Answer:
[tex]y = 250x + 4000[/tex]
[tex]y = 400x + 400[/tex]
The slope of the second option(financing) is greater than the first option(leasing) meaning that the monthly payments for the financing option are greater than the monthly payments of leasing.
The y-intercept of the first option(leasing) is greater than the y-intercept of the second option(financing) meaning that the initial payment of the first option is greater than the initial payment of the second option.
Step-by-step explanation:
The general slope-intercept form is given by
[tex]y = mx + b[/tex]
First option leasing:
The given equation is
[tex]250x - y + 4000 = 0[/tex]
We need to convert this equation into the slope-intercept form.
[tex]y = 250x + 4000[/tex]
where x represents the number of months of ownership and y represents the total amount paid for the car after ‘x' months.
The slope of the equation is 250 which represents the rate at which the value of y is increasing with respect to x.
When x = 0 then y = 4000 which represents the initial payment.
Second option financing:
We are given two points,
[tex](x_1, y_1) = (0,400)[/tex]
[tex](x_2, y_2) = (10,4400)[/tex]
The slope of the equation(m) is given by
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{4400 - 400}{10 - 0} \\\\m = \frac{4000}{10} \\\\m = 400[/tex]
To find the value of the y-intercept (b), substitute any of the given point into the slope intercept equation
[tex]y = mx + b \\\\y = 400x + b \\\\400 = 400(0) + b \\\\b = 400[/tex]
So the equation of the second option is
[tex]y = 400x + 400[/tex]
The slope of the equation is 400 which represents the rate at which the value of y is increasing with respect to x.
When x = 0 then y = 400 which represents the initial payment.
Comparison in terms of slope:
The slope of first option leasing = 250
The slope of second option financing = 400
The slope of the second option(financing) is greater than the first option(leasing) meaning that the monthly payments for the financing option are greater than the monthly payments of leasing.
Comparison in terms of y-intercept:
The y-intercept of first option leasing = 4000
The y-intercept of second option financing = 400
The y-intercept of the first option(leasing) is greater than the y-intercept of the second option(financing) meaning that the initial payment of the first option is greater than the initial payment of the second option.
geometry question please help
Answer:
see below
Step-by-step explanation:
Alright, geometric probability.
We need to find
the area of the rectanglethe area of the equilateral triangle the area of the square the area of the part of the circle that does not include the squareand the area of the part of the rectangle that does not include the square, circle, or triangle.To find those, we need to find the areas of:
the outer rectanglethe circlethe equilateral trianglethe squareLet's start off with the easiest figure. The circle.
The circle has a radius of 10. Therefore, its area is is π[tex]r^2[/tex]. 100π is roughly 314.159265.
The circle has an area of around 314.159265.
Half of the diagonal of the square is 10m. That means that the full diagonal of the square is 20 m.
Formula for side of square using diagonal:
a = q / √2
20/√2 = 14.142135623731
The area of a square is a^2
14.142135623731^2= 200
The area of the square is 200 m^2. (28)
Using this, and the area of the circle, we can find the area of the part of the circle that does not include the square.
314.159265 - 200= 114.159265
The area of the part of the circle that does not include the square is 114.159265.
Now, the most important calculation (because it lets us find the total area of the rectangle); the equiangular triangle.
The height of this triangle is 30m. Therefore, the area is 519.6152422706632.
The area of the equiangular triangle is 519.6152422706632.
The side length of the equiangular triangle is 34.64101615137755.
The area of the rectangle= l times w.
l = 34.64101615137755
w= 30
30 times 34.64101615137755= 1039.23048454133
The total area is 1039.23048454133.
Now that we have the denominator of our fraction (total area), lets go back to our questions.
We need to find
the area of the equilateral triangle the area of the square the area of the part of the circle that does not include the squareand the area of the part of the rectangle that does not include the square, circle, or triangle.The area of the equilateral triangle = 519.6152422706632
519.6152422706632/1039.23048454133 = .5
The geometric probability that a point chosen randomly inside the rectangle is inside the equilateral triangle is .5
The area of the square = 200
200/1039.23048454133 = 0.19245008973
The geometric probability that a point chosen randomly inside the rectangle is inside the square is 0.19245008973
The area of the part of the circle that doesn't include the square: 114.159265
114.159265/1039.23048454133= 0.10984980396
The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle that doesn't include the square is 0.10984980396
The part of the rectangle that doesn't include the square, circle or triangle.
Area of triangle = 519.6152422706632
(The triangle contains the circle and square).
1039.23048454133- 519.6152422706632 = 519.61524227067
519.61524227067 /1039.23048454133 = 0.5
The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle doesn't include the square, circle, or triangle is 0.5
Hope this helped! Let me know if I made an errors, or if my answers are incorrect.
