The length of the line is 5 units.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that, endpoints are (-1,4) and (2,0) of the line segment.
The length= √(2+1)²+(0-4)²
=5units
Hence, The length of the line is 5 units.
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Mrs. Knight is saving money for a trip. She already has some money saved in 1 point
her savings account and will add the same amount to her account each
week. At the end of 2 weeks, she has $130. At the end of 8 weeks, she has
$280. Write a linear function to represent the amount of money (y)
Mrs. Knight has saved after x weeks
The equation of line is given by y = 25x + 80.
What is an equation of a line?The equation of a line is expressed as y = mx + b where m exists the slope and b exists the y-intercept
y - y₁ = m ( x - x₁ )
Where, y be the y-coordinate of second point
y₁ be y-coordinate of point one
m be the slope
x be the x-coordinate of second point
x₁ be the x-coordinate of point one
Let the equation of slope m be
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Equation of line be represented as A
The two points are given as A ( 2 , 130 ) and B ( 8 , 280 )
The slope of the line between the two points exists given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 280 - 130 ) / ( 8 - 2 )
simplifying the above equation, we get
m = 150 / 6
m = 25
Now , the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 130 = 25 ( x - 2 )
On simplifying the equation , we get
y - 130 = 25x - 50
Adding 130 on both sides , we get
y = 25x + 80
The equation is of the form y = mx + b where b is the y intercept.
Therefore, the equation of line is given by y = 25x + 80
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The equation of line is given by y = 25x + 80, this represent the linear function between the amount of money and the saved amount.
What is an equation of a line?The equation of a line is expressed as y = mx + b where m is called the slope and b is called the y-intercept
y - y₁ = m ( x - x₁ )
Where, y be the y-coordinate of second point
y₁ be y-coordinate of point one
m be the slope
x be the x-coordinate of second point
x₁ be the x-coordinate of point one
Let the equation of slope m be
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Equation of line be represented as A
The two points are given as A ( 2 , 130 ) and B ( 8 , 280 )
The slope of the line between the two points exists given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 280 - 130 ) / ( 8 - 2 )
simplifying the above equation, we get
m = 150 / 6
m = 25
Now , the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 130 = 25 ( x - 2 )
On simplifying the equation , we get
y - 130 = 25x - 50
Adding 130 on both sides , we get
y = 25x + 80
The equation is of the form y = mx + b where b is the y intercept.
Therefore, the equation of line is given by y = 25x + 80
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Find the area of the largest rectangle that can be inscribed in the ellipse x2 / a2 + y2 / b2 = 1.
The maximum area of the rectangle inside the ellipse is 2ab.
Given that,
Ellipse = x2 / a2 + y2 / b2 = 1
we know the general coordinates of any point in an ellipse of the equation
x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)
So, we take general vertices of rectangles as
(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)
So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ
So, its area will be ab4sinθcosθ (Length x Breadth)
Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A
Now A=2absin2θ
Now as the area is the maximum given in the question, we have to differentiate it with respect to θ
dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)
Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ = π / 2 and θ=π / 4
So now we to put θ=π / 4 in the equation of area which is A=2absin2θ
We get as A=2absin2π / 4=2absinπ / 2=2ab
Hence the max area of the rectangle inside the ellipse is 2ab.
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For Drew’s week 1 classes identify the domain and range is the relation a function? Explain
From the table for Drew's week 1 classes:
Domain = {English, Math, History, Biology, Biology Lab}
Range = {60. 90, 45, 0}
What is domain and range?A function's domain is the set of values that can be plugged into it. This set contains the x values in a function such as f. (x). A function's range is the set of values that it can take. This is the set of values that the function returns when we enter an x value. They are the y values.
A function can be thought of as a machine on an assembly line. On one end of the assembly line, there are a few screws and bolts, and on the other end, there is a car. The function is represented by the machine in the middle. The domain consists of the screws and bolts that we insert into the machine (our function).
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Please Help?
The amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining.
Answer:
ok, the correct answer should be R(1.5)=R(2)!
Step-by-step explanation:
I did this my class before!
PLZ HELP ME QUICK!!
Does the data provide convincing statistical evidence that at women pay more than men for the same catalytic converter repair?
Answer:
Yes the data provide convincing statistical evidence that at women pay more than men for the same catalytic converter repair
Is it a perfect square trinomial X² 10x 25?
Yes, it is a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."
The equation X² + 10X + 25 can be factored into (X + 5)²,
which is a perfect square trinomial. In general, a perfect square trinomial is any polynomial of the form A² + 2AB + B² where A and B are constants or variables.
This is because such a polynomial can be factored into (A + B)².
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Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio
The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.
Now, According to the question:
What is meant by ratio?
When expressed in numbers or amounts, a ratio is a relationship between two things. For example, if a room contains ten boys and thirty girls, the boy-to-girl ratio is 1:3, or one to three.A ratio, or getting rationed, on the occurs when replies to a tweet vastly outnumber likes or retweets. This means that people are reacting negatively to the tweet's content.It usually means that your comment has received more replies than likes. This implies that there are more people who disagree with your comment than agree with it.Therefore, simplifying the equation then we get,
if you take the ranges (y) and subtract one from the other you get 0.42.
(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42
(23.26 - 22.84)/(3 - 2) = 0.42
(23.68 - 23.26)/(4 - 3) = 0.42
Hence, The common difference is 0.42
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Please help!
ponential functions are in the form y = a(b)'.
What values of b make it an exponential growth function?
What values of make b it an exponential decay function?
Points p and q are negative integers plotted on a number line. If |p| > |q|, which statement is true?
A. Point p is closer to 0 than point q, and to the right of point q.
B. Point p is closer to 0 than point q, and to the left of point q.
C. Point p is further from 0 than point q, and to the right of point q.
D. Point p is further from 0 than point q, and to the left of point q.
Point p is further from 0 than point q, and to the left of point q.
The correct option is D.
What is an absolute value?The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.
Given:
Points p and q are negative integers plotted on a number line.
And |p| > |q|.
That means,
The absolute value of p is greater than the absolute value of q.
|p| and |q| are the positive integers.
So, p < q.
So, the q is closer to zero.
And p is left to point q.
Therefore, the q is closer to zero and p is left to point q.
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helppppppppppppp pleaseeeee
Answer:
e = 54
f = 20
d = 106
Step-by-step explanation:
Opposite angles are the same. Also, straight lines always equal 180 degrees.
Hope that this helps!
On Friday, 134 MP3s were downloaded from an online music store. Of the 73 country songs. 52 were downloaded by women. Of the 61 alternative
songs. 47 were downloaded by men.
a. Make a two-way frequency table for the data.
b. What is the joint relative frequency of men who downloaded a country song?
c. What is the marginal relative frequency of people who downloaded an alternative song?
Answer:
13
Step-by-step explanation:
Each boy in a class has 11 pockets and each girl in the class has 13 pockets. How many boys and how many girls are in this class if all 21 students have a total of 251 pockets? Please answer ASAP and please no links.
Answer:10 girls and 11 boys
Step-by-step explanation:
Mattie is twice as old as Pat. Jon is twice as old as Mattie. In 4 years the sum of their ages will be 61. How old is each person?
Answer:
Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.
So (x + 4) + (2x + 4) + (4x + 4) = 61.
7x + 12 = 61 => 7x = 49 => x = 7.
So the answer is
Pat = 7
Mattie = 14
Jon = 28
The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.
If we take Pat's age as = 'x' years,
so, Mattie's age will be = '2x' years.
and then, Jon would be = 2(2x)
= '4x' years.
Now, the sum of their ages after 4 years =
=> (x+4) + (2x+4) + (4x+4) = 61
=> 7x+12 = 61
=> 7x= 61-12
=> 7x= 49
=> x= 49/7
=> x = 7
Therefore, Pat's age is = 7 years.
