None of the equation is true from the given equations.
What is true equation?
Verify your math to ensure that the values on either side of the equals sign are the same in order to create a true equation. To create a true equation, make sure the numbers on both sides of the "=" sign are equal.
We define a true equation as an equation where the thing at the left is equal to the thing on the right, so we need to check that for all the given equations.
1) 62 − 22 = 4 + 7⋅22
We just solve each side, we will get:
40 = 158
This is not a true equation.
2) 54 ÷ 6 + 3² = 4 + 4²
9 + 9 = 4 + 16
18 = 20
This is not a true equation.
3) 8042 = 10 − 22 − 1
Clearly, this is not a true equation.
4) 19 − 2⋅5 = 9⋅73 −9
19 - 10 = 657 - 9
9 = 648
This is not a true equation.
Hence, none of the equation is true from the given equations.
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nswer the following question by entering the numeric value with appropriate units. if the length of one side of a square is 12.0 m m , what is the perimeter of the square? express the perimeter with the appropriate units.
A hexagonal aquarium is 15. 5 on each side of its base and 28. 5cm high. Whats the area
The area of the hexagons having side 15.5 cm and height 28.5 cm will be 662.625 cm^2.
A hexagon or sexagon is a six-sided polygon or 6-gon that forms the shape of a cube in geometry. The sum of any basic hexagon's interior angles is 720°.
The hexagon has six sides in mathematics; what makes this specific form so fascinating is because it best fills a plane with equal size units and leaves no wasted space. Because of its 120-degree angles, hexagonal packing also reduces the perimeter for a given area.
As we have,
Area of Hexagon = 3/2 x s x h
Where, s = side of hexagons
h = height of hexagons.
So, for determining the value of area of hexagons, we will put the value of (s) and (a) in the above formula.
So, we will get the area of hexagons as:
(3/2) * 15.5 * 28.5 =662.625 cm^2
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what point do we get when we rotate $(3,2\sqrt 3)$ around the point $(2,\sqrt 3)$ by $60^\circ$ counterclockwise?
The new point we will get P([tex]1,2\sqrt{3}[/tex]) when we rotate the point [tex](3,2\sqrt 3)[/tex] around the point (2, [tex]\sqrt{3}[/tex]) by 60⁰ counterclockwise.
Rotating point A [tex](3,2\sqrt 3)[/tex][tex](3,2\sqrt 3)[/tex] around point O[tex](2,\sqrt 3)[/tex] by 60⁰ counterclockwise.
Let us get point P as result.
so, assuming O is the center of a circle which has radius = r
r = [tex]\sqrt{(2-3)^2 + (\sqrt{3}-2\sqrt{3})^2 }[/tex]
or r = 2
And point A and P(x,y) are on the circumference of the circle.
so, the coordinates of point P(x,y) will as follows
x = Oₓ + (Aₓ-Oₓ)cosθ - (Ay-Oy)sinθ
or x = 2 + (3-2)cos60⁰ - [tex]\sqrt{3}[/tex]sin60⁰ = 2+1/2-3/2 = 1
And y = Oy + (Aₓ-Oₓ)sinθ + (Ay-Oy)cosθ
y = [tex]\sqrt{3}[/tex] + [tex]\sqrt{3} /2[/tex] + [tex]\sqrt{3} /2[/tex] = [tex]2\sqrt{3}[/tex]
so, P([tex]1,2\sqrt{3}[/tex]}
Therefore, the new point we will get P([tex]1,2\sqrt{3}[/tex]) when we rotate the point [tex](3,2\sqrt 3)[/tex] around the point (2, [tex]\sqrt{3}[/tex]) by 60⁰ counterclockwise.
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The polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written in the form: ax^3 + bx^2 + cx + d where a, b, c, and d are constants. What are the values of a, b, c, and d? Show your work. .
The values of a, b, c, and d in the polynomial ( x - 2 )( x² + 1 ) - x( x - 3 ) in the form of the form ax³ + bx² + cx + d are 1, -3, 4 and -2 respectively.
What are the values of a, b, c, and d?Given the expression in the question;
( x - 2 )( x² + 1 ) - x( x - 3 )
To simplify, apply distributive property
( x - 2 )( x² + 1 ) - x( x - 3 )
x( x² + 1 ) - 2( x² + 1 ) - x( x - 3 )
x( x² ) + x(1 ) - 2( x² ) + (-2)( 1 ) - x( x ) - (-x)3
x³ + x - 2x² - 2 - x² + 3x
Collect and add like terms
x³ - 2x² - x² + x + 3x - 2
x³ - 3x² + 4x - 2
Comparing to the form ax³ + bx² + cx + d
a = 1
b = -3
c = 4
d = -2
Therefore, the values of a, b, c, and d are 1, -3, 4 and -2 respectively.
