The square root of negative number can be negative imaginary number (complex number)
As we know the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.
Finding a square root of number is an inverse method of squaring a number.
A radical symbol '√' used to represent the square root of number.
If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],
We can write above relation as, m² = n
We know that square of any real number is positive.
For example, 3² = (3 × 3) = 9
(-3)² = (-3) × (-3) = 9
i.e., the square root of 9 is 3 and -3
Thus the square root of a negative number is undefined among the set of Real Numbers.
As we know the set of real numbers is subset of complex numbers.
In complex numbers, the imaginary number 'i' is the square root of negative 1.
When an imaginary number is squared, the result is negative number.
Consider example,
[tex]\sqrt{-16}\\\\ =\sqrt{16} \times \sqrt{-1}\\\\ =(\pm 4)\times i\\\\=\pm4i[/tex]
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A recipe for crumb cake says to mix 3/8 cup of brown sugar and 1/3 cup of white sugar.
From this sugar mixture, set aside 1/4 cup for the crumb topping.
The remaining sugar mixture is used to make the cake.
What amount of the sugar mixture is used to make the cake?
A.) 17/24
B.) 11/24
C.) 1/2
D.) 7/12
Answer:
C) 1/2
Step-by-step explanation:
We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.
From this sugar mixture, 1/4 cup is set aside for the crumb topping.
To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.
We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)
3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.
1/4 cup is set aside for the crumb topping.
So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup
Two angles have measures of 6315' 47" and 116°44'13" The angles are
complementary
supplementary
neither complementary or supplementary
5. A line that passes through (4, 5) and (0, -12]
Answer: Your answer would be y = 17/4 x - 12
Step-by-step explanation:
I hope this helps!
Answer:
y=17/4x-12
Step-by-step explanation:
Find the following areas under the normal curve
A. -1.43 < z < 0.68
B. 0.58 < z < 1.74
C. -1.55 < z < 0.44
D. z > 1.34
2 find the standardized score (z-score) closest to the following percentiles
A. 35th percentile
B. First Quartile QI
C. The observation with 12% of the data falling above it
3. Given a normal distribution of heights of 5 year olds (in inches) with a mean of 36 and a standard deviation of 10, find the following areas under the curve:
A. x < 31 inches
B. x > 49 inches
C. 40 < x < 50 inches
D. 70% of 5 year olds are below what height?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
Explain about the normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution. Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.
Using the inverse standard normal calculator, we can determine the height at which 70% of 5-year-olds are below it, yielding a z-score of 0.84162. Using the formula x = mean + (z-score * standard deviation), this z-score can be used to determine the corresponding x value, which in this case would be
36 + (0.84162*10) = 42.4 inches.
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Which two sentences from the text serve as examples of parallelism as a rhetorical strategy?.
We were able to recognize the following two sentences because parallelism involves the repetition of grammatical structures in a sentence or text.
Today, 25 years ago, America underwent a change of heart and a change of direction.
She is currently working on a project to find low-cost strategies to minimize pollution and share them with smaller businesses with businesses situated near three Ohio rivers.
Describe parallelism.
The repetition of the same grammatical structure is known as parallelism. It can be used as a rhetorical device or just as a method of disseminating data more effectively. In a text, parallelism helps prevent ambiguity and confusion.
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How do you find the length of the third side of an acute triangle?.
There are several ways to find the length of the third side of an acute triangle, depending on the information given about the triangle and the sides. Some common methods include:
Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the length of the third side. The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Using the Law of Cosines: If you know the lengths of two sides and the measure of the angle between them, you can use the law of cosines to find the length of the third side.
Using the Law of Sines: If you know the lengths of two sides and the measure of the angle opposite one of them, you can use the law of sines to find the length of the third side.
It's important to note that you need to know at least 2 sides and an angle or the side opposite to the right angle (if the triangle is a right triangle) in order to find the length of the third side.
Work out the value of a and the value of n[tex](ax^{6} )^\frac{1}{n} = 7x^{3}[/tex]
In the expression (ax⁶)^(1/n) = 7x³ the values of a and n are
49 and 2 respectivelyHow to solve for a and nThe expression (ax⁶)^(1/n) = 7x³is simplified as follows
Information from the problem
(ax⁶)^(1/n) = 7x³
to make x⁶ to be equal to x³ we use the powers
6 * y = 3
y = 1/2
hence n = 2
substituting n = 2 and solving
(ax⁶)^(1/2) = 7x³
√(a) x³ = 7x³
dividing both sides by x³
√a = 7
squaring both sides of the equation wil result to
√a = 7
(√a)² = 7²
a = 7²
a= 49
We can therefore say that a = 49 and n = 2
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QUICK!!