Simplify: |3r−15| if r<5
Answer:
[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]
Step-by-step explanation:
Given that:
r < 5
To simplify:
|3r−15|
Solution:
First of all, let us learn about Modulus function:
[tex]f(x) =|x| =\left \{ {x, \ if\ {x>0} \atop -x\ if\ {x<0}} \right.[/tex]
In other words, we can say:
Modulus function has a role to make its contents positive.
If the contents are positive, the result will be equal to its contents only.
If the contents are negative, it will add a negative sign to the contents to make it positive.
Now, let us consider the given condition:
[tex]r < 5[/tex]
Multiply both sides with 3. (As 3 is a positive number, the equality sign will not change.)
[tex]3r < 15[/tex]
Subtracting 15 from both sides:
[tex]3r-15<15-15\\\Rightarrow 3r-15<0[/tex]
Now, we know that [tex]3r-15<0[/tex], let us use the definition of Modulus function.
Add a negative sign to the contents because the contents are already negative.
[tex]\\\Rightarrow |3r-15| = -(3r-15)\\\Rightarrow -3r+15[/tex]
So, the answer is:
[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]
Use the graph to evaluate the function below for specific inputs and outputs.
Answer:
y = G(x) = 6, when x = -4
y = G(x) = -2, when x = 3
Step-by-step explanation:
From the attached graph tracing the first point to the graph and then to x axis.
y = G(x) = 6
as shown on the attachment(by the thick line)
y = G(x) = 6, when x = -4
From the attached graph tracing the second point to the graph and then to x axis.
y = G(x) = -2
as shown on the attachment(by the thin line)
y = G(x) = -2, when x = 3
A taut string of length 10 inches is plucked at the center. The vibration travels along the string at a constant rate of c inches per millisecond in both directions. If x represents the position on the string from the left-most end, so that 0≤x≤10, which of the following equations can be used to find the location x of the vibration after 0.3 milliseconds? A. | x -5 | =0. 3 B. ∣cx−5∣=0.3 C. | x -0.3 | = 5 D. | x - 10 | =0.3c
Answer:
The correct option is
[tex]A. \ \dfrac{1}{c} \times \left | x - 5 \right | = 0.3[/tex]
Step-by-step explanation:
The parameters given are;
The length of the string = 10 inches
The speed or rate of travel of the wave = c inches per millisecond
The position on the string from the left-most end = x
The time duration of motion of the vibration to reach x= 0.3 milliseconds
The distance covered = Speed × Time = c×0.3
Given that the string is plucked at the middle, with the vibration travelling in both directions, the point after 0.3 millisecond is x where we have;
The location on the string where it is plucked = center of the string = 10/2 = 5 inches
Distance from point of the string being plucked (the center of the string) to the left-most end = 5 inches
Therefore, on the left side of the center of the string we have;
The distance from the location of the vibration x (measured from the left most end) to the center of the string = 5 - x = -(x -5)
On the right side of the center, the distance from x is -(5 - x) = x - 5
Therefore, the the equation that can be used to find the location of the vibration after 0.3 milliseconds is [tex]\dfrac{1}{c} \times \left | x - 5 \right | = 0.3[/tex] or [tex]\left | x - 5 \right | = 0.3 \times c[/tex] which gives the correct option as A
Nzjksjsjdidnxnskusxh
Answer:
99cm^2
Step-by-step explanation:
Look at pic
HELP ME ASAP Check all that apply. If cos0=15/17 , than: A. sec0 = 17/15 B. csc0 = 17/15 C. sin0 = 15/8 D. tan0 = 8/15
Answer:
D. tan 0 = 8/15 and A. sec 0 = 17/15
Step-by-step explanation:
Cos 0 = adjacent/ hypotenus
Adj = 15 and Hyp =17
Using pythagoras theory
Opp^2 = 17^2 - 15^2
Opp^2 = 289 - 225
Opp^2 = 64
Therefore Opp = 8 which is the square root of 64
tan 0 = opp/adj
tan 0 = 8/15
Sec 0 is the multiplicative inverse of cos 0
6,666,666×666,666 /1+2+3+4+5+6+5+4+3+2+1 − 777,777×777,777/1+2+3+4+5+6+7+6+5+4+3+2+1
Answer:
111111 [tex]\times[/tex] 1111110 is the simple expression.
Step-by-step explanation:
The expression to be solved:
[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}[/tex]
First of all, let us solve the first term:
[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111[/tex]
Now, the right term:
[tex]\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111[/tex]
So, the expression to be solved becomes:
[tex]1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110[/tex]
Q2:
Which expression is equivalent to 4(x + 1) – 7(x + 3)?
