It's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle,
What are the slopes of the two lines?
The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter m.
The slopes of the two lines that Laurie graphed, -2 and 1/2, are negative reciprocals of each other, which means that their product is -1.
In a Cartesian coordinate system, lines that are perpendicular to each other will have slopes that are negative reciprocals of each other, and the product of their slopes will be -1.
However, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle.
The two lines could be skew lines that never intersect and thus cannot be perpendicular.
Another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
When working with slope, we always assume that the lines are defined on a 2D Cartesian coordinate system, if that is not the case, it could cause the lines to not appear as perpendicular.
Hence, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle, another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
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Express the following measure in radians.
675°
Answer:
[tex]\frac{15\pi }{4}[/tex]
Step-by-step explanation:
Degrees to radians, multiply by pi/180
675pi/180
use a calculator to simplify
You get 15pi/4
The value of 675 degree is equivalent to [tex]\frac{15pi}{4}[/tex].
What is the formula to convert degree to radian?
The relation between radian and degree is given by Angle in radian=angle in degree*[tex]\frac{pi}{180}[/tex].
What is the conversion of 675degree?We will substitute 675 for angle in degree into the formula to get the value in radian.
[tex]\frac{675*pi}{180}[/tex]
This will be [tex]\frac{15pi}{4}[/tex].
Therefore, the correct answer is [tex]\frac{15pi}{4}[/tex].
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write an equation for the exponential function represented in the graph below.
Answer
150
Step-by-step explanation:
No hay explanation
How many hours of sleep do you get each night? Is this a statistical question
Answer:
Yes.
Step-by-step explanation:
This is a statistical question because a statistical question is a question that can be answered by collecting data that vary. The question that you provided would have different answers from different people.
Another example of a statistical question could be: "How old are the students at my school?" This would be statistical because once again, the ages will vary from different people.
Hello, I am stuck on this question which is a exchange rate question
if 1 sar is worth 0.05 US dollars, how many south african rand is 1 US dollar worth?
Answer:
0.05 US$=1 sar
then,1 US$=1/0.05 sar.
Need with this … substitution method..
Answer:
The solution is the point (-3,2)
Step-by-step explanation:
x + 2y = 1 Subtract 2y from both sides
x + 2y - 2y = 1 - 2y
x = 1 - 2y Substitute 1 - 2y in for x in the second equation and solve for y.
5x -4y = -23
5(1 - 2y) -4y = -23 Distribute the 5
5(1) - 5(2y) - 4y = -23
5 -10y - 4y = -23 Combine like terms
5 -14y = -23 Subtract 5 from both sides
5 -5 - 14y = -23 -5
-14y = -28 Divide both sides by -14
[tex]\frac{-14y}{-14}[/tex] = [tex]\frac{-28}{-14}[/tex]
y = 2
Solve for y
x + 2y = 1 Substitute in 2 for y and solve for x
x + 2(2) = 1
x + 4 = 1 Subtract 4 from both sides
x + 4 - 4 = 1 - 4
x = -3
The solution is the point (-3,2)
Check:
2 + 2y = 1
-3 + 2(2) = 1
-3 + 4 = 1
1 - 1 checks
5x - 4y = -23
5(-3) - 4(2) -23
-15 - 8 = -23
-23 = -23
No math apps, my teacher said they don’t work ♀️
x^3 – 27 = 0
Answer:
hope this helps you
Answer =3
The weights of a sample of nine football players are 78, 72, 68, 73, 75, 69, 74, 73, 72. Find the variance and the standard deviation.
Answer:
The variance is of 8
Step-by-step explanation:
To find the variance and the standard deviation, first we need to find the mean.
