As we know that slope is denoted by the letter m and is calculated by the formula:
[tex]\red{\boxed{\sf{Slope (m) \: = \: \dfrac{y_{2} \: - \: y_{1} }{x_{2} \: - \: x_{1}} }}} \: \bigstar[/tex]★ We have :
x₁ = 3x₂ = 5y₂ = 7y₁ = 1★ Putting the values :
[tex]: \: \longrightarrow \: \sf{Slope (m) \: = \: \dfrac{ 7 \: - \:1 }{5\: - \:3 } } \\ \\ : \: \longrightarrow \: \sf{Slope (m) \: = \: \dfrac{6 }{5\: - \:3 } } \\ \\ : \: \longrightarrow \: \sf{Slope (m) \: = \: \dfrac{6 }{2} } \\ \\ : \: \longrightarrow \: \sf{Slope (m) \: = \: \cancel\dfrac{6 }{2} } \\ \\ : \: \longrightarrow \: \pink{\bf{Slope (m) \: = \: 3 }}[/tex]
Additional Information :
★ Centroid of a triangle :-
[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]★ Distance Formula :-
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]★ Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]a line that includes the point (7,-9) has a slope of -2. v
Answer:
y = - 2x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (7, - 9 ) into the partial equation
- 9 = - 14 + c ⇒ c = - 9 + 14 = 5
y = - 2x + 5 ← equation of line
In parallelogram ABCD, m∠B = 32 + 35 and m∠D = 52 + 13. Find m∠C.
Answer:
113°
Step-by-step explanation:
1) according to the condition m(∠B)=m(∠D)=67°;
2) m(∠C)=180°-m(∠B)=180°-m(∠D);
m(∠C)=180-67=113°.
At a local high school, enrollment in the drama club increases by 5% each year. what is the common ratio in this situation? 0.05 0.95 1.05 1.95
At a local high school, enrollment in the drama club increases by 5%. the common ratio will be 1.05.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
At a local high school, enrollment in the drama club increases by 5%.
Let an initial number of students in high school be 'a'.
so next year increase in students will be = 5% of a
= 5/100 × a
= 0.05a
and total number of the students will be = ( a + 0.05a )
= ( 1.05a )
So common ratio of the geometric square formed
( 1.05a )/ a = 1.05
Therefore, the common ratio will be 1.05.
Learn more about percentages;
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What is the circumference of a circle with a diameter of 8 inches?
a 12.56
b 25.12
c 50.24
d 200.96
A Circle is a closed plane geometric shape figure. The diameter of a circle is the longest chord of a circle. The radius drawn perpendicular to the chord bisects the chord. A Circle is always lie at an equal distance from a center point. Circles having different radius are similar.
Circumference of Circle:The circumference of a circle is the product of pi and length of the diameter of a circle. Mathematically;
[tex]\longrightarrow \tt{Circumference_{(circle)} = \pi{D}}[/tex]
Here, D is the diameter of the circle or distance between the circle.
Elucidation:We are asked to find the circumference of the circle if the diameter is 8 inches.
We know that, The circumference of a circle is the product of pi and length of the diameter of a circle. Therefore;
[tex]\implies \tt{Circumference_{(circle)} = \pi{D}}[/tex]
[tex]\implies \tt{Circumference_{(circle)} = 3.14 \times 8}[/tex]
[tex]\implies \boxed{\pmb{\tt{Circumference_{(circle)} = 25.12}}}[/tex]
Hence, the circumference of the circle is 25.12 inches. So option (B) is correct.
Answer:
Circumference of circle = 25.12 inchesThus Option B is correct .Step-by-step explanation:
In the question we are given that diameter of circle is of 8 inches . And we have asked to find the circumference of the circle .
For finding circumference of circle we must have to know that what is the formula for finding circumference of circle. So :
[tex] \quad \quad \: \red{\underline{\pink{ \boxed{ \frak{Circumference \: of \: Circle =2 \pi r }}}}}[/tex]
Where ,
π refers to 3.14 r refers to radius of circleSolution : -
As in the question we are given length of diameter . So for finding circumference we need to find the radius of circle .
