23. Describe the slopes of perpendicular lines
Answers
Answer:
The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m. For example, we found that the slope of the line y = (1/2)x + 3 is 1/2.
The slopes of perpendicular lines when multiplied together gives the product as -1.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
Suppose the two perpendicular lines have equations as follows,
y = m₁x + c₁ and y = m₂x + c₂.
Suppose m₁ = tan θ
Then, m₂ = tan (90° + θ)
Apply the trigonometric identity to obtain,
m₂ = tan (90° + θ) = -cot θ
Now, m₁ × m₂ = tan θ × -cot θ = -1
Thus, the products of slopes is -1.
Hence, the product of slopes of two perpendicular lines is -1.
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Related Questions
Translate the sentence into an equation.
Eight times the sum of a number and 5 equals 7 .
Answers
Let the number be represented by the variable "x". Then, the sentence can be translated into the following equation:
8(x + 5) = 7
Sara works 40 hours per week and earns $660. Which graph shows the unit rate for this situation?
Answers
Answer: $16.5/hour
Step-by-step explanation:
The unit rate is the relationship between y and x if x = 1
660/40 = 16.5
That means, if x = 1, y = 16.5
Therefore, $16.5/hour
6 4 0,409, 210
onas period
ones
The number name for this number is six hundred forty million, four hundred
nine thousand, two hundred ten.
1Expanded form is a way to write a number as the sum of each
digit multiplied by its place value. Fill in the blanks to write the
number in expanded form.
Answers
The expansion of 6 4 0,409, 210 is given below with the solution.
What does "expanded form" mean?The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so on, results in the expanded form of the number. The expanded version of the number is the one that is represented by the sum of each digit times its place value.
6 4 0,409, 210 = 6 × 10,00,00,000 + 4 × 100,00,000 + 0 × 10,00,000 + 4 × 100,000 + 0 × 10,000 + 9 × 1000 + 2 × 100 + 1 ×10 + 1 × 0
A number is displayed in expanded form according to the place values of its digits.
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voces são de que pais?
which country are you from?
Answers
seriously bro
listen if you want to make friends or relationship please PLEASE NOT HERE THERE ARE KIDS HERE PEOPLE and the massage is not only for u
. The marching band packed 3060 сans of juice into boxes for a
band competition. Each box holds 18 cans. How many boxes did
the band members have to carry?
Answers
Answer: 170 boxes
Step-by-step explanation:
You simply divide 3060 by 18.
If you draw one card from a deck of 12 cards, numbered 1 through 12, what is the probability you will get an odd number or a number divisible by 4? (Enter your probability as a fraction.)
also,
A cube has 2 faces painted red, 2 painted white, and 2 painted blue. What is the probability of getting a red face or a white face in one roll? (Enter your probability as a fraction.)
and,
Rob Lee knows that he can compete successfully in a single track mountain bike race unless he gets a flat tire or his chain breaks. In such races, the probability of getting a flat is 0.1, of the chain breaking is 0.09, and of both occurring is 0.02. What is the probability that Rob completes the race successfully?
also,
A cube has 2 faces painted red, 2 painted white, and 2 painted blue. What is the probability of getting a red face or a white face in one roll? (Enter your probability as a fraction.)
and,
Rob Lee knows that he can compete successfully in a single track mountain bike race unless he gets a flat tire or his chain breaks. In such races, the probability of getting a flat is 0.1, of the chain breaking is 0.09, and of both occurring is 0.02. What is the probability that Rob completes the race successfully?
Answers
The probability that Rob completes the race successfully is:
1 - 0.1 - 0.09 + 0.02 = 0.83
The probability of getting an odd number or a number divisible by 4 can be found by adding the probabilities of getting an odd number and a number divisible by 4, and subtracting the probability of getting a number that is both odd and divisible by 4 (which is 4). The probabilities of getting an odd number, a number divisible by 4, and a number that is both odd and divisible by 4 are:
Odd number: There are 6 odd numbers out of 12 total numbers, so the probability of getting an odd number is 6/12 = 1/2.
Number divisible by 4: There are 3 numbers divisible by 4 (4, 8, 12), so the probability of getting a number divisible by 4 is 3/12 = 1/4.
Number that is both odd and divisible by 4: The only number that is both odd and divisible by 4 is 4, so the probability of getting this number is 1/12.
