Answer:
the given statement is true.
Step-by-step explanation:
The given lines are
2x - 3y = 1 and 2x + 3y = 2
Write these equations in slope intercept form of a line y = mx +b
For the first equation
[tex]2x-3y=1\\\\3y=2x-1\\\\y=\frac{2}{3}x-\frac{1}{3}[/tex]
For the first equation
[tex]2x+3y=2\\\\3y=-2x+2\\\\y=-\frac{2}{3}x+\frac{2}{3}[/tex]
The slope and y-intercepts of first line are 2/3 and -1/3 respectively.
The slope and y-intercepts of second line are -2/3 and 2/3 respectively.
Since, the slopes and y-intercepts of these lines are different.
Hence, these lines are intersecting.
Therefore, the given statement is true.
True or false
Two points determine a plane
ind the area of an octagon with a radius of 6 meters. Round your answer to the nearest tenth.
19. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.
6 numbers per cube
if one is a 1, then the other one has to be a 2, 4 or 6 to be an odd sum
1+2=3, 1+4=5,1+6=7
since there are 3 numbers you can get that would be a 3/6 ( reduce to 1/2) probability
so 1/2 probability
1/2 is wrong, I put it on my exam and got it wrong:/
Each week Rosario drive to an ice-skating rink that is 60 miles away. The road trip takes 2.75 hours. If he averages 55 mph on his way to the rink, which equation can be used to find X, the number of miles per hour he averages on his way home?
Answer: The number of miles per hour he averages on his way home is 36 mph.
Step-by-step explanation:
Since we have given that
Distance traveled by Rosario = 60 miles
Time taken for road trip = 2.75 hours
Speed at which he on his way to the rink = 55 mph
Let X be the speed at which he averages on his way home.
So, According to question, we get that,
[tex]\dfrac{60}{55}+\dfrac{60}{x}=2.75\\\\1.09+\dfrac{60}{x}=2.75\\\\\dfrac{60}{x}=2.75-1.09\\\\\dfrac{60}{x}=1.659\\\\x=\dfrac{60}{1.659}\\\\x=36.16\\\\x=36\ mph[/tex]
Hence, the number of miles per hour he averages on his way home is 36 mph.
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x= 12 + y
18x – 12y= 18
The roof of a house is being reconstructed to accommodate heavy snows. the current 32 foot roofline makes an 18.2° angle with the horizontal. the owner has decided to construct the new roof so that it makes a 50° with the horizontal as shown below. what will be the length of the new roofline?
To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.
Explanation:To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:
tan(50°) = 32/x
To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:
x = 32/tan(50°)
Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:
x ≈ 32/1.1917
By calculating this, we find that the length of the new roofline is approximately 26.9 feet.
Use the remainder theorem to determine the remainder when 3t2 + 5t − 7 is divided by t − 5. A. 93 B. 43 C. 107 D. 57
Write the equation of the ellipse with its center at the origin. the height of the ellipse is 12 units and the width is 14 units.
I need help and I'm not sure if the answer is A so can you pls help!
Which expression represents the area of triangle ABC in square meters?
Answer:
the correct answer is A. 1/2 x 14 x 57
Step-by-step explanation:
i got it right on my test
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
Final answer:
To convert 28.7251 degrees to degrees, minutes, and seconds, take the whole number of degrees (28) and multiply the decimals (.7251) by 60 to get the minutes (43). Then multiply the remaining decimal of the minutes (.506) by 60 to get the seconds (30), resulting in 28 degrees, 43 minutes, and 30 seconds (28° 43' 30").
Explanation:
To convert 28.7251 degrees to degrees, minutes, and seconds, you follow a multi-step process which involves converting the decimal part of the degrees into minutes and then into seconds. First, identify the whole number of degrees, which is 28 in this case.
To convert the decimal part (.7251) to minutes, multiply by 60. Using the operation provided in the reference, with 0.7251 × 60, you get 43.506 minutes. The whole number part, 43, is the minutes.
To convert the remaining decimal part of minutes (.506) into seconds, again multiply by 60. This gives you (.506 imes 60) 30.36 seconds, which when rounded to the nearest second is 30 seconds.
Therefore, 28.7251 degrees is equal to 28 degrees, 43 minutes and 30 seconds (28° 43' 30").
Jenna surveyed the students at her dance class to find out if they like salsa and/or ballet. The results of her survey are shown in the two-way table below:
Like Salsa
Do Not Like Salsa
Total
Like Ballet
32
42
74
Do Not Like Ballet
22
4
26
Total
54
46
100
If a student does not like ballet, what is the probability that student also does not like salsa?
