Answer:
y = -1.6x + 4
Step-by-step explanation:
y = mx + b
y = (-1.6)x + (4)
y = -1.6x + 4
The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = - 1.6x + 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Slope of the line (m) = - 1.6
And, The y - intercept = 4
We know that;
The slope intercept form of an equation of line is,
⇒ y = mx + b
Where, 'm' is slope of the line and 'b' is y - intercept of the line.
Hence, The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = mx + b
⇒ y = - 1.6x + 4
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triangle ABC has veritices A(-2,3), B(0,3), and C (-1,-1). Find the coordinates of the image after a reflection over the x-axis.
Answer:
A' = (-2, -3)
B' = (0, -3)
C' = (-1, 1)
I did this on edg
Step-by-step explanation:
Since it's a reflection over the x axis, the x coordinates will stay the same while the y coordinates will be opposite of what they are.
After reflected: A'(-2,-3), B'(0,-3), C'(-1,1)
One batch of cookies requires the following ingredients:
2 1/3 cups of flour
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 1/2cups of brown sugar
3/8of a cup of white sugar
1/2 of a teaspoon of salt
Eric wishes to triple the recipe.
How much of each ingredient should he use? Select all that apply.
A) 9/12 cup of chocolate chips
B) 6/5 cups of chopped almonds
C) 1/6 of a teaspoon of salt
D) 1 1/8 cups of white sugar
E) 6 1/3 cups of flour
F) 2 1/2 cups of brown sugar
Can some one help me plz
Answer:
4h
2d
Step-by-step explanation:
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+3y=8te^−t+6e^−t−(9t+6)
with initial values y(0)=2andy′(0)=2.
We're given the ODE,
y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) - (9t + 6)
(where I denote exp(x) = eˣ )
First determine the characteristic solution:
y'' + 4y' + 3y = 0
has characteristic equation
r ² + 4r + 3 = (r + 1) (r + 3) = 0
with roots at r = -1 and r = -3, so the characteristic solution is
y = C₁ exp(-t ) + C₂ exp(-3t )
For the non-homogeneous equation, assume two ansatz solutions
y₁ = (at ² + bt + c) exp(-t )
and
y₂ = at + b
• y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) … … … [1]
Compute the derivatives of y₁ :
y₁ = (at ² + bt + c) exp(-t )
y₁' = (2at + b) exp(-t ) - (at ² + bt + c) exp(-t )
… = (-at ² + (2a - b) t + b - c) exp(-t )
y₁'' = (-2at + 2a - b) exp(-t ) - (-at ² + (2a - b) t + b - c) exp(-t )
… = (at ² + (b - 4a) t + 2a - 2b + c) exp(-t )
Substitute them into the ODE [1] to get
→ [(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c)] exp(-t ) = 8t exp(-t ) + 6 exp(-t )
(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c) = 8t + 6
4at + 2a + 2b = 8t + 6
→ 4a = 8 and 2a + 2b = 6
→ a = 2 and b = 1
→ y₁ = (2t ² + t ) exp(-t )
(Note that we don't find out anything about c, but that's okay since it would have gotten absorbed into the first characteristic solution exp(-t ) anyway.)
• y'' + 4y' + 3y = -(9t + 6) … … … [2]
Compute the derivatives of y₂ :
y₂ = at + b
y₂' = a
y₂'' = 0
Substitute these into [2] :
4a + 3 (at + b) = -9t - 6
3at + 4a + 3b = -9t - 6
→ 3a = -9 and 4a + 3b = -6
→ a = -3 and b = 2
→ y₂ = -3t + 2
Then the general solution to the original ODE is
y(t) = C₁ exp(-t ) + C₂ exp(-3t ) + (2t ² + t ) exp(-t ) - 3t + 2
Use the initial conditions y (0) = 2 and y' (0) = 2 to solve for C₁ and C₂ :
y (0) = C₁ + C₂ + 2 = 2
→ C₁ + C₂ = 0 … … … [3]
y'(t) = -C₁ exp(-t ) - 3C₂ exp(-3t ) + (-2t ² + 3t + 1) exp(-t ) - 3
y' (0) = -C₁ - 3C₂ + 1 - 3 = 2
→ C₁ + 3C₂ = -4 … … … [4]
Solve equations [3] and [4] to get C₁ = 2 and C₂ = -2. Then the particular solution to the initial value problem is
y(t) = -2 exp(-3t ) + (2t ² + t + 2) exp(-t ) - 3t + 2
Find the measurement of
an interior angle of a regular
decagon (10-sided figure).