Therefore, the probability of getting an odd number or a number divisible by 4 is:
1/2 + 1/4 - 1/12 = 5/12
The probability of getting a red face or a white face can be found by adding the probabilities of getting a red face and a white face. The probability of getting a red face is 2/6 = 1/3, and the probability of getting a white face is also 1/3. Therefore, the probability of getting a red face or a white face is:
1/3 + 1/3 = 2/3
To find the probability that Rob completes the race successfully, we need to subtract the probability of getting a flat tire, the probability of the chain breaking, and the probability of both occurring from 1 (the probability of completing the race successfully). The probability of getting a flat tire is 0.1, the probability of the chain breaking is 0.09, and the probability of both occurring is 0.02. Therefore, the probability that Rob completes the race successfully is:
1 - 0.1 - 0.09 + 0.02 = 0.83
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please answer ASAP!!
At a science museum, Julia compares the length of a T-rex tooth and a crocodile tooth. The T-rex tooth is 7/12 foot long. The crocodile tooth is 1/4 foot long.What expression can be used to find how much longer the T-rex tooth is than the crocodile tooth?
Choose 1 answer:
A. 7/16 -3/16
B. 7/12-3/12
C. 7/16-1/16
D. 7/12-1/12
Answers
Answer:
B. 7/12-3/12
Step-by-step explanation:
make 1/4 to have the same denominator as 7/12
1/4=?/12
1×12=12
12/4
3
3/12
7/12-3/12
Graph linear equations in slope-intercept form. Y = 2x + 1
Answers
Answer:
Here's how to graph it!
since the function is in a slope-intercept form we see both the slope, 2x, and the y-intercept, +1, present in the equation
First, start at the y-intercept. In this function, it is positive 1.
After you have placed your first point at ( 0, 1 ), begin with the slope. In this function, the slope is 2 or 2/1. This means you will go 2 points up and 1 point to the right.
What should be done for an experiment to be considered verifiable?
Answers
We know that an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.
For an experiment to be considered verifiable, several things should be done. Firstly, the experiment should be designed in a way that allows others to replicate it and obtain the same results. This means that all procedures, materials, and variables used should be clearly documented and made available to others.
Secondly, the experiment should be conducted in a controlled environment, where all external factors that could influence the results are minimized or eliminated.
Thirdly, the data obtained from the experiment should be analyzed and interpreted objectively, without any bias or preconceived notions. Finally, the results should be subjected to peer review and scrutiny by experts in the relevant field to ensure that they are valid and reliable.
By following these steps, an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.
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explain how you can find 3/8 of $800
Answers
Answer:
by adding 2 zeros after the 3 and 8 in 3/8
Answer:
turn the problem into 3/8 divided by 800/1. then reciprocal. which leave it at 3/8 x 1/800. cross cancel. 3/1 x 1/100 answer is 3/100 .
Aisha has been taking music lessons. This year, she has taken 3 piano lessons for every 2 guitar lessons If Aisha has taken 48 piano lessons this year, how many guitar lessons has she taken?
Answers
Answer:
32 guitar lessons
Step-by-step explanation:
3 piano lessons : 2 guitar lessons = 48 piano lessons : x guitar lessons
3/2 = 48/x
(3)(x) = (48)(2) Cross multiply
3x = 96
x = 32
f(x)=
−x − 4 , x < 3
x^2 − 7 , 3 ≤ x ≤ 10
120/x + 5 , x > 10
f(4)=
Answers
In the given function, the value of f(4) is 9
What is a function?A function is a process or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.
To find the value of f(4), we need to evaluate the function f(x) at x = 4. Let's substitute x = 4 into the appropriate piece of the function:
f(4) = x² - 7
f(4) = 4² - 7
f(4) = 16 - 7
f(4) = 9
Therefore, the value of f(4) is 9.
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Troy started at the fire station. He walked to the library and then rode his bike to the post office. If Troy only traveled along the grid lines and took the shortest route, how far did he travel? please helllllllppppppppppppppp my last one
Answers
Answer:
14 blocks
Step-by-step explanation:
next time plz add a grid :(
A troop leader recorded whether the members from two troops prefer hiking or swimming. He plans to create a two-way table to display his results. Which describes the variables he can use in the first row and first column to create his table?
troop number and number who prefer hiking
troop number and activity preference
activity preference and number of troop 1 members
activity preference and number of troop 2 members
Answers
Answer:
B: troop number and activity preference
Step-by-step explanation:
I took the quiz :)
Answer:
The answer would be B. troop number and activity preference
Step-by-step explanation:
I took the test.
Help me please://///
Answers
Answer:
\(\frac{59}{11}\)
Step-by-step explanation:
The "b" value is when the x value is 0 (or the y intercept).
Lets first find the slope so we can find the y intercept.
Slope Formula:
\(\frac{y_1-y_2} {x_2-x_1}\)
Plug into the formula.
\(\frac{6-5}{7--4}\) (\(\frac{1}{11}\))
Slope is 1/11.
Now we can start forming a equation.
y = 1/11x + b
Slope of 1/11 means that every 11 gone right, 1 goes up. Lets use another formula to calculate.