A
11x + 25
B
11x – 17
C
–3x – 17
D
–3x + 25
Answer:
The expression equivalent to the given equation is -3x - 17
Step-by-step explanation:
4(x + 1) - 7(x + 3)
Distribute 4 to (x + 1) and distribute 7 to (x + 3).
4x + 4 - 7x - 21
Combine like terms.
-3x - 17
If 3x-5=10x+9, what is 4(x+7)?
Answer: not sure
Step-by-step explanation:
Answer:
Hey there!
3x-5=10x+9
-5=7x+9
-14=7x
x=-2
4(x+7)
4(-2+7)
4(5)
20
Hope this helps :)
F(x)3x+5/x what is f(a+2)
Answer:
3a+6+5/(a+2)
Step-by-step explanation:
To do this you replace x with a+2, meaning that 3x+5/x turns into 3(a+2)+5/a+2. Simplified this is 3a+6+5/(a+2)
Some one HELP PLEASE
THE ANSWER IS NOT 40,5 20 -20
Answer:
x = 20
Step-by-step explanation:
If AE is a bisector then it divides the angle in half
BAE = EAC
x+30 = 3x-10
Subtract x from each side
30 = 2x-10
Add 10 to each side
40 = 2x
Divide by 2
40/2 =2x/2
20 =x
A triangle is drawn on a coordinate plane. Point A is at (2,6), Point B is at (4,10), and Point C is at (8,5). What is the midpoint of side AB
?
Answer:
I(3,8)
Step-by-step explanation:
to answer this question we must use this relation :
let I be our midpoint I([tex]\frac{2+4}{2}[/tex];[tex]\frac{6+10}{2}[/tex])I(3,8)Combine the like terms to create an equivalent expression: -n+(-3)+3n+5
Answer: 2n+2
Step-by-step explanation:
1. Remove the parentheses
-n-3+3n+5
2. Collect like terms
2n-3+5
3. Calculate the sum
2n+2
√12 a rational number or an integer?
Answer:
Square root of 12 is a interfering because it isn’t a perfect square.
Answer:
It is an integer.
Step-by-step explanation:
Integers are all types of numbers may it be negative or positive but rational numbers are positive and negative fractions or decimals. So √12 is an integer.
Hope this helps.
Match each power of a power expression with its simplified expression.
Answer:
(-4^9)^2 = -4^18
(4^6)^-3 = 1/4^18
(4^0)^-9 = 4^0
(4^-3)^-3 = 4^9
Step-by-step explanation:
Here, we want to match what we have on the left with the expressions on the right.
(-4^9)^2
= -4^18
(4^6)^-3
= 4^-18 = 1/4^18 according to laws of indices
(4^0)^-9 = 4^0
(4^-3)^-3
= 4^9
Answer:
(-4^9)^2 = -4^18
(4^6)^-3 = 1/4^18
(4^0)^-9 = 4^0
(4^-3)^-3 = 4^9
Step-by-step explanation:
HELP ME PLEASE PLEASE IM BEGGING
Answer:
The solution is the triplet: (a, b, c) = (-3, 0, 0)
Step-by-step explanation:
Let's start with the second equation, and solving for "a":
a - b = -3
a = b - 3
Now replace this expression for a in the third equation:
2 a + b = -6
2 (b - 3) +b = -6
2 b - 6 +b = -6
3 b = -6 +6
3 b = 0
b = 0
So if b = 0 then a = 0 - 3 = -3
now we can replace a= -3, and b = 0 in the first equation and solve for c:
2 a - b + c = -6
2 ( -3) - 0 + c = -6
-6+ c = -6
c = -6 + 6
c = 0
Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)
6 • 14 - (9 + 8) 2 =
Answer:
50
Step-by-step explanation:
For this question you would follow the BIDMAS rule - (Brackets, Indices, Division, Multiplication, Addition, Subtraction.)
The first thing in this question you need to solve it (9 + 8)
we do this because, when we follow BIDMAS, the first rule is brackets
so, 9 + 8 = 17
The second step is to multiply, as this rule is second,
so, 17 x 2 = 34
Our final step is to solve the last bit, which is 6 x 14
and we know that 6 x 14 = 84
So now that we have 84 and 34, we need to subtract the two numbers as shown,
84 - 34 = 50
And this is how you get the answer 50
i hope this has helped you, please comment if you did not understand it and i will explain it in another way : )
Use pemdas
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Do parenthesis first: (9+8)=17
6x14-17x2
Then do multiplication
6x14=84 17x2=34
Now do subtraction
84-34=50
Therefore your answer is 50
Please help ! ;v; A coordinate plane is shown. A line passes through the point (-4,1) and through the y-axis at 4. What is the y-intercept of the line shown?