We know that diameter of circle is two times its radius ,
[tex] \qquad \: \rm {Diameter = 2 × Radius }[/tex]
So for radius we are dividing both side with 2 :
[tex]\qquad \: \rm { \dfrac{Diameter}{2} = \dfrac{ \cancel{2} × Radius}{ \cancel{2}} }[/tex]
We get that ,
[tex] \qquad \: \rm {Radius = \dfrac{Diameter}{2} }[/tex]
Therefore , we can say that radius of circle is half of its diameter .
Now using this , firstly we are finding radius of circle . So :
[tex] \longmapsto \quad \: \boxed{\rm{ Radius = \frac{8}{2} \: \: inches}}[/tex]
Therefore , radius of circle is 4 inches .Now , we are moving towards our final solution .
So ,
[tex] \longmapsto \quad Circumference_ { (Circle)} =2 \times 3.14 \times 4 [/tex]
Multiplying 2 with 3.14 :
[tex]\longrightarrow \quad Circumference_ { (Circle)} = 6.28 \times 4 [/tex]
Multiplying 4 and 6.28 :
[tex]\longrightarrow \quad \purple{{\boxed{\frak{Circumference_ { (Circle)} = 25.12\: inches }}}}[/tex]
Therefore , circumference of circle having diameter 8 inches is 25.12 inches and hence option b is correct .#Keep LearningWhile mining, Joan found a large metal bar that weighed 20 ounces. Joan was also able to determine that the bar contained 65% tin. How many ounces of tin are in the metal bar? Round your answer to the nearest whole number if necessary.
(I will mark brainliest if you answer+explain)
Answer: 13 ounces
Step-by-step explanation:
To answer this question, we will find 65% of 20. A percent divided by 100 becomes a decimal that can be used to solve.
65% / 100 = 0.65
0.65 * 20 = 13
There are 13 ounces of tin in the metal bar.
Answer:
The metal bar contains 13 ounces of tin.
Step-by-step explanation:
Multiply '20 ounces' by 0.65, obtaining 13 ounces.
The metal bar contains 13 ounces of tin.
Which of the following statements must be true of a function?
A. Every output value corresponds to only one input value.
B. Every input value corresponds to only one output value.
C. No inout values are repeated.
D. No output values are repeated
Answer:
B: Every input value corresponds to only one output value.
Amin has 16 pots of equal size. He used 9 bags of potting soil to fill 12 of the pots. At that rate, how many bags of potting soil does Amin need to fill the remaining 4 pots?
Answer:
5 1/3 bags
Step-by-step explanation:
12/9 = 1 1/3 bags per pot
4 * 1 1/3 = 5 1/3 bags to fill the pots
Answer:
3 bags
Step-by-step explanation:
Given
Amin has 16 potsHe fills 12 of them with 9 bags of soilSolving
No. of bags per pot = 9/12No. of bags per pot = 0.75Remaining pots = 3Bags needed = 0.75 x 3 = 2.25 bags3 bags (nearest whole number)Solve 2(x+1)=2x+5
-------------------------------------------
All real numbers
No solution
0
3
The answer is "no solution"
If you place 6 blue 3 yellow and 5 pink marbles in a bag close your eyes and choose a marble what is the probability that it will be blue
Answer:
6/14 or simplify it to 3/7
Step-by-step explanation:
this is because you have a total of 14 marbles
Diego borrowed $915 for nine months with monthly payments of $108.00.
What is the amount of total payments?
O $1,023
$1,002
S972
$915
Step-by-step explanation:
108 x 9 = 972
so it's 972 dollars
ANSWER THIS!!!!!!!! PLEASEEEEEE!!!!! CLICK ON THIS ONE!!
The line looks like it is around 6, the square root of 61 is 7.810249675906654, so that would be the closest to our estimate.
Answer:
I think the answer is 11
Step-by-step explanation:
because if u count under the lines from one point to another u get 6
then count up from where ur at and u get 5
and then ig just add it up
6+5
look
A traveler pulls a suitcase, as shown in the figure. (image below)
The force acting on the handle is 35 N at an angle of θ = 30°. How much work is done if the traveler moves 110 meters? Round to the nearest whole number.
