Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.
What are opposite values?Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.
In general, the temperature equation for Portland, Maine is stated mathematically as
PoT=-PhT
As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,
PoT=-PhT
PhT =+PoT
Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.
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statement that is assumed to be true without proof is . A statement that has been shown to be true by vigorous application of logic is . is a statement that is believed to be true but hasn't been proven.
An axiom is a statement that is assumed to be true without proof.
What are the types of statements?In logic, a statement could be shown to be valid or true by the use of premises that lead to a sound conclusion.
The following terms can be used to describe the statements;
Axiom - a statement that is assumed to be true without proofTheorem - a statement that has been shown to be true by vigorous application of logicHypothesis - a statement that is believed to be true but hasn't been proven.Learn more about mathematical statements:https://brainly.com/question/17029275?
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Answer:
The answer is axiom, theorem, and then conjecture
Step-by-step explanation:
Using Triangle Congruence Theorems
There are a total of five theorems congruent triangles. They are summarized as:
SASSSSAASRHS and ASA.What are the definitions of the Theorems of Congruent Triangles?SAS - Side Angle Side
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
SSS - Side Side Side Rule
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.
AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.
ASA - Angle Side Angle rule
According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.
RHS - Right Angle- Hypotenuse side Rule
According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.
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Answer:
AD=BC (given)
DC=DC (reflexive property)
DE=CE (converse of isosceles triangle thm)
<BCD=<ADC (given)
<ECD=<EDC (CPCTC)
TriangleADC=TriangleBCD (SAS)
Another day, another math problem 3
Answer:
[tex]2\sqrt{x+1}-3\\domain:[-1, \infty)[/tex]
Step-by-step explanation:
[tex]g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\[/tex]
the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1
A carpenter wants to cut an 84 inches long board into two-pieces such that one piece is twice as long as the other piece. Set up an equation and find the length of each piece.
Answer:
small piece = 28 inches
large piece = 56 inches
Step-by-step explanation:
The carpenter has one piece of wood 84 inches long. He wants to cut that piece of wood into two pieces. One piece will be 2 times as long as the other. Let's let x = the small piece of wood
2x + x = 84
In this equation, the longer piece is 2 times the shorter piece and the shorter piece is added, which equals 84 inches. Lets solve:
2x + x = 84
3x = 84
3x/3 = 84/3
x = 28
This means that the shorter piece is 28 inches. To find the longer piece, multiply 28 by 2 because the longer piece is twice the shorter piece. Therefore the longer piece is
28 × 2 = 56
Finally, we figured out that the short piece is 28 inches and the longer piece is 56 inches
We can double check this by doing 56 + 28 and making sure it equals 84
A comedy club's nightly revenue from the sale of x tickets is given by R = 15x and its
nightly costs are given by C= 1.25x + 495. How many tickets need to be sold each night
to break even? In other words, when will revenue equal costs?
Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.
What is the break-even point?The break-even point is when the revenue and the costs are equal.
In this problem, the equations are given as follows:
R(x) = 15x.C(x) = 1.25x + 495.At the break-even point:
R(x) = C(x)
15x = 1.25x + 495
13.75x = 495
x = 495/13.75
x = 36.
36 tickets have to be sold each night to break even.
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Simplify the root below
\frac{a}{b} \sqrt[]{ \frac{405}{324} }
Answer:
(√5)/2
Step-by-step explanation:
To simplify the root, we remove perfect squares.
__
Factors that are the same in numerator and denominator cancel. A square under the radical can have its root brought out of the radical.
[tex]\sqrt{\dfrac{405}{324}}=\sqrt{\dfrac{9^2\cdot5}{9^2\cdot2^2}}=\boxed{\dfrac{\sqrt{5}}{2}}[/tex]
help pls i jusiot jiojfgnio43nfginfmowenfviowngognior3
Answer:
i dont know
Step-by-step explanation:
sorry please be a bit more clear on what help you would like
Find the value of: (4/5)^1 A. 4/5 B. 1 C. 0 D. 16/25
Answer:
A. 4/5
Step-by-step explanation:
Answer:
4/5 (option a)
Step-by-step explanation:
by following the exponent rule of [tex]a^1 = a[/tex], we know that
[tex](\frac{4}{5} )^1[/tex] = [tex]\frac{4}{5}[/tex]
So, the value of
[tex]\frac{4}{5}^{1}[/tex] is 4/5
Mrs. Juergen's class is building a model city from craft sticks. each house requires 267 sticks. the class will build 93 houses. About how many sticks will be needed?
