Answer:
a. The railing is transversal to the posts
b. In order to make the posts parallel, the angle between the posts and the transversal should be = 78°
c. The angle between the post and the ramp is 102° as we reach the post from the bottom and 102° and 78° immediately after the post
d. 1) Alternate interior angles = 78° and 102°
2) Alternate exterior angles = 102°
3) Corresponding angles = 78° and 102° depending on the side of from which we approach the post
4) Consecutive interior = 78° and 102° depending on the side of from which we approach the post
e. The interior angles are supplementary
f. Horizontal spacing between posts = 2.93 ft.
Spacing between posts along the length of the railing = 3 ft. spacing
Step-by-step explanation:
a. A transversal is a line crossing two or more parallel lines which are in a plane at different points
Therefore, the railing is transversal to the posts
b. Whereby the ramp rises at an angle of 12°, the railing, which is the transversal is therefore inclined at 12° to the horizontal and the posts which will be vertical erect will be at 90° to the horizontal
Therefore, in order to make the posts parallel, the angle between the posts and the transversal should be 90° - 12° = 78° for each post to railing.
c. The angle between the post and the ramp before the post as we ascend the ramp is therefore, 180 - 78 = 102° and 78° after the post
d. The alternate interior angles lie on the opposite sides of the transversal = 78° on one side and 102° on the other (Sum of angles on a straight line) which are the angles on the transversal
The alternate exterior angles lie on the exterior opposite sides of the transversal = 102°
Corresponding angles are the angles located in the corresponding positions on the transversal = 78° on one side and 102°as we cross the post (Sum of angles on a straight line)
Consecutive interior angles are the angles that are located on the same part of the transversal = 78° and 102° (Sum of consecutive interior angles of parallelogram = 180°
e. For the posts to be parallel, the consecutive interior angles should be supplementary or equal to 180°
f. Whereby we have a 12-ft rail inclined at 12°, we have;
Horizontal distance covered by the rail = 12 × cos(12) = 11.74 ft
Since we have 5 posts, there 4 equal spaces between them which gives
Spaces between posts = 11.74/4 = 2.93 ft. horizontally and 3 ft. spacing between each post along the railing.
The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, sold by the company: Part A: What
Answer:
dollars
Step-by-step explanation:
solve the inequality 7(v + 8) ≥ 7v + 1
Answer:
True all for v
Step-by-step explanation:
7(v+8)≥7v+17v+56≥7v+17v+56−7v≥7v+1−7v56≥156−56≥1−560≥−55All real numbers are solutions.
One side of a rectangle is X+7 units long, and the other side is X+3 units long. Express the area of the rectangle as a polynomial. If the value of X is 10, what is the value of the Polynomial?
Answer:
area as a polynomial: x^2 + 10x +21
If the value is 10: 221 units square
Step-by-step explanation:
to solve for the polynomial just do (x+7)(x+3) use the box method if your unfamiliar with this
to solve for the value just plug it in the polynomial you got from the previous answer
hope this helps
IM TIMED Find an ordered pair that represents the vector from (-3.7,2) to (-4, -5).
a.
(-7.7,-3)
c.
(1.3,7)
b.
(-0.3,-7)
d.
(7.7,3)
Answer:
<-0.3, -7>
Step-by-step explanation:
Re: a vector from (-3.7,2) to (-4, -5).
This has two components: a horizontal one and a vertical one.
The horizontal component is -4 - (-3.7) = -0.3.
The vertical component is -5 - 2 = -7
Thus, the desired vector is <-0.3, -7>
Answer:
B on edge
Step-by-step explanation:
got it right (2021)
7 movie tickets cost $35
Unit rate
Answer:
$5 per ticket
Step-by-step explanation:
If you put it into a ratio of movie tickets to cost it will be 7 : 35
When you simplify it the ration will be 1 : 5
Answer:
$5 per ticket . # Unit rate.
