Please please help
Engineers have determined that the strengths of a rectangular beam varies as
the product of the width w and the square of the depth d of the beam, that is,
S = kwd2 for some constant k > 0.
a A particular cylindrical log has a diameter of 48 cm. Use Pythagoras' theorem
to show that s = kw (2304 - w²).
b Hence find the dimensions of the strongest rectangular beam that can be cut from
the log.
Answers
Answer:
The dimensions of the strongest rectangular beam that can be cut from the log are:
depth d = 16√6 cmwidth w = 16√3 cmStep-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Part (a)From observation of the given diagram, the diameter of the circle is the hypotenuse of a right triangle (with legs w and d). Given that the diameter is 48 cm, substitute the values into Pythagoras' Theorem and rearrange to create an expression for d²:
[tex]\begin{aligned}w^2+d^2&=48^2\\w^2+d^2&=2304\\d^2&=2304-w^2\end{aligned}[/tex]
Substitute the found expression for d² into the given strength equation:
[tex]\begin{aligned}s&=kwd^2\\s&=kw(2304-w^2)\end{aligned}[/tex]
Hence showing that s = kw (2304 - w²).
Part (b)To find the value of w that will maximise the strength of the rectangular beam, first differentiate the equation for s in terms of w:
[tex]\begin{aligned}s&=kw(2304-w^2)\\s&=2304kw-kw^3\\\implies \dfrac{\text{d}s}{\text{d}w}&=2304k-3kw^2\\&=3k(768-w^2)\end{aligned}[/tex]
Set the differentiated equation to zero and solve for w:
[tex]\begin{aligned}3k(768-w^2)&=0\\ 768-w^2&=0\\w^2&=768\\w&=\sqrt{768}\\w&=\sqrt{256 \cdot 3}\\w&=\sqrt{256}\sqrt{3}\\w&=16\sqrt{3}\\\end{aligned}[/tex]
Substitute the value of w that maximises the strength of the beam, together with the given hypotenuse of 48 cm, into Pythagoras' Theorem and solve for d:
[tex]\begin{aligned}w^2+d^2&=48^2\\768+d^2&=2304\\d^2&=2304-768\\d^2&=1536\\d&=\sqrt{1536}\\d&=\sqrt{256 \cdot 6}\\d&=\sqrt{256}\sqrt{6}\\d&=16\sqrt{6}\end{aligned}[/tex]
Therefore, the dimensions of the strongest rectangular beam that can be cut from the log are:
depth d = 16√6 cmwidth w = 16√3 cmRelated Questions
The 4th term of a geometric sequence is -25 and the 9th term is 25/32. find the 15th term
Answers
The 15th term of the geometric progression is a₁₅ = 25/2048
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the 15th term of the geometric progression be a₁₅
Now , the 4th term of the GP is a₄ = -25
The 9th term of the GP is a₉ = 25/32
Now , nth term of a GP is aₙ = arⁿ⁻¹
Substituting the values in the equation , we get
a₄ = ar³ = -25 be equation (1)
a₉ = ar⁸ = 25/32 be equation (2)
Divide equation (2) by equation (1) , we get
r⁵ = -( 1/32 )
r⁵ = - ( 1/2 )⁵
So , the common ratio r = -1/2
Now , the first term of the GP a is calculated by
ar³ = -25
when r = -1/2
a ( -1/2 )³ = -25
a/8 = 25
a = 200
Now , the 15th term of the geometric progression a₁₅ = ar¹⁴
Substituting the values in the equation , we get
a₁₅ = 200 ( -1/2 )¹⁴
a₁₅ = 200/16,384
a₁₅ = 25/2048
Hence , the 15th term of the GP is 25/2048
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Simplify the expression. Enter the answer in the box 3 1/2+(-7 1/5) = 3+(-7) + 2/5 + (-1/5)
Answers
The required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3 1/2+(-7 1/5) = 3+(-7) + 2/5 + (-1/5)
7/2 - 34/5 = -4 + 2/5 + -1/5
-33/10 = -4 + 1/5
-33/10 ≠ -19/5
Thus, the required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.
