Write the following equation in slope-intercept form.
3
Q1. If a and b are rational number and √2+2√3 2√√2+√3 a+b√6, then find the values of a and b.
Q2. Find the length and breadth of a rectangle whose area is 6x²-29x + 30. Also find its perimeter.
Answer:Q1. The values of a and b cannot be determined from the given information. To find the values of a and b, additional information is needed to solve the equation √2+2√3 = (a + b√6)/(2√2+√3).
Q2. To find the length and breadth of a rectangle, you need to factor the polynomial expression 6x² - 29x + 30. Then, you need to identify two numbers that multiply to 30 and add up to -29. The expression 6x² - 29x + 30 can be factored as (2x - 5)(3x - 6). The length of the rectangle is 2x - 5, and the breadth is 3x - 6. The perimeter of the rectangle is (2 * length) + (2 * breadth) = 2(2x - 5) + 2(3x - 6) = 4x + 4.
Step-by-step explanation:
Q1. The values of a and b cannot be determined from the given information. To find the values of a and b, additional information is needed to solve the equation √2+2√3 = (a + b√6)/(2√2+√3).
Q2. To find the length and breadth of a rectangle, you need to factor the polynomial expression 6x² - 29x + 30. Then, you need to identify two numbers that multiply to 30 and add up to -29. The expression 6x² - 29x + 30 can be factored as (2x - 5)(3x - 6). The length of the rectangle is 2x - 5, and the breadth is 3x - 6. The perimeter of the rectangle is (2 * length) + (2 * breadth) = 2(2x - 5) + 2(3x - 6) = 4x + 4.
a family of four averages 4 showers a day for a month. the showers last on average of 10 minuetes each. calculate how much water the family would use each month just on showering if they only had standard floe shower heads in their house that delivered 5 gal/min. a
The family would use: 6000 gallons of water per month on showering.
In each day, the family would use;
4 showers/day * 10 minutes/shower
= 40 minutes of shower time per day.
In a month with 30 days, the family would use
40 minutes/day * 30 days
= 1200 minutes of shower time per month.
If each shower head delivers 5 gallons/minute, then the family would use 1200 minutes * 5 gallons/minute = 6000 gallons of water per month on showering.
The amount of water used by this family just on showering is more than half of the total amount of water used by the average family in a month.
Additionally, using standard flow shower heads can help to reduce water usage. Many cities have adopted regulations that require new shower heads to have a maximum flow rate of 2.5 gallons per minute or less. By using low-flow shower heads, this family could potentially reduce their water usage by half.
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2. Ana hace recuerdos para bodas con velas en forma de pirámide cua- drangular decoradas con semillas. a) Si un lado de la base mide 7 cm y la altura de la pirámide es de 15 cm, ¿qué volumen de cera ocupará para hacer 40 velas?
It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles
How do you calculate a quadrangular pyramid's volume?The volume of a pyramid with a square base can be calculated using the formula V=13s2h, where s is the length of the base's sides. A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume = (1/3) base area height, where height is the height from the base to the apex, is the basic formula for a pyramid's volume.
Given,
side = 7cm
height = 15cm
Volume = 1/3 × h × 5/2 × s
⇒ volume = 15×7 ×5/6
⇒ volume = 87.5 cm³
It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles
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Complete Question -
Ana makes wedding favors with candles in the shape of a quadrangular pyramid decorated with seeds. a) If one side of the base measures 7 cm and the height of the pyramid is 15 cm, what volume of wax will it take to make 40 candles?
What is log 2 called?
The binary logarithm, sometimes referred to as log base 2, is the inverse function of the power of two functions.
According to the generic logarithm, can be represented in exponential form as for every real number n.
n = [tex]a^x[/tex]
The logarithm form is expressed as Log base 2 is the power to which the number 2 must be raised to acquire the value of n.
[tex]log_a n[/tex] = x
In this case, "a" is a positive real integer that is used as a base and "x" is an exponent. The formulas for log base 2 functions are given for any real value x as
x = [tex]log_{2}n[/tex]
Which is equal to
[tex]2^x[/tex] = n
The real number system does not specify the logarithm of base 0 or logarithms of negative values.
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Write 7/4 as a mixed fraction.
I need an answer fast!
it's inverted but still this is answer
What are the steps in solving quadratic equation by factoring give one example?
Steps which are required to solve quadratic equation by factoring are as follow :
1. Convert the equation into standard form.
2. calculate the factors of the equation by splitting or formula method.
3. Equate the factors to zero and get the value.
Example : Factors of x² + 4x + 4 = 0 are x = -2.
As given in the question,
Steps required to solve quadratic equation by factoring are given by :
Standard quadratic equation is : ax + by + c = 0
Two methods to solve quadratic equations are:
a. Splitting method
b. Formula : x = ( - b ± √b² -4ac ) / 2a.
