Answer:
y = -2(x + 1)
Step-by-step explanation:
x-intercept of -1 means y=0 when x=-1, so you have your (x₁, y₁) value of (-1, 0).
Slope is -2 so m=-2.
Plug into point-slope formula:
y = m(x - x₁) + y₁
y = (-2)(x - (-1)) + (0)
y = -2(x + 1)
help pls will give brainliest
Answer:
9 * 10^7.
Step-by-step explanation:
(3 * 10^5) * (3 * 10^2)
= 3 * 3 * 10^5 * 10^2
= 9 * 10^(5+2)
= 9 * 10^7.
Three numbers form a geometric progression. If the second term is increased by 2, then the progression will become arithmetic and if, after this, the last term is increased by 9, then the progression will again become geometric. Find these three numbers.
The three numbers forming the geometric progression are [tex]4/7, 32/7,[/tex] and [tex]81/7.[/tex] The second term is increased by [tex]2[/tex], then the progression will become arithmetic and if, after this, the last term is increased by [tex]9[/tex], then the progression will again become geometric.
Let's denote the three numbers forming the geometric progression as [tex]a[/tex], [tex]ar[/tex], and [tex]ar^2}[/tex], where a is the first term and [tex]r[/tex] is the common ratio.
If the second term is increased by [tex]2[/tex], then the progression becomes arithmetic. This means:
[tex]ar+2=2ar-a[/tex]
[tex]2=ar-a \\2=a(r-1)[/tex]
If after this, the last term is increased by [tex]9[/tex], then the progression becomes geometric again. This means: [tex]ar^2} +9=(ar+2)r[/tex]
[tex]ar^2} +9=ar^2} +2r \\9=2r \\r=9/2[/tex]
Now, we have found the value of [tex]r[/tex], which is the common ratio. Let's substitute [tex]r=29[/tex] into the equation [tex]2=a(r-1)[/tex] to find the value of a:
[tex]2=a((9/2)-1) \\2=a(9-2/2) \\2=a(7/2) \\a=4/7[/tex]
So, the first term a is [tex]4/7.[/tex]
Now, let's find the second term by substituting [tex]a=4/7[/tex] into the equation [tex]ar+2=2ar-a:\\4/7.9/2+2=2.4/7.9/2-4/7 \\18/7+2=36/7-4/7 \\32/7=32/7[/tex]
This equation is satisfied, so the second term is [tex]32/7.[/tex]
Finally, let's find the third term by multiplying the first term by the common ratio:
[tex]4/7.(9/2)2=7.4/4.1/8=81/7[/tex]
So, the three numbers forming the geometric progression are [tex]4/7, 32/7,[/tex]and [tex]81/7.[/tex]
We used the properties of geometric and arithmetic progressions to set up and solve equations to find the three numbers. First, we found the common ratio r by solving the equations derived from the given conditions. Then, we found the first term a and used it to find the second term. Finally, we found the third term by multiplying the first term by the common ratio squared.
COMPLETE QUESTION:
Three numbers form a geometric progression. If the second term is increased by [tex]2[/tex], then the progression will become arithmetic and if, after this, the last term is increased by [tex]9[/tex], then the progression will again become geometric. Find these three numbers.
The three numbers are 4, 18, and 81.
Let the three numbers forming the geometric progression be [tex]\( a, ar, \)[/tex] and [tex]\( ar^2 \)[/tex], where [tex]\( r \)[/tex] is the common ratio.
Given that increasing the second term by 2 makes it an arithmetic progression, we have:
[tex]\[ar + 2 = a + 2d\][/tex]
where d is the common difference in the arithmetic progression.
Similarly, after increasing the last term by 9, the progression becomes geometric again, so:
[tex]\[ar^2 + 9 = (ar + 2)r\][/tex]
From the first equation, [tex]\( d = (ar - a)/2 \)[/tex], and substituting this into the second equation, we get:
[tex]\[ar^2 + 9 = (ar + 2)r\][/tex]
[tex]\[ar^2 + 9 = ar^2 + 2r\][/tex]
[tex]\[9 = 2r\][/tex]
[tex]\[r = \frac{9}{2}\][/tex]
Substituting [tex]\( r = \frac{9}{2} \)[/tex] into the first equation, we find [tex]\( d = \frac{a}{2} \)[/tex].
