Answers
Answer:
Option (a) is correct.
The equation of the line is expressed using expression [tex]\frac{y}{x}=\frac{1}{4}[/tex]
Step-by-step explanation:
Given : The graph shows a line and two similar triangles.
We have to find the expression that finds the equation of line.
Since, given two triangles are similar.
So, Δ ABC ≅ Δ ADE
Thus, There corresponding sides are in same proportion.
[tex]\frac{AC}{AD}=\frac{CB}{DE}= \frac{AB}{BE}[/tex]
Substitute, we get,
[tex]\frac{1}{y}=\frac{4}{x}= \frac{AB}{BE}[/tex]
Rearrange, we have,
[tex]\frac{1}{4}=\frac{y}{x}= \frac{AB}{BE}[/tex]
Also, finding slope of line AE,
Coordinate of B is (4,1) and Coordinate of A is (0,0)
Th equation of line is y = mx + c
Where, m is slope and c is x intercept
Since, [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{1-0}{4-0}[/tex]
Simplify, we have,
[tex]m=\frac{1}{4}[/tex]
And c = 0
Thus, equation of line is[tex]y=\frac{1}{4}x[/tex]
We re-writing we get,
[tex]\frac{y}{x}=\frac{1}{4}[/tex]
Thus, The equation of the line is expressed using expression [tex]\frac{y}{x}=\frac{1}{4}[/tex]
Related Questions
Write a function perfect that determines whether parameter number is perfect number
Answers
Construct a polynomial function of least degree possible using the given information.
Real roots: -2, 1/2 (with multiplicity 2) and (-3, f(-3))=(-3,5)
Answers
As given in the problem, there are two roots: –2 and 1/2. The multiplicity of 1/2 is 2 meaning that the root 1/2 repeats twice. So the function f(x) can be written like this.
f(x) = k• (x – (–2))(x – 1/2)^2 = k•(x + 2)(x – 1/2)^2
We're supposed to find the coefficient k to complete the function.
Given that f(–3) = 5, we can plug –3 in for x and 5 in for f(x).
So 5 = k •(–3 + 2)(–3 – 1/2)^2
5 = k(–1)(–7/2)^2
5 = -k•49/4
Then 5 • 4/49 = -k
Or k = –20/49
So the function with the least degree is
f(x) = –20/49 (x + 2)(x – 1/2)^2.
find the y-intercept of the line represented by 6x-7y=12
Answers
6x - 7y = 12
-7y = -6x + 12
y = 6/7x - 12/7
The y-intercept of the line represented by the equation 6x - 7y = 12 is (0, -12/7). Hope this helps and have a fabulous day!
Find the work done by the force field f(x, y, z) = y + z, x + z, x + y on a particle that moves along the line segment from (1, 0, 0) to (5, 3, 2).
Answers
[tex]\nabla\times\mathbf f(x,y,z)=\mathbf 0[/tex]
which means [tex]\mathbf f[/tex] is conservative. This means there is some scalar potential function [tex]f(x,y,z)[/tex] such that [tex]\nabla f(x,y,z)=\mathbf f(x,y,z)[/tex]. If we can find such a function, then we only need to evaluate the difference of [tex]f(5,3,2)[/tex] and [tex]f(1,0,0)[/tex] (because the gradient theorem holds in this case).
We're looking for a function [tex]f(x,y,z)[/tex] that satisfies
[tex]\dfrac{\partial f}{\partial x}=y+z[/tex]
[tex]\dfrac{\partial f}{\partial y}=x+z[/tex]
[tex]\dfrac{\partial f}{\partial z}=x+y[/tex]
Integrate the first equation with respect to [tex]x[/tex] to get
[tex]f(x,y,z)=xy+xz+g(y,z)[/tex]
Differentiate with respect to [tex]y[/tex], then we must have
[tex]\dfrac{\partial f}{\partial y}=x+z=x+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=z[/tex]
[tex]\implies g(y,z)=yz+h(z)[/tex]
[tex]\implies f(x,y,z)=xy+xz+yz+h(z)[/tex]
Differentiate with respect to [tex]z[/tex], and we have to have
[tex]\dfrac{\partial f}{\partial z}=x+y=x+y+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]
[tex]\implies h(z)=C[/tex]
[tex]\implies f(x,y,z)=xy+xz+yz+C[/tex]
Now, by the gradient theorem, we have
[tex]\text{work}=\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(5,3,2)-f(1,0,0)=31[/tex]
where [tex]\mathcal C[/tex] is the line segment.
