Answer:
The 61st term is -52
Step-by-step explanation:
Many counties in Texas missed many school days in the fall of 2017 due to hurricanes
that year. A solution for how to make up those
days was to add time to each school day
for a portion of the year. It was decided that in order to make up a 6 hour school day, 10
minutes would be added to each day. How many extended days would be needed to
make up 3 school days?
A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?
Answer:
4x+12
Step-by-step explanation:
A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?
(5+2x)+(7+2x)
The perimeter would be 4x+12
Hope I helped!
Please mark Brainliest!!!
Answer:
The answer is A. 4x+12
Step-by-step explanation:
Just took the test on edge 2020 :D
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
(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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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.
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
2. How much interest is earned on a principal of $200 invested at an interest rate of 9% for eight
years?
Answer:
Answer: 177
Step-by-step explanation:
Evaluate the function f(x) = -2x + 9 when x = 2
Answer:
I think x= 5
Step-by-step explanation:
because u put 2 where x is supposed to go so it would be -2(2)+9 and -2(2)=-4 and then add 9 and that =5
Which expression is equivalent to (2x^2+3x-4)-(x^2-2x+4)
Answer:
3x + 2 = 14
Step-by-step explanation:
I am unable to understand how to solve this question, please send the working out.
Answer:
[tex](9x)^{\frac{1}{2} }.(8x^{\frac{-1}{2} })^{\frac{1}{3} }\\\\=9^{1/2}.x^{1/2}.8^{1/3}.x^{-1/2.1/3} \\\\=3.2.x^{1/2}.x^{-1/6} \\\\\\=6.x^{1/2-1/6}\\\\=6x^{1/3}[/tex]
Step-by-step explanation:
Margo studied for 20 minutes. How many seconds did she study?
A. 1,200
B. 800
C. 620
D. 120
Answer:
1200 because 12*60 is 1200
3 + 2p - 4 = 11
algebra 1 solving equations
Answer: the variable is p=6 .
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable
Answer:
p = 6
Step-by-step explanation:
Step 1: Simplify both sides.
3 + 2p − 4 = 11
3 + 2p + −4 = 11
(2p) + (3+−4) = 11 (Combine Like Terms)
2p + −1 = 11
2p − 1 = 11
Step 2: Add 1 to both sides.
2p − 1 + 1 = 11 + 1
2p = 12
Step 3: Divide both sides by 2.
2p/2 = 12/2
p=6
A machine can pack 70 boxes of spaghetti in 5 minutes. At this rate, how
many boxes can they pack in 8 minutes.
Answer:
112 boxes
Step-by-step explanation:
Answer: 112 boxes
Step-by-step explanation: 112 boxes in 8 minutes. To find how many boxes the machine packs per minute, you divide 70 by 5 and you get 14. You then multiply 14 boxes by 8 minutes giving you the product of 112.
WILL MARKDOWN BRAINLIEST
Answer:
1. $539
2. $300
3. C
Step-by-step explanation:
May I have brainliest?
a, = 5 +0.2(n-1)
f(n)
Answer:
a=4.8
Step-by-step explanation:
may be wrong tho
The quotient below is shown without the decimal point. Use number sense to place the decimal point correctly.
340.1 ÷ 9.5 = 358
Answer:
35.8
Step-by-step explanation:
[tex]\frac{340.1}{9.5}[/tex] = 358
We know that our answer can never be greater than 358 since the dividend
is 340.1 and the divisor is 9.5;
Also,
Both values are to one decimal places and we can use this to solve the problem;
9 can divide 340 in about 37 place with a remainder of 7,
So, it is appropriate to make the solution 35.8
find the value of x PLEASE EXPLAIN
Answer:
x = 57, x = 111
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180, that is
x + 67 + 56 = 180
x + 123 = 180 ( subtract 123 from both sides )
x = 57
---------------------------------------------------------------------
Similarly
x + 47 + 22 = 180
x + 69 = 180 ( subtract 69 from both sides )
x = 111
We can say that:
In the first triangle, x = 57°In the second triangle, x = 111°Let's go!We must know that the sum of all the internal angles of a triangle is equal to 180°. So, just solve an equation to determine x in each triangle.
First triangle:67 + 56 + x = 180 → Sum:123 + x = 180 → We move 123 to the other side, changing its signal.x = 180 - 123 → Subtract:x = 57°Second triangle:22 + 47 + x = 180 → Sum:69 + x = 180 → We move 69 to the other side, changing its signal.x = 180 - 69 → Subtract:x = 111°________________
Hope this helps! Good studies! ☺
Can someone please solve this before I get my phone taken away?
Answer:
option 1 or should be
Step-by-step explanation:
4/1.5 is 2.6 and 2/3 as a fraction is 66666 so yeah
Lexi jarred 2.3 liters of jam after 2 days. How many days does Lexi need to spend making jam if she wants to jar 4.6 liters of jam in all?
Answer:
bruh 4 days duh
Step-by-step explanation:
What is 708 divided by 67 with a remainder?