Thus, [tex]\( a + 2 = a + \frac{a}{2} \)[/tex], and solving for [tex]\( a \)[/tex], we find [tex]\( a = 4 \)[/tex].
Then, using [tex]\( r = \frac{9}{2} \)[/tex], we find [tex]\( ar = 18 \) and \( ar^2 = 81 \)[/tex].
Therefore, the three numbers are 4, 18, and 81.
What is a equation of a line that passes threw the points (3,1) and (-2,4)
Answer:
y-1=-3/5(x-3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-1)/(-2-3)
m=3/-5
m=-3/5
y-y1=m(x-x1)
y-1=-3/5(x-3)
Mai biked 7 and 1/4 miles today, and Noah biked 3 5/8 miles. How many times the length of Noah's bike ride was Mai's bike ride?
Answer:
The distance cover by Mai's bike is 2 time the distance cover by Noah's bike
Step-by-step explanation:
Given as :
The distance cover by Mai's bike = [tex]d_1[/tex] = 7 [tex]\dfrac{1}{4}[/tex] miles
I.e [tex]d_1[/tex] = [tex]\dfrac{28+1}{4}[/tex] miles
Or, [tex]d_1[/tex] = [tex]\dfrac{29}{4}[/tex] miles
The distance cover by Noah's bike = [tex]d_2[/tex] = 3 [tex]\dfrac{5}{8}[/tex] miles
I.e [tex]d_2[/tex] = [tex]\dfrac{24 + 5}{8}[/tex] miles
Or, [tex]d_2[/tex] = [tex]\dfrac{29}{8}[/tex] miles
let the number of times that Noah's bike ride was Mai's bike ride = n
So, The distance cover by Mai's bike = n × The distance cover by Noah's bike
Or, [tex]d_[/tex] = n × [tex]d_[/tex]
Or, [tex]\dfrac{29}{4}[/tex] miles = n × [tex]\dfrac{29}{8}[/tex] miles
Or, n = [tex]\frac{\frac{29}{4}}{\frac{29}{8}}[/tex]
∴ n = [tex]\dfrac{8}{4}[/tex]
I.e n = 2
Hence The distance cover by Mai's bike is 2 time the distance cover by Noah's bike . Answer
why would 3/2 be a rational number?
Explanation: All fractions positive or negative are rational numbers so 3/2 must be rational. Another way to think about rational numbers is that if you can turn the number into a fraction, it's rational. Since 3/2 is already in fraction form, it's a rational number.
domain of the function f(x)=3x3 is 2,5 what is the function range?
Domain of the function f(x)=3x^3 is 2,5 what is the function range?
Answer:
The range of given function is {24, 375}
Solution:
Domain of the function is possible input of the function that is "x" and range of the function is possible output of the function that is f(x)
So we can substitute the given domain values of "x" in f(x) and find the range of function
As per the given question:
The domain of the function [tex]f(x) = 3x^3[/tex] is, [2, 5]
We have to find the range of the function
At x = 2:Substitute x = 2 in f(x)
[tex]f(x) = 3x^3[/tex]
[tex]f(2) = 3 (2)^3 = 3(8) = 24[/tex]
At x = 5:Substitute x = 5 in f(x)
[tex]f(5) = 3(5)^3 = 3 \times 125 = 375[/tex]
Therefore range of given function is {24, 375}
The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x. Using the relationship between interior and exterior angles, find the value of x.
The value of x is 30
Solution:
Given that measure of exterior angle of regular polygon is 2x
The measure of interior angle is 4x
To find: value of x
The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)
measure of exterior angle + measure of interior angle = 180
2x + 4x = 180
6x = 180
x = 30
Finding the measure of an exterior angle
measure of exterior angle = 2x = 2(30) = 60 degrees
Finding the measure of interior angle
measure of interior angle = 4x = 4(30) = 120 degrees
Find the equation of the line through the point (6, 9) that has a slope of 4?