Mean:
Sum of all values divided by the number of values. So
[tex]M = \frac{78+72+68+73+75+69+74+73+72}{9} = 72.67[/tex]
The standard deviation is of 2.83
Variances:
Sum of the difference squared between each value and the mean, divided by the number of values. So
[tex]V = \frac{(78-72.67)^2+(72-72.67)^2+(68-72.67)^2+(73-72.67)^2+(75-72.67)^2+(69-72.67)^2+(74-72.67)^2+(73-72.67)^2+(72-72.67)^2}{9} = 8[/tex]
The variance is of 8
Standard deviation:
Square root of the variance. So
[tex]S = \sqrt{V} = \sqrt{8} = 2.83[/tex]
The standard deviation is of 2.83
Directions: Find the sum for each of the following arithmetic series below. Use the summation
formula to find the sums.
1. A series with six terms, the first term is five, and the common difference is five.
2. A series with six terms, the first term is nine and the common difference is twelve.
3. A series with five terms, the first term is 5.7 and the common difference is 1.4.
Therefore , the solution to the given problem of arithmetic mean comes out to be 1. 105, 2. 234 and 3. 42.5
Arithmetic mean: What is it ?The combination of the amount of all of the values in a list and the number of items in the that list, split by both, is the arithmetic average or mean of the group. The mathematical progression is same to this. This mean of the digits 5, 7, and 9 is 4,
For example, as expression 5 + 7 + 9 is 21, and 21 divided by 3 [there are actually three numbers] equals 7.
Given:
1) There are six terms in AP, with terms a and d each being worth five points.
2) There are 6 terms in AP, with terms 9 and 12 respectively.
3) In AP, there are five terms, where an is 5.7 and d is 1.4.
4) In AP, = 20, t21 = 400
5) In AP, t100 = 99 and a = 0
Find the sum of the terms in the arithmetic series.
As is common knowledge, Sn in the AP equals n/2[2a+(n-1)d]
To determine: the total terms in the arithmetic series
The AP sum of n words is well known. Sn = (n-1)/2[2a+(n-1)d]
1) There are 6 terms in the case where a = 5 and d = 5, as shown by S6 = [2(5)+(61)5] = 3[10+5(5)] = 3[10 + 25] = 3(35) = 105
2) There are 6 terms in the case where a = 9 and d = 12, where S6 = [2(9)+(61)12] = 3[18+5(12)] = 3[18+60] = 3(78) = 234
3) There are 5 terms total, with terms a = 5.7 and d = 1.4.
S5= [2(5.7)+(5—1)1.4] = 2.5[11.4+4(1.4)] = 2.5[11.4+5.6] = 2.5(17) = 42.5
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नीचे दिर गर दक्वि व्यंजनी वाले दो दो शब्द लिखिए
म्म
Answer:
give Ff id let's play ......
look at the picture pls pls pls i need help
Answer: 39.5 ft^2
Step-by-step explanation:
1. Find the area of the rectangle using the formula length * width
8 ft * 4 ft = 32 ft2. Find the area of one of the triangles (the top one) using the formula 1/2(b*h)
2 ft * 3 ft * 0.5 = 3 ft3. Find the area of the other triangle (the bottom one) using the formula 1/2(b*h)
3 ft * 3 ft * 0.5 = 4.5 ft4. Add 'em all up to get the total area
32 ft + 3 ft + 4.5 ft = 39.5 ft ^2Circle Review Worksheet
Please help
Answer/Step-by-step explanation:
Recall: circumference of a circle, C = πd or C = 2πr
Where d = diameter
Radius (r) = ½ of diameter
1. Radius (r) = 3 cm
Diameter (d) = 2(3) = 6 cm
Circumference = πd = π*6
C = 18.8495559 ≈ 18.8 cm (nearest tenth)
2. Radius (r) = 6 in.
Diameter (d) = 2(6) = 12 in.
