A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?
Answers
Answer:
y = (-3/7)x + 9 ( -1.5x − 3.5y = -31.5)
Step-by-step explanation:
Normally, there's a list of possible answers associated to this question, and the answer is usually in the form of -1.5x − 3.5y = -31.5 (equivalent to y = (-3/7)x + 9)
You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.
In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).
We see on the image that the line PQ is perpendicular to AB. That means that its slope is -3/7.
So, we have a slope of -3/7 and we know it passes through point P (7,6), let's see if we can find the missing term.
y = (-3/7) x + b
6 = (-3/7) 7 + b
6 = -3 + b
b = 9
So the equation of the line forming the street PQ is y = (-3/7)x + 9
Related Questions
PLEASE HELP I NEED THE ANSWER
QUICK!!!
Answers
Step-by-step explanation:
ΔADG - NO (it's an equilateral triangle)
ΔAFH - NO (it's an equilateral triangle)
ΔBCH - NO (it's an equilateral triangle)
ΔBEH - NO (it's an equilateral triangle)
ΔBFG - YES
ΔCDG - YES
ΔEFG - YES
ΔDFG - NO (it's an equilateral triangle)
All equilateral triangles have the sides equal a√2 (a - length of edge).
ΔBFG has sides a, a√2 and a√3.
From Inverse Pythagorean Theorem:
a² + (a√2)² = (a√3)²
a² + 2a² = 3a²
3a² = 3a² CORRECT :)
ΔCDG and ΔEFG have sides a, a and a√2.
From Inverse Pythagorean Theorem:
a² + a² = (a√2)²
2a² = 2a² CORRECT :)
if i have a 0.75 ( F ) and i get an A x2 what will my grade be
Answers
Answer:
Maybe a C if the grade is summative
Step-by-step explanation:
F's are not hard to raise, you're gonna need more than 2 A's to get a "passing grade." Try extra credit!
The longest river in the UK is the river Severn which has a length of 24 cm on a map. If the map is drawn at a scale of 1:1,500,000, then how many kilometers is the river actually?
Answers
Answer:
360 km
Step-by-step explanation:
we know that
The scale of the map is
1:1,500,000
That means
1 cm on a map ------> represent 1.500.000 cm in the actual
or
1 cm on a map ------> represent 15,000 m in the actual
or
1 cm on a map ------> represent 15 km in the actual
therefore
In this problem
24 cm on a map-------> represent 24*15=360 km actually
The actual length of the river Severn is 360 kilometers.
To determine the actual length of the river Severn, we need to apply the map scale to the map length. The scale given is 1:1,500,000, which means that 1 unit of measurement on the map corresponds to 1,500,000 of the same units in reality.
The map length of the river Severn is given as 24 cm. To find the actual length, we multiply the map length by the scale factor:
[tex]\[ \text{Actual length} = \text{Map length} \times \text{Scale factor} \] \[ \text{Actual length} = 24 \, \text{cm} \times 1,500,000 \][/tex]
Since the scale is in centimeters to kilometers, we need to convert the map length from centimeters to kilometers before multiplying by the scale factor. There are 100,000 centimeters in a kilometer, so:
[tex]\[ 24 \, \text{cm} = \frac{24}{100,000} \, \text{km} \] \[ 24 \, \text{cm} = 0.00024 \, \text{km} \][/tex]
Now, we multiply this by the scale factor:
[tex]\[ \text{Actual length} = 0.00024 \, \text{km} \times 1,500,000 \] \[ \text{Actual length} = 360 \, \text{km} \][/tex]
Therefore, the actual length of the river Severn is 360 kilometers.
Use the table from a random survey about the preferred service for streaming movies. Out of 750 people, how many would you expect to prefer Company B?
Answers
Answer:
The correct answer option is 192.
Step-by-step explanation:
We are given the results of a random survey about the preferred service for streaming movies.
We are to find the number of people we would expect to prefer Company B.
