1. The equation of the perpendicular line is: y = -x + 4
2. The equation of the parallel line is: y = -x + 4
What are the Equations of Parallel and Perpendicular Lines?The equations of two lines that are parallel to each other will have the slope (m), while the equations of two lines that are perpendicular to each other will have slope values that are negative reciprocals of each other.
The slope-intercept form for the equation of a line is, y = mx + b, where b is the y-intercept and m is the slope of the line.
1. The slope (m) of y = x - 4 is 1. The line that is perpendicular to y = x - 4 would have a slope (m) of -1.
Substitute (a, b) = (1, 3) and m = -1 into y - b = m(x - a):
y - 3 = -1(x - 1)
Rewrite in slope-intercept form:
y - 3 = -x + 1
y = -x + 1 + 3
y = -x + 4
2. The slope (m) of y = -x - 4 is -1. The line that is parallel to y = -x - 4 would have a slope (m) of -1.
Substitute (a, b) = (3, 1) and m = -1 into y - b = m(x - a):
y - 1 = -1(x - 3)
Rewrite in slope-intercept form:
y - 1 = -x + 3
y = -x + 3 + 1
y = -x + 4
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Please this awnser asap pls no equation just the awsner pls
Answer: 296 with a remainder of 1 (I'm guessing this by mental math, btw, why not just use a calculator, the calc is your best chance for a right answer anyway)
Edit: Used calc, was close lol, 296.5 is the exact answer
Step-by-step explanation:
P.S: Question, is that supposed to be divided or square rooted?
Anyway, I'll explain it since I can't leave it hanging:
2*2 = 4 so 5-4 = 1 and bring 9 down, after that 2*9 = 18, so it becomes 1, and then bring down 3 for 13, and 6*2 = 12, so 13-12 = 1, and that is 296 with a remainder of 1.
Kindly solve these in copy and send pic !! Plis urgent
Answer:
log(m) - log(n) + 1/2 log(p)
log(m/n) + log(√p)
log[(m*√p)/n]
A coach asked her athletes if they enjoy running. Forty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
a tree diagram shows athletes branching off into two categories of enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories of enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two sub-categories of enjoys cycling and does not enjoy cycling
What is the total percentage of the athletes who do not enjoy cycling?
50%
24.5%
13.5%
11%
Based on the percentage of those who love running and those who don't, the total percentage of the athletes who do not enjoy cycling is 24.5%.
What percentage doesn't like cycling?The percentage who don't enjoy cycling are:
= Percentage who enjoy running and but not cycling + Percentage who don't enjoy running or cycling
Solving gives:
= ((1 - 70%) x 45%) + ( (1 - 45%) x (1 - 80%))
= (30 % x 45%) + (55% x 20%)
= 24.5%
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Identify the property of addition described as commutative, associative, or identity.
The sum of any number and zero is the original number.
When two numbers are added, the sum is the same regardless of the order of addends.When three or more numbers are added, the sum is the same regardless of how the addends
are grouped.
The sum of any number and zero is the original number: Identity property
When two numbers are added, the sum is the same regardless of the order of addends: Commutative property
When three or more numbers are added, the sum is the same regardless of how the addends are grouped: Associative property
What is the Commutative Property of Addition?A + B = B + A if A and B are any two whole numbers.
In other words, the sum of two whole numbers is true regardless of how the addends—or real numbers—are arranged.
Any order will work for adding the numbers. Even if the numbers are rearranged, the sum of the two numbers remains the same.
What is the Additive Identity of Addition?When an is a whole number, A + 0 equals 0 + A.
In other words, the number itself is equal to the sum of any whole number and zero. In other words, zero is the only whole number that when added to, does not alter the value (identity) of the original number.
The additive identity or identity element for the addition of whole numbers is the integer 0 (zero).
When zero is added to a number, the result is unchanged.
What is the Associative Property of Addition?If any three whole numbers are A, B, and C, then (A + B) + C = A + (B + C)
In other words, whole number addition is associative.
Any group or placement of the numbers has no effect on the sum when three or more are added.
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2.7 and 5.9 find the distance
Answer:
The distance between both numbers is 3.2.