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how many lines can pass through a given pair of two distinct points?
Answer: Only one line can pass through two distinct points.
what is an angle whose vertex is on the circle and sides are chords?
The angle whose vertex is on the circle and the sides of the angle are the chords is called an Inscribed Angle .
What is an Inscribed Angle ?
An inscribed angle in the circle is formed by the two chords which have a common end point on circle and this common end point is called the vertex of inscribed angle.
The arc formed by the inscribed angle in the circle is called as the intercepted arc .
also the Inscribed Angle Theorem states that inscribed angle on the circle is half the measure of central angle that subtends the same arc .
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Does anyone know this?
Answer:
Area = 50
Step-by-step explanation:
x2 = 36
x = 6
36 + 6 + 6 + 1 + 1 =50
the small squares = 1
How much water, in ounces, do you drink on average per day? Let Y be the amount of water, in ounces, a randomly selected student drinks on average per day. Y is a (continuous or discrete)?
If Y represents the amount of water a randomly selected student drinks per day, it follows that the variable Y in this scenario is a discrete variable.
What is the difference between a discrete and continuous variable?A discrete variable is a variable that takes on distinct, countable values while- A continuous variable on the other hand, is one which takes on any value within a range, and the number of possible values within that range is infinite.
Hence, since it is possible to put a count to the amount of water one drinks per day, it follows that variable, Y in this scenario is discrete.
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What is the YYY intercept of y =- 3 7xy − 3 − 7x?
After solving, the y-intercept of line7x−y+3=0 is 3.
In the given question, we have to find the y-intercept of 7x−y+3=0.
The general equation of line is y = mx + c, where m is the slope of line and c is the y-intercept of the line.
We express the following equation in slope-intercept form, which is to obtain the slope and y-intercept.
To find the y-intercept of 7x−y+3=0 we firstly convert the equation in the form y = mx + c.
7x−y+3=0
We firstly isolate the y.
subtract y on both side, we get
y = 7x + 3
When we compare the equation by y = mx + c
So, c = 3
Hence, the y-intercept of 7x−y+3=0 is 3.
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The complete question is:
What is the y-intercept of 7x−y+3=0?
silmutaneous equation
Step-by-step explanation: Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.
the general manager, marketing director, and 3 other employees of company a are hosting a visit by the vice president and 2 other employees of company b. the eight people line up in a random order to take a photo. every way of lining up the people is equally likely.
The probability that the maid of honor is in the leftmost position is 0.00034.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
We have to find the probability that the maid of honor is in the leftmost position.
There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: 7*2 = 14
∴ The required probability = 14/8! = 1/2880 = 0.00034
Thus, the probability that the maid of honor is in the leftmost position is 0.00034.
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The probability that the maid of honor is in the leftmost position is 0.00034.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
We have to find the probability that the maid of honor is in the leftmost position.
There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: 7*2 = 14
∴ The required probability = 14/8! = 1/2880 = 0.00034
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Write an expression for the sequence of operations described below.
raise 10 to the 2nd power, subtract the result from 5, then multiply z by what you have
Do not simplify any part of the expression.
The expression is (10² -5)z. The variable is z. The simplest form of the expression is 95z.
What are algebraic operations?
The four fundamental algebraic operations are as follows:
Addition, Subtraction, Multiplication, Division
We always categorize the terms in our algebraic equations as like and unlike terms in each of the algebraic operations we perform.
The given sequence of operations are:
1) Raise 10 to the 2nd power
2) Subtract the result from 5
3) Then multiply z
The mathematical representation of the first statement is:
10².
Then apply the second operation:
10² - 5
Then apply the third operation:
(10² - 5)z
Now simplify the above expression:
= (100 - 5)z
= 95z
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scores at a truck pull were based on the distance the truck stopped from the finish line. order these scores from least to greatest: -5 3/4 , -7.2 , 9 , and 3 1/8
The scores, in order from least to greatest, are:
-7.2, -5 3/4, 3 1/8, 9. Therefore, the final order is: -7.2, -5 3/4, 3 1/8, 9
What is the Decimal form?A decimal form is a way of expressing numbers in the base-10 number system, which is the number system we use in everyday life. In decimal form, a number is represented by a combination of digits, where the rightmost digit represents units (ones), the next digit represents tens, the next represents hundreds, and so on. Each digit is multiplied by a power of 10, determined by its position in the number.
