Answer:
Step-by-step explanation:
The distance between a point (x,y) and the point (-3,4) is
d1= [tex]\sqrt{ (x+3)2+(y-4)2}[/tex] .
The distance between a point (x,y) and the point (0,0) is
d2= [tex]\sqrt{x2+y2}[/tex] .
You know what y is from the equation of the line, so substitute that, set d1=d2, and solve for x.
The coordinates of the point on the straight line y=3x+1 that is equidistant from the origin and (−3, 4) is (-33/18, 39/6)
The distance formula is expressed as:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\[/tex]
For the coordinate point (x,y) to (-3, 4), the distance is expressed as:
[tex]D_1 = \sqrt{(x+3)^2+(y-4)^2}\\[/tex]
For the coordinate point (x,y) to (0, 0), the distance is expressed as:
[tex]D_2=\sqrt{(x-0)^2+(y-0)^2}\\D_2 = \sqrt{x^2+y^2}[/tex]
Since the distance are equidistant, then D1 = D2
[tex]\sqrt{(x+3)^2+(y-4)^2} = \sqrt{x^2+y^2}\\ (x+3)^2+(y-4)^2 = x^2+y^2\\x^2+6x+9+y^2-8y+16 = x^2+y^2\\6x+9-8y+16=0\\6x-8y+25=0[/tex]
Substitute y = 3x+1 and get x
6x - 8y + 25 = 0
6x-8(3x+1) - 25 = 0
6x -24x-8-25=0
-18x-33 = 0
-18x = 33
x =-33/18
Sincey= 3x + 1
y = 3(33/18) + 1
y = 33/6 + 1
y = 39/6
Hence the required coordinates is (-33/18, 39/6)
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If g(x) =4x+2 and f(x) =3x-10
find g(f(3))
Answer:
[tex]g(f(3))=-2[/tex]
Step-by-step explanation:
So we have the two functions:
[tex]g(x)=4x+2\text{ and } f(x)=3x-10[/tex]
And we want to find g(f(3)).
So, let's find f(3) first:
[tex]f(3)=3(3)-10[/tex]
Multiply:
[tex]f(3)=9-10[/tex]
Subtract:
[tex]f(3)=-1[/tex]
Therefore, we can substitute -1 for f(3):
[tex]g(f(3))=g(-1)[/tex]
Now, find g(-1):
[tex]g(-1)=4(-1)+2[/tex]
Multiply:
[tex]g(-1)=-4+2[/tex]
Add:
[tex]g(-1)=-2[/tex]
And we're done!
So:
[tex]g(f(3))=-2[/tex]
A gym employee is paid monthly. After working for three months, he had earned $4,500. To
determine how much money he will make over a six-month period, he created the table below.
Write an equation to represent the constant of proportionality
Answer:
$9000
Step-by-step explanation:
A gym employee has earned in 3 months =$4500
Then his monthly salary =$4500/3 =$1500
After six months he will earn = 6 × his monthly salary
= 6×$1500=$9000
Suppose that J and K are points on the number line.
If JK = 10 and J lies at -17, where could K be located?
If there is more than one location, separate them with commas.
Answer:
-7, -27
Step-by-step explanation:
J is at -17. K is 10 units from J.
Start at point J, -17:
a) If you go 10 units to the right, you end up at -17 + 10 = -7
b) If you go 10 units to the left, you end up at -17 - 10 = -27
J can be at -7 or at -27
Answer: -7, -27
solve m = 10x - x for x
Answer:
X = M/9
Step-by-step explanation:
Please answer this question! it's due in a few hours if you don't mind!
Answer: 45 Seconds
Step-by-step explanation: Because if you do 3/4=0.75 or 75%. Knowing that a minute is 60 seconds long. 75% of 60 is 45 Seconds.
Hope this helped!