1,893 Nm
1,925 Nm
2,703 Nm
3,334 Nm
Answer:
3334 N·m
Step-by-step explanation:
Work is the product of force and distance. The force used in the product is the force that is in the direction of motion.
__
The horizontal component of the applied force is ...
F = (35 N)cos(30°) ≈ 30.311 N
Then the work done is ...
W = Fd
W = (30.311 N)(110 m) = 3334 N·m
The cost for a teacher to offer an art class is represented by the function f(s)=15s+75, where s is the number of students enrolled. What does each parameter represent in this situation? Drag and drop the explanation to the parameter it represents. HELP. Will reward 20 points.
Answer:
look below
Step-by-step explanation:
Slope = materials cost per student
Y—intercept = cost of renting the classroom
two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds:
y = – (x – 5)2 + 3
y = –3(x –3)2 + x + 1
30 POINTS !! To make sure the flip is in unison, after how many seconds should the flip occur?
2 seconds
3 seconds
4 seconds
5 seconds
To make sure the flip is in unison, after 4 seconds should the flip occur, as given by the option C: 4 seconds.
What does synchronized motion mean?Synchronized motion is a motion of two or more system which goes in syncronization with each other.
For this case, the flip will occur such that both gymnasts are synchronized and flip is unison (simultaneous).
For that, we need the time(x) and the height (y) same.
Since the motion paths are:
[tex]y= -(x-5)^2 + 3\\\\y = -3(x-3)^2 + x + 1[/tex]
Therefore, we need to find the values of x for which same y comes as output.
Let x = t be the time for which the height y is same, then:
[tex]-(t-5)^2 + 3 = -3(t-3)^2 + t + 1[/tex] = height achieved by both gymnasts.
Solving it further:
[tex]-(t-5)^2 + 3 = -3(t-3)^2 + t + 1\\3(t^2 + 9 -6t) -(t^2 + 25 -10t) -t + 2 = 0\\\\2t^2 -9t + 4 = 0\\2t^2 -8t - t + 4 = 0\\2t(t-4) -1(t-4) = 0\\(2t -1)(t-4) = 0\\\\t = 4, t = 1/2[/tex]
Assuming they planned to do flip after integral number of time in seconds, the correct option is t = 4 seconds.
Thus, to make sure the flip is in unison, after 4 seconds should the flip occur, as given by the option C: 4 seconds.
Learn more about solving system of equations here:
https://brainly.com/question/2825832
Answer:
5 seconds
Step-by-step explanation:
Put the equations in desmos and you will see they intersect at 5 seconds.
This is definitely correct. Here is proof:
The school auditorium has 120 seats. The school is selling tickets for 3 performances of the school play. How many tickets are available. Show your work.
Answer:
Friday: 18 tickets Saturday:24 tickets Sunday: 2 tickets
Step-by-step explanation:
120-102=18 tickets
120-96=24 tickets
120-118=2 tickets
TYSM I REALLY NEEDED IT TY!!
it helped me
You pick a card at random, put it back, and then pick another card at random.
1 2 3 4
What is the probability of picking a number greater than 1 and then picking a number greater
than 2?
Answer:75% percent chance of picking a card greater than 1 and a 50% chance of picking a card greater than 2
Step-by-step explanation:
please pick me as brainliest
Write an example problem(s) for area.
Answer:
Example 1.
A square with side lengths of 5.
5*5 = 25.
So the area would be 25 units ^2
Example 2.
A rectangle with a length of 9 and a width of 4
9*4 = 36
So the area is 36 units ^2
There are 420 fans at a high school basketball game. The ratio of students to parents is 5 to 2. Exactly how many more students are there than
parents at the game?
Answer:
180 more students than parents at the game
Step-by-step explanation:
There are 5 students for every 2 parents equalling 7 people in one set of students to parents ratio.
There are 420 fans at the game. Divide the 420 by the 7 people per set.
