Answer:
1) The slope-intercept and standard forms are [tex]y = -5\cdot x + 1[/tex] and [tex]5\cdot x +y = 1[/tex], respectively.
2) The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x -\frac{9}{2}[/tex]. The standard form of the line is [tex]-5\cdot x +2\cdot y = -9[/tex].
3) The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x + 5[/tex]. The standard form of the line is [tex]-5\cdot x +2\cdot y = 10[/tex].
4) The slope-intercept and standard forms of the family of lines are [tex]y = \frac{2}{7}\cdot x -\frac{c}{7}[/tex] and [tex]2\cdot x -7\cdot y = c[/tex], [tex]\forall \,c \in \mathbb{R}[/tex], respectively.
5) The slope-intercept form of the line is [tex]y = 2\cdot x-7[/tex]. The standard form of the line is [tex]-2\cdot x +y = -7[/tex].
Step-by-step explanation:
From Analytical Geometry we know that the slope-intercept form of the line is represented by:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
In addition, the standard form of the line is represented by the following model:
[tex]a\cdot x + b \cdot y = c[/tex] (2)
Where [tex]a[/tex], [tex]b[/tex] are constant coefficients, dimensionless.
Now we process to resolve each problem:
1) If we know that [tex]m = -5[/tex] and [tex]b = 1[/tex], then we know that the slope-intercept form of the line is:
[tex]y = -5\cdot x + 1[/tex] (3)
And the standard form is found after some algebraic handling:
[tex]5\cdot x +y = 1[/tex] (4)
The slope-intercept and standard forms are [tex]y = -5\cdot x + 1[/tex] and [tex]5\cdot x +y = 1[/tex], respectively.
2) From Geometry we know that a line can be formed by two distinct points on a plane. If we know that [tex](x_{1},y_{1})=(1,-2)[/tex] and [tex](x_{2},y_{2}) = (3,3)[/tex], then we construct the following system of linear equations:
[tex]m+b= -2[/tex] (5)
[tex]3\cdot m +b = 3[/tex] (6)
The solution of the system is:
[tex]m = \frac{5}{2}[/tex], [tex]b = -\frac{9}{2}[/tex]
The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x -\frac{9}{2}[/tex].
And the standard form is found after some algebraic handling:
[tex]-\frac{5}{2}\cdot x +y = -\frac{9}{2}[/tex]
[tex]-5\cdot x +2\cdot y = -9[/tex] (7)
The standard form of the line is [tex]-5\cdot x +2\cdot y = -9[/tex].
3) From Geometry we know that a line can be formed by two distinct points on a plane. If we know that [tex](x_{1},y_{1})=(-2,0)[/tex] and [tex](x_{2},y_{2}) = (0,5)[/tex], then we construct the following system of linear equations:
[tex]-2\cdot m +b = 0[/tex] (8)
[tex]b = 5[/tex] (9)
The solution of the system is:
[tex]m =\frac{5}{2}[/tex], [tex]b = 5[/tex]
The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x + 5[/tex].
And the standard form is found after some algebraic handling:
[tex]-\frac{5}{2}\cdot x+y =5[/tex]
[tex]-5\cdot x +2\cdot y = 10[/tex] (10)
The standard form of the line is [tex]-5\cdot x +2\cdot y = 10[/tex].
4) If we know that [tex]a = 2[/tex] and [tex]b = -7[/tex], then the standard form of the family of lines is:
[tex]2\cdot x -7\cdot y = c[/tex], [tex]\forall \,c \in \mathbb{R}[/tex]
And the standard form is found after some algebraic handling:
[tex]-7\cdot y = -2\cdot x +c[/tex]
[tex]y = \frac{2}{7}\cdot x -\frac{c}{7}[/tex], [tex]\forall \,c\in\mathbb{R}[/tex] (11)
The slope-intercept and standard forms of the family of lines are [tex]y = \frac{2}{7}\cdot x -\frac{c}{7}[/tex] and [tex]2\cdot x -7\cdot y = c[/tex], [tex]\forall \,c \in \mathbb{R}[/tex], respectively.