The ladder in a fire station is 29 feet (ft) tall. The ladder is anchored to the basement floor and the second floor ceiling. The basement floor is 12 feet below ground level. Identify the integers of the ends of the ladder below and above the basement floor
Answer:
top = 17ft
bottom = -12ft
Step-by-step explanation:
As seen in the badly drawn picture attached in this question we are trying to find the point at the top of the ladder and the point at the bottom of the ladder. As seen in the picture ground level has an altitude of 0 ft meaning that lower than this would be in the negatives. Since the basement floor is 12 feet below ground level then this point would be -12 ft. Now since we know that the ladder is 29ft tall we simply add this height to the basement floor value to get the value of the 2nd floor ceiling (top of the ladder).
29ft + ( -12ft) = 17ft
Therefore we can see that the point at the top of the ladder is 17ft.
Which are valid rearrangements of F=95C+32? Select the two correct answers. response - incorrect 95C−F=32 F+95C+32=0 C=59(F−32) C=95(F−32) F−32=95C
Answer:
F+95C+32=0 & F−32=95C
Step-by-step explanation:
f=95c+32
Answer:
1st and the last one
Step-by-step explanation:
Find the difference
16-(-4)
i need help ASAP
Evaluate R - Y for R = -2 and Y= -7
Answer:
5
Step-by-step explanation:
Replace variables with integers
(-2) - (-7)
Solve.
-2 - (-7) --> -2 + 7 --> 5
If I want to buy a pair of sunglasses and the original price is $120, how much will I pay if they are 50% off? What if they were 25% off?
Answer:
$60, $90
Step-by-step explanation:
Amount paid when 50% off
=$ 120 - 50/100 * 120 = $ 120 - $60 = $60
Amount paid when 25% off
=$ 120 - 25/100 * 120 = $ 120 - $30 = $90
A square rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the correct significant digits.
Answer:
38.3
Step-by-step explanation:
multiply l x w to get your answer then just round. Hope it helps!!
If t = -3, what is
[tex] \sqrt{6 - 25t} [/tex]
Answer:
[tex]9[/tex]
Step-by-step explanation:
So we have the expression:
[tex]\sqrt{6-25t}[/tex]
And we want to find the value of the expression when t is -3.
So, substitute -3 for t:
[tex]\sqrt{6-25(-3)}[/tex]
Multiply:
[tex]=\sqrt{6+75}[/tex]
Add:
[tex]=\sqrt{81}[/tex]
Evaluate:
[tex]=9[/tex]
So, our answer is 9.
And we're done!
only question one. please answer and show full working out. will reward with brainliest.
Answer:
48 meters squared or 48m^2
(Both are correct. Whichever you prefer is fine.)
Step-by-step explanation:
The formula to find area is A=height*base
So since the base = 6 and height = 8
Just multiply to combine the two
6*8=48
If you want to show with only numbers write this.
A=b*h
6*8=48
48 meters squared or 48m^2
-7=-x
One step equations ( Find X)
Answer:
answer of your question is
-x= -7
1/3 (6y - 9) = -2y + 13
Answer: 3,75 ( 15/4)
Step-by-step explanation:
1/3 (6y - 9) = -2y + 13
6y/3 - 9/3 = - 2y + 13
2y - 2 = - 2y + 13
2y + 2y = 13 + 2
4y = 15
y = 15/4
y = 3,75
X to the second power(x to the fifth power)
What are the correct answers for this?
Choose the midpoint of the line segment with endpoints at (5, 9) and (11, 15).
A) (16,24)
B) (6,6)
C) (8,12)
D) (-6,-6)
Answer:
C) (8,12)
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )\\MP= (\frac{5+11}{2} )(\frac{9+15}{2} )\\MP= (\frac{16}{2} )(\frac{24}{2} )\\MP= (8,12)[/tex]
Ronald rents a car from Cheap Rent-a-Car for $25 plus $0.05 per mile. Dixon rents a car
from Great Cars for S40 plus $0.03 per mile. How many miles must they both drive for
their rental fees to be the same?
