The length of a rectangle is 3m more than the width. The area is 70m². Find the dimensions of the rectangle.
If it were a square it would be 17.5meters on every side, but we are not solving for a square we are solving for a rectangle. The dimensions for this rectangle are 19 long 16 wide.
Answer:
304m?
Step-by-step explanation:
okay bye
bye
Solve the differential equation y" + 3y' + 2y = P1 where, y" = d2y/dx2, y' = dy/dx, P1 = P1(x)) and the initial conditions are y(0) = 0, y'(0) = 0. The input function is given by P1() = { 0, < 0 1, 0 ≤ ≤ 1 0, > 1
Answer:
[tex]y(x) = 0[/tex]
Step-by-step explanation:
Let P(1) = 0, the differential equation becomes:
y" + 3y' + 2y = 0
Also let y' = my and y'' = m²y
Substitute
m²y+3my+2y = 0
(m²+3m+2)y = 0
The auxiliary equation is expressed as:
m²+3m+2 = 0
Factorize
m²+2m+m+2 = 0
m(m+2)+1(m+2) = 0
(m+1)(m+2) = 0
m+1 = 0 and m+2 = 0
m₁ = -1 and m₂ = -2
Since the value of m is real and distinct, the solution to the differential equation will be expressed as:
[tex]y = C_1e^{m_1x}+C_2e^{m_2x}\\[/tex]
[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\[/tex]
Given the initial condition y(0) = 0
[tex]y(0) = C_1e^{-0}+C_2e^{-2(0)}\\0 = C_1+C_2\\C_1+C_2 = 0 ................. 1[/tex]
If y'(0) = 0
[tex]y'(x) = -C_1e^{-x}-2C_2e^{-2x}\\y'(0) = -C_1e^{-0}-2C_2e^{-2(0)}\\0 = -C_1-2C_2\\C_1-2C_2 = 0...................... 2[/tex]
Solve eqn 1 and 2 simultaneously
From 1:
C₁ = -C₂ .......... 3
Substitute equation 3 into 2:
-C₂-2C₂ = 0
-3C₂ = 0
C₂ = 0
Substitute the constant into the differential equation.
[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\\\y(x) = 0[/tex]
During an investigation on speed, a ball rolls down a ramp a distance of 8 m in a time of 2 seconds. What is the average speed of the ball in m/s?
Answer:
4 m/s
Step-by-step explanation:
To find the average speed of the ball, divide the number of meters by the number of seconds:
8/2
= 4
So, the average speed of the ball is 4 m/s
Question 5 please. I need help with thus.
Answer:
TU = 63.84 in
Step-by-step explanation:
Since T lies on RU, then
RT + TU = RU, substitute values
9x - 2.64 + 11x - 4.36 = 117, that is
20x - 7 = 117 ( add 7 to both sides )
20x = 124 ( divide both sides by 20 )
x = 6.2
Thus
TU = 11x - 4.36 = 11(6.2) - 4.36 = 68.2 - 4.36 = 63.84 in
The value in dollars, f(x), of a certain car after x years is represented by the equation f(x) = 25,000(0.86)^x. To the nearest dollar, how much more is the car worth after 2 years than after 3 years?
a. $18,490
b. $34, 391.40
c. $15,901.40
d. $2,588.60
Answer:
588.6
Step-by-step explanation:
Multiply
0
by
0.86
x
.
f
(
x
)
,
x
y
e
a
r
s
,
f
(
x
)
=
25
,
0
,
2
y
e
a
r
s
,
3
y
e
a
r
s
,
a
,
18
,
490
,
b
,
34
,
391.4
,
c
,
15
,
901.4
,
d
,
2
,
588.6
I need help solving all the questions.
1. Rakesha claims that the equation f(n) 5 5n 2 7 is the function notation for the sequence that is
represented by the explicit formula an 5 22 1 5(n 2 1). James doesn’t understand how this can be
the case.
a. Help James by listing the steps to write the explicit formula of the given sequence in function
notation. Provide a rationale for each step.
b. Graph the function. Label the fi rst 5 values of the sequence on the graph.
2. Determine whether each table of values represents a linear function. For those that represent
linear functions, write the function. For those that do not, explain why not.
find the value of x if n(x)=-6x+10 when n(x)=58
Answer:8
Step-by-step explanation:
6x+10=58
6x=48
X=8
Which of the following is equivalent to 5x-6y=20?