Step-by-step explanation:
7 tickets costs =$35
therefore, 1 ticket cost = $35÷ 7
= $5
Sarah is organizing a party at the Vine House Hotel. The Vine House Hotel provides her with the following
information: $750 for the room rental plus $20 per person attending the party.
a. If C dollars is the cost of a party for P people, write an equation to determine the cost.
b. Sarah is inviting 60 people to the party. She calculates her cost to be $1200. Is she correct? Show your work and
explain.
Answer:
A) 750+20P=C
B) No, it will not be $1200. It will be $1950. $1200 is only the cost for the people and does not include the room rental.
Step-by-step explanation:
A) 750+20P=C
B) 750+20(60)=C
750+1200=C
1950=C
No, it will not be $1200. It will be $1950. $1200 is only the cost for the people and does not include the room rental.
Answer:
a. C = 750 + 20P
b. If Sarah is inviting 60 people to the party,
L.H.S. = 750 + 20 x 60
= 750 + 1200
= 1950 dollars
R.H.S. = 1200
because L.H.S is not equal to R.H.S.
no she is wrong
whats 4x^(3)-12x^(2)-16x factored? pls explain too! i give brainliest
Answer:
4x(x-4)(x+1)
Step-by-step explanation:
Please see the picture.
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. c 22 and 15 Answer: < 3rd side
Answer:
| a - b | < length of third side < a + b
Step-by-step explanation:
Visualize the two given sides of the triangle (let's call then a and b), joined at the vertex of the triangle, and forming an angle. We can join the other free end of these two segments, with another segment whose length would vary according to how tiny or large the angle is. We can spread the aperture of the angle they form as much as we can just below [tex]180^o[/tex] (not reaching this angle measure, because in such case, there will be no triangle of tangible area. In such case, the length of the joining segment will be limited by the addition of the two sides:
length of third side < a + b
In the case the aperture of the angle formed by the two given sides is diminished as much as possible to still form a measurable triangle, the angle has to be just larger than zero, and in such case, the segment joining the other to ends of a and b would be just larger than the absolute value of the difference between a and b:
length third side > | a - b|
These are the two extreme cases, and the length of the third side must be within these limits.
Answer:
7<x<37
Step-by-step explanation:
Here is the formula to solve range questions:
22-15<x<22+15
Can anyone plz help me
Answer:
vertex (-4,-1)
2nd point ( 0,31)
Step-by-step explanation:
f(x) = 2x^2 + 16x + 31
First find the vertex
The x coordinate of the vertex is -b/2a where ax^2 +bx +c
-16/ 2(2) = -16/4 = -4
Substitute into the function
f(-4) = 2 ( -4)^2 +16(-4) +31
= 2 *16-64 + 31
= 31 -64 +31
= -1
The vertex is at ( -4,-1)
Another point can be x=0
f(0) = 0+16(0)+31
= 31
( 0,31)
the letter v has an unknown value. If you multiply v by ten, the product is two . What value does v have?
Answer:
0.2
Step-by-step explanation:
10v=2
v=2/10
v=0.2
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 7?
Answer:
line of slope 1 move up 7, so that there is a y-intercept of 7
Step-by-step explanation:
Answer:
There should be a y intercept of seven. :)
PLEASE HELP! WILL MARK BRAINLIEST! 13 POINTS! THX! Two bicycles are driving on the circle in the same direction with speeds of 9 mph and 5 mph respectively. How many points are there on the circle where the two bicycles meet.
Answer
The points where the two bicycles meet after every 6hr at 30 miles and 54 miles.
37.4
Solve for x and y.
A. x = 26.4 y = 20.4
B. x = 26.4, y = 17
C. x = 18.3. y = 20.4
D.
x = 18.3. y= 17
FIRST WILL GET BRAINLLEST Each group of students receives a bag that has 8 red cubes, 2 green cubes, and 10 blue cubes. If each group makes 100 pulls and replaces the cube after each pull, how many times would you expect them to draw a green cube?
Answer:
10
Step-by-step explanation:
We can do the ratio of 8:2:10. If we add it all up, we get 20. We do 100/20 and get 5, so each number equals 5. Then we do 2*5.