Circumference = πd = π*12
C = 37.6991118 ≈ 37.7 in. (nearest tenth)
3. Radius (r) = 9 mm
Diameter (d) = 2(9) = 18 mm
Circumference = πd = π*18
C = 56.5486678 ≈ 56.5 mm (nearest tenth)
4. Radius (r) = ½(4.8) = 2.4 cm
Diameter (d) = 4.8 cm
Circumference = πd = π*4.8
C = 15.0796447 ≈ 15.1 cm (nearest tenth)
5. Radius (r) = ½(7) = 3.5 cm
Diameter (d) = 7 cm
Circumference = πd = π*7
C = 21.9911486 ≈ 22.0 cm (nearest tenth)
6. Radius (r) = ½(14) = 7 cm
Diameter (d) = 14 cm
Circumference = πd = π*14
C = 43.9822972 ≈ 44.0 cm (nearest tenth)
help me!! asap!! please!!
Answer:
y^6/x^4
Step-by-step explanation:
It's the last answer because 1/x^4*y^6 is equal to y^6/x^4
HELP PLEASEEEEEEEEO ITS EASY IF U LIKE RECTANGLESoo
Answer: 5 feet
Step-by-step explanation: I used a ruler
Express using a radical
Answer[tex]\sqrt[4]{6}[/tex][tex]\sqrt[4]{b^3}[/tex][tex]\sqrt[4]{c}[/tex]
Step-by-step explanation:
You have 48 in a yellow ribbon and 64 inches of red ribbon you want to cut the ribbon into pieces of equal length with no leftovers what is the greatest length of pieces that you can make?
Answer:
16inchs
Step-by-step explanation:
the gcf of 48 and 64 is 16
Answer:
16 because it is the GCF
Step-by-step explanation:
The lowest recorded temperature in Wisconsin is -55°F on February 4, 1996. Use the expression 5(F-32)/9 to find this temperature in degrees Celsius. Round to the nearest tenth. Explain its meaning
Answer:
-48.3° Celsuis
Step-by-step explanation:
Mark as brainllest
Parent function Math test, (give me the answers please).
Answer:
Step-by-step explanation:
no thx for 50points
4) You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2? ________
6% of the salary is $366
The total amount that would in the retirement account in the account each month is $732.
The amount that would be in the retirement account when you retire is $345,418.50.
The amount of money that you put in the account is $162,504.
The amount of money that the employer put in the account is $162,504.
The interest that was gained over the years is $20,410.50.
3% of the salary is $183.
The total amount that would in the retirement account in the account each month is $366.
The amount that would be in the retirement account when you retire is $172,709.25.
The amount of money that you put in the account is $81,252
The amount of money that the employer put in the account is $81,252
The interest that was gained over the years is $10,205.25.
How much would be in the retirement account?6% of the salary = salary x percentage
6% of the salary = 6% x $6,100
6% of the salary = 0.06 x $6,100 = $366
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $366 + $366 = $732
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $732 x 12 x (62 -25)
$732 x 12 x 37 = $325,008
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50
Amount the employer put in the account = $325,008 \ 2 = $162,504
Interest earned = $345,418.50 - $325,008 = $20,410.50
3% of the salary = salary x percentage
3% of the salary = 3% x $6,100
3% of the salary = 0.03 x $6,100 = $183
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $183 + $183 = $366
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $366 x 12 x (62 -25)
$366 x 12 x 37 = $162,504
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25
Amount the employer put in the account = $162,504 \ 2 = $81,252
Interest earned = $172,709.25 - $162,504 = $10,205.25
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The second side of a triangular deck is 5 feet longer than the shortest side. The third side of the deck is 5 feet shorter than twice the length of the shortest side. If the
perimeter of the deck is 60 feet, what are the lengths of the three sides?
The shortest side of the deck is feet.
(Simplify your answer.)
Answer:
Step-by-step explanation:
60= s+5 + 2s-5 + s
60 = 4s
15 = s
the short side is 15
the 2nd side is 20
the 3rd side is 25
What is the spread of Cassandra’s grades?
The box plot shows Cassandra’s grades in science this year. Use the box plot to answer the following question:
Answer:i THINK 79, i dont know fully, but i think 79
Which of the following is a sum of cubes?