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Find the missing side of each triangle. Round to the nearest tenth if necessary.
Answers
I found the answer with the ruluer it's 11.3
-2/5(5-10e) = e + 1/3(6e-12)
Answers
Step-by-step explanation: To solve for e in this equation, you can start by isolating e on one side of the equation.
First, distribute the -2/5 on the left side of the equation:
-2/55 - 2/510e = e + 1/36e - 1/312
Now, you can combine like terms on both sides of the equation:
-2 - 4e = e + 2e - 4
Next, you can add e to both sides of the equation:
-2 - 3e = 2e - 4
Now you can add 3e to both sides of the equation:
-2 = 5e - 4
Now you can add 4 to both sides of the equation:
-6 = 5e
Finally, you can divide both sides of the equation by 5:
e = -6/5
So the value of e that satisfies the equation is -6/5.
2000 a month for 15 months with 4% interest
Answers
Answer:
1200
Step-by-step explanation:
4% of 2000 is 80 then do 80*15 and you get 1200
Scott fixed two vases if flowers for Lana. Vase J contained 14 carnations and half a dozen of roses. Vase K contained 15 carnations and a dozen daises. Which statement is true?
A.The probability of randomly selecting a carnation from Vase J is greater than the probability of randomly selecting a carnation from Vase K.
B. The probability of randomly selecting a carnation from Vase K is less than 50%.
C. The probability of randomly selecting a carnation from Vase J is 1/14
D. The probability of randomly selecting a carnation from vase K is greater than the probability of randomly selecting a carnation from vase J.
Answers
The answer to option D) is yes. The likelihood of choosing a carnation at random from vase K is higher than the likelihood of choosing one at random from vase J.
What are examples and probability?The possibility is determined on the range of potential outcomes. the estimated number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping the coin and receiving heads is 1 in 2. (a head or tail). We write P(heads) = 12 here.
What in mathematics is probability?Roughly simply, probability is the chance that everything will exist. When we wouldn't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes.
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consider the continuous random variable x, which has a uniform distribution over the interval from 40 to 44. the variance of x is approximately _____. a. 46 b. 1.333 c. 1.155 d. 0.333
Answers
The variance of 'x' for the continuous distribution over the interval 40 to 44 is approximately b) 1.333
The variance of a continuous uniform distribution over the interval [a, b] is:
Calculate the variance using the formula:
Var(x) = (b-a)^2/12
where [a, b] is the interval over which the continuous uniform distribution is defined
But putting a= 40 and b = 44, calculate the variance by putting them in the above formula
So, Var(x) = (44-40)^2/12
Var(x) = 4^2/12
Var(x) = 16/12
Var(x) = 4/3
Var(x) = 1.333
Therefore, the variance of 'x' for the continuous distribution over the interval 40 to 44 is approximately b) 1.333
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Ben helped his dad make soup. Their recipe made 15 cups. If they eat 2 cups, will their leftovers fit in a 64-ounce container.
Answers
Answer:
No, it would not fit because one cup is 8 ounces and if you times 8 and 13 it 104 so it would not fit they would need another container.
Step-by-step explanation:
hope it helps
Write a system of linear equations for the graph below.
Y=
Y=
Answers
The system of linear equations for the given graph is: y = 1/2x + 6; y = -3x - 1
The graph of a linear equation.The graph of a linear equation follows a slope-intercept form y= mx + b, where m is the slope and b is the y-intercept. We can determine the graph of a linear equation by merely looking at the graph and finding two points on the graph from which the slope of the graph can be determined the represent it as a linear equation.
The linear equation can now be converted to a standard form to determine the system of the linear equation.
From the graph.
The first upper graph to the right shows the point (-2, 5) and (0,6)
The second graph to the left shows the point (-2, 5) and (0,-1)
The slope of the first graph = (6 - 5 )/(0--2) = 1/2; The y-intercept = 6
In slope-intercept form, we have:
y = 1/2x + 6 ----- (1)
The slope of the second graph = (-1 - 5)/(0--2) = -6/2 = -3
The y-intercept = -1
In slope-intercept form: y = -3x - 1 ------- (2)
y = 1/2x + 6
y = -3x - 1
Therefore, we can conclude that the system of linear equations for the given graph is: y = 1/2x + 6; y = -3x - 1
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for a 13-person team, on average, how many overtime hours will each person need to work?