5) If we know that [tex](x,y) = (3,-1)[/tex] and [tex]m = 2[/tex], then the y-intercept of the line is:
[tex]3\cdot 2 + b = -1[/tex]
[tex]b = -7[/tex]
Then, the slope-intercept form of the line is [tex]y = 2\cdot x-7[/tex].
And the standard form is found after some algebraic handling:
[tex]-2\cdot x +y = -7[/tex] (12)
The standard form of the line is [tex]-2\cdot x +y = -7[/tex].
g(x) = x + 2h (x) = x^2 – 4Find: g(x) • h(x)
See attachment for math work and answer.
4x < 8
And how to graph it?
Answer:
x<2
put a circle (unsahded) on number 2 and a line on all the sides to the left of 2 , like through 1, 0 , -1 ....
Step-by-step explanation:
4x<8
divide by 4
x<2
To plot the point (5, -3) you would move up 5, then left 3.
1. False
2. True
Answer:
False
Step-by-step explanation:
Positive in the X-axis is always to the right and negative is left and in the Y-axis positive is up and negative is down
PLEASE HELP I HAVE 5 MIN TO TURN THIS IN!!!!
There are two gardens, garden A and garden B are shown in the image below.
Determine if statement 1 is true or false and explain why the statement was true or false
Answer:
TrueStep-by-step explanation:
Perimeter of Garden A
P = 2(w + l)P = 2(2x - 3 + 5(2x - 3) = 2(2x - 3 + 10x - 15) = 2(12x - 18) = 24x - 36The statement is TRUE
I’ll give brainliest. Pls help me
Answer:
Interpolation refers to using the data in order to predict data within the dataset. Extrapolation is the use of the data set to predict beyond the data set.
Step-by-step explanation:
Extrapolation and interpolation are both used to estimate hypothetical values for a variable based on other observations. There are a variety of interpolation and extrapolation methods based on the overall trend that is observed in the data.
pls help me 98+29 x=96+33x
Answer:
x=1/2
Step-by-step explanation:
98+29x=96+33x
Step 1: Simplify both sides of the equation.
29x+98=33x+96
Step 2: Subtract 33x from both sides.
29x+98−33x=33x+96−33x
−4x+98=96
Step 3: Subtract 98 from both sides.
−4x+98−98=96−98
−4x=−2
Step 4: Divide both sides by -4.
−4x
−4
=
−2/−4
x=1/2
charges competition fees of $250 plus $75 per week for classes. What is the
total charge for 40 weeks?
Answer:
$3,250
Step-by-step explanation:
You take the initial fee of 250 then add 75x40
250x75(40)=$3250
I need to know 2/7 divided by 6 =
Answer: 1/21
[tex]\frac{2}{7}:6=\frac{2}{7}.\frac{1}{6}=\frac{2}{42}=\frac{1}{21}[/tex]
Step-by-step explanation:
what is the solution to the inequality? 2 3/5
Answer: c b< 3 2/15
The following graph shows the time required to install fencing of different lengths. 1 1 2 2 3 3 4 4 5 5 20 20 40 40 60 60 80 80 100 100Time (hours)Length of fencing (meters) Which statements about the graph are true? Choose all answers that apply:
Answer:
b is the answer
Step-by-step explanation:
4 is hours and 60 m
Answer:
The answer is B
Step-by-step explanation:
"The point shows (4,60) shows that it takes 4 hours to install 60m of fencing"
I did this on khan too
hope this helps :)
Look at picture please !! I really need help thank you !
please help will mark brainliest if right
Answer:
1 & 5
4&8
3& 7
Step-by-step explanation:
Annie needs $30 to buy a coat she has saved $12 and plans to work as a baby siter to earn $6 per hour which inequality shows the minimum number of hours, n, that annie should work as a babysitter to earn enough to buy a coat?
a 12 + 6n ≤ 30, so n ≤ 3
b 12 + 6n ≥ 30, so n ≤ 3
c 6n ≥30 + 12, so n ≥ 7
d 6n ≤30 + 12, so n ≤ 7
Answer:
The answer would be B.
Step-by-step explanation:
This is because the total cost is $30 so it can't be c or d. A shows that Annie can only have at least $30. this means that B is the only option left.
If this answer is wrong, I deeply apoligize. I hope you have a great day.
