The Pythagorean Theorem indicates the following relationship between the squares and triangles.
Part A
The relationship between the areas of the squares is that the area of the large square is the sum of the areas of the other two squares.Part E
The point that the length c on one triangle is equal to the length n on the other triangle and that the other two sides of both triangles are congruent, the two triangles are congruent by SSS congruency rule.What is the Pythagorean Theorem?Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
Part A
The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached
The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²
Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.
Part E
The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n
It was shown that c² = n²
Therefore;
c = n
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4. A farmer is taking a break
to watch a movie that is 25
minutes long. He doesn't have
time to watch the whole thing
in one day. So he watched 20
minutes the first day and 12
minutes the next day. How
much more of the movie does
he have left to watch?
(jk−1)÷j when j=−4 and k=−0.9
The numerical value of the expression ( jk−1 )÷j when j=−4 and k=−0.9 is -0.65.
What is the numerical value of the given expression?Given the expression in the question;
( jk − 1 ) ÷ jj = -4k = -0.9To determine the numerical value of the expression, plug in the values of j and k and then simplify.
( jk − 1 ) ÷ j
Plug in j = -4 and k = -0.9
( jk − 1 ) ÷ j
( (-4 × -0.9) − 1 ) ÷ (-4)
Simplify
( 3.6 − 1 ) ÷ (-4)
( 2.6 ) ÷ (-4)
-0.65
Therefore, the value of the expression is -0.65.
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PLEASE HELP! WILL GIVE BRAINLIEST!
1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4
2. Using the function table, the test average for science class is after the second test is: 84.
3. f(4) = 79.8
4. g(4) = 80
5. Science class was higher.
What is a Linear Function?The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.
The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79
Write the linear function for science class;
Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1
Slope (m) = -2
Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:
82 = -2(3) + b
82 = -6 + b
82 + 6 = b
88 = b
b = 88
Substitute m = -2 and b = 88 into g(x) = mx + b:
g(x) = -2x + 88
Part 1:
Substitute x = 2 into .f(x) = 0.2x + 79
.f(2) = 0.2(2) + 79
.f(2) = 79.4
Test average for maths class after 2 test is: 79.4
Part 2:
Using the function table, when x = 2, the test average for science class is: 84.
Part 3:
Substitute x = 4 into .f(x) = 0.2x + 79
.f(4) = 0.2(4)+ 79
.f(4) = 79.8
Part 4:
Substitute x = 4 into g(x) = -2x + 88
g(4) = -2(4) + 88
g(x) = 80
Part 5:
Science class had a higher test 4 average of 80.
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Referring to the figure, find the perimeter of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Referring to the Fig. in Question #1, find the area of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Answer:
Perimeter = 18√3 = 18SQR(3)
Area = 27√3 = 27SQR(3)
Step-by-step explanation:
The sides of a regular polygon are congruent.
Therefore, as the triangle is a regular polygon, it is an equilateral triangle since its sides (and interior angles) are congruent.
The interior angles of a triangle sum to 180°. Therefore, each interior angle of the equilateral triangle is 60°.
Therefore, the right triangle formed inside the equilateral triangle by the perpendicular bisectors is a 30-60-90 triangle with hypotenuse of 6 units.
The ratio of the side lengths of a 30-60-90 triangle is b : b√3 : 2b, where:
b = shortest side opposite the 30° angle.b√3 = side opposite the 60° angle.2b = longest side (hypotenuse) is opposite the right angle.As the hypotenuse of the 30-60-90 right triangle is 6 units:
[tex]2b = 6 \implies b=3[/tex]
Therefore, the length of the longest leg of the right triangle is 3√3.
As this is half the length of one side of the equilateral triangle:
[tex]\implies \sf Perimeter = 6 \times 3 \sqrt{3}=18\sqrt{3}\; units[/tex]
Heron's Formula allows us to find the area of a triangle in terms of its side lengths.
Heron's Formula
[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
where:
a, b and c are the side lengths of the triangle.s is half the perimeter.Given:
Each side length = 6√3 unitsHalf perimeter = 9√3 unitsSubstitute these values into the Heron's formula to calculate the area of the equilateral triangle:
[tex]\begin{aligned}\implies \sf Area &= \sf \sqrt{9\sqrt{3}(9\sqrt{3}-6\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(3\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(81\sqrt{3})}\\&=\sf \sqrt{2187}\\&=\sf \sqrt{729 \cdot 3}\\&=\sf \sqrt{729}\sqrt{3}\\&=\sf 27\sqrt{3} \;\;units^2\end{aligned}[/tex]
Identify the correct command to find the derivative ofywith respect toxof the following equation:y=4x∧4−3x∧2+6x+14dydx=polyder([4,0,−3,6],14)dydx=polyder([4,0,−3,6,14])dydx=polyder(4,0,−3,6,14)dydx=polyder([4,−3,6],14) Explanation: When taking the derivative of a polynomial, the coefficients of the polynomial must be arranged in decending powers, being careful to specify zero for missing terms. The constant (i.e.,xto the zero power) is included in the array of coefficients.
