The length of the rafter as detailed in the question is approximately; 22.80 yards
How to use Pythagoras theorem?
The formula for Pythagoras theorem is;
a² + b² = c²
where;
a and b are adjacent and opposite sides of the triangle formed
c is the hypotenuse
Now, a rafter is a sloped member of a roof structure. Thus, if the rafter is raised to a height of 18 yeards, it means that is the vertical height of the top of the rafter to the bottom of the kingpost.
Now, if half the length run is 14 yards, it means that half of the tie beams is 14 yards. Thus, from the base of the rafter to the center of the tie beams is 14 yards. Thus, we will use Pythagoras theorem to find the length of the rafter.
c = √(14² + 18²)
c = √520
c = 22.80 yards
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When 1,2504 is written in its simplest radical form, which value remains under the radical?
O 10
O 6
O 5
02
The value that remains under the radical is 2
How to determine the value under the radical?The correct expression in the question is:
1250^4
This can be rewritten as:
[tex]\sqrt[4]{1250}[/tex]
Express 1250 as product
[tex]\sqrt[4]{(2 * 5^4)}[/tex]
Expand the expression
[tex]\sqrt[4]{2} * \sqrt[4]{5^4}[/tex]
Simplify
[tex]\sqrt[4]{2} * 5[/tex]
Evaluate the product
[tex]5\sqrt[4]{2}[/tex]
Hence, the value that remains under the radical is 2
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KM=
Help me asap pleasee
Answer: 3
Step-by-step explanation:
By the intersecting chords theorem,
[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]
Given that polygon PQRS≅ polygon LMNO, identify the congruent corresponding part for PQ
(NO GRAPH PROVIDED)
Answer:
LM
Step-by-step explanation:
Usually these problems would already be in order, so since PQ are the first 2 letters of polygon PQRS, then for LMNO, it's LM.
for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).
Answer:
k = 18=========
GivenLine 13x - ky + 7 = 0Line 2Passing through the points (4, 3) and (5, - 3)To findThe value of k, if the lines are perpendicularSolutionWe know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.
Find the slope of line 1 by converting the equation into slope-intercept from standard form:
Info:
standard form is ⇒ ax + by + c = 0, slope - intercept form is ⇒ y = mx + b, where m is the slope3x - ky + 7 = 0ky = 3x + 7y = (3/k)x + 7/kIts slope is 3/k.
Find the slope of line 2, using the slope formula:
m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6We have both the slopes now. Find their product:
(3/k)*(- 6) = - 1- 18/k = - 1k = 18So when k is 18, the lines are perpendicular.
Which graph correctly shows f(x)=x+3 / x^2-4
Step-by-step explanation:
it isnot looking well here so go on geogebra. org/calculator and you will see. have a nice day :))
Answer:
C on Edge 2022
Step-by-step explanation:
Just did it and got it right
What is the answer to the question below
The distance between the two given points coordinates is; Option C: √85
How to find the distance between two coordinates?Formula for the distance between two coordinates is;
d = √((x₂ - x₁)² + (y₂ - y₁)²)
We are given the coordinates as;
(-2, 3) and (5, -3). Thus;
d = √((-2 - 5)² + (-3 - 3)²)
d = √(49 + 36)
d = √85
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Which expression is equivalent to the given expression?
Answer:
The third option.
Step-by-step explanation:
[tex](\frac{4xy^3}{x^2})^2\\\\=(\frac{4y^3}{x})^2\\\\=\frac{16y^6}{x^2}[/tex]
Hence the 3rd option.
what is the positive angle less than 2π that is coterminal with 14π/6
Coterminal angles are angles that are made by the positive x-axis of the coordinate plane. The positive angle that is less than 2π and is coterminal with 14π/6 is 1/3π.
What are coterminal angles?Coterminal angles are angles that are made by the positive x-axis of the coordinate plane.
The angle that 14π/6 makes from the positive x-axis is 1/3π, which is equal to 60°.
Hence, the positive angle that is less than 2π and is coterminal with 14π/6 is 1/3π.
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the missing side of the triangle
Answer:
x = √95Step-by-step explanation:
from the sign on the picture it is a rigth triangle
we use pythagoras
x² = 12² - 7²
x² = 144 - 49
x² = 95
x = √95
(x = 9.75)
Answer:
x = [tex]\sqrt{95}[/tex]
Step-by-step explanation:
In this problem, we need to use the Pythagorean theorem.
Pythagorean theorem is a theorem where you can find a side length in a right triangle.