How can you use multiplication and division to solve an inequality?
Answer:
If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.
But if you multiply or divide both sides of an inequality by a negative number, the inequality is no longer true.
Step-by-step explanation:
hope it helps<3Answer:
The multiplication property of inequality states that if one side of the inequality is multiplied or divided by a positive number, we can multiply and divide the other side of the inequality by the same number without changing or disturbing the direction sign of the inequality.
Step-by-step explanation:
what is x? please help
Answer:
x = 132
Step-by-step explanation:
The sum of interior angles in parallelogram equals 360. Opposite angles are congruent. (have equal measures)
360 = 48 x 2 + 2x
360 = 96 + 2x
(subtract 96 from both sides)
264 = 2x
(divide both sides by 2)
132 = x
Check:
2x + (48 x 2) = 360
(132 x 2) + 96 = 360
264 + 96 = 360
360 = 360
Answer: 132 Degrees
Step-by-step explanation: Since you know all the angles have to add up to 360 and one of the angles is 48. Alternate angles are always equal so you would do 48 and double that making 96. 360-96 leaves you with 264. Using the same alternate angles rule you would just divide that by 2 which leaves you with 132 degrees.
How do you graph y <- 2x 4?.
To depict the curve, we will make use of the idea of slope and intercept in linear equations.
A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.
When y = 2x - 4 is put into comparison with the generic form, we get
The curve has a slope of 2 and a y-intercept of -4.
To assist us plot the graph, let's take two points along the line y = 2x – 4.
The line y = 2x - 4 passes through since its y-intercept is equal to -4. (0, -4)
In the formula y = 2x - 4, replace y with 0.
0 = 2x - 4
2x = 4
x = 2
the line therefore goes through (2, 0).
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Full Question = Which graph represents the function y = 2x - 4?
Answer in simplest radical form if necessary (NO DECIMALS!). Copy and paste this symbol if needed: √
The value of x from the given figure is 16 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given figure,
Using Pythagoras theorem to ΔBDC
Now, BC²=8²+4²
BC=√80
In ΔABD,
AB²=BD²+AD²
AB²=8²+x² ------(I)
In ΔABC
AC²=AB²+BC²
(x+4)²=AB²+80
AB²=(x+4)²-80 ------(II)
From equation (I) and (II), we have
64+x²=x²+8x+16-80
8x=128
x=16
Therefore, the value of x from the given figure is 16 units.
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Points A, B and Clie on the circumference of a circle, centre O.
LABC= 37°.
37
B
Diagram not drawn to scale
Q7
Q8 09 Q10 Q11 Q12
O
Calculate the size of the reflex angle ZAOB.
(2 marks)
Answer:
286°
Step-by-step explanation:
You want the measure of the reflex angle AOB, whose vertex is the center of the circle in which inscribed angle ACB has measure 37°.
Inscribed angleAn inscribed angle is half the measure of the arc it intercepts, so short arc AB is 2·37° = 74°.
Central angleA central angle is equal to the measure of the arc it intercepts. Long arc ACB is 360° -74° = 286°. That means the measure of the reflex central angle AOB is ...
reflex ∠AOB = 286°
__
Additional comment
The total of arcs around a circle is 360°.
Kelli call her grandmother every month. Every other month, Kelli alo call her couin. If Kelli call her couin in January, how many call will Kelli have made to her grandmother and her couin by the end of Augut
Kelli has made 12 calls to her grandma and her cousin by the end of August.
Kelli has already placed 12 calls other, according to this.
She starts calling her cousin every other month in January, so she will call four times in January, March, May, and July.
By using the unitary method
The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.
The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.
Consequently, 8+4=12
Kelli has already placed 12 calls.
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There are 9 thirds in 3 ones.
The number 3 is a special number that carries a lot of meaning in various cultures and religions.
