Answer:
The distance between the lines: 4x+3y-11 and 8x+6y=15 is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
You have two parallel and different lines. The form of the implicit equations is:
A*x + B*y + C= 0
A'*x + B'*y + C'=0
Since the two lines are parallel, the coefficients of their general equations must satisfy that the slopes are equal.
Therefore, the equations can be transformed so that the coefficients A and B are equal, multiplying or dividing one of them by a constant.
So, the distance between two lines can be expressed as follows:
[tex]d=\frac{|C-C'|}{\sqrt{A^{2} +B^{2} } }[/tex]
In this case, you have:
4x+3y-11= 0 Multiplying this equation by 2 you get: 8x +6y -22=08x+6y-15 =0Then, you have:
A= 8B=6C= -22C'= -15Replacing in the definition of distance:
[tex]d=\frac{|-22-(-15)|}{\sqrt{8^{2} +6^{2} } }[/tex]
Solving:
[tex]d=\frac{|-7|}{\sqrt{8^{2} +6^{2} } }[/tex]
[tex]d=\frac{7}{\sqrt{8^{2} +6^{2} } }[/tex]
[tex]d=\frac{7}{\sqrt{64+36 } }[/tex]
[tex]d=\frac{7}{\sqrt{100 } }[/tex]
[tex]d=\frac{7}{10}[/tex]
The distance between the lines: 4x+3y-11 and 8x+6y=15 is [tex]\frac{7}{10}[/tex]
Green River State Park had 312,684 visitors in one summer. Blue Sky State Park had 441,902 visitors.
1. How many fewer visitors did Green River State Park have than Blue Sky State Park? 2. Ashlee said that both state parks had a total of 753,586 visitors. Is Ashlee correct? Explain your reasoning.
Answer:
1. 129,218 fewer vistors than Blue Sku State Park
2. Ashley is not correct, since 441902 + 312684 is 754,586; not 753,586. She made a mistake on the thousands place, which she probably added one extra on accident.
Step-by-step explanation:
Oki, subtract for question one:
441902 - 312684 = 129218
Add for two:
441902 + 312684 = 754586
For problem, number two; I recommend writing it in your own words instead of copying off mines.
identify the domain of the function shown in the graph
What is the slope of the line represented by the equation y = 4/5x - 3?
Answer:
The slope is 4/5 and the y intercept is -3
Step-by-step explanation:
The equation is in slope intercept form
y= mx+b where m is the slope and b is the y intercept
y = 4/5x -3
The slope is 4/5 and the y intercept is -3
Solve the simultaneous equation
2x-4y=19
3x+5y=1
Plz help me I’ve been stuck on this for a while 20 points
Answer:
x=4.5
y=-2.5
Step-by-step explanation:
Multiply 2x-4y=19 by 3
Multiply 3x+5y=1 by 2
Solve simultaneously
Answer:
[tex]x=\frac{9}{2} =4.5, y=-\frac{5}{2} =-2.5[/tex]
Step-by-step explanation:
[tex]2x-4y=19, multi ply- by 5\\10x-20y=95 , Eq I\\3x+5y=1, multiply - by 4\\12x+20y=4, Eq II\\Add -EQI -and- EqII\\\\10x-20y+12x+20y=95+4\\22x=99\\x=\frac{99}{22}=\frac{9}{2} =4.5\\3(\frac{9}{2})+5y= 1\\5y=1-\frac{27}{2} =-\frac{25}{2}\\y=-\frac{25}{2}*\frac{1}{5} =-\frac{5}{2} =-2.5\\[/tex]
A coin is tossed and a spinner with three equal-sized sections labeled 3, 6, and 9 is spun. What is the probability of getting heads and a number greater than 3? Express as a fraction in simplest form.
Answer:
The answer is 1/3.
Step-by-step explanation:
A coin has either heads or tails. The odds of a coin getting heads is 1/2.