Answer:
144°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Sum of Angles: 180(n - 2)Step-by-step explanation:
Step 1: Define
Number of sides n = 10
Step 2: Find
Substitute: 180(10 - 2)Subtract: 180(8)Multiply: 1440°Step 3: Find 1 angle
We have 10 sides.
Divide: 1440/10 = 144Find an equation of the line that passes through the point (23, 22) and is
parallel to 2x=3-5y
Answer:
The equation of the line is y= -2/5x+156/5
Step-by-step explanation:
y=mx+b
m= -2/5 ( 23,22)
y-y=m(x-x¹)
y-22=-2/5(x-23)
y-22=-2/5x+46/5
+22 +22
y= -2/5x+156/5
can commas be used to separate the ones, tens and hundreds
Answer: no? because the comma goes after every three numbers.
The elves are loading all of the toys from Santa's workshop to the sleighs. They filled 2 small sleighs and 9 big sleighs with 241 toys. Later, they filled 14 small sleighs and 13 big sleighs with 437 toys. How many toys can fit on each type of sleigh?
Answer:
2*9=18 14*13=182 18+182=200
Step-by-step explanation:
well you multiply 2 times 9 and you get 18 and then you multiply 14 times 13 and you get 182 and then you 18+182 and that will give you 382.
Graph the line that passes through the point (0,-7) and (-3,-9) and determine the equation of the line
Answer:
The equation is y=2/3x-7
Step-by-step explanation:
-9-(-7) /-3-0
-2/-3
that's your answer
Find the area of the trapezoid below by decomposing the shape into
rectangles and triangles.
6
5
8
3
Answer:
72 square units
Step-by-step explanation:
The area of the rectangle in the middle: 6x8 = 48 square units
The area of the triangle on the left: (5x6)/2 = 30/2 = 15 square units
The area of the triangle on the right: (3x6)/2 = 18/2 =9
(The 6 for the height of the triangle on the right is from the left side of the rectangle in the middle, they have to be the same length)
48+15+9 = 72 square units
Help me please I’m dying
Answer:
[tex]\boxed{x = 2+2\sqrt{6} ~~or~~x = 2 - 2 \sqrt{6} }[/tex]
.
Step-by-step explanation:
To find x, use pythagoras form
[tex]c^2 = a^2 + b^2[/tex]
[tex](x + 4)^2 = x^2 + (x + 1)^2[/tex]
[tex]x^2 + 8x + 16 = x^2 + x^2 + 2x + 1[/tex]
[tex]2x^2 + 2x + 1 - x^2 - 8x - 16 = 0[/tex]
[tex]x^2 - 6x - 15 = 0[/tex]
[tex]x^2 - 6x = 15[/tex]
[tex](x - 3)^2 - 9 = 15[/tex]
[tex](x - 3)^2 = 15 + 9[/tex]
[tex](x - 3)^2 = 24[/tex]
[tex]x - 2 = \pm \sqrt{24}[/tex]
[tex]x = 2 \pm 2\sqrt{6}[/tex]
.
[tex]x_1 = 2 + 2\sqrt{6}[/tex]
[tex]x_2 = 2 - 2\sqrt{6}[/tex]
.
Happy to help :)
Solve the system of equations using the elimination method.
(8x +11y = 37
8x+y=7
Carle is cutting pieces of string that are exactly inches long. How many pieces can she cut from a ball of string that has 100 feet?
Answer:
Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet? 1 foot= 12 inches. A) 49 pieces.Oct 14, 2016
Step-by-step explanation:
Dawn purchased 6 quarts of motor oil for $14.12. What is the Unit Price per quart rounded to
the nearest cent?
Answer:
$2.35 per quart (rounded to nearest cent)
Step-by-step explanation:
6 quarts --- $14.12
1 quart --- [tex]\frac{1}{6}[/tex] × $14.12 = $2.35 (rounded to nearest cent)
Wrote a linear function f with the values f(-4)=0 and f(4)=2
Answer:
y = (1/4)x + 1
Step-by-step explanation:
The points mentioned are (-4,0) and (4,2).
We can find the slope m:
(2-0)/(4-(-4)) = 2/8 = 1/4
We now have the equation y = (1/4)x + b
Now we must find the y-intercept.