Number of people using service B = 32
Total number of people = 125
Number of people expected to prefer Company B = [tex] \frac{32}{125} \times 7 5 0 [/tex] = 192
Answer: Option A
192 people[
Step-by-step explanation:
From the participation survey
[tex]n =75+32+18=125[/tex] people
Among these 125 people, only 32 preferred the company B
Now assuming that this sample is representative of the total population, then the probability that a randomly selected person prefers company B is:
[tex]P =\frac{X_B}{n}[/tex]
Where
[tex]X_B=32[/tex]
[tex]n=125[/tex]
[tex]P =\frac{32}{125}[/tex]
[tex]P =0.256[/tex]
Finally, the expected number of people who prefer company B is:
[tex]E = P * m[/tex]
Where m is the number of people in the total population. [tex]m = 750[/tex]
[tex]E=0.256*750[/tex]
[tex]E=192\ people[/tex]
Which of the following give the correct graph and phase shift for y = 3 cos ( θ +20) – 4?
Answers
Answer:
See picture attached below
Step-by-step explanation:
We can easily find the answer to your question, if we plot the equation with a graphing calculator or any plotting tool.
The equation is
y = 3 cos (θ + 20) - 4
See attached picture below
phase_shift = 20
max_amplitude = -1
min_amplitude = -7
Period = 2π
solve the equation 2y²=13y
Answers
Step-by-step explanation:
2y² = 13y
2y² − 13y = 0
y (2y − 13) = 0
y = 0, y = 13/2
It can be tempting to divide by y at the beginning, but if you do, you lose one of the solutions. Instead, move everything to one side and factor.
The solutions to the equation 2y²=13y are y = 0 and y = 6.5. This is achieved by setting up the equation to zero, factoring it out and applying the zero product property.
Explanation:To solve the provided equation, 2y²=13y, you'll need to set the equation to zero by moving all the terms to one side: 2y² - 13y = 0. This becomes a quadratic equation in the form ax² + bx + c = 0.
Factor the equation by taking out a common factor of 'y', yielding y(2y - 13) = 0. According to the zero product property, if a product is zero then at least one of the factors must be zero. This means that y = 0 or 2y - 13 = 0. Solving the second equation gives y = 6.5.
So, the solutions of the equation are y = 0 and y = 6.5.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
#SPJ3
Please help me, I need to divide this problem (-2/7)(5/-8)
Answers
Answer:
5/28 (Decimal: 0.178571)
Step-by-step explanation:
(−2/7) (5/−8)
= −2/7 (5/−8)
=−2/7 (−5/8)= 5/28
The definition of an angle uses the undefined term_______.
line
plane
point
ray
Answers
Answer:
I believe the answer is C. Point
Step-by-step explanation:
Hope my answer has helped you!
Answer:
The correct answer is option C - point
Step-by-step explanation:
The definition of an angle uses the undefined term : POINT
An angle has two rays that share a common endpoint.
This common point is also referred to as the vertex.
Angles that meet at 90 degrees are called right angles.
Angles that are less than 90 degrees are called acute angles.
Angles that are exactly 180 degrees are called straight angles.
Give the slope of y- 4 = 5(x - 2) and a point on the line.
A. The slope is 5 and (-2,-4) is on the line.
B. The slope is 5 and (2, 4) is on the line.
C. The slope is 4 and (2,5) is on the line.
D. The slope is 2 and (5, 4) is on the line.
Answers
Answer:
B. The slope is 5 and (2, 4) is on the line.Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the equation:
[tex]y-4=5(x-2)[/tex]
Therefore
m = 5
(x₁, y₁) = (2, 4)
Answer:B The slope is 5 and (2,5) is on the line
Step-by-step explanation:
.
The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 210 minutes, the monthly cost will be $108.5. If the customer uses 620 minutes, the monthly cost will be $252.
A) Find an equation in the form
y
=
m
x
+
b
,
where
x
is the number of monthly minutes used and
y
is the total monthly of the NextFell plan.
Answer:
y
=
B) Use your equation to find the total monthly cost if 979 minutes are used.
Answer: If 979 minutes are used, the total cost will be
dollars.
Get help: Video
Answers
Answer:
1. y=0.35x+35
2. If 979 minutes are used, the total cost will be $377.65 dollars.
Step-by-step explanation:
1. Let $x be the flat monthly fee and $y be the amount of money paid per minute used on the phone.
If a customer uses 210 minutes, the monthly cost will be $108.5, thus
[tex]x+210y=108.5[/tex]
If the customer uses 620 minutes, the monthly cost will be $252, then
[tex]x+620y=252[/tex]
Subtract from the second equation the first one:
[tex]x+620y-(x+210y)=252-108.5\\ \\x+620y-x-210y=143.5\\ \\410y=143.5\\ \\y=0.35[/tex]
Substitute it into the first equation
[tex]x+210\cdot 0.35=108.5\\ \\x=108.5-73.5\\ \\x=35[/tex]
We get the flat fee is $35 and the amount of money per minure used is $0.35. So, the equation of the function is
[tex]y=35+0.35x,[/tex]
where x is the number of monthly minutes used and y is the total monthly of the NextFell plan.
2. When x=979, then
[tex]y=35+0.35\cdot 979=377.65[/tex]
Pocket contains 15 white eight pink three yellow and 10 blue golf balls. A ball is chosen at random, not replaced then another is chosen at random. What is the probability of blue, then pink
Answers
Answer:
4/63
Step-by-step explanation:
The probability of first choosing a blue golf ball and then a pink golf ball, without replacement, from the pocket is 4/63.
The question asks for the probability of selecting a blue golf ball and then a pink golf ball from a pocket that contains 15 white, 8 pink, 3 yellow, and 10 blue golf balls, without replacement. To solve this, we need to find the probabilities of each event happening sequentially and then multiply them.
Firstly, the probability of choosing a blue ball initially is 10 out of the total number of balls (15 white + 8 pink + 3 yellow + 10 blue), which gives us 36.
Therefore, the probability is 10/36 or 5/18. Once a blue ball has been chosen, it is not replaced, so the total count of balls is reduced by one, making it 35, and the count of blue balls is now 9.
Secondly, with the blue ball removed, we now calculate the probability of choosing a pink ball. There would still be 8 pink balls, so the probability of now choosing a pink ball is 8 out of the remaining 35 balls. This gives us the probability of 8/35.
To find the overall probability of both events happening in sequence (first a blue ball, then a pink ball), we multiply the individual probabilities: (5/18) × (8/35) = 40/630, which can be simplified to 4/63.
i dont know the answer. Can someone help me ?
Answers
Answer:
V = 18 pi unit ^3
Step-by-step explanation:
Volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = pi * (3)^2 *2
V = pi *9(2)
V = 18 pi unit ^3
The volume of a cylinder is
(Pi) x (radius squared) x (height) .
Using this, you can FIND the volume of any cylinder, even when you don't know it. This one is 18 pi cubic units.
The surface area of a sphere is 16 square units. The radius of the sphere measures
Answers
The answer to this question is 2.
Probability of getting HH
Answers
Answer:
The experimental probability is 3% greater than the theoretical probability.
Step-by-step explanation:
We are given the results of flipping two coins with their outcomes and number of times they were tossed.
We are to compare the experimental and theoretical probability of getting HH.
The theoretical Outcomes are: HH HT TH TT
So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%
Total number of outcomes = [tex]28+22+34+16[/tex] = 100
So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%
Therefore, the experimental probability is 3% greater than the theoretical probability.
Given the following triangle, if c = 25 and 2 A= 20°, find a.
Answers
Answer: A=2
Explanation:
1: c=25
2: 2a=20
3: 1 a=20
Which word describes an angle with a measure of 98"?
A) Obtuse
B) Right
C)Acute
D) Complementary
Answers
Answer:
A) Obtuse.
Step-by-step explanation:
Angles of value between 90 and 180 degrees are called obtuse.
Answer:
obtuse
Step-by-step explanation:
because an obtuse angle is any angle from 91°-180°
what changes in the parent graph y= |x| would you see if you graphed y= |x+3| ?
Answers
Answer:
The graph is shifted 3 units to the left
Step-by-step explanation:
Answer:
The parent graph will shift 3 units to the right.
Step-by-step explanation:
We are given that there is this parent graph with the equation [tex] y = | x | [/tex] and if we graph [tex] y = | x + 3 | [/tex], what are the changes that will be made to the parent graph to get this.
Since there is addition of 3 units in x, therefore the parent graph will shift 3 units to the right side.
Can you Solve |2a-1|=7
Answers
Answer: a=4 or a= −3, so you can use anyone of the answers.
Step-by-step explanation:
Solve Absolute Value.
|2a−1|=7
We know either 2a−1= 7or 2a−1 = −7
2a−1=7(Possibility 1)
2a−1+1=7+1(Add 1 to both sides)
2a=8
[tex]\frac{2a}{2} = \frac{8}{2}[/tex] (Divide both sides by 2)
a=4
OR,
2a−1=−7 (Possibility 2)
2a−1+1= −7+1 (Add 1 to both sides)
2a= −6
[tex]\frac{2a}{2} =\frac{-6}{2}[/tex] (Divide both sides by 2)
a= −3
Therefor the answers are a=4 or a= −3
* Hopefully this helps:) Mark me the brainliest:)!!
PLEASE HELP!!!
Driving across country, mike drove for 3 hours at a certain rate and for 4 hours at a rate 10 mph faster. If his total distance covered was 495 miles, then what was his slower rate?
Answers
Answer:
50 miles per hour
Step-by-step explanation:
What is 50 percent of 62?
Answers
Answer:
31
Step-by-step explanation:
An entire amount is 100% of the amount.
50% is half of 100%, so 50% means the same as half.
Half of 62 is the same as 62/2 = 31
Answer: 31
Generally you would need to do a [tex]\frac{part}{whole}[/tex] proportion but there is a shorter way to do just the specific question. If you would like to know how to do the proportion version let me know
Since it asks for 50% of 62 it means that it's looking for half of 62, so all you have to do is divide 62 by 2 which is...
62/2 = 31
31 is 50% of 62
Hope this helped!
What is the equation for the line of reflection
Answers
Answer:
B
Step-by-step explanation:
The image is a reflection of the original in the y- axis
The equation of the y- axis is x = 0 → B
Answer:
The correct option is B.
Step-by-step explanation:
The coordinates of polygon ABCDE are A(-2,2), B(-1,2), C(1,1), D(0,-1) and E(-2,1).
The coordinates of polygon A'B'C'D'E' are A'(2,2), B'(1,2), C'(-1,1), D'(0,-1) and E'(2,1).
The relation between preimage and image is
[tex]P(x,y)\rightarrow P'(-x,y)[/tex]
From the given figure it is clear that the figure ABCDE reflected across the y-axis.
If a figure reflected across the y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
The equation of y-axis is x=0, so the given figure reflected across x=0.
Therefore the correct option is B.
Which statement describes the rate of change of the following function?
f(x) = 9x - 4
A.
The function has a constant rate of change, decreasing for all x at a rate of 4.
B.
The function has a constant rate of change, increasing for all x at a rate of 9.
C.
The function has a varying rate of change when x > 9.
D.
The function has a varying rate of change when x < 4.
Answers
Answer:
answerbis 2.25
Step-by-step explanation:
f(x)=9/4
f(x)=2.25
it would be a because of the -4
The graph given above shows the following function
y= cos(x)
What is the amplitude of the function?
a. 2
b. pi
c. 2pi
d. 1
Answers
Answer:
D,1
Step-by-step explanation:
look at the wavelengths
Answer: For plato user the correct answer is C
Step-by-step explanation:
Just took the test and got it correct
If it takes John 10 hours to paint the fence, how long will it take John and his 2 friends to do the job if they work at the same rate? If it takes John 10 hours to paint the fence, how long will it take John and his 2 friends to do the job if they work at the same rate?
Answers
Answer:
3.3 hours
Step-by-step explanation:
10/3≈3.3
Answer:
You just have to divide 10 by 3 since John takes 10 hours to paint the fence
it would take 3.3 hours for john and his friends to finish painting the fence
Step-by-step explanation:
Raquel has created a program for a robot. The robot travels 10 meters and stops. The program is designed for wheels that are 2.5 cm in diameter. When Raquel replaces the wheels with ones having a 2.75 cm diameter, how should she adjust the number of rotations so that the robot travels the same distance?