There are three equal-sized sections with numbers 3, 6 and 9 on the spinner. There are two sections with numbers greater than 3, which are 6 and 9. The odds of getting a number greater than 3 is 2/3.
To find the overall probability of both incidents occurring, the two fractions are multiplied together, which is 1/2 * 2/3 = 1/3
Answer:
0.333/1/3
Step-by-step explanation:
Well, the probability of getting heads is 1/2 since there are 2 sides to a coin. There are 2 numbers on the spinner greater than three (6,9) which is 2/3.
1/2 times 2/3=0.33. The probability of getting heads and getting a number that is greater than is 0.333 or 1/3.
Jay volunteers at a food bank he volunteered 2 5/6 hours on Saturday 2 1/3 hours on Wednesday how many hours did he volunteered in all
Answer:
5 1/6 hours
Step-by-step explanation:
Add the hours he volunteers
2 5/6 + 2 1/3
Get a common denominator of 6
2 5/6 + 2 1/3*2/2
2 5/6 + 2 2/6
4 7/6
This is an improper fraction
4 6/6 + 1/6
5 1/6
Whoever answers first and it is correct I will award Brainliest!!!
Consider circle C with a radius of 5 cm and a central angle measure of 60°.
Circle C is shown. Line segments R C and S C are radii with length of 5 centimeters. Angle R C S is 60 degrees.
What fraction of the whole circle is arc RS? 1/6
What is the approximate circumference of the circle?
cm
What is the approximate length of arc RS?
cm
Answer:
below
Step-by-step explanation:
that is the procedure above
fraction of arc RS
ANGLE RcS = 60 °
60°/360°
=1/6
therefore the total fraction is 1/6
The fraction of the whole circle is arc RS = (1/6)
approximate circumference of the circle = 31.4 cm
approximate length of arc RS = 5.23 cm
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
As per the given data:
Radius of circle with center C = 5 cm
central angle = 60°
∠RCS = 60°
To find out the fraction of the whole circle is arc RS:
arc length = radius × θ {θ is in radians}
∠RCS = 60° = 60° × (π/180°) = π/3
fraction of the whole circle = arc length / circumference
= [tex]\frac{r \times \frac{\pi}{3}}{2\pi r}[/tex] = (1/6)
approximate circumference of the circle = 2πr
= 2π(5)
= 31.4 cm
approximate length of arc RS = r × θ
= 5 × (π/3)
= 5.23 cm
Hence, the fraction of the whole circle is arc RS = (1/6)
approximate circumference of the circle = 31.4 cm
approximate length of arc RS = 5.23 cm
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El equipo de corredores de la escuela organizo una carrera de 20 kilometros para ello deberan corre un circulito de 1000 metros. Cada integrante de los equipos corrio una distancia acorde a su resistencia. Para calcular los kilometros recorridos por cada uno de los integrantes
Answer:
corrieron 50 kilómetros de la escuela a la casa
The original price of a computer was reduced by $250.
If p= the computer’s original price in dollars, which algebraic expression represents the reduced price?
a. 250p
b. 250 + p
c. p - 250
d. 250 - p
Answer:
the awnser is c. p-250 + p
8) Round 2.3428 to the nearest hundredth.
Help me please!!! I really need it!
Answer: The value of x can be either 5 or 10.
Step-by-step explanation:
We are given:
Total profit, P = $5600
The given equation follows:
⇒ P = 600 + 1500x - 100x²
Putting value of P in above equation, we get:
⇒ -100x² + 1500x + 600 = 5600
⇒ -100x² + 1500x - 5000 = 0
⇒ 100x² - 1500x + 5000 = 0
Solving this equation by middle term split, we get:
⇒ 100(x² - 15x + 50) = 0
⇒ (x² - 10x - 5x + 50) = 0
⇒ x(x - 10) - 5(x -10) = 0
⇒ (x - 10)(x - 5) = 0
⇒ x = 10, 5
Hence, the value of x can be either 5 or 10.
