Answer:
(x+7)(x-2)
Step-by-step explanation:
=x^2+5x-14
=x^2+(7-2)x-14
=x^2+7x-2x-14
=x(x+7)-2(x+7)
=(x+7)(x-2)
Answer: (x+7)(x-2)
We're looking for two numbers that multiply to -14 and also add to 5. Through trial and error, you should find those numbers are 7 and -2.
You can use the FOIL rule to confirm that (x+7)(x-2) expands out to x^2+5x-14
(x+7)(x-2) = x^2-2x+7x-14 = x^2+5x-14
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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Help mee pleaseeeeee!!!!
Answer:
c bye have a good day
Step-by-step explanation:
Brenna saved 36% on a $15 pair of sunglasses. Choose the correct expression to find 36% of $15.
A 36 x 15
B 36 x 0.15
C 3.6 x 15
D 0.36 x 15
Answer:
D
Step-by-step explanation:
HoPe THiS hElpSCalculate the side lengths a and b to two decimal places.
Answer:
Can confirm, it’s a=16.23 and b=17.99
5)Ten less than 6 times a number is greater than or equal to 2 more than twice the number.
Answer:
6n-10 >= 2+2x2
Step-by-step explanation:
Answer:
Step-by-step explanation:
6x - 10 ≥ 2x + 2 Subtract 2x from both sides
6x-2x - 10 ≥ 2x - 2x +2 Combine
4x - 10 ≥ 2 Add 10 to both sides
4x - 10+ 10 ≥ 2 + 10 Combine
4x ≥ 12 Divide by 4
4x/4 ≥ 12/4 Combine
x ≥ 3
The perimeter of the rectangle below is 94 units. Find the length of side WX.
Write your answer without variables.
Answer:
24units
Step-by-step explanation:
2(4y + 3) + 2(5y - 1) = 94
18y + 4 = 94
y = 5
WX = 5y - 1 = 5(5) - 1 = 24units
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First we need to find the value of y .
[tex]Perimeter = 2 \times ( \: (4y + 3) + (5y - 1) \: ) \\ [/tex]
[tex]Perimeter = 2 \times (9y + 2)[/tex]
[tex]Perimeter = 18y + 4[/tex]
Question told us that perimeter is 94 ,
Thus :
[tex]94 = 18y + 4[/tex]
[tex]18y + 4 = 94[/tex]
Subtract sides 4
[tex]18y + 4 - 4 = 94 - 4[/tex]
[tex]18y = 90[/tex]
Divide sides by 18
[tex] \frac{18y}{18} = \frac{90}{18} \\ [/tex]
[tex]y = 5[/tex]
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The face sides in the rectangular are same.
Thus :
[tex]VY = WX[/tex]
So ;
[tex] WX = 5y - 1[/tex]
[tex]WX = 5(5) - 1[/tex]
[tex]WX = 25 - 1[/tex]
[tex]WX = 24[/tex]
Done...
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PLEASE HELP ILL GIVE BRAINLEST
Circle the like terms:
⅓ x 4x2 8xy -x -5x
Answer:
8xy im pretty sure
Step-by-step explanation:
find the slope of the graph given below
Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
Which of the following sets of numbers could represent the three sides of a triangle?
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.
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
A car travels 355 miles in 5 hours. How many miles did they travel per hour?
Answer:
71 miles in 1 hour
Step-by-step explanation:
divide the total amount of miles by the total amount of hours: 335/5
you get 71 mph
Answer:
71 miles per hour
Step-by-step explanation:
355 divided by 5 is 71
71 x 5 = 355
355 divided by 71 is 5
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:
what’s the value of y??
Answer:
90.6
Step-by-step explanation:
that what i think and thanks
Picture shown below help
Answer:
measure of angle 2 and angle 3 are both 97
Step-by-step explanation:
angle 2 and angle 3 are vertical angles
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?
5) A firm has $30,000 in a bank account at the beginning of the year. Interest will be paid at a rate of 2% at the end of the year. How much interest will the firm receive for the year?
Answer:
10%
Step-by-step explanation:
10% i think
write an equation in point slope form to represent a line that passes through the points (-6,-14) and (12,16)
Answer:
y + 14 = 3/5(x + 6)
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
please help ASAP!
i will give brainliest!! :)
Answer:
its c i took the test trust me
Step-by-step explanation:
“Explain or show why 4:3 and 3:4 are not equivalent ratios.” Pls this is due today at 12:00 p.m
Please help meeeeeee
I need the answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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°
Kona’s mother realized that her age is the difference of Kona’s age squared and four. If k represents Kona’s age, which expression represents Kona’s mother’s age?
k squared minus 4
k cubed minus 4
k squared + 4
k cubed + 4
Answer:
k squared minus 4/ A
Step-by-step explanation:
took the test
Answer:A. k squared minus 4
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?
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 :)✨
Of the relations graphed below, three are functions and one is not.
Which of the relations is NOT a function?
4 graphs. Graph A is a curved line, graph b is horizontal, vertical, and then horizontal, graph C is a line with positive slope, graph D is a parabola.
Answer:
vertical line
Step-by-step explanation:
If it is possible to draw any vertical line (a line of constant x) which crosses the graph of the relation more than once, then the relation is not a function.
Answer:
the answer is b
Step-by-step explanation
PLEASE HELP I DONT WANT TO FAIL
A rollercoaster rises 160 feet into the air before dropping 190
feet. What is the height of the rollercoaster
Answer:
190
Step-by-step explanation:
27686+05446535
gfytf+ wtdf gufyhfedhe. b1+3533
⚠️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
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:
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8a+5 = 7b+4 = 5c + 2
Answer:
a= -5/8
b= -4/7
c= -2/5
Step-by-step explanation:
8a + 5 = 7b + 4 =5c + 2
I'm not sure what you want with this incomplete question, but I assume it's to find the values of a, b, and c.
Therefore, to find the value of a,
8a+5=0
8a= - 5
a= -5/8
7b + 4=0
7b = - 4
b= -4/7
5c + 2=0
5c= - 2
c= -2/5
Therefore, the values of a, b, and c are -5/8, -4/7 and -2/5
PLEASE HELP NEED ASAP
Help please!!! Solve for a: a+3(4a+8)=128
Answer:
A= 8 !!
Step-by-step explanation:
Answer:
a=8
Explanation:
distribute and simplify the left side of the equation
a
+
12
a
+
24
=
128
13
a
+
24
=
128
subtract 24 from both sides
13
a
=
128
−
24
=
104
divide both sides by 13
a
=
104
13
=
8
I give Brainliest!
Using Angle Side Relationship Theorem, use the side measures to list the angle measures of the triangle in order from biggest to smallest.
Q
R
P
Answer:
∠Q, ∠P, ∠R
From largest to smallest.
Step-by-step explanation:
Remember that the largest side is always opposite from the largest angle.
26 is the longest side. The angle opposite is 26 is ∠Q. So, ∠Q is the largest angle.
21 is the second longest side. ∠P is the angle opposite to 21. So, ∠P is the second largest angle.
Finally, 17 is the shortest side and ∠R is opposite to 17.
So, ∠R is the smallest angle.
Therefore, the measures of the angles from biggest to smallest is:
∠Q, ∠P, ∠R