Final Answer:
Word done = 31 units
Explanation:
To find the work done by a force field [tex]$\mathbf{F}(x, y, z)$[/tex] on a particle moving along a path, we can use the line integral of the force field along that path.
First, we need to define the force field [tex]$\mathbf{F}(x, y, z)$[/tex] and the parametric equations for the line segment.
Given the force field
[tex]$$\mathbf{F}(x, y, z) = \langle y + z, x + z, x + y \rangle,$$[/tex]
we have the following components:
[tex]F_x &= y + z, \\\\F_y &= x + z, \\\\F_z &= x + y.[/tex]
Now, let's find the parametrization of the line segment from the point (1,0,0) to the point (5,3,2). We can define a vector [tex]$\mathbf{r}(t)$[/tex] that describes this line segment by
[tex]$$\mathbf{r}(t) = \mathbf{r_0} + t(\mathbf{r_1} - \mathbf{r_0}),$$[/tex]
where [tex]$\mathbf{r_0} = \langle 1, 0, 0 \rangle$[/tex] is the starting point, [tex]$\mathbf{r_1} = \langle 5, 3, 2 \rangle$[/tex] is the ending point, and t is a parameter that goes from 0 to 1.
So we have
[tex]\mathbf{r}(t) &= \langle 1, 0, 0 \rangle + t(\langle 5, 3, 2 \rangle - \langle 1, 0, 0 \rangle) \\\\ &= \langle 1, 0, 0 \rangle + t\langle 4, 3, 2 \rangle \\\\ &= \langle 1 + 4t, 3t, 2t \rangle.[/tex]
From the parametric equation, we have the components:
[tex]x(t) &= 1 + 4t, \\\\y(t) &= 3t, \\\\z(t) &= 2t.[/tex]
The line integral of the force field along the path can be computed by
[tex]$$W = \int_C \mathbf{F} \cdot d\mathbf{r},$$[/tex]
where [tex]$d\mathbf{r}$[/tex] is the differential element along the path C, and the dot product represents the scalar product of the force field and the differential path element.
We can express [tex]$d\mathbf{r}$[/tex] in terms of t as
[tex]$$d\mathbf{r} = \mathbf{r}'(t) dt = \langle \frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt} \rangle dt = \langle 4, 3, 2 \rangle dt.$$[/tex]
Then the work done is
[tex]W &= \int_{t=0}^{t=1} \mathbf{F}(x(t), y(t), z(t)) \cdot \mathbf{r}'(t) dt \\\\ &= \int_{0}^{1} \langle 3t + 2t, 1 + 4t + 2t, 1 + 4t + 3t \rangle \cdot \langle 4, 3, 2 \rangle dt \\\\ &= \int_{0}^{1} [(5t)(4) + (6t + 1)(3) + (7t + 1)(2)] dt \\\\ &= \int_{0}^{1} [20t + 18t + 3 + 14t + 2] dt \\\\ &= \int_{0}^{1} [52t + 5] dt \\\\ &= [26t^2 + 5t]_{0}^{1} \\\\ &= 26(1)^2 + 5(1) - (26(0)^2 + 5(0)) \\\\ &= 26 + 5 \\\\ &= 31.[/tex]
So, the work done by the force field [tex]$\mathbf{F}(x, y, z)$[/tex] on the particle as it moves along the line segment from (1, 0, 0) to (5, 3, 2) is 31 units of work.