420 / 7 = 60 (There are 60 sets of 5 students to 2 parents ratio)
Multiply the 60 sets by 5 students and 2 parents, respectively:
60 x 5 = 300 students
60 x 2 = 120 parents
Subtract the number of parents from number of students:
300 students - 120 parents = 180 more students
If 1/5 of those in a high school are freshmen, and 40% of the freshmen are women, and 3/5 of those in the other grades are women, how many men are enrolled in the high school, given that there are 600 students altogether? a. 240.
b. 264.
c. 300.
d. 336.
e. 360
There are 264 male students in the high school containing 600 students.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
There are 600 students altogether, hence:
Number of freshmen = (1/5) * 600 = 120
Number of other graders = 600 - 120 = 480
Number of male freshmen = 120 - (0.4 * 120) = 72
Number of male other graders = (1 - 3/5) * 480 = 192
Total number of male = 72 + 192 = 264
There are 264 male students in the high school containing 600 students.
Find out more on equation at: https://brainly.com/question/1214333
Express the following in p/q form, where p and q are integers and q is not equal to 0.
(i) 1.272727..... (ii) 0.1282828.......
pls give the answer with steps
thank you!!!
(i) 1.272727...
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1.\overline{27}}}}[/tex] [tex]\bf{i.}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{Let\:x\:be\:1.\overline{27}}}}[/tex]
Multiplying both the sides by 100.
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{x\:*\:100=1.\overline{27}\:*\:100}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{100x=127.\overline{27}}}}[/tex] [tex]\bf{ii.}[/tex]
Subtracting [tex]\bf{i.}[/tex] from [tex]\bf{ii.}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{100x\:-\:x=127.\overline{27}\:-\:1.\overline{27}}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{99x=126}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{126}{99}}}}[/tex]
Reducing it to lowest form
[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{14}{11}}}}[/tex]
[tex]\gray{\rule{300pt}{0.3em}}[/tex]
(ii) 0.1282828...
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{0.1\overline{28}}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{Let\:x\:be\:0.1\overline{28}}}}[/tex]
Multiplying both sides by 10
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{x\:*\:10=0.1\overline{28}\:*\:10}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{10x=1.\overline{28}}}}[/tex] [tex]\bf{i.}[/tex]
Multiplying both sides by 100
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{10x\:*\:100=1.\overline{28}\:*\:100}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1000x=128.\overline{28}}}}[/tex] [tex]\bf{ii.}[/tex]
Subtracting [tex]\bf{i.}[/tex] from [tex]\bf{ii.}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1000x\:-\:10x=128.\overline{28}\:-\:1.\overline{28}}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{990x=127}}}[/tex]
[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{127}{990}}}}[/tex]
[tex]\gray{\rule{300pt}{0.3em}}[/tex]
Hope it helps..♪Convert.
pints = 61 quarts
Match Term Definition
Triangle A) shape created when a rectangle is rotated about the y-axis
Rectangle B) perpendicular cross section of a cylinder
Circle C) parallel cross section of a sphere
Cylinder D) perpendicular cross section of a pyramid
Cone E) shape created when a right triangle is rotated about the y-axis
Answer:
Perpendicular cross section of a pyramid ------- triangle.
Perpendicular cross section of a cylinder ------- rectangle
parallel cross section of a sphere ------ circle
shape create.... ----- cylinder.
Step-by-step explanation:
Imagine you cut pyramid like that. Height of pyramid would be height of your triangle. and sides of pyramid would be sides of triangle.
diameter of a base of cylinder would be one side of rectangle and height of cylinder would be other side of rectangle. (pair of sides)
when you cut sphere a side would apear with shape of circle.
one side of rectangle would be hight of cylinder and other would be radius of it.
last one is cone. If you place right angle in coordinate beginning (0.0) and one of shorter sides to lie on y axis other would be on x axis. when rotated you get cone.
What is the quotient of (x3 – 3x2 3x – 2) ÷ (x2 – x 1)? x – 2 x 2 x – 4 x 1
The quotient of the equation is x-2.
What is the quotient?The quotient is the number that is generated when we perform division operations on two numbers. Basically, it is the result of the division method.
The given equation is;
[tex]\rm \dfrac {x^3 - 3x^2 + 3x -2}{ x^2 - x + 1}\\\\[/tex]
By fraction, a quotient is a number obtained by dividing the dividend by the divisor which is a simple division of numerator and denominator.
The solution of the equation is determined in the following steps given below.