The hypotenuse (The longest side) squared equals the other two side lengths added together after being squared.
In numbers, this will be: (12)^2 = (7)^2 + (x)^2.
144 = 49 + x^2.
95 = x^2
x = [tex]\sqrt{95}[/tex]
We cannot simplify [tex]\sqrt{95}[/tex], so that is the final answer.
Question 17 of 25
how many solutions does the following system of equations have?
y=5/2x+2
2y=5x+4
a. zero
b. one
c.infinitely many
d. two
Answer:
c
Step-by-step explanation:
y = [tex]\frac{5}{2}[/tex] x + 2 → (1)
2y = 5x + 4 ( divide through by 2 )
y = [tex]\frac{5}{2}[/tex] x + 2 → (2)
the 2 equations are the same and will have infinitely many solutions
HELPPPPPPP PLEASEEEEEEE
Find the solutions of the quadratic equation:
Answer:
Answer A is correct
Step-by-step explanation:
Let us use completing square method for this.
[tex]x^{2} -5x -10=0\\\\x^{2} -5x=10\\\\x^{2} -5x+\frac{25}{4}=10+ \frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{10*4}{1*4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40}{4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40+25}{4} \\\\(x+\frac{5}{2}) ^{2} =\frac{65}{4} \\\\(x+\frac{5}{2}) = \±\sqrt{\frac{65}{2} }\\\\(x+\frac{5}{2}) =\±\frac{\sqrt{65}}{4}\\\\x=\±\frac{\sqrt{65}}{4}-\frac{5}{2}[/tex]
∴ [tex]x=-\frac{5}{2} \±\frac{\sqrt{65}}{4}[/tex]
Two systems of equations are shown:
System A System B
6x + y = 2 2x − 3y = −10
−x − y = −3 −x − y = −3
Which of the following statements is correct about the two systems of equations?
The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.
They will have the same solution because the first equations of both the systems have the same graph.
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical.
The correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D
How to determine the right statement
6x + y = 2 2x − 3y = −10 System A
-x − y = −3 −x − y = −3 System B
Let;s solve for x and y in system A
6x + y = 2
Make 'y' the subject
y = 2-6x
Substitute in the other equation
-x -y = -3
-x - (2-6x) = -3
-x -2+6x = -3
Collect like terms
5x = -3+2
x = -1/5
Substitute in y = 2-6x to find 'y'
y = 2- 6(-1/5)
y = 2+ 6/5
y = [tex]\frac{10+ 6}{5}[/tex]
y = 16/5
For system B
-x-y = -3
Make y subject, we have
-x + 3 = y
y = -x + 3
Substitute in the other equation, we have
2x − 3y = −10
2x - 3(-x+3) = -10
2x + 3x -9 = -10
Collect like terms
5x -9 = -10
5x = -10 + 9
x = 1/5
Substitute into y = -x + 3 to find 'y'
y = -(1) + 3
y = 2
Thus, the correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D
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"I am thinking of a number. If you
multiply my number by 4 and then add 3
times my number, you will get 175. What is
my number?"
Answer:
y =25Step-by-step explanation:
y×4+3×y=175 4y+3y=175 7y=175 divide by 7 both side with make value of y y=25. this is my answerFrom the diagram below, given the side lengths marked, and if we know that < C is congruent to < E, we can say that ___.
Select one:
a.
the two triangles are similar by SAS
b.
the two triangles are not similar
c.
the two triangles are congruent
d.
the two triangles are similar by AA
Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.
The properties of similar triangles.In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Ratio = BC/AC = 6/3 = 2.
Ratio = FE/DE = 4/2 = 2.
Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.
Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.
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An airplane travels 640 miles from Topeka to Houston in 3.2 hours, going against the wind. The return trip is with the wind, and takes only 2 hours. Find the rate of the airplane with no wind. Find the rate of the wind.
A) The airplane flies at 210 mi/h with no wind. The rate of the wind is 50 mi/h.
B) The airplane flies at 210 mi/h with no wind. The rate of the wind is 60 mi/h.
C)The airplane flies at 260 mi/h with no wind. The rate of the wind is 60 mi/h.
D)The airplane flies at 260 mi/h with no wind. The rate of the wind is 50 mi/h.
The airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:
(a - b)3.2 = 640
a - b = 200 (1)
Also:
(a + b)2 = 640
a + b = 320 (2)
The solution to equation 1 and 2 is:
a = 260, b = 60
The airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.