Consider a example:
x² + 4x = -4
1. Convert into standard from
x² + 4x + 4 = 0
solve it by splitting method :
x² + 2x + 2x + 4 = 0
⇒ x(x + 2 ) + 2 ( x + 2 ) =0
⇒ ( x + 2 ) ( x+ 2 ) = 0
⇒ x + 2 = 0
⇒ x = -2
Therefore, the steps required to solve quadratic equation are :
1. Convert the equation into standard form.
2. calculate the factors of the equation by splitting or formula method.
3. Equate the factors to zero and get the value.
Example : Factors of x² + 4x + 4 = 0 are x = -2.
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A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A|B)=
%
b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A'|B') =
%
a) The probability that a person has the virus given that they have tested positive is 0.5.
b) The probability that a person does not have the virus given that they test negative is 0.9.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
Virus infects one in every 400 people.
Let A = be the event of being infected.
Let A' = be the event of not being infected.
Let B = be the event of being tested positive.
Let B' = be the event of being tested negative.
Let the population = 1,00,000
So, now the number of infected people are -
Infected people = (1/400) 100000
Infected people = 250
The number of non-infected people are -
Non-Infected people (T') = 100000 - 250
Non-Infected people (T') = 99750
The test is 80% positive when the person has the virus -
N(A|B) = 0.80 × 250
N(A|B) = 200
So, the probability value for N(A|B) -
P(A|B) = 200/400 = 0.5
The test is 10% positive when the person does not have the virus -
N(A'|B) = 0.10 × 99750
N(A'|B) = 9975
Number of people who test negative when they don't have the virus -
N(A'|B') = (T') - N(A'|B)
N(A'|B') = 99750 - 9975
N(A'|B') = 89775
So, the probability value for N(A'|B') -
P(A'|B') = 89775/99750 = 0.9
Therefore, the probabilities are 0.5 and 0.9.
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G = the square root of m/t^2.
m = 6. 1 x 10^-5
t = 1. 7 x 10^-6
What is the value of G? wrote your answer in standard form correct to 3 s. F.
m is increased by 8%
t is increased by 5%
What is the new value of G?
Give your answer in standard form correct to 3 s. F.
Any help with these 2 questions would be extremely appreciated :)
The required required value of G is 1) 2.11 × 10^7 2) 2.06 × 10^7.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
According to question:We have,
1) m = 6. 1 x 10^-5, t = 1. 7 x 10^-6
G = m/t^2
G =6. 1 x 10^-5/(1. 7 x 10^-6)^2
G = 2.11 × 10^7
2)m is increased by 8%
New m = 6.59 x 10^-5,
t is increased by 5%
New t = 1.79 x 10^-6
So
G = m/t^2
G = 6.59 x 10^-5/(1.79 x 10^-6)^2
G = 2.06 × 10^7.
Thus, required value of G is 1) 2.11 × 10^7 2) 2.06 × 10^7.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
Solving the expression:
3−9/3+(2)(9)
=3−3+(2)(9)
=0+(2)(9)
=0+18
=18
o is the centre of the circle and abc and edc are tangents to the circle what is bcd if o is 152
The requried measure of the angle m∠BCD is 28°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
From the figure,
m∠BOD = 2m∠BFD
= 2 × 76°
= 152°
OD perpendicular to CE simultaneously OB perpendicular to CA
m∠ODC = m∠OBC = 90°
m∠ODC + m∠OBC + m∠BOD + m∠BCD = 360
90 + 90 + 152 + m∠BCD = 360
m∠BCD = 28°
Thus, the requried measure of the angle m∠BCD is 28°.
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Pls someone help me on this
On solving the provided question we can say that from the graph, we can say as both sides are similar angle D is congruent to angle D'
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
from the graph, we can say as both sides are similar
Angle D is congruent to angle D'
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What is the length of Line segment B C?
Answer:
(c) 15 units
Step-by-step explanation:
Given a right triangle with hypotenuse 17 and one leg 8, you want the measure of the other leg.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the sides of a right triangle:
a² +b² = c² . . . . . . where c is the hypotenuse
Applicationa² +8² = 17² . . . . . . using given values of b, c
a² = 289 -64 = 225 . . . . subtract 8²
a = √225 = 15
The length of segment BC is 15 units.
__
Additional comment
These side lengths {8, 15, 17} can be considered to be a "Pythagorean triple." It is one of a few that often appear in algebra and geometry problems. Others include {3, 4, 5}, {5, 12, 13}, {7, 24, 25}. Multiples of these are also commonly seen, such as 2×{3, 4, 5} = {6, 8, 10}.
I want to delete this question. How do I do it?
