Hence, It is proved that, Pythagorean theorem, is verified.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
A triangle has sides with lengths 8, 15, and 17.
so, here, 8^2 + 15^2
=64 +225
=289
=17^2
Hence, It is proved that, Pythagorean theorem, is verified.
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Multiply left-parenthesis x plus 2 right-parenthesis left-parenthesis x minus 6 right-parenthesis
Answer options
A.
x squared minus 8 x minus 12
B.
x squared plus 8 x minus 12
C.
x squared minus 4 x minus 12
D.
x squared plus 4 x minus 12
E.
x squared minus 4 x plus 12
Answer:
[tex]x^{2}-4x-12[/tex]
Step-by-step explanation:
(x+2)(x-6)
STEP 1 - USE FOIL
(FOIL is a standard way of multiplying 2 fractions, just multiply in the following order):
Forward
Outside
Inside
Last
(x+2)(x-6) becomes this when you FOIL it:
[tex](x^{2} )(-6x)(2x)(-12)[/tex]
STEP 2 - COMBINE ALL THE TERMS
[tex]x^{2}[/tex] has to stay by itself because there are no other squares. [tex]-6x+2x=-4x[/tex] because you're adding two to -6 which effectively is 6 - 2 but you're adding a negative sign. And [tex]-12[/tex] stays the same because there are no x's in it.
STEP 3 - WRITE THE SOLUTION
All in all, the final solution, once you put everything together, is:
[tex]x^{2} -4x-12[/tex]
Fill in the missing term and select the
missing description. Simplify any fractions.
6(a + 2)
a + 2 =3
a =
Subtract 2 from both side
The value of a in the equation a + 2 = 3 is 1.
How to calculate the valueAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
a + 2 = 3
Subtract 2 from both sides
a + 2 - 2 = 3 - 2
a = 1
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+Ready
Practice Write and Solve Mulo-Step Equations-Quid-Level
Three sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches.
The perimeter of the quadrilateral is 40 inches.
Write an equation that represents
the situation.
+
9
3
7
40
11
7
9
9
The equation that represents the situation is q = 40 - 7
How to determine the perimeterThe formula for the perimeter of a quadrilateral is expressed as;
P = a + b + c + d
Where the sides, a , b , c and d are all the sides of the quadrilateral
From the information given, we have that;
The sides are a, the fourth is 7
The perimeter = 40 inches
Substitute the values
40 = 7 + q
collect the like terms, we get
q = 40 - 7
subtract the values
q = 33 inches
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E(t)E, left parenthesis, t, right parenthesis models the daily amount of energy (in kilojoules, \text{kJ}kJstart text, k, J, end text) that a solar panel in Pago Pago generates, ttt days after the autumn equinox. Here, ttt is entered in radians. E(t) = {624}\sin\left({\dfrac{2\pi}{365}}t\right) + {8736}E(t)=624sin( 365 2π t)+8736E, left parenthesis, t, right parenthesis, equals, 624, sine, left parenthesis, start fraction, 2, pi, divided by, 365, end fraction, t, right parenthesis, plus, 8736 What is the first day after the autumn equinox that the solar panel generates 8400\text{ kJ}8400 kJ8400, start text, space, k, J, end text?
The first day after the autumn equinox that the solar panel generates 8400 kJ is approximately 39.2 days, or 0.107 radians, after the equinox.
To find the first day after the autumn equinox that the solar panel generates 8400 kJ, we need to solve the equation:
624sin(2π/365)t + 8736 = 8400
Simplifying the equation, we get:
sin(2π/365)t = 0.958
Taking the inverse sine of both sides, we get:
(2π/365)t = 1.296 or (2π/365)t = 3.846
Solving for t in each equation, we get:
t ≈ 78.97 or t ≈ 235.62
Since t is measured in radians, we need to convert it to days by dividing by 2π/365:
t ≈ 78.97 / (2π/365) ≈ 86.75 or t ≈ 235.62 / (2π/365) ≈ 256.73
Therefore, the first day after the autumn equinox that the solar panel generates 8400 kJ is either day 87 or day 257.
