Answer:
Hi! I think you are referring to the Pythagorean Theorem.
Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.
The formula is a squared + b squared = c squared
If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:
3 squared + 4 squared = x squared
(Let x = the longer side)
3 squared = 9
4 squared = 16
9+16 = x squared
25 = x squared
x = 5
So there you go, that's the Pythagorean theorem.
Let me know if this helped!
Answer:
a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Step-by-step explanation:
The three dot plots together are the scores of teenagers in three samples from this population. Which of the three samples is most representative of the population? Explain how you know.
The sample that is most representative of the population is: sample 3.
What is a Representative Sample of a Population?A representative sample of a population can be defined as a subset of that particular population that reflects almost or same characteristics of the main population such as the shape, center, and spread.
From the three dot plots given, the one that has almost same pattern and characteristics is sample 3 considering it has almost similar spread and shape.
Thus, the most representative sample is: sample 3.
Learn more about the representative sample of a population on:
https://brainly.com/question/27829028
#SPJ1
find the solution set. 7x^2-5x-2=0
Answer:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
, we get that
x
=
−
2
,
0.6
Explanation:
Rearrange the equation so that it becomes:
5
x
2
+
7
x
−
6
=
0
The quadratic formula is:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
In our equation above,
a
=
5
b
=
7
c
=
−
6
Plugging these values into the quadratic equation gives:
x
=
−
7
±
√
7
2
−
4
(
5
)
(
−
6
)
2
(
5
)
x
=
−
7
±
√
49
+
120
10
x
=
−
7
±
√
169
10
x
=
−
7
±
13
10
x
=
−
2
,
0.6
vertex of y = −2(x−4)2 + 3
and identify it as a minimum or a maximum.
An equation is formed of two equal expressions. The vertex of the equation y=-2(x-4)²+3 will lie at (4,3).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
If we plot the graph of y=-2(x-4)²+3, then the vertex of the graph will lie at (4,3).
Hence, the vertex of the equation y=-2(x-4)²+3 will lie at (4,3).
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
What is the solution to the trigonometric inequality sin^2(x) > cos(x) over the interval 0<= x <= 2pi radians?
The solutions to the trigonometric inequality in the interval is given by:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex], or [tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
What is the trigonometric inequality?It is given by:
[tex]\sin^{2}{x} > \cos{x}[/tex]
We have the following identity:
[tex]\sin^2{x} = 2\sin{x}\cos{x}[/tex]
Hence:
[tex]2\sin{x}\cos{x} > \cos{x}[/tex]
[tex]2\sin{x} > 1[/tex]
[tex]\sin{x} > \frac{1}{2}[/tex]
Between the first and second quadrant, the solution is:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex]
Between the third and fourth quadrants, the solution is:
[tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
More can be learned about trigonometric equations at https://brainly.com/question/24680641
#SPJ1
Slopes of parallel \perpendicular lines
Hello, the answer should be [tex]m=\frac{6}{5}= 1,2[/tex].
First, let's edit the given function as [tex]y[/tex] parameter leave alone.
[tex]15x+18y=270\\\\18y=270-15x\\\\y=\frac{270-15x}{18}\\ \\y=\frac{270}{18}-\frac{15x}{18}[/tex]
IMPORTANT!If the given equation looks like;
[tex]y=f(x)\\\\y=ax+b[/tex]
then, the slope of the equation is the coefficient of [tex]x[/tex] parameter ([tex]a[/tex])
The slope(m);
[tex]m=\frac{-15}{18}=\frac{-5}{6}[/tex]
The product of the slopes of two perpendicular lines must be [tex]-1[/tex]. By that way, the slope of a line perpendicular to the given line is below:
[tex]m_{expected}=\frac{-1}{m_{given}} \\\\m_{expected}=\frac{-1}{\frac{-5}{6} }=\frac{6}{5}[/tex]
Good luck. If you have any questions, then feel free to ask in comments!
Which graph represents f(x)= | x+3|
The graph of the function looks like V. And the vertex of the function will be at (-3, 0).
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = |x + 3|
Then the graph of the function looks like V. And the vertex of the function will be at (-3, 0).
The graph of the function is given below.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
In a school,The ratio of the number of boys to the number of girls is 8:5. One quarter of the boys and 1/15 of the girls wear glasses. When another 48 students who wear glasses join the school,the total number of students becomes 216. How many boys wore glasses at first?
Answer:
hi look here https://www.louisianabelieves.com/docs/default-source/assessment/grade-6-answer-key.pdf?sfvrsn=293b981f_2
Step-by-step explanation:
How many hours must Miguel worked to receive $10,000 in total pay?
Using the linear equation, Miguel must work for 160 hours to receive $10,000 in total pay
Complete Question:Miguel works as a technician in a company. If his hourly rate and flat pay are $50 and $2000, how many hours must Miguel worked to receive $10,000 in total pay?
How to determine the number of hours?Let the number of hours be x and the total pay be y.
The equation that represents the total pay is represented as:
y = Rate * x + Base pay
From the question, we have:
Base pay = 2000
rate = 50.
