Answers
Answer:
k = 3/2
Step-by-step explanation:
3/2 is equal to 1.5
Flip the triangle on the left to match the triangle on the right if you multiply the right triangle values by 1.5 (3/2) you get the same values as the one on the left.
Related Questions
okay here they are there is only 2 things right now but I am making more right now
Answers
Answer:
So whats the question?
Step-by-step explanation:
A curve is such that (dy)/(dx) = 12/(2x + 1) ^ 2 and P(1, 5) is a point on the curve . (i) The normal to the curve at P crosses the x-axis at Q. Find the coordinates of Q (ii) Find the equation of the curve. (iii) A point is moving along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.3 units per second. Find the rate of increase of the y-coordinate when x=1
Answers
(i) The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].
(ii) The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].
(iii) The rate of increase of the y-coordinate is 1.2 units per second.
(i) By analytical geometry, we know that the slope of a line normal of a curve ([tex]m_{\perp}[/tex]) by the following expression:
[tex]m_{\perp} = - \frac{1}{\frac{dy}{dx} }[/tex] (1)
Where [tex]\frac{dy}{dx}[/tex] is the slope of the line tangent to the curve.
If we know that [tex]x = 1[/tex], then the slope of the normal to the curve is:
[tex]\frac{dy}{dx} = \frac{12}{2\cdot (1)+1}[/tex]
[tex]\frac{dy}{dx} = 4[/tex]
And the slope of a line normal of a curve is:
[tex]m_{\perp} = -\frac{1}{4}[/tex]
By definition of secant curve we calculate the remaining coordinate of the point Q:
[tex]m_{\perp} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (2)
Where:
[tex]x_{P}[/tex], [tex]x_{Q}[/tex] - x-coordinates of points P and Q. [tex]y_{P}, y_{Q}[/tex] - y-coordinates of points P and Q.If we know that [tex](x_{P}, y_{P}) = (1, 5)[/tex], [tex](x_{Q}, y_{Q}) = (x, 0)[/tex] and [tex]m_{\perp} = -\frac{1}{4}[/tex], then the remaining coordinate of point Q is:
[tex]-\frac{1}{4} = \frac{0-5}{x-1}[/tex]
[tex]-\frac{1}{4}\cdot (x-1) = -5[/tex]
[tex]-\frac{1}{4}\cdot x +\frac{1}{4} = -5[/tex]
[tex]\frac{1}{4}\cdot x = \frac{21}{4}[/tex]
[tex]x = 21[/tex]
The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].
(ii) The equation of the curve is derived by separating the variables and integrating the resulting expression:
[tex]dy = \frac{12}{2\cdot x + 1}\,dx[/tex]
[tex]\int\, dy = 6\int {\frac{2\,dx}{2\cdot x + 1} }[/tex]
[tex]\int \, dy = 6\int {\frac{du}{u} }[/tex]
[tex]y = 6\cdot \ln u[/tex]
[tex]y = 6\cdot \ln (2\cdot x + 1)+C[/tex]
And the integration constant is found for [tex](x,y) = (1, 5)[/tex]:
[tex]5 = 6\cdot \ln(2\cdot 1 + 1) + C[/tex]
[tex]C = -1.592[/tex]
The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].
(iii) The rate of increase of the y-coordinate by using the differential equation presented in statement and the definition of rate of change:
[tex]\frac{dy}{dt} = \left(\frac{12}{2\cdot x +1}\right)\cdot \frac{dx}{dt}[/tex] (3)
If we know that [tex]\frac{dx}{dt} = 0.3[/tex] and [tex]x = 1[/tex], then the rate of increase of the y-coordinate is:
[tex]\frac{dy}{dt} = \left[\frac{12}{2\cdot (1)+1} \right]\cdot (0.3)[/tex]
[tex]\frac{dy}{dt} = 1.2[/tex]
The rate of increase of the y-coordinate is 1.2 units per second.
To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/25731911
i). The coordinates of Q is equal to:
[tex](x,y) = (21, 0)[/tex]
ii). The equation of the curve is:
[tex]y = 6. In(2.x + 1) - 1.592[/tex]
iii). The rate of increase for y-coordinate when x = 1:
[tex]1.2 units[/tex] per second
i). Using analytical geometry,
[tex]xp[/tex] and [tex]xq[/tex] are the P and Q's x-coordinates.
