The degree and terms of the polynomial are explained and an example is also discussed.
What are polynomials?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. It is a mathematical expression made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division (No division operation by a variable).
The expression's components that are divided up by the operators "+" or "-" are referred to as polynomial terms. In polynomials, like terms are ones that share the same variable and power. Unlike terms are those that have dissimilar variables and/or dissimilar powers.
The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. A polynomial equation's maximum number of solutions can be calculated using the degree.
The different types of polynomials based on terms are:
Monomial - Single termBinomial - Two termsTrinomial - Three termsThe different types of polynomials based on the degree are:
Constant polynomial - Zero degreeLinear polynomial - Degree is oneQuadratic polynomial - Degree is twoCubic polynomial - Degree is 3Example,
Consider a polynomial 3x² + 5x + 4
Number of terms = 3 (Trinomial)
Degree = 2 (Quadratic polynomial)
Therefore the degree and terms of the polynomial are explained and an example is also discussed.
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The answer is:
⇨ belowWork/explanation:
Here's how we classify polynomials based on the number of terms:
monomial - has only one term
binomial - has two terms
trinomial - has three terms
polynomial - has four terms or more
As for degrees, those are the highest exponents the polynomial.
Example: Classify [tex]\bf{2p^2+p}[/tex].
It has 2 terms so it's a binomial.
Its highest exponent is 2 so it's a second degree binomial.
Hence, that's how we classify polynomials.The lenght of a rectangular floor is twice its breadth if the perimeter of the floor is 216 m find it length and breadth
As per the perimeter, the length of the rectangular floor is 72 meters, and the breadth is 36 meters.
Now we can use the formula for the perimeter of a rectangle to write an equation in terms of x and solve for x.
Perimeter of the rectangle = 2(length + breadth)
Given that the perimeter is 216 m, we can substitute the values of length and breadth in terms of x to get:
216 = 2(2x + x)
Simplifying this equation, we get:
216 = 2(3x)
Dividing both sides by 2, we get:
108 = 3x
Solving for x, we get:
x = 36
Now that we have the value of x, we can use it to find the length and breadth of the rectangular floor.
Length = 2x = 2(36) = 72 m
Breadth = x = 36 m
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prove the following:
1. the altitudes of a triangle are the angle bisectors of the orthic triangle
2. the circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle
The altitudes of a triangle are the angle bisectors of the orthic triangle is true because the orthic triangle is formed by the feet of the altitudes of the original triangle. The circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle is true because circumcircle of a triangle passes through all three vertices.
To prove the first statement, we can use the fact that the altitudes of a triangle are perpendicular to the sides and intersect at the orthocenter. The orthic triangle is formed by the feet of the altitudes of the original triangle.
1. Let ABC be the original triangle and D, E, F be the feet of the altitudes from A, B, and C, respectively.
2. Since AD is an altitude, ∠ADB and ∠ADC are right angles.
3. Similarly, ∠BEC and ∠BFC are right angles.
4. Therefore, ∠BDC and ∠EDF are supplementary angles, meaning they add up to 180 degrees.
5. Since ∠BDC and ∠EDF are supplementary and they share a common side, they are also the angle bisectors of the orthic triangle DEF.
6. The same logic can be applied to the other two altitudes to show that they are also angle bisectors of the orthic triangle.
To prove the second statement, we can use the fact that the circumcircle of a triangle passes through all three vertices.
1. Let ABC be the original triangle and D, E, F be the feet of the altitudes from A, B, and C, respectively.
2. Let O be the circumcenter of the original triangle ABC.
3. Since the circumcircle passes through all three vertices, OD, OE, and OF are all radii of the circle.
4. Since all radii of a circle are equal, OD = OE = OF.
5. Therefore, the circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle, as they are all equidistant from the center of the circle.
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Did I do the FOIL method right on this equation?
f(x)=4(x+1)^2-3
f(x)=4(x+1)(x+1)-3
f(x)= 4x^2+1x+1x+2-3
& if so, what do I do next?
Thank you
Yes, you have correctly applied the FOIL method to the equation f(x)=4(x+1)²-3.
The next step would be to simplify the equation by combining like terms.
This would result in the equation f(x)=4x²+2x-1. From here, you can either set the equation equal to zero and solve for x, or you can find the vertex, axis of symmetry, and other characteristics of the quadratic function.
Here is a step-by-step explanation of the FOIL method and simplification process:
1. Start with the original equation: f(x)=4(x+1)²-3
2. Apply the FOIL method to the (x+1)² term: f(x)=4(x²+2x+1)-3
3. Distribute the 4 to each term inside the parentheses: f(x)=4x²+8x+4-3
4. Combine like terms: f(x)=4x²+8x+1
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Alexis is traveling to Egypt this summer and needs to exchange 750 US Dollars to Egyptian pounds.
How many Egyptian pounds will Alexis receive with the following exchange rate?