Sorry if this is wrong.
Solve |3x + 9| + 6 = 6 Question 5 options: A) x = 3 B) x = 3 or x = –3 C) No solutions D) x = –3
Answer:
Hey there!
We have |3x + 9| + 6 = 6. Subtracting 6 from both sides gives us |3x + 9| = 0.
3x+9=0
3x=-9
x=-3
Hope this helps :)
Answer:
-3
Step-by-step explanation:
Subtracting 6 from both sides yields |3x + 9| = 0. For this to be true, 3x + 9 must be 0, and so x must be -3.
hi can you please help me and explain step by step if possible thank you
Answer: see image
Step-by-step explanation:
Count how many spaces the vertex is away from the line x = -1. Then place that vertex the same distance on the other side of the line x = -1.
im badd i kinda understand but not really understanding it
Answer:
40
Step-by-step explanation:
if you add all the numbers up it becomes 96 and 96 goes Into. 480 5 times so you multiply 5 times the number of giant swallow tails
Answer:
If they are proportional we can expect 40
lol iready
if you were to take a dime and 500 pennies and 5 quarters how much money would you have
Answer:
$6.35
Step-by-step explanation:
5*25=125
125+500=625
625+10=635
635/100=6.35
Answer:
$6.35
Step-by-step explanation:
500 pennies = $5.00
5 quarters = $1.25
.10+1.25+5=6.25
A bag contains 5 blue marbles, 2black marbles ,and 3 red marbles. A marine is randomly drawn from the bag The probability of not drawing a red marble is___ . The probability of drawing a red marble is
The probability of not drawing a red marble is 7/10
The probability of drawing a red marble is 3/10
=======================================================
Explanation:
We have 3 red marbles out of 5+2+3 = 10 total. Therefore, the probability of selecting a red marble is 3/10.
The probability of not selecting a red marble is 7/10 because 3/10+7/10 = 1. Put another way, we have 7 marbles that aren't red (the 5 blue and 2 black ones) out of 10 total.
Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 45 quarts of 2% butterfat milk. The mixture should contain _______quarts of the 4% butterfat milk.
Answer:
15
Step-by-step explanation:
30 quarts of 1 percent combined with 15 quarts of 4 percent would equal 45 quarts of 2%
AD= 36 cm. Points C, B∈AD, such that AB:BC:CD=2:3:4. Find the distance of midpoints of the segments AB and CD.
Answer:
The distance of the midpoint of AB = 4 cm
The distance of the midpoint of CD = 28 cm
Step-by-step explanation:
The given information are;
Segment AD = 36
Point C and point B are points on AD such that AB:BC:CD = 2:3:4
Which gives;
The proportion of AB in AD = 2/(2+3+4) = 2/9
The length of AB = 2/9×36 = 8 cm
The proportion of BC in AD = 3/(2+3+4) = 3/9
The length of AD = 3/9×36 = 12 cm
The proportion of CD in AD = 3/(2+3+4) = 4/9
The length of AD = 4/9×36 = 16 cm
The coordinate of the midpoint of AB = 8/2 = 4 cm from A
The distance of the midpoint of AB = 4 cm
The coordinate of the midpoint of CD = 8 + 12 + 16/2 = 28 cm from A
The distance of the midpoint of CD = 28 cm.
Find the mean of the data in the dot plot below.
Answer:
1.6
Step-by-step explanation:
So, first, write down the number of jokers in each deck of cards.
That would be: 0, 1, 2, 2, 3
Then, add up all those numbers.
0+1+2+2+3=8
Now, divide that sum by the number of decks or cards shown in the data set, which would be 5.
8/5=1.6
So, the mean of the data in the dot plot shown is 1.6.
The mean of the data in the dot plot below is 1.6.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
Jokers in each of Marcie's decks of card would be 0, 1, 2, 2 and 3.
The mean,
= 0 + 1 + 2 + 2 + 3/5
= 8/5
= 1.6
Therefore, the mean is 1.6.