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Divide 12x5 - 36x4 - 6x³ by 6x².
O 2x² + 6x + 1
O 2x² - 6x - 1
2x³ + 6x² + x
O 2x³-6x²-x
Answer:
D. 2x^3−6x^2−x
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors.
Hope this helps.
name the ray that is opposite FH.
Answer: Ray HF is opposite of Ray FH
Step-by-step explanation:
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The solution of the system is the set of all points (x, y) that satisfy both equations, and the points in the solution set are (-1, 3) and (2, -2).
What is System of Equation?
A system of equations is a collection of one or more equations with several variables. The variable mappings that satisfy all component equations—that is, the places where all of these equations intersect—are the solutions of systems of equations.
To solve the system of equations graphically, we can plot each equation on the same set of axes.
Here is how to solve the system of equations:
y = -x² + 4x - 2
4x + 2y = 12
The points of intersection between the two lines are the solutions of the system of equations. We can see from the graph that there are two points of intersection, at approximately (-1, 3) and (2, -2).
Therefore, the solution of the system is the set of all points (x, y) that satisfy both equations, and the points in the solution set are (-1, 3) and (2, -2).
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Beth added 1 1/4
pounds of fruit to a fruit basket. Her son took 2 3/8 pounds
of fruit out of the basket. What was the total change in pounds of fruit in the
fruit basket?
Answer: To find the total change in pounds of fruit in the basket, we need to subtract the amount taken out from the amount added.
First, let's convert all the fractions to decimals:
1 1/4 = 1.25
2 3/8 = 2.375
Now, we can subtract:
1.25 - 2.375 = -1.125
So, the total change in the fruit basket was -1.125 pounds, meaning the basket had 1.125 pounds less fruit after the removal.
Step-by-step explanation:
Pre cal due tonight pls help
The dot product a . b is -22
What is the dot productThe dot product, also known as scalar product or inner product, is a binary operation that takes two vectors and returns a scalar (single-valued) quantity. The dot product of two vectors is equal to the product of the magnitude (length) of the vectors and the cosine of the angle between them.
Given two vectors, A and B, the dot product is defined as:
A ∙ B = |A| * |B| * cos(θ)
where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.
a = <3, -2>
b = <-2, 8>
a . b = (3 * -2) + (-2 * 8)
a . b = -6 + - 16
a . b = -22
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Sanjay made cookies for a bake sale and has tracked his sales by cookie shape. cat 36 star 14 dog 35 Considering this data, how many of the next 51 cookies sold should you expect to be in the shape of a dog?
The number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
The probability of cookies sold in shape of dog is:
P = 35/85
The number of cookies sold that would be in the shape of the dog in the next 51 cookies is:
N = 51 (P)
N = 51 (35/85)
N = 21
Hence, the number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.
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Gina wilson all things algebra unit 4: congruent triangles homework 7: proofs review: all methods page 1
In geometry, two triangles are said to be congruent if they are the same size and shape. This means that all corresponding angles and sides are equal.
To prove that two triangles are congruent, we must use one of the five congruency tests: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).The SSS test states that if all three sides of two triangles are equal, then the triangles are congruent. The SAS test states that if two sides and the included angle of two triangles are equal, then the triangles are congruent. The ASA test states that if two angles and the included side of two triangles are equal, then the triangles are congruent. The AAS test states that if two angles and a non-included side of two triangles are equal, then the triangles are congruent. Lastly, the HL test states that if the hypotenuse and a leg of a right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are congruent.In order to prove that two triangles are congruent, we must show that one of the five congruency tests is true. To do this, we can use techniques such as the Reflexive Property, the Symmetric Property, and the Transitive Property. We can also use logical reasoning, such as if two angles are equal and their corresponding sides are proportional, then the triangles must be congruent.
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What is the definition of congruent triangles?