The derivative of the given polynomial equation is 16x³ - 6x + 6.
We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
The equation is given below.
y = 4x^4 - 3x² + 6x + 14
dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)
dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)
dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]
dy/dx = 16x³ - 6x + 6
Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.
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A population of values has an unknown distribution with
ll
= 83.3 and o
= 10.4. You intend to draw a random
sample of size n
= 212.
What is the mean of the distribution of sample means?
flie
(Please enter an exact answer.)
What is the standard deviation of the distribution of
sample means?
Ox
(Please report your answer accurate
to 2 decimal places.)
By using the concept of mean and standard deviation, it can be obtained that
The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714
What is mean and standard deviation?
Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used
For Standard deviation, at first, it is important to know about variance
Variance is the sum of the square of deviation from mean.
Square root of variance is the standard deviation
A population of values has an unknown distribution with
[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212
So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714
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pls help me i’ll give brainliest
Answer:
25/0 aka infinity
Step-by-step explanation:
Equation used:
(y2-y1)/(x2-x1)
1. Plug in the values to get (27-2)/(9-9)
2. Simplify to get 25/0
3. This results in an infinity
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?
1, –0.25, –1.5, –2.75, –4, . . .
1, 2.25, 3.5, 4.75, 6, . . .
4, 2.75, 1.5, 0.25, –1, . . .
4, 5.25, 6.5, 7.75, 8
The sequence that can be defined by the recursive formula is (c) 4, 2.75, 1.5...
How to determine the elements of the recursive definition of f?The function definition is given as
f(1) = 4
f(n + 1) = f(n) - 1.25 for n ≥ 1
Set n = 1
So, we have the following representation
f(1 + 1) = f(1) - 1.25
This gives
f(2) = f(1) - 1.25
So, we have
f(2) = 4 - 1.25 = 2.75
Set n = 2
So, we have the following representation
f(2 + 1) = f(2) - 1.25
This gives
f(3) = f(2) - 1.25
So, we have
f(3) = 2.75 - 1.25 = 1.5
So, we have
4, 2.75, 1.5...
The sequence that matches 2.75, 1.5... in the options is (c) 4, 2.75, 1.5...
Hence, the sequence is (c) 4, 2.75, 1.5...
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Answer:
C
Step-by-step explanation:
Because i got it right
A farmer has 20 boxes of eggs
there are 6 eggs in each box
write as a ratio, the number of eggs in two boxes to the total number of eggs
Give your answer in its simplest form
Answer:
1 : 10 is the answer.
Step-by-step explanation:
Total number of eggs in 2 boxes = 6 x 2 = 12
Total number of eggs in 20 boxes = 120
12 : 120
1 : 10
Answer:
1:6
Step-by-step explanation:
ella has 1/3 as many trading cards as kip. Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. write an expression for the total number of cards the groups has. writ an expression for the total number of cards?
If Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. The expression for the total number of cards the groups has is: 1/3 ⋅9+(3+0.5⋅18)+18.
How to determine the expression?Given data:
Number of trading cards = 1/3
Adira number of cards = 23 more than 50%
Kip number of cards = 18 cards
Now let formulate an expression and then make use of the formulated expression to find the number of cards
Hence,
Number of cards = 1/3 ⋅9+(3+0.5⋅18)+18
Number of cards = 1/3 ⋅9+(3+9)+18
Number of cards = 1/3 ⋅9+(12)+18
Number of cards =3 + 12+18
Number of cards = 33 cards
Therefore the expression is : 1/3 ⋅9+(3+0.5⋅18)+18.
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how many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row? a) 70 b) 604,800 c) 120 d) 3,628,800 e) 17 f) none of the above.
The correct option c) 120; for the assignment of 7 students to 10 seats in a row.
What is referred as the combination?Combinations are mathematical techniques that count the number of potential arrangements for a set of elements only when order of the selections is irrelevant. You can choose the constituents of combos in any order.The procedure for determining how many arrangements are feasible when only a few items are selected from a set of items that are unique is as follows:The formula for finding the combination is-
ⁿCₓ = n!/ x!(n - x)!
Where,
n = total value.x = selected valueFor the given question.
Total students to be assigned a seat = 7.
Total seats in a classroom = 10.
Thus, Applying combination;
¹⁰C₇ = 10!/7!(10 - 7)!
¹⁰C₇ = 120
Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.
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A fast food restaurant was selling 2 boxes of chicken nuggets for $4.52
A competing restaurant was selling 4 boxes of chicken fingers for $9.44
Which food has a higher unit price?