Answer:
(0, 4)
Step-by-step explanation:
The y-intercept is where the graph crosses the y-axis when x = 0. Since you are given the graph, you can see that when x = 0, the graph crosses y = 4, so our y-int is (0, 4).
Solve the inequality 5(2h + 8) < 60
Step-by-step explanation:
5(2h+8) <60
10h +40< 60
10h + 40-40 < 60-40
10h < 20
10h/10 < 20/10
h < 2
Given: JP = KP; PX = PY Prove: ΔPYJ ≅ ΔPXK Triangles P Y J and P X K overlap and intersect at point Z. Point X of triangle P X K is on side J P of triangle P Y J. Point Y of triangle P Y J is on side K P of triangle P X K. Which best describes the missing reasons? ♣: ♦:
Answer:
Which best describes the missing reasons?
♣:reflexive property
♦: SAS
Step-by-step explanation:
I just did it.
The missing reasons is ♣: reflexive property
We have given that,
JP = KP; PX = PY
ΔPYJ ≅ ΔPXK Triangles P Y J and P X K overlap and intersect at point Z. Point X of triangle P X K is on side J P of triangle P Y J. Point Y of triangle P Y J is on side K P of triangle P X K.
We have to determine which best describes the missing reasons.
What is the reflexive property?
The reflexive property of equality states that a number is always equal to itself. Reflexive property of equality. If a is a number, then. a = a. a=a.
♣: reflexive property
♦: SAS
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A hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters did he descend? Ju Chan answered the question by writing the following: 4(−15) meters = −60 meters. Which word in the problem indicates that a negative number should be used?
Answer:
"descends"
Step-by-step explanation:
(just had the same question).
Solve the system of equations by substituion,
-5x + y = 3
7.5x - 1.5y = 3
helpppppp pleaseeeeee
Answer:
HL, the two triangles both share a side and have right angles.
Step-by-step explanation:
Congruent Triangles - Hypotenuse and leg of a right triangle. (HL) Definition: Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. If, in two right triangles the hypotenuse and one leg are equal, then the triangles are congruent.
What does x(x - 2) equal?
Answer:
x^2 - 2x
Step-by-step explanation:
Distribute the x to every term in the parenthesis.
Answer:
x^2 -2x
Step-by-step explanation:
x(x - 2)
Distribute
x*x - 2*x
x^2 -2x
i mark brainliest for all my questions that are answered right :) thx for helping me
Determine the solution to f(x) = g(x) using the following system of equations: (5 points) f(x) = 3x − 23 g(x) = −4.5x + 7
Answer:
(The solution is (4, -11).
Step-by-stp explanation:
Let f(x) = g(x) = y:
y = 3x − 23
y = -4.5x + 7 Subtract the second equation from the first to eliminate y:
0 = 7.5x - 30
7.5x = 30
x = 4
Plug this into the first equation:
y = 3(4) - 23
y = -11.
Approximate 5.7255 to the nearest thousandth
Answer:
5.726
Step-by-step explanation:
First, find the thousandths place value. Note the place values:
5 (one's place value)
.
7 (tenth's place value)
2 (hundredth's place value)
5 (thousandth's place value)
5 (ten thousandth's place value)
Find the thousandths place value. Look at the number located directly next to it (ten thousandth's place value).
Note that:
If the number is 4 or less, round down.If the number is 5 or greater, round up.Since the number is 5, round up.
5.7255 rounded to the nearest thousandths place value is 5.726
~
(4x + 9)/2 1/3= 3x/0.5
The value of x is 9/10.
The given equation is [tex]\frac{4x+9}{2\frac{1}{3} } =\frac{3x}{0.5}[/tex].
What is an equation?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
Now, [tex]\frac{4x+9}{\frac{7}{3} } =\frac{3x}{\frac{1}{2} }[/tex]
⇒(4x+9)×3/7=3x×2
⇒12x+27=42x
⇒30x=27
⇒x=9/10
Therefore, the value of x is 9/10.
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Help!!!!! please!!!!!
With steps , please .
Answer:
Θ=15
Step-by-step explanation:
AD=DC so triangle BCD is isosceles, so angle DBC = angle BCD = Θ
So angle BDC=180-Θ-Θ=180-2Θ
angle BDE = 180- angle BDC = 180-180+2Θ=2Θ
in triangle BDE all angles must add up to 180
angle BED= 180- angle BEA=180-90=90
so
90+4Θ+2Θ=180
90=6Θ
Θ=15