Write the equation of the given line in slope-intercept form.
Answer:
y = 2x - 1
Step-by-step explanation:
The line passes through points A(1, 1) and B(2, 3).
The slope-intercept form of the equation of a line is
y = mx + b,
where m = slope, and b = y-intercept.
We see from the graph that the y-intercept is -1, so b = -1, and we have
y = mx - 1
Going from point A to point B, we go up two units and right 1 unit. Slope = m = difference in y over difference in x, so
m = 2/1 = 2
The equation is
y = 2x - 1
Answer: 2x + -1
Step-by-step explanation: In this problem, we're asked to write the equation of the given line in slope-intercept form.
Slope-intercept form is the same thing as y = mx + b form where m represents the slope of the line and b represents the y-intercept. So our first step is to find the slope and the y-intercept of the given line.
To find the slope, we use the ratio rise over run between any two points on the line. To get from point A to point B along this line, we rise 2 units and run 1 unit. So our slope or rise over run is 2/1 or just 2.
Next, to find the y-intercept, it's important to understand that the y-intercept is the point where the line crosses the y-axis. Notice that this line crosses the y-axis at the point (0,-1) which means that the y-intercept is -1.
Therefore, m = 1/2 and b = -1 and we substitute these values into our formula for m and b to get y = 2x + -1.
So the equation of the given line in slope-intercept form is y = 2x + -1.
Is abc def name the postulates that applies
Answer:
The answer is C. AAA is not a congruency postulate because the side lengths may be different sizes although the angles are the same.
triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate.
In other words, if two triangles have all three corresponding sides equal, then the triangles are congruent.
So the answer to the question is B. Congruent - SSS.
If triangles ABC and DEF are congruent, and if so, to name the postulate that applies.
The triangles are congruent because they have the same side lengths and angles. This can be seen from the following:
AD = BE (given)
∠ADB=∠BED (vertical angles)
AB = EF (given)
∠ABD=∠EBD (corresponding angles when AD ∥ EF )
BC = DF (given)
Therefore, triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate
A total of 626 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
351 adults and 275 students
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 626 tickets were purchased, then s+a=626.
We also know that 74 fewer student tickets then adult tickets. So s+76=a, the number of student tickets plus 76 will be the number of adult tickets.
We will solve by substituting one equation into the other. We substitute a=76+s into s+a=626. Simplify and isolate the variable a.
s+a=626
s+76+s=626
2s+76=626
2s+76-76=626-76
2s=550
s=275
This means that 275 students attended and 351 adults attended since 275+351=626.
By setting up a system of equations and solving for the number of adult tickets, we are able to determine that 350 adult tickets were sold for the school play.
To find out how many adult tickets were sold, we can set up an equation to model the situation. Let A be the number of adult tickets and S be the number of student tickets. We are given that a total of 626 tickets were sold, which can be described by the equation A + S = 626. We are also told that there were 74 fewer student tickets sold than adult tickets, described by the equation S = A - 74.
To solve for A, we can substitute (A - 74) for S in the first equation, giving us A + (A - 74) = 626. Simplifying this, we get 2A - 74 = 626. Adding 74 to both sides, we get 2A = 700. Finally, dividing both sides by 2, we find A = 350.
Therefore, 350 adult tickets were sold.
Five out of six residents of Mayville have library cards. Which tool will best allow Darren to simulate this scenario and predict whether a randomly chosen resident has a library card? A coin a 5-sector spinner a number cube a bag of 11 marbles
Answer:a number cube
Step-by-step explanation:
Answer: A number cube is correct to chosen five out of six residents of Mayville have library cards.
Step-by-step explanation:
A number cube is the best to simulate this scenario and predict whether a randomly chosen resident has a library card.
As Coin has only 2 outcomes "Head" and "Tail".
A 5-sector sector spinner has only 5 outcomes we need six outcomes.
A bag of 11 marbles has no differentiated with respect to colors etc.