Answers
Answer:
Raquel should adjust the number of rotations to 115.81 rotations
Step-by-step explanation:
step 1
Find the circumference of the wheels that are 2.5 cm in diameter
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=2.5/2=1.25\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14) (1.25)[/tex]
[tex]C=7.85\ cm[/tex]
step 2
Find the number of rotations
Divide 10 meters by the circumference
[tex]10\ m=1,000\ cm[/tex]
[tex]1,000/7.85=127.39\ rotations[/tex]
step 3
For a diameter of 2.75 cm find how should she adjust the number of rotations so that the robot travels the same distance
Find the circumference of the wheels
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=2.75/2=1.375\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14) (1.375)[/tex]
[tex]C=8.635\ cm[/tex]
step 4
Find the number of rotations
Divide 10 meters by the circumference
[tex]10\ m=1,000\ cm[/tex]
[tex]1,000/8.635=115.81\ rotations[/tex]
The general term of an arithmetic sequence is tn = 32 + 3n, where n ∈N and n ≥ 1. The sequence is A) 32, 35, 38, 41, 44, 47,... B) 32, 96, 288, 864, 2592, 7776,... C) 34, 39, 44, 49, 54, 59,... D) 35, 38, 41, 44, 47, 50,...
Answers
Answer:
35,38,41,44,47,50,....
Step-by-step explanation:
n ∈N means that n is an element of Natural numbers
Natural numbers are whole non-negative numbers
n ≥ 1, means that n = 1, 2, 3, 4, 5, 6,........
tn = 32 + 3n
the first term t1 = 32 + 3(1)
32 + 3 = 35
the second term t2 = 32 + 3(2)
32 + 6 = 38
the third term t3 = 32 + 3(3)
32 + 9 = 41
The native bird population in a city is decreasing at a rate of 10% per year due to industrialization of the area by humans. The population of native birds was 14,000 before the decrease began.
Complete the recursively-defined function to describe this situation.
f(0) = ____
f(n) = f(n - 1) · 0.9 , for n ≥ 1
After 3 years, _____ birds will remain.
Answers
Answer:
The recursively-defined function to describe this situation is:
f(0) = 14000 f(n) = f(n - 1) · 0.9 , for n ≥ 1 After 3 years, 10206 birds will remain.Step-by-step explanation:
To solve the number of birds that there will be after three years, you must recognize that the function f(0) means the number of birds at time zero, in which the birds are complete (that is, the 14,000 birds), by their part, following the equation provided below we have the following calculation:
f(n) = f(n-1) * 0.9So:
f(1) = f(0) * 0.9 = 14000 * 0.9 = 12600 f(2) = f(1) * 0.9 = 12600 * 0.9 = 11340 f(3) = f(2) * 0.9 = 11340 * 0.9 = 10206Therefore, the final number of birds after three years in decline is 10206.
Which equation would best help solve the following problem?
Maria releases a javelin 1.5 m above the ground with a initial vertical velocity of 22 m/s. How long will it take the javelin to hit the ground?
(Possible answer in picture)
Answers
Answer:
- 4.9t + 22t= 1.5 is the answer
Does anyone know this?
Answers
Answer:
There are two inputs for which the output is 5.
The vertex of its graph is at (0,-2)
Step-by-step explanation:
ANSWER
2nd
4th
5th
EXPLANATION
The given function is
[tex]y = |x| - 2[/tex]
The value of this function cannot be negative: False.
y = |1| - 2=-1
Its graph has a V-shape. This is true because it is the graph of y=|x| shifted downwards by 2 units.
There is only one input for which this function is zero. False
both -2 and 2 will make this function zero.
There are two inputs for which this function is 5. True, x=7 and x=-7
The vertex is (0,-2). This is true because it is the graph of y=|x| shifted downwards by 2 units.
The equation of a circle is given. What is the diameter of the circle? Round to the nearest tenth.
(x-2)2 + (y+3)2 = 52
Answers
Answer:
14.2 is the diameter.
Step-by-step explanation:
The radius squared = 52.
What you have given is the general equation of the circle with a center at (2,-3) and a radius of sqrt(52)
You can break the 52 down.
sqrt(52) = sqrt(4 * 13) = 2 sqrt(13). Notice that 4 is a perfect square.
d = 2*radius.
d = 2(2 sqrt(13) )
d = 4 sqrt(13)
That is the diameter. You want it to the nearest 1/10
d = 14.222 but it is to the nearest 1/10
d = 14.2