The length of the unknown side of the right triangle is 13
What is a right angle triangle?A right triangle (American English), sometimes known as a right-angled triangle (British), is a triangle with one angle that is a right angle (i.e., a 90-degree angle), or two sides that are perpendicular. The link between is the basis of trigonometry.
between the right triangle's angles and sides.
The side across from the right angle is the hypotenuse (side c in the figure). Legs are the sides closest to the ideal angle (or catheti, singular: cathetus). The side a that is next to angle B and across from angle A is referred to as side b, and the side a that is next to angle A and across from angle B is referred to as side a.
Right triangles are referred to as Pythagorean triangles and their side lengths as Pythagorean if all three of their sides are integer lengths.
[tex]\sqrt{(12)^2+(5)^2}=13[/tex]
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eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. how many distinguishable ways are there to construct the octahedron? (two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)
There are 1680 ways to construct the octahedrons.
Here,
Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron.
An octahedron has 8 equilateral triangles.
We have to find number of ways to construct the octahedron.
What is Regular octahedron?
An octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
Now,
An octahedron has 8 equilateral triangles.
We have to fix 2 faces before applying the colors.
So, the first face that can be fixed for any of the 8 faces but each faces are similar.
Hence, there are 8/8 ways.
And, When we fix one face, three adjoining faces are similar.
So, we have 7 colors for the second face.
Hence, 7/3 ways
Now, we can place any color anywhere, it will be different arrangement.
So, 6! ways.
Hence, Total number of ways = (8/8) * (7/3) * 6! = 7 * 6 * 5 * 4 *2 = 1680
So, There are 1680 ways to construct the octahedrons.
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Leila wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are feet. Suppose each can of paint will cover square feet. How many cans will she need to paint the ceiling?
Answer: Find the square roots and the multiply that by 4
Step-by-step explanation:
hope this helped
Meri paid $19.24 for 10.5 gallons of
gas. What was the cost of one
gallon?
What did Raya do wrong? Use complete sentences to describe her mistake.
During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.
How to Evaluate an Expression?Given the expression, a³ - b³ / 5, where:
a = 2
b = -3
Substitute the values into the expression
Step 1: (2)³ - (-3)³ / 5
Evaluate
Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)
Step 3: 8 + 27/5
Step 4: 35/5 [addition]
Simplify
Step 5: 35/5 = 5 [division]
Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.
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A piece of machinery depreciates at a fixed rate of 12% per year for 7 years. If the machinery is valued at $100,000 after 7 years, how much would the machinery have initially cost rounded to the nearest dollar?
a.
$113,636
d.
$45,235
b.
$40,868
e.
$244,692.86
c.
$244,693
The price the machinery have initially cost rounded to the nearest dollar is $244,693
Exponential equationThe formula for calculating depreciation is expressed according to the formula:
P(t) = P0e^-rt
Given the following parameters
P(t) = $100,000
rate = 12% = 0.12
time =7 years
Substitute
100,000 = P0e^-(0.12)(7)
100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693
Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693
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5/6 x -4 1/2 x -2 1/5
Find the product. Write your answer as a fraction in simplest form.
Answer:
8 1/4 or 33/4
Step-by-step explanation:
How to muliply fractions: just multiply all the denominators together and the numerators together
However, if your mulitplying whole numbers, you have to change those into improper fractions using the formula: Whole number x denomiator + numerator
**Make sure to put the same numerator as you had before when you change to an improper fraction!!!
-4 1/2 = -9/2
-2 1/5 = -11/5
5 -9 -11 5 x -9 x -11 -45 x -11 (use a calculator) 495
-- x -- x --- = --------------- = ------------- = ------------
6 2 5 6 x 2 x 5 12 x 5 60
1 33
= 8.25 or 8 ---- = --------
4 4
Describe the pattern, then list the next three numbers in the sequence.
4.5, 7, 12, 22, 42 __, __, __
Answer:
82 , 162, 322
Step-by-step explanation:
So basically add the number by two and then subtract that number by 2. 4.5(2)=9 9-2=7 and 7(2)=14 14-2=12 and so on
1.) The weight of the tea in 100 identical tea bags is 8 ounces. What is the weight, in ounces, of the tea in 3 tea bags? Show your work.
Answer:
0.24 ounces for 3 teabags.
Step-by-step explanation:
Since this is a 1 digit number, we should find out how much each teabag weighs. We can do this by dividing 8 by 100, which gives us 0.08.
Now we can multiply that by 3, which gives us 0.24, so 3 teabags are 0.24 ounces.
Find car A and car B speed in km/h
Answer:
72 km/h and 48 km/hStep-by-step explanation:
Let the speed of the cars be x and y.
When moving in opposite directions, the speeds add up and when moving in the same direction the speeds subtracted.
Convert time from minutes to hour:
4 minutes = 4*1/60 hr = 1/15 hr20 minutes = 20*1/60 hr = 1/3 hrOpposite direction(x + y)*1/15 = 8x + y = 8*15x + y = 120Same direction(x - y)*1/3 = 8x - y = 8*3x - y = 24Add up the two equations and find the value of x:
x + y + x - y = 120 + 242x = 144x = 72Find y:
72 + y = 120y = 120 - 72y = 48What is four hundred in standard form
Answer: 4x10²
Step-by-step explanation:
gerber product's gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† if you want to provide your child with 300 calories and 74 grams of carbohydrates, how many servings of each should you use? gerber mixed cereal for baby serving(s) gerber mango tropical fruit dessert serving(s)
Number of servings of Gerber mixed cereal for baby = 1
Number of servings of Gerber mango tropical fruit dessert for baby = 3
Given information about Gerber products are,
Gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.
Gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.
We have to find the number of servings of each to provide exactly 300 calories and 74 grams of Carbohydrates. So we need to find the appropriate combination of numbers 60 and 80 to make 300 and combinations of 11 and 21 to get 74.
Since 1 x 60 + 3 x 80 = 60 +240 = 300
and 1 x 11 + 3 x 21 = 11 + 63 = 74 ,
we can conclude that 1 serving of Gerber mixed cereal and 3 servings of Gerber mango tropical fruit dessert will do.
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x^2y(7xy^4)
helppppp
Create an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six.
15 points to whoever can answer this pleeease help
Answer:
1.3^24 / 1.5)^18
Step-by-step explanation:
[1.5^3 / 1.3^4]^-6
= 1.5^(3*-6) / 1.3^(4*-6)
= 1.5^(-18) / 1.3^(-24)
= 1.3^24 / 1.5)^18
This table represents function f. If function g is a quadratic function that contains the points and , which statement is true over the interval ? A. The average rates of change of f and g cannot be determined from the given information. B. The average rate of change of f is less than the average rate of change of g. C. The average rate of change of f is the same as the average rate of change of g. D. The average rate of change of f is more than the average rate of change of g.
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.
What is an average rate of change?An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of function f over the interval [-3, 0]:
a = -3; f(a) = -4.5
b = 0; f(b) = 0
Substituting the given parameters into the formula, we have;
Average rate of change = (0 - (-4.5))/(0 - (-3))
Average rate of change = 4.5/3
Average rate of change = 1.5.
Also, we would determine the average rate of change of function g over the interval [-3, 0]:
a = -3; f(a) = 5
b = 0; f(b) = 14
Substituting the given parameters into the formula, we have;
Average rate of change = (14 - 5)/(0 - (-3))
Average rate of change = 9/3
Average rate of change = 3.
In conclusion, the average rate of change of function f is less than the average rate of change of function g.
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Answer:
The average rate of change of f is less than the average rate of change of g.
Step-by-step explanation:
Plato/Edmentum
Lock 4 (screen will be blank until you crack the code for lock #3) Awe-sum! You have reached the last lock. Use your equation solving skills to find the value of each variable. Use the values you calculate to help you move along in the puzzle and find all of the missing variables. When you have found all of the variables Imove to the next screen.
Problems:
4a +2= -10
a(2+ b) = -12
-5c+b= 22
7(c+d) = 14
d-c-e= 17
Answers:
a=
b=
c=
d=
e=
The values of the variables are:
a = -3
b = 2
c = -4
d = 6
e = -7
Given, the expressions are:
4a + 2 = -10
4a = -10-2
4a = -12
a = -3
substitute a value in the next expression.
a(2+b) = -12
-3(2+b) = -12
-6-3b = -12
-3b = -12+6
-3b = -6
b=6/3
b = 2
now substitute b value in the next expression.
-5c+b= 22
-5c+2 = 22
-5c = 22-2
-5c = 20
c = -20/5
c = -4
substitute c value in the next expression.
7(c+d) = 14
7(-4+d) = 14
-28+7d = 14
7d = 14+28
7d = 42
d=42/7
d=6
In the last expression substitute c and d values to find e.
d-c-e= 17
6-(-4)-e = 17
6+4-e = 17
10-e = 17
-e = 17-10
-e = 7
e = -7
hence we get the values of all the variables.
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a janitor had 3/5 of a spray bottle of a cleaning solution . he used 1/9 of the soloution in a day. how much of the bottle did he use?
The Janitor used 8/15 of the bottle
How to calculate the amount of the solution of the bottle used ?