Mattie's age is = 14 years (2×7).
Jon's age is = 28 years (4×7).
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Which is equal to 100%?
A. 0.001
B. 1/100
c. 0.1
D 1/10
Need ASAP
Answer:
1/100
or we can say 100/1
expand this expression using the distributive property. 4(-2g+4-3t)
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801kg. Write an exponential function that models the
decay of the material.
Answer:
m(t) = 801 * (1/2)^(t/85)
Step-by-step explanation:
m(t) = 801 * (1/2)^(t/85)
m(t) is the mass after t days
difference between -0.4 and 44.4
Answer:
44.8
Step-by-step explanation:
44.4 - (-0.4) = 44.8
L)
express the given in terms os sin x or cos x
sin ( 4pi - x )
how
The value of sin(4π-x) is -sinx
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given that, express the given in terms of sinx or cosx sin (4π-x)
sin(4π-x) = sin(2π+2π-x)
We know, that, sin(a+b) = sina·cosb+sinb·cosa
Here, a = 2π and b = 2π-x
Therefore,
sin(2π+2π-x) = sin2πcos(2π-x)+sin(2π-x)cos2π
Now, sin2π = 0 and cos(2π) = 1
Therefore,
sin2πcos(2π-x)+sin(2π-x)cos2π
= sin(2π-x)
As we know that, sin(2π-x) = -sinx
Hence, sin(4π-x) = -sinx
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Find the area of the shaded region in the above sided figure. Take = 3.14
Step-by-step explanation:
The Radius of the larger semi circle = [tex]\frac{12}{2}[/tex] = [tex]6[/tex][tex]cm[/tex]
Area of the 2 larger semi Circles = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]
= [tex]\frac{3.14X(6)^{2} }{2} X 2[/tex]
= [tex]\frac{113.04}{2} X2[/tex]
= [tex]113.04[/tex] [tex]cm^{2}[/tex]
Radius of the smaller semi circle = [tex]\frac{5}{2} = 2.5cm[/tex]
Area of the smaller semi circle = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]
= [tex]\frac{3,14X(2.5)^{2} }{2} X 2[/tex]
= [tex]196.25[/tex][tex]cm^{2}[/tex]
Combined Area = [tex]113.04 + 196.25[/tex]
= [tex]309 . 29cm^{2}[/tex]
Find the gradients of lines A and B.
Answer: The Gradient of line A and B are
2 and -1
Step-by-step explanation:
For the given two points A(x1, y1) and B(x2, y2)
The gradient of the line AB is y2-y1/x2-x1
So the gradient of line A is
5-1/2-0
2
the gradient of line B is
5-0/0-5
-1
Which function has zeros at x=23 and x=−4?
Answer:
g(x) = a(x - 23)(x + 4)
Step-by-step explanation:
Weren't there possible answer choices to share?
if this function has zeros at 23 and -4, then the function has the following form:
g(x) = a(x - 23)(x + 4)
A laboratory uses liquid nitrogen tanks of two different sizes. The combined volume of 3 large tanks and 2 small tanks is 24 liters. The combined volume of 2 large tanks and 3 small tanks is 21 liters. What is the volume of each size of tank? JUSTIFY YOUR ANSWER.
The size of the large tank is 6 liters and the size of the small tank is 3 liters.
What is the size of each type of tank?The first step is to form a system of equations using the information provided in the question:
3l + 2s = 24 equation 1
2l + 3s = 21 equation 2
Where:
l = volume of the large tank s = volume of the small tankThe elimination method would be used to solve the equations:
Multiply equation 1 by 2 and equation 2 by 3:
6l + 4s = 48 equation 3
6l + 9s = 63 equation 4
Subtract equation 3 from equation 4:
5s = 15
Divide both sides of the equation by 5
s = 15 / 5
s = 3 liters
Substitute for s in equation 1 :
3l + 2(3) = 24
3l + 6 = 24
3l = 24 - 6
3l = 18
l = 18 / 3
l = 6
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How can you solve inequalities explain and give an example?