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Helppp meeeeee pleasseeeeeeeeeee
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Given the domain {-2, 1, 5}, what is the range for the relation 4x + y = 3?
Answer:
Step-by-step explanation:
Domain is the set of all possible inputs (x) for the function f(x)
The range is the set of all possible values for that domain
This function is 4x + y = 3 which can be re-written as y = 3-4x
Plug in each of the domain values and you will get the range
For -2 : y = 3-4(-2) = 3 + 8 = 11
For 1: y = 3-4(1) = -1
For 5: y = 3-4(5) = -17
So range is {-17, -1, 11}
PLEASE HELP ASAP THANK YOU!!
Answer:
Second graph
Step-by-step explanation:
See attached image.
what type of polynomial is -3
Answer:
a monomial, a constant
Step-by-step explanation:
It has only 1 term, so it's a monomial.
Also, the term is a constant.
Find dy/dx by implicit differentiation.
(sin pix + cos piy)^8 = 17
dy/dx =
please help quickly
dy/dx by implicit differentiation is cos(πx)/sin(πy)
How to find dy/dx by implicit differentiation?Since we have the equation
(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.
So, [(sin(πx) + cos(πy)⁸ = 17]
d[(sin(πx) + cos(πy)⁸]/dx = d17/dx
d[(sin(πx) + cos(πy)⁸]/dx = 0
Let sin(πx) + cos(πy) = u
So, du⁸/dx = 0
du⁸/du × du/dx = 0
Since,
du⁸/du = 8u⁷ and du/dx = d[sin(πx) + cos(πy)]/dx= dsin(πx)/dx + dcos(πy)/dx
= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)
= πcos(πx) - πsin(πy) × dy/dx
So, du⁸/dx = 0
du⁸/du × du/dx = 0
8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0
8[(sin(πx) + cos(πy)]⁷ × (πcos(πx) - πsin(πy) × dy/dx) = 0
Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0
(πcos(πx) - πsin(πy) × dy/dx) = 0
πcos(πx) = πsin(πy) × dy/dx
dy/dx = πcos(πx)/πsin(πy)
dy/dx = cos(πx)/sin(πy)
So, dy/dx by implicit differentiation is cos(πx)/sin(πy)
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What are the zeros of this function?
A. X=2 and x=-4
B. x=0 and x=4
C. X=0 and x=2
D. X=0 and x=-4
Answer:
The answer is B: x = 0 and x = 4
Step-by-step explanation:
The zeroes of a function are the x-intercepts, or the x values of the points that are on the x-axis. (The x-axis is the numbered horizontal line.)
One of the zeroes passes through the origin, which is (0,0). The other point is right before the number 5 on the x axis, which means that the point is (0, 4). If you look at the x-values of the ordered pairs of the zeroes, that's the answer.
(x, y)
Please help me figure out where they all belong to
The values of the trigonometric functions are
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{13}{12}[/tex]
Trigonometric functionsFrom the question, we are to determine the values of the given trigonometric functions
From the given information,
[tex]sec \theta =\frac{13}{5}[/tex]
∴ [tex]\frac{1}{cos \theta} =\frac{13}{5}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
Thus,
Adjacent = 5
Hypotenuse = 13
Opposite = ?
Using the Pythagorean theorem
|Opp|² = |Hyp|² - |Adj|²
|Opp|² = 13² - 5²
|Opp|² = 169 - 25
|Opp|² = 144
|Opp| = √144
|Opp| = 12
∴ Opposite = 12
Thus,
By using SOH CAH TOA
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{1}{tan\theta}[/tex]
∴ [tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{1}{sin\theta}[/tex]
∴ [tex]csc\theta = \frac{13}{12}[/tex]
Hence, the values of the trigonometric functions are
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{13}{12}[/tex]
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2. Try It #2 The population of a small town increased from 1,442 to 1,868 between 2009 and 2012 . Find the change of population per year if we assume the change was constant from 2009 to 2012 .
Answer:
If it is assumed that the change was constant from 2009 and 2012 , then change of population is 142 .
Step-by-step explanation:
In the question, it is given that the population of a small town increased from 1442 to 1868 between 2009 and 2012 .
It is asked to find the change of population if it is assumed that the change was constant from 2009 and 2012 .
Step 1 of 2
Population in 2012 is given to be 1868 and
Population in 2009 is given to be 1442 .
Duration of year is given by 2012-2009 which is 3 years.
Change in population is given by 1868-1442 which is 426 .
Step 2 of 2
Change in population per year is given by dividing the change in population and the duration of years it took to happen the change.
