperature is getting hotter.
so -23 +5= -18
Second, minus the answer by 7 since the temperature is now falling down after the sunset.
so -18 -7 = -25
or...
this step can be simplified as:
-23 +5 -7 =. -25
The population of a large U.S. city is 2,707,210. Which of the following best expresses this population?
A 2.7 × 106 C 2.707 × 106
B 2.7 × 107 D 27.07 × 106
Answer:
2.707 * 10^6
i think it is the best expression
The length, breadth and thickness of a brick is 18 cm, 8 cm, and 5 cm respectively. Find the area of the widest part of the brick. Also find the volume of the brick.
Answer:
area = 8 × 18 = 144 cm^2
volume 8×18×5 = 720cm^3
The perimeter of a rectangle is given by the formula P=2w+2l,where w is the width and l is the length.Rearrange the formula for the length ( ).
Answer:
l = (p - 2w)/2
Step-by-step explanation:
A rectangular box contain 782 apples. If there are 23 rows in a box, how many columns are there?
Answer:
34
Step-by-step explanation:
This is because you will have to simply divide 782 by 23.
782 / 23 =
34 :D