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Seven girls and three boys are waiting to audition for a school play. To be fair the staff is
choosing candidates at random for the auditions. If the first two selections were boys, how
does that affect the probability of the third candidate being a girl?
The first two selections do not affect the probability of the third candidate.
It increases the probability of a girl being the third candidate.
It decreases the probability of a girl being the third candidate
Since there is only one boy left, a girl will definitely be the third candidate.
If the first two selections were boys, the way that it affects the probability of the third candidate being a girl is; It increases the probability of a girl being the third candidate.
How to solve conditional probability?Conditional probability in mathematics is defined as the type of probability that depends on the occurrence or outcome of another event.
Now, we are told that in the school;
Number of Girls = 7
Number of boys = 3
Since the staff is choosing the candidates at random, then it means everyone has an equal chance to be picked.
Now, since we are told that 2 boys are selected first, it means that there would be only 1 boy left and as such the probability of selecting a girl will increase because there would now be seven girls out of 8 people.
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Find the equation of a line that passes through the point (0,3) and has a gradient of 2. Leave your answer in the form y = m x + c.
The equation of a line that passes through the point (0,3) and has a gradient of 2 is: y = 2x + 3
We know that the point-slope form of equation of line is:
(y - y₁) = m(x - x₁)
where m is the slope (also called as gradient)
Here, we have been given a point (0, 3) and the slope of the line is 2.
Let us assume that (x₁, y₁) = (0, 3)
and slope (m) = 2
Using point-slope form of equation of line,
(y - y₁) = m(x - x₁)
(y - 3) = 2(x - 0)
y - 3 = 2x
y - 3 + 3 = 2x + 3
y = 2x + 3
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Graphing equations for algebra
The solution for the inequality -4x-3>-5x+8 is x>11.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
1) -11+x≥-3
Move all terms not containing x to the right side of the inequality.
x≥8
2) -x/4 <7
Move all terms not containing x to the right side of the inequality.
-x<28
x>-28
3) The highest waterfall in the world is Angel falls in Venezuela at 1000 meters.
So, the inequality represent the height of waterfall is h≤1000.
4) -4x-3>-5x+8
Add 5x on both the sides of an inequality, we get
x-3>8
Add 3 on both the sides of an inequality, we get
x>11
5) Given that, Area≤48
Here, 1/2 ×8×x≤48
4x≤48
x≤12
6) -2x-9<-x-4
Add x on both the sides of an inequality, we get
-x-9<-4
Add 9 on both the sides of an inequality, we get
-x<5
x>-5
7) 1/2 x-8>-3
Move all terms not containing x to the right side of the inequality.
Here x>10
Therefore, the solution for the inequality -4x-3>-5x+8 is x>11.
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Sadie got food and drinks if it cost $22.50 and there is a 9% meals tax, how much is the bill
Answer:
Step-by-step explanation:
Tax would be about 2 dollars
how many quarters are in thirty dollars
Answer: 120 quarters
Step-by-step explanation:
There are 4 quarters in a dollar.
For 30 dollars, there are 3 * 40 = 120 quarters
120 quarters are in thirty dollars
In DIY store the height of a door is given as 195 cm to the nearest cm write down the bound for the height of the door
220 cm serves as the door's maximum height allowance.
The dimensions of a door are what?The standard door height is 80 inches, which is often mandated by construction rules, and is used in both commercial buildings and private dwellings. The usual standard door width for an external door is 36 inches, while the average standard door width for an interior door is 28 to 32 inches. Door widths vary more frequently.The door height can be determined by taking a measurement from the top of the door panel to the bottom of the door edge. Next, determine the sidelight's height or the distance between the interiors of the top and bottom jambs.To learn more about height refer to:
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6 , then
x = 7 - 6 = 1
x = 7 + 6 = 13
Given g(x)=√x - 4 + 3 find g-¹(5)=
A 26
B 67
C4
D 8
Answer:
D
Step-by-step explanation:
D.D.D..D.D.D.D.D.D.D.D D D. D.D.D.
The polynomial 2x³+x²-3x+ p has a remainder 20 when divided by (x - 2). Find the value of constant p.
The value of constant p is 6. Polynomials are algebraic formulas with variables and coefficients. Variables are also known as indeterminates.
How to get the value?Remainder for f(2) = 20.
F(2)=2(23)+22−3(2)+p=20
16+4−6+p=20
14+p=20
P=6
To divide polynomials, divide each term independently by the monomial (as mentioned above), and sum the quotients of each division to get the result. Polynomial long division is a procedure in algebra for dividing a polynomial by another polynomial of the same or lower degree, which is an extended version of the well-known arithmetic approach known as long division. It is simple to accomplish by hand because it divides an otherwise difficult division problem into smaller ones.
