Answer:
Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.
For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.
Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.
Draw squares on each of these sides.These squares have areas p²,b² and h².
For any right angled triangle with sides of length p,b and h;
[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]
[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
From (i); p²=h²-b²
[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
Similarly,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
Step-by-step explanation:
[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]
Marc Gasol scored 18 points on Monday, 29 points on Wednesday, and 8 points on Saturday. What
was his average number of points per game for those three nights?
Answer: 18.33 ppg
Step-by-step explanation:
He played three games
18+29+8=55
55/3=18.33
Lydia is making tickets for her class
concert. Each ticket measures 4cm by
3cm. What is the maximum number of
the tickets that can be cut off a sheet of
bristol board measuring 48cm by 36cm
A group of 25 classmates visits an amusement park. When they arrive, 3/5 of the students want to ride the fastest roller coaster first. How many students is this?
Find 3/5th of the classmates
3/5 of 253/5(25)3(5)15studentsThey are 15 students
Answer:
15 students
Step-by-step explanation:
To find 3/5 of 25 students, simply swap the word "of" for the multiplication symbol and calculate:
[tex]\begin{aligned}\sf \dfrac{3}{5}\:of\:25\:students & = \sf \dfrac{3}{5} \times 25\\\\& = \sf \dfrac{3 \times 25}{5}\\\\& = \sf \dfrac{75}{5}\\\\& = \sf 15\:students\end{aligned}[/tex]
The function fis defined as follows.
f(x)=2x²+3
If the graph of fis translated vertically downward by 6 units, it becomes the graph of a function g.
Find the expression for g(x).
The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3
How to Interpret Graph Translations?
We are given the function;
f(x) = 2x² + 3
Now, when we translate a function f(x) downwards, the new function becomes;
g(x) = f(x) - a
where a is the amount of units by which the graph was translated.
Thus for translation of 6 units vertically downwards;
g(x) = 2x² + 3 - 6
g(x) = 2x² - 3
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what is linear relationship
Step-by-step explanation:
a linear relationship is simply a straight line relationship.
any equation that can be pot in the form of y = mx + b is a linear relationship.
linear = straight
hope this helps
HELP ILL GIVE MONEY
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 27 liters per minute. There are 700 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let I represent the total number of minutes that water has been added. Write an equation
relating W to T. Then use this equation to find the total amount of water after 17 minutes.
Equation:__
Total amount of water after 17 minutes: __liters
Answer: Equation: 27t +700 = w
Total amount of water after 17 minutes: 1159 L
Step-by-step explanation:
Equation: 27t +700 = w
let t = minutes
let w = total amount of water in pond (liters)
Total amount of water after 17 minutes: 1159 L
t = 17
therefore
27(17) +700 = 1159
Answer:
425 l
Step-by-step explanation:
The area of the base of a cylinder is 36 square inches and its height is 10 inches. A cone has the same area
for its base and the same height. What is the volume of the cone?
The volume of the cone is
in³.
I need help:((
URGRENNTTT PLSS HELPP 50 POINTSS!!!!! Students were asked to simplify the expression cotangent theta plus tangent theta over cotangent theta. Two students' work is given.
Student A
Step 1: cotangent theta over cotangent theta plus tangent theta over cotangent theta
Step 2: 1 plus tangent theta over the quantity 1 over tangent theta end quantity
Step 3: 1 + tan2 θ
Step 4: sec2 θ Student B
Step 1: the quantity 1 over tangent theta end quantity plus tangent theta over the quantity cotangent theta
Step 2: the quantity 1 plus tangent squared theta end quantity over tangent theta all over cotangent theta
Step 3: secant squared theta over tangent squared theta
Step 4: csc2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 3: 1 + tan²(Ф)Step 4: sec²(Ф)Student 2:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]Step 3: sec²(Ф)/tan²(Ф)Step 4: csc²(Ф)As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
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a fridge costs €336 after a price increase of 40%. what was the original price
the original cost is "x", which is the 100% of the original price, and we also know that €336 is its price increased by 40%, namely 100% + 40% = 140%, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 336& 140 \end{array} \implies \cfrac{x}{336}~~=~~\cfrac{100}{140} \\\\\\ \cfrac{x}{336}=\cfrac{5}{7}\implies 7x=1680\implies x=\cfrac{1680}{7}\implies x=240[/tex]
A play has tickets available for 8 orchestra seats and 12 balcony seats. The next person to buy a ticket will be randomly assigned to one of those seats. What is the probability that the next person will be assigned an orchestra seats?
The probability that the next person will be assigned an orchestra seats is 2/5.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, Available Orchestra seats = 8
Balcony seats = 12
Total available seats = 12 + 8 = 20
Probability = Favorable Outcome / Total Outcome
Probability of getting orchestra ticket = 8/20
= 2/5
Thus, the probability that the next person will be assigned an orchestra seats is 2/5.
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Bob wants to take his wife, Mary, to Europe in three years to commemorate their 40th wedding anniversary. He recently received a $25,000 inheritance from an uncle, which he plans to put towards the trip. Bill calculates that the trip will cost $30,000 and that he can earn 6% yearly compound interest on his investment. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, F (From the tables provided, select the appropriate factor(s).)
To calculate the future value, fill out the table below. Will he be able to pay for the trip with the money he has saved up? (Round up your totals to the nearest whole dollar amount.)
Answer:
10%
Explanation:
Use future value formula
Future Value = Present Value ((1+r)^n)
26,600 = 20,000 ((1+r)^3
26,600/20,000 = (1+r)^3
1.33 = (1+r)^3
1.33^1/3 = 1+r
1.0997 = 1+r
1.0997 - 1 = r
r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)
(pls give brainliest)
Question 14 of 14
Rachel buys
1
gallon of milk. Her sister Abby uses
1
1
2
quarts of the milk in a recipe. Then her mother uses
3
cups of the milk in a different recipe.
Select all of the true statements below.
A.
Rachel's mother uses more milk than her sister Abby uses.
B.
There are
56
fluid ounces of milk left.
C.
There are
9
cups of milk left.
D.
There is more than
1
4
gallon of milk left.
E.
There is more than
1
2
gallon of milk left.
The true statements are:
There are 56 fluid ounces of milk left.
There is more than 1 / 4 gallon of milk left.
What are the true statements?
The first step is to convert gallons to cups.
1 cup = 16 gallons
Then, convert quarts to cups
1 quart = 4 cups
1 1/2 x 4
3/2 x 4 = 6 cups
Total cups left = 16 - 6 - 3 = 7 cups
1 cup = 8 ounces
Total milk left in ounces: 8 x 7 = 56 ounces
1 cup = 1/16 gallons
Total milk left in gallons: 1 / 16 x 7 = 7/16 gallons
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Find the area of the yellow region.
Round to the nearest tenth.
DCH
6 in
-6 in-
Area = [?] in²
Answer:
A = 3.9 in²
Step-by-step explanation:
To find the area of the shaded region, you need to find the (1) area of the entire square, then (2) find the area of the 1/2 circles, then (3) subtract them and divide by 2. Because the 1/2 circles are identical, you can combine them and just use the circle area equation.
Area of the Square:
A = l x w
A = 6 in x 6 in
A = 36 in²
Area of Combined 1/2 Circles:
A = πr²
r = 6 in / 2
r = 3 in
A = π(3)²
A = 9π -----> 28.3 in²
Area of Shaded Region:
A = (Area Square - Area Circle) / 2
A = (36 in² - 28.3 in²) / 2
A = 7.7 in² / 2
A = 3.9 in²
find the area and the circumference of a circle with the diameter 6 yards
Answer:
area = 28.27
circumference = 18.85
Step-by-step explanation:
Using the formulas for area,
A = πr^2
d = 2r
Solving for area,
A = 1/4 πd^2 = 1/4 × π × 6^2 ≈ 28.27yd²
Using the formulas for circumference,
C = 2 πr
d = 2r
Solving for circumference,
C = πd = π × 6 ≈ 18.85yd
if for 5 pounds of beans it cost 4 dollars than how much money is needed for 50 pounds of beans
Answer:
40 dollars
Step-by-step explanation:
We can use a ratio to solve the problem
5 pounds 50 pounds
---------------- = -----------------
4 dollars x dollars
Using cross products
5 * x = 4 * 50
5x = 200
Divide by 5
5x/5 = 200/5
x = 40
40 dollars
Step-by-step explanation:
[tex]\sf 5 \: pounds \longrightarrow 4 \: dollars[/tex]
[tex]\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars[/tex]
[tex]\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars[/tex]
[tex]\sf \longmapsto 40 \: dollars[/tex]
3. Which test do you stretch your muscles by reaching for your toes?
Answer:
I think it's sit and reach sorry if I'm wrong
A petri dish contains cells of a certain strain of bacteria. Each bacterial cell in the dish divides in half approximately every 6 minutes. The curve of best fit that models the number of bacterial cells in the dish is given by the equation f(x) = 4.2 • 1.1x, where x represents the number of minutes and y represents the number of cells. Approximately how many bacterial cells will be in the petri dish after 30 minutes?
The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the number of cells after x minutes, hence:
y = 4.2(1.1)ˣ
After 30 minutes:
y = 4.2(1.1)³⁰ = 73.3
The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3
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Every day carla spends 2/3 of a hour cleaning her room. How long will she spend cleaning her room in 4 days
Answer:
see photo
Step-by-step explanation:
see photo for answer
sometimes when there is a fraction in the question it's a good idea to keep things as fractions and not decimals
please help me Fast!!!!! slove the question in picture
Step-by-step explanation:
A)
Class Width=8
Median= 28.1
Modal Class= 20.5-28.5
B)
Mean=31.34
Solve f (9) for f(x) = -13 + 2x
ƒ(9) = [?]
The value of f(9) for the given function is 5
Evaluating the value of a functionFrom the question, we are to determine the value of f(9)
The given function is
f(x) = -13 + 2x
To determine f(9), we will put x = 9 in the given function
That is,
f(x) = -13 + 2x becomes
f(9) = -13 + 2(9)
f(9) = -13 + 18
f(9) = 5
Hence, the value of f(9) for the given function is 5
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Solve the system of equations 4x + 3y = 3 and y = 2x + 6.
O The solution is (-0,3).
O The solution is (-1,5).
O The solution is (-2,3).
O There are no solutions.
Step-by-step explanation:
4x + 3y = 3
y = 2x + 6 ->
2x - y = -6
let's multiply the modified second equation by 3 and add both equations :
4x + 3y = 3
6x - 3y = -18
--------------------
10x + 0 = -15
x = -1.5
4x + 3y = 3
4×-1.5 + 3y = 3
-6 + 3y = 3
3y = 9
y = 3
and so the solution is (-1.5, 3).
which is not in the list of your answer options.
so, something must have been wrong in your problem definition.
either you changed something in the 2 equations, or subverting is missing in the answer options, or you even mixed up problem and answer options of 2 different questions.
but I also checked by using the numbers in the 2 equations, but (-1.5, 3) is indeed the correct solution for the given 2 equations.
PLEASE HELP ME I HAVE A F IN MATH
Answer:
pattern 0 i believe would be just the 4 red squares
Step-by-step explanation:
its adding a blue square on the 3 sides and adding enough green squares to cover the middle, or however many blue squares there are on the top and side, multiply them together. like in figure 1 i noticed that 1×1=1 so that's how many green squares there are. Figure 2: 2 blue× 2 blue= 4 green. if that makes sense. Figure 3: 3×3=9 i dont know if that made sense. but that's what i could think of!!
PLEASE I NEED THE ANSWER (JUST THE ANSWER)
Select the graph of y=cot x.
Answer:Suppose y= cot x is our parent function then remember general rules of transformation.1) y= -f(x), reflects the graph of f(x) across x-axis.2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.Now, apply these rules to y= -4 cot(x)the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.
Which pair of angles is an example of supplementary angles?
Answer:
Angle1 and Angle2 are supplementary.
Step-by-step explanation:
There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.
Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:
1&2
2&4
3&4
1&3
5&6
6&8
7&8
5&7
Since angles don't have to touch in order to be supplementary there are many more pairs.
The price of a new shirt was slashed from N1 500 to N1 250. Find the percentage decrease in the price of the shirt.
Answer:
The percent decrease is 16.67%.
Step-by-step explanation:
percent change = (new price - old price)/(old price) × 100%
percent change = (N1250 - N1500)/(N1500) × 100%
percent change = -250/1500 × 100%
percent change = -16.67%
A negative percent change is a percent decrease.
The percent decrease is 16.67%.
Solve for x.
Your answer must be simplified.
−x<−29
Step-by-step explanation:
if you made no typo or left things out, this is very simple :
-x < -29
x > 29
remember that when you multiply an inequality by -1 (or any negative value), the orientation of the inequality changes.
Are these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 > > > > 1. Rational 2. Irrational please answer quickly
Answer:
hope you can understand
Solve the equation using the Square Root Property
2(x+1)^2=50
SHOW ALL YOUR STEPS/WORK
A football stadium holds 17,700 seats. The lower level has 300 seats less than 4 times the number of seats in the upper level. The middle level has 500 more seats than twice the number of seats in the upper level. Let x represent the seats in the upper level. Which equation can be used to find the number of seats in the upper level?
7 x + 200 = 17,700
6 x + 200 = 17,700
7 x minus 200 = 17,700
6 x minus 200 = 17,700
Answer:
6x + 200 = 17,000
Step-by-step explanation:
Lower level = 4x - 300
Mid level = 2x + 500
Combine the two equations to find the number of seats in the upper level
(2x + 500) × (4x - 300) = 17,000
Combine like terms
4x × 2x + 500 - 300 = 17,000
6x + 200 = 17,000