Answer:
its 10 with the remainder of 38
Step-by-step explanation:
The result of the division is remainder = 38 and quotient = 10
What is division?Division is the opposite of multiplying. When we know a multiplication fact, we can find a division fact: Example: 3 × 5 = 15, so 15 / 5 = 3. Also, 15 / 3 = 5.
Given that, 708 divided by 67
When dividing 708 by 67 will get 10 as quotient and 38 remainder
Hence, the result of the division is remainder = 38 and quotient = 10
Learn more about division, click;
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#SPJ2
Solve.
24 + d = 30
d =
Answer:
I think d = 6 because 24 + 6 = 30
Answer:
d=6
Step-by-step explanation:
5 (2k - 8 ) - 15 = -25
how do I solve this?
Answer:
3=k
5(2k-8)-15=-2510k-40-15=-2510k-55=-2510k=-25+5510k=3030÷103=kLESS THAN 5 MIN!!! WILL GIVE BRAINLIEST
Raise to the power:
(–xn)^4
Answer:
x^4n^4
Step-by-step explanation:
Answer:
[tex]n^{4} x^{4}[/tex]
I really hope this helps!
The post office sold 39-cent
commemorative stamps in sheets
of 25 stamps. What was the price
for the sheet of stamps?
Answer: $9.75.
Step-by-step explanation:
Given: Cost per stamp = 39 cents
since 1 dollar = 100 cent , so 1 cent = 0.01 dollar
So, Cost per stamp = $0.39
Total stamps = 25
Cost of 25 stamps = (Cost per stamp) x (Cost per stamp)
=$0.39 x 25
= $9.75
Hence, the price for the sheet of stamps = $9.75.
what isthe area of the circle or semicircle 2.5
Answer:
I don't know what your question was but the radius would eqaul .089 so the area is 2.5
Answer:
0.89
Step-by-step explanation:
the area of the. ..............
Parallel or perpendicular 3x+5y=10 and 5x-3y=-6
What is the discriminant of the quadratic equation, 4x^2-8x-5=0
Answer:
Step-by-step explanation:
4x^2-8x-5=0
The discriminant is the number under the √. In this case it's 144
Answer:
[tex]\Delta=144[/tex]
Step-by-step explanation:
For a quadratic in standard form, the discriminant is given by:
[tex]\Delta=b^2-4ac[/tex]
We have the equation:
[tex]4x^2-8x-5=0[/tex]
Hence, our a=4; b=-8; and c=-5.
Substituting into our formula, we acquire:
[tex]\Delta=(-8)^2-4(4)(-5)[/tex]
Evaluate:
[tex]\Delta=64+80[/tex]
Add:
[tex]\Delta=144[/tex]
Therefore, our discriminant is 144.
Notes:
Since our discriminant is a positive value, this tells us that our quadratic has two real roots.
What is the value of the expression 4/7 ÷ 12/21
Answer:
Step-by-step explanation:
[(24÷12)⋅6]+3⋅8÷2
2.Evaluate the expression.
(26÷13)⋅(−7)+14−4
3.Simplify this expression.
9 + 3 × 2
15
21
24
48
4.What is the value of this expression?
6⋅[(32−8)÷4+2]
5.Simplify.
6y+5z+8y−3z
11y + 5z
14y +2z
14y + 8z
16yz
does this help
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
hiiii please help if u can <3
Answer:
Step-by-step explanation:
given: triangle EDC is right angle isosceles triangle,AD and BC is perpendicular to AB.
statement reason
1. in triangle AED and BEC
a.∠ADE=∠EBC a.given( AD and BC is perpendicular to AB)
b.∠AED+∠DEC=∠EBD+∠ECB b. exterior angle of triangle is equal to two ∠AED =∠ECB opposite interior angle and substracting
(∠DEC=∠EBD=90°) from both side
c.ED=EC c corresponding sides of equal angle in
isosceles triangle are equal
2 ∴ triangle AED is congruent to BEC 2. by A.A.S axiom
What is the expanded form of 720.058
Answer:
Standard Form:
720.058
Expanded forms can be written like a sentence or stacked for readability as they are here.
Expanded Notation Form:
720.058 =
700
+ 20
+ 0
+ 0.0
+ 0.05
+ 0.008
Expanded Factors Form:
720.058 =
7 × 100
+ 2 × 10
+ 0 × 1
+ 0 × 0.1
+ 5 × 0.01
+ 8 × 0.001
Expanded Exponential Form:
720.058 =
7 × 102
+ 2 × 101
+ 0 × 100
+ 0 × 10-1
+ 5 × 10-2
+ 8 × 10-3
Word Form:
720.058 =
seven hundred twenty and fifty-eight thousandths
Step-by-step explanation:
Answer:
700 + 20 + 0 + 0.050 + 0.008
Step-by-step explanation:
Can someone please help me with this proof?!
Given: AC and BD bis, each other.
Prove: ABCD is a parallelogram
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: