Line PQ is parallel to BC and splits AB into lengths of x + 8 and x. The other side, AC, is split into lengths of x + 13 and x + 1. What is the length of AC? Image Not to Scale.
Answer:
AC = 18.Step-by-step explanation:
The problem is about proportions, because we have two parallels line being intercepted by two transversal. So, the proportion would be:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}[/tex]
Solving for [tex]x[/tex]:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}\\(x+1)(x+8)=x(x+13)\\x^{2} +8x+x+8=x^{2} +13x\\9x+8=13x\\8=13x-9x\\4x=8\\x=\frac{8}{4}=2[/tex]
Now, to find the length of AC, we just have to use the value found and replace it in the proper expression:
[tex]AC=x+13+x+1=2x+14=2(2)+14=4+14=18[/tex]
Therefore, the length of AC is 18.
Catie is making bracelets for her friends using small rubber bands. She has 364 rubber bands and she wants to make 6 bracelets. How many rubber bands will she use for each bracelet? How many rubber bands will be left over?
If the average cost of hotel stay per night is about $85 plus 18% of hotel tax, estimate the total stay. Round answer to the hundredths place
Haley is at the store buying some supplies for an art project. She decides to buy some colored pencils for $3.95 and a drawing tablet. The total cost of the supplies before sales tax is $6.94.
Which equation could not be used to find the cost of the drawing tablet?
$3.95 + x = $6.94
$6.94 + x = $3.95
x = $6.94 - $3.95
$6.94 - x = $3.95
An office building casts a 90 foot shadow. At the same time of day, a 5 foot woman standing near the building casts an 8 foot shadow. What is the approximate height of the building to the nearest foot?
Lily forgot the security code for her apartment building. the code is two different numbers followed by a letter. how many different possible codes are ther?
What is 24.051 rounded to the nearest hundredth? How did you solve it?
two ninths of the eighteen people in the bakery are eating cookies how many people are eating cookies
Final answer:
To find out how many people are eating cookies, you multiply the total number of people in the bakery, which is 18, by two-ninths. The result is four, meaning four people are eating cookies.
Explanation:
If two-ninths of the eighteen people in the bakery are eating cookies, we need to calculate 2/9 of 18 to find out how many people are eating cookies. This is a basic fraction multiplication problem.
To solve this, we multiply 18 (the total number of people) by the fraction 2/9:
18 × (2/9) = (18 × 2) / 9
18 × 2 = 36
36 / 9 = 4
Therefore, four people in the bakery are eating cookies.
True or false.
1) Adjacent angles are supplementary?
2) Same-side interior angles are supplementary?
3) Vertical angles are congruent?
Find a polynomial function with integer coefficients that has given zeros. (There are many correct answers)
0, 0, 4, 1+i
15 points to help answer these two questions?
1) How can graphing methods be used to solge a system of linear equations and how can you determine the equations of the two lines by analyzing the graph?
2) Solve this system of equations and explain what method you used to find your solution.
8x-y=-9
4x-3y=-22
(3x^2a - 4y^a z^3a) ^2 ...?
Jason bought 8 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 40 cards left. how many cards did jason start with
Jason started with 72 baseball trading cards. To find out how many baseball trading cards Jason started with, let's break down the information given step by step.
1. Jason bought 8 new baseball trading cards: This implies that Jason's collection increased by 8 cards.
Let's denote the number of cards Jason had before buying the new ones as X . After buying the new cards, Jason would have X + 8 cards.
2. The next day his dog ate half of his collection: If his dog ate half of his collection, this means that the number of cards left after the incident is half of what Jason had before. So, after the dog ate half of the collection, Jason would have [tex]\( \frac{1}{2} \times (X + 8) \)[/tex] cards remaining.
3. There are now only 40 cards left: This information tells us that the number of cards left after the incident is 40. So, we have the equation:
[tex]\[ \frac{1}{2} \times (X + 8) = 40 \][/tex]
Now, let's solve for X:
[tex]\[ \frac{1}{2} \times (X + 8) = 40 \][/tex]
[tex]\[ X + 8 = 40 \times 2 \][/tex]
X + 8 = 80
X = 80 - 8
X = 72
So, Jason started with 72 baseball trading cards.
To verify, let's check the steps:
1. Jason initially had 72 cards.
2. He bought 8 new cards, totaling 72 + 8 = 80 cards.
3. After his dog ate half of his collection, he was left with [tex]\( \frac{1}{2} \times 80 = 40 \)[/tex] cards, which matches the given information.
Therefore, Jason started with 72 baseball trading cards.
The complete question is:
Jason bought 8 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 40 cards left. how many cards did jason start with?
77/8 as a mixed number
Find sin x/2, cos x/2, and tan x/2, if cos x = -12/13, 180 degrees is less than x which is less than 270 degrees
Gabriela works at a nearby electronics store. she makes a commission of 14% on everything she sells. if she sells a camera for $589 how much money does gabriel make in commission?