A. 8x^3 -27y^6
B. 3x^3 +8y^6
C. X^3 +8y^6
D. 125x^6 -9y^3
Answer:
C. X^3 +8y^6
Step-by-step explanation:
X³ +8y⁶ = (X + 2 y²) (X² - 2 X y² + 4 y⁴)
What is the domain of the function with the graph given below?
Answer:
(-∞, 1] or {x|x<=1}
Step-by-step explanation:
pls help i don’t understand
Answer: 495 is the answer
Step-by-step explanation:
11 for the table is 880
11 for the graph is 385
880-385
To construct an angle that has a measure of 55°, another ray can be drawn that
starts at point W and passes through —
Your answer:
A. X
B. M
C. S
D. Not here
38 points!
"-12<-3x-15" less than or equal to 36
Answer:
-17 ≤ x < 1
Step-by-step explanation:
-12 < -3x - 15 ≤ 36
Add 15 to all 3 "sides."
-12 + 15 < -3x - 15 + 15 ≤ 36 + 15
3 < -3x ≤ 51
Divide all 3 "sides" by -3. Remember that when you multiply or divide an inequality by a negative number, you much change the direction of the inequality sign.
3/(-3) > -3x/(-3) ≥ 51/(-3)
-1 > x ≥ -17
Rewrite in standard order.
-17 ≤ x < 1
A quantity with an initial value of 860 grows continuously at a rate of 20% per year. What is the value of the quantity after 24 months, to the nearest hundredth? Various forms and units
Answer:
In this equation, the 100 represented the initial quantity, and the 0.50 was the percent ... If a bank offers a 24 month CD with an annual interest rate of 1.2% ... up an exponential function, with our initial amount of $1000 and a growth rate of r ... An initial substance weighing 20g is growing at a continuous rate of 12% per day.
Step-by-step explanation:
What is the value of k and why
Answer:
b is the answer
Step-by-step explanation:
The value of k in the equation sin (k - x) = cos (x) would be k = π/2
Given that,
An expression is defined as,
sin (k - x) = cos (x)
Used the concept of trigonometry formula which stated that,
sin (90 - θ) = cos (θ)
Here, the expression is given as,
[tex]sin (k - x) = cos (x)[/tex]
Substitute k = π/2 in the above equation,
[tex]sin (\dfrac{\pi }{2} - x) = cos (x)[/tex]
Apply the above formula,
[tex]\text {cos x } = \text {cos x }[/tex]
So, the value of k is π/2.
Hence, option c is true.
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Find x. Round your answer to the nearest tenth of a degree.
15
x
10
Answer:
x is approximately 48.2.
Step-by-step explanation:
Use the trig function of cosine, or adjacent over hypotenuse.
cos theta = adjacent / hypotenuse
Substitute variables.
cos x = 10 / 15
Apply inverse cosine to both sides.
x = cos^-1(10/15)
Evaluate.
x ≈ 48.2
Answer:
x ≈ 48.2°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10}{15}[/tex] , then
x = [tex]cos^{-1}[/tex] ([tex]\frac{10}{15}[/tex] ) ≈ 48.2° ( to the nearest tenth )
A recipe for 8 pancakes needs the following:
1 1/4 cups of milk
1 1/2 cups of flour
1 egg
Maria has these ingredients.
1 quart of milk
8 cups of flour
12 eggs
How many more cups of milk does Maria need to make 40 pancakes in total?
Answer:
2 1/4 cups
Step-by-step explanation:
the first step is to determine how many cups would be needed for 1 pancake
1 1/4 ÷ 8
5/4 x 1/8 = 5/32 cups
the second step is to determine how many cups would be needed for 40 pancakes
5/32 x 40 = 25/4 = 6 1/4
The next step is to convert quart to cups
1 quart = 4 cups
So Maria has 4 cups of milk.
the cups she needs more = 6 1/4 - 4 = 2 1/4 cups
Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on