Answer: The competing restaurant
Step-by-step explanation:
If you divide the 4.52 by 2 you get 2.26 for the first restaurant's unit price
If you divide the 9.44 by 2 you get 2.36 for the second restaurant's unit price
Hope this helps :)
a nurse researcher conducted an in-depth study of anxiety in patients undergoing chemotherapy. the researcher coded data from interviews with 20 patients, and a coinvestigator independently coded 8 of the 20 interviews. the coding of the two researchers was then compared. which quality-enhancement strategy was the researcher using?
The researcher was using Investigator triangulation quality-enhancement strategy.
The Investigator triangulation strategy make use of more than one researcher, investigator or interviewer to study the data.This research strategy can help you improve the credibility and the validity of your findings.
Including the Investigator triangulation strategy , there are basically four types of triangulation strategies . The other three are listed below :
- Data Triangulation
- Theory Triangulation
- Methodological Triangulation
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a rectangle with a diagonal of length xx is twice as long as it is wide. what is the area of the rectangle?
A rectangle with a diagonal of length x is twice as long as it is wide, the area of the rectangle is (B) 2x²/5..
How to find the area of the rectangle?Given that we have a rectangle with a diagonal of length x is twice as long as it is wide.
Let
L = length of rectangle,
W = width of rectangle and
D = length of diagonal = x
Given that the length of diagonal, x is twice as long as it is wide, we have that
L = 2W
Also, since it is rectangle, we have that
D² = L² + W²
D² = (2W)² + W²
D² = 4W² + W²
x² = 5W²
W² = x²/5
W = x/√5
W = x√5/5
since the length of the rectangle, L = 2W, we have that
L = 2W
= 2x√5/5
The area of the rectangle
The area of the rectangle is given by A = LW where
L = length of rectangle and
W = width of rectangle
So, A = LW
= 2x√5/5 × x√5/5
= 2x² × 5/25
= 2x²/5
So, the area of the rectangle is (B) 2x²/5
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A painter work 7 3/4 hours per hour. How.
many hours does this painter work in 5
days a week
Answer: 38.75 hours
Step-by-step explanation: so one thing real quick, you said “A painter worked 7 3/4 hours per hour” that’s not possible so instead I’m guessing you meant 7 3/4 hours per day.
Turn 7 3/4 hours into 7.75 hours then it’s simple, you multiply 7.75x5! You get 38.75 hours!
Answer:
38 3/4
Step-by-step explanation:
7 3/4 times 5 =
7 3/4 = 31/4
31/4 times 5 = 155/4
= 38 3/4
−12+(−20)
Enter your answer in the box.
Answer:-32
Step-by-step explanation:
-12+(-20)
-12-20
-32
Answer: -32
Step-by-step explanation:
−12+(−20)=
-12 - 20= ==> adding a negative number is equal to subtracting by the positive version of that number. ?-20=?+(-20)
-(12+20)=-32
what is the gcf of 70x^3z and 45y^4z^2
The GCF of the expressions given as 70x³z and 45y⁴z² is 5z
How to determine the GCF of the expressions?From the question, we have the following expressions
70x^3z and 45y^4z^2
Rewrite the given expression as follows
This is represented using
70x³z and 45y⁴z²
Factor out z from the expression
So, we have the following representation
70x³ and 45y⁴z => Factored z
Factor out 5 from the expression
So, we have the following representation
14x³ and 9y⁴z => Factored 5z
So, we have
Factored = 5z
This represents the GCF
Hence, the GCF is 5z
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The ratio 20mins to 1 hour can be written in the form 1:n find the value of n.
Answer:
1:3
n=3
Step-by-step explanation:
1 hour = 60 minutes
20:60
20÷20=1
60÷20=3
1:3
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint?
The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.
So, the ratio of gallons of blue paint to gallons of yellow paint is
= 5 to 9 or 5:9
Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint
= 1- 5/9
=4/9
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth
Step-by-step explanation:
imagine a circle with the center at the vertex of the angle x, and the radius 72 ft.
cos(x) = 28/72 = 7/18 = 0.388888888...
x = 67.11461952...° ≈ 67.1°
[tex]x^{2}-6x+1=0[/tex]
Solve the quadratic equation using the quadratic formula.
Show exact answers in simplified radical form; no rounded decimals.