At the start of a party, a drink dispenser contains 912 quarts of iced tea. After the party only 7 cups of tea remain. How many cups of iced tea did people drink during the party?
Amount of iced-tea consumed during party was 92 cups, which is equivalent to 23 quarts. It's important to note difference between volume units such as cups and quarts, and the conversion factor between them.
To determine the number of cups of iced-tea that were consumed during the party, we need to subtract the amount that remained from the total amount that was in the drink dispenser at the start of the party.
One cup of iced tea is equal to 1/16 of a quart, so 7 cups is equal to
7 * (1/16) = 7/16 quarts.
Thus, the total amount of iced tea that was consumed during the party is 912 quarts -
7/16 quarts = 912 - 7/16
= 912 - 7 * (1/16)
= (912 * 16 - 7 * 1) / 16
= 1476 / 16
= 92.25 cups, rounded down to the nearest whole number, which is 92 cups.
It is important to note that the answer is given in cups and not quarts. Quarts is a unit of volume and cups is a unit of volume as well, but they are not equivalent. 1 quart is equal to 4 cups. If we wanted to express the amount of iced tea consumed in quarts, we would multiply the answer by 1/4.
In conclusion, the number of cups of iced tea consumed during the party is 92 cups, and if we express this in quarts it is equivalent to
92 * (1/4) = 23 quarts.
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A little boy accidentally let go of his ballioon, and it floated away. It was 2 meters above the
ground when he let go, and it steadily rose 1 meter per second.
Write an equation that shows the relationship between the number of seconds since the boy
let the balloon go, x, and its elevation in meters, y.
y=
Answer:
Step-by-step explanation:
y=2+x
1m per second.
2+1x=2+x=y
find the relational column formula.
find the selling price if
cost price is R720 with a profit of 40%
Answer:
R1008
Step-by-step explanation:
720 X 1.4 = R1008
I used 1.4 because there is a 40 percent profit
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The barber cuts 61 haircuts in 4 days. Determine the rate for a ratio of the two different quantities.
61 over 65 haircuts per day
4 over 65 haircuts per day
4 over 61 haircuts per day
61 over 4 haircuts per day
Answer:
61 over 4 haircuts per day
What is a ratio?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
A way to solve for the number of haircuts per day is to use this equation:
total number of haircuts ÷ number of days = haircuts per dayYou could also use this fraction:
[tex]\frac{total-number-of-haircuts}{number-of-days}[/tex]Inserting the numbers into the fraction::
[tex]\frac{61}{4}[/tex]Therefore, the rate for a ratio using the two different quantities is 61 over 4 haircuts per day.
select the number that comes next in the sequence of numbers below 6 12 20 26 34 40
GIVE BRAINLIEST PLEASE!
thank you and have a good day :)
Answer:
48
Step-by-step explanation:
the sequence of numbers alternates between adding 6 and 8.
6 + 6 = 12
12 + 8 = 20
20 + 6 = 26
26 + 8 = 34
34 + 6 = 40
40 + 8 = 48!
i hope this helps :)
Answer:48
Step-by-step explanation:The sequence adds 6 first then adds 8
3x-1=5x+10x= 5 1/2
please explain to me what did i do wrong and correct it
The requried correct expression 3x - 1 + 5x + 10x = 5 1/2, and solution of the equation is x = 7.5/18
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
The equation as written doesn't have a unique solution, as the left-hand side and right-hand side are not equal.
To correct the equation, you would need to provide more information about what you intended to do with the two equations and format the right-hand side of the equation properly. For example, if you meant to add the two equations, you could write,
3x - 1 + 5x + 10x = 5 + 2.5
18x = 7.5
x = 7.5/18
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Martin has 156 liters of soda. Each glass can hold 13 of a liter of soda. How many glasses can Martin completely fill with soda?