A) y = 6x + 4
B) y = 3x + 121
C) y = 4x + 15
D) y = 4x - 15
Answer:
D Y=4x-15
Step-by-step explanation:y=Mx+b
6x-2y=10 for y when x=2
Answer: 1
Step-by-step explanation:
6 times 2 minus 2y = 10
first 6x2=12
12-2y=10
minus 12 from each side =0
so now you have;
-2y= -2
divide & you get one!
<33333
8(19-17) number- number
Answer:
16
Step-by-step explanation:
8(19-17)=8(2)=16
A chicken farm produces ideally 600,000 eggs per day. But this total can vary by as many as 5,000 eggs. What is the maximum and minimum expected production at the farm?
Answer:
max.600,000
min.595,000
Step-by-step explanation:
Solve for X. Thanks for the help!!!!
Check the picture below.
what is 9 out of 100 as a percent ?
Answer:
9%
Step-by-step explanation:
9/100 = 0.09
To convert to a percent, multiply by 100 and add a percent sign:
0.09 * 100 = 9%
Answer: 9%
Step-by-step explanation:
I Looked it up online.
A construction crew has just finished building a road. The road is 10 kilometers long. If the crew worked for 4 2/3 days, how many kilometers of road did they build each day? (Assume they built the same amount each day.)
2.14 kilometers of road is built each day
Solution:
Given that road is 10 kilometers long
The crew worked for [tex]4\frac{2}{3}[/tex] days
To find: Kilometers of road build each day
Assume they built the same amount each day
Length of road = 10 km
number of days worked = [tex]4\frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3}[/tex]
Kilometers of road build each day is given as:
Kilometers of road build each day = total length of road divided by number of days the crew worked
[tex]\rightarrow \frac{10}{\frac{14}{3}}=\frac{10}{1} \times \frac{3}{14}=2.14[/tex]
Thus 2.14 kilometers of road is built each day
(SAT Prep) Find the value of x in each of the following exercises:
Answer:
[tex]x=115^o[/tex]
Step-by-step explanation:
Angles Inside a Polygon
A polygon of n sides must have the sum of its internal angles
[tex]S=180^o(n-2)[/tex]
The polygon shown in the figure has n=5 sides, so the sum of its internal angles is
[tex]S=180^o(5-2)=540^o[/tex]
The construction of the internal angles of the polygon is shown in the image below. The sum of them is
[tex]50+180-x+180-x+360-x+x=540[/tex]
Reducing
[tex]-2x+770=540[/tex]
Solving
[tex]\displaystyle x=\frac{770-540}{2}[/tex]
[tex]\boxed{x=115^o}[/tex]
Answer:
x is 115 degrees
Step-by-step explanation:
shondra wants to cut a cloth into 10 squares strips. how wide would each strip get?
To find the width of each strip, divide the total width of the cloth by the number of strips required.
Explanation:To find the width of each strip, we need to divide the total width of the cloth by the number of strips required. Let's assume the width of the cloth is W. So, each strip would get a width of W/10.
Please i want to calculate summation of 0.30+0.60+0.90............+3.0
what is the formulae to get it
Answer:
16.5.
Step-by-step explanation:
This is an arithmetic series because the increase is a constant 0.30.
Sum of n terms = (n/2)[a + l) where n = no.of terms a = first term , l = last term.
There are 3/ 0.3 = 10 terms so
Sum = (10/2) (0.3 + 3.0)
= 5 * 3.3
= 16.5.
Emily participates in a trivia quiz show. In each round, 20 points are awarded for a correct answer and 10 points are deducted for an incorrect answer. Emily answered 7 questions correctly and 8 incorrectly in the first round. What was her first-round score? Emily answered 4 questions correctly and 11 incorrectly in the second round. What was her score in the second round? The final score is the average of the two rounds, what is Emily's final score?