A researcher wishes to estimate, with % confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within % of the population proportion.
Answer:
The minimum sample size required is 1068.
Step-by-step explanation:
The complete question is:
A researcher wishes to estimate, with 95% confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 3% of the population proportion.
No preliminary estimate is available. Find the minimum sample size needed.
Solution:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
[tex]MOE=0.03\\\text{Confidence level}=95\%[/tex]
Assume that the sample proportion is 50%.
The critical value of z is, 1.96.
Compute the minimum sample size required as follows:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times\sqrt{0.50(1-0.50)}}{0.03}]^{2}\\\\=1067.1111\\\\\approx 1068[/tex]
Thus, the minimum sample size required is 1068.
this 5th question ...please answer
Answer:
Im 47 and i have no idea
Step-by-step explanation:
thanks for 5 points
Please do for me thank you I am
4.) top row: 1, 2, 4, 6, 8, 10
bottom row: 25, 50, 100, 150, 200, 250
5.) top row: 1, 2, 4, 6, 8, 10
bottom row: 50, 100, 200, 300, 400, 500
HELP ME I HAVE TO PASS
What is the value of x in the solution to this system of equations?
3x+5y=94
x=2y−9
A.x = 7
B.x = 13
C.x = -13
D.x = 10
what is the composition f•g if f(x)=4-2x and g(x)=3x^2
Answer: 4-6x^2
Step-by-step explanation:
f•g = f(g(x))
f(g(x)) = 4-2(3x^2) = 4-6x^2
4
A line has slope 3. Through which two points could this line pass?
a. (24, 19), (8, 10)
b. (10,8), (16, 0)
C. (28, 10), (22, 2)
d. (4, 20), (0, 17)
Find the value of x!!!!!
Answer:
96 degrees
Step-by-step explanation:
The 144 degrees is on a straight line, meaning the angle next to it inside the triangle and 144 are supplementary. They add up to 180 degrees.
Coincidentally, the other two angles plus the third, unlabeled angle will add up to 180 degrees as well, meaning that the the 48+x = 144 degrees (according the property of equality, which is if a=b and b=c, then a=c). Solve for x from there:
x = 144-48
x = 96
Answer:
I attached a photo of the answer
I know it’s extremely late! But I seriously need help!!
Kong took
15
%
15%15, percent fewer seconds than Nolan took to complete his multiplication timed test. Kong took
85
8585 seconds.
How many seconds did Nolan take?
Answer:
100
Step-by-step explanation:
=(100x-15x )/100=85
=85x/100=85
=85x=8500
=x=8500/85
=x=100
what odd number is less than 12
Answer:
theirs many 1, 3, 5, 7, or 9.
Step-by-step explanation:
Answer:
1, 3, 5, 7, 9, 11
Step-by-step explanation:
I Hope That This Helps! :)
The function f(x) = 4x + 5 has domain 0sxs 50. What is its range?
The range of the function is
9514 1404 393
Answer:
range: 5 ≤ f(x) ≤ 205
Step-by-step explanation:
You can put the extreme values of x in this linear function to see its range:
f(0) = 4·0 +5 = 5
f(50) = 4·50 +5 = 205
The range is 5 ≤ f(x) ≤ 205.
MARK YOU BRAINLIST PLEASE ANSWER A small airplane flies from Big Lake to Pine City every day, with a 30-minute layover in Summerville. The distance between Big Lake and Summerville is 375 miles, and the distance between Summerville and Pine City is 525 miles. If the airplane flies at an average speed of 200 mph, how long does the whole trip (including any stops) from Big Lake to Pine City take?
Answer:
5 hours
Step-by-step explanation:
Please answer all ASAP (no explanation needed), extra points and will mark brainliest (don’t comment “idk” it’s not helpful :(, u will be reported)