The solutions of the quadratic equation using the quadratic formula is x = 3 + 2√2 and x = 3 - 2√2
Solving Quadratic equation using the Quadratic formulaFrom the question, we are to solve the given quadratic equation using the quadratic formula
The given quadratic equation is
x² - 6x + 1 = 0
Using the quadratic formula,
x = [-b±√(b² - 4ac)] / 2a
a = 1, b = -6, and c = 1
Thus,
x = [-(-6) ±√((-6)² - 4(1)(1))] / 2(1)
x = [6 ±√(36 - 4)] / 2
x = [6 ±√(32)] / 2
x = [6 ± 4√2] / 2
x = [2(3 ± 2√2)] / 2
x = 2(3 ± 2√2) / 2
x = (3 ± 2√2)
x = 3 + 2√2 and 3 - 2√2
Hence, the roots are 3 + 2√2 and 3 - 2√2
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can someone help pls
Answer:
4 hostel rooms
Step-by-step explanation:
okay so for this all you need to do is read the chart
go to 4-7 and read across to see how many hostel rooms have this many guests go to 20-23 and read across to see how many hostel rooms have this many guests there are 5 rooms with 4-7 guests (because 5 is halfway between 4 and 6 on the chart)there is only 1 room with 20-23 guests (because 1 is halfway between 0 and 2)work out the difference: 5-1 = 4rewrite 16r^2s^2 as a power of a product
Answer: 16r²s²=(4rs)²
Step-by-step explanation:
[tex]16r^2s^2=\\\\4^2r^2s^2=\\\\(4rs)^2[/tex]
It take Jada 20 minute to walk to chool. It take Andre 80% a long to walk to chool. How long doe it take Andre to walk to chool?
Andre takes 36 minutes to walk to the school.
Given, It take Jada 20 minutes to walks to school.
It takes Andre 80% a long to walk to school.
As, Andre takes 80% more to walk to school
So, the time Andre takes = 20×180/100
the time Andre takes = 2×18
the time Andre takes = 36 minutes
Hence, Andre takes 36 minutes to walk to the school.
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Triangles geometry . I really neeed it. Teacher don’t explain at all.
The value of x is 32.5°(degree) when isosceles triangle has a base angle of (4x-3)degrees and non base angle is 54 degrees.
How to calculate the value of x?We know that an isosceles triangles is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180°(degrees).
According to given data,
⇒ 180 - {(4x-3)+54}= 0
⇒180 - 4x + 3 - 54 = 0
⇒130 = 4x
∴ x = 32.5°(degree).
That means that each base angle is 32.5°(degree).
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Apply the distributive property to
create an equivalent expression.
(-7c + 8d)0.6
Answer: -4.2c + 4.8d
Step-by-step explanation:
Multiply each number by 0.6 to get -4.2c + 4.8d.
Please help me I WILL GIVE BRAINLY IF CORRECT!!<3 Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions LC)
Rewrite 30 - 6x³ using a common factor.
O2(15-3x³)
O 2x(15-3x²)
O6(5-6x³)
O6x(5-x²)
By factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])
The expression is given,
30 - [tex]6x^3[/tex]
The expression is the mathematical sentence that consist of different types of variables, numbers and the mathematical operators. The mathematical operators will be addition, subtraction, division and multiplication. The expression does not contains a equal sign or inequality signs
The expression is given,
30 - [tex]6x^3[/tex]
Take a common term outside
Here the common term is 2
30 - [tex]6x^3[/tex] = 2((30/2) - [tex]6x^3[/tex] /2)
= 2(15 - [tex]3x^3[/tex])
Hence, by factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])
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The radius of Earth's moon is about 173,700,000 cm. Which of the following is the number in scientific notation?
1Points
""
Earth's moon
Radius of Earth's moon is [tex]1.737*10^{8}[/tex]
Explain Scientific notationVery big or very small numbers can be presented in a simpler way using scientific notation. Although whole numbers can be stretched to infinity, humans are unable to write such enormous numbers on paper. Additionally, it was necessary to represent the numbers that appear at the millions place after the decimal in a more straightforward manner. The extended form of a few numbers is therefore difficult to represent. So, we employ scientific notations.
Given, radius of Earth's moon is 173,700,000.
As we know, in scientific notation there is only one number to the left.
So, we need to move the decimal to 8 places.
Therefore, radius of Earth's moon is [tex]1.737*10^{8}[/tex].
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Write down three different factors of
360 with a sum between 90 and 100.
Answer: 90 x 4 x 1
Step-by-step explanation:
90 x 4 x 1 = 360
Please thank and rate <3
Answer:
360
Step-by-step explanation:
2³x3²x5
Please thank you and rate
At 61°F, a certain insect chirps at a rate of 99 times per minute, and at 64°F, they chirp 117 times per minute. Write an equation in slope-intercept form that represents the situation.
An equation in slope-intercept form that represents the situation is C(x) = -267 + 6x.
What is the equation in slope intercept form?A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that can slope either upward or downward.
The general form of a linear equation is
y = mx + b
Where:
b = intercept y = dependent variable x = independent variable m = slopeSlope = change in the chirps / change in the temperature
Slope = (117 - 99) / (64 - 61)
Slope = 18 / 3
Slope = 6
99 = a + 6x
99 = a + 6(61)
99 = a + 366
a = 99 - 366
a = -267
C(x) = -267 + 6x
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