So, we have:
10000 = 50 * x + 2000
Subtract 2000 from both sides
8000 = 50x
Divide both sides by 50
x = 160
Hence, Miguel must work for 160 hours
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
Find slope and intercept of the line 3x - 2y - 7 = 0
The slope and intercept of the line 3x - 2y - 7 = 0 are -1.5 and -3.5 respectively
How to determine the slope and the intercept?The equation of the line is given as:
3x- 2y - 7 = 0
Add 7 to both sides
3x - 2y = 7
Subtract 3x from both sides
-2y = -3x + 7
Divide both sides by -2
y = -1.5x -3.5
A linear equation is represented as:
y = mx + c
Where m represents slope and c represents the intercept
By comparison;
m = -1.5 and c = -3.5
Hence, the slope and intercept of the line 3x - 2y - 7 = 0 are -1.5 and -3.5 respectively
Read more about linear equation at:
https://brainly.com/question/14323743
#SPJ1
if 3\2 =x\12 what is the value
[tex]\frac{3}{2} =\frac{x}{12}[/tex]
---Cross multiply
2x = 36
---Divide both sides by 2
x = 18
Hope this helps!
What is the value of
(1/8)^-1/3
PLEASE I NEED THE AWNSER QUICK PLEASE AND TY
Answer:
2.66666666667
Step-by-step explanation:
(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.
what's the answer
1. The function below shows the weekly earnings of Alice from her job last summer.
a) We kindly invite to check the image attached below to see a detailed graph of the piecewise function.
b) The piecewise function is continuous.
How to understand a piecewise functionA piecewise function is a conditional combination of two or more functions, whose expression depends on which value of the domain is the function evaluated at.
a) The piecewise function described in the question is plotted on a graphing tool (i.e. Desmos), whose result is presented in the image attached below.
b) A function is continuous if and only if there is one value from range for every value of domain. The piecewise function is continuous as linear functions are continuous and the two functions of the conditional combination have the same value for x = 30.
To learn more on piecewise functions: https://brainly.com/question/12561612
#SPJ1
Dean Field is a bookkeeper for a retail shop. He is super excited about his upcoming two-week vacation to Hawaii. His flight leaves to Honolulu at 7pm on Friday. At 4:45pm on Friday he realizes the company’s trial balance is a mess and it does not balance. He places random numbers in the General Ledger system to make it balance and leaves the office to catch his flight. He knows he can correct the situation when he returns from his vacation. What are your thoughts about this case?
The fact that Dean Field places random numbers in the general ledger system to make it balance and leaves the office to catch his flight is wrong.
What is a ledger?It should be noted that a ledger simply means a record of the balance of each of the accounts of a business.
In this case, when he realizes the company’s trial balance is a mess and it does not balance, he should have waited and ensured that he re calculated it and made it balance.
Learn more about ledgers on:
brainly.com/question/1436327
#SPJ1
write down the equation for the following expression and then solve it.
The product of 3 and 4 less than a number is 12.
Answer:
x = 24
Step-by-step explanation:
x - (3 · 4) = 12
x - 12 = 12
+ 12 + 12
x = 24
If I have $1,050 dollars, and I want to buy something 6 times for $45 dollars, how much times can I buy it until I run out of money?
Answer:
140
Step-by-step explanation:
here,
You have 1050
now
$1050(45×6)
=140 items
HELP PLSSSSSSSSS WIL GIVE BRAINLEST Nathan needs 10 ounces of lemonade.
He needs to know how much liters that is.
A 16
B 5
C 943
D 0.295735
The volume of 10 ounces of lemonade in litres is 0.295735 litres.
How to convert from ounces to litres?
He needs 10 ounces of lemonade.
To know the volume in litres, we have to convert from ounces to litres.
Therefore,
1 ounces = 0.0295735 litres
10 ounces = ?
cross multiply
volume in litres = 0.0295735 × 10
volume in litres = 0.295735
Therefore, the volume of the lemonade in litres is 0.295735 litres.
learn more on litres here: brainly.com/question/15322533
#SPJ1
A community organization wants to determine area support for the construction of a new skate park in the center of town. The organization decides to survey 500 people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park.
What is the best way to randomly choose these 500 people?
The method that can be used to randomly choose these 500 people is the use of systematic random sampling.
What is random sampling?Random sampling is defined as the method of sampling in which the whole sampling frame is being considered.
In order the survey a community of people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park, both the male and female should be considered.
The systematic random sampling will give the both male and female equal opportunity to the chosen.
Learn more about random sampling here:
https://brainly.com/question/17831271
#SPJ1
1. IDENTIFY THE DIFFERENT PARTS OF THE THERMOMETER 100 20 10 30 AN 000
9.80 x 10^-3 + 1.60 x 10^-4
Answer:
0.00016098
Step-by-step explanation:
First multiply 9.8 by 10^-3 which equals 0.0098
Then add 0.0098 to 1.6 which equals 1.6098
Then multiply 1.6098 by 10^-4 which equals 0.00016098
Therefore, 0.00016098 is your answer
even numbers less than 9
Answer:
2, 4, 6, 8
Step-by-step explanation:
even numbers are numbers that can be equally split in half.