Answers
Based on the numerical data, we can estimate that 26 more labor hours will be necessary to satisfy the labor hours required without overtime.
What is Overtime?The Fair Labor Standards Act, enacted by the federal government, places a cap on the number of hours per week (40 hours) that businesses may demand their employees to perform in exchange for regular pay. Employers were now required to give employees who put in more than 40 hours of work additional compensation in the form of overtime pay.
Hence,
Overtime pay is usually 1.5 times the employee's regular hourly wage.
So, if an employee is paid $15 per hour, their overtime rate is $22.50 per hour ($15 multiplied by 1.5).
If another employee is paid $25 per hour, overtime is $37.50 per hour ($25 x 1.5).
It would require 26 more labor hours will be necessary to satisfy the labor hours required without overtime.
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Find the perimeter of the composite figure below. (semicircle). Round to the nearest tenth. Use π = 3.14
Answers
take upper base = 12
take upper base = 12right side= 20
take upper base = 12right side= 20apply pythagorus
take upper base = 12right side= 20apply pythagorus .
take upper base = 12right side= 20apply pythagorus .= 13
now semi circle= 2 pi r/2 = pi × (11/2)
add all
12 +20+13× 5.5pi
Answer:
64.27cm
Step-by-step explanation:
Total perimeter =
semicircle + Length of rectangle + Breadth of rectangle and triangle +
hypotenuse of Triangle
semicircle = pi x r (r = radius)
= 3.14 x 11/2
= 17.27 cm -----------------(1)
Length of rectangle = 12cm (Given) ----------------------(2)
Base (rectangle and triangle) = 20cm (Given) --------------------(3)
Hypotenuse = Root of (20-11)^2 + 12^2
= Root of 9^2 + 12^2
= Root of 81 + 144
= Root of 225
= 15cm ---------------------------(4)
By adding (1), (2), (3) and (4) we get
= 17.27 + 12 + 20 + 15
= 64.27cm
how much hamburger will it take to make 300
Answers
It all depends on how you want your hamburger. If you're serving it as a main dish, 300 hamburger patties (each around 4 ounces) should be plenty to feed 300 people. If you utilize hamburger meat as a topping or filler in a meal, you'll need a different amount.
What is arithmetic operation?Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic mean is a number calculated by dividing the sum of a set's elements by the number of values in the set.
Here,
It all depends on how you want to eat the hamburger. If you're serving it as a main course, 300 hamburger patties, each weighing around 4 ounces, should plenty to satisfy 300 people. It will need a different quantity of hamburger meat if you use it as a topping or filler in a dish.
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Complete question:
How much hamburger will it take to make 300 three oz patties with a 20% shrinkage?
what is the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended waranty
Answers
The probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty = 0.493
Here, 21% of customers purchase extended warranty.
So, the probability p = 0.21
It takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty is nothing but none of the first three buy.
This means, we find probability P(X = 0) when n = 3.
Using Binomial distribution formula for probability,
P(X = 0) = ³C₀ (0.21)⁰ (1 - 0.21)⁽³ ⁻ ⁰⁾
P(X = 0) = ³C₀ (0.21)⁰ (0.79)⁽³ ⁻ ⁰⁾
P(X = 0) = 0.493
Therefore, the required probability is 0.493
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The complete question is:
The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible
items are chosen at random one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who
purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independentWhich of the following is closest to the probability that X > 3;
that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?
Rearange the equation to make b the subject. a = 1/4 b.
Answers
The value of the equation a = (1/4)×b in terms of a is b = 4a.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression a = (1/4)×b.
Now, Making 'b' the subject is the same as solving for 'b'.
We know when a term is multiplied by another term moving it to the other side we have to take its reciprocal.
Therefore, a = (1/4)×b.
b = a×(4/1).
b = 4a.