\(b = y_1 - mx_2\)
Plug in.
\(b = 5 - \frac{1}{11} (-4) \\b = 5-\frac{-4}{11}\\b = 5 + \frac{4}{11} \\b = \frac{59}{11}\)
Use the figure and information below to find the length of each line segment
7th grade math please help me
Answers
Answer:
7. 6
8. 6
9. 12
10. 6
11. 12
12. 24
Step-by-step explanation:
The length of each segment is AB = 6, BC = 6, AC = 12, CD = 6, CE = 12, AE = 24
What is the length?It is the measure of distance between the two points is called a length.
D is the mid-point of CE. Then
CD = DE = 6
B is the mid-point of AC. Then
AB = BC
C is the mid-point of AE. Then
AC = CE
AB + BC = CD + DE
AB + AB = CD + CD
2 AB = 2 CD
AB = CD
AB = 6
Then
AB = 6
BC = AB = 6
AC = AB + BC = 6 + 6 = 12
CD = DE = 6
CE = CD + DE = 6 + 6 = 12
AE = AB + BC + CD + DE = 6 + 6 + 6 + 6 = 24
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FOR 20 POINTS FIND X PLEASE!!
Answers
Hi there!
We can find the values of x using right triangle trig.
Recall: SOHCAHTOA
sin = O/H (Opposite / Hypotenuse)
cos = A/H (Adjacent / Hypotenuse)
tan = O/A (Opposite / Adjacent)
Thus:
6. A = 14, H = 15
cos x = 14/15
cos⁻¹ (14/15) = x
x = 21.04° ≈ 21°
7. O = 19, A = 23
tan x = 19/23
tan⁻¹(19/23) = x
x = 39.56° ≈ 40°
8. A = 9, H = 17
cos x = 9/17
cos⁻¹(9/17) = x
x = 58.03 ≈ 58°
9. O = 43, H = 45
sin x = 43/45
sin⁻¹(43/45) = x
x = 72.85° ≈ 73°
Between which two integers is
\( \sqrt{60} \)
Answers
there is a 150% markup on a $399 laptop and there is a sale for 25% what is the sale price?
Answers
Answer:
99.9
Step-by-step explanation:
The graph of a linear function passes through (−8,−4) and (4, 5). What is the equation of the function? A. y = −34x + 2 B. y = 34x + 2 C. y = −43x + 6 D. y = 43x + 6
Answers
Answer:
y = 3/4x + 2
Step-by-step explanation:
Not sure if you wrote your answer choices incorrectly, but if B is y=3/4x + 2 then the answer is B
To KeianaLol thanks :)
Answers
Answer:
PAGE 1
16.) c
PAGE 2
11.) e
12.) a
PAGE 3
13.) e
14.) d
15.) b
PAGE 4 (SCREENSHOT)
Step-by-step explanation:
PAGE 1
16.) C b/c if you draw a line through it you have line of symmetry and a regular hexagon has rotational symmetry.
PAGE 2
11.) P(6, 2) ----(6*3, 2*3) -----> P'(18, 6)
So e is the answer
12.) The compound transformation should read
Dilation with center at origin and scale factor of 1/2
Reflection across the x-axis
Reflection across the x-axis rule is (x, y) -->(x, -y)
a is the answer b/c A(-1, -2) --> A'(-1/2, -1) --> (-1/2, 1)
PAGE 3
13.) The scale of the dilation is 1/4 b/c ---> 25*1/4 = 6.25 and 64*1/4 = 16
So 16*1/4 = 4 and 10*1/4 = 2.5, so e is the answer
14.) Dilation b/c you can either enlarge or reduce the pre-image.
15.) A heptagon has 7 lines of symmetry b/c it is equal to the number of sides
PAGE 4
SCREENSHOT
Hope this helps ya pal!!!
P.S. I added the screenshots that you didn't get the other time!
And on some of the graphs I forgot to put A'' or A''' so you will have to add the extra ' things it depends on how many transformations there are if there are 3 you but 3 ' on the red triangles.
In ALMN, the measure of ZN=90°, MN = 5 feet, and LM = 7-3 feet. Find the measure
of ZL to the nearest tenth of a degree.
M
7.3
5
79
N
L
PLEASE HELP ME
Answers
Answer:43.2
Step-by-step explanation:
find the area of a pentagon with an apothem of 7 centimeters
Answers
If the side length of the pentagon is 19.27 centimeters. Then the area of the pentagon will be 337.225 square cm.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The apothem of the pentagon is 7 cm.