Step-by-step explanation:
How to find the answer is to:
1. Subtract the 9 and 7 to get 2.
2. Place your decimal point behind the 2 to make .2
3. Do 5 minus 2 to get 3.
Your answer is 3.2.
Sketch the graph using partial factoring.
y = 2x^2 - 6x + 5
(You don't need to draw it if you answer. Just show how to find the vertex and zeros.)
Answer:
(3/2,1/2)
Step-by-step explanation:
y=2x^2-6x+5
a=2
b=-16
substitute the coefficients into the expression
x= - -6/2x2
x=3/2
y=2x^2-6x+5, x=3/2
calculate the function value for x=3/2
y=1/2
(3/2,1/2)
A large window is made of a semicircle and a square. The square section is made of 9 square window panes. The builder wants to buy glass for each of the parts of the window.
a. What is the area, in square inches, of the semicircular pane of glass the builder needs? Round the answer to the nearest tenth, if necessary. You can disregard the width of the white window trim in your calculations.
_____in^2
b. What is the area, in square inches, of each of the 9 panes of glass for the square part of the window? Round the answer to the nearest tenth, if necessary.
_____in^2
c. What is the perimeter, in inches, of the entire window? Round the answer to the nearest tenth, if necessary.
_____in.
The 2 ft 3 in. semicircular section of the window and the 4 ft 6 in. by 4 ft 6 in. of the square section gives;
a. The area of the semicircular pane is approximately 1145.1 in.²
b. The square section is 2916
c. The entire window has a perimeter of approximately 354.82 inches
How can the area and the perimeter of the shapes be found?a. The given radius of the semicircular pane, r = 2 ft. 3 in. = 27 in.
The area of a semicircle, A = 0.5•π•r²The area of the semicircular pane is therefore;
A = 0.5 × π × 27² ≈ 1145.1
The area of the semicircular pane is approximately 1145.1 in.²b. The area, A, of the 9 panes of glass, disregarding the window trim is found using the equation for the area of a square, as follows;
A = Side × Side
The area of the 9 panes is therefore;
A = 4 ft. 6 in. × 4 ft. 6 in.
Which gives;
A = 54 in. × 54 in. = 2916 in.²
The area of the square section is 2916 in²c. The perimeter of the entire window, P, is given by the sum of the perimeter of the semicircular pane, P1, and the perimeter of the 9 square window panes, P2, as follows
P1 = 54 + π×27
P2 = 4 × 54
P = P1 + P2Which gives;
P = 54 + π × 27 + 4 × 54 ≈ 354.82
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what are all the possible values of sin cos and tan
Answer: What are the values of sin, cos and tan?
Sin Cos Tan Chart
Angles (in degrees) 0° 60°
Sin θ 0 √3/2
Cos θ 1 1/2
Tan θ 0 √3
Cot θ ∞ 1/√3
Step-by-step explanation: hope this helps a little!!!!
Which is the correct definition of perpendicular lines?
A. A part of a line that is bounded by two distinct endpoints.
B. A set of points that extends infinitely in two directions.
C. Two lines that intersect at a right angle.
D. Two lines that never cross.
(Note: the selected answer is the image is not guaranteed to be correct)
By definition of perpendicularity, plane, point and line, we find that two lines are perpendicular if they intersect at a right angle. (Correct choice: C)
When are two lines on a plane perpendicular?
According to Euclidean geometry, two pairs of opposite angles are created by generating two lines with different slopes on the same plane. Two lines with same slope never cross on the plane and are known as parallel lines.
Opposite angles have the same measure and the two lines are perpendicular to each other if and only if each pair of opposite angles are right angles. Right angles have a measure of 90° (π / 2 radians), then each of the four angles must have a measure of 90° (π / 2 radians).
In summary, two lines set on a plane are perpendicular to each other if they intersect at a right angle.
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The distance from Earth to the moon is 2.4 × 105 miles. The distance from Earth to the sun is 9.3 × 107 miles.
Complete the sentence by typing numbers in the boxes.
The distance from earth to the sun is 387.5 times greater than the distance from the earth to the moon.