Hence, A number cube is correct to chosen five out of six residents of Mayville have library cards.
can someone plz help with this but with work shown
Use the substitution method to solve the system of equations
You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).
In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.
The result is
[tex] 14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8 [/tex]
So, the second equation turned to be an equality, i.e. an equation where both sides are the same.
This implies that the system has infinitely many solutions, because every couple [tex] (n,m) [/tex] such that [tex] n=-7m-4 [/tex] is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.
Compare using the quadratic formula to find solutions to a quadratic equation having irrational roots to that of one that has rational roots.
For a general quadratic equation with rational coefficients
[tex]ax^2+bx+c=0,\,\,\,\,a,b,c \in Q[/tex]
the two solutions are:
[tex]x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-b\pm\sqrt{D}}{2a}[/tex]
where D is the determinant.
Clearly, a solution will a rational number as long as [tex]\sqrt{D}[/tex] is rational. However, it can be shown that a square root of an integer is only rational if its value is an integer. In other words, [tex]\sqrt{D}[/tex] is rational if and only if the determinant is a perfect square, [tex]D=n^2, \,\,\,n\in N[/tex], otherwise the square root is irrational. Therefore the coefficients of quadratic equations that are to have rational solutions must satisfy the following condition:
[tex]b^2-4ac=n^2\,\,\,n\in N[/tex]
HELP I HAVE TO GO IN A MINUTE Which function has a y-value of 12, if the x-value is 3?
y = x - 6
y = 4x
y = x + 8
y = 3x
An object moves according to the law s = t2 + 5t - 8. what is the exact rate of change of s with respect to t when t = 1.5 seconds?
Answer:
ds/dt =8 when t =1.5
Step-by-step explanation:
s = t^2 + 5t - 8
We want to find ds/dt
ds/dt = 2t +5
evaluated when t=1.5
ds/dt = 2(1.5) +5
ds/dt = 3+5
ds/dt =8 when t =1.5
Replace t with 1.5 seconds and solve for s:
s = 1.5^2 + 5(1.5) -8
s = 2.25+7.5-8
s= 9.75 -8
s = 1.75
Rate of change is S/t
Rate of change = 1.75 / 1.5
Rate of change of s = 1.17
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
Use the imaginary numberi to rewrite the expression as a complex number
Answer:
i think the answer would be C
Step-by-step explanation:
since it seemed you had to divide the numbers a hundred would turn into ten and ninety would turn into nine and because you have one negative and one positive that means it would have to be a negative so it would be
10 - 9i
Answer: B
Step-by-step explanation:
[tex]\sqrt{100} + \sqrt{-81}[/tex]
[tex]\sqrt{100} = 10[/tex][tex]\sqrt{-81} = \sqrt{-1} * \sqrt{81} = i * 9 = 9i[/tex][tex]\sqrt{100} + \sqrt{-81}[/tex]
= 10 + 9i
A company had a competition to see which team could load trucks at the loading dock the fastest. On day one, team one loaded 5 1?2 trucks. The leader of team three said her team could load 3 1?2 times that number when it was their turn to participate. How many trucks does that team expect to load?
Answer:25
Step-by-step explanation:cause it is
To calculate the number of trucks Team Three expects to load based on the information provided.
To calculate the number of trucks Team Three expects to load:
Calculate 3.5 times the number of trucks loaded by team one: 5.5 trucks x 3.5 = 17.5 trucks.
Therefore, team three expects to load 17.5 trucks.
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 4 rows of the same length, he has 3 chairs left over. If he arranges the chairs in 2 rows of that same length, he has 15 left over. How many chairs does Liam have?
Find the solution to the system of equations graphed here:
Answer: (1,3)
All you're doing is looking for where the two lines cross, or the point of intersection. What you can do is draw a vertical line through this intersection point to see that the vertical line lands on x = 1 on the x axis. At the same time, draw a horizontal line to the y axis and it will get to y = 3.