Answer:
1. Emily scored 60 points in the first round
2. Emily scored minus 30 points in the second round
3. Emily's final score is 15 points.
Step-by-step explanation:
1. Let's review all the information given to us to answer the questions correctly:
Points awarded for a correct answer = 20
Points deducted for a incorrect answer = 10
2. Let's calculate the score of Emily in the first round:
Score = 7 * 20 - 8 * 10
Score = 140 - 80
Score = 60
Emily scored 60 points in the first round
3. Let's calculate the score of Emily in the second round:
Score = 4 * 20 - 11 * 10
Score = 80 - 110
Score = - 30
Emily scored minus 30 points in the second round
4. Let's calculate the final score of Emily:
Final score = (Score 1st round + Score 2nd round)/2
Final score = (60 + - 30)/2
Final score = (60 - 30)/2 = 30/2 = 15
Emily's final score is 15 points.
What is -4x+y=-8 equal to
Answer:
y=4x+8
Step-by-step explanation:
I assume you want this rewritten in slope intercept form. That means we need to isolate the y.
-4x+y=-8
Add 4x to both sides
y=-8+4x
Now let's rewrite it in slope intercept form. Recall slope intercept form is y=mx+b. That means our 'b' (8) must be on the end of the equation.
y=4x+8
Out of 1,000 tickets in a raffle, one ticket will win a $710 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
Answer:
The probability of winning = 0.001 and hence the expected payoff = $0.
Step-by-step explanation:
There is a lottery contest and there are 1000 entries.
Only one will win and will get a prize of $710. All others would be given nothing.
We have to find the probability of the person winning.
Probability = [tex]\frac{number of favorable events}{total number of events}[/tex]
Number of favorable events = 1
Total number = 1000
So probability of winning the payoff = [tex]\frac{1}{1000}[/tex] = 0.001
Hence the expected payoff = $0
if r equals 35 and s equals to 5t t=2u and u≠0 what is the value of rst/u³
2. before last nights game a basketball player has scored an average ( arithmetic mean) of 20 points per game . she scored 25 points in last nights game raising her average go 21 points per game. how many games did she play before last night's game
@3 (b)4(c)5(d)6(e)7
Question:
before last nights game a basketball player has scored an average ( arithmetic mean) of 20 points per game . she scored 25 points in last nights game raising her average go 21 points per game. how many games did she play before last night's game
Answer:
She played 4 games before last night's game
Step-by-step explanation:
Given:
Average of last night basketball games = 20
Points scored in last night game = 25
Rise in average after last night game = 21
To Find:
The number of games played last night = ?
Solution:
Let the number of games played before last night's game be x
Then
The average of x games =20
That is
[tex]\frac{\text{ Total points scored in x games}}{x}= 20[/tex]
Total points scored in x games = 20x
In last night game she scored 25 points
So now the total score will be = 20x+25 and
the number of games will be x+1
Now the
The average of x+1 games = 21
[tex]\frac{20x+25}{x+1}[/tex] =21
[tex]20x+25 =21 \times (x+1) [/tex]
[tex]20x+25 =21x+ 21[/tex]
[tex]25-21 =21x-20x[/tex]
x=4
Find the Polynomial with roots 3, -2, and 0.
Urgent!!! Help
Answer:
Step-by-step explanation:
Answer:
f(x) = x³ - x² - 6x
Step-by-step explanation:
If a polynomial f(x) has roots x = a and x = b then the factors are
(x - a) and (x - b) and the polynomial is the product of the factors, that is
f(x) = (x - a)(x - b)
Here the roots are x = 3, x = - 2 and x = 0, thus
(x - 3), (x - (- 2)) and (x - 0) are the factors, that is
(x - 3), (x + 2) and x , hence the polynomial is
f(x) = x(x - 3)(x + 2) ← expand the pair of factors
= x(x² - x - 6) ← distribute parenthesis by x
= x³ - x² - 6x
5x+8=23 what is the variable in this equation
Answer: The variable is 3.
Step-by-step explanation: 5x3=15. 15+8=23
Please Mark Me Braineilest
What are the steps for solving, 7,542÷3
Answer:
2514
Step-by-step explanation:
Do the long division and you'll find the answer.