-7.2 , -5 3/4 , 3 1/8, 9
The numbers are already in decimal form, so we can compare them directly.
-7.2 is less than -5.75
-5.75 is less than 3.125
3.125 is less than 9
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How do you solve for two unknown angles?
We can solve two unknown angles in a triangle only if the exterior angle is already given and then put the sum of all the angles equal to 180 degrees.
We know that,
If the exterior angle of a triangle is θ and the two opposite interior angles are θ₁ and θ₂, then the sum of θ₁ and θ₂ will be equal to the θ.
⇒θ = θ₁ + θ₂
Also,
If the angles of a triangle are θ₁, θ₂ and θ₃, respectively. Then the sum of θ₁, θ₂ and θ₃ is equal to 180°.
⇒θ₁ + θ₂ + θ₃ = 180°
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a coral reef is 3 kilometers due south of its closest point along a straight shoreline. a visitor is staying in a tent that is 14 kilometers east of that point. the visitor is planning to go from the tent to the coral reef. suppose the visitor runs at a rate of 12 kmph and swims at a rate of 1 kmph. how far should the visitor run to minimize the time it takes to reach the coral reef? round to two decimal places.
3.6miles the visitor have to run to minimize the time it takes to reach the coral reef.
How do you find the time in math?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.The equation for calculating time is [Time = Distance ÷ Speed].Seconds, minutes, hours, days, weeks, months, and years are the fundamental units of time. To determine the time of day, we use seconds, minutes, and hours; to determine the date, we use days, months, and years. The smallest units of time are seconds, minutes, and hours, while the larger ones are days, months, and years.Correct question :
A visitor is staying in a cabin that is 3 miles west of the closest point on a shoreline to a coral reef. The coral reef is 2 miles due south of the shoreline. The visitor plans to travel from the cabin to the coral reef by running and swimming. If the visitor runs at a rate of 7 mph and swims at a rate of 2 mph, how far should the visitor run to minimize the time it takes to reach the coral reef
Given data :
distance of tent from the closest point on shore-line, d=3miles.
distance between shoreline point and coral reef, x=2miles
The shortest distance (say l) that the visitor runs towards the reef in order to swim a minimum distance which takes least time.
∴ l² = d² + x²
l = [tex]\sqrt{3^{2} +3^{2} }[/tex]
l = 3.6 miles
Now on reaching at the shore at this point the visitor will have to swim the least distance due east to reach coral reef.
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1. In Luguru Academy, each lesson in lower primary and upper primary classes lasts 30 minutes and 40 minutes respectively. The first time the two bells ring at the same time, the pupils go out for a tea break if lessons of the whole school start at 8:30am. a) At what time does tea break start? b) How many upper primary lessons take place before break? 2. A bottle contained 6 litres of milk. Malimoto took of the remainder. How much milk remained in the bottle? 3. An irregular pentagon has the following four interior angles 110°, 108° 135°, and 152°. Determine the value of the exterior angle adjacent to the fifth interior angle. 4. A candidate scores 45, x and y percent in an interview, what is his average score?
Using LCM, the pupils go out for a tea break at 10.30 a.m, Using property of pentagon, The value of the exterior angle adjacent to the fifth interior angle is 145°.
How do I figure out LCM?Step 1: Use the repeated division method to identify the prime factors of the supplied numbers.
Write the numbers in exponent form in step two. Only those prime factors' product with the highest power should be sought.
Step 3: The LCM of the provided numbers is the product of these factors with the highest powers.
a) Find the moment when two bells will ring simultaneously.
In 30 minutes, the first bell rings.
The second bell will ring in 40 minutes, and classes will begin at 8:30. LCM of 30, 40, equals 120 minutes.
Bath bells sound at the same time at 8.30 a.m. plus 2 hours after 120 minutes, which is 10.30 a.m.
b) 40 + 40 + 40 = 120 minutes
∴ 3 classes will take place before break in upper primary.
An irregular pentagon has the following four interior angles 110°, 108° 135°, and 152°. Determine the value of the exterior angle adjacent to the fifth interior angle.
Sum of angles of pentagon = 540°
⇒ 110° + 108° + 135° + 152 + x = 540
⇒ x = 35
The value of the exterior angle adjacent to the fifth interior angle is 180 - 35 = 145°
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How do you draw an inverse relation graph?
To see the points of draw an inverse graph.
Choose some points on the given relation (graph).Interchange the x and y coordinates of each point to get new points.Plot all these new points and join them by a curve which gives the graph of the inverse relationship.Now, According to the question:
Inverse Relation of a Graph
If a relation is given as a graph, then its inverse is obtained by reflecting it along the line y = x. This is because the inverse of a relation is nothing but the interchanged ordered pairs of the given relation. To graph the inverse of a relation that is given by a graph,
Choose some points on the given relation (graph).Interchange the x and y coordinates of each point to get new points.Plot all these new points and join them by a curve which gives the graph of the inverse relationship.Learn more about Inverse graph at:
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Solve the following system of equations for all three variables.
9x+4y+6z= -8
9x+4y+6z= -5
x-8y+8z= -6
There is no solution for the system of equations because the determinant of A is zero.
What are matrices?A matrix is an array of rows and columns containing numbers, symbols, or expressions that is rectangular in shape.
In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.
Given the equations,
9x + 4y + 6z = -8
9x + 4y + 6z = -5
x - 8y + 8z = -6
solving by matrix method,
A = [tex]\left[\begin{array}{ccc}9&4&6\\9&4&6\\1&-8&8\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}-8\\-5\\-6\end{array}\right][/tex]
X = [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
X = A⁻¹B
for A⁻¹, calculate the determinant of A
|A| = [tex]\left|\begin{array}{ccc}9&4&6\\9&4&6\\1&-8&8\end{array}\right|[/tex]
|A| = 9(32 + 48) - 4(72 - 6) + 6(-72 - 4)
|A| = 720 - 264 - -456
|A| = 0
since |A| is zero there are no solutions for the equation.
Hence there are no solutions for a system of equations.
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you invest a total of $5000 between two saving accounts. account A pays 2% annual interest and account B pays 4% annual interest. after one year, you have earned a total of $135 in interest. How much did you invest in each account
The Investment in Account A is 1750, Investment in Account B is 3250
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
The total investment = 5000
Let the amount invested in account A be x
Therefore, the amount invested in account B = 5000-x
In Account A, rate of interest = 4% per year
Thus, interest earn in one year
= x*4*1/100
= 4x/100
Now, The interest in account B = 2% per year
Thus, the interest earn in one year
= (5000-x)*2*1/100
= 2(5000-x)/100
Therefore, total interest;
(x*4*1/100)*((5000-x)*2*1/100)
(2x+10000)/100=35
x=1750
Hence, investment with interest in account A and account B will be $1750 and 5000-1750 = $3250
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15 POINTS HELP MEEEEEE!!!!!!
The distance between the points (2, 4) and (5, -2) is 3√5 units.
How to find the distance between points?The distance between the point (2, 4) and (5, -2) using Pythagoras theorem can be calculated as follows:
Using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuseTherefore,
d = √(y₂ - y₁)² + (x₂ - x₁)²
using (2, 4) and (5, -2)
x₁ = 2
x₂ = 5
y₁ = 4
y₂ = -2
Hence,
d = √(-2 - 4)² + (5 - 2)²
d = √(-6)² + (3)²
d = √36 + 9
d = √45
d = √9 × 5
Therefore,
distance = 3√5 units
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a plane flew at a constant speed and traveled 762762762 miles in 555 hours. how many miles would the plane travel in 333 hours at the same speed? miles
The plane travel 457657656.894 miles in 333 hours at the same speed.
The plane is travelling at a speed of 762762762 miles in 555 hours.
Considering that the plane traveled 762762762 miles in 555 hours.
If I write that as a fraction it is 762762762mi/555hours.
I can make this a unit rate by saying,
762762762 / 555 = 762762762 ÷ 555= 1374347.318.
This means plane is travelling at a speed of 152.4 miles in an hour.
So distance travelled by plane in 333 hours can be find out
By using,
Distance = speed x time
=1374347.318 x 333
=457657656.894
So plane travel 457657656.894 miles in a span of 333 hours.
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find the area of shaded regions below. give your answer as a completely simplified exact values in terms of pi
The area of the shaded portion is 36pi cm² -72
What is a segments?A segment of a circle is part of the circle cut off by the chord. A chord is a straight line that touches a circle at two points. Do well also to understand that a chord is a straight line touching two points on the circumference of a circle.
A circle's area is calculated as pi*r², so a semicircle is pi*r² / 2, and a quarter circle is pi*r² / 4.