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Gina Wilson all things algebra Unit 6 Homework 5
Answers
The simplified monomials are:
-2a³b²xy(7 - 2x)3a⁷-x¹⁰k⁴15x⁷-12x⁵y⁵10b⁸/a³16y⁸a⁸b¹⁰c¹⁵d³/216c³1/64a⁷-576x¹¹y⁸64b¹⁵/a³c⁹3/d²3a⁴/2b-4x²yz³8y⁵/581x⁸/y¹²-5a³bLet's simplify each monomials we have.
3a³b² - 5a³b² = -2a³b² --> both exponents are already equal
5xy - 2x²y + 2xy = 7xy - 2x²y
= xy (7 - 2x)
-6w : -2w = 3
a⁴ . a³ = a⁽⁴⁺³⁾
= a⁷
(-x⁵)² = - x ⁽⁵ˣ²⁾
= - x¹⁰
k⁹ / k⁵ = k⁽⁹⁻⁵⁾
= k⁴
-5x³ . (-3x⁴) = 15x⁷
(-2x²y)² . (-3xy³) = (4x⁴y²) . (-3xy³)
= -12x⁵y⁵
2a⁻⁵b⁶ . 5a²b² = 10 a⁻³b⁸
= 10b⁸ / a³
(-4y⁴)² = 16y⁸
(a²bc³)⁴ . (b²c)³ = (a⁸b⁴c¹²) . (b⁶c³)
= a⁸b¹⁰c¹⁵
(6cd⁻¹)⁻³ = 1 / (6cd⁻¹)³
= (d/6c)³
= d³ / 216c³
(4a)⁻³ . a⁻⁴ = 1/(4a)³ . (1/a⁴)
= 1/64a³ . 1/a⁴
= 1/64a⁷
(3xy)² . (-4x³y²)³ = (9x²y²) . (-64x⁹y⁶)
= -576x¹¹y⁸
(4a⁻¹b⁵c⁻³)³ = (4b⁵ / ac³)³
= 64b¹⁵ / a³c⁹
9d⁸/3d¹⁰ = 3/d²
6a⁵b² / 4ab³ = 3a⁴/ 2b
32x³y²z⁵ / -8xyz² = -4x²yz³
(2y⁵)⁴ / 10y¹⁵ = 16y²⁰ / 10y¹⁵
= 8y⁵ / 5
(3x⁵y³ / x³y⁶)⁴ = (3x²/y³)⁴
= 81x⁸ / y¹²
(-6a⁵b)² - 8a³b = 36a¹⁰b² - 8a³b
12a⁷b 12a⁷b
= 3a⁵b - 8a⁵b
= -5a⁵b
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the chi square value of a given dihybrid analysis is 0.47. if the degrees of freedom in the analysis were 3, would the null hypothesis be rejected?
Answers
If the chi square value of a dihybrid analysis is 0.47 , and degree of freedom in analysis were 3 , then the null hypothesis will not be rejected because 0.47 < 7.815 .
To determine whether to reject or accept the Null Hypothesis, a critical value of chi-square with a given level of significance is used.
If the calculated chi-square value is greater than the critical value, then the null hypothesis is rejected. and
If the calculated chi-square value is less than or equal to the critical value, then the null hypothesis is not rejected.
The critical value of chi-square for a level of significance and degrees of freedom can be found using a chi-square distribution table.
With a level of significance of 0.05 and 3 degrees of freedom, the critical value of chi-square is 7.815.
that means ⇒ 0.47 < 7.815, the null hypothesis would not be rejected at a level of significance of 0.05 .
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7. Fill in the blanks below to make each statement true.
a. Fewer than 15% of coins were
of the coins were quarters.
b. Exactly
c. Nickels, dimes, and quarters account for
of the total number of coins.
Answers
Fewer than 15% of coins were quarters. Exactly 80% of the coins were nickels, dimes, and quarters. Nickels, dimes, and quarters account for 95% of the total number of coins.
What is the quarters?Quarters are coins that are used in many countries as a form of currency. Quarters are generally made of metal and are round in shape. They are typically smaller than other coins, such as dimes and nickels, and have a value of 25 cents (or one-fourth of a dollar). Quarters are often used in everyday transactions, such as buying candy or a newspaper, or to pay for parking. In the United States, there are five different designs of quarters in circulation, each representing a different state or territory.