[tex]\rm = \dfrac {x^3 - 3x^2 + 3x -2}{ x^2 - x + 1}\\\\\rm = \dfrac {( x^2 - x + 1)(x-2)}{ x^2 - x + 1}\\\\=x-2[/tex]
Hence, the quotient of the equation is x-2 .
Learn more about quotient here;
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if 500(.85)^x = 30(1.15)^x what is X
Answer:
x = log 17frac 23 (3)
(50)
Step-by-step explanation:
500 x 0.85 x at the top =30x1.15 x at the top again.
Which transformation is this an example of?
A. reflection
B. rotation
C. translation
D. None of these
Answer:
B. rotation
Step-by-step explanation:
A reflection would mean that the shape would be mirrored across the y-axis or the x-axis. A translation means that nothing about the shape changes except for the location. A dilation (not an answer option but still helpful to know) is the change in size of the shape. And finally, the correct answer for this problem, a rotation means that the shape is rotated at a specific point.
I included a picture that uses a shape to help explain this idea. I hope this helps! Have a lovely day!! :)
Using the distributive property to find the product (y−4x)(y2 4y 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x. what is the value of a in the polynomial? 4 8 16 32
The product (y−4x)(y^2 + 4y + 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x then the value of a is 16.
What is distributive property?The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is
A(B + C) = AB + AC
This property is known by distributive law and applies to subtraction also.
First let w = y-4x make distribution a bit easier
(y−4x)(y^2 + 4y + 16)
[tex]w(y^2 + 4y + 16)\\wy^2 + w4y + w16\\[/tex]
now put the values of w in the equation
[tex](y-4x)y^2 + (y-4x)4y + (y-4x)16\\y^3-4xy^2 + 4y^2-16xy+16y-64x\\[/tex]
Here the value of a is 16.
Learn more about the distributive property:
https://brainly.com/question/26207297
Answer:
16
Step-by-step explanation:
Point m lies between points l and n on line segment l n . the space between l and m is 10 x 8. the space between m and n is 5 x minus 4. if ln = 12x 16, what is the length of line segment l n in units? 16 units 40 units 48 units 64 units
The length of line segment l n on which point m lines in between is 64 units. Option 4 is the correct option.
What is the length of line segment?Length of a line segment is the distance of both the ends of it.
Point m lies between points l and n on line segment l n .
The space between l and m is 10x 8. The space between m and n is 5x -4.The value of line segment LN is,
[tex]LN = 12x +16[/tex]
The sum of LM and LN is equal to the line segment LN. Thus,
[tex]LM+MN=LN\\10x +8+(5x-4)=12x+ 16\\10x +8+5x-4=12x+ 16\\10x+5x-12x=16 -8+4\\3x=12\\x=\dfrac{12}{3}\\x=4[/tex]
Put this value of x in the equation of line segment LN,
[tex]LN = 12(4) +16\\LN=48+16\\LN=64\rm\; units[/tex]
Thus, the length of line segment l n on which point m lines in between is 64 units. Option 4 is the correct option.
Learn more about the line segment here;
https://brainly.com/question/2437195
• A principal is planning for 120 parents
to attend the Eighth Grade Open House.
In the multipurpose room, round tables
seat 6 and square tables seat 8. Let x
equal the number of round tables needed.
Let y equal the number of square tables
needed. Write an equation that represents
this situation. Then use the equation to
determine the number of round tables
needed if no square tables are used.
Answer:
✏If the rod is held straight then the angle alpha equals 90°,therefore the required solution is 45°
Step-by-step explanation:
Algebra Find the value of x.
Answer:
8 :)
Step-by-step explanation:
Side 1: 15
Side 2: 14
Side 3: 7 + x
Side 1 and 3 are the same length so we subtract :D
15 - 7 = 8
Have an amazing day!!
Please rate and mark brainliest!!
In a class of students, the following data table summarizes how many
students have a cat or a dog. What is the probability that a student
chosen randomly from the class has a dog?
Answer:
22/29
Step-by-step explanation:
First, add up all of the numbers given:
16 + 4 + 6 + 3 = 29
Now since there are 16 students who have a dog and a cat, and 6 who only have a dog, we add those numbers:
16 + 6 = 22
Now since there are 29 total numbers, that will be the number of outcomes out of the 22 people with dogs:
22/29