We have a quarter circle of radius 12, of which the area is pi*(12² / 4) = 36pi.
In conclusion, this means that the shaded area is 36pi - 72.
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The figure shows the dimensions of a city park in feet.
Part B: The city plans to cover the park with grass. One square of grass covers 60 square feet. How many squares of grass will need to be ordered to fill the entire park?
A. 18 squares
B. 21 squares
C. 20 squares
D. 19 squares
When Dan makes chocolate chip cookies at home, he typically mixes x ounces of chocolate chips into the batter. In his last batch, he decided to make the cookies extra delicious and used 30% more chocolate chips.
Pick all the expressions that represent how many ounces of chocolate chips Dan used in his last batch.
0.3x
1.3x
x+0.3x
x+1.3x
All of the expressions that represent the total number of ounces of chocolate chips which Dan used in his last batch include the following:
B. 1.3x
C. x + 0.3x
How to write the required expressions?In order to write the required expressions, we would assign variables to the ounces of chocolate chips and the number of cookies, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the ounces of chocolate chips.Let the variable y represent the total number of cookies.Since Dan typically mixes x ounces of chocolate chips into the batter and decided to make the cookies extra delicious and used 30% more chocolate chips, the required expressions are given by;
y = x + (30% of x).
y = x + (30/100 × x)
y = x + 0.3x ....expression 1.
y = 1.3x ....expression 2.
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Elliot earned $49 last month walking his neighbor's dog. He earns $7 each time he walks the dog. How many times did Elliot walk his neighbors dog last month?
Answer: 7
Step-by-step explanation:
49/7 = 7
What is a 180 degree angle called?
Angles that are 180 degrees (θ = 180°) are known as straight angles.
A straight angle is a 180-degree angle in mathematics. Straight refers to the fact that it appears as a straight line. Angles are formed when two rays are linked end to end, according to the definition of angles in mathematics.
As a result, the two rays of the 180-degree angle are subtended in the opposite direction, where the rays are united at the ends.
In radians, the 180-degree angle is measured in pi (π). To point the opposite way, the straight angle changes the direction. A 180-degree is also considered supplementary.
Thus, Angles that are 180 degrees (θ = 180°) are known as straight angles.
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If the product of two successive positive integers is 4556, find the sum of these two numbers.
The sum of two successive positive integers is : 135
Let m and (m + 1) be two successive positive integers.
Given that the product of two successive positive integers is 4556
So, we get an equation,
m × (m + 1) = 4556
We need to find these two successive positive integers.
We solve above equation to find the value of m.
m² + m = 4556
m² + m - 4556 = 0
After factorizing above quadratic equation we get,
(m - 67)(m + 68) = 0
m - 67 = 0 OR m + 68 = 0
m = 67 OR m = -68
Sine the required numbers are positive integers we consider m = 67
For m = 67, the two successive positive integers: 67, 68
and the sum of integers would be: 67 + 68 = 135
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What is the number and types of solutions of the quadratic equation x² 7x 12 0?
The number of solutions of the quadratic equation x² 7x 12 0 is two, and the types of solutions are real and distinct.
x2 - 7x - 12 = 0
(x - 6)(x + 2) = 0
x - 6 = 0 or x + 2 = 0
x = 6 or x = -2
Therefore, the number of solutions of the quadratic equation x2 7x 12 0 is two, with real and distinct solutions of x = 6 and x = -2.
The quadratic equation x² 7x 12 0 can be solved by factoring. After factoring the equation, we get
(x - 6)(x + 2) = 0.
This equation can be simplified further to x - 6 = 0 or x + 2 = 0. Solving for x in each equation, we get x = 6 and x = -2. This means that the number of solutions of the quadratic equation x² 7x 12 0 is two, with real and distinct solutions of x = 6 and x = -2. The solutions of the quadratic equation can be used to find the x-intercepts of the graph of the equation, which can be used to graph the equation.
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please help me Multiply (3)(2x+5)
Answer:
6x + 15
Step-by-step explanation:
(3)(2x+5)
6x + 15
(2x+5)(3) = 2x × 3 + 5 × 3 = 6x+15
How many exercises are in class 10 polynomials?
In class 10 mathematics chapter 2 (Polynomials), there are 4 exercises.
'What are polynomials?'
Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
The Greek words "polynomial" and "nominal" are the origins of the word polynomial, which is translated as "many phrases" when combined. There is no limit to the number of terms that a polynomial can have.
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