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a rectangle has a length of 4 meters and a width of 150 centimeters what is the perimeter of the rectangle in meters
Answers
The perimeter of the rectangle with a length of 4 meters and a width of 150 centimeters is 11 meters.
What is the perimeter of the rectangle?A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
Perimeter = 2( length + width )
Given the data in the question;
Length of rectangle = 4 metersWidth of rectangle = 150 cm = ( 150/100 )m = 1.5 metersPerimeter = ?Plug the values into the above equation.
Perimeter = 2( length + width )
Perimeter = 2( 4 meters + 1.5 meters )
Perimeter = 2( 5.5 meters )
Perimeter = 11 meters
Therefore, the perimeter is 11 meters.
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Mary, Katherine, and Alex share the bill at a restaurant after a meal. Mary pays for of the bill, Katherine pays for of the bill, and Alex
pays for the rest. What is the ratio of Mary's share to Katherine's share to Alex's share?
Answers
The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.
To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.
So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.
To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.
Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1
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FIND AREA PLS HELP ASAP
Answers
The area of the rhombus is 54 sq. units
Area of the trapizium is 115 sq. units.
What is a Rhombus and Trapizium ?A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
A parallelogram's general characteristics are as follows:
Angles on the opposite sides are congruent or equal.The opposing sides are parallel and equal in size.Diagonals cut each other in half.Any two parallel or following angles add up to 180 degrees.In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.
The area of a rhombus = ½ x (product of the lengths of the diagonals)
= ½ *18*6 = 54 sq. units
Area of the trapizium = ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
=½ *(17 + 29) * 5 = 115 sq. units.
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Here is the graph y = f(x)
(2,-1)
y=f(x)
What are the coordinates of the point
shown after the transformation
f(-2x)?
X
Answers
The coordinates of the point shown after the transformation f(-2x) are given as follows:
(-4,-1).
How to apply the transformation?The original coordinates of the the point in this problem are given as follows:
(2,-1).
Hence:
The x-coordinate is of 2.The y-coordinate is of -1.The transformation is given as follows:
f(-2x).
Meaning that the x-coordinate is multiplied by -2, hence the coordinates of the point shown after the transformation f(-2x) are given as follows:
(-4,-1).
(as 2 x -2 = -4).
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if we throw uniformly at random a point on segment [0,1], then its expected position is 1/2. what are the expected positions of two random points on segment [0,1]?
Answers
If we throw uniformly at random a point on segment [0,1], then its expected position is 1/2. the expected positions 1/3 and 2/3 of two random points on segment [0,1] are [0,1/3],[1/3,2/3]and[2/3,1]
In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen. Given the interval is [0,1]
Then it's expected position is 1/2
So [0,1/2] and[1/2,1]
Now we get the two expected positions
I. E three intervals
So (1-0)/3
=1/3
So 1/3 and 2/3 are expected positions
They are [0,1/3],[1/3,2/3]and[2/3,1]
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what is the sum (two-fifths x startfraction 5 over 8 endfraction) (one-fifth x minus one-fourth)? three-fifths x startfraction 1 over 8 endfraction three-fifths x startfraction 3 over 8 endfraction three-fifths x startfraction 5 over 8 endfraction three-fifths x startfraction 7 over 8 endfraction
Answers
The sum of the expressions 2x/5 + 5/8 + x/5 - 1/4 is option b) 3x/8 + 3/8
Here we have 2x/5 + 5/8 + x/5 - 1/4
Now since we have constants as well as variables here, to add these up, we will add the constants and variables separately.
The constants are the ones with just numbers, while the variables are those terms that have the term x with them.
Hence adding up the constants will give us
5/8 - 1/4
The LCM of denominators 8, and 4 is 8
Hence, we get
5/8 - 2/8
= 3/8
Now adding the variable gives us
2x/5 + x/5
= 3x/5
Hence the sum is
3x/5 + 3/8
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Complete Question
2x/5 + 5/8 + x/5 - 1/4
a) 3x/5 + 1/8
b) 3x/5 + 3/8
c) 3x/5 + 5/8
d) 3x/5 + 7/8
It is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.