To learn more about the mean;
brainly.com/question/13451489
#SPJ3
10 points are placed on a circle. How many triangles is it possible to form, such that their vertices will be the given points?
Answer:
120
Step-by-step explanation:
The total number of triangles that can be made are 120.
We have a circle and 10 points are placed on it.
We have to find how many possible triangles can be made such that their vertices will be the given points.
What is a Combination?A combination can be defined as the number of possible arrangements of elements without taking into consideration the order of selection. The number of possible combinations can be given by -
[tex]\frac{n!}{(n-r)!r!}[/tex]
In the question given to us - we have 10 points on circle. Only three points are needed to make a triangle. The order does not matter here, therefore -
[tex]\frac{10!}{(10-3)!3!}\\\\\frac{10!}{7!\times3!} \\\\\frac{10\times9\times8\times7!}{7!\times3\times2\times1}[/tex]
10 x 3 x 4 = 120
Hence, the total number of triangles that can be made are 120.
To solve more questions on combinations, visit the link below -
https://brainly.com/question/13387529
#SPJ2
Find the mean of the data in the bar chart below.
puppets
Puppets made by each puppeteer
5
Number of puppets
0
Alex
Kalin
Bruce
Davi
Puppeteer
Just look at the picture
Answer:
2.5
Step-by-step explanation:
the mean, better known as the average, can be found by finding the sum of all numerical data and dividing by the amount of your data. so 1+4+3+2=10 and 10 divided by 4=2.5
Answer:
2.5
Step-by-step explanation:
Determine if the two triangles shown are similar. If so, write the similarity statement. options: A) ΔUVW ∼ ΔFGH B) The triangles are not similar. C) ΔWUV ∼ ΔFGH D) Impossible to determine.
Answer:
B (from down below) They are similar but your q does not match up with the picture
Step-by-step explanation:
to determine if two triangles are similar you have to make sure the ratios are the same. So 10 / 8 = 1.25, so all sides should have this ratio. 15 / 12 is also 1.25 so you know to sides are similar and also the triangles ARE SIMILAR. So The statement would be KMN is similar to KLP.
plz help me i have a fever and i don't want to do math
Answer:
Four books because there are the most dots over that spot on the bottom number line thingy
A farmer has the same number of chickens, cows and goats. Together, all these animals have 210 legs. How many chickens live on this farm?
Answer: 35 chickens
Step-by-step explanation:
210/3=70
70/2=35
Help me out :O What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side length.
Answer:
Step-by-step explanation:
[tex]s = \frac{1}{3}ft\\[/tex]
Volume of a cube = s³ ft³
Volume of 3 cubes = 3 * s³
[tex]= 3 * \frac{1}{3} * \frac{1}{3} *\frac{1}{3}\\\\= \frac{1}{3} *\frac{1}{3}\\\\=\frac{1}{3*3}\\\\=\frac{1}{9} ft^{3}[/tex]
What is the length of the hypotenuse in the right triangle shown below?
Answer:
A. 6 √2
Step-by-step explanation:
If a triangle is a 45-45-90 triangle then,
Theorem 5-13: If each acute angle of a right triangle has a measure of
45 degrees, then the measure of the hypotenuse is the square root of two times as long as a leg (45, 45, 90 Theorem).
so the hypotenuse is x√2, and x = 6 (side length)
on day in the fall, mark raked the leaves on 5 peoples lawns in 2.5 hours. one day in the summer, he mowed 6 peoples lawns in 1.2 hours. the daily rate mark rakes lawns in the fall is what % of the daily rate he mowes lawns in the summer, assuming he works at a constant rate
Assuming he works at a constant rate, the daily rate Mark rakes lawns in the fall is 40% of the daily rate he mows lawns in the summer.
Step-by-step explanation:
Fall:
5 neighbors' lawns / 2.5 hours = 2 lawns per hour
Summer:
6 neighbours' lawns / 1.2 hours = 5 lawns per hour
2 x 100% / 5 = 40%
2 is 40% of 5