What is number?Number is a mathematical concept that is used to count, measure, or label. It is used to quantify or quantify objects, events, or ideas. In mathematics, numbers can be classified as either rational or irrational. Rational numbers include integers, fractions, and decimals, while irrational numbers include pi and square root. Numbers are also used to represent data and can be used to represent a variety of objects and concepts including digits, dates, and time.
It is often seen as the number of unity and harmony, as it is comprised of three individual parts. In Christianity, the number 3 is associated with the Holy Trinity. In Hinduism, Buddha, and other Eastern religions, the number 3 is associated with the three qualities: action, knowledge, and devotion.
In mathematics, 3 is a prime number, meaning that it cannot be divided by any other number except itself and 1. It is also an odd number, and the third number in the Fibonacci sequence.
The number 3 is a powerful number and is often associated with creativity and luck. It is also seen as a number of growth and expansion. In literature, 3 is often used as a symbol of completeness and wholeness.
The number 3 is also associated with balance and harmony. It is seen as the number of perfection and balance between opposites. It is seen as the number of the divine and is often used in spiritual practices.
The number 3 is often used in art and design. Its three distinct parts make it a perfect number for creating a pleasing and attractive composition.
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The number 3 is a special number that carries a lot of meaning in various cultures and religions.
What is number?Number is a mathematical concept that is used to count, measure, or label. It is used to quantify or quantify objects, events, or ideas. In mathematics, numbers can be classified as either rational or irrational. Rational numbers include integers, fractions, and decimals, while irrational numbers include pi and square root. Numbers are also used to represent data and can be used to represent a variety of objects and concepts including digits, dates, and time.
It is often seen as the number of unity and harmony, as it is comprised of three individual parts. In Christianity, the number 3 is associated with the Holy Trinity. In Hinduism, Buddha, and other Eastern religions, the number 3 is associated with the three qualities: action, knowledge, and devotion.
In mathematics, 3 is a prime number, meaning that it cannot be divided by any other number except itself and 1. It is also an odd number, and the third number in the Fibonacci sequence.
The number 3 is a powerful number and is often associated with creativity and luck. It is also seen as a number of growth and expansion. In literature, 3 is often used as a symbol of completeness and wholeness.
The number 3 is also associated with balance and harmony. It is seen as the number of perfection and balance between opposites. It is seen as the number of the divine and is often used in spiritual practices.
The number 3 is often used in art and design. Its three distinct parts make it a perfect number for creating a pleasing and attractive composition.
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The complete question is-
Please explain there are 9 thirds in in 3 ones.
How do I do this problem?
No, these statements are not needed to prove that ABCD is a parallelogram.
What is parallelogram?A parallelogram is a type of four-sided geometric shape with two pairs of opposite sides that are parallel. Each side of the parallelogram is a line segment, and all four of the interior angles are equal. The opposite sides of a parallelogram are also equal in length. Parallelograms can be found in a variety of applications, including engineering, architecture, and other fields. The most common types of parallelograms are squares, rectangles, and rhombuses.
A parallelogram is defined as a four-sided shape with opposite sides that are equal in length and with opposite angles that are equal in measure.
To prove that ABCD is a parallelogram, it is necessary to show that two of its sides are parallel and that its opposite sides are equal in length.
The statements provided do not show any of these properties, and so are not needed to prove that ABCD is a parallelogram.
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Sydney is deciding between two parking garages. Garage A charges an initial fee of
$12 to park plus $4 per hour. Garage B charges an initial fee of $7 to park plus $5 per
hour. Let A represent the amount Garage A would charge if Sydney parks for t hours,
and let B represent the amount Garage B would charge if Sydney parks for t hours.
Write an equation for each situation, in terms of t, and determine the hours parked,
t, that would make the cost of each garage the same.
The equation for Garage A can be expressed as A = 12 + 4t, and the equation for Garage B as B = 7 + 5t.
Write an equation for each situation?In order to determine the hours parked, t, that would make the cost of each garage the same, we first set the two equations equal to each other, A = B.Then, we can solve for t by subtracting 7 from both sides of the equation and dividing by -1.This gives us t = -5. Since we cannot park for a negative number of hours, this tells us that the cost of each garage will never be the same.The equation for Garage A is A = 12 + 4t, while the equation for Garage B is B = 7 + 5t. To find the number of hours, t, that would make the cost of each garage the same, we must set A = B and solve for t.Therefore, 12 + 4t = 7 + 5t, and subtracting 7 from both sides of the equation yields 5t = 5, and t = 1. Thus, if Sydney parks for 1 hour, the cost of both Garage A and Garage B would be the same.A = 12 + 4t
B = 7 + 5t
12 + 4t = 7 + 5t
4t - 5t = 7 - 12
-t = -5
t = 5 hours
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how much work is done when a 100 lb rock is lifted to a height of 3 ft?