The expression
(2/5 * 5/8) + (1/5 * x - 1/4)
can be simplified as follows:
2/5 * 5/8 = 1/8
1/5 * x - 1/4 = (1/5 - 1/4) x = -3/20 x
So the expression becomes
1/8 + (-3/20 x) = (1/8 - 3/20 x).
This is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.
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Graph the inequality.
र
y ≥ x-5
Answers
Answer:
Step-by-step explanation:
In circle B with the measure of minor arc AC= 126°, find m/ADC.
Answers
Answer:
Step-by-step explanation:
=63
The measure of arc ADC in circle B with the measure of minor arc AC= 126° is 234°.
Given that the measure of minor arc AC = 126°, we can find the measure of arc ADC using the following formula:
m/ADC = 360° - m/AC
Plugging in the values, we get:
m/ADC = 360° - 126° = 234°
Therefore, the measure of arc ADC is 234°.
Here is the explanation:
A minor arc is an arc that is less than 180°.
The measure of a minor arc is equal to the measure of the central angle that intersects it.
The measure of a whole circle is 360°.
Therefore, the measure of arc ADC is equal to the difference between the measure of the whole circle and the measure of minor arc AC. This difference is 360° - 126° = 234°.
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Using the graph attached, find all the point(s) such that the sum of their coordinates is equal to 7.
Answers
Answer: B, C, A.
Step-by-step explanation: positive, not negative
question in the number 7,567.23, how does the value of the 7 in the ones place compare to the value of the 7 in the thousands place?
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The value of the 7 in the one's place is 1/1000 times the value of the 7 in the thousand places.
According to the question,
The number is 7,567.23.
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in the number.
The difference in place value in one's place and thousand places is 1000.
The 7 in the thousands place is 1000 times the value of the 7 in the one's place.
So, The value of the 7 in the one's place is 1/1000 times the value of the 7 in the thousand places.
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unit 4 homework 6 congruent triangles proofs
#4 and 6
Answers
1) The proof that ΔFEH ≅ΔFGH is given as follows:
ΔFH bisects ∠EFG (Given)
∠FEH ≅ ∠ FGH.
FH = HF (Given)
∠EFH ≅ ∠FHG (Angle Bisector Theorem)
Thus, ΔFEH ≅ΔFGH (Angle - Side - Angle Theorem)
2) The proof that ΔPQR ≅ ΔTSR is:
∠RPQ ≅ ∠RTS - Given
R is the midpoint of QS - Given the Definition of Midpoint
QR ≅ RS - Definition of Midpoint
∠PRQ ≅ ∠SRT Vertical Angles
Thus: ΔPQR ≅ ΔTSR - Angle - Angle - Side Theorem.
3) the proof that ΔABC ≅ Δ DCB is given as follows:
ΔABC and ΔDCB are Right Angled Triangles
AB ≅ DC - Given
BC ≅CB - Reflective Properties; thus
ΔABC ≅ ΔDCB - Hypothenus Leg Theorem.
What is the Hypotenuse Leg Theorem?
According to the hypotenuse-leg (HL) theorem, if the hypotenuse and a leg of a right triangle are both congruent with the corresponding hypotenuse and leg of another right triangle, the triangles are congruent. According to the HL theorem, these triangles are congruent.
There is one exception to this rule: when the angles are straight angles. Using words: The triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle.
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PLEASE HELP RIGHT AWAY When angle A + angle B = 90 deg what relationship formed by tan angle A and tan angle B? Select all that apply.
Answers
The relationship between tan A and tan B is: tan A * tan B = 1
How to determine the relationshipFrom the question, we have the following parameters that can be used in our computation:
angle A + angle B = 90 deg
When angle A + angle B = 90 degrees,
The two angles are complementary, meaning they add up to 90 degrees.
In this case, the relationship between tan A and tan B is:
tan A * tan B = 1
This is known as the tangent addition formula.
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What is the image of (-6,-5) after a reflection over the x-axis?
Answers
Answer:
6,5
Step-by-step explanation:
