What is the equation of the line that passes through the points (4,-1 ) and (-7,4 )?
Answer:
[tex] \large{ \tt{❃ \: STEP- BY - STEP \: EXPLANATION}} : [/tex]
Let the equation of line passes through the points A ( 4 , - 1 ) and B ( - 7 , 4 ) . Let A ( 4 , -1 ) be ( x₁ , y₁ ) & B ( - 7 , 4 ) be ( x₂ , y₂ )[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]
Using two - point form of the equation of straight line , we have :[tex] \boxed{ \large{ \bf{❀ \: y -y _{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1}} (x - x_{1)}}}}[/tex]
- Plug the values :
[tex] \large{ \bf{⇢ \: y - ( - 1) = \frac{4 - ( - 1)}{ - 7 - 4}(x - 4) }}[/tex]
[tex] \large{ \bf{⇢y + 1 = \frac{4 + 1}{ - 11} (x - 4)}}[/tex]
[tex] \large{ \bf{⇢ \: y + 1 = - \frac{5}{11} (x - 4)}}[/tex]
[tex] \large{ \bf{⇢y + 1 = - \frac{5}{11}x + \frac{20}{11} }}[/tex]
[tex] \large{ \bf{⇢y + 1 = \frac{ - 5x + 20}{11} }}[/tex]
[tex] \large{ \bf{⇢11(y + 1) = - 5x + 20}}[/tex]
[tex] \large{ \bf{⇢11y + 11 = - 5x + 20}}[/tex]
[tex] \large{ \bf{⇢5x + 11y + 11 - 20 = 0}}[/tex]
[tex] ⇢ \boxed{\large{ \bold{\bf{5x + 11y - 9 = 0}}}}[/tex]
♕ Hence , 5x + 11y - 9 = 0 is the required equation of the line.✺ The two most important days in your life are the day you are born and the day you find out why ! ♪
♡ Hope I helped! ツ
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divide x^4+x^2-2x^2+x+1 by x-1
Answer:
= 0
Step-by-step explanation:
by using reminder theorem,
let, x - 1 = 0
then,
x = 1
plag in
1^4 + 1^2 - 2(1)^2 + 1 + 1
1 + 1 - 4 + 2
2 - 4 + 2
2 - 2
= 0
that's what I think.
What is the mean for 46 47 52 55 64 69 70 78
answer: 60.125
step-by-step explanation:
46 + 47 + 52 + 55 + 64 + 69 + 70 + 78 is 481, then you divide it by the amount of numbers you have which is 8 and you get 60.125
please help me i suck at this
Answer:
x = 10
Step-by-step explanation:
We know that in a parallelogram base angles are supplementary angle (add up to 180°)
Given that;
∠U = 9x + 15
∠V = 6x + 15
we can say that:
∠U + ∠V = 180°
(9x + 15) + (6x + 15) = 180
Combining like terms we get;
15x + 30 = 180°
15x = 180 - 30
15x = 150
x = 150/15
x = 10
Hope this helps!
I need help no files just type the whole thing in
Answer:
the answer to C. Is 3/8.
The answer to D. Is 5/8.
Step-by-step explanation:
1. solve for p: p - 17 = 13
2. solve for m: 23 + m = 31
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
1st Question :-[tex]p - 17 = 13 \\ p = 13 + 17 \\ p = 30[/tex]
✍ The value of p is 30.
2nd Question :-[tex]23 + m = 31 \\ m = 31 - 23 \\ m = 8[/tex]
⎆ The value of m is 8.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
Answer:
p=30, m=8
Step-by-step explanation:
1. if p - 17 = 13, then p = 13+17, which is equal to 30
2. if 23 + m = 31, then m = 31-23, which is equal to 8
Do the opposite of the sign, for instance in question 1 it's -17, so you would +17 to calculate p.
!! Solve for the following equation step by step and justify your steps when using an exponential property.
(7^(x))^(4)=(7^(2)*7^(3))/(7^(3x))
Answer:
x = 5/7
Step-by-step explanation:
Here, we want to get the value of x
Firstly, according to indices;
(a^m)^n = a^(m * n) = a^mn
Also;
a^m * a*n = a^(m + n)
a^0 = 1 (any number raised to zero as its power is 1)
And lastly;
a^m divided by a^n = a^(m-n)
So using these we can have;
7^4x = 7^( 2 + 3)/7^3x
7^4x = 7^5/7^3x
7^4x = 7^(5-3x)
Since we have the same bases, we have to equate the powers
4x = 5-3x
4x + 3x = 5
7x = 5
x = 5/7
two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1600. what are the rate charged per hour by each mechanic. if the sum of the two rates are $215 per hour.
The rate charged per hour by the first mechanic = $105,
And the rate charged per hour by the second mechanic = $110.
Use the concept of ratio defined as:
A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x: y, which is equivalent to x/y.
Where x and y are individual amounts of two quantities.
And, the Total quantity gives after combining as x + y.
Given that,
Two mechanics worked on a car.
The first mechanic worked for 10 hours.
The second mechanic worked for 5 hours.
Together, they charged a total of $1600.
The sum of the two rates charged per hour is $215.
Assume that,
The rate charged per hour by the first mechanic is = x dollars,
The rate charged per hour by the second mechanic is = y dollars.
The first mechanic worked for 10 hours,
The total amount earned by the first mechanic would be 10 times their hourly rate = 10x dollars.
Similarly,
The second mechanic worked for 5 hours,
The total amount earned by the second mechanic would be 5 times their hourly rate = 5y dollars.
Set up two equations based on the given information:
The first equation is the sum of the two rates, which is,
x + y = 215 ......(i)
The second equation is the total amount earned by both mechanics,
10x + 5y = 1600 .....(ii)
Use substitution to find the values of x and y:
From the first equation, we can express x in terms of y as,
x = 215 - y
Substitute this value of x into the second equation:
10(215 - y) + 5y = 1600
Expanding the equation, we get,
2150 - 10y + 5y = 1600
Combining like terms, we have:
-5y = 1600 - 2150
-5y = -550
Dividing both sides of the equation by -5, we get:
y = 110
Now that we have the value of y,
Substitute it back into the first equation to find x:
x + 110 = 215
Subtract 110 from both sides, and we get:
x = 105
Hence,
The rate charged per hour by the first mechanic is $105, & the rate charged per hour by the second mechanic is $110.
Learn more about the ratio visit:
https://brainly.com/question/12024093
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One number is six less than a second number. Twice the first is 4 more than times 6 the second. Find the numbers.
Answer:
[tex]\text{First number: }-10, \\\text{Second number: }-4[/tex]
Step-by-step explanation:
We can write the following system of equations:
Let the first number be [tex]f[/tex] and the second number be [tex]s[/tex]:
[tex]\begin{cases}f+6=s, \\2f-4=6s\end{cases}[/tex]
Solving, we get:
[tex]\int\limits^a_b {x} \, dx \begin{cases}f+6=s, \\2f-4=6s\end{cases},\\2f-4=6(f+6),\\2f-4=6f+36,\\-40=4f,\\f=\boxed{-10}[/tex]
Solving for [tex]s[/tex]:
[tex]f+6=s,\\-10+6=s,\\s=\boxed{-4}[/tex]
Akash draws a 4 from ten cards numbered 1 through 10. He replaces the card. Then Ramesh draws a 7. What is the probability of getting a 4 and a 7?
Answer:
1/100
Step-by-step explanation:
P(4 then 7) = 1/10 x 1/10
r(s to the power of 2)(t) when r=2, s=3, and t=5
Plzzz help
Answer:
90
Step-by-step explanation:
2(3)²(5)
2(9)(5)
18(5) = 90
Please help me with either one, (all both) I’ve been struggling with this
Answer:
x = 12, x = 7
Step-by-step explanation:
The 2 legs of the triangle are congruent, both 2x + 7, then
2x + 7 + 2x + 7 + x + 11 = 85 ← equation for perimeter
5x + 25 = 85 ( subtract 25 from both sides )
5x = 60 ( divide both sides by 5 )
x = 12
-----------------------------------------------------------
Opposite sides are congruent, then
2(2x) + 2(5x + 3) = 104 ← distribute and simplify both sides
4x + 10x + 6 = 104
14x + 6 = 104 ( subtract 6 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7
Answer:
x=12 x=7 yup thank me later
Bobby E. Lee has completed 57% of the race. If he has completed 114 laps, how many total laps are in the race?
Answer:
100% is 200 laps
Step-by-step explanation:
Answer:
200 laps
Step-by-step explanation:57%=114 1%=114/57=2 100%=2x100=200 laps
A runner runs a distance of 640 metres in a time of 80 seconds.
What is his average speed?
Answer:
8 meters per second
Step-by-step explanation:
We can divide meters by seconds to get his average speed in meters per second. -- 640 m / 80s = 8 m/sec (meters per second). We can also figure out his average speed in minutes by multiplying 8 by 60 (because there are 60 seconds in a minute), 8 * 60 = 480 m/min (meters per minute).
Answer:
8m/s
Step-by-step explanation:
Speed is equal the distance upon time.
640/80
so speed is equal to 8m/s
Mrs. Rashad is baking 3 pies. She needs 16 cups of strawberries for each pie. How many cups of strawberries does she need in all?
Make an equation to solve the problem. Move numbers and a symbol to the blanks to make the equation. If there is no whole number in the
answer, put a 0 in the box after the equals sign.
Answer:
48
Step-by-step explanation:
1 pie = 16 cups
you need 3 pies
add 16 three times
16+16+16=48
Orange gray produce 133,952 oranges. If a crate holds 92 oranges, how many crates were needed for shipping? (Write operation and answer) no links
Answer:
1,456 crates needed
Step-by-step explanation:
oranges = 133,952
crate capacity = 92
133,952 / 92 = 1,456 crates needed
Three airlines serve a small town in Ohio. Airline A has 48% of all scheduled flights, airline B has 35% and airline C has the remaining 17%. Their on-time rates are 81%, 70%, and 41%, respectively. A flight just left on-time. What is the probability that it was a flight of airline A
Answer:
If a flight just left on-time, the probability that it was a flight of airline A is 56.06%.
Step-by-step explanation:
Since three airlines serve a small town in Ohio, and Airline A has 48% of all scheduled flights, airline B has 35% and airline C has the remaining 17%, and their on-time rates are 81%, 70%, and 41%, respectively, if a flight just left on-time, to determine what is the probability that it was a flight of airline A the following calculation must be performed:
A = 0.48 x 0.81 = 38.88
B = 0.35 x 0.7 = 23.5
C = 0.17 x 0.41 = 6.97
38.88 + 23.5 + 6.97 = 100
38.88 = X
69.35 = 100
38.88 = X
38.88 x 100 / 69.35 = X
3,888 / 69.35 = X
56.06 = X
Therefore, if a flight just left on-time, the probability that it was a flight of airline A is 56.06%.
What is the range of the function?
Answer:
j -last one
Step-by-step explanation:
the range represents all values of y so the answer is J
x^2+21x+1=5x+4
solve by completing the square show all work
(will give brainliest)
Answer:
x = 0.1854 and x = -16.1854
Step-by-step explanation:
refer to photo
Hi could someone solve this for me i have been stuck for an hour now XD
Answer:
The anwser is 40.82
Step-by-step explanation:
Pie times radius
Answer:
[tex] \large{ \tt{☄ \: STEP - BY- STEP \: EXPLANATION}} : [/tex]
We are provided the diameter of circle ( d ) i.e 13 cm & value of pi ( π ) i.e 3.143. We are asked to find out the circumference of the given circle ( C ).[tex] \large{ \tt{✎ \: LET'S \: START} }: [/tex]
[tex] \boxed{ \large{ \tt{❃ \: Circumference \: of \: a \: circle = \pi \: d}}}[/tex]
- Plug the given values & Multiply 3.142 by 13
[tex] \large{ \tt{↬ \: 3.142 \times 13}}[/tex]
[tex] \boxed{ \large{↬ \tt{40.846 \: cm}}}[/tex] [ Don't forget to write the units i.e cm ]
[tex] \boxed{ \boxed{ \tt{⟿ \: OUR \: FINAL \: ANSWER: \boxed{ \underline{ \tt{40.846 \: cm}}}}}}[/tex]
[tex] \large{ \tt{✺ \: STUDY \: TIPS}} : [/tex]
If you realize you've been studying for hours : Grab a snack to refuel your body and watch a sitcom to refuel your brain then back to the books! ♪♡ Hope I helped! ツ
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Help please explain
Given:
[tex]\sin^{-1}\left(\dfrac{5}{8}\right)=A[/tex]
To find:
The correct equivalent equation.
Solution:
We have,
[tex]\sin^{-1}\left(\dfrac{5}{8}\right)=A[/tex]
Taking sin on both sides, we get
[tex]\sin \sin^{-1}\left(\dfrac{5}{8}\right)=\sin A[/tex]
[tex]\dfrac{5}{8}=\sin A[/tex] [tex][\because \sin (\sin^{-1}\theta )=\theta][/tex]
Interchanging the sides, we get
[tex]\sin A=\dfrac{5}{8}[/tex]
Therefore, the correct option is 4.
In the circle above, DE = 2, CE = 6, and BE = 3.
What is the measure of EA?
A) 2
B) 3
C) 6
D) 4
Answer: The correct option is (D) 4.
Step-by-step explanation:
According to the intersecting chords theorem, if two chords intersect in a circle then the products of the length of the chord segment are equal.
Given:
DE = 2
CE = 6
BE = 3
Now calculating the the value of EA.
As per theorem:
[tex]DE\times CE=BE\times EA[/tex]
Now putting the all the given values in this expression, we get:
[tex]2\times 6=3\times EA\\\\EA=4[/tex]
Therefore, the measure of EA is 4.
I really need help lol so please do me a favor
Answer:
the answer should be 5/8.
Step-by-step explanation:
look at number of x.
Answer:
3/4
Step-by-step explanation:
When you simplify 6/8 (you get this by subtracting 1/8 from 7/8) , you get 3/4.
If someone vapes for every 15 minutes in a total of 16 hours how many times would they vape in those 16 hours
Answer:
64 times
Step-by-step explanation:
There are 4 sessions of 15 minutes in an hour. Meaning that a person would vape 4 times in an hour. 4 * 16 = 64. A person vapes 64 times in 16 hours. o-o dont vape kids.
Answer and Step-by-step explanation:
We are given the ratio of 1 vape every 15 minutes. We need to convert the time to hours, then multiply the hours by 16.
1 : 15
We know that there are 60 minutes in 1 hour, so we need to multiply 15 by 4 to get 60.
15 × 4 = 60
We also need to multiply 1 by 4, so that the result will be a multiple of the beginning number and so that we didn't get random numbers from somewhere.
1 × 4 = 4
Now we have the ratio 4 : 60, which means that the person vapes 4 times every 60 minutes, or every hour. But since we turned the minutes into an hour, this turns the 60 into a 1. 4 : 1
Now, we have to multiply 4 and 1 by 16 to get the amount of vapes done in 16 hours.
4 × 16 = 64
1 × 16 = 16
So, we have the ratio 64 : 16
This means that the person smokes 64 times in the 16 hours.
#teamtrees #PAW (Plant And Water)
PLS HELP ILL GIVE BRAINLIST AND FOLLOW U
Answer:
61.2
Step-by-step explanation:
base=6
height=10
Area of parellelogram=base x height
=6x 10.2
=61.2 sq.ft
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
The average height of 3 apartment blocks is 145.6 m the height of block A is 128.7 m and the height of block C is 138.9 m what is the height of block B?
Answer:
[tex]H_B=169.2m[/tex]
Step-by-step explanation:
From the question we are told that:
Average height of blocks [tex]H_{ABC}=145.6[/tex]
Height of block A [tex]H_A=128.7[/tex]
Height of block C [tex]H_C=138.9[/tex]
Generally the equation for Height of block C is mathematically given by
Since
[tex]H_{ABC}=\frac{H_A+H_B+H_C}{3}[/tex]
Therefore
[tex]H_B=(H_{ABC}*3)-(H_A+H_B)[/tex]
[tex]H_B=(145.6*3)-(128.7+138.9)[/tex]
[tex]H_B=169.2m[/tex]
Which equation represents an exponential function with an initial value of 500?
O f(x) = 100(5)^x
Of(x) = 100(x)^5
O f(x) = 500(2)^x
Of(x) = 500(x)^2
Answer:
[tex]o \: f(x) = 500 {(x)}^{2} [/tex]
Step-by-step explanation:
[tex]f(x) = 500 {(x)}^{2} \\ f(0) = 500 {(0)}^{2} \\ = 500[/tex]
Write three ratios equal to 7/42
A. 7/42 7/49 7/56
B. 1/7 2/14 3/21
C. 2/10 3/15 4/20
D. 1/6 2/12 3/18
whoever does it i will give brainiest answer pls help
product of the polynomial (2y+3)(3y^2+4y+5)
A.15y3 + 17y2 + 22y + 15
B.6y3 + 17y2 + 22y + 15
C.6y3 + 20y2 + 22y + 15
D.6y3 + 17y2 + 22y + 25
i need need help on this
Answer:
points A, B and D are all in the same plane but not all are on the same line
Step-by-step explanation:
points A, C, D are all collinear which means they must also be coplanar