Answer: 12
Step-by-step explanation:
we divide 156 by 13, however, we can stop as soon as we reach the tenths column as we only care about full glasses.
if done correctly, you get 13
In my own words, write the 4 steps in finding the unknown angle of the givin right triangle
Answer:
Step-by-step explanation:
This question of of Trigonometry
Tan means the ratio of sides which are opposite to the given angle divided by the adjacent side to the angle (NOT THE HYPOTENUSE)
So Tan(Unknown angle) = 5/14
Unknown angle = 19.6 Degrees
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The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then ∠FGN = ∠FJN.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The line segment GF = NJ and FN bisect the angle ∠GFJ.
In triangles ΔGFN and ΔJFN, then we have
GF = NJ (Given)
∠GFN = ∠JFN (Given)
NF = NF (Common sides)
The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then we have
∠FGN = ∠FJN
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State if the lines are Parallel, Perpendicular, or Neither. 4x+y=5 3x+12y=-6
The lines 4x+y=5 and 3x+12y=-6are neither parallel nor perpendicular
How to determine the relationship between the linesFrom the question, we have the following parameters that can be used in our computation:
4x+y=5 3x+12y=-6
Make y the subject in the equations
So, we have
y = -4x + 5
y = -1/4x - 1/2
The slopes of the lines are -4 and -1/4
These numbers are not equal and they are not opposite reciprocals
This means that the lines are neither parallel nor perpendicular
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question 10
help me asap
Note that the lenght of segment LN = 55.14 (Option D)
This is arrived at using the Chord Bisector Theorem and the lengths of the sides of a right-angled triangle.
What is the Chord Bisector Theorem?According to the theorem, the line that goes through the circle's center and is perpendicular to the chord also bisects it.
This means that LK (as per the attached image) is the same as MK.
The Right Angle Postulate also means that:
LX = √[KX² - LK²]
LX = √[29² - 9²]
LX = √(841 81)
LX = √760
LX = 27.57
Since LN = LX *2
LN = 27.57 * 2
LN = 55.14
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Part Two Using the diagram above, answer the following questions. Answer both parts of each question. For questions 7 and 8, identify the process as either cellular respiration, photosynthesis or both. True or False. The arrow labeled C represents a transfer of chemical energy to mechanical energy. Explain why this is true or false. True or False. The arrow labeled A represents a transfer of solar energy to chemical energy. Explain why this is true or false. Which arrow or arrows represent a release of carbon dioxide? What process is occurring at the arrow(s) you selected? Which arrow or arrows indicate a process that cycles carbon from living or nonliving organisms? Describe the process or processes you selected. Which arrow or arrows represent reactions that demonstrate a conservation of mass and energy? Explain your answer.
The arrow labeled C represents a transfer of chemical energy to mechanical energy. False, this is because, the gas released does not do any work.
The arrow labeled A represents a transfer of solar energy to chemical energy. True, chemical energy is stored in starch molecules
The arrows that represent the release of carbon dioxide is C. This is combustion and it occurs in nonliving things. The process involves the burning of carbon materials.
The conservation energy is demonstrated by arrow A since we can show it by a chemical reaction.
What is the carbon cycle?
The carbon cycle is the process by which carbon atoms circulate through the Earth's atmosphere, oceans, and landmasses. In the carbon cycle, carbon is exchanged between the atmosphere, biosphere, hydrosphere, and geosphere. The main components of the carbon cycle include photosynthesis, cellular respiration, decomposition, and combustion.
In photosynthesis, plants take in carbon dioxide from the atmosphere and convert it into organic compounds, which serve as food for the plants and are stored in their tissues.
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It says its wrong is it?
Answer: Yes, it's wrong.
Step-by-step explanation:
In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.
r = d/2 = 3/2 = 1.5 ft
[tex]A=\pi r^{2}\\[/tex]
≈ 3.14 x 1.5
= 4.71
4 Write an expression
explaining the depth of
an Olympic pool that
goes to 50 ft. deep.
The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:
d = 50 ft.
What is olympic pool?
Olympic pool is a type of swimming pool that is used for competitive swimming and diving events. These pools typically have a uniform depth, a smooth and flat bottom and multiple lanes for swimmers to compete in.