Work done when a 100 lb rock is lifted to height of 3 ft is 9652.215 ft-lb.
What is meant by work done?
The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the rock, which is equal to the force of gravity acting on it.
The weight of an object is given by the formula:
W = mg
Where m is the mass of the object (in this case, 100 lb) and g is the acceleration due to gravity (approximately 9.8 m/s^2 or 32.17405 ft/s^2).
So the weight of the rock is:
W = (100 lb)(32.17405 ft/s^2) = 3,217.405 ft-lb
The work done on the rock is equal to the force applied (its weight) multiplied by the distance it is lifted (3 ft), so the work done is:
Work = (3,217.405 ft-lb) x (3 ft) = 9652.215 ft-lb
Therefore, the work done when a 100 lb rock is lifted to a height of 3 ft is 9652.215 ft-lb.
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A storage silo for grain can house 18,000 bushels of grain. Answer the following questions using the fact that 1 ton equals to 2000 pounds.
1) Given that one bushel of oats weight 32 pounds, how many tons of oats can be stored in the silo?
2) Given that one bushel of barley weighs 48 pounds, how many tons of barley can be stored in the silo?
3) Given that one bushel of wheat weighs 60 pounds, how many tons of wheat can be stored in the silo?
1. 288 tons of oats can be stored in the silo.
2. 432 tons of barley can be stored in the silo.
3. 540 tons of wheat can be stored in the silo.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A storage silo for grain can house 18,000 bushels of grain.
1. One bushel of oats weighs 32 pounds which is equal to 32/2000 tons.
= 0.016 tons.
Therefore, The number of tons of oats that can be stored is,
= 0.016×18000.
= 288 tons.
2. One bushel of barley weighs 48 pounds or 48/2000 = 0.024 tons.
Therefore, The number of tons of barley that can be stored is,
= 0.024×18000.
= 432 tons.
3. One bushel of wheat weighs 60 pounds or 60/2000 tons = 0.03 tons.
Therefore, The number of tons of wheat that can be stored is,
= 0.03×18000.
= 540 tons.
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A football team has an away game. And the buses breakdown the coaches aside to drive the players to the game in cars and vans for players can ride in each car six players can run Ageman they’re 48 players on the team the equation 4X plus 6Y equals 48 models situation where X is a number of cars and why is the number of vans
The graph of the equation 4x+6y=48 is given below.
And the intercepts are (0, 8) and (12, 0).
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given:
A football team has an away game, and the bus breaks down.
The coaches decide to drive the players to the game in cars and vans.
Four players can ride in each car.
Six players can ride in each van.
There are 48 players on the team.
The equation 4x+6y=48 models this situation, where x is the number of cars and y is the number of vans.
And the graph with in intercepts is given in the attached image.
Therefore, (0, 8) and (12, 0) are the intercepts.
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The complete question:
A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation 4x+6y=48 models this situation, where x is the number of cars and y is the number of vans.
Graph the equation.
Interpret the intercepts.
helllo need this due in 5 minutes
The numerical value of the slope and its meaning include the following: C. 312; velocity increases at rate of 312 kilometers per minute as the time increases.
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be modeled by using this equation:
y = mx + c
Where:
m represents the slope.x and y represents the data points.Based on the information provided above, a function which represents the speed of a spaceship that is been launched from the station is given by:
v(t) = 5,924 + 312t
where:
v represents the velocity measured in kilometers per minute.t represents the number of minutes after the spaceship is launched.By comparison, we can logically deduce that the slope is equal to 312 and it represents the rate of change of velocity with respect to time.
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√54
simplify the square root
Answer:
7.3
Step-by-step explanation:
i need help please thank you
The line of reflection for this problem is defined as follows:
x = -1.
The line of reflection is drawn on the image given at the end of the answer.
How to obtain the line of reflection?The vertices of the two triangles have the same y-coordinates, while the x-coordinates are different, hence the reflection line is a vertical line.
