When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
what is Pythagoras theorem ?Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.
given
by Pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
To know more about Pythagoras theorem visit:-
https://brainly.com/question/343682
#SPJ1
Matthew scored a total of 168 points in his basketball season. He scored 147 of those points in the regular season and the rest were scored in his playoff game. What percent of his total points did he score in the playoff game?
Answer:
168 - 147 = 21
21/168 = 12.5
What’s the equation to find angles in a parallelogram
b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
Cost (in dollars)
2
10
3
9
15 45
The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $50:
Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.
The best way to find out how many people will go to movie with $50 is by looking at the table.
So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,
Step-by-step explanation:
What are the 3 parts to a chemical word equation?
The three main parts to a chemical word equations are the reactants , the products and the arrow .
What is a Chemical Equation ?
A chemical equation is defined as a representation of a chemical reaction expressing it in in terms of symbols of the substances.
The three main parts of the Chemical Equation are :
(i) The Reactants : During a chemical reaction, these elements combine and undergo some chemical changes. They are present on left side of reaction equation.
For Example : [tex]CH_{4} + 2O_{2}[/tex] ;
(ii) The Arrow : It indicates formation of products from reactant . It is represented as " → " ;
(iii) The Products : Products are the result of chemical reactions between their reactants. It is present on right side of the chemical equation.
For example, : [tex]CO_{2} +2H_{2} O[/tex]
So , overall Chemical Equation can be written as : [tex]CH_{4} + 2O_{2}[/tex] → [tex]CO_{2} +2H_{2} O[/tex] .
Learn more about Chemical Equations here
https://brainly.com/question/19626681
#SPJ4
Audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (–1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)
The reasonable solutions for this situation is (1, 3.5) and (2, 2)
What is Graph?A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.
Audrey has x pounds of red grapes and y pounds of green grapes.
She has less than 5 pounds of grapes in all, hence:
x + y < 5
Also, x ≥ 0, y ≥ 0
a) The option (–1, 2) is wrong because x = -1 < 0
b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5
c) The option (2, 2) is correct because 2 + 2 = 4 < 5
d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.
e) The option (5, 0) is wrong because 5 + 0 is not less than 5
To learn more about Graphs visit:
https://brainly.com/question/17267403
#SPJ4
What happens when you log an e?
When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.
For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.
In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.
To know more about the log refer to the link brainly.com/question/28596588
#SPJ4
find the area of the rectangle whose length is 16cm and breath is 8cm
Answer:
128cm²
Step-by-step explanation:
Formula to find area of rectangle is l×b
In order to find the area of the rectangle we need to apply that formula
[tex]A =lb[/tex]
[tex]A = 16[/tex]×[tex]8[/tex]
[tex]A = 128[/tex][tex]cm[/tex]²
Hence , the area of the given rectangle is 128cm²
How do you solve systems by substitution step by step?
Answer:
1.Solve one of the equations for either variable.
2.Substitute the expression from Step 1 into the other equation.
3.Solve the resulting equation.
4.Substitute the solution in Step 3 into one of the original equations to find the other variable.
5.Write the solution as an ordered pair.
6.Check that the ordered pair is a solution to both original equations.
Step-by-step explanation:
Can someone help me please? Picture attached
Answer:
Step-by-step explanation:
A^2 + B^2 = C^2
12^2 + B^2 = 18^2
144 + B^2 = 324
Subtract 144 from both sides
B^2 = 324 - 144
B^2 = 180
[tex]\sqrt{180}[/tex] = 13.416
B^2 = 13.4
Simplifying algebraic expression
Answer:
42
Step-by-step explanation:
2 + 3(5) + 5(5)
2 + 15 + 25
Which equals..
42
Answer:
42
Step-by-step explanation:
IF b=5
Now,
2+3b+5b
=. 2 + 3*5 + 5*5
=. 2 + 15 + 25
=. 42
Does 4 8 10 make a right triangle?
No, 4, 8 and 10 cannot be the sides of a right triangle. So 4, 8 and 10 does not make a right triangle.
In a right triangle, the side opposite the right angle (the hypotenuse) is the longest side. The side opposite the 90-degree angle is the hypotenuse and it follows the Pythagorean theorem which states that the square of the hypotenuse is equal to the sum of the squares of the legs, so:
c² = a² + b²
In this case, c = 10, a = 8 and b = 4,
so 8² + 4² = 64 + 16 = 80 ≠ 10²
That is it does not follows the theorem. Therefore, 4, 8 and 10 cannot be the sides of a right triangle.
To know more on right triangles
https://brainly.com/question/2254532
#SPJ4
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.
What is a ratio?A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.
What does the ratio 5:73 mean?5 : This is the number of baseball players who are in 8th-grade
73: This is the total of players. You get this number if you add all the numbers given.
Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".
Learn more about athletes in: https://brainly.com/question/17404705
#SPJ1
Show youR WORK please send. A photo it could help
Answer:
Step-by-step explanation:
1 ft= 12 inches
So 5ft = 60 Inches
4= 0.3
Thus, Its 60.3
45. Sliding Down a Hill
Ojemba is sitting on a sled on the side of
a hill inclined at 60°. The combined weight of Ojemba and the
sled is 160 pounds. What is the magnitude of the force required
for Mandisa to keep the sled from sliding down the hill?
If Ojemba is sitting on a sled on the side of a hill inclined at 60° and weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N .
the inclination angle of the the side of the hill is = 60° ;
the compound mass of Ojemba and Sled is = 160 pounds ,
On conversion we get the mass in Kg is = 72.57 Kg .
the acceleration due to gravity is , [tex]g = 9.8 m/s^{2}[/tex] ;
The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;
[tex]F = mgSin\theta[/tex] , Substituting the values ,
we get ;
[tex]F = 72.57\times 9.8\times Sin(30\textdegree)[/tex]
[tex]F = 72.57\times 9.8\times \frac{1}{2}[/tex] ;
So , [tex]F = 355.59 N[/tex] .
The required magnitude of the force is 355.59 N .
Learn more about Force here
https://brainly.com/question/29006132
#SPJ4
What is the degree of 2 polynomial?
A polynomial with a degree of two is referred to as a quadratic polynomial.
What is a quadratic polynomial?When the highest power of a variable term in a polynomial expression equals 2, the term is considered a quadratic polynomial. The exponent of a polynomial is all that is considered when determining its degree. It does not account for the power of a coefficient or constant term.
When a quadratic polynomial is equated to 0, it generates a quadratic equation or a quadratic function. The solutions to a quadratic equation are known as its roots or zeros.
A quadratic polynomial is a second-degree polynomial with the highest degree term having the value 2 as its coefficient. A quadratic equation is written in its general form as ax² + bx + c = 0.
Learn more about quadratic polynomial
https://brainly.com/question/17489661
#SPJ4
In ΔSTU, = 670 inche, u = 630 inche and ∠U=67°. Find all poible value of ∠S, to the nearet degree
The measure of ∠S is 59.4° for trignometric identities
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
ΔSTU:
s = 50 inches
t = 58 inches
u = 630 inches
Applying the cosines rule on ΔSTU.
s² = t² + u² - 2 x t x u x cos S
cos S = (t² + u² - s²) / 2tu
cos S = (58² + 27² - 50²) / (2 x 58 x 27)
cos S = (3364 + 729 - 2500) / 3132
cos S = 0.5086.
∠S = (0.5086)
∠S = 59.4°
Thus,
∠s angle value is 59.4°.
Learn more about trigonometric identities here:
brainly.com/question/14746686
#SPJ4
Solve equations - two sides
(135a)
Solve
2x - 7=7x +5
Answer:
x=-12/5
Step-by-step explanation:
2x-7=7x+5
2x-7x=5-(-7)
-5x=5+7
x=12/-5
x=-12/5
Nolan is a waiter at a restaurant. Each day he works, Nolan will make a guaranteed wage of $25, however, the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on. How much would Nolan expect to earn in a day on which he waits on 12 tables? How much would Nolan expect to make in a day when waiting on tt tables?
Nolan would expect to earn $157 in a day when he waits in 12 tables.
Now, According to the question:
We have the following information:
Each day Nolan works, Nolan will make a guaranteed wage of $25, however the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on.
Now, for waiting on 12 tables, he will get the fixed amount of 25 dollars and the amount for 12 tables.
So, the total amount will be:
25+11 × 12
$157
Hence, Nolan would expect to earn $157 in a day when he waits in 12 tables.
Learn more about expected earning at:
https://brainly.com/question/29252733
#SPJ4
What is the height of the triangle 12 units?
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
what is triangle ?
A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
Given, side length, a = 12 units.
the height of equilateral triangle, h = (a√3)/2.
Substituting the value of 'a',
h = (12√3)/2 = 6√3 =
10.39 units.
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ4
How do you determine area?
Answer:
You multiply one side and then the other. Basically doing hxw
6. Jenna wants to hang outdoor stringed lights on her house along the roof line
and horizontally across, connecting the ends of the roof line to create a triangle.
What is the approximate length, in feet, of lights that she needs to create one
triangle?
A. 48
B. 64
C. 80
D. 98
The approximate length, in feet, of lights that she needs to create one triangle is 64
This is an approximate estimate as the exact length would depend on the specific measurements of the roof line. However, if the roof line is a typical house roof and the string lights are hung horizontally across to connect the ends of the roof line, creating a triangle, the approximate length of lights needed would be the hypotenuse of the triangle (the longest side) which is equal to the square root of (leg 1^2 + leg 2^2).
A typical house roof is approximately 40 feet wide and 20 feet tall, which creates a right triangle with legs of 40 and 20. The hypotenuse of this triangle (the length of lights needed) would be approximately 64 feet (the square root of (40^2 + 20^2) = 64).
Learn more about geometry and measuring lengths here: https://brainly.com/question/1578168
#SPJ4
HELP!!! I WILL GIVE YOU 24 POINTS!!!THINK SMaRTER| Sense or Nonsense? . Emilio and Julia used different ways to find ‡ + 4. Emilio used a rodel to find the quotient. Julia used a related multiplication equation to find the quotient. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Answer:
24
Step-by-step explanation:
24 it's could be ok. I think 24 is good.
Answer: I think it's nonsense??? Not quite sure...
Step-by-step explanation:
Solve the answer please
Answer:
A
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
140° is an exterior angle of the triangle , then
∠ B + 90° = 140° ( subtract 90° from both sides )
∠ B = 50°
∠ ACB and ∠ DCB are a linear pair and sum to 180° , that is
∠ ACB + 140° = 180° ( subtract 140° from both sides )
∠ ACB = 40°
How much money should be put into a savings account now that earns 6.0% a year compounded weekly if you want to have 70000 in 15 years?
If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.
How does compound interest work?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.
Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.
A = P(1 +r/n)^(nt)
where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, we have ...
70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)
P = 70000/2.4583 = 28474.96
You would need to deposit 28474.96 in order to have 70000 in 15 years.
To know more about compound interest visit :-
https://brainly.com/question/14295570
#SPJ1
300 grams of type a raisin bran is mixed with 500 grams of type b raisin brad to produce a mixture which is 11% raisins. Type A raisin bran has twice as many raisins per kilogram as type b. What percentage of raisins are each type of raisin bran?
The blend contains 16% of type A and 8% of type B.
What is meant by percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Let p be the percentage of type b used for the mix
2p be the percentage of type a used for the mix
2p × 300 + p × 500 = 0.11 × 800
simplifying the above equation, we get
p = 0.08 or 8%
Substitute the values in the above equation
2p = 2 × 0.08 = 0.16 or 16%
16 % of type a and 8 % of type b exists utilized for the mix.
To learn more about percentage refer to:
https://brainly.com/question/24877689
#SPJ1
The required percentage of raisins are each type of raisin bran are 16% and 8%.
What is meant by percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Let p be the percentage of type b used for the mix
2p be the percentage of type a used for the mix
2p × 300 + p × 500 = 0.11 × 800
simplifying the above equation, we get
p = 0.08 or 8%
Substitute the values in the above equation
2p = 2 × 0.08 = 0.16 or 16%
16 % of type a and 8 % of type b exists utilized for the mix.
To learn more about percentage refer to:
brainly.com/question/24877689
#SPJ1
a ski area claims that its lifts can move 47000 people per hour. if the average lift carries people about 200m (vertically) higher, estimate the maximum total power needed?
The peak is located at R=1 according to a power curve analysis. To put it another way, the load and source resistance must match.
At what point does maximum total power occur?The ski area's name needs to be changed first. Squaw is not a kind way to refer to a woman. It is an expression that refers to female genitalia. (a decent slang equivalent in English begins with "c" and rhymes with "runt") During my time as a teacher in an Indian school, I learned this in a very embarrassing manner.
If we suppose that each person weighs roughly 70 kilograms (154 lbs) on Earth, then the power required to simply raise the people is P = W/t, and since W = mgh in this situation, P = W/t = mgh/t = (47,000 people)(70 kg/person).
(2 MW) = (1791222.222 W)(9.8 N/kg)(200 m)/(3600 s).
The complete question is:
Squaw Valley ski area in California claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.
To learn more about maximum total power refer to:
https://brainly.com/question/14837464
#SPJ4
Amy operates a coffee kiosk and is blending her special house coffee. She is mixing Kenya beans that cost $9. 00 per pound with Colombia
beans that cost $7. 50 per pound to create a 30 pound blend that sells for $8. 50 per pound. How many pounds of Kenya beans and how many
pounds of Colombia beans does Amy need to use to create her blend?
So Amy needs to use 2 pounds of Colombia beans and 32 pounds of Kenya beans to create her blend.
Define Unitary Method.The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What is direct and indirect variation in the unitary method?We are aware that an inverse variation or indirect variation occurs when two values are coupled in a way that a rise in one generates a corresponding reduction in the other, and vice versa.
Let x be the number of pounds of Kenya beans and y be the number of pounds of Colombia beans. We know that:
x + y = 30 (since the blend is 30 pounds)
We also know that the blend sells for $8.50 per pound, so the total cost of the blend is:
8.50(x + y) = 8.50(30) = $255
We know that the cost of the Kenya beans is $9.00 per pound and the cost of the Colombia beans is $7.50 per pound, so the total cost of the Kenya beans is:
9.00x and the total cost of the Colombia beans is 7.50y
We can set up the following equation:
9x + 7.5y = 255
We have 2 equations and 2 variables, we can solve this system of equation by different methods, one of them is substitution:
x + y = 30
9x + 7.5y = 255
We can substitute the first equation into the second equation
9(x + y) + 7.5y = 255
9(30) + 7.5y = 255
270 + 7.5y = 255
7.5y = -15
y = -2
So Amy needs to use 2 pounds of Colombia beans. We can substitute that value into the first equation to find the amount of Kenya beans:
x + (-2) = 30
x = 32
So Amy needs to use 32 pounds of Kenya beans.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ4
Please solve area of figure
Formula and radius of figure in the picture
Area of circle and formula and radius of circle is 9 pi ( x y ^3 )^3.
How can you calculate area using pi and radius?A circle's area is equal to pi times the radius squared (A = r2).
Pi times the radius r squared equals the area of a circle.
π ⋅ ( r a d i u s)2
In the formula for the area of a circle, substitute the value of the radius r =3. 3.14 is about how big a number pi is.
pi * 3^2
Raise 3 to the power of 2 to arrive at 9.
pi * 9
9 must be moved to the left of. 9 pi ( x y ^3 )^3.
Area of circle and formula and radius of circle is 9 pi ( x y ^3 )^3.
To learn more about radius refer to:
https://brainly.com/question/24375372
#SPJ1
What are the 4 steps to solve by elimination?
Elimination is a very easy method when it comes to solving simultaneous equations.
First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.
The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given
Now take one of the equations and multiply it by -1.
Add the equations up to eliminate the variable and derive the other variable(s)
To learn more about elimination visit
https://brainly.com/question/14619835
#SPJ4
f(x)=3^√x-1
Find f(27) and f(-343)
need to find cube root
On solving the provided question, we can say that - the value of the cube root is 19683 = 27
what is cube root?In mathematics, y3 = x since the cube root of a number x equals a number y. Each non-zero real integer has precisely one real cube root, one set of complex conjugate cube roots, and three different complex cube roots. When a number is multiplied three times, the result is the cube root of that number. Three cube roots, the final cube root, is the symbol for the cube root. The opposite of cubing an integer is finding the cube root of that number. Prime factorization is a fairly straightforward technique that may be used to get a number's cube root. The sign stands for a cube root.
here,
we have f(27)
cube will be [tex]( 27 )^3[/tex] = 19683
and f(-343) = -7
To know more about cube root visit:
https://brainly.com/question/30038389
#SPJ1