Answers
============================================================
Explanation:
Use the pythagorean theorem to tie together the three sides of the right triangle.
[tex]a = x-3 = \text{horizontal leg}\\b = x+5 = \text{vertical leg}\\c = 9 = \text{hypotenuse}[/tex]
[tex]a^2 + b^2 = c^2\\(x-3)^2 + (x+5)^2 = 9^2\\x^2-6x+9 + x^2+10x+25 = 81\\2x^2+4x+34 = 81\\2x^2+4x+34-81=0\\2x^2+4x-47=0\\[/tex]
From here, we use the quadratic formula to solve for x.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(4)\pm\sqrt{(4)^2-4(2)(-47)}}{2(2)}\\\\x = \frac{-4\pm\sqrt{392}}{4}\\\\x \approx \frac{-4\pm19.79898987}{4}\\\\x \approx \frac{-4+19.79898987}{4} \ \text{ or } \ x \approx \frac{-4-19.79898987}{4}\\\\x \approx \frac{15.79898987}{4} \ \text{ or } \ x \approx \frac{-23.79898987}{4}\\\\x \approx 3.94974747 \ \text{ or } \ x \approx -5.94974745\\\\[/tex]
We'll ignore the negative x value because it makes the sides x+5 and x-3 to be negative numbers. Negative side lengths make no sense.
The only practical solution is roughly x = 3.94974747; rounding to 3 sig figs leads to the final answer of x = 3.95
In this case, 3 sig figs means that we're rounding to 2 decimal places.
Related Questions
An equilateral triangle and a rectangle have the same perimeter.
How do you find the side lengths of the equilateral triangle and the rectangle?
Answers
I think you already got the explanation part
I've just solved for 'x' in here
And to check if the answer is correct or not, you just put in this value of x and try finding the perimeter for each.
You'll get 24 units!
I'm sorry, but it wouldn't let me answer earlier XD
Use point-slope form to write the equation of a line that passes through the point
(-6,3) with slope – 2.
Answers
Answer:
y = -2x - 9
Step-by-step explanation:
Slope = - 2
Using the slope = -2 and the point (-6, 3) substitute into y= mx + b and solve for "b"
y = mx + b
3 = -2(-6) + b
3 = 12 + b
3 - 12 = b
-9 = b
The equation of the line is y = -2x - 9
clara has a positive acceleration for 5 minutes
Answers
Answer:
The answer is C.
Step-by-step explanation:
Bacteria colonies can triple in size every 4 days. If you start with 150 bacteria microorganisms, how large would the colony be after 16 days? First, complete the equation: Future Amount = 150(1+[?]
Answers
Answer:
But notice that the colony tripled 4 times in 16 days, or it tripled 16 / 4 = 4 times.
Step-by-step explanation:
150 x 3 x 3 x 3 x 3 = 150 x 34 = 150 x 81 = 12,150.
Hope this helps
Answer:
ha i got nothing
Step-by-step explanation:
he i got nothing
For every 20 penguins at the North Pole there are 9 polar bears. If you encountered 27 polar bears, how many penguins would you expect to see?
Answers
Answer:
60 penguins
Step-by-step explanation:
We need to find out how many times 9, the number of polar bears for every 20 penguins, was multiplied by, so that we can multiply 20 penguins by the same amount.
27/9 = 3
20*3 = 60
Answer: 60
Step-by-step explanation:
The ratio is 20:9. If you times both sides by 3, you will get 60:27, which means 60 penguins per 27 polar bears.
The chances that you will be ticketed for illegal parking on campus are about 1/3. During the last nine days, you have illegally parked every day and have NOT been ticketed (you lucky person!). Today, on the 10th day, you again decide to park illegally. The chances that you will be caught are:
Answers
6/10=3/5
3/5 chance to be caught
The required probability of getting caught on the 10th day is 3/5.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Probability of getting caught in 9 days
= [1 - 1/3]*9=6
The probability of getting on the tenth day is given as,
= 6/10
=3/5
Thus, the required probability of getting caught on the 10th day is 3/5.
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Plsss some one help with this
Answers
Answer:
the answer is c and the entire equation means that the tickets each cost $15 and the service fee is $12
Isabelle ran a distance of about 26 miles during a marathon. In other countries, kilometers is used to measure length. There are approximately 8 kilometers in 5 miles.
Which measurement is closest to the number of kilometers Isabell ran?
Answer
A
16.3 kilometers.
B
41.6 kilometers.
C
7.2 kilometers.
D
53.5 kilometers.
Answers
Answer:
Step-by-step explanation:
b
If the point (2K-3, K+2) lies on the graph of the equation 2x+y+14=0, find the value of k.?
Answers
Answer:
k = -2
Step-by-step explanation:
Substitute 2k-3 for x and k+2 for 2
2x + y + 14 =0
2(2k-3) + (k + 2) + 14 = 0
4k - 6 + k + 2 + 14 = 0
4k + k - 6 + 2 + 14 = 0
5k + 10 = 0
5k + 10 - 10 = 0 - 10
5k = -10
[tex]\frac{5k}{5} = \frac{-10}{5}[/tex]
k = -2
what skills are needed to learn derivatives in math
Answers
Answer:
smart
be smart
Please help me please
Answers
Step-by-step explanation:
m +2 = 4
m = 2
x = 1
y +1 = 2
y = 1
z = -1
-5x - 25= 78; her work is shown below identify the error and where it was made
Answers
[tex]-5x = 78 + 25 <=> -5x = 103 <=> x = -103/5[/tex]
Choose all of the proportional relationships that have a greater unit rate than the unit rate of this graph.
10
9
8
7
6
5
4
3
2
1
5
7
B
00
9 TD
X
y
2
5
10
15
low
y
3
6
9
6
12
18
6
y = 2x
y = 0.25%
y
2
4
y
3
6
9
8
16
24
8
12
Answers
The proportional relationships that have a unit rate that is greater than that of the one of the graph are: the first and third tables, and y = 2x.
How to Determine the Unit Rate of a Proportional Relationship?The unit rate can be calculated as, m = y/x. In an equation that represents a proportional relationship, y = mx, the value of m is the unit rate.
Using a point on the graph, (5, 2):
Unit rate of the graph = y/x = 2/5
Unit rate = 0.4.
Unit rate for the first table = 3/5 = 0.6 [greater than 0.4]
Unit rate for the second table = 2/6 = 0.3 [less than 0.4]
Unit rate for y = 2x, is 2 [greater than 0.4].
Unit rate for y = 0.25x, is 0.25 [less than 0.4].
Unit rate for the third table = 2/4 = 0.5 [greater than 0.4]
Unit rate for the second table = 3/8 = 0.375 [less than 0.4]
Those that have a unit rate that is greater than the one of the graph are: the first and third tables, and y = 2x.
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A farmer has two tractors. The probability that
tractor 1 will break down is 3% and the
probability that tractor 2 will break down is
5%. What is the probability that both tractors
will break down on a given day? Give your
ansineras
Answers
Step-by-step explanation:
the break down probabilities are for the same given day ? one day ?
if that is so, then the expected value for a break down day for tractor 1 will be 34 days (rounded up 100%/3%), and for tractor 2 20 days (100%/5%).
that would be horrible. a tractor would only work for about a month without major repair.
because normally such probabilities are given for a warranty period like 1 or 3 or 5 years.
but the description does not say anything about that. so, we have to go with the primary assumption.
so, the question is about the probability that both things happen at the same time (the same day).
this is like asking for the probability of rolling a double 6 with two dice - both events (a 6 on a die) have to happen "together". so it is the probability of one event multiplied by the probability of the second event : 1/6 × 1/6 = 1/36
5% = 0.05 (5% is 5 hundredths) = 5/100
3% = 0.03 (3% is 3 hundredths) = 3/100
now both events (break-down of both tractors) happen together means 5/100 × 3/100 = 15/10000 = 0.0015
that means the probability in % is 0.15%
that means in other words, this event (both tractors breaking down on the save day) is expected to happen 15 times in 10000 days, or once every 667 days (or roughly every 2 years).
Find the slope (-10,-3) (7,2)
Answers
Answer:
Let (-10,-3) be (x1, y1)
and (7, 2) be (x2, y2).
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Substitute in values:
[tex]\frac{2-(-3)}{7-(-10)} =\frac{5}{17}[/tex]
Answer:
5/17
Step-by-step explanation:
Slope = Change in /Change in X
Slope = 2 - (-3) / 7 - (-10)
Slope = 5/17
-Chetan K
Write the statement "--5 times x subtracted from 22 is less than 9 more than
x" as a mathematical inequality. I dont know this sorry
Answers
Answer:
5x-22<9<x
Step-by-step explanation:
5 times x = 5x
subtract 22 = 5x-22
less then = 5x-22<
9 more then x = 5x-22<9<x
What is a unit rate?
What are the steps for
finding a unit rate?
Each 12-ounce bottle of
shampoo cost $2.15.
What is the cost
per ounce?
Answer all please
Answers
Answer:
1. Cost of a quantity of 1.
2. Divide the cost by quantity.
3. $0.18 per ounce
work: 2.15 / 12 = 0.1791666666666 and round
During a sale, a store offered a 20% discount on a camera that originally sold for $650. After the sale, the discounted price of the camera was marked up by 20%. What was the price of the camera after the markup? Round to the nearest cent.
Answers
Answer:
$624
Step-by-step explanation:
650 * .80 = 520
520 * 1.20 = 624
I need this solved with the answer as an ordered pair
Answers
Answer:
look at the picture i have sent
Zachary wants to ride his bicycle 26.8 miles this week. He has already ridden 8 miles.
If he rides for 4 more days, write and solve an equation which can be used to
determine m, the average number of miles he would have to ride each day to meet his
goal.
Answers
Answer:
4.7 ~~~ :D
Step-by-step explanation:
t = total...i = initial amount ridden......d = days..... m = average amount of miles
---------------
t = i +dm
26.8 = 8 + 4m
----------------- solve -----------------
26.8 = 8 + 4m ----> 18.8 = 4m ----> 4.7 = m
The expression is 26.8 = 8 + 4m and the average number of, miles he would have to ride each day to meet his goal is 4.7.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Let the attributes be, t = total, i = initial amount ridden, d = days, and m = average amount of miles.
The required expression can be written as below:-
t = i +dm
26.8 = 8 + 4m
The value of average miles will be calculated by solving the expression:-
26.8 = 8 + 4m
18.8 = 4m
4.7 = m
Therefore, the expression is 26.8 = 8 + 4m and the average number of, miles he would have to ride each day to meet his goal is 4.7.
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Please explain step-by-step! Thanks!
Random answers will be reported
Answers
Step-by-step explanation:
what is your questions?????An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. At the end of the night, the driver calculates his profits and makes a graph to analyze the data. What is the average rate of change for the from the 1st hour to the 4th hour? Be sure to include the correct units of measurement
Answers
The rate of change is in Y over the change in X.
Y is the dollar amount at 4 is 78 at 1 it is 54, the change is 78 - 54 = 24.
X is the time the change from 4 to 1 is 3 ( 4 - 1 = 3)
The rate of change is 24 / 3 = 8.
The answer is 8 dollars per hour.
An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. the average rate of change from the 1st hour to the 4th hour is 8.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer.
At the end of the night, the driver calculates his profits and makes a graph to analyze the data.
The rate of change is in Y over the change in X.
Y is the dollar amount at 4 = 78 ,
at 1 = 54
the change is 78 - 54 = 24.
X is the time the change from 4 to 1 = 3
The change is ( 4 - 1 = 3)
The rate of change = 24 / 3 = 8.
Therefore, The answer is 8 dollars per hour.
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what is the slope of the equation above?
Answers
This shake is made from five congruent triangles. Find the total area of the shape
Answers
Area of one triangle = [tex]A = \frac{a·b}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9 {cm}^{2} \\ [/tex]
For 5 triangles = [tex]9 \times 5 = 45 {cm}^{2} [/tex]
- BRAINLIEST answerer
the person who answes my question can u stay because i have more thankyou
Answers
Answer:
c. 60 mins
Step-by-step explanation:
12 * 5 = 60
15 * 4 = 60
1. £1000 is invested for 2 years at 5% per annum with compound interest. Work out the total amount in the account after 2 years.
Answers
Answer:
A = £1102.50
Step-by-step explanation:
Use the compound amount formula:
A = P(1 + r)^t, where P is the principal, r is the interest rate as a decimal fraction, and t is the number of years.
Here A = £1000·(1 + 0.05)^2, which evaluates to A = £1102.50
Find the equation of a line parallel to y = -5x – 10 that passes through the point
(-5,0).
Answers
Answer:
8684787
Step-by-step explanation:
Q.no 21 solve it.
Plz. Plz
Answers
Answer:
Hamm i don't know sorry a want yo help You Buy a can't because a don't know sorry
Amy buys 16 envelopes for 14p each and pays with a £5 note.
How much change does she get?
Give your answer in pounds, £.
Answers
Answer:
£2.76
Step-by-step explanation:
The cost of Amy's purchase is ...
16×(£0.14) = £2.24
Her change from £5.00 is ...
£5.00 -2.24 = £2.76 . . . . Amy's change
Which figure best demonstrates the setup for the box method of finding the area of a triangle? On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and share 2 sides with the triangle. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and the 3 points of the triangle touch the sides of the box. The box is 2 units larger than one side of the triangle. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and all 3 points of the triangle are on the sides of the box. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and 2 points of the triangle are on the box.
Answers
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The answer is C in Edge. Just took the assigment. Hope this helps! :)