Write an equation in slope intercept form of the line that passes through the points (1,−6) and (5,−6).
slope intercept form = y=mx+b
m= slope
b= y-intercept
the slope is rise over run, so if the points are (1, -6) and (5, -6), the slope is 0
the y intercept is -6
y = 0x-6
or
y = -6
HELP VERY URGENT!!!!!!
Answer:
Step-by-step explanation:
D is greater than -2
Answer:
A, C, D
Step-by-step explanation:
All of them have a larger x-coordinate than -2.
A = .5
C = -1
D = -1.5
Hope that this helps!
Which is true about the functional relationship shown in the graph?
Answer:
Explanation: Since, a function is always the type of y= f(x), where x is independent variable and y is dependent variable which is dependent on the value of x. Here, a graph of Olivia's earning per hour is given. ... Thus, we can say that earning is dependent variable while hours is independent variable
ILL MARK AS BRAINLESS PLS HELP
Answer:
95-3^4=14
Step-by-step explanation:
3^4=81
95-81=14
Part A: 176
Part B: First, I did is multiple 3 to the common denominator by 4 times with the same number and that would give you a positive number of 81, then I combined 81 with 95 and your solution is 176.
Step-by-step explanation:
Part A:
-3^4 = -3x-3x-3x-3
-3^4 = 81
95+81 = 176
Harry buys 6 yards of rope to make a swing. Lenny spends $16 on rope.
How much do the two boys spend in all?
We are doing indices can someone help me please.
1. y^6/y^2=
2.5^2*5^4=
Answer:
1. y⁴
2. 15625
Step-by-step explanation:
1. y^(6-2)
= y⁴
2. 5^(2+4)
= 5⁶
= 15625
If <3 measures 123, what is the measure of <7?
Madison
River
A bridge crosses over the Madison River.
The opposite banks of the river are parallel
and the bridge is a transversal.
A. 90°
B. 123
C. 180°
D. 57
Answer: B
Step-by-step explanation: I just took the quiz
The measurement of angle 7 is 123°.
What are corresponding angles?The corresponding angles are angles that have the same relative position or measurement in two similar figures. They are formed when two lines, parallel or not, are intersected by a transversal. They are located on the same side of the transversal. Corresponding angles formed by parallel lines and a transversal are congruent.
Given is scene of two parallel line intersected by a transversal,
∠3 = 123°, We need to find the value of ∠7,
We see that, the angles, ∠3 and ∠7 are corresponding angles,
Therefore,
∠3 = ∠7 by the definition of corresponding angles between parallel lines,
Therefore, ∠7 = 123°.
Hence, the measurement of angle 7 is 123°.
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Can I please have help on 3, 4 will mark brainiest thank you.
Answer:
4) Alternate angles
Step-by-step explanation:
Alternate angles are on the opposite corners of the line of the angle, and 10 and 14 are on opposite corners, so that makes them alternate angles. I hope this helped you!
what is the volume of a cone with a radius of 12 and a height of 8?
Answer:
Volume of a cone= [tex]\frac{1}{3} \pi r^{2}h[/tex]
=[tex]\frac{1}{3}[/tex]×[tex]\frac{22}{7}[/tex]×144×8
=[tex]\frac{22}{21}[/tex]×144×8
=1206.86[tex]cm^{2}[/tex]
Step-by-step explanation:
Find the equation of the line passing through the point (-1,5) and perpendicular to
the line y = - 3x + 4.
Answer:
1/3x+16/3
Step-by-step explanation:
Perpendicular equations slope is the negative reciprocal of the original problem.
So, the slope of the new equations is 1/3
1/3(-1)+b=5
b= 16/3
After that incident, the Civil defense team decided to buy new trucks with ladders higher than 100 feet. They found 2 different trucks with same height of ladders. The first truck costs $145,000 and will cost $0.31 per mile traveled based on the current gas prices. The second truck will cost $160,000 but gets better gas mileage, costing $0.27 per mile. They need to decide which truck is the best deal.