Is AABCDEF? If so, identify the similarity postulate or theorem that
applies.
A
B
16 105⁰
36
с
D
4
LLI
E
9
-105⁰
F
OA. Similar - AA
OB. Similar - SSS
OC. Similar - SAS
OD. Cannot be determined
4
Answer:
C
Step-by-step explanation:
C is the correct answer as both triangles have a similar angle of 105⁰ and both side lengths of triangle ABC are being divided by 4 to have the same two side lengths as triangle DEF
The triangles ΔABC and ΔDEF are similar triangles by SAS theorem
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔABC
The measure of side AB = 16
The measure of side AC = 36
And , the measure of ∠ABC = 105°
Let the first triangle be ΔDEF
The measure of side DE = 16
The measure of side DF = 36
And , the measure of ∠DEF = 105°
Now , the ratio of sides of the triangles is given by
AB / DE = AC / DF
4/16 = 9/36
1/4 = 1/4
So , corresponding sides of similar triangles are in the same ratio
And , the measure of angles = 105°
Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , they are similar triangles
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If Jenny walks 2 miles in 40 minutes, then Jenny will walk how far in 100
minutes if she walks at the same speed the whole time? If necessary, round
your answer to the nearest tenth of a mile.
Answer:
Five miles
Step-by-step explanation:
if 2=40 then 1=20 so 5=100
4x² + 24x + 20
common factor =
which of the following expresses the coordinates of the foci of the conic section shown below? (x-2)^2/4+(y+5)^2/9
Step-by-step explanation:
[tex] \frac{(x - 2) {}^{2} }{4} + \frac{(y + 5) {}^{2} }{9} = 1[/tex]
This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a
The formula for the foci of the vertical ellipse is
(h,k+c) and (h,k-c).
where c is
Our center (h,k) is (2, -5)
[tex] {c}^{2} = {a}^{2} - {b}^{2} [/tex]
Here a^2 is 9, b^2 is 4.
[tex] {c}^{2} = 9 - 4[/tex]
[tex] {c}^{2} = 5[/tex]
[tex]c = \sqrt{5} [/tex]
So our foci is
[tex](2, - 5 + \sqrt{5} )[/tex]
and
[tex](2, - 5 - \sqrt{5} )[/tex]
What are the roots for the quadratic equation below?
3x^2+9x-2=0
Answer:
[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
Given: 3x² + 9x - 2 = 0
⇒ a = 3, b = 9, c = -2
Substitute the given values into the formula and simplify:
[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Therefore, the correct answer is A.
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In the last three years Frederic’s basketball team win 40 more games than they lost
Answer:
Wht is the total matches they played?
3xy - ² + 4x for x = -2, y = - and = 6?
Answer:
See below
Step-by-step explanation:
Not sure what you are asking....do you want to know what y is when x = -2 and the equation = 6 ?
3 xy^2 + 4x = 6 or is that 3 xy^(-2) + 4x = 6
Could use some serious editing of your question if you are able ....
Describe the change in the graph of the parabola f(x) when it transforms into g(x) =
The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).
The parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).
The parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).
The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Answer:
(d) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
We assume you intend ...
f(x) = equation of a parabola
g(x) = 2/3·f(x)
Multiplying a function by a factor of 2/3 will cause it to be compressed vertically to 2/3 of its original height. When the function is a parabola, this has the effect of making it appear wider than before the compression.
__
The compression factor is positive, so points on the graph remain on the same side of the x-axis. The direction in which the graph opens is not changed.
The attachment shows parabolas that open upward and downward, along with the transformed version.