1. After buying some bottle caps for $81.74, Peter has $6.74 left. How much money did Peter have to begin with?
2. Henry has $97.95 and Marilyn has $74.71. How much more does Henry have than Marilyn?
3. Helen has $84.51 and Joseph has $17.93. How much money do they have together?
4. Emily has $27.09 and David has $6.17. How much more does Emily have than David?
5. Cynthia has $74.45 and Amy has $38.44. How much more does Cynthia have than Amy?
6. After buying some Skittles for $71.18, Irene has $17.36 left. How much money did Irene have to begin with?
7. Steven has $98.25 and Joe has $4.97. How much money do they have together?
8. Ralph starts with $74.53 and spends $4.97 on candies. How much money does Ralph have left?
9. Christopher has $26.34 and Beverly has $4.15. How much money do they have together?
10. Eugene gives $2.89 to Sarah. If Eugene started with $56.03, how much money does he have left?
11. Keith has $56.49 and Theresa has $3.43. How much money do they have together?
12. Peter gives $20.85 to Nancy. If Peter started with $84.26, how much money does he have left?
13. Bruce has $67.72 and Charles has $29.62. How much more does Bruce have than Charles?
14. Sandra gives $9.13 to Stephen. If Sandra started with $11.66, how much money does she have left?
15. After buying some marbles for $93.52, Donald has $6.35 left. How much money did Donald have to begin with?
science pls answer I give brainliest
Answer:
b
Step-by-step explanation:
because air is cooler in the mountains so it'll be cold not humid
A cake is removed from an oven. The temperature, in degrees Fahrenheit, of the cake after t minutes can be modeled by the equation, f(x)=70+140e^-0.024t.
What is the temperature of the cake at the moment it is removed from the oven and about how long will it take for the cake to reach a temperature of 80F ? Round your answer to the nearest whole minute.
Thank you (:
9514 1404 393
Answer:
210 °F110 minutesStep-by-step explanation:
A graphing calculator answers the questions easily.
At t=0, f(0) = 210 . . . degrees F
f(t) = 80 at about t=109.96, so it takes about 110 minutes to reach 80 °F.
__\
Working "by hand"
The exponential term is 1 at t=0, so the temperature then is ...
f(0) = 70 +140·1 = 210 . . . degrees F
The temperature of the cake from the oven is 210 °F.
__
The time when the temperature is 80 °F will be ...
80 = 70 +140e^(-.024t)
10 = 140e^(-.024t)
10/140 = e^(-.024t)
ln(1/14) = -0.024t
t = ln(1/14)/-0.024 ≈ 109.9607
t ≈ 110 when f(t) = 80
It takes about 110 minutes for the cake to cool to 80 °F.
I'm not sure what to do about this problem, so please help me out.
Answer:
21
Step-by-step explanation:
Let the three consecutive integers be;
x , x + 1 and x + 2:
The sum of squares of the two smaller numbers:
The two smaller numbers are x and x+ 1
Sum of their squares:
x² + (x+1)²;
x² + x² + 2x + 1 = 2x² + 2x + 1
It is 45 more than the square of the larger number:
Larger number = x + 2
(x+2)² = x² + 4x + 4
45 more;
x² + 4x + 4 + 45 = x² + 4x + 49
Both are equal:
2x² + 2x + 1 = x² + 4x + 49
2x² - x² + 2x - 4x + 1 - 49 = 0
x² - 2x - 48 = 0
x² - 6x + 8x - 48 = 0
x(x - 6) + 8(x - 6) = 0
(x + 8)(x-6) = 0
x + 8 = 0 or x - 6 = 0
x = -8 or x = 6
We choose x = 6 because it makes the solution true as a positive integer
Sum of the three numbers:
x + x + 1 + x + 2 = 6 + 6 + 1 + 6 + 2 = 21
What are all of the factors pairs of 25
Answer:
Step-by-step explanation:
1, 5, 25 are the factor pairs and the multiples are 50.
Factor pairs of 25 :
1 , 5, 25
Given ,
Factors of 25 .
Now,
Factor is a number that divides the given number completely and remainder will be zero .
So,
25 = 5*5
25 = 5²
And,
1 and the number itself is an universal factor of any number .
Thus the factors of 25 are:
1, 5 , 25 .
Know more about factors,
https://brainly.com/question/29155845
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What single percentage change is equivalent to a 8% increase followed by a 15% increase?
Answer:
24.2%
Step-by-step explanation:
If we take 100 for example, an 8% increase would make it 108, and a further 15% increase would make it 124.2 and 124.2 is 124.2% of 100 and if we minus the initial value of 100% it would be 24.2%