[tex]yp[/tex] and [tex]yq[/tex] are the P and Q's y-coordinates.
Since ([tex]xp[/tex], [tex]yp[/tex]) = (1,5) and ( [tex]xq[/tex], [tex]yq[/tex]) = [tex](x, 0)[/tex] and m⊥ = - 1/4, the left coordinate of Q's point:-
-1/4 = (0-5)/(x - 1)
∵[tex]x = 21[/tex]
Thus, the coordinates of y = (21, 0)
ii). Through isolating the variables and employing integration:-
[tex]dy = \frac{12}{(2.x + 1)} dx[/tex]
by integration and integration constant (1,5), the equation is:
[tex]y = 6. In(2.x + 1) - 1.592[/tex]
iii). The rate of increase for y-coordinate:
[tex]dy/dt[/tex] = [tex]\frac{(12)}{(2.1 + 1)} .0.3[/tex]
∵ [tex]dy/dt[/tex] [tex]= 1.2[/tex]
Thus, the rate of increase for y-coordinate when x = 1 is 1.2 units per second.
Learn more about "Co-ordinates" here:
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I need to know ASAP! Thanks ^^
Answers
Answer:
PQ=30
Step-by-step explanation:
Knowing that the segment has 3 parts that are 3:1:1 and sum up to 50, you could find how much 1 would equal by finding the total in relation to the ratio (doing 3+1+1) which gets you 5 parts. Then you can divide the total (50) by 5 to figure out how much one part would equal (10). Now, since you know that 1 part is equal to 10 and that PQ is 3 parts, you can find that PQ is equal to 3x10, or 30.
pls complete it (picture)
Answers
Answer:
The answer to your question is 24cm.
Step-by-step explanation:
6 multiplyed by 8 equals 48, and 48 divided by 2 equals 24.
Hope I helped. Have a spectacular day! ;)
Which statement is true of the mapping?
PLEASE HELP MEE
Answers
Answer:
C
Step-by-step explanation:
pleaseeee hurryyy i needd helppp
How many solutions are there for this equation? Why?
2(m+2)=12−6m
Select the option that correctly answers both questions.
a. There is one solution, because the coefficients of the variables on both sides of the equation are the same.
b. There are no solutions, because the coefficients of the variables on both sides of the equation are different.
c .There is one solution, because the coefficients of the variables on both sides of the equation are different.
d. There are no solutions, because the coefficients of the variables on both sides of the equation are the same.
Answers
Answer:
C. There is one solution, because the coefficients of the variables on both sides of the equation are different.
Step-by-step explanation:
The solution is m = 1
~theLocoCoco
Tony is making a circular, glass tabletop with a radius of 22 inches. Approximately how much glass does he need to make the tabletop?
A.
138.16 square inches
B.
379.94 square inches
C.
1,519.76 square inches
D.
6,079.04 square inches
Answers
the area of a circle with a radius of 22 is 1,520.5344 which leads you to answer C
Marsha is driving 600 total miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?
A. 120 miles
B. 240 miles
C. 300 miles
D. 360 miles
Answers
Solve each equation for x. 1.3x + 9x = 6x + 42
Answers
Answer:
Just use a calcultor...
Step-by-step explanation:
Martha wants to go to band camp this summer that costs $103.50 she has $10 and plans to save $5.50 each week. How many weeks will it take her to save the money? In algebra pls
Answers
Answer:
19 weeks
Step-by-step explanation:
You'll be looking for an equation the form of
y=mx+b
Given:
b = $103.50
m = $5.50
x = ? (where x is in weeks)
Next, set y = 0
--> mx+b = 0
Rearrange
x = (-b/m)
Plug in b and m:
x = (-(-103.5)/5.5) = 18.818
Rounding up, it will Martha 19 weeks to save enough money.
7 times the difference of x and 8
Answers
Answer:
7(x - 8)
Step-by-step explanation:
times means multiplication
difference means subtraction
7 times the difference of x and 8 -> 7 * (x - 8) -> 7(x - 8)
Simplify if needed.