Plugging in the first point:
0 = (1/4)*(-4) + b
0 = -1 + b
1 = b
y = (1/4)x + 1
A person saving for retirement makes an initial deposit of $1,000 to a bank account earning interest at a rate of 3% per year compounded monthly, and each month she adds an additional $200 to the account For each nonnegative integer n, let An be the amount in the account at the end of n months. Find a recurrence relation relating Ak to Ak-1. Use iteration to find an explicit formula for An.
Answer:
Step-by-step explanation:
(a)
From the given information:
Let An denote the amount in the account at the end of n month
Thus,
[tex]A_o[/tex] =1000
After the first month ends, interest = [tex]=A_o \times \dfrac{3}{100} \times \dfrac{1}{12}[/tex]
= [tex]0.0025A_o[/tex]
Additional deposit = $200
Now,
[tex]A_1 = A_o + 0.0025A_o + 200[/tex]
[tex]=1.0025A_o + 200 --- eqn(1)[/tex]
Interest after 2nd month, = [tex]A_1 \times \dfrac{3}{100} \times \dfrac{1}{2}[/tex]
Additional deposit = $200
[tex]A_2 = A_1 + 0.0025A_1 + 200[/tex]
[tex]=1.0025A_1 + 200 --- eqn(2)[/tex]
Thus:
[tex]A_n = 1.0025A_{n-1} +200[/tex]
(b)
From above;
[tex]A_1 = 1.0025A_ 0+ 200[/tex]
Thus;
[tex]A _2 = 1.0025A_ 1+ 200[/tex]
[tex]A_2 = 1.0025( 1.0025A_ 0+ 200)+ 200[/tex]
[tex]A_2 = 1.0025^2A_o +200 ( 1+1.0025)[/tex]
[tex]A _3 = 1.0025A_ 2+ 200[/tex]
[tex]A _3 = 1.0025( 1.0025^2A_o +200 ( 1+1.0025))+ 200[/tex]
[tex]A _3 = 11.0025^3A_o +200 ( 1+1.0025 + 1.0025^2)[/tex]
To continuity...
[tex]A_n = 1.0025^n A_o + 200 (1+1.0025 +1.0025^2 +...+ 1.0025^{n-1} ) ---- (3)[/tex]
Thus, we have a geometric term [tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1}[/tex]
where:
a = 1 (first term)
r = 1.0025>1 (common ratio)
Thus;
[tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1} = \dfrac{a(r^n -1)}{r-1}[/tex]
[tex]= \dfrac{1(1.0025^n -1)}{1.0025-1}[/tex]
[tex]= 400(1.0025^n -1)[/tex]
From equation(3)
[tex]A_n = (1.0025^n \times 1000) + 80000(1.0025^n -1)[/tex]
[tex]A_n = 1.0025^n \times 81000-80000[/tex]
Given the vectors u and v.
On a coordinate plane, vector u has origin (0, 0) and terminal point (7, 8). Vector v has origin (0, 0) and terminal point (negative 3, 5).
What is u · v?
19
59
61
160
Answer:
A. 19
Step-by-step explanation:
edge 2020
The dot product of the vector u and v is 19 if option (A) is correct.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
We have:
On a coordinate plane, vector u has an origin (0, 0) and terminal point (7, 8). Vector v has origin (0, 0) and terminal point (negative 3, 5).
Vector u = <(7-0, (8-0)> = <7, 8>
Siimilarly, v = <-3, 5>
u · v = (7×(-3)) + (8×5) = -21 + 40 = 19
Thus, the dot product of the vector u and v is 19 if option (A) is correct.
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Consider drawing two cards, without replacement, from a standard deck of 52 cards. That means we are drawing the first card, leaving it out, and then drawing the second card.what is the probability that both cards selected for black?
Given:
Two cards are drawn from a standard deck of 52 cards without replacement.
To find:
The probability that both cards selected for black.
Solution:
We know that,
Total number of cards = 52
Total number of red cards = 26
Total number of black cards = 26
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Probability of selecting first black card is
[tex]\text{Probability}=\dfrac{26}{52}[/tex]
[tex]\text{Probability}=\dfrac{1}{2}[/tex]
Number of remaining total cards = 52-1 = 51
Number of remaining black cards = 26-1 = 25
Probability of selecting second black card is
[tex]\text{Probability}=\dfrac{25}{51}[/tex]
So, the probability that both cards selected for black is
[tex]\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}[/tex]
[tex]\text{Probability}=\dfrac{25}{102}[/tex]
Therefore, the required probability is [tex]\dfrac{25}{102}[/tex].