8.7%
15.4%
18.2%
84.6%
Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π 3 rad.
Final answer:
To find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3 rad, we need to differentiate the formula for the area of a triangle with respect to time.
Explanation:
Rate of Change of Triangle Area with Increasing Angle
To find the rate at which the area of the triangle is increasing, we need to differentiate the formula for the area of a triangle with respect to time.
The formula for the area of a triangle is given by: A = 0.5 × a × b × sin(C), where a and b are the lengths of the two sides and C is the angle between them.
By differentiating this formula with respect to time, we can find the rate of change of the area with respect to time.
When the angle between the sides is π/3 rad, substitute the length of the sides and the rate at which the angle is increasing, and solve for the rate of change of area.
If five cakes cost 5 pounds how much do 2 cakes cost
PLEASE HELP!!!! IMAGE ATTACHED FIND THE MEASURE OF ANGLE 3
If one u.s. dollars equals 5.76 egyptian pounds and one u.s. dollar equals 0.56 british pound, how many egyptian pound equal one british pound?
A point is on a circle if the distance from the center of the circle to the point is equal to the
a) area.
b)circumference.
c)radius.
d)diameter.
The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)?
Number of Hours Distance from Lighthouse
(in oceanic miles)
2 53
4 95.5
6 138
8 180.5
10 223
12 265.5
14 308
16 350.5
y = 42.5x + 10.5
y = 10.5x + 32
y = 21.5x + 10.5
y = 12.25x + 28.5
y = 12.5x + 10.5
Answer:
y=21.5x+10.5
Step-by-step explanation:
Find the missing number in the proportion. 8/56 = ?/49
Write a point-slope equation for the line that has slope 5 and passes through the point (6, 22). Do not use parenthesis on the y side.
If the x-axis is Quantity and the y-axis is Price, which of the following is the best summarization of the supply shift from S1 to S2?
A)The supply decreased.
B) The supply stayed the same.
C) The supply increased.
D) The supply outweighed demand.
Answer:
Option B is correct.
Step-by-step explanation:
We have been given x-axis representing quantity
And y-axis representing price
S1 and S2 are supply
So, these two supply have parallel lines which means they will never intersect they will remain same throughout the domain.
Therefore, the supply stayed the same.
Option B is correct.
Which double-angle or half-angle identity would you use to verify that 1+cos2a=2/1+tan2a?
In this case or scenario,
the double-angle identity that should be used is the one for cosine.
In totality, we shall need the following three trigonometric
identities to end up with the equality:
1. cos (2a) = cos² (a) - sin² (a)
2. sin² (a) + cos² (a) = 1
3. tan² (a) + 1 = sec²
(a)
Using identities 1 and 2 on the left-hand side of the
equation, we get the following:
1 + cos (2a) = 1 + cos² (a) - sin² (a) = 2 cos² (a)
Recalling that cos² (a) = 1 / sec² (a) and applying identity
3, we find the following:
2 cos² (a) = 2 / sec² (a) = 2 / (1 + tan² (a))
Therefore giving us:
2 cos² (a) = 2 / (1 + tan² (a))
Answer:
Its C. cos2a=cos^2a-sin^2a on ed
Write the equations in graphing form, then state the vertex of the parabola or the center and radius of the circle.
x^2+y^2+y+2=8
What is the intersection of this sphere with the yz-plane? find an equation of the sphere with center (−3, 2, 9) and radius 6?
The equation of the sphere with center (-3, 2, 9) and radius 6 is (x + 3)² + (y - 2)² + (z - 9)² = 6². The intersection of this sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.
Explanation:The equation of a sphere with center (-3, 2, 9) and radius 6 is given by:
(x + 3)² + (y - 2)²+ (z - 9)² = 6²
To find the intersection of this sphere with the yz-plane, we need to set x = 0 in the equation:
(0 + 3)² + (y - 2)² + (z - 9)² = 6²
Simplifying this equation gives:
(y - 2)² + (z - 9)² = 27
So, the intersection of the sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.
How would you represent 4 eighth notes as a fraction?
Transform both equations in each system of equations so that each coefficient is an integer.
***I also need it to be solved using substitution method.
△LMN, with vertices L(2,2), M(3,5), and N(6,1), is rotated 90° about the origin. What is the location of M′?
What is the equation of a quadratic graph with a Focus of (8,-8) and directrix of y=-6
On the blueprint of a house, 45 millimeters represents 10 meters. The length of the living room is 36 millimeters on the blueprint. What is the actual length of the living room?
45/10= 36/x
cross multiply
360/45X
360/45 = 8
the length is 8 meters
Convert the following using dimensional analysis:
13.2 cm to ft & in