7(x - 8)
~Distribute
2x - 56
Best of Luck!
Use the graph to find the cost of 8 hats.
Cost of Hats
110
100
90
80
($) 1803
10
8 7 8 10 11
Number of hats
O A. The cost of 8 hats is $7.50.
ООО
B. The cost of 8 hats is $75.00
O C. The cost of 8 hats is $8.00.
PREVIOUS
Answers
Answer:
are you missing a option because for me one option that has the same exact numbers that you mentioned is the cost of 8 hats is 60
Step-by-step explanation:
Please help meeeeeee
I need the answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
4x + 6x + y = 180
6x + y = x + 5y
10x + y = 180 ........... (1)
5x - 4y = 0 .............. (2)
(1) - 2 × (2)
y + 8y = 180 ⇒ y = 20
6x + 20 = x + 100 ⇔ 5x = 80 ⇒ x = 16
64° , 116°
Which of the following sets of numbers could represent the three sides of a triangle?
Answers
Answer:
{5, 15, 19}
Step-by-step explanation:
According to the triangle inequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.
Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:
a + b > c
b + c > a
a + c > b
Where a and b are the smaller side lengths, and c is the length of the longest side.
Let's check each set of numbers given to see if any satisfies this condition.
✍️Option 1: {6, 20, 28}
6 + 20 is not greater than 28
20 + 28 > 6
6 + 28 > 20
❌This set of numbers does not represent the sides of a ∆.
✍️Option 2: {4, 11, 15}
4 + 11 = 15
11 + 15 > 4
4 + 15 > 11
❌This set of numbers does not represent the sides of a ∆.
Option 3: {9, 19, 30}
9 + 19 is not greater than 30
19 + 30 > 9
9 + 30 > 19
❌This set of numbers does not represent the sides of a ∆
Option 4: {5, 15, 19}
5 + 15 > 19
15 + 19 > 5
5 + 19 > 15
✅This set of numbers does not represent the sides of a ∆
Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.
Find the number of terms in this polynomial.
-8f^2
Answers
Answer:
3 terms
Step-by-step explanation:
Tyson bought four roses for $8.88. If the cost per rose is constant, how much would 6 roses cost?
Answers
Answer:
6 roses = $13.32
Step-by-step explanation:
4 roses = $8.88
(divide by 4)
1 rose = $2.22
(multiply by 6)
6 roses = $13.32
unit 6 lesson 9: linear functions sample work
its asking suppose you are constructing a lego technic land rover defender with a total of 2573 pieces. Every minute you had 5 pieces. So how would I write an equation in slope- intercept form to model the number of pieces placed in relation to time.
Answers
Answer:
Initially, you have 2573 pieces.
You use 5 pieces each minute.
Right when you start, you have 2573 pieces.
One minute after that, you have 2573 - 5 pieces.
Another minute after, you have 2573 - 2*5 pieces.
Another minute after, you have 2573 - 3*5 pieces.
And so on.
You can see the pattern here, and with this, we can find the linear equation that represents the number of pieces that you have as a function of time.
Then, if the variable t represents the number of minutes that passed since you started, we can write the equation:
f(t) = 2573 - 5*t
That represents the number of pieces that you have after t minutes.
find the slope of the graph given below
Answers
Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
Can someone please help me with this proof?!
Given: AC and BD bis, each other.
Prove: ABCD is a parallelogram
Answers
Answer:
because AC and BD bis => AX = XC; BX = XD
ΔAXD ≅ ΔCXB (SAS) because: AX = CX
DX = BX
m∠AXD = m∠BXC ( 2 opposing angles)
because ΔAXD ≅ ΔCXB (SAS)
=> AD = BC and m∠DAX = m∠BCX
because m∠DAX = m∠BCX => AD//BC
ABCD has AD = BC and AD//BC => ABCD is a parallelogram
Step-by-step explanation:
1. What are the different offensive and defensive strategies that are used in water polo?
2. Which strategies do you think are the most difficult to accomplish? Why?
3. Which strategies do you think are the easiest to achieve? Why?
Answers
Answer:
A defensive way is use all your might to jump when the ball is coming at you, because as you might know is it takes a lot of effert to jump in a pool, the gravity is very strong in the pool! Or if you get the ball you can throw and swing your arm as strong as you can a HIT that ball! You wanna hit it hard so the players on the other side of the pool don’t get the ball,instead it will go over them and you WIN!
