Answer:
[tex]y = \dfrac 12x -5[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (6,-2)~ \text{and}~ (x_2,y_2) = (12,1)\\\\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{1+2}{12-6}= \dfrac{3}{6} = \dfrac 12\\\\\text{Equation of line,}\\\\~~~~~~~~y-y_1 =m(x-x_1)\\\\\implies y+2=\dfrac 12 (x-6)~~~~~~~~~~~~~~;[\text{Point -slope form}]\\\\\implies y = \dfrac 12 x -3 -2\\\\\implies y = \dfrac 12x -5~~~~~~~~~~~~~~~~~~~~~;[\text{Slope-intercept form.}][/tex]
Select the correct expressions. 1 Identify each expression that represents the slope of a tangent to the curve y= * +1 at any point (x, y)
The expressions which represents the slope of a tangent to the curve [tex]y=\frac{1}{x+1}[/tex] at any point (x, y) are:
[tex]f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}[/tex]
The slope of a tangent to the curve.Mathematically, the slope of a tangent line to the curve is given by this equation:
[tex]f'(x) =limh \rightarrow 0\frac{f(x+h)-f(x)}{h}[/tex]
Given the function:
[tex]f(x)=y=\frac{1}{x+1}[/tex]
When (x + h), we have:
[tex]f(x+h)=y=\frac{1}{x+h+1}[/tex]
Next, we would find the derivative of f(x):
[tex]f'(x) =limh \rightarrow 0\frac{\frac{1}{x+h+1} -\frac{1}{x+1}}{h}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -(x+h+1)}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -x-h-1}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}\\\\f'(x) = \frac{-1}{(x+1)(x+1)} \\\\f'(x) = \frac{-1}{(x+1)^2}[/tex]
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Identify the center and the radius of each circle.
C. X^2+2x+1+y^2+4y+4=9
Answer:
[tex]Center =(-1,\: -2),\: radius = 3\: units[/tex]
Step-by-step explanation:
[tex] x^2 +2x + +1 + y^2++4y+4=9[/tex] (Given equation of circle)[tex]\implies (x^2 +2x + +1) + (y^2++4y+4)=(3)^2[/tex][tex]\implies (x+1)^2 + (y+2)^2=(3)^2[/tex]Comparing the above equation with standard form of circle i.e. [tex](x-h)^2+(y-k)^2=r^2[/tex], we find:[tex]h=-1, \: k = -2,\: r = 3[/tex][tex]Center =(h, \: k )=(-1,\: -2),\: radius = 3[/tex]Joe has 7/8 yards of string. What is the maximum number of 1/16 yards of string Joe can be cut from the string? 11 points
Answer:
14
Step-by-step explanation:
7/8 = 14/16
A sequence is represented by the formula an=-5+a(n-1). If a4 = 20, what is the 6th term in the sequence?
PLEASE HELP!!
Answer:
10
Step-by-step explanation:
Formula :
aₙ = -5 + aₙ₋₁Finding a₅ :
a₅ = -5 + a₄a₅ = -5 + 20a₅ = 15Finding a₆ :
a₆ = -5 + a₅a₆ = -5 + 15a₆ = 10If as = 24, a, = 40, then find a20
Answer:
[tex]a_{20}[/tex] = 84
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + ( n - 1 )d
~~~~~~~~~~~~~
[tex]a_{5}[/tex] = [tex]a_{1}[/tex] + (5 - 1)d = 24
[tex]a_{9}[/tex] = [tex]a_{1}[/tex] + (9 - 1)d = 40
[tex]a_{1}[/tex] + 4d = 24 ........... (1)
[tex]a_{1}[/tex] + 8d = 40 ........... (2)
(2) - (1)
4d = 16 ⇒ d = 4
[tex]a_{1}[/tex] + 8(4) = 40 ⇒ [tex]a_{1}[/tex] = 8
[tex]a_{20}[/tex] = 8 + ( 20 - 1 ) × 4 = 84
Can one of u guys help me I need help asap
Answer:
See below ~
Step-by-step explanation:
The three inequalities (listed below) have been plotted on a graph :
y ≤ 8y ≥ -3x + 4y > 2x - 4Consider the diagram.
2 triangles are connected at their hypotenuse to form a rectangle. The rectangle has a length of 7 meters and width of 6 meters.
Mia plans to build a fence to divide her rectangular garden into two triangular areas. Use the diagram to find the length of fence she will need to divide the garden. Round up to the nearest hundredth.
Mia will need a fence that is
meters long.
The length of fence she will need to divide the garden is 9.22 m.
What is a Rectangle?A Rectangle is a quadrilateral having four sides and four right angles in which both sides are parallel and opposite to each other.