Answer:
750 miles
Step-by-step explanation:
Ronald
Rental fee = fixed cost + variable cost
= $25 + $0.05x
Where x = number of miles
Dixon
Rental fee = fixed cost + variable cost
= $40 + $0.03x
How many miles must they both drive for their rental fees to be the same?
Equate the two equations
$25 + $0.05x = $40 + $0.03x
Collect like terms
0.05x - 0.03x = 40 - 25
0.02x = 15
Divide both sides by 0.02
x = 15 / 0.02
= 750 miles
HELP ME PLEASE I NEED THIS <3333
Answer:
214°
Step-by-step explanation:
The arc subtending an angle at the centre are equal, that is
arc ED = 90° and
arc DF = 360° - (90 + 146)° = 360° - 236° = 124°
Thus
arc EDF = arc ED + arc DF = 90° + 124° = 214°
1. Brie knows there is a relationship between the grades on
her math tests and the time she spends studying for those
tests. Identify the independent quantity and the dependent
quantity in this problem situation.
Time is the independent variable as it can be treated as a controllable constant against which changes in a system can be measured. How much time you spend effects how much time you study, making studying the dependent.
what is the range of this function(–11, 8) (13, 7) (14, 7)
Answer:
The range is { 7,8}
Step-by-step explanation:
The range of the functions is the output values
We do not list the repeated values more than one and normally list them from smallest to largest
The range is { 7,8}
Whoever answers first gets the brainliest Given : f(x)=-|x+9|
What direction does the graph move?______ How far?_____
What axis does the graph reflect over?____
Answer:
See below.
Step-by-step explanation:
f(x) = -|x + 9|
compared to
f(x) = |x|
has a graph that opens downward in an upside down V shape.
It has been moved 9 units left compared to the graph of f(x) = |x|.
It reflects over the x-axis.
SO Problem -3.62 + 18.57 =
Answer:
18.57- 3.62___________________
14.95The Ford Mustang can travel at a rate of 160 miles in 2 hours. The Toyota Corolla can travel at a rate of 210 miles in 3 hours. Which car has faster rate?
Answer:
The Ford Mustang can travel at a faster rate.
Step-by-step explanation:
160/2 = 80/1 miles/hour -Ford Mustang
210/3 = 70/1 miles/hour - Toyota Corolla
n-8=-4+5n solve for n.
Step-by-step explanation:
Hey there!!!
Here,
Firstly, Shift n to right side and -4 to the left side, because we always try to have variable as positive.
[tex] - 8+4 = + 5n-n[/tex]
Now, Simplify them.
[tex] - 8 + 4 = 5n - n[/tex]
[tex] - 4 = 4n[/tex]
You should divide now.
[tex]n = \frac{ - 4}{4} [/tex]
Therefore the value of n is -1.
{ As now you can keep it on left side. We generally find the vallue of variable by keeping it on left side. But we kept it right side in solution to avoid our confusion because if we kept it on left side and you would get harder to find the value at last as we need to transpose (-) to the right side value of n}.
Hope it helps...
A letter in the word UNIVERSITY is chosen. What is the theoretical probability of choosing an I? *
Answer:
There is a 1 in 5 chance that the letter will be I.
Step-by-step explanation:
There are ten letters in the word and 2 are I's. 2/10 simplifies to 1/5.
Answer:
2/10 or 20%
Step-by-step explanation:
if you were to pick at random
out of all i would have a 20 percent chance to be chosen
Find AC if AB = 17 and BC = 9
Answer:
ANSWER:-
Step-by-step explanation:
AB+BC=AC
17+9
=26 is the answer.
(9+33-6)-3-7?
can someone also explain it i don't really understand :( thx!
Answer:
26
Step-by-step explanation:
APPLY PEMDAS:
Evaluate the numbers in the parentheses before evaluating the whole equation.
[tex](9+33-6)-3-7\\\\36 - 3 -7\\\\33-7\\\\\boxed{26}[/tex]
Hope this helps.
What is 17 1/3 x 8 and how much water will each group get
Answer:
The Answer to 17 1/3 x 8 is 138.67
There is not enough context to answer the second question.