So together x = 1 and y = 3 pair up to get (x,y) = (1,3)
The table below shows the temperature in degrees for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature: 68 77 83 85 89 94 96 99
Number of cones: 403 447 457 465 489 503 543 576
about how many ice cream cones would you expect the shop to sell if the temperature one day is 106 degrees?
Answer:
We have to find the equation of least squares regression line in order to find the number of ice cream cones that the shopkeeper to sell if the temperature is 106 degrees. We can use excel regression data analysis tool to find the equation of the regression line. The excel output is attached here.
The equation of the least squares regression line is:
[tex]\hat{y}=46.587+5.080x[/tex]
Now, if the temperature is 106 degrees, then the number of cones expected to be sold is given below:
[tex]\hat{y}=46.587+5.080 \times 106[/tex]
[tex]=585.1 \approx 585[/tex]
Therefore, the number of ice cream cones that the shopkeeper would expect to sell if the temperature is 106 degrees is 585.
Identify the perimeter and area of an equilateral triangle with height 12√2 cm. Give your answer in simplest radical form. HELP PLEASE!!!
Answer:
perimeter = 24√6 cmarea = 96√3 cm²Step-by-step explanation:
The edge length (s) of an equilateral triangle is (2/3)√3 times the height. This means the edge length of your triangle is ...
... s = (2/3)√3 × 12√2 = 8√6
The perimeter is 3 times the side length:
... p = 3s = 3×8√6 = 24√6 . . . cm
The area is half the product of edge length and height:
... a = (1/2)sh = (1/2)(8√6)(12√2) = 48√12 = 96√3 . . . cm²
The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².
To find the perimeter and area of an equilateral triangle with a given height, we can follow these steps:
First, let's denote the side length of the equilateral triangle as a. In an equilateral triangle, the height (h) can be found using the formula:
h = (a√3)/2
We know the height is 12√2 cm. Therefore,12√2 = (a√3)/2
To find the side length a, we can rearrange the equation: a = 2 * 12√2 / √3
Simplify the expression: a = 24√2 / √3
Multiplying numerator and denominator by √3 to rationalize the denominator: a = 24√6 / 3
a = 8√6
Now, the perimeter (P) of the equilateral triangle is given by: P = 3a
Substitute the value of a: P = 3 * 8√6
P = 24√6 cm
Next, we calculate the area (A) using the formula: A = (base * height) / 2
In an equilateral triangle, the base is equal to the side length a, and the height is given as 12√2 cm:
A = (8√6 * 12√2) / 2
Multiplying the bases and simplifying: A = (96√12) / 2
Since √12 can be simplified to 2√3: A = (96 * 2√3) / 2
A = 96√3 cm²
The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².
The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.
What does 1−x represent in the expression?
percent of original price being paid
original price of shorts
discount price of the shorts
percent of discount
Answer:
1-x represents the percent of the original price being paid.
Step-by-step explanation:
The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.
For example , 10% is the discount percentage
1 - 10% = 90% will be the percentage of original price to be paid
Here x represents the percent of the discount
so 1-x represents the percent of the original price being paid.
Answer:
percent of original price being paid
Step-by-step explanation:
The pie store is having a 20\%20% off sale on all of its pies. If the pie you want regularly costs \$18$18, how much would you save with the discount? \$
Answer:
$3.6
Step-by-step explanation:
We are told that the pie store is having a 20% off sale on all of its pies. The pie you want regularly costs $18.
To find the amount saved with the discount let us find 20% of 18.
[tex]\text{The amount saved with discount}=\frac{20}{100}\times 18[/tex]
[tex]\text{The amount saved with discount}=0.20\times 18[/tex]
[tex]\text{The amount saved with discount}=3.6[/tex]
Therefore, the amount saved with the discount is $3.6.
Write a function rule for the given graph. Identify the value of y when x=12.
Answer: f(x) = x + 2; f(12) = 14
Step-by-step explanation:
The parent function of f(x) = x has been shifted up 2 units
⇒ f(x) = x + 2
f(12) = 12 + 2
= 14
the equation for distance is d= st. if a car has a speed of 35 m/s for 15 seconds, how far does it go ?