Hence, change in population per year is
[tex]$\frac{426}{3}=142$[/tex]
Hence, the population was changed by 142 per year from 2009 to 2012 .
31. Lefties Find the sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of three percentage points, and use a confidence level of 99%. a. Assume that pn and qn are unknown. b. Assume that based on prior studies, about 10% of Californians are left-handed. c. How do the results from parts (a) and (b) change if the entire United States is used instead of California
a. The required sample size when pn and qn are unknown then n = 1844
b. The required sample size when about 10% of Californians are left-handed is n = 664
c. There would have been no effect on parts a and b if entire US has been chosen
According to statement
a. No estimate of proportion is given so we will assume:
{p} = {q} = 0.5
For 99% confidence, z = 2.576
E = 0.03
Hence, Required sample size
n = (0.5)*(0.5)*(2.576/0.03)^2
n = 1844
b. {p} = 0.10
{q} = 1 - {p}
{q} = 1 - 0.10
{q} = 0.90
For 99% confidence, z = 2.576
E = 0.03
Hence, Required sample size n = (0.1)*(0.9)*(2.576/0.03)^2 = 664
c. There would have been no effect on parts a and b if entire US has been chosen because minimum sample size required is not dependent on population size.
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Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
3. 72,162
Answer:
The greatest common factor of 72 and 162 is 18.
Step-by-step explanation:
In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 72 is 2*2*2*3*3, and the prime factorization of 162 is 2*3*3*3*3 (you can make a factor tree for both of these numbers to verify this). The common primes factors for both of these numbers are 2, 3, and 3 (both 72 and 162 have one 2 and at least two 3s). 2*3*3 is 18, which is the greatest common factor.
Work out
(4 × 10³) – (7 × 10²)
Give your answer in standard for
Answer:
3300
Step-by-step explanation:
This can be worked out using PEMDAS:
First you solve in the PARENTHESIS:
(4 × 10³) – (7 × 10²)
Then, you look at the EXPONENTS:
(4 × 10³) = (4 × 1000)
(7 × 10²) = (7 × 100)
After that, look at the MULTIPLICATION:
(4000) - (700)
Since there is only subtraction left, subtract it:
3300
Answer:
Parenthesis:
4 *1000 = 4000
7*100= 700
4000-700=3300
Step-by-step explanation:
Celo used the simple interest formula uppercase a = uppercase p (1 r t) to calculate the interest he earned on his savings last month. which equation is equivalent to the simple interest formula?
The equation which is equivalent to the given simple interest formula is
[tex]P=\frac{A}{1+rt}[/tex].
What is an equivalent equation?
Equivalent equations are algebraic equations that have identical solutions.
According to the given question.
We have a simple interest formula.
[tex]A=P(1+rt)[/tex]
Now, the equivalent equation for the above formula can be given as
[tex]A=P(1+rt)[/tex]
⇒[tex]P=\frac{A}{1+rt}[/tex]
Hence, the equation which is equivalent to the given simple interest formula is [tex]P=\frac{A}{1+rt}[/tex].
Thus, option A is correct.
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How many units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$
56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$
Properties of triangles are:
A triangle has three sides and three angles.
The sum of the angles of a triangle is always 180 degrees.
The exterior angles of a triangle always add up to 360 degrees.
The sum of consecutive interior and exterior angle is supplementary.
How to solve?Given:
Height: ha = 7
Height: hb = 24
Height: hc = 25
Sum to sides is:
25 +7 + 24 =56 units.
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Which graph represents an exponential function?
The first graph is the exponential function.
What is exponential function?The exponential function serves as the positive-valued function with respect to real variable. and the values denoted as X which is exponential is all real numbers.
Analyzing the first graph, moving down the graph, we can see that x value increases.
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Answer:
First Graph
Step-by-step explanation:
Edge
On a coordinate plane, 2 trapezoids are shown. Trapezoid M O N P has points (negative 5, 4), (negative 2, 5), (negative 2, 2), and (negative 5, 3). Trapezoid C D E F has points (3, negative 5), (4, negative 5), (5, negative 2), (2, negative 2).
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. Which congruency statement applies to the trapezoids?
CDEF ≅ NPOM
CDEF ≅ MNPO
CDEF ≅ NMOP
CDEF ≅ MOPN
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The correct option is C.
What is a Trapezoid?A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. The congruency statement that applies to the trapezoids is CDEF ≅ NMOP.
Hence, the correct option is C.
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