A y=5/6x
B y=5/6x-10/3
C y=6/5x+4
D y=-5/6x
Answer:
y = [tex]\frac{5}{6}[/tex]x - [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Given expression:
5x - 6y = 20
To solve this problem, we make y the subject of the expression:
Solution
5x - 6y = 20
Add -5x to both sides of the expression;
-5x + 5x - 6y = 20 + (-5x)
-6y = 20 - 5x
Now, multiply both sides by [tex]-\frac{1}{6}[/tex] ;
[tex]-\frac{1}{6}[/tex] x (-6y) = [tex]-\frac{1}{6}[/tex] (20 - 5x )
y = [tex]-\frac{20}{6}[/tex] + [tex]\frac{5}{6}[/tex]x
y = [tex]\frac{5}{6}[/tex]x - [tex]\frac{10}{3}[/tex]
The band boosters sell snickers bars for 75¢ each. Which of the following statements are true? Select all that apply.
A. If Tom spent $6.00 on snickers bars, he bought 9.
B. When the band boosters sell 10 snickers bars they make $7.50.
C. For every 4 snickers bars sold the band boosters earn $3.00.
D. If Tom bought 6 snickers bars, he paid $3.50. E. 75¢ is the unit price for a snickers bar.
Answer:
B, C, and E
Step-by-step explanation:
B because 0.75*10=7.5. C because 4*0.75=3. And E because 0.75 is how much each snickers bar is is that is the unit price
please help! giving brainliest to the person who’s correct :)
She counted the squares instead of using the scale.
The scale, the numbers on the x amd y axis dont fo by ones, they go by sixes
Answer: the secound one
Step-by-step explanation:
A line passes through the point (-9,1) and has a slope of -2/3
Answer:
y - 1 = (-2/3)(x + 9)
Step-by-step explanation:
Here you are given a point on a line and the slope of the line. You'll need to apply the "point-slope" formula
y - k = m(x - h) (Memorize this)
Then m = slope = -2/3, h = -9 and k = 1.
Making the appropriate substitutions, we get:
y - 1 = (-2/3)(x + 9)
If f(x) = x? - x, what is f(-5)?
Answer: f(-5)= -5
Step-by-step explanation:
If f(x)=x then f is one and 1 times -5 is -5
Solve forx: (x – 3)/ 3 =4
Answer:
x = 15
Step-by-step explanation:
=> x - 3 = 12
=> x = 15
Answer:
your answer is 9/4 check google
Step-by-step explanation:
could some one please help I'm not that good with math
Answer:
D and E
Step-by-step explanation:
It is acute because all angles are under 90 degrees. This means that it cannot be F, obtuse. It cannot be A because A scalene triangle is a triangle in which all three sides have different lengths. It cannot be B either because it has 3 sides of equal angles. It cannot be right because non of the angles are 90 degrees. It is equilateral.
Hope this helps.
What is the slope of the line that contains these points?
Pls help
Answer:
-1
Step-by-step explanation:
m=y2-y1/x2-x1
-6-(-5)=(-1)
6-5=1
-1/1=(-1)
hope this helps :3
if it did pls mark brainliest
PLEASE ANSWER IT CORRECT PLEASE!!!
Answer:
11. y=1 1/3x-3
12. y-4=3(x-2)
Step-by-step explanation:
here ya go
I need help please.................................
Answer:
The answer is in the photo.
if y= -4 when x=2, find y when x=-6.
Answer:
y=12
Step-by-step explanation:
2*-2=-4
-6*-2=12
y=12
Answer: erbgv
Step-by-step explanation:
-3a + b when a
=
-4 and b = 9.
Answer:
12+9=21
Step-by-step explanation:
The equation p = 3.25b can be used to find the price, p, in dollars, of b pounds of blueberries at a particular supermarket. Each of the tables gives the prices of various pounds of blueberries at a different supermarket. Which of these tables represents blueberries that are more expensive than those represented by the equation? Select all that apply.
