Answer:
[tex]\textsf{1.} \quad 2[/tex]
[tex]\textsf{2.} \quad -4[/tex]
[tex]\textsf{3.\quad und\:\!efined}[/tex]
[tex]\textsf{4.} \quad 0\;\;\textsf{(zero)}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Question 1Given points:
(x₁, y₁) = (0, -1)(x₂, y₂) = (2, 3)Substitute the given points into the slope formula:
[tex]\implies \textsf{Slope}=\dfrac{3-(-1)}{2-0}=\dfrac{4}{2}=2[/tex]
Question 2Given points:
(x₁, y₁) = (6, -10)(x₂, y₂) = (2, 6)Substitute the given points into the slope formula:
[tex]\implies \textsf{Slope}=\dfrac{6-(-10)}{2-6}=\dfrac{16}{-4}=-4[/tex]
Question 3Given points:
(x₁, y₁) = (3 ,2)(x₂, y₂) = (3, 5)Substitute the given points into the slope formula:
[tex]\implies \textsf{Slope}=\dfrac{5-2}{3-3}=\dfrac{3}{0}=\textsf{und\:\!efined}[/tex]
Question 4Given points:
(x₁, y₁) = (2, 3)(x₂, y₂) = (5, 3)Substitute the given points into the slope formula:
[tex]\implies \textsf{Slope}=\dfrac{3-3}{5-2}=\dfrac{0}{3}=0[/tex]
consider ventilation of a well-mixed room. the differential equation for mass concentration in the room as a function of time is given as follow,
consider ventilation of a well-mixed room, the differential equation for mass concentration in the room as a function of time is given as follow:
There are three characteristic parameters in such a situation:
L, a characteristic length scale of the room (assume L = V^1/3); V the volume flow rate of fresh air into the room, and [tex]c_{limit}[/tex], the maximum mass concentration that is not harmful.
Using these three characteristic parameters, define dimensionless forms of all the variables in the equation. c* = c/[tex]c_{limit}[/tex].)
Rewrite the equation in dimensionless form, and identify any established dimensionless groups that may appear.
V = dc/dt = S - [tex]V_c[/tex] - c[tex]A_sk_w[/tex]
Although several models are available in legal contexts, the current implementations seem to be unable to correctly simulate concentration changes that actually occur in volatile mixtures and in particular in thin films.
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Full question:
Consider ventilation of a well-mixed room as in The differential equation for mass concentration in the room as a function of time is given in and is repeated here for convenience,
V = dc/dt = S - [tex]V_c[/tex] - c[tex]A_sk_w[/tex].
Calculate length of bc
Answer:
a) BC = 8.66
b) BC = 4.33
Step-by-step explanation:
a)
solution:
cos30°=BC/AC
or, BC=0.866*10
BC=8.66
b)
solution:
BC=5*0.866
BC=4.33
two years ago, elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. she was promised 4% simple interest.
The interest that Elizabeth will get based on the information is $480.
How to calculate the interest?From the information, Elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. The profit deposited will be:
= 1/2 × $12000
= $6000
The simple Interest will be calculated thus:
= Principal × Rate × Time
= $6000 × 4% × 2
= $6000 × 0.04 × 2
= $480
The interest is $480.
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Two years ago, elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. she was promised 4% simple interest. How much was the interest?
iready jonah hill has recorded 32 shows using his cable television service. each week he record 6 new shoes. write an expression to show the totel number of shows jonah her recorded after w weeks
The expression to show the total number of shows Jonah hill recorded after w weeks is 32 + 6w
How to use expression to represent a situation?Jonah hill has recorded 32 shows using his cable television service. Each week he record 6 new shows.
The expression to show the total number of shows Jonah hill recorded after w weeks is as follows:
Hence,
let
w = number of weeks
Therefore, the expression to represent the situation is as follows:
total number of shows = 32 + 6w
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If the 20th term of a number sequence is 50, what will be the 21st term? (Non-serious answers will be reported because I need this to prepare for a Maths exam which is on Thursday.)