To Solve the inequalities , we take the variables on a side and the numbers on the other side and then apply mathematical operations to solve it .
What is Inequality ?
The Inequality is defined as a relationship between two values that are not equal to each other .
The method of solving the inequalities is a little different than solving equations.
To solve the inequalities, some simple rules should be followed .
(i) The inequality does not change if any number or variable is added or subtracted from both sides.
Similarly, the value of inequality is not affected if the same number is multiplied on both the sides.
(ii) If the inequality is divided by a negative variable or number on both sides, then the inequality sign gets reversed.
(iii) On dividing inequality by a positive number, there is no change.
For Example : Solve the inequality [tex]4x+6 > 3x+7[/tex] ;
subtracting [tex]3x[/tex] from both the sides ,
we get ;
[tex]x+6 > 7[/tex],
Now subtracting [tex]6[/tex] from both sides of the inequality;
we get ;
[tex]x > 1[/tex] .
Therefore , the solution of the inequality [tex]4x+6 > 3x+7[/tex] is [tex]x > 1[/tex] .
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WILL GIVE BRAINLIEST!!!!
How are you doing today?
(This is for a survey for a class) We are learning percentages.
Answer: Hope This Helps!
Step-by-step explanation:
Im doing good today. And I hope you have a good rest of the day!
HELP HELP HELP I WILL BRAINLIEST U
Answer:
2x+3y-(-4x+3y)=6-12
2x+3y+4x-3y. =-6
6x. = -6
X=-1
no
Answer:
No
Step-by-step explanation:
So, lets go over what we know:
Our x and y values are (0,2)
This means:
x=0
y=2
Lets plug these in for each equations:
2x+3y=6
=
2(0)+3(2)=6
=
0+6=6
=
6=6
So thie first equation is correct.
But we dont know if the second one will check out yet!
Lets plug our values in once more, only on the second equation instead of the first:
-4x+3y=12
=
-4(0)+3(2)=12
0+6=12
6=12
Uh oh...Thats not right.
So this means that (0,2) is not a solution to both equations.
Answer:
No
Hope this helps! :D
Line C passes through the points (-3,-6) and (-1,-12). What is the slope of the line perpendicular to the line C
Answer:
The slope of the line perpendicular to the line C is 1/3.
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-12-(-6))/(-1-(-3))
m=(-12+6)/(-1+3)
m=-6/2
m=-3
perpendicular lines have negative reciprocal slopes.
What is the percent of change if the price changes from $150 to $100? Round to the nearest whole percent if necessary.
Answer:
Percentual change= 33.33% decrease
Step-by-step explanation:
Giving the following information:
Present value (PV)= $150
Future value (FV)= $100
To calculate the percentual change, we need to use the following formula:
Percentual change= [(PV - FV) / PV]*100
Percentual change= [(150 - 100) / 150]*1''
Percentual change= 0.3333*100
Percentual change= 33.33% decrease
Identify whether this angle is acute, obtuse, right, or straight.
an angle that measures about one hundred thirty seven degrees
Acute
Obtuse
Right
Straight
pleaseeee helppp meee!!!
Answer:
x=800
Step-by-step explanation:
first you gonna take 3×x= 3x
then
3×200= 600
(3x+600)=3000
3x=3000-600
3x=2400
3x÷3=2400÷3
x=800
I need help with this question please
The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.
It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)
The square brackets [] is used to mean the end points as shown is inclusive
What is average rate of change in quadratic equation?A quadratic equation is a polynomial of degree two
The average rate of change here is not constant and is usually specified by the two points to which it is measured
For instance using points (-3, 0) and (0, -1) we have
= (y₀ - y₁) / (x₀ - x₁)
= (-1 - 0) / (0 - (-3))
= -1/3
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