Pythagoras TheoremThe Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
Let us consider the length of the fence be 'x'
Using Pythagoras Theorem,
x² = 6² + 7²
[tex]x^{2} =36+49\\x^{2} = 85[/tex]
x = 9.22 m
So, the length of fence is 9.22 m.
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Answer:
9.22
Step-by-step explanation:
edge
Two stores have movies to rent.
• The first store charges a $10.50-per-month membership fee plus
$1.50 per movie rented.
• The second store has no membership fee but charges $2.50 per movie
rented.
What is the minimum number of movies a person would need to rent in a month
for the first store to be a better deal?
Answer:
4 movies because ďòê ánş vianna sausage says so i dont know im barely passing math myself
Expand and simplify 3(x-4)(2x+5)
3(x-4)(2x+5)
= 3×(x-4)×(2x+5)
= (3x-12)(2x+5)
= 6x²+15x-24x-60
= 6x²-9x-60
[tex]3( {2x }^{2} + 5x - 8x - 20) \\ 3( {2x}^{2} - 3x - 20) \\ {6x}^{2} - 9x - 60 \\(6x + \frac{5}{2} )(x - 4)[/tex]
A group of 3 people are sharing chocolates.Each person wants 8 chocolates and each box has 4 chocolates.How many boxes do they need?
Answer:
6
Step-by-step explanation:
you times it and you get the answer
Which of the following options have the same value as 10% of 33?
Choose 3 answers:
0.1.0.33
® 10.33
©
1
10
33
0.1.33
10
100
33
3o
Answer:
1
Step-by-step explanation:
THE DISTRIBUTIVE PROPETY
3(4+3r)
Answer:
12+9r
Step-by-step explanation:
3(4+3r) = 3*4+3*3r = 12+9r
Which statement is true
Answer:
the answer is only 5
Step-by-step explanation:
What is the solution of logx 729=3?
The answer is 9 (B) on edge.
Answer:
x = 9
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{x}[/tex] 729 = 3 then
729 = x³
note 729 = 9³ , so
9³ = x³ ( equating the bases) , gives
x = 9
HELP ASAP THIS IS DO TOMORROW!
Answer:
The volume of the box is 250cm³
Step-by-step explanation:
V = Length * Width * Height
V = 5cm * 5cm * 10cm
V = 250cm³
The volume of the given box (rectangular prism).
Solution:[tex]V = whl[/tex]
[tex]V = 10 \times 5 \times 5[/tex]
[tex]\large\boxed{\sf{V = 250 \: {cm}^{3}}}[/tex]
Therefore, the volume of the given box (rectangular prism) is 250 cubic centimeters.
sophie leaves school and travels east at an average speed of 40km/h, jenny leaves school one hour later and travels west at an average speed of 50km/h, determine how many hours after jenny leaves school they will be "400km" apart
Considering the speeds given, it is expected Sophie and Jenny are 400 km apart after a total of 5 hours.
How will their position change over time?Jenny:
1 hour later: 40 km east2 hours later: 80 km east3 hours later: 120 km east4 hours later: 160 km east5 hours later: 200 km eastSophie:
1 hours later: 0 km2 hours later: 50 km west3 hours later: 100 km west4 hours later: 150 km west5 hours later: 200 km westWhen wil they be 400 km apart?It is expected 5 hours later they are 400km apart because at this time each of them will be 200km away from school.
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The diameter of a cylindrical construction pipe is 3 ft. If the pipe is 12 ft long,
what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole
number.
Be sure to include the correct unit in your answer.
Work Shown:
d = 3 = diameter
r = d/2 = 3/2 = 1.5 = radius
h = 12 = height or length of the pipe
pi = 3.14 approximately
V = volume of the cylinder pipe
V = pi*r^2*h
V = 3.14*(1.5)^2*12
V = 84.78
V = 85
The cylindrical pipe's volume is about 85 cubic feet.
I need help PLEASE HELPP
Answer:
1 and 5 are corresponding angle
8 and 4 are corresponding angle
4 and 6 are alternate interior angle
2 and 8 are alternate exterior angle
7 and 3 are corresponding angle
2 and 6 are corresponding angle
3 and 5 are alternate interior angle
1 and 7 are alternate exterior angle
HELP NOW PLESAE
WHat is m
An inscribed angle (like angle RTS) is half its intercepted arc.
Angle RTS = 51
Then, we just have a triangle to look at. Remember that the interior angles of a triangle add up to 180.
67 + 51 + x = 180
118 + x = 180
x = 62
Answer: angle RST = 62 degrees
Hope this helps!