Answer: 52.5
Step-by-step explanation: We can divide 50 by 20 to find what the number is. In this problem, the number is 2.5. Since we know this, we can multiply 2.5 and 21 to get 52.5.
hope this helps!
please give brainliest!
Answer:
21st term = 52.5
Step-by-step explanation:
Given that,
→ 20th term of a sequence is 50.
The common difference is,
→ 50 ÷ 20
→ 50/20
→ 2.5
Now the 21st term will be,
→ n × 2.5
→ 21 × 2.5
→ 52.5
Hence, the answer is 52.5.
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
O (x,y) - (x + 5, y- 3)
O (x,y) - (x + 5, y + 3)
O (x,y) - (x-3,y +5)
O (x.y) - (x + 3, y +5)
The rule to describe the translation is (x , y) ---> ( x + 3 , y + 5 )
Translation is Changing scale , shifting or reflection of a parent figure.
Scale means Changing size and shape of figure
Shifting means moving the figure to new location this could be upwards downwards , left and right
Reflection means making a mirror image or figure to different quadrant or along different axis.
According to the question,
A rectangle on a coordinate plane whose coordinates are (x, y) is translated 5 units up and 3 units to left
Shifting a plane upwards means changing the y coordinates so ,
y +5
shifting towards left means shifting to left side of x - axis
so , x + 3
Hence , the rule to describe this translation is
(x , y) ---> ( x + 3 , y + 5 )
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Nadia is a stockbroker.She earns 11% commission each week. Last week, she sold $7,000 worth of stocks. How much did she make the last week in commission? If she averages that same amount each week, how much did she make in commission in 2011
Answer:
$770
$40,040
Step-by-step explanation:
Last week: 11% of $7,000
11% of $7000 = 11/100 × $7000 = $770
Full year is 52 weeks.
52 × $770 = $40,040
PLEASE HELP ME WITH THIS!
What is the remainder when x3 1 is divided by x 1?.
The remainder when x³ + 1 is divided by x + 1 is 0
Given,
The polynomial functions; x³ + 1 and x + 1
We have to find the remainder when x³ + 1 is divided by x + 1
Polynomial function;-
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Here,
p(x) = x³ + 1
g(x) = x + 1 = 0
x = -1
Then,
p(x) = x³ + 1
p(-1) = -1³ + 1 = -1 + 1 = 0
That is,
The remainder when x³ + 1 is divided by x + 1 is 0
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In the Bayesian linear model, the priors for the intercept and for the slope are independent. True or false: in the posterior distribution, the intercept and slope may be correlated. true or false?
(a) The statement about Bayesian model "For the Bayesian linear model, the priors for intercept and slope are independent" is False .
(b) The statement about posterior distribution "in posterior distribution, intercept and slope may be correlated" is False .
In the question ,
it is given that ,
Part(a) ,
the statement is given to be "In Bayesian linear model, the priors for the intercept and slope are independent" , we have to check whether the statement is True or False .
We have the linear model as [tex]y_{i}= \alpha +\beta x_{i} +A_{i}[/tex] , where [tex]A_{i}[/tex]≈N(0,σ²) , α is the intercept and β is the slope .
we know that priors [tex](\hat{\alpha } , \hat{\beta })[/tex] are not independent ,
Cov [tex](\hat{\alpha } , \hat{\beta })[/tex] = [tex]\frac{-\bar{x}}{S_{xx} }[/tex] *σ² ,
So , the priors for the intercept and for the slope are independent ,
hence the statement is False .
Part(b) ,
the statement is given to be "In posterior distribution, intercept and the slope may be correlated" ,
For Posterior distribution , as [tex]A_{i}[/tex]≈N(0,σ²) ,
and 2 + [tex]\beta x_{i}[/tex] is a non random part of the model ,
and Cov([tex](A_{i} , A_{i} )[/tex] = 0 for i ≠ j .
hence , we can say that the intercept and slope are not Corelated ,
the statement is False .
Therefore , both the given statement are False .
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What is the measure of angle JMF?
The measure of angle EMJ is 66°.
Answer:
18
Step-by-step explanation:
66-48=18
What are the 3 angle bisectors of a triangle intersect?.