The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:
d = 50 ft.
Where d is the depth of the pool. This expression simply states that the depth of the pool is equal to 50 ft.
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A spinner is split into eight wedges numbered 0-7.
Drag the numbers into the correct position to complete the
Venn diagram. Then use the diagram to answer the probability
questions.
The required Venn diagram is given in the picture.
What is the Venn diagram:The graphic representation of the differences and affinity between the two concepts is a Venn diagram.
In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship among sets and their contents.
Note: "The set of natural numbers starts from 1, hence '0' is not included in the set of natural numbers."
Here we have
A spinner is split into eight wedges numbered 0-7
The set of numbers = 0, 1, 2, 3, 4, 5, 6 and 7
The set of numbers that is less than 5 = {0, 1, 2, 3, 4 }
The set of numbers that are natural numbers = {0, 1, 2, 3, 4, 5, 6, 7 }
The set number that natural number and less than 5 = {1, 2, 3, 4 }
Hence,
The required Venn diagram is given in the picture.
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[ Complet Question is given in picture ]
What algebraic expression could represent the average of 2x, 3 + x and 6x?
The algebraic expression in simplified form representing the average is 3x + 1.
To solve this question, one must know the formula of average. It is as follows -
Average = sum of the numbers / quantity of numbers
Now, we see that there are 3 expressions in the question. Hence, quantity of numbers will be 3.
Sum of the numbers = 2x + 3 + x + 6x
So, keep the values in formula to find the expression -
Average = 2x + 3 + x + 6x/ 3
Simplifying the expression to find average
Average = 9x + 3/3
Performing division on Right Hand Side of the equation
Average = 3x + 1.
Hence, required algebraic expression is 3x + 1.
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a gambler has a fair coin and a two-headed coin in his pocket. he selects one of the coins at random; when he flips it, it shows heads. what is the probability that it is the fair coin?
The probability of selecting the fair coin when a gambler has both a fair coin and a two-headed coin in his pocket is 50%.
This is because, when he selects one of the coins at random, it is equally likely that he has chosen either the fair coin or the two-headed coin. If he flips the coin and it shows heads, then the probability that it is the fair coin is still 50%, because either coin could have been selected and both would show heads.This is an example of a classical probability problem, which is based on the law of equal chances. This law states that when an event has multiple possible outcomes, each of those outcomes is equally likely to occur. In this case, there are two possible coins that could have been chosen, so each coin has a 50% chance of being selected. This means that the probability of selecting the fair coin is 50%.This also applies to events that have multiple outcomes which are not equally likely. For example, if a gambler has a fair coin, a two-headed coin, and a three-headed coin in his pocket, the probability of selecting the fair coin is still 50%. This is because the gambler has an equal chance of selecting any of the coins, regardless.
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Can someone explain this
Step-by-step explanation:
This is a family of curves represented by the equation:
y = a (x + 4) (x − 2)
Different values of the a coefficient result in different quadratic functions.
The vertex of the parabolas is halfway between the zeros, at x = -1.
y = a (-1 + 4) (-1 − 2)
y = -9a
So to find the value of a, divide the y-coordinate of the vertex by -9. For example, curve A has a vertex at (-1, -3), so the value of the a coefficient is -3 / -9 = ⅓.
A. y = ⅓ (x + 4) (x − 2)
B. y = (x + 4) (x − 2)
C. y = 2 (x + 4) (x − 2)
D. y = -⅓ (x + 4) (x − 2)
E. y = -2 (x + 4) (x − 2)
Solve for x.
X
A
=
2
C
1
B
1
E
X
D
Step-by-step explanation:
ABC and ADE are similar triangles.
that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.
so, we see that AB = 2, AD = 2+1 = 3
the scaling factor f from AB to AD is then
AB × f = AD
2 × f = 3
f = 3/2
the same scaling factor now applies between BC and DE (= x).
BC × f = x
1 × 3/2 = x
x = 3/2 = 1.5