1)A student earned a grade of 80% on a math test that had 60 problems. How many
problems on this test did the student answer correctly?
Answer:
48
Step-by-step explanation:
80% = .8
60 x .8 = 48
Answer: 48
Step-by-step explanation:
80% of 60 or 80/100 x 60 = 48
Complete the table so that the cost per banana remains the same.
number of
bananas
cost in
dollars
unit price
(dollars per banana)
4
0.50
6
0.50
7
0.50
10
0.50
10.00
0.50
16.50
0.50
Step-by-step explanation:
No. of banana Cost Unit price
4 2 0.50
6 3 0.50
7 3.5 0.50
20 10 0.50
20 10 0.50
33 16.50 0.50
Cost = No of banana x unit price
Cost = 4 x 0.50 = 2
Cost = 6 x 0.50 = 3
Cost = 7 x 0.50 = 3.50
Cost = 20 x 0.50 = 10
No of banana = Cost / Unit price
No of banana = 10 / 0.50 = 20
No of banana = 16.50 / 0.50 = 33
Answer ASAP will give brainliest, thanks.
Answer:
B
Step-by-step explanation:
4x+2y=6
6x-4y=-12
2y=6-4x
y=3-2x
6x-4(3-2x)=-12
6x-12+8x=-12
2x-12=-12
2x=0
x=0
4(0)+2y=6
2y=6
y=3
(0,3)
7 1/2÷3/4 Please help this mom out!!
Answer:
10
Step-by-step explanation:
give me brainly
am i correct? let me know
winston earns $140.00 by selling 56 hotdogs at a concession stand at school. by using the same rate for the cost of one hotdog , how many more would Winston need to sell to earn $175.00?
URGENT !!
A popular television show recently released a video
preview for the upcoming season on íts website As
fans of the show discover the video, the number of
views of the preview video has grown each day
during the last 2 vweeks. The number of days since
the release of the video and the natural log of the
number of video views ís shown in the scatterplot.
Answer:C
Step-by-step explanation:
Jared a beekeeper placed 120 hives in a apple orchard
Answer: 20
Step-by-step explanation:
How much money will i get in 5.4 hours if i get $4 per 6 hours
Answer:
3 dollars and 60 cents
Step-by-step explanation:
6) A climber is on a hike. After 2 hours she is at an altitude of 400 feet. After 6 hours, she is at an
altitude of 700 feet. What is her rate of change?
Answer:
Her rate of change is 75 ft/h
Step-by-step explanation:
Rate of Change
It measures how one quantity varies with respect to another. The second variable usually is the time.
The climber is hiking. We are given two points of her progress: At 2 hours, she is at 400 ft. This corresponds to the point (2,400).
At 6 hours, she is at 700 ft. This is the point (6,700)
The rate of change is the slope between these two points or the quotient of the variations of each variable:
[tex]\displaystyle m=\frac{700\ ft-400\ ft}{6\ h-2\ h}[/tex]
[tex]\displaystyle m=\frac{300\ ft}{4\ h}[/tex]
[tex]m=75\ ft/h[/tex]
Her rate of change is 75 ft/h
18 ≤ -2x = what?? please answer im in class
Answer:
-9
Step-by-step explanation:
can you help me please
Answer:
Please check the explanation.
Step-by-step explanation:
Given that
|v|=38
Ф = 120°
Finding the horizontal component
The horizontal component can be obtained using the formula
Vx = |v| cos Ф
= 38 cos 120°
= 38 (-0.5)
= -19
Thus, the horizontal component is:
Vx = -19
Finding the vertical component
The vertical component can be obtained using the formula
Vy = |v| sin Ф
= 38 sin 120°
= 38 (0.86)
= 32.68
Thus, the vertical component is:
Vy = -19
A vector 'v' with magnitude |v| and direction Ф can be written as:v = |v| cos Ф i + |v| sin Ф j
As
|v|=38
Ф = 120°
Thus, the vector is
v = 38 cos 120° i + 38 sin 120° j
or
v = -19 i + 32.68 j
You increase your walking speed from 1 m/s to 3 m/s in a period of 1 s.
What is your acceleration?
Answer:
2 m/s
Step-by-step explanation:
Answer:
2m/s²
Step-by-step explanation:
acceleration= v-u/t
=3-1/1
=2m/s²