The x-coordinates will be equidistant to the reflection line, just on opposite coordinates.
Considering that the reflection changes the "faces" of the triangles, D and E are equivalent vertices, thus the reflection line is given by the mean of the x-coordinates of these two points, hence:
x = (-3 + 1)/2
x = -1.
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(6cd-¹)-3
Simplify
The -1 is an exponent that needs to be made positive
The solution of the expression is 216(cd)³.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the exponential expression is (6cd⁻¹)⁻³. The expression will be simplified as below,
E = (6cd⁻¹)⁻³.
Use the property of the exponents to multiply the powers and now solve.
E= (6cd³)
E = 6³ x (cd³)
E = 216(cd³)
Therefore, the simplified value of the expression is 216(cd)³.
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How do I find the first term of geometric progression when the ration is 2 and the sum of the first 6 terms is 7?
Answer:
The first term is 1/9-----------------------------
Let the first term be a.
The common ratio is r = 2 and the sum of the first 6 terms is S₆ = 7.
Use the sum of first n terms formula:
Sₙ = a(rⁿ - 1)/(r - 1)Substitute and solve for a:
7 = a(2⁶ - 1)/(2 - 1)7 = a(64 - 1)/17 = 63aa = 7/63a = 1/9What is the inverse of +9?.
The inverse of the expression +9 is -9.
Expression in math is defined as any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
Here we have the expression +9 and we need to find the inverse for it.
As we all know that the term inverse in math is known as a function or operation which reverses the order or operation of another function or operation
Based on the definition, the given expression is written as,
=> +9
Now, the inverse of the expression is written as in the negative form such that,
=> -9
Therefore, the resulting value is -9.
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Burj Khalifa i the tallet building in the world. It height i approximately 89,800 cm. The contruction team i planning to intall a 60 m long lightning rod on top of it. What will be the total height of the tructure , in metre , after the intallation of the rod
The total height of the structure after the installation of the rod will be 898.60 metres.
60 metres (rod) + 828 metres (Burj Khalifa height) = 888 metres
888 metres + 10 metres (approximate height of the lightning rod) = 898.60 metres
The Burj Khalifa is the world's tallest building with a height of 828 metres. It is located in Dubai, United Arab Emirates. The construction team is planning to install a 60 metre long lightning rod on top of the Burj Khalifa. This will increase the total height of the structure to 898.60 metres. The lightning rod is necessary for protecting the structure from lightning strikes which can cause significant damage. This will make the Burj Khalifa even taller, and will ensure the safety of the building as well as the people living in and around it.
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Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $305. How much did each computer cost before finance charges?
Using algebraic expressions, cost before finance charges is $2019.63 and $1669.63.
Algebraic Expressions: Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can be solved using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of algebraic expressions. Additionally, Boolean algebra is essential to algebraic expressions.
In the basics of algebraic expressions, the letters x, y, and z stand in for an unknown value. Variables are the names given to these letters. Both variables and constants can be present in an algebraic expression. They combine to create the algebraic expression.
Let x = cost of desktop computer;
then x - 350 = cost of laptop computer
converting % to decimals, 7% = 0.07 and 9.5% = 0.095
Then, 0.07x + (x - 350)0.095 = $305
0.07x + 0.095x - 33.24 = $300
0.165x = $333.24
x = $2019.63
then x - 350 = $1669.63
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Does someone mind helping me with this problem? Thank you!
Answer:
the answer to get x = 116 and y=54
Step-by-step explanation:
What is the equation of this trend line? Enter your answers by filling in the boxes.
K = __ J +__
Equation of this line is K = -2J + 28.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Step 1:
The equation can be written in slope intercept form which is y = mx + b
Step 2:
Calculate slope of the line, m = (y2 - y1)/(x2 - x1)
⇒ m = (24 - 20)/(2 - 4)
= 4/-2)
= -2
Step 3:
Find y-intercept of the line
⇒ b = 28
Step 4:
Substitute values in the equation
⇒ K = -2J + 28
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Pleaes help me. The points in the table lie on a line. Find the slope of the line.
0/1/2/3
-1/0/1/2
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-(-1)}{3-0}[/tex] = [tex]\frac{2+1}{3}[/tex] = [tex]\frac{3}{3}[/tex] = 1