A. 300m
B. 50 M
C.2.33 M
D.525 M
Answer:
D.525 M
Step-by-step explanation:
We know the equation
d = st
where d is the distance, s is the speed and t is the time
The problem gives us the speed of 35 m/s and the time of 15 seconds
s = 35 m/s and t =15 s, we can substitute them in
d =st
d = 35 * 15
d = 525 m
Answer:
525 m
Step-by-step explanation:
Is the movie is 28 minutes and 58 seconds and we have watched 13 minutes and 44 second how much long do we have before we finish the movie
Final answer:
To find out how much longer we have before we finish the movie, subtract the time already watched from the total duration of the movie.
Explanation:
To find out how much longer we have before we finish the movie, we need to subtract the time we have already watched from the total duration of the movie.
Given that the movie is 28 minutes and 58 seconds long, and we have already watched 13 minutes and 44 seconds, we subtract the time already watched from the total duration:
28 minutes 58 seconds - 13 minutes 44 seconds = 15 minutes 14 seconds.
Therefore, we have 15 minutes and 14 seconds left before we finish the movie.
A student in an intro stats course collects data at her university. she wants to model the relationship between student jobs and gpa. she collects a random sample of students and asks each for their gpa and the number of hours per week they work. she checks the conditions and makes a linear model with gpa as the response variable. she finds that the r-squared statistic is 12.7%. what is the correct interpretation of this number?
Answer:
We are given:
[tex]R^{2}=12.7\%[/tex]
The interpretation of [tex]R^{2}[/tex] is the amount of variation in response variable that is explained by the explanatory variable in the model
Therefore, the interpretation of [tex]R^{2}=12.7\%[/tex] is 12.7% of variation in gpa response variable is explained by the jobs explanatory variable in the given linear regression model.
the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.
The R-squared statistic, often denoted as R², measures the goodness of fit of a linear regression model. In this context, where the R-squared statistic is 12.7%, it means that approximately 12.7% of the variability in GPA can be explained by the linear relationship with the number of hours per week students work.
More specifically:
- 12.7% of the variation in GPAs among the students in the sample can be accounted for by the linear regression model with the number of hours worked as the predictor variable.
- The remaining 87.3% of the variability in GPAs is not explained by this model and is attributed to other factors or sources of variation that are not included in the model.
In summary, the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.
Learn more about R-squared statistic here
https://brainly.com/question/11743185
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This question is worth Points and Brainliest!!!!! HURRY
Which of the following is the solution to the equation 4 over 5n = 20?
A) n = 4
B) n = 12
C) n = 16
D) n = 25
Answer:
D) n=25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
I didi the quiz
Find the degree of the polynomial: 7.5x^3yz+x^7z^2+2x^3y^3z−x^4z
The degree of this polynomial is 9
Answer:
Answer in image
Step-by-step explanation:
Answer in image
WILL GIVE BRAINLIEST
Solve for x
Answer:
6x^2 +81x - 17
---------------------
7x-15
Step-by-step explanation:
We cannot solve for x since this is an expression
((6x+9) (x+12) -sqrt(49+76) ^2
--------------------------------------------
(49+7x) -64
Lets simplify the numerator
((6x+9) (x+12) -sqrt(49+76) ^2
Simplify what is inside the last parentheses
((6x+9) (x+12) -sqrt(125) ^2
Squaring a square root leaves the original number
((6x+9) (x+12) -(125)
FOIL the first two terms
First 6x*x = 6x^2
Outer: 6x*12 = 72x
Inner: 9x
Last : 9*12 = 108
Add them together
6x^2 +72x+9x+108 = 6x^2 +81x+108
Subtract the 125
6x^2 +81x+108-125
6x^2 +81x - 17
Now lets simplify the denominator
(49+7x) -64
49+7x-64
7x-15
6x^2 +81x - 17
---------------------
7x-15
Jason spends 1/3 of each day sleeping.What is the total numbers of days that jason spend awake in 1 week?