How many times greater is the distance from Earth to the Sun than Earth to the Moon?Given Data;
The distance from earth to the sun = 9.3 x 10⁷ miles
The distance from the earth to the moon = 2.4 x 10⁵ miles
The distance ES to EM
Then we need to divide the distance from earth to the sun by the distance from the earth to the moon
= 9.3 x 10⁷ miles / 2.4 x 10⁵ miles
= 387.5 times is greater.
Therefore, The distance from earth to the sun is 387.5 times greater than the distance from the earth to the moon.
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val runs 1 1/2 miles each day. She has run for 4 days. How far has she run altogether
Answer:
6 miles
Step-by-step explanation:
1 1/2 miles x 4 days= 6 miles over 4 days
Convert the percent to a reduced fraction, mixed number, or whole number.
0.2%
Answer:
2/10 or 20
Step-by-step explanation:
the only one i could figure out was the reduced fraction and the whole
The length of a rectangle is four less than twice its width. If the perimeter of the rectangle is 76 units, what is its width?
a
13
b
14
c
20
d
26
e
28
Answer: the width of the rectangle is 14 units
Let's denote the length of the rectangle to be x and the width to be y.
The first sentence tells us that the length, x , is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. x = 2y - 4.
In the question given that the perimeter of the rectangle is 76 units
Perimeter of a rectangle is 2( length + breadth )
According to the question :
76 = 2(x + y)
76 = 2(2y – 4 + y)
76 = 2(3y – 4 )
76 = 6y – 8
84 = 6y
y = 14 units
putting the value of in x = 2y – 4
x = 2(14) – 4
x = 24 units
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-135.4 + 78 1/2 =___
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
∠ B = 23°
Step-by-step explanation:
vertical angles are congruent , so
∠ B = ∠ A , that is
5x - 17 = x + 15 ( subtract x from both sides )
4x - 17 = 15 ( add 17 to both sides )
4x = 32 ( divide both sides by 4 )
x = 8
Then
∠ B = 5x - 17 = 5(8) - 17 = 40 - 17 = 23°
Vertically opposite angles are equal
So,[tex]x + 15 = 5x - 17 \\ 15 + 17 = 5x - x \\ 32 = 4x \\ x = 8[/tex]
Therefore;[tex] \sf \: \angle \: a = x + 15 = > 8 + 15 = 23 \degree[/tex]
[tex] \sf \: \angle \: b= 5x - 17 = > 5 \times 8 - 17 = > 40 - 17 = 23 \degree[/tex]
Find the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares
The volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.
for given question,
We need to find the volume of the solid whose base is the region bounded between the curve y = x³ and the y-axis from y = 0 to y = 1 and whose cross section taken perpendicular to the y-axis are squares.
Now we rewrite given curve y = x³ in terms of x.
[tex]x=\sqrt[3]{y}[/tex]
Since the length of the side of each cross sectional square is [tex]2\sqrt[3]{y}[/tex], the cross sectional area A(y) can be given by
A(y) = [tex](2\sqrt[3]{y})^2[/tex]
A(y) = [tex]4y^{\frac{2}{3} }[/tex]
The region is bounded from y = 0 to y = 1
so, the volume V can be found by,
[tex]V=\int\limits^1_04y^{\frac{2}{3} }~dy\\\\V=4\int\limits^1_0 y^{\frac{2}{3} }~dy\\\\V=4\times \frac{3}{5} \\\\V=\frac{12}{5}\\\\V=2.4[/tex]
Therefore, the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.
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You are running a camp of 30 students, including johnand jane.3
What is the total possible ways you can arrange2 focus groupsof students one group being size 4 , and the othersize 6.?
The total possible ways of arranging 30 students in two groups of sizes 4 and 6 respectively are 6309453150, which is obtained by using the prerequisite knowledge of combinations.
What is the combination?
A combination is a mathematical procedure that deduces the number of feasible selections in a collection of articles in which the order of the selection does not matter. In combinations, you can choose any items in any order. Its formula is given by C(n,r) = n! / (n - r)! r!)
Calculation of the total possible ways of arranging two focus groups of students with sizes 4 and 6 respectively
Given a group of 30 students
Two focus groups are to be arranged in sizes 4 and 6 respectively
Total number of possible ways to arrange the two focus groups = C(30,4) × C(26,6)
Using the formula for combination, we get,
T.F.O = [30! / (26! 4!)] × [26! / (20! 6!)]
T.F.O = 27405 × 230230
= 6309453150
Hence, the required possible ways to arrange two groups are given by 6309453150.
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a powdered drink calls for 3 scoops powder to 8 ounces of water. how much powder do you need if you have 32 ounces of water
Answer:
12
Step-by-step explanation:
This is a ratio problem where 3 is to 8 as x is to 32. Set up as fractions and solve:
3/8 = x/32 solve for x
Find the equation of the line.
Use exact numbers.
y= x+
Answer:
y = 3/4x -2
Step-by-step explanation:
We first find the slope of the line using two points
(0,-2) and (8,4)
m = ( y2-y1)/(x2-x1)
m = ( 4---2)/(8 - 0)
= (4+2)/(8)
= 6/8
= 3/4
We can write the equation in slope-intercept form using
y = mx+b where m is the slope and b is the y-intercept
b is where it crosses the y axis. It crosses at -2
y = 3/4x -2
Write 4.13 ×10 with exponent -5 in standard form.
Answer: 0.0000413
Step-by-step explanation:
The -5 exponent is the amount of zeros that go behind 413.
A population of 10000 grows 3% annually. Write an equation that represents the growth of this population
Answer: How do you write a population growth equation?
The annual growth of a population may be shown by the equation: I = rN (K-N / K), where I = the annual increase for the population, r = the annual growth rate, N = the population size, and K = the carrying capacity.
Step-by-step explanation: hope this helps!!!
Answer:
Step-by-step explanation:
The annual growth of a population may be shown by the equation: I = rN (K-N / K), where I = the annual increase for the population, r = the annual growth rate, N = the population size, and K = the carrying capacity.
Describe
and correct the error in naming opposite rays in
the diagram (problem 26 only)
The error was the use of just a line on each name instead of a line with an arrow head pointing to the right. It should be: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex]are opposite rays.
How to Name Opposite Rays?To name two rays that are opposite each other, start the name of each of the rays with the letter of the endpoint that connects both rays together, then use the letter of the point where each of the rays extend to infinity.
The line on top both of the letters of the rays must have an arrow head, "→" that points to the right.
In problem 26, the letters used in naming the opposite rays were correct, but, the line on each letter that was used had no arrows pointing to the right. They are wrong.
The correct way of naming the opposite rays is: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex].
Therefore, we can conclude that, the error was the use of just a line on each name instead of a line with an arrow head pointing to the right. It should be: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex]are opposite rays.
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The right triangle on the right is a scaled copy of the right triangle on the left. Identify
the scale factor. Express your answer as a whole number or fraction in simplest form.
13
13
13/3
13/3
Answer:
Step-by-step explanation:
To find the scale factor, take the value of one side length from the scaled copy and divide it by the value of the corresponding side length of the original.
39/13 = 3
Therefore, the scale factor is 3.
A car dealership sells suvs and passenger cars. for a recent year,80 more subs were sold than passenger cars. if a total of 310 vehicles were sold, determine the number of each type of vehicle sold
The total number of SUVs sold = 195
and the total number of passenger cars were sold = 115
For given question,
Let x be the total number of SUVs and y be the total number of passenger cars sold.
For a recent year,80 more SUVs were sold than passenger cars.
So we get an equation,
x = y + 80 .............(1)
A total of 310 vehicles were sold.
So we get an equation,
x + y = 310 .............(2)
Substitute the value of x from (1) in an equation (2),
(y + 80) + y = 310
2y + 80 = 310
2y = 230
y = 115
This means, total 115 passenger cars were sold.
Substitute the above value of in equation (1),
x = 115 + 80
x = 195
This means, total 195 SUVs were sold.
Therefore, the total number of SUVs sold = 195
and the total number of passenger cars were sold = 115
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Statement: If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?
The geometry term represented by the statement "If two points are given, then exactly one line can be drawn through those two points." is "geometric postulate".
What are termed as the geometric postulate?Postulates are assertions that are believed to be correct in the absence of evidence.