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Measures of ___ describe the spread of the data.
A. Center
B. Frequency
C. Statistic
D. Variability
Answer: The Answer is D. Variability
Answer: D: Variability
Hope this helped!
how many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same? (in other words, two arrangements are considered the same if i can rotate and/or reflect one arrangement to get the other. assume that each square gets exactly one bead.)
There are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same. We can solve this problem using Burnside's Lemma.
Burnside's Lemma states that for a group action on a set, the number of fixed points is given by the average over the group of the number of fixed points under a particular group element, where the average is taken over all group elements.
In this case, the group action is the action of rotating and reflecting the grid, and the set is the set of all possible bead arrangements in the grid. To use Burnside's Lemma, we need to find the number of fixed points (i.e., bead arrangements that are unchanged) under each group element, and then take the average over all group elements.
There are a total of $4$ rotations and $2$ reflections possible for a 2x3 grid.
The identity transformation keeps the grid in its original position, and thus there are
6!/(2!3!) = 60
The $90 rotation keeps $3 beads in the same place and switches the other $3, and similarly $180 and $270 rotation also keeps $3 beads in the same place and switches the other $3$, thus there are
3! = 6
The reflection on the horizontal axis keeps $3 beads in the same place and switches the other $3, and similarly the reflection on the vertical axis also keeps $3 beads in the same place and switches the other $3, thus there are
3! = 6
So the average number of fixed points is $(6+6+6+60)/8 = [tex]\frac{78}{8}[/tex] = 9.75$
So, there are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same.
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show the equation of V²=U²+2as
Answer: V² = U² + 2as
This equation is known as the equation of motion, and it relates the final velocity (V) of an object to its initial velocity (U), acceleration (a), and displacement (s).
The equation states that the square of the final velocity is equal to the square of the initial velocity plus twice the product of acceleration and displacement.
The equation can be used to calculate the final velocity of an object if the initial velocity, acceleration, and displacement are known, or it can be used to calculate the displacement of an object if the initial velocity, final velocity, and acceleration are known.
This equation is based on the concepts of physics and it's used to calculate the velocity of an object under constant acceleration.
Step-by-step explanation:
8) In 1992, 1219 monk parakeets were observed in the United States. For the next 11 years, about 12% more parakeets were observed each year.
How many parakeets are there in 2006?
The number of parakeets are there in 2006 are approximately equal to 4240 monk parakeets.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables , constants and exponents.
Given, expressions
In 1992, 1219 monk parakeets were observed in the United States. For the next 11 years, about 12% more parakeets were observed each year.
The initial amount is 1219 . The percent growth is 12%.
So the growth factor is 1+0.12 = 1.12
Therefore,
The model us M = 1219 (1.12)^t
where M is the number of monk parakeets after t years.
M(11) = 1219(1.12)^11
M(11)=4240.35
There will be approximately 4240 monk parakeets in 2003.
M = 1219 (1.12)^t. In 2023, there will be approximately equal to 4240 monk packets.
Hence, The number of parakeets are there in 2006 are approximately equal to 4240 monk parakeets.
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Parallelogram ABCD is given. Draw line EF such that it goes through vertex C, point E lies on side AD, and point F lies on the extension of BA.
Prove that AECD ~ ACFB.
Solving the provided question, we can say that area of parallelograms = 1/2[( a +b)/ 2 ] = 1/2[( AB+EF)/ 2 ]
What is parallelograms?A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.
we have
area of parallelograms = 1/2[( a +b)/ 2 ]
a = AB and b = EF
area of parallelograms = 1/2[( AB+EF)/ 2 ]
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For what value of k does the pair of linear equations has an infinite many solution KX 4y 3 6x 12y 9?
The required value of k will the system of linear equations has infinite number of solutions is 2.
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
According to question:We know that
KX + 4y - 3 = 0 . ..........(1)
6x + 12y - 9=0 ..........(2)
Because there are infinity many solutions to linear equations.
[tex]\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]
⇒ k/6 = 4/12 = -3/-9
k/6 = 1/3
k = 2
Thus,required value of k is 2.
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An image of a rhombus is shown.
A rhombus with a base of 18 inches and a height of 16 inches.
What is the area of the rhombus?
288 in2
144 in2
136 in2
68 in2
If a rhombus with a base of 18 inches and a height of 16 inches has an area of 288 square inches
What is Polygon?a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
A rhombus is a quadrilateral whose four sides all have the same length.
Given that rhombus with a base of 18 inches and a height of 16 inches.
Height = 16 inches
Base = 18 inches
Area of the rhombus = Base × Height
=16×18
288 square inches.
Hence, if a rhombus with a base of 18 inches and a height of 16 inches has an area of 288 square inches.
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Answer:
288
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