Step-by-step explanation:
Hope this helped :)✨
If
3x+y = 7, what is the value of x/y?
SOMEONE HELP I NEED IT QUICK!! plsss
Answers
Answer:
x=2 y=1
Step-by-step explanation:
3 times 2 =6
plus 1 = 7
Parallel or perpendicular 3x+5y=10 and 5x-3y=-6
Answers
Michael has five different stocks that he watches on a daily basis the table shows the change in each stock price in dollars at the end of a trading day
Answers
Answer:
a
Step-by-step explanation:
A store offers four different brands of a product. It decides to eliminate the brand that is most likely to be returned. The table shows the number of items of each brand that were returned over the past year and the total sold. which brand should the store eliminate? A. Brand A B. Brand B C. Brand C D. Brand D
Answers
Answer:
Brand b
Step-by-step explanation:
2) 5x 3 x 2
what is the order of operations
Answers
Answer:
PEMDAS
Step-by-step explanation:
parentheses
exponents
multiplication
division
subtraction
5x3x2=30
Parentheses, exponents, multiplication, division, addition, subtraction
5x3 is first equaling 15
15x2 is next equaling 30
The answer is 30
Which expressions simplify to a rational answer?
Select each correct answer.
Answers
Answer: the answers are the second one and the last one
Step-by-step explanation:
please help ASAP!
i will give brainliest!! :)
Answers
Answer:
its c i took the test trust me
Step-by-step explanation:
⚠️PLEASE HELP FAST⚠️ Camie and Jorge each begin saving money
for a new computer. Camie saves $5 per
week plus $50 she receives for her birthday.
Jorge saves $7 per week. Which of the
following can be used to find w, the number
of weeks until Jorge has saved at least the
same amount as Camie?
A.7w = 5W + 50
B.50 + 5w < 7w
C.5W + 50 >_7w
D.7W >_5W + 50
Answers
Answer:
The answer is A
Step-by-step explanation:
Camie: $5x + $50 = $55 ( for now/i think)
Jorge: $7x
The equation to represent Jorge has saved at least the same amount as Camie is 7w = 5W + 50.
The correct option is (A)
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
Camie saves $5 per week plus $50 she receives for her birthday.
Jorge saves $7 per week.
Now, Jorge have to achieve the same amount as Camie.
let w be the number of weeks.
Then equation can be represented as
7w = 5W + 50
Here 7w is amount by Jorge and 5W + 50 is amount of Camie.
Hence, the equation to represent Jorge has saved at least the same amount as Camie is 7w = 5W + 50.
Learn more about equation here:
https://brainly.com/question/10413253
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Water begins to slowly leak from David’s water bottle right after he fills it. After 5 minutes, he notices the bottle has 26 ounces of water remaining. After 30 minutes, he notices the bottle has 16 ounces of water remaining. Let x represent the number of minutes that have passed and let y represent the amount of water remaining in the bottle.
a) Without calculating, will the rate of change (slope) for the water bottle be positive or negative? Explain how you know.
b) What is the rate of change (slope) of this situation (in ounces per minute)?
c) Write an equation to model this situation:
d) How much water was in David’s bottle immediately after he filled it?
e) After how many minutes will David’s bottle be completely empty?
Answers
Some one help :( I’ll mark you brilliant
Answers
Answer:
1. 8
2. 9
3. 3
4. 60
5. 1/60
Step-by-step explanation:
1. The coefficient of x is 8. This is m(slope) in the equation y=mx+b.
2. To find the slope, choose to points. (4,36) and (6,54). Now use the formula (y2-y1)/(x2-x1). 18/2 is also 9.
3. Use the same formula as before. (13-10)/(9-8)= 3/1= 3.
4.Use the same formula as before. (240-120)/(4-2)= 120/2= 60.
5. Use the same formula as before. (3-2)/(190-130)= 1/60
PLZ GIVE ME BRAINLIEST