15 points. Would the rules for interference work the same for light waves as they do for sound waves? Explain why or why not.
Answer:
Yes, because when waves are at the same place at the same time, the amplitudes of the waves simply add together and this is really all we need to know!
Step-by-step explanation:
The sum of two waves can be less than either wave, alone, and can even be zero. This is called destructive interference.
If we place the waves side-by-side, point them in the same direction and play the same frequency, we will have constructive interference.
Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6. The equation is y− = (x− )
Answer:
y + 9 = 6(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 6 and (a, b) = (4, - 9), thus
y - (- 9) = 6(x - 4), that is
y + 9 = 6(x - 4)
the student council orders 12 sandwhiches for the school dance. each sandwich is 6 feet long cut into sections that are 4 inches long. how many small sandwiches will they have?
1ft = 12inch
The school council will have 216 small sandwiches.
Step-by-step explanation:
Sandwiches ordered = 12
Length of one sandwich = 6 feet
1 foot = 12 inch
6 feet = 12*6 = 72 inches
Length of one sandwich in inches = 72 inches
As one small sandwich is 4 inches,
Number of small sandwiches in one sandwich = [tex]\frac{72}{4}=18[/tex]
One sandwich = 18 small sandwiches
12 sandwiches = 18*12 = 216 small sandwiches
The school council will have 216 small sandwiches.
Keywords: multiplication, division
Learn more about multiplication at:
brainly.com/question/10710410brainly.com/question/10717746#LearnwithBrainly
What is the mean of: 3.7,5, 9.2,4,6.1,5,2.6, 4.5.2,5?
A. 4.88
B. 4.5
C. 4
D. 6.6
The mean of 3.7,5, 9.2,4,6.1,5,2.6, 4,5.2,5 is 4.88.
Explanation:Mean is referred in mathematics to as average of the mentioned numbers. Average can be virtually imagined as a center position giving every number equal weight. Average can be calculated by diving the sum of all the numbers by count of total numbers.
For example, 2, and 4 will have average of 3. Average of 2,3,4 will be also 3. This is because [tex]\frac{(2+4)}{2} = 3, and\ also\ \frac{(2+3+4)}{3} = 3[/tex].
So considering the above Question, count of all the above numbers is 10.
Sum = 3.7 + 5 + 9.2 + 4 + 6.1 + 5 + 2.6 + 4 + 5.2 + 5 = 488
Mean = Average = [tex]\frac{Sum}{Count}[/tex]
Mean = [tex]\frac{488}{10}[/tex] = 4.88
Answer:
its 4.88
Step-by-step explanation:
it was on my test
find the exact values of sin 2θ and cos 2θ for sin θ= 5/11 on the interval 0° ≤ θ ≤ 90°
pls help asap!
Answer:
Below in bold.
Step-by-step explanation:
sin ^2x + cos ^2 x = 1, so
cos^2x = 1 - (5/11)^2 = 96/121
cos x = √96/11
= 4√6/11.
sin 2x = 2 sinx cosx = 2 * 5/11 * 4√6/11.
= 40√6/121.
cos2x = 2cos^2 x - 1
= 2 * 96/121 - 1
= 192/121 - 121/121
= 71/121.
A study will investigate the effectiveness of a new early reading program on
Prekindergarten students' reading abilities. The samples (n = 30 and
n =40) included in the study are taught by two preschool teachers.
Which of the
following are possible limitations of the study? Select all that apply.
A. The sample size is too small.
B. The teachers may differ in number of years teaching.
C. The teachers may differ in early childhood experience.
D. The teachers may differ in number of years teaching reading.
Answer:
B, C, D
Step-by-step explanation:
The information given about the teachers is limited to the fact they teach preschool.
B and D. If a teacher has more experience teaching, they are probably better at teaching. Even if the subject is not reading, they gain transferable teaching skills with experience.
C. Although both teachers teach preschool, one may have many more years of experience or other qualifications, which will likely help them to teach better in generally.
A. The samples 30 and 40 students in a typical class are enough to show different students' various learning styles and strengths. The sample size is big enough.