Rya uses 4 gallons of gas ro drive 120 miles on the highway. If she gets that samw gas mileage, how many miles can she drive on 1 gallon of gas?
Answers
so Rya gets 30 miles off of 1 gallon of gas
Write an equation of the line that passes through (0, 5) and (−1.5, 1)
Answers
STEP-BY-STEP SOLUTION:
Let's establish the formula we will be using to achieve the equation of the line.
y - y1 = m ( x - x1 )
m = gradient / slope of line
To use the previous formula, we will need to first find the gradient ( m ) using the below formula. We will be substituting the values of the points given in the problem into this formula.
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( 5 - 1 ) / ( 0 - ( - 1.5 ) )
m = ( 5 - 1 ) / ( 0 + 1.5 )
m = 4 / 1.5
m = 8 / 3
Now we will substitute the value of ( m ) from above into the formula for the line. We will also be substituting the values of one of the given points into the formula. In this example, we will be using the point ( 0, 5 ).
y - y1 = m ( x - x1 )
y - 5 = ( 8 / 3 ) ( x - 0 )
y - 5 = ( 8 / 3 )x
y = ( 8 / 3 )x + 5
FINAL ANSWER:
The equation of the line is:
y = ( 8 / 3 )x + 5
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The equation of the line that passes through (0, 5) and (−1.5, 1) is y = 8/3 x + 5
The equation can be represented as follows:
y = mx + b
where
m = slope
b = y-intercept
lets find the slope
(0, 5) (−1.5, 1)
m = 1 - 5 / -1.5 - 0 = - 4 / -1.5 ≈ 8 / 3
we multiplied the numerator and denominator by 2
b = 5, b is the value of y when x = 0.
Therefore, the equation will be as follows:
y = 8/3 x + 5
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Find the value of c for which the line 3x +cy= 5 is parallel to the y axis,
Answers
and our sharpest value for that, is our very good friend Mr Zero, c = 0, cy = 0y = 0.
check the picture below.
Veronique and Lily compare their investment accounts to see how much they will have in the accounts after seven years. They substitute their values shown below into the compound interest formula. Compound Interest Accounts Name Principal Interest Rate Number of Years Compounded Veronique $1,000 5% 7 Once a year Lily $1,800 9% 7 Once a year mc017-1.jpg Which pair of equations would correctly calculate their compound interests? Veronique: mc017-2.jpg, Lily: mc017-3.jpg Veronique: mc017-4.jpg, Lily: mc017-5.jpg Veronique: mc017-6.jpg, Lily: mc017-7.jpg
Answers
Answer:
A
Step-by-step explanation:
The pair of equations that would correctly calculate their compound interests are:
Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10
Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.
What is the compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n)^(nt)
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
For Veronique, we have:
A = 1000(1 + 0.05/1)⁷ = $1,407.10
For Lily, we have:
A = 1800(1 + 0.09/1)⁷ = $3290.47
To calculate the compound interest for each account, we subtract the principal amount from the final amount:
For Veronique:
Interest = A - P = $1,407.10 - $1,000 = $407.10
For Lily:
Interest = A - P = $3,290.47 - $1,800 = $1,490.47
Therefore, the pair of equations that would correctly calculate their compound interests are:
Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10
Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.
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Scott puts some sports stickers in rows. He makes 6 rows with 5 stickers in each row. If he puts the same number of stickers in 5 equal rows, how many stickers would be in each row?
Answers
Answer:
6 stickers.
Step-by-step explanation:
We have been given that Scott makes 6 rows with 5 stickers in each row.
The total number of stickers in 6 rows would be:
[tex]\text{The total number of stickers}=6\times 5[/tex]
[tex]\text{The total number of stickers}=30[/tex]
Therefore, there are 30 stickers in 6 rows.
We need to find the number of stickers in 5 rows having the same number of stickers.
Since there are 30 stickers in total, so the number of stickers in each row would be 30 stickers by 5 rows.