Answer:
Given the statement: Jason spends 1/3 of each day sleeping
Since, a day has 24 hours and
Jason spends each day [tex]\frac{1}{3}\times 24 = 8 hours [/tex] in sleeping .
Remaining Jason spend awake each day, 24 - 8 = 16 hours.
In 1 day = Jason spend 16 hours in awake
then;
in 1 week(i.e, 7 days) = [tex]16 \times 7 = 112 hours[/tex] spend in awake.
To find the total number of days Jason spend awake in 1 week.
Divide 112 hours by 24 we get;
[tex]\frac{112}{24} = \frac{14}{3} =4\frac{2}{3}[/tex] days
therefore, [tex]4\frac{2}{3}[/tex] is the total number of day that Jason spend awake in 1 week.
PLEASE HELP ASAP 25 POINTSS
Given Equations :
✿ 5x + 3y = -6 -------------- [1]
✿ 3x - 2y = 4 -------------- [2]
Multiplying Equation [1] with 2, We get :
⇒ 10x + 6y = -12 ----------- [3]
Multiplying Equation [2] with 3, We get :
⇒ 9x - 6y = 12 ---------- [4]
Adding Both Equations [3] and [4], We get :
⇒ (10x + 6y) + (9x - 6y) = -12 + 12
⇒ 19x = 0
⇒ x = 0
Substituting x = 0 in Equation [1], We get :
⇒ 5(0) + 3y = -6
⇒ 3y = -6
⇒ y = -2
⇒ (x , y) = (0 , -2)
Option (a) is the Answer
Answer: A (0, -2)
Step-by-step explanation:
5x + 3y = -6 → 2(5x + 3y = -6) → 10x + 6y = -12
3x - 2y = 4 → 3(3x - 2y = 4) → 9x - 6y = 12
19x = 0
x = 0
Now, input "x = 0" into one of the equations and solve for y:
5x + 3y = -6
5(0) + 3y = -6
3y = -6
y = -2
The time a basketball player spends in the air when shooting a basket is called the "hang time." the vertical leap l measured in feet is related to the hang time t measured in seconds by the equation equals=4t squared 4t2. suppose that a basketball player has a vertical leap of 44 feet 1111 inches. find the hang time for this leap.
Answer: 1.1 seconds
Step-by-step explanation:
leap = 4t² ; leap = 4 ft 11 inches, find t
[tex]4\frac{11}{12} = 4t^2[/tex]
[tex]\frac{59}{12} = 4t^2[/tex]
[tex]\frac{59}{48} = t^2[/tex]
[tex]\sqrt{\frac{59}{12}} = \sqrt{t^2}[/tex]
[tex]\sqrt{1.23} = t[/tex]
1.1 = t
Please help this is so confusing to me
First multiply C by F by multiplying each row in C by each column in F:
12 * -2 + 0*0 + 1.5*2 12*0 + 0*8 + 1.5*1
1*-2 -6*0 +7.2 1*0-6*8 +7*1
to get a matrix of:
-21 1.5
12 -41
Now subtract that matrix from B:
2- -21 = 2+21 = 23
8 - 1.5 = 6.5
0.6 - 12 = -11.4
3 - -41 = 3+41 = 44
So you have:
23 6.5
-11.4 44
Which makes C the correct answer.
Write a linear function that passes through the points (-5, -6) and (2, 8).
Answer:
y = 2x+4
Step-by-step explanation:
We need to find the slope
m = (y2-y1)/(x2-x1)
= (8--6)/(2--5)
= (8+6)/(2+5)
= 14/7
=2
Now we can use the point slope form of a line
y-y1 = m(x-x1)
y--6 = 2 (x--5)
y+6 = 2(x+5)
If we want it in slope intercept form
Distribute the 2
y+6 = 2x+10
Now subtract the 6 from both side
y+6-6=2x+10-6
y = 2x+4
If FGA and BGC each measure 30°, which does EGD measure?
Answer:
Answer is B) 120