The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.
Given:
the 3 angle bisectors of a triangle intersect.
when three angle bisector of a triangle intersect then that point of concurrency is called incenter.
Incenter:
The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.
Incenter formula:
= (ax1+bx2+x3 / a+b+c , ay1+by2+y3 / a+b+c).
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if speed varies inversely as the time it takes to drive and kris takes 5 hours driving at 55 mph, what speed will martin need to drive if he wants to take 512hours
The speed that will martin need to drive, if he wants to take the 512 hours is 0.537 mph.
What does proportionality's constant look like?Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.
Speed and travel time vary in opposite directions.,
So v ∝ 1/t.
speed = v
time = t
So
=> v = k/t, k=constant of proportionality.
Since it takes Kris 5 hours when driving at 55 mph,
=> v = 55mph and t = 5 hours.
=> 55 = k/5
by doing cross multiply
=> k = 55*5
=> k = 275
Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t
=> v = 275/512
=> v = 0.537 mph
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What is the solution to this system of linear equations yx 6 y x =- 10 O (- 2 8 O (- 8 2 O 6/10 O (- 10 6?.
This set of linear equations, y - x = 6, and y + x = - 10, has the following solution.
What are linear equation systems?
In mathematics, a system of linear equations is the collection of two or more linear equations that share the same variables. The maximum power of the variable in the linear equations in this situation is 1, making them first-order equations. A linear equation may have one, two, or three variables.
Knowing that;
Y - x = 6
Y + x = -10
Since both equations are equivalent to y, let's equalize them.
x + 6 = - x - 10
By additional computation;
x + x = - 10 - 6
2x = - 16
Subtract 2 from both sides;
x = -8
In either equation, x should be changed to the appropriate value;
y - x = 6
y - (-8) = 6
Hence, we do;
y + 8 = 6
y = 6 - 8
y = - 2
Therefore,the answer to this set of linear equations is y + x = -10 and y - x = 6. (-8, -2).
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The players on a basketball team decided that they wanted
to score 750 points by the end of the season. The coach
promised pizzas if the team scored within 50 points of its
goal. Solve the inequality |x - 750| ≤ 50, which represents
the total possible number of points the team could score to earn pizzas.
The total possible number of points the team could score to earn pizzas is 700, using the inequality |x - 750| ≤ 50
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Based on the given conditions, formulate: 750 -50
Calculate the sum or difference will be 700
Hence, the inequality possible number of points the team could score to earn pizzas is 700
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What is the value of k when k3 =
1
125
?
A.
1
25
B.
1
5
C.
5
D.
25
The value of k in k^3=1/125 is 1/5 (optionB)
What is Indices?Indices is the power or exponent which is raised to a number or a variable. For example, in number 2^5, 5is the index of 2 which means 2×2×2×2×2. The plural form of index is indices.
From the law of Indices,
a^-1= 1/a
similarly, 1/125= (125)^-1
from the expression, K^3= (125)^-1
K^3= (5^3)^-1
therefore K^3=(5)^-3
multiply the power of both sides by 1/3
=K^3×1/3= (5)^-3×1/3
therefore k= 5^-1=1/5
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Describe and correct the error
the student made when writing the equation
of the line that passes through (-8, 5) and is
perpendicular to y = 4x - 2.
The equation of line that passes through the point (-8, 5) and perpendicular to y = 4x - 2 is, [tex]y=-\frac{1}{4}x+3[/tex].
What is point slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Consider the given equation of line
y = 4x - 2
And the point is (-8, 5).
We have to find the equation of line that passes through the given point and perpendicular to the given line.
First to find the slope of the line.
Since, slope of the perpendicular line is negative reciprocal of the slope of the given line.
Here, slope of the line is 4.
So, the slope of the perpendicular line is -1/4.
Now, consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1) = (-8, 5), m = -\frac{1}{4}[/tex]
[tex]y-5=-\frac{1}{4}(x-(-8)) \\y-5=-\frac{1}{4}(x+8)\\ y-5=-\frac{1}{4}x-2\\y=-\frac{1}{4}-2+5\\ y=-\frac{1}{4}+3[/tex]
Hence, the equation of line perpendicular to the given line is, [tex]y=-\frac{1}{4}x+3[/tex].