Answer:
D.) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
I got it right on the test :)
stay hydrated.
what is golden ratio, and explain it's history
Answer:
The golden ratio is a proper term in the field of mathematics, but it finally covers more than the research in the field of mathematics. According to the current literature discussion, we can say that the discovery of the Golden ratio and how it evolved is still a mystery. But studies have shown that the Pythagorean school of ancient Greece in the 6th century BC studied the formation of regular 5-sided and regular 10-sided plots, leading modern mathematicians to conclude that the Pythagorean school had touched on and even mastered some of the rules of the golden ratio and also discovered irrational numbers. It focuses on the relationship from mathematics, to explore the principle of beauty and that beauty is harmony and proportion, according to the proportional relationship can form beautiful patterns, this is actually a digital proportional relations, the line is divided into two parts, a long and a short period of the ratio of the equal to the ratio of length to a long, their proportion is around 1.618:1, This mathematical principle is also embodied in the famous Frederikian sequence, in which everything in this proportion shows the harmony and balance of its internal relations.
In the 4th century BC, the Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion. Around 300 BC, Euclid absorbed the research results of Eudoxus in writing The Elements of Geometry and further systematically discussed the Golden Section, which became the earliest treatise on the golden Section (i.e. the middle and the end ratio) [5].
After the Middle Ages, the golden ratio was shrouded in mystery. Italian mathematician Luca Pacioli called the middle and the end of the ratio sacred and wrote a book about it. The German astronomer Johannes Kepler called the divine ratio the Golden Ratio. Golden in the 19th century the name only gradually, and the evidence is that German mathematician Martin Ohm (English: Martin Ohm) wrote the second edition of the basic pure mathematics annotation wrote about the interpretation of the golden ratio: "people used to put any straight line along the way will be divided into two parts, the method of known as the golden mean". And in the ninth edition of the Encyclopaedia Britannica, published in 1875, Sully notes: "The interesting, experimental and strong idea put forward by Frederick... proclaimed the supposed superiority of the 'golden Section' in visual proportion." So the Golden Section was already popular. In the 20th century, American mathematician Mark Barr gave it the name Phi. The Golden Section has many interesting properties and has been widely used by humans to make it famous today. The most famous example is the golden ratio or 0.618 method in optimization, which is first proposed in 1953 by Jack Kiefer (English: Jack Kiefer), an American mathematician, and is promoted in China in 1970s.
Select The correct answer.
Segment AB Is tangent to the circle at point B. Which equation describes the relationship between the tangent and secant line segments?
B
D
OA
(AD)² = (AC) (AB)
OB. (AB)2 = (AC)(CD)
OC. (AB)2 = (AC)(AD)
OD. AB=(AC + AD)
According to the tangent-secant theorem, the relationship of the tangent and secant in the given circle is: C. AB² = (AC)(AD).
What is the Tangent-Secant Theorem?The secant tangent theorem defines the relationship between the lengths of the secant and the tangent line segments when they meet outside a circle.
Based on the tangent-secant theorem, using the image given, the equation that describes the relationship of the tangent and secant in the given circle is:
C. AB² = (AC)(AD)
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Answer: C
Step-by-step explanation:
got it right on my test!!
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
triangle a is a right angled triangle with a height | of 8cm base of 5cm and missing hypotenuse
triangle b is a right angled triangle with a height | of 12cm and a hypotenuse of 17cm with a missing base
The length of the missing sides of triangles A and B are 9.43 cm and 12.04 cm respectively.
Pythagoras theoremTriangle A:
Height = 8cmBase = 5cmHypotenuse = x cmHypotenuse² = height ² + base²
x² = 8² + 5²
= 64 + 25
x² = 89
x = √89
x = 9.43 cm
Triangle B:
Height = 12cmBase = x cmHypotenuse = 17 cmHypotenuse² = height ² + base²
17² = 12² + x²
17² - 12² = x²
289 - 144 = x²
145 = x²
x = √145
x = 12.04 cm
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PLEASE HELPP!!!!!
Question 9 of 13
Which of the following scatterplots represents the data shown below?
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47),
(9,34), (10,3), (11, 33), (12, 35)
The attached graph below can represent the scatter plot of the points. the correct option is B.
How to find the function which was used to make graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given:
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47), (9,34), (10,3), (11, 33), (12, 35)
The above points would be plotted using the following scale such as:
x: axis -> 1 interval = 10 units
y: axis -> 1 interval = 10 units
The attached graph below can represent the scatter plot of the points. the correct option is B.