Postulates serve two functions: they explain undefined terms and they serve as a foundation for proving those certain statements. The Postulates of Euclid: A line segment is defined by two points.A line segment can be enlarged along a line indefinitely.A postulate is a fundamental concept in geography that denotes a hypothesis that is believed to be correct in the given factor.In this sense, the main feature of the postulate is its widespread acceptance by the scientific community, that is, by the vast majority of scientists who are committed to its investigation.
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HELP ASAP!!! WILL MARK BRAINLIEST!!!
Line A: y = 1/2x + 2
Line B: y = -1/2x + 7
Line C: y = 2x + 4
Line D: y = 1/2x + 5/4
Which lines are perpendicular?
A. B & C
B. A & D
C. A & B
D. A & C
Answer:
A
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
A y = [tex]\frac{1}{2}[/tex] x+ 2 ← has slope m = [tex]\frac{1}{2}[/tex]
B y = - [tex]\frac{1}{2}[/tex] x + 7 ← has slope m = - [tex]\frac{1}{2}[/tex]
C y = 2x + 4 ← has slope m = 2
D y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{4}[/tex] ← has slope m = [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes
• the product of the slopes of perpendicular lines = - 1
- [tex]\frac{1}{2}[/tex] × 2 = - 1
then lines B and C are perpendicular
A student ran a distance of 2 1/2 miles each day for 5 days. Then the student ran a distance of 3 1/4 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
- - - - - - - - - - - - - - - - - - - - - - - -
First I'd like to convert the fractions into decimals.
2 1/2 = 2.5
3 1/4 = 3.25
Now, multiply each number by how many days that distance was reached.
2.5 x 5 = 12.5
3.25 x 5 = 16.25
We add our products:
28.75 (28 3/4)
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck! :)
(Consider leaving a Brainliest if this helped!)
~pinetreee
each side of the base of a right octagonal prism is 7 in. long. the altitude of the prism measures 12 in. find the lateral area.
The lateral area of the right octagonal prism is 672 square inches
How to determine the lateral areaThe formula for lateral area of a right octagonal prism is expressed as;
Lateral area = 8ah
Where;
a is the side length = 7 Inchesh is the height of the prism = 12 InchesSubstitute the values into the formula
Lateral area = 8 × 7 × 12
Multiply through
Lateral area = 672 square inches
Thus, the lateral area of the right octagonal prism is 672 square inches
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The sales tax rate for South Salt Lake is 7.05%.
What is the state sales tax on a $21,900 car in South Salt Lake?
The state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.
We are given that:
The rate of tax on sales for South Salt Lake is = 7.05 %
That is:
Sale tax rate = r = 7.05 %
Now, we are given that the selling price of a car = $ 21,900
Selling price = $ 21,900
Now we need to find the sales tax amount that will be imposed on the car.
For this, we will calculate the percentage.
Sales tax = 7.05 % of $ 21,900
Sales tax = 7.05 % × $ 21,900
Sales tax = 7.05 / 100 × $ 21,900
Sales tax = 7.05 × $ 219
Sales tax = $ 1543.95
Therefore, we get that the state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.
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did I do Question A right and I need help for (B)
the Math question is on the Image.
"The ratio of the number of male staff to the number of female staff is 2:3."
This means if [tex]x[/tex] is the number of male staff, and [tex]y[/tex] is the number of female staff, then these numbers occur in a fixed ratio such that
[tex]\dfrac xy = \dfrac23[/tex]
The sentence does not say anything about the actual number of staff members. There's no reason to believe that there are 50 people working.
What it does say is that 2/5 = 40% of the team is made of males and 3/5 = 60% is made of females.
(a) Of the males, 20% = 1/5 of them are under the age of 20. This means that 20% of 40% of the entire staff is made up of males under 20, or
2/5 × 1/5 = 2/25 = 8%
Of the females, 40% = 2/5 are under the age of 20. So 40% of 60% are females under 20, which comes out to
3/5 × 2/5 = 6/25 = 24%
Adding these up, we get a total of 8% + 24% = 32%.
(b) Yes, any change to the team would adjust this percentage.
Consider a smaller example of a team of 4, 1 each of male/female and under/over 20. 1/4 = 25% of this team is female and under 20. If we add one more under-20 female, the new ratio is 2/5 = 40%. If we add one more member to any other group, the new ratio is 1/5 = 20%.