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A student is assessing the correlation between the number of workers in a factory of and the number of units produced daily. The table shows the data:
Number of workers
(x)
10 20 30
50 60 70
80
Number of units
(y)
52 102 152 202 252 302 352 402 452
Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What do the slope and y-intercept of the plot indicate? (3 points)
The slope and y intercept of the line formed are 5 and 2 respectively .
How are the values from the table related?Part A:
Yes. There is a correlation between the number of workers in a factory and the number of units produced daily.
Let us consider the coordinates [tex](x_{1},y_{1})\text{ and }(x_{2},y_{2})[/tex] to be (10, 52) and (20, 102)
The slope = m
[tex]m =\frac{y _{2}-y_{1}}{x_{2}- x _{1}} \\\\=\frac{102-52}{20- 10} \\\\= \frac{50}{10} \\\\= 5[/tex]
The value of slope = m = 5
The slope - intercept form of the equation is y = mx + b ----(1)
Let us find y intercept b (x = 0),
From the given table,
When x = 0 , y = 2
So ,b = 2
Substituting m = 5 and b =2 in the equation (1)
y = 5x + 2
Thus, there is a correlation between the number of workers in a factory and the number of units produced daily.
Part B :
Substituting m = 5 and b =2 in the equation (1)
y = 5x + 2
So, y = 5x + 2 is the function that best fits the data.
Part C:
The slope = m = 5Here, the slope indicates that the rate of change of number of units produced daily over the rate of change of number of workers.
The y - intercept is b = 2The y - intercept indicates that the number of units produced daily by the number of workers.
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Translate: 3 less than the product of 7 and a number
Answer:
3-7n
Step-by-step explanation:
Answer:6
Step-by-step explanation:
Three less than the product of 7 is 6
Just translate the sentence into a equation:7n-3=6
What is the slope of the line that passes through the points (-3, 3), and (1, -5)?
-1/2
2
1/2
-2
the base of a triangle is 4 meters shorts than its height. what are the height and base of the triangle if its area is 48 square meters?
Height and base of a triangle with given area 48 square meters is 12meters and 8 meters respectively.
As given ,
Area of the triangle = 48 square meters
Let 'y' meters represents the height of the triangle
Then 'y - 4' meters represents the base of a triangle.
Area of a triangle = ( 1/2 ) × base × height
Substitute the values we get
48 = ( 1 / 2) × ( y - 4 ) × y
⇒ 96 = y² - 4y
⇒ y² - 4y - 96 = 0
⇒ y² - 12y + 8y - 96 = 0
⇒ ( y - 12 ) ( y + 8 ) =0
⇒ y = 12 or y = -8
Height cannot be negative.
⇒y = 12meters
Base = 12 -4
= 8 meters
Therefore, height and base of a triangle with given area is 12 meters and 8 meters respectively.
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What can be received at 45 F 7 C?.
The item that can be received at 45°F (7° C) is Milk , the correct option is (b) .
In the question ,
the receiving temperature of the items is given ,
we have to identify the item that can be received at 45°F (7° C) .
From the given options ,
we see that cold feed is received at 41°F (5° C) ,
Milk at 45°F (7° C) and Hot Food at 135°F (57° C) .
So , we can conclude that the option (b) Milk can be received at 45°F (7° C) .
Therefore , The item that can be received at 45°F (7° C) is Milk , the correct option is (b) .
The given question is incomplete , the complete question is
Temperature criteria for receiving items is given as follows ;
(a) Cold Food is received at 41°F (5° C) or lower ,
(b) Milk is received at 45°F (7° C) or lower ,
(c) Hot Food is received at 135°F (57° C) or lower .
Find the item that can be received at 45°F (7° C) ?
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how will the volume of the pyramid change if each side is multiplied by a factor of one-half?
Answer:
I think it will be one eighth times the volume
Step-by-step explanation:
rigoberto invests $8,000, at 6% interest, compounded semiannually for 1 year. use the compound interest formula to calculate the compound interest for his investment.