[tex]\text{The number of stickers in each row}=\frac{30}{5}[/tex]
[tex]\text{The number of stickers in each row}=6[/tex]
Therefore, there would be 6 stickers in each row.
Curve passes through the point (0,8)(0,8) and has the property that the slope of the curve at every point pp is four-times the y-coordinate. what is the equation of the curve
Answers
Slope of tangent line at a given point = value of derivative of function at that point.
Thus, dy/dx = derivative = 4y
Thus, dy/dx = 4y. Rearrange this with all y on one side and all x on the other:
dy
--- = 4dx
y
Integrating both sides, we get ln|y| = 4x + ln C, or ln|y| - ln C = 4x
|y|
Then ln -------- =4x. This can be written as an exponential function:
C
|y|
--- = e^(4x). Thus, |y| = C*e^(4x). Given that this curve passes thru (0,8),
C
8 = C*e^0, so C = 8. Then the function question is y = 8e^(4x).
If total liabilities are $200,000 and total assets are $325,000, owner's equity would be: 2)
a. $525,000
b. $200,000
c. $125,000
d. impossible to determine from the given data
Answers
$325,000-$20000 (of liabilites) thus= $125,000
6 tractors take 10 days to collect the harvest. How long would it take 15 tractors to do the same amount of work
Answers
bc 6/10 equals .375, then 15/ .375 is 40, divided by 10 is 4?
A line has a slope of between the points (10,5) and (16,n).
What is the value of n?
8
2
10
16
6
Answers
Any way, I can show you how to calculate the answer given a generic value of the slope.
Assuming that the slope values m, you can use the formula:
m = rise / run = change in y / change in x
=> m = (n - 5) / (16 - 10)
=> n - 5 = m (16 - 10)
=> n - 5 = 6m
=> n = 6m + 5
Now I am going to calculate the value of n for several values of the slope (m):
m n = 6m + 5 answer
1/2 n = 6(0.5) + 5 = 8 the first option
-1/2 n = 6(-0.5) + 5 = 2 the second option
5/6 n = 6(5/6) + 5 = 10 the third option
11/6 n=6(11/6) + 5 = 16 the fourth option
1/6 n = 6(1/6) + 5 = 6 the fifth option
Now you have the procedure and the answer for several values of the slope, so you do not have problems to answer this question.
Find the volume of a sphere with a diameter 40 cm in length. Approximate pi as 3.14 and round your answer to the nearest tenth.
Answers
now lets sub
V = 4/3 * 3.14 * 20^3
V = 4/3 * 3.14 * 8000
V = 32,000/3 * 3.14
V = 100480/3
V = 33493.3 cm^3 <===
You and your frend step into identical row-boats. you notice that your boat sinks into the water twice as far as your friends. what can you say about your friend's weight compared with yours? your friend weighs twice as much as you your friend weighs the same as you your friend weighs half as much as you your friend weighs one fourth your weight
Answers
The correct answer would be: "your friend weighs half as much as you"
Hope this Helps, and May the Force Be With You!
-Jabba
The perimeter of a rectangle is 36 yards. The width is 18 yards less than twice the length. Find the length and the width of the rectangle
Answers
Here W = 2L-18 and 2L + 2W = 36. Subst. 2L-18 for W:
2L + 2(2L-18) = 36. Then 6L - 36 = 36, and 6L = 72. Therefore, L = 12 yd.
W = 2(12 yd) - 18 yd = 24 yd - 18 yd = 6 yd
The rectangle's dimensions are 6 yd (width) by 12 yd (length).
Note that P = 2(6) + 2(12) = 36, as required.
The length of the rectangle is 12 yards and the width is 6 yards. The problem is solved with algebra using the formulas for the perimeter of a rectangle and given relation between the length and width.
Explanation:This problem involves the use of algebra in solving geometrical problems. The question provides information about the perimeter and the relationship of length to width using algebraic expressions. To find the length and the width, we can use the formulas for the perimeter of a rectangle (P=2L + 2W) and the given width (W=2L-18).
Let L represent the length. Then, 2L+W=18 represents the width. Setting 2L + 2W equal to the given perimeter of 36, we get 2L + 2(2L - 18) = 36.
Solving this equation gives: L = 12, and substituting L=12 into W=2L - 18, we get: W=6. Hence, the length is 12 yards and the width is 6 yards.
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What is 0.69 expressed as a fraction in simplest form?
Answers
––
100
would be the answer
what are the term in the expression 4x^2-2x-x^2+3x+1
Answers
Harry worked seven hours last week this is 1/3 as many hours as Aiden worked how many hours did Aidan work
Answers
Multiply 7 by 3.
7 * 3 = 21
Answer: 21 hours.
Pretty much, if 7 is 1/3 of how many hours Aiden worked, then all you do is multiply 7 by 3.
Hope that helps!
Factor the following
Answers
This can be rewritten as:
(x + 2)(x + 2)
Multiply everything in the second parenthesis by x.
x^2 + 2x
Multiply everything in the second parenthesis by 2.
2x + 4
Add these equations together.
x^2 + 2x + 2x + 4
Combine like terms.
x^2 + 4x + 4
Hope this helps!
Suppose investment of $6200 doubles in value every 13 years how much is the ivestment worth after 78 years
Answers
The investment will be doubled 6 times over 78 years
So the investment worth
A=6,200×2^(6)=396,800
Hope it helps!
A vendor sold 72 hotdogs and hamburgers during a football game if the ratio of hotdogs to hamburgers sold was 8:1 how many of each food did vendor sell?
Answers
What's the answer? I need help. Thank you :)
Answers
= 27/4 / 3/4 = 27/4 * 4/3 = 27 /3 = $9 Answer
... Divide the cost by the weight.
... The quotient is the cost per pound of nuts.
... Whichever column you choose, the answer is always the same. So pick the column with the fractions that you think will be easiest to divide.
The whole purpose of this question is to practice dividing mixed numbers and fractions. It actually has nothing to do with pecans. It could be the same table for pistachios, apples, or M & M's.
A homeowner is draining her swimming pool. The volume of water in the pool changes by −12 gallons every minute.
What is the change in volume over 60 minutes?
Answers
To answer this question, multiply -12 gallons / minute by 60 minutes.
That comes to -720 gallons, the volume by which the water in the pool decreases in an hour.
So, water decreases by 12 gallons EVERY minute.
How much water will decrease in 60 minutes?
[tex]12*60=720[/tex] gallons
So, the volume changes by 720 gallons in 60 minutes.
ANSWER: Volume decreases 720 gallons in 60 minutes.
the line L1 has equation 2x + y = 8. The line L2 passes through the point A ( 7, 4 ) and is perpendicular to L1 . Find the equation of L2.
Answers
y=mx+c
m= gradient
c= y intercept
first find what is the gradient of L1. In order to get the gradient make y the subject. thus,
2x+y=8
y=-2x+8
thus, the gradient of L1 is -2.
The question states that L2 is perpendicular to L1, thus the gradient of L2 is reciprocal to gradient of L1.
Thus, gradient of L2 will be
m= 1/2
In order for the gradient to be reciprocal, it needs to be perpendicular.
thus so far the equation of L2 is
y= 1/2x+c
Now the question states that is passes through A(7,4). Thus you need to sub in x=7 and y=4 into equation of L2 to find what is the y intercept.
4= 1/2(4)+c
c=2
thus the equation of L2 is
y=1/2x+2
Answer: [tex]x-2y+7=0[/tex]
Step-by-step explanation:
Given : The line[tex]L_1[/tex] has equation [tex]2x + y = 8[/tex]
In intercept form : [tex]y =-2x+8[/tex]
The slope of [tex]L_1[/tex] =-2 [in intercept form equation of line [tex]y =mx+c[/tex], m is slope ]
Let p be slope of [tex]L_2[/tex]
We know that when two lines are perpendicular then the product of their slopes is -1.