The manufacturing cost of an air-condioning unit is $544, and the full-replacement extended warranty costs $113. If the manufacturer sells 506,970 units with extended warranties and must replace 20% of them as a result, how much will the replacement costs be? (Note: Assume manufacturing costs and replacement costs are the same.) a. $55,158,336 b. $11,457,522 c. $2,129,274 d. $66,717,252
Answer:
It's A
Step-by-step explanation:
This is what i got on edge 2020, hope this helps <3
Answer: A) $55,158,336
hope this helps <3
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (Do not use mixed numbers. Round your answers to three decimal places.)
(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
_____ ft/sec
20 feet away from the wall
_____ ft/sec
24 feet away from the wall
_____ ft/sec
...?
last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez
x2+y2=25calculus says
2xx′+2yy′=0and you are told that
y′=2so you know
2xx′+4y=0or
x′=−2yxThe area of desert a is eight times the area of desert
b. if the sum of their areas is 900,000 square miles, find the area of each desert
In a circus a tightrope is stretched from the top of a 10 ft. pole to the top of a 25 ft pole. The poles are 36 feet apart and vertical. How long is the tightrope?
Show your work.
Final answer:
To find the length of the tightrope between two poles of different heights and a known distance apart in a circus using the Pythagorean theorem.
Explanation:
The length of the tightrope can be calculated using the Pythagorean theorem.
Given:
Height of the first pole = 10 ftHeight of the second pole = 25 ftDistance between the poles = 36 ftUsing the Pythagorean theorem:
Length of the tightrope = √(36^2 + (25-10)^2)
Length of the tightrope = √(1296 + 225)
Length of the tightrope = √1521
Length of the tightrope = 39 ft
what is 0.9 as a percentage
0.9 as a percentage is 90 percent.
Explanation:To convert a decimal to a percentage, you need to multiply the decimal by 100. In this case, 0.9 times 100 equals 90. Therefore, 0.9 as a percentage is 90 percent.
Learn more about Conversion decimal to percentage here:https://brainly.com/question/30775491
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A bookstore charges a standard rate for paperback or hardback books. The cost of a paperback book is 11 dollars less than the cost of a hardback book. Recently one day of sales totaled $784.10. That day the bookstore sold 53 paperback books and 45 hardback book. Write a system representing the situation. Use the graph test made the solution of the system. What does the solution mean to the situation? How much does each type of book cost? You substitution to verify your solution.
The required price of the paperback book and hardback book is $2.95 and $13.95 respectively.
Given that,
The cost of a paperback book is 11 dollars less than the cost of a hardback book. Recently one day of sales totaled $784.10. That day the bookstore sold 53 paperback books and 45 hardback book.
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let the price of paperback be x and price of hardback books be y,
According to the question,
x = y - 11 - - - (1)
53x + 45y = 784.10 - - - (2)
From equation 1
53 [y - 11] + 45y = 784.10
y = $13.95
Now,
y = 13.95 - 11
y = $2.95
Thus, the required price of the paperback book and hardback book is $2.95 and $13.95 respectively.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
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A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. The perimeter is 19 inches.
What is the measure of x?
(A) 2
(B) 3
(C) 5
(D) 9 ...?
Answer:
9
Step-by-step explanation:
Final answer:
To find the value of x in a triangle where one side is x and the other two are each 4 inches less than x with a perimeter of 19 inches, set up an equation and solve it to find that x = 9 inches. The correct option is D.
Explanation:
The question involves finding the value of x when a triangle has one side that measures x, and the other two sides each measure 4 inches less than x. The perimeter of the triangle is given as 19 inches.
To solve this, we use the formula for the perimeter of a triangle, which is the sum of the lengths of its sides. Therefore, the equation can be set up as:
x + (x - 4) + (x - 4) = 19
Simplifying this equation:
Combine like terms: 3x - 8 = 19Add 8 to both sides: 3x = 27Divide both sides by 3: x = 9Therefore, the measure of x is 9 inches which corresponds to option D.
This problem is a basic algebra problem that requires understanding of how to set up equations based on given conditions and solving them to find unknown variables.
one pipe fills a storage pool in 8 hours. A second pipe fills the same pool in 4 hours when a third pipe is added and all three are used to fill the pool,it takes only 2 hours. find how long it takes the third pipe to do the alone.
Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π].
Mrs. Donley's math class has a total of 25 students. On Friday, the class was given an eight question quiz on fractions. The number of incorrect answers given by the students is shown below.
Incorrect Answers Number of Students
0 5
1 7
2 4
3 6
4 2
5 1
What is the relative frequency of students that missed 1 question on the quiz?
A. 0.28
B. 0.48
C. 0.35
how do you do factoring the gcf out of a binomial
Choose the correct simplification of (7x3 − 8x − 5) + (3x3 + 7x + 1).
10x3 − x − 4
10x3 + x + 4
4x3 − 15x − 6
4x3 + 15x + 6 ...?
the correct simplification of (7x^3 − 8x − 5) + (3x^3 + 7x + 1),
Is 10x^3 − x − 4
Simplify 5 log2 k – 8 log2 m + 10 log2 n
...?
Answer:
your answer is log2 k to the fifth power n to the tenth power over m to the eighth power
Step-by-step explanation:
The number of pizzas eaten at the class party is equal to one-fourth the number of students, plus two more pizzas for the adults. If nine pizzas are eaten, how many students are there?