Please help. I dont understand a thing. lol
Answer:
39 in²
Step-by-step explanation:
Area of triangle = 1/2 * b * h, where,
b = Base of Triangle
h = Height of triangle
Area of 4 triangles = 4 * 1/2 * 3 in * 5in
Area of 4 triangles = 2 * 3 in * 5 in
Area of 4 triangles = 30 in²
Area of square = a², where,
a = Each side of square.
Area of square = (3 in) ²
Area of square = 9 in²
Total surface area of pyramid = 30 inch² + 9 inch²
Total surface area of pyramid = 39 in²
Answer:
39 in^2 (Please mark me brainliest)
Step-by-step explanation:
3*3+3*2*5
=39
Find the values of x and y in parallelogram PQRS. PT=y, TR=2x+1, QT=5y, TS=6x+13 x= ? and y= ?
Answer:
Step-by-step explanation:
The coordinates of the endpoints of the diameter of a circle are (-1, 5) and (3, -1). The center of the circle has coordinates
Answer: (1,2)
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so using the midpoint formula, we get the answer to be [tex]\left(\frac{-1+3}{2}, \frac{5-1}{2} \right)=\boxed{(1,2)}[/tex]
e. In a survey, it was found that the ratio of people who like tea and coffee is 9:8. If 25% liked tea and coffee both, 80 liked none of these and 20% liked tea only, find the total number of people participated in the survey.
8x+5y=16 8x+10y=56 what strategy could you apply to use the linear combination method to solve the system?
Answer:
elimination
Step-by-step explanation:
Can someone please help me with b and C questions
Answer:
(b) 33919
(c) 8 ¹/₃
Step-by-step explanation:
⇒ 317 × 107 = (300 + 10 + 7)(100 + 7)
= 300(100 + 7) + 10(100 + 7) + 7(100 + 7)
= 30000 + 2100 + 1000 + 70 + 700 + 49
= 30000 + 2000 + 100 + 1000 + 70 + 700 + 40 + 9
= 30000 + 2000 + 1000+ 700 + 100 + 70 + 40 + 9
= 30000 + 3000 + 800 + 110 + 9
= 30000 + 3000 + 800 + 100 + 10 + 9
= 30000 + 3000 + 900 + 10 + 9
= 33919
[tex]\begin{aligned} 5\frac{2}{3}+3\frac{1}{2}-\frac{5}{6}&=\dfrac{5 \times3+2}{3}+\dfrac{3 \times 2+1}{2}-\dfrac{5}{6}\\\\&=\dfrac{17}{3}+\dfrac{7}{2}-\dfrac{5}{6}\\\\& =\dfrac{17 \times 2}{3\times 2}+\dfrac{7\times 3}{2\times 3}-\dfrac{5}{6}\\\\ & = \dfrac{34}{6}+\dfrac{21}{6}-\dfrac{5}{6}\\\\ & = \dfrac{34+21-5}{6}\\\\ & = \dfrac{50}{6}\\\\&=8\frac{1}{3}\end{aligned}[/tex]
Find x if f(x)=2x-7 and f(x) = 18.
Answer:
x = 12.5
Step-by-step explanation:
f(18)=2x-7
18+7=2x
25=2x
x=12.5
Give brainiest please!
Hope this helps :)
Write and simplify an expression that represents the sum of the perimeters of the square and the triangle.
A square with side length 6x. A triangle with side lengths 3x, 3x, and x - 2.
Answer:
To solve this question, you simply apply algebraic formulas to geometric relationships.
The perimeter is simply the sum of the lengths of the sides of a shape. However, in this case, there is an "x" involved, so you must add algebraically.
Simply add the length of the sides up.
[3x] + [6x-2] + [x+3] + [4x+1] + [5x-2] = Perimeter
Now, simplify. Since adding is commutative, you can simply put all the variables first and constants next, no matter where they come from within the expression.
3x + 6x + x + 4x + 5x + -2 + 3 + 1 + -2
19x + 0 (-2-2 + 3+1 cancel out)
The perimeter of this pentagon is 19x.
Step-by-step explanation:
RIGHT triangular prisms A and B are congruent. What is the volume of prism B? A) 420 in3 B) 1080 in3 C) 2160 in3 D) 32400 in3
Answer: B
Step-by-step explanation:
6. The three side lengths of a triangle are given. Which triangle is a right triangle?
A. Triangle 1: 13, 6, 7
B. Triangle 2: 7, 8, 13
C. Triangle 3: 10, 11, 12
D. Triangle 4: 10, 9,8
Illustrate on a number line the solution set of each pair of simultaneous inequalities. x>-2;-4 <x <2
The intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have two inequalities:
x>-2 and
-4 <x <2
or
x ∈ ( -2, ∞) and x ∈ (-4, 2)
The intersection region will be(from the graph)
x ∈ (-2, 2)
Thus, the intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
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