1. Write an equation that represents the total cost of each truck.
2. How many miles the trucks will have to drive for the costs of the trucks to be equal?
3. Which truck should the Civil defense team buy? Explain your reasoning using Mathematical terms.
Answer:
Step-by-step explanation:
the cost difference between the first truck and the second truck = $160,000-$145,000 = $15,000
the difference of gas cost between the first truck and the second truck = $0.31 - $0.26= $0.05 per mile.
so,
I think, this is a very significant number of truck cost compared with gas cost
for the best deal, the first truck is the best choice.
Hope this answer helps you :)
Have a great day
Mark brainliest
Answer:
buy truck 2 since it cheaper
, if u do it in a graph after they intersect usee that truck num 1 increases while truck num 2 decreases
Step-by-step explanation:
1.
First Truck: Y = 0.31x + 145,000
Second Truck: Y = 0.27x + 160,000
2.
Y = 0.31x + 145,000
Y = 0.27x + 160,000
- 0.31x + y = 145,000
- 0.27x + y = 160,000
- 0.31x + y = 145000
0.27x – y = -160000
- 0.04 = -15000
X=375000
- 0.31 x 375000 + y =145000
Y = 261250
(x , y) = (375000 , 261250)
What is the measure of ∠4?
Answer:
80 degrees
Step-by-step explanation:
angle 1 is equal to 100 because of the law of exterior angles. And since andgle 1 and 2 make 180 degrees we can subtract 80 from 100 and we get the measure of angle 2. Angle 2 and 4 are the same becasue of the law of adjacent angles.
PLEASE HELP!! GIVEN THE FOLLOWING TABLE OF DATA FROM A QUADRATIC EQUATION
the last numbers are 9/7 and 10/16
Please anwser one question!!
Answer:
I think d is 9°.......
Step-by-step explanation:
(6d+8)°+(3d+1)°=90°
d =9°
please answer with method you did please fast
Answer:
LM = 8 cm
Step-by-step explanation:
LM = KN = x + 7
NM = KL = x + 7 + NQ = x + 7 + 2 = x + 9
KN×NM = 80
(x+7)(x+9) = 80
x² + 7x + 9x + 63 = 80
x² + 16x + 63 = 80
x² + 16x - 17 = 0
solution of a quadratic equation
x = (-b ± sqrt(b² - 4ac))/(2a)
a=1
b=16
c=-17
(-16 ± sqrt(256 + 4×17))/2 = (-16 ± sqrt(256+68))/2 =
= (-16 ± sqrt(324))/2 = (-16 ± 18)/2
x1 = (-16 + 18)/2 = 2/2 = 1
x2 = (-16 - 18)/2 = -34/2 = -17
x2 as negative value is no valid solution for a side length.
so, only x1 remand as solution.
=> x=1, LM = KN = 1+7 = 8, NM = KL = 1+9 = 10
I need this done quick please help
Answer:
you have to use proportion equation
a business want to increase its number of employees by 65% to 20,460. How many employees does the company currently have?
Answer:
12,400
Step-by-step explanation:
Let the current employees be x
65% increase in number = 0.65x
If the total number of employees after the increase is 20,460, then;
x + 0.65x = 20,460
1.65x = 20,460
x = 20,460/1.65
x = 12,400
Hence the current number of employees is 12,400
Explain how to find the percent for a fraction that does not have a denominator which is a factor of 100
Answer: Use division to convert the fraction to a decimal: 1/4 = 1 ÷ 4 = 0.25.
Multiply by 100 to get percent value: 0.25 × 100 = 25%
Step-by-step explanation:
Graph the linear function passing through point B with a slope of -2
Answer:
sorry but that will go off so need the area rl
tell it in the comments!