The Janitor has 3/5 of a spray bottle solution
He uses 1/9 of the solution in a day
The amount of solution used can be calculated as follows
3/5 × 1/9
= 3/45
= 1/15
The initial amount in the bottle is
3/5 - 1/15
= 8/15
Hence the amount of solution he has used is 8/15
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perform the indicated operation and simplify the result leave yuour answer in factored form 4x/x2 - 1
The simplified result is :
[tex]4x/x^{2}[/tex] - 1
= 4/x -1
4-x / x.
Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.
An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.
In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.
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You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,
How to calculate the amount of sodium we can consume?To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:
2300mg - 125mg = 175mgAccording to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).
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please help
see attached picture
Answer:
See Explanation
Step-by-step explanation:
For cement block:Given is a square cement block, thus, it's width and height would be equal.-> length (l)= h, width (w)= 2x, height (h) = 2x [tex]V_{cement \: block} = lwh[/tex][tex]\implies V_{cement \: block} = h(2x)(2x)[/tex][tex]\implies V_{cement \: block} = 4x^2h.....(1)[/tex]For cylinder:Radius (r) = 2x/2 = x, height (h) = h[tex]V_{cylinder} = \pi r^2 h[/tex][tex]\implies V_{cylinder} = \pi x^2 h.....(2)[/tex]Subtract (2) from (1), we find:[tex]V_{cement \: block}-V_{cylinder} = 4x^2h- \pi x^2 h[/tex][tex] V(cement \: block\: without\: cylinder)= x^2h(4- \pi)[/tex]Thus proved To solve 6.2.1 and 6.2.2 plug the given values in [tex]x^2h(4- \pi)[/tex] and calculate.− 2/ 3 is a/an . (check all that applies.) \sqrt{5} 5 is a/an . (check all that applies.) natural number integer rational number real number irrational number
The -2/3 is an integer and rational number.
It is required to choose the number.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given:
-2/3 is an integer and rational number.
The square root of 25 is 5 is an Natural numbers, whole number, integer, and rational number.
Natural numbers are positive whole numbers (1, 2, 3, 4, 5, ...)
Whole numbers are positive numbers start with zero (0, 1, 2, 3,...)
Integers are positive and negative whole numbers or zero (..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)
Rational numbers include all integers as well as positive or negative numbers that have fractional parts ( -2.0, -3/4, 0.25, 2.1, 5, etc.)
Irrational numbers are numbers that can not be written as a simple fraction. Its decimal goes on forever without repeating (π = 3.14159....)
5 is a natural number, whole number, integer, and rational number.
Therefore, the -2/3 is an integer and rational number.
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Carla earned a total of $84 for 7 hours of babysitting. After a total of 8 hours of babysitting, how much money will Carla have earned? Assume the relationship is directly proportional.
40 . a guest orders a drink that contains 4 ½ ounces of 80-proof liquor. approximately how many drinks does this beverage contain?
Number of drinks = 3
From the question we are told that:
Ordered drink 4 1/2 ounces of 80-proof liquor
Generally,
80-proof liquor contains 40\% alcohol
Giving the drink a standard 1.5 ounce of distilled spirit
Therefore,
Number of drinks = 4.5 / 1.5
So, Number of drinks = 3
What do you mean by ounces?A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified. The avoirdupois ounce, or precisely 28.349523125 g, is 116 of an avoirdupois pound and is used in both the United States and the United Kingdom. Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items. Although the avoirdupois ounce is the standard unit of mass for most applications.
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7. Health experts recommend the average female older than 50 years of age to
consume about 1,800 calories per day.
• Mrs. Keith has already consumed 950 calories today.
She plans to consume the same number of calories per hour for
the next 5 hours.
.
Which inequality represents d, the number of calories Mrs. Keith could eat each hour
for the next 5 hours without exceeding her recommended daily caloric intake?
Hayley wants to be a marine biologist when she grows up. Her entire room is ocean-themed, so she is painting her bed frame blue to match. She estimates that she will need 800 milliliters of paint, but the hardware store only sells paint in liters. If Hayley buys 1 liter of paint, how many milliliters will she have left?
Answer:
Hayley will have 200 milliliters of paint left.
Step-by-step explanation:
1 liter=1000 milliliter
1000-800=200
Answer:
305
Step-by-step explanation:
There are 1,000 milliliters in 1 liter.solveYou need to find how many milliliters of blue paint Annie has left. But first, you need to know how many milliliters she started with.There are 1,000 milliliters in a liter, so multiply 0.5 liters by 1,000.0.5×1,000=500Annie started with 500 milliliters of blue paint.Now, add to find how much blue paint Annie used for her beach painting. She used 75 milliliters of blue paint for the sky and 120 milliliters for the ocean.75+120=195Annie used 195 milliliters of blue paint in all.Now, find how much blue paint Annie has left. She started with 500 milliliters. Subtract the 195 milliliters she used.500–195=305Annie has 305 milliliters of blue paint left.
A tennis player hits the ball with an initial speed of 55 feet per second at an angle of 17°, from a height of 1.8 feet. How far away does the ball land in feet?
The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.
What is the projectile motion?An item or particle that is thrown toward the planet's surface and moves somewhere along a curved route only under the influence of gravity is said to be experiencing projectile motion.
Let u be the initial speed and θ be the angle at which the ball hits. Then the range of the call is given as,
R = (u² sin 2θ) / g
Where 'g' is the acceleration due to gravity.
A tennis player strikes the ball at a height of 1.8 feet with an initial speed of 55 feet per second and an angle of 17°.
R = [55² x sin (2 x 17°) ] / 9.81
R = [3025 x sin 34° ] / 9.81
R = 172.43 meters
The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.
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Answer:
61.988 feet
Step-by-step explanation:
I took the test and got it right :)
someone pls help me w this. I rlly need this!! thank uu!
"write the equation of a line that is parallel to y=2x-3 and passes through the point (1, 6)"
Write a function g with the parent function f(x) = /x/ that has a vertex at (-2, 4)
The answer for the given function g(x) is |x - 4|² - 2.
Given parent function is f(x) = |x|
Given vertex (h, k) = (-2, 4)
The simplest function in a family of functions, a parent function maintains the definition of the entire family.
The parent function that has vertex must be used to create the function of g, as shown below.
vertex form can be written as
a ( x - k )² + h
Here a = 1 , k = 4, h = -2
Now the function g(x) = | x -4 |² + ( -2)
g(x) = |x - 4|² - 2
Therefore, the function g(x) is found to be |x - 4|² - 2.
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Maria needs to be at the airport terminal at 16:15. It will take 1 1/3
hours to drive to the airport from her home, and a further 25 minutes to park and get to the terminal.
What is the latest time she should leave home?
Give your answer as a time in the 24-hour clock.
Maria should leave home for the airport terminal at 14:30.
How to convert hour into minutes?Local time is the time of a location as determined by the apparent motion of the sun. The fixed time for locations on the same meridian set by law in a country is referred to as standard time. Changes in real time as longitude changes. The same applies to a specific country.We all know that one hour equals sixty minutes.
As a result, 6 hours = (6 × 60) minutes = 360 minutes.
For, the given question;
The time at which Maria need to be at airport terminal is 16:15.
Time taken for the driving is 1 1/3 = 4/3 hours.
convert this in minutes;
= 4×60/3
= 80 minutes.
Now, extra 25 minutes is requires to park.
Total time = 80 minutes + 25 minutes
Or we can write 60 minutes + 45 minutes.
Total time = 1 hour + 45 minutes.
The time at which Maria has to reach = 16:15 - 1:45 = 14:30
Therefore, the time at which Maria must reach the airport is 14:30 in 24-hour clock.
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The slope of the graph
Answer:
5 x + 4 y = 4 b
Step-by-step explanation:
You haven't specified what form you need. Here is the Standard form, but you can also calculate the Slope intercept form points and the Point-Slope form.
Find the equation of the line in standard form with the properties:
slope: m = -5/4
At least two parameters must be provided to determine a line equation:
Since the line is incompletely determined, compute the equation assuming an arbitrary y-intercept b
Substitute the slope m = -5/4 into the slope-intercept equation y = m x + b:
y = -(5 x)/4 + b
Add (5 x)/4 to both sides:
(5 x)/4 + y = b
Multiply both sides by 4:
4 ((5 x)/4 + y) = 4 b
Distribute: 4 ((5 x)/4 + y) = 5 x + 4 y:
Answer: 5 x + 4 y = 4 b
Solve the given word problem.
Ms. Enriquez asked a carpenter to construct a rectangular bulletin board for his classroom. She told the carpenter that the length of the board is 7 ft. Longer than its width and its area is 18 square feet. Find the dimensions of the given bulletin board.
Pls solve the question
The dimensions of the bulletin board is 2 ft and 9 ft.
Let the width of board = x
Then, the length of board = 7+x
Area of board = 18 ft²
Area of rectangle = L×W
so, (7+x) × x = 18 ft²
7x + x² = 18 ft²
7x + x² + 18 = 0
x² + 9x -2x -18 = 0
x(x+9) -2(x+9) = 0
(x+9) (x-2) = 0
x+9 =0, x -2 = 0
Dimension can not be in negative number, so
x = 2, Width = 2 ft
Length = 2+7 = 9 ft
Hence, the dimensions of board will be:
The width of board = 2 ft
And, the length of bard = 9 ft.