Example:
2 ⇒ 1 - 14 ⇒ 2 - 26 ⇒ 3 - 38 ⇒ 4 - 4what is a conditional statement that correctly and accurately represents the statement all people who vote in US elections must be 18 or older
A conditional statement to demonstrate the situation presented would be: If a person can vote -> Then they are over 18 years old. An alternative to this would be: If a person is 18 years or older -> Then they can vote in the United States elections.
What is a conditional statement?A conditional statement is a type of structure to express the relationship between two dependent variables. Its structure is as follows:
If P, then Q...
According to the above, two conditional statements about voting in the United States would be:
If a person can vote -> Then he is over 18 years old. If a person is 18 years old or older -> Then they can vote in the United States elections.Learn more about conditional statement in: https://brainly.com/question/18152035
#SPJ1
Drag the tiles to the correct boxes to complete the pairs.
Match the systems of equations with their solution sets.
y + 12 = 1² + s
s+y = 3
y - 17 = 12 -9r
- + y = 1
Solution Set
(2,3) and (8,9)
(-2,3) and (7-6)
(-2,5) and (3,-5)
(-5,8) and (3,0)
y-15 = -12 + 4s
=+y=1
y + 5 = 1²-3r
2s + y = 1
Linear-Quadratic System of Equations
Answer:
y+12=1+s = (-5,8)(3,0)
y-17=12-9r = (2,3)(8,9)
y-15=-12+4x = (-2,3)(7,-6)
y+5=x-3x = (-2,5)(3,-5)
A grocery wants to make two kinds of coffee. One consoles for $1.40 pound, and the other cells for $2.95 a pound. He wants to makes a total of 21 pounds and sell it for $2.60 per pound. How many pounds of each kind should he use in the new mix? (round off the answers to the nearest hundredth)
Step-by-step explanation:
a lot of typos in the problem description.
I assume the price of the mix is 1:1 related to the prices of the individual types of coffee.
so, from what I understood we can define
x = pounds of the first type of coffee.
y = pounds of the second type of coffee.
x + y = 21 pounds
1.4x + 2.95y = 2.6(x + y) = 2.6×21 = $54.60
in the second equation we have to bring the given "$2.60 per pound" to the total price, which is $2.60 times the total amount of pounds (which is 21).
from the first equation we get
x = 21 - y
and that we use in the second equation
1.4×(21 - y) + 2.95y = 54.6
29.4 - 1.4y + 2.95y = 54.6
1.55y = 25.2
y = 25.2 / 1.55 = 16.25806452... ≈ 16.26 pounds
x = 21 - y = 4.741935484... ≈ 4.74 pounds
so, he should mix 4.74 pounds of the first (cheaper) type and 16.26 pounds of the second (expensive) type.
Please answer correctly!
Answer:
I. Evaluate the largest angle when x = 15
Explanation:
First, solve for x:
x + 8x + x + 30 = 180
10x = 180 - 30
10x = 150
x = 15
Here in the question, his friend wants to find the largest angle in triangle.
So, input x = 15 in the largest angle.
Which is, 8x = 8(15) = 120° <--- largest angle in the triangle.
A) 16/12
B) 12/20
C) 12/16
D) 16/20
Answer:
COA opposite/ adjacent
16/12
A
Find the value of cos (2pie/3)
Answer:
-1/2 or - 0.5
Step-by-step explanation:
[tex]cos (\frac{2\pi }{3}) = cos 120^{o} = -\frac{1}{2}[/tex]
√17 is a number between
Y
5
What is the equation of the graphed line written in
standard form?
4
3
2
1
O 2x + 3y = -6
O 2x + 3y = 6
O y=-{x-2
O y=x-2
5-4-3-2 12
1 2 3 4 5
x
2
-3
The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex] and for line 2x + 3y = 6 will be,[tex]\rm y = \frac{-2}{3}x+2[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
a) 2x + 3y = -6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2[/tex]
To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.
b) 2x + 3y = 6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2[/tex]
Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex]
To learn more, about equations, refer;
https://brainly.com/question/10413253
#SPJ1
What is the equation of the graphed line written in standard form?
2x + 3y = -6, 2x + 3y = 6
Summary:
a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.
b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.
please help will give branliest
This proof was correctly started by both eric and maggie.
The next step in the proof is to set the right side of the equations equal.
This would be done by the transitive property of equality.
What is a Mathematical Proof?This refers to the use of inference to make an argument to show the logical conclusion to a set of assumptions.
Based on the given diagram that shows Triangle XYZ and the mathematical proof that both Eric and Maggie are trying to prove, they both give the correct proof and the next step was to make the right side of the equations equal.
Read more about the law of sines here:
https://brainly.com/question/2807639
#SPJ1
Answer:
1: both
2: set the right side
3: transitive property
Step-by-step explanation:
got it right on plato :)
39. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 5 exterior angles and equate to 360
5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is
23x + 15 = 360 ( subtract 15 from both sides )
23x = 345 ( divide both sides by 23 )
x = 15