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Which statements are true? Select three options O The line x = O is perpendicular to the line y = -3 O All lines that are parallel to the y-axis are vertical lines. O All lines that are perpendicular to the x-axis have a slope of O. O The equation of the line parallel to the x-axis that passes through the point (2, -6) is x = 2. O The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1
The statements which are true among the answer choices are;
The line x = O is perpendicular to the line y = -3.All lines that are parallel to the y-axis are vertical lines. Which statements among the answer choices are true?In the concept of straight line graphs (linear graphs) the statements are evaluated as follows;
The line x = O is perpendicular to the line y = -3. - This is true because the former is a vertical line while the latter is horizontal.All lines that are parallel to the y-axis are vertical lines. - True, because the y-axis itself is a vertical line.All lines that are perpendicular to the x-axis have a slope of O. - False, because all lines perpendicular to the X axis are vertical lines and have do not have slope 0.The equation of the line parallel to the x-axis that passes through the point (2, -6) is x = 2. - False, because a line parallel to the x-axis is defined by y.The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1. - True.Read more on parallel and perpendicular lines;
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Simplify
[tex]\left(\frac{123}{321}\right)\left(\frac{456}{654}\right)\left(\frac{789}{987}\right) \left(\frac{123}{321}\right)^{-1}\left(\frac{456}{654}\right)^{-1}\left(\frac{789}{987}\right)^{-1}[/tex]
Answer:
1
Step-by-step explanation:
using the rule of exponents
[tex](\frac{a}{b}) ^{-1}[/tex] = [tex]\frac{b}{a}[/tex] , then
[tex]\frac{123}{321}[/tex] × [tex]\frac{456}{654}[/tex] × [tex]\frac{789}{987}[/tex] × [tex]\frac{321}{123}[/tex] × [tex]\frac{654}{456}[/tex] × [tex]\frac{987}{789}[/tex]
[ [tex]\frac{123}{321}[/tex] × [tex]\frac{321}{123}[/tex] = 1 , [tex]\frac{456}{654}[/tex] × [tex]\frac{654}{456}[/tex] = 1 , [tex]\frac{789}{987}[/tex] × [tex]\frac{987}{789}[/tex] = 1 ]
= 1 × 1 × 1
= 1
Where does billy bob johns
Answer:
in ur moms house
Step-by-step explanation:
Answer:
he doesn't
Step-by-step explanation:
Find the area of a 150° sector of a circle whose radius is 3.
Answer: [tex]\frac{15\pi}{4}[/tex]
Step-by-step explanation:
[tex]A=\pi(3^{2})\left(\frac{150}{360} \right)=\boxed{\frac{15\pi}{4}}[/tex]
Can anyone Help I have 25 questions, 2hr 40mins remaining,
Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
How do we add polynomials?We add polynomials combining the like-terms, that is, adding terms with the same exponent.
In this problem, the polynomials are:
[tex]f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}[/tex][tex]g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3[/tex]Combining the like terms, the addition is given by:
[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
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g(x) f(x) = −6x − 3 cosine function with y intercept at 0, negative 3 h(x) = 2 cos(x + π) − 1 Using complete sentences, explain which function has the greatest y-intercept. (10 points)
full step by step process please.
A function assigns the values. The function that has the greatest y-intercept is h(x).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
There are three function, g(x){given in the graph below}, f(x)= -6x-3, and -3h(x) = 2 cos(x + π) − 1, the y-intercept of the function is the point at which the graph intersects the y-axis. Therefore, the y-intercept are,
g(x) = -3
f(x) = -3
h(x) = 1
Hence, the function that has the greatest y-intercept is h(x).
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What is the value of x?
E
(2x)°
xº
D
Answer:
30°
Step-by-step explanation:
Since ED = FD, the ∠DEF = ∠EFD
Since ∠DEF = 2x, ∠EFD is also equal to 2x
The sum of the 3 angles of a triangle is 180°
So x + 2x + 2x = 180
6x = 180
x = 30
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Step-by-step explanation:
[tex]29 {}^{ \frac{x}{2} } [/tex]
[tex]((29) {}^{ \frac{1}{2} } ) {}^{x} [/tex]
The answer is A
A 13 -ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving away at the rate of 15 ft/sec.
a. What is the rate of change of the height of the top of the ladder?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?