P = $8,000 is the principal value;
r = 0.06 or 6% interest rate;
m = 2 is the number of compounding periods per year;
t = 1 year;
i = r/m = 0.06/2 = 0.03 is the interest rate per period;
n = mt = 2*1 = 2 is the number of compounding periods;
A = is the future value;
the interest is 8487.2 - 8000 = $487.2.
Rigoberto invests $8,000, at 6% interest, compounded semiannually for 1 year the compound interest for his investment is 8487.2
A = P(1 + r/n)²
In the formula
A = Accrued amount (principal + interest)
P = Principal amount = 8000
r = Annual nominal interest rate as a decimal = 0.06
R = Annual nominal interest rate as a percent
r = R/100
n = number of compounding periods per unit of time
t = time in decimal years;
A = 8000(1 + 0.06/2)²
= 8000(1 + 0.03)²
= 8000(1.0609)
= 8487.2
Therefore, the compound interest for his investment is 8487.2
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P is inversely proportional to the square root of m. P = 10 when m = 1/4 Work out the value of m when P = 2
The required value of m is given as 25/4 as of the given proportionality.
Given that,
P is inversely proportional to the square root of m. P = 10 when m = 1/4 to work out the value of m when P = 2.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
According to the question,
P ∝ 1 / √m
Now,
P₁/P₂ = √m₂/√m₁
Substitute the value in the above equation,
10/2 = √m₂/√1/4
√m₂ = 5/2
m₂ = 25/4 researchers
Thus, the required value of m is given as 25/4 as of the given proportionality.
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The number of miles driven by Zoe is directly proportional to the number of gallons
she used.
Number of Gallons Used
9
28
40
Number of Miles Driven
348.3
1083.6
1548
How many miles would she drive on 47 gallons?
Answer:
1818.9 mi
Step-by-step explanation:
If the num of miles is directly proportional, then we can find out that she drives 348.3/9 = 38.7 mi/gal (this also works for the other two pairs)
To find the distance with 47 gallons, you multiply 38.7 by 47, to get 1818.9 mi.
Anthony has 40 books, and Tommy has 50 books. If Vlad has twice as many books as Anthony and Tommy combined, then what does Vlad have?
A.) 180
B.) 90
C.) 245
D.) 115
Answer:
180
Step-by-step explanation:
first we combine what Anthony and Tommy have by adding
40+50
90
And twice as many is multiplying by 2
2x90
180
Hopes this helps please mark brainliest
Answer:180
explanation:40+50=90
90x2=180
a trapezoid has a perimeter of 14 feet. what will the perimeter be if each side length is increased by a factor 7?
If the point P(x, 3) is equidistant from the points Q(3, 5) and R(−4, −2), find the value of x.
The value of the coordinate x in the point P(x, 3) s -2
How to find the value of x?From the question, we have the following coordinate points
Point P = (x, 3)
Point Q = (3, 5)
Point R = (-4, -2)
The point P is equidistant from the points Q and R
This means that
PQ = PR
These lengths can be calculated using the following distance formula
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, we have
PQ = √[(x - 3)² + (3 - 5)²]
PR = √[(x + 4)² + (3 + 2)²]
Recall that PQ = PR
So, we have
√[(x - 3)² + (3 - 5)²] = √[(x + 4)² + (3 + 2)²]
Square both sides
(x - 3)² + (3 - 5)² = (x + 4)² + (3 + 2)²
So, we have
(x - 3)² + 4 = (x + 4)² + 25
Open the brackets
x² - 6x + 9 + 4 = x² + 8x + 16 + 25
Evaluate the like terms
8x + 6x = 9 + 4 - 16- 25
Evaluate the like terms
14x = -28
This gives
x = -2
Hence, the value of x is -2
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what is 459.63? is it irrational?
Answer:
No it is not irrational
Step-by-step explanation:
459.63 is a rational number.
Irrational numbers are numbers that can't be shown as simple fractions
Examples of irrational numbers are:
√2, π(Pi), 0.45445544455544445555.. (because it doesn't end)
