Given a right triangle, find the length of the missing leg given the hypotenuse is 13 cm and the other leg is 5 cm. (Round to two decimal places.)
Answers
The length of the missing leg is 12 cm.
Explanation:
a² + b² = c² (Pythagoras theorem)
c is the hypotenuse (longest length) of a triangle.
a and b are the two other side of the triangle excluding the longest one.
Let x cm be the length of the missing leg of the right triangle.
x² + 5² = 13² (Pyth. Thm.)
x² = 13² - 5²
x² = 169 - 25
x² = 144
x = √144
x = 12
Hope it helps! Mark me brainliest if it’s correct.
The length of the missing leg given the hypotenuse is 13 cm and the other leg is 5 cm would be 12 cm.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
a² + b² = c² (Pythagoras theorem)
where, c is the hypotenuse (longest length) of a triangle.
And a and b are the two other side of the triangle excluding the longest one.
Let x be the length of the missing leg of the given right triangle.
x² + 5² = 13²
x² = 13² - 5²
x² = 169 - 25
x² = 144
x = √144
x = 12
Hence, the length of the missing leg given the hypotenuse is 13 cm and the other leg is 5 cm would be 12 cm.
Learn more about Pythagoras theorem;
https://brainly.com/question/343682
#SPJ2
Related Questions
Kareem says that the ratio 4 : 1 is equivalent to the ratio 12 : 9 because 4 1 8 5 12 and 1 1 8 5 9. Is Kareem correct? Explain how you know.
Answers
\(\bf Step-by-step~explanation:\)
Kareem's statement: 4:1 is equal to 12:9. Let's see if this is correct.
\(\bf Step ~1:\)
We have to simplify the ratios. Since 4:1 is already simplified, we do not have to do anything with it. 12:9 could be simplified. To do so, we need to find the greatest common factor (GCF) of both numbers. The GCF of 12 and 9 is 3. Since 3 is the GCF for both numbers, we divide them by 3.
\(\bf 12 /3=4\\9/3=3\)
First number: 4
Second number: 3
Ratio: 4:3
\(\bf Step~2:\)
We compare the ratio 4:3 to 4:1. Since they have different values, they are not equivalent to each other.
\(\large\boxed{\bf Our~final~answer: ~Kareem~is~wrong.}\)
\(\bf {Explanation~in~Step~1}\)
4 : 1 and 12 : 9 are not equivalent
Kareem is wrong
Correct question:
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because
4 + 8 = 12 and 1 + 8 = 9. Is Kareem correct? Explain how you know
4 : 1 is in its simplest form already
12 : 9
= 12/9
= 4/3
= 4 : 3
Therefore,
4 : 1 and 12 : 9 are not equivalent
Kareem is wrong based on his assumption that 4 + 8 = 12 and 1 + 8 = 9
https://brainly.com/question/17352744
SELECT THE EQUIVALENT EXPRESSION
(6^-4 x 8^-7)^-9
A. 6^36•8^63
B. 1/6^13•8^16
Answers
Answer:
A
Step-by-step explanation:
Calculate the products in the multiple choice and see if any equal the product in the problem.
Hence as the products calculated in choice A equal that in the problem;the answer is A
A new gaming chair costs $309.99. You have already saved $144.99 and earn $27.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
27.5w − 144.99 = 309.99; w = 17
27.5 + 144.99w = 309.99; w = 6
27.5w − 309.99 = 144.99; w = 17
27.5w + 144.99 = 309.99; w = 6
Answers
The linear equation we need to solve is:
$27.50*w = $309.99 - $144.99
And the solution is w = 6.
How to write and solve the equation?
We know that the cost of the gaming chair is $309.99.
To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:
f(w) = $144.99 + $27.50*w
So the linear equation we need to solve is:
$144.99 + $27.50*w = $309.99
To solve this we need to isolate w.
$144.99 + $27.50*w = $309.99
$27.50*w = $309.99 - $144.99
w = ($309.99 - $144.99)/$27.50 = 6
So they can buy the chair after 6 weeks.
Learn more about linear equations at:
brainly.com/question/13763238
#SPJ1
The graph of f(x)=x2 was transformed to create the graph of g(x)=−f(x−1)+2 Which is the graph of g ?
Answers
1. Shift the graph of f(x) to the right by 1 unit, which means replacing x with (x - 1) in the equation. This gives us: f(x - 1) = (x - 1)^2.
2. Reflect the graph of f(x - 1) about the x-axis by multiplying the expression by -1. This gives us: -f(x - 1) = -(x - 1)^2.
3. Shift the graph of -f(x - 1) up by 2 units. This gives us: g(x) = -f(x - 1) + 2 = -(x - 1)^2 + 2.
Therefore, the graph of g(x) is a downward-facing parabola that has been shifted 1 unit to the right and 2 units up from the graph of f(x) = x^2.
Antonio is in a bowling league. His goal is to score an average of at least 100 points per game. His scores so far are 105,95,97,82, and 110. How many points can Antonio score in his next game to reach his goal? Show your work.
Please show work I need it so please have step by step I will give brainly thanks!
Answers
Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.
What are basic arithmetic operations?
Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.
To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:
Total points needed = (number of games + 1) × average score goal - total points scored so far
In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:
105 + 95 + 97 + 82 + 110 = 489
Substituting these values into the formula, we get:
Total points needed = (6) × (100) - 489
Total points needed = 600 - 489
Total points needed = 111
Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.
To learn more about arithmetic operations, visit:
https://brainly.com/question/4721701
#SPJ1
your backyard is shaped like a rectangle and measure's 45 1/2 feet by 50 feet. you want to put a fence around your backyard. how much fence will you need?
Answers
Answer:
191 ft
Step-by-step explanation:
If it's 45.5ft x 50ft, we'll need to put fence around two 45.5ft sides and two 50ft sides.
2*45.5ft + 2*50ft = 91ft + 100ft = 191ft
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Answers
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
Read more on function here: https://brainly.com/question/10687170
#SPJ1
I need help ☹️ anybody know if it’s a b c or d
Answers
Answer:
C
Step-by-step explanation:
3(7-9k)+23k=4x-(24-k)
Answers
Jannah places a rectangle in the coordinate plane so that the lower left vertex is at the origin and the longer side of the rectangle is along the x-axis.
Jannah knows that the length of the rectangle is 3 times its width. She labels the coordinates of the lower right vertex as (3a, 0).
What coordinates should Jannah use to label the upper right vertex of the rectangle?
(a, 3a)
(a over 3,0)
(3a, 3a)
(3a, a)
(3a, a over 3)
Answers
Answer:
(d) (3a, a)
Step-by-step explanation:
You want to know the upper right vertex of a rectangle with long-side coordinates (0, 0) and (3a, 0) such that the side in the x-direction is 3 times the side in the y-direction.
WidthIf the length is 3a and is 3 times the width, then the width is 'a'.
VertexThe point at upper right will have its x-coordinate equal to 3a, and its y-coordinate equal to 'a'. That point is (3a, a).
BRAINLIEST!!!!!!!!!!!
Answers
y = 6(1/2)^x
what is the answer for 6x + 3(x-2)
Answers
Answer:
9x - 6
Hope this helps! <3
(If you need a step by step lmk)
Answer:
6x+3(x-2)
6x+3x-6
9x-6
I need help with my math
Answers
Step 1: Pick any two points
The points are represented as (x1,y1), (x2,y2).
where x1= -4, y1= -8, x2= 0, y2= 4
Step 2: Write out the formula of the equation to use
\(\frac{y-y_1}{x-x_1}=\text{ }\frac{y_2-y_1}{x_2-x_1}\)Step 3: Substituting the values and to get the equation
\(\begin{gathered} \frac{y-(-8)_{}}{x-(-4)}=\text{ }\frac{4-(-8)}{0-(-4)} \\ \frac{y+8}{x+4}=\frac{4+8}{0+4} \\ \frac{y+8}{x+4}=\text{ }\frac{12}{4} \end{gathered}\)\(\begin{gathered} \frac{y+8}{x+4}=\text{ 3} \\ \text{Cross multiply} \\ y+8=\text{ 3(x+4)} \\ y+8=\text{ 3x+12} \\ \text{Collect like terms} \\ y=\text{ 3x+12-8} \\ y=\text{ 3x + 4} \end{gathered}\)The equation that represents the graph is y= 3x+4.
Option A is the correct answer.
Dr Wyzard passed out bags of Starburst for the best students. One bag contains 5
orange, 2 pink, and 3 yellow. What is the probability of randomly selecting an orange
candy, eating it, then randomly selecting another orange?
Answers
4/10 or 2/5 simplified
Hope this helps you out!
Hello -- can you please assist with this assignment? Thank you.
Answers
Note that:
f(x) = y can be writtten in coordinate form as (x, y)
Following the rule above. the statements below can be translated into coordinate points as folllows
a) f(-1) = 1
(-1, 1)
b) h(2) = 7
(2, 7)
c) g(1) = -1
(1, -1)
d) k(3) =
please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
Is (-3,2) a solution of the equation x + y = 3?
Answers
explanation:
-3+2=3
-1=3
not a solution
Answer:
no
Step-by-step explanation:
plug the numbers in.
(‐3) + (2) = 3
-1 is not equal to 3.
a certain hurricane charles at 20.80 km per hour the distance from people to key west is 145 km right in south multiplication to find out how long will it take for meridian to travel from cuba to key west
Answers
The distance from Cuba to Key West is 145 km, and if Hurricane Charles is travelling at 20.80 km per hour, it will take 6.97 hours to travel that distance. To calculate this, use the following equation: 145 km / 20.80 km/h = 6.97 hours.
The time it takes for Hurricane Charles to travel from Cuba to Key West can be calculated using the formula time = distance / speed. In this case, the distance is 145 km and the speed is 20.80 km per hour. Plugging in these values gives:
Time = 145 km / 20.80 km per hour
Time = 6.97 hours
Therefore, it will take Hurricane Charles approximately 6.97 hours to travel from Cuba to Key West.
Here you can learn more about distance formula https://brainly.com/question/25841655
#SPJ11
Please help me I’ll mark you brainly
Answers
On solving the provided question, we can say that - here in graph we have on solving equation \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
from graph, x= 2
y = 1
\(2x^2+ 9y^2 \\\)
\(8 + 9 = 17\)
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
PLEASE DON'T GUESS! I NEED THE CORRECT ANSWER!!!! THIS IS A TEST!!!!
Answers
Answer:
Option D "The graph on the left is..."
Step-by-step explanation:
because there's no graph that ever starts on 81 lol
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
Answers
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
Read more on function here: brainly.com/question/10687170
#SPJ1
Find the angle marked x in each of these polygons
Answers
The angles marked x in each of the polygons are 128° and 82° respectively.
What are Concave Polygons?Concave polygons are closed two dimensional figures whose at least one of the interior angle is more than 180 degrees.
The given polygons are named as ABCDEFGH and PQRSTU as shown below.
1) An interior angle and a corresponding exterior angles are supplementary.
Interior angle ∠B = 180° - 42° = 138°
Similarly,
Interior angle, ∠E = 180° - 34° = 146°
Also, angle around a point = 360°
Interior angle at G = 360° - 141° = 219°
Sum of the angles of a polygon = (n - 2) 180°, where n is the number of sides.
Here, number of sides, n = 8
x + 138° + 107° + 145° + 146° + 126° + 219° + 71° = (8 - 2) 180°
x + 952° = 1080
x = 1080 - 952
x = 128°
2) The dotted line implies that the shape is symmetrical.
∠Q = ∠U and ∠R = ∠T
∠Q = ∠U = 34°
Exterior angle at T = 87°
Interior angle at T = 360° - 87° = 273°
So ∠R = ∠T = 273°
Again number of sides, n = 6
x + 34 + 273 + 24 + 273 + 34 = (6 - 2) 180
x + 638 = 720
x = 720 - 638 = 82°
Hence the angle are 128° and 82°.
Learn more about Concave Polygons here :
https://brainly.com/question/3658258
#SPJ9
Solve for p. −8.4p=24.36
Enter your answer in the box.
Please help my life depends on this question and 19 more!
Answers
Answer:
p= -2.9
Step-by-step explanation:
24.36/-8.4=-2.9
Charis muffin recipe calls for 1/2 cups of flour for the muffins and a quarter cup of flour for the topping she makes half of the original recipe how much flour she use
Answers
Answer:
1/2=2/4
2/4+1/4=3/4 cups of flour
Step-by-step explanation:
Please need help don't understand please explain
Answers
Answer:
Combine like terms for the than you do to other side the multiply last for least you divide both sides
Step-by-step explanation:
In the figure 302 648 719. what is the place value of the digit 2?
Answers
Answer:
Millions
Step-by-step explanation:
2 is in the millions place
The Place Value of digit 2 = 2000000 , 2 million.
What is Place Value ?The place value is the position of each digit in a number. The place value of digits is determined as ones, tens, hundreds, thousands,ten-thousands and so on, based on their position in the number.
Each digit has a value depending on its place called the place value of the digit.
Place Value of a digit = (face value of the digit) × (value of the place).
6 is in ten place. Hence, the place value of 6 in 64 = 6 x 10 = 60.
The digit 2 in 302 648 719
Place Value of digit 2 = (2) × (1000000)
Place Value of digit 2 = 2000000
Therefore Place Value of digit 2 = 2000000 , 2 million .
To know more about Place Value
https://brainly.com/question/27734142
#SPJ2
Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used. 2 one half 4 one fourth
Answers
Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)
Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).
The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,
A' = 2A
A'(8, -12) = 2×A(4, -6)
These facts are all you need to know to choose the correct answer (shown above).
Answer: 1/2
Step-by-step explanation:
I took the quiz!
Algebra Question
Let v = (-7,6,-6) and w = (-5,-3,-6) be vectors in R^3. Find the orthogonal projection of v onto w.
Answer:
Projection on w: (-54/14, -159/70, -159/35)
I have the correct answer but I don't know how they got it.
Answers
The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).
To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:
proj_w(v) = (v⋅w) / (w⋅w) * w
where ⋅ denotes the dot product.
Calculating the dot product of v and w:
v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53
Calculating the dot product of w with itself:
w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70
Now, substituting these values into the formula, we have:
proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)
Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).
In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.
for such more questions on vector
https://brainly.com/question/15519257
#SPJ8
Hove
Find the average rate of change indicated below.
y = 4x+1
[-1, 1)
A.15
B.3.75
C.1.875
D.7.5
Answers
The average rate of change of the function over the interval is 4
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
y = 4x + 1
The interval is given as
[-1, 1)
The function is a linear function
This means that it has a constant average rate of change
From y = 4x + 1, we have
Rate = 4
Hence, the rate is 4
Read more about average rate of change at
https://brainly.com/question/17131025
#SPJ1
Define a variable, using let statements, set up an equation, then solve. On the album "1989" by Taylor Swift, Blank Space is 12 seconds longer than Shake it Off. if the combined time of the two songs is 7 minutes and 30 seconds how long is Shake It Off? Give your answer in minutes and seconds.
Answers
Let Blank space be represented as b
Let shake it off be represented as s
Blank Space is 12 seconds longer than shake it off
mathematically,
b = s + 12
this means the total time for blank spacce is the summation of shake it off recording time and 12seconds
if the two of the aongs were recorded for 7mimutes 30 seconds
Blank space + shake it off = 7.5 minutes
b + s = 7.5 minutes
let convert 7.5 minutes to seconds
60s ==== 1min
xsec === 7.5min
x * 1 = 60 x 7.5
x = 450seconds
therefore
b + s = 450
b = s + 12 ------- equation 1
b + s = 450 ------- equation 2
substitute b = s + 12 into equation 2
s + 12 + s = 450
collect the like terms
s + s = 450 -12
2s = 438
divide both sides by 2
2s / 2 = 438 /2
s = 219 seconds
convert to minutes
60s ===== 1 min
219s ==== xmin
cross multiplication
x * 60 = 219 x 1
60x = 219
divide both sides by 60
60x / 60 = 219/60
x = 3.65 minutes
x = 3minutes 39 seconds
therefore, shake it off was recorded for 3 mins 39seconds
The answer is 3 minutes 39 seconds