[tex]\Rightarrow\ -2\times p=-1\\\\\Rightarrow\ p=\dfrac{1}{2}[/tex]
The equation of line having slope 'm' and passing through (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Then , equation of line [tex]L_2[/tex] will be :-
[tex](y-7)=\dfrac{1}{2}(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7[/tex]
You can buy 4 pounds of peaches for $5.96. What do 4 1/2 pounds of peaches cost?
Answers
Hopefully not too confusing lol
In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. 2a, 2a2b, 2a3b2, 2a4b3. . .
Answers
Answer:
a). it is an Infinite Sequence.
b). This sequence is Geometric Progression.
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Step-by-step explanation:
Given: A Sequence 2a , 2a²b , 2a³b² , [tex]2a^4b^3[/tex]
To find: a). Given Sequence is finite or infinite
b). Pattern of the sequence
c). Sixth term
a). Since, there is no detail about no. of terms of the sequence.
Therefore, It implies it is an Infinite Sequence.
b). Given 1st term = 2a , 2nd term = 2a²b , 3rd term = 2a³b²
First we find the difference of 1st and 2nd term
d = 2a²b - 2a ⇒ d = 2a (ab - 1)
Now, Difference of 2nd and 3rd term,
d = 2a³b² - 2a²b = 2a²b (ab - 1)
So, This Sequence is not a Arthematic Progression.
Now, we find the ratio of 2nd term to 1st term,
[tex]r\:=\:\frac{2a^2b}{2a}\,=\,ab[/tex]
Ratio of 3rd term to 2nd term,
[tex]r\:=\:\frac{2a^3b^2}{2a^2b}\,=\,ab[/tex]
Since, the ratio is common.
This sequence is Geometric Progression.
So, Pattern is next term of this sequence has 1 more in power of a and b
⇒ [tex]nth\,term\,of\,this\,GP\,=\,2a^{n}b^{n-1}[/tex]
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^{6}b^{6-1}[/tex]
[tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Therfore, a). it is an Infinite Sequence.
b). This sequence is Geometric Progression.
c). [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]
Stu is laying brick down to make a patio. He plans for the patio to be 12.5 feet by 18.3 feet. He orders enough brick for 247 square feet. Which statement about the amount of brick is correct?
Answers
Answer:
Stu estimated correctly by rounding up.
He ordered enough brick.
The exact area is [tex]228.75[/tex] square feet
Step-by-step explanation:
we know that
the area of the patio is equal to
[tex]A=bh[/tex]
In this problem we have
[tex]b=12.5\ ft, h=18.3\ ft[/tex]
substitute in the formula
[tex]A=12.5*18.3=228.75\ ft^{2}[/tex]
[tex]228.75\ ft^{2}< 247\ ft^{2}[/tex]
the sum of three consecutive integers if the last integer is z.
a.) 3z+3
b.) 3z+6
c.)3z-3
d.)3z
Answers
The sum is therefore
(z-2)+(z-1)+z=3z-3.
The sum of three consecutive integers where the last integer is z is 3z - 3.
Explanation:The sum of three consecutive integers can be derived using the concept of arithmetic series. For instance, if z represents the last of the three consecutive integers, we know that the numerals preceding it are z-1 and z-2. Hence, the sum of these three integers would be (z-2) + (z-1) + z.
Simplifying this, we get 3z - 3 which corresponds to option c.)3z-3 in the question's list.
Remember, an important aspect of sequences and series is that the numbers are arranged in a specific order.
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Michael did 45 pushups in 3 minutes. Michelle did 36 pushups in 2 minutes.Who did pushups at a faster rate? How much faster was that person? Answer with supporting work.
Answers
Micheal: 45/3 equals 15 push ups per minute
Michelle: 36/2 equals 18 push ups per minute