Then the area of the pentagon will be
\(\rm Area = 5 \times \dfrac{1}{2} \times apothem \times side \ length\)
The side length of the pentagon will be
\(\rm Side \ length = 2 \times 7 \tan 54^o \\\\Side \ length = 19.27\ cm\)
Then the area will be
\(\rm Area = 5 \times \dfrac{1}{2} \times 7\times 19.27\\\\Area = 337.225\)
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oscar finally found his dog on the fourth day. if he searched in a for two days and b for two days (not necessarily in that order) what is the probability that he found his dog. alive?
Answers
the probability that he found his dog. alive is 15%.
What is probability?
The chance of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Probability theory is a branch of mathematics that focuses on calculating the likelihood that an event will occur. Probability measures how likely something is to happen.
if he searched in a for two days and b for two days
P(A) = 0.4
P(B) = 0.6
P(Dn D-1 F-1)= n n+2
P(FnA, Sn, F-1) = 0.25
P(FB, S, F-1) = 0.15
Hence the probability that he found his dog. alive is 15%.
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A field in the shape of a right triangle is boarded on one side by a stream, on another side by a road, and on a third side by a fence. What angle does this stream make with the road
Answers
The angle that the stream makes with the road in the given right triangle is approximately 53 degrees (rounded to the nearest degree).
To determine the angle that the stream makes with the road in the given right triangle, we can use the trigonometric function called inverse tangent (arctan). The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the stream is the side opposite the angle we want to find, and the road is the side adjacent to the angle. The length of the stream is 27 yards, and the length of the road is 20 yards.
Using the arctan function, we can calculate the angle:
θ = arctan(opposite/adjacent)
θ = arctan(27/20)
Using a calculator, we can find the arctan of this ratio. The result is approximately 53.13 degrees.
Therefore, the angle that the stream makes with the road in the given right triangle is approximately 53 degrees (rounded to the nearest degree).
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Note: The complete questions is
A field in the shape of a right triangle is bordered on one side by a stream, on another side by a road, and on a third side by a fence.
What angle does this stream make with the road?
Round only your final answer to the nearest degree.
plz plz plz help me....
the product of digits in a two digit number is 12. the number formed by interchanging the digits of that number will be 9 less than the original number. find the original number.
Answers
Answer:
Let the tens digit of the required number be x and the units digit be y. Then,
x+y=12 .........(1)
Required Number = (10x+y).
Number obtained on reversing the digits = (10y+x).
Therefore,
(10y+x)−(10x+y)=18
9y−9x=18
y−x=2 ..........(2)
On adding (1) and (2), we get,
2y=14⟹y=7
Therefore,
x=5
Hence, the required number is 57.
Step-by-step explanation:
Hope it is helpful...
Step-by-step explanation:
Let X be the 1st digit and Y be the 2nd digit of the two digit number.
We have X * Y = 12 and (10X + Y) = (10Y + X) + 9.
=> XY = 12 and 9X = 9Y + 9
=> XY = 12 and X = Y + 1
Therefore X = 4 and Y = 3. => Number is 43.
Charlie buys a pack of 8 thank you cards for 1.20$ using the pickles shown below. How much does he spend on each thank you card?
Answers
Answer:
0.15
Step-by-step explanation:
You are the director of the customer service center in Company Alpha. You find that the mean time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective response time is 11 minutes with a standard deviation of 20 minutes. (a) Identify the following parameters: ta
tθ
∂a
∂θ
ra:
rθ:
Answers
The identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
ta: Mean time between calls to the center
tθ: Effective response time
∂a: Standard deviation of the time between calls to the center
∂θ: Standard deviation of the effective response time
ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)
rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)
Given information:
Mean time between calls to the center (ta) = 6 minutes
Standard deviation of time between calls (∂a) = 4 minutes
Effective response time (tθ) = 11 minutes
Standard deviation of effective response time (∂θ) = 20 minutes
Using this information, we can determine the values of the parameters:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/ta = 1/6 minutes^(-1)
rθ = 1/tθ = 1/11 minutes^(-1)
So, the identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
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I really need some help. Plz show your work, Thanks!
Answers
Answer:
Step-by-step explanation:
What is the interest practice of combining campaign contributions from several sources into one larger contribution from the group, so as to increase the groups impact on the candidate
Answers
The interest practice described in the question is known as "bundling." Bundling refers to the act of combining individual campaign contributions from multiple sources into a single larger contribution from a group or organization.
Bundling allows interest groups or individuals to pool their resources and present a more substantial contribution to a candidate. By consolidating smaller contributions into a larger sum, bundlers can demonstrate greater financial support and influence.
This practice is often employed by special interest groups, lobbyists, or individuals with shared political objectives who want to maximize their influence on the political process. Bundlers can leverage their collective financial power to gain access to candidates, shape policy agendas, and potentially gain favorable treatment or influence over decision-making.
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