Answer:
Table C, Table D, Table E
Step-by-step explanation:
See attachment for tables
Given
[tex]p = 3.25b[/tex]
Required
Which of the tables is more expensive than the given function
To answer this question, we simply determine the equation of each table and then compare the equation with [tex]p = 3.25b[/tex]
Table A:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1,2.75)[/tex]
[tex](b_2,p_2) = (4,11)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{11 - 2.75}{4 - 1}[/tex]
[tex]m = \frac{8.25}{3}[/tex]
[tex]m = 2.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 2.75 = 2.75(b-1)[/tex]
[tex]p - 2.75 = 2.75b-2.75[/tex]
[tex]p = 2.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.75 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
Table B:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1.5,3.75)[/tex]
[tex](b_2,p_2) = (6,15)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{15 - 3.75}{6 - 1.5}[/tex]
[tex]m = \frac{11.25}{4.5}[/tex]
[tex]m = 2.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 3.75 = 2.5(b-1.5)[/tex]
[tex]p - 3.75 = 2.5b- 3.75[/tex]
[tex]p = 2.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.5 < 3.25[/tex]
Hence:
This equation is also less expensive than [tex]p = 3.25b[/tex]
Table C:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2,7)[/tex]
[tex](b_2,p_2) = (4,14)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{14 - 7}{4 - 2}[/tex]
[tex]m = \frac{7}{2}[/tex]
[tex]m = 3.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 7 = 3.5(b - 2)[/tex]
[tex]p - 7 = 3.5b - 7[/tex]
[tex]p = 3.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.5 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table D:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2.5,10)[/tex]
[tex](b_2,p_2) = (5,20)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{20 - 10}{5 - 2.5}[/tex]
[tex]m = \frac{10}{2.5}[/tex]
[tex]m = 4[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 10 = 4(b - 2.5)[/tex]
[tex]p - 10 = 4b - 10[/tex]
[tex]p = 4b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]4 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table E:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (6, 22.5)[/tex]
[tex](b_2,p_2) = (12,45)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{45 - 22.5}{12 - 6}[/tex]
[tex]m = \frac{22.5}{6}[/tex]
[tex]m = 3.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 22.5 = 3.75(b - 6)[/tex]
[tex]p - 22.5 = 3.75b - 22.5[/tex]
[tex]p = 3.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.75>3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table F:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (7, 21)[/tex]
[tex](b_2,p_2) = (14,42)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{42 - 21}{14 - 7}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m = 3[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p -21 =3(b -7)[/tex]
[tex]p -21 =3b -21[/tex]
[tex]p = 3b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
If 3 + w=b, which expression is equivalent to w?
Answer:
W= B-3 or 3=B-W
Step-by-step explanation:
just add or subtract either
Answer:
w = b - 3
Step-by-step explanation:
3 + w = b
-3 -3
w = b - 3
Hope this helps!
line I is the perpendicular bisector of MN. find m
Answer:
m = 68
Step-by-step explanation:
MN bisects it or splits it in half so we know N = M, which we could also write as 8x-12 = 5x+18 because they give us those equations
once you have 8x-12 = 5x+18 you can subtract 5x from both sides, so you will get 3x-12 = 18, then you can add 12 to both sides and you will get 3x = 30. Once you have narrowed down to this you can divide three by both sides making x = 10
Now that we know x =10 we can insert it into the equation
5(10) + 18 = m
50 + 18 = m
m = 68
Which Expression has a value of 2/3
Answer:
(8 + 24) ÷ (12 x 4)
Step-by-step explanation:
w = 8.75h
What is an impossible value for h?
Answer:
h = 0.1 142857 w
Step-by-step explanation:
Answer:
hayy
Step-by-step explanation:
Find the missing numbers:
x2 – 9x + 20 = (x – ?)(x – ?)
Answer:
bloop
Step-by-step explanation:14 and 30
[tex]74 \times 54 + 7 \div 20[/tex]
slove this?
(Will mark brainliest if you’re right)
How are linear inequalities used for financial analyst? Written in a Paragraph
Answer:
It allows you to find the slope of the gross income that you are earning. Linear inequalities show how much money you earn from the maximum to the potential minimum. Linear lines are straight so they show the average or the best fit of your financial status.
Step-by-step explanation:
Hope this helps!
The quotient of a number and twelve is the sum of eight and the number.
Answer: n/12=8+n
Answer:
Step-by-step explanation:
12(n/12 = 8 + n)
n = 96 + 12n
-11n = 96
n = -96/11
Answer:
-96/11 or -8 8/11
Step-by-step explanation:
For this, create an equation, x/12=x+8.
Any number without a denominator has a denominator of 1, so x/12=(x+8)/1.
Now, cross multiply to get 1*x=12(x+8).
Simplify that to x=12x+96.
Subtract 12x from both sides, and you have -11x=96.
Divide by -11, and x=-96/11.
How many solutions does the following equation have? 3(y + 9) = 12y+ 13
Answer:
asddsdaddd
Step-by-step explanation:
1. The center of circle S is (9,2), and the radius of the circle is 5 units. Which point is on the circle?
Answer:
Find the equation of the circle that is shifted 5 units to the left and 2 units down from the circle ... If one circular table has a radius of 4 feet and a center at C(-4, 6), find the center and ... The points (-5, 2) and (-5, 8) lie on a circle with a radius of 3.
Step-by-step explanation:
hope this helps