1 USD = 18.48 Egyptian pounds
Enter the correct answer in the box.
( ) Egyptian pounds
Answer:
13,860 egyptian pounds
Answer:
Step-by-step explanation:
1 USD = 18.48 Egyptian pounds
∴ 750 USD = 750 × 18.48 Egyptian pounds
= 13860 Egyptian pounds
For parallelogram ABCD, Find m∠1.
The measure of angle 1 would be equal to 59 degrees.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We have been given the angles as 31 degrees and 90 degree
We know that the sum of angle of triangle is 180 then the angle 1 will be;
31 + 90 + m∠1 = 180
m∠1 = 180 - 90 - 31
m∠1 = 59
Hence, m∠1 = 59
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The following equation models the amount of aspirin in a person's blood in milligrams, t hours after ingesting a dose: f(t) = 300 * (1/2) ^ (1/30)
a. How much aspirin is in the dose?
b. Find and interpret ƒ (60).
c. When will the aspirin level be less than 10 milligrams?
A. The amount of aspirin in the dose is 22.066 milligrams.
B. ƒ (60) = 7.483 milligrams
This means that 60 hours after ingesting a dose of 22.066 milligrams of aspirin, the amount of aspirin in the person's blood will be 7.483 milligrams.
C. The aspirin level will be less than 10 milligrams after approximately 45.06 hours.
a. The initial amount of aspirin in the dose can be found by evaluating f(0):
f(0) = 300 * (1/2)^(1/30) ≈ 22.066
Therefore, there are approximately 22.066 milligrams of aspirin in the dose.
b. We can find f(60) by substituting t = 60 into the equation:
f(60) = 300 * (1/2)^(1/30 * 60) ≈ 7.483
Therefore, there are approximately 7.483 milligrams of aspirin in the person's blood 60 hours after ingesting the dose. This is significantly less than the initial amount of 22.066 milligrams, indicating that the aspirin is being metabolized and eliminated from the body over time.
c. We want to solve for t when f(t) < 10:
300 * (1/2)^(1/30t) < 10
Dividing both sides by 300:
(1/2)^(1/30t) < 1/30
Taking the natural logarithm of both sides:
ln[(1/2)^(1/30t)] < ln(1/30)
Using the properties of logarithms:
(1/30t)ln(1/2) < ln(1/30)
Simplifying:
-0.6931t < ln(1/30)
Dividing both sides by -0.6931 (which is ln(1/2)):
t > ln(1/30) / (-0.6931)
t > 45.06
Therefore, the aspirin level will be less than 10 milligrams after approximately 45.06 hours.
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The dashed triangle is the image of the solid triangle for a dilation with center at the origin. What is the scale factor?
The scale factor using in that dilation of the dashed triangle would be = 3:1
What is a scale factor?A scale factor is defined as the ratio that exists between an original size of an object and the new formed size of the same object.
The formula that can be used to calculate the scale factor ;
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Using the base of the triangle from the centre of origin in the graph;
The dimension of the new shape = 18
The dimension of the original shape = 6
scale factor = 18/6 =3
That is, the scale factor = 3:1
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Find the common ratio of a geometric sequence, whose first term is 2 and the third term is 242.
The common ratio of the geometric sequence is 11.
What is the common ratio of the sequence?To determine the common ratio r, we can use the formula for the nth term of a geometric sequence. The formula is expressed as;
aₙ = a₁ × r^(n-1)
where a1 is the first term, r is the common ratio, and n is the term number.
We are given that;
First term a₁ = 2Third term a₃ = 242.We can use these values to write two equations:
aₙ = a₁ × r^(n-1)
a₃ = a₁ × r^(3-1) = 2r² = 242
Solving for r, we get:
r² = 121
r = ±√121
r = ±11
However, we need to determine the sign of the common ratio.
Since the third term is larger than the first term, the common ratio must be positive. Therefore, r = 11.
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I need help please and thank you
The solution is, distance from the point to the line is 22√10 feet.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
The distance from point (x, y) to the line ax+by+c=0 is given by ...
d = |ax +by +c|/√(a²+b²)
In general for, the equation of the line is ...
y = x/3 - 4
i.e. x -3y -12 = 0
so the distance formula is ...
d = |x -y -12|/√(1² +(-3)²) = |x -y - 12|/√10
For the given point, the distance is ...
d = |-6 -4 -12|/√10
= 22/√10
d = 22/√10 . . . .
distance from the point to the line = 22/√10
now, distance = 22/√10 * 10
=22√10 feet.
Hence, The solution is, distance from the point to the line is 22√10 feet.
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please i need help im in a desperate situation
Answer:
Step-by-step explanation:
When calculating this equation you simply insert the x value into the equation given, in this case (x-2)^2
for example you are given 4 to 4 which is achieved by the method previously described, like this (4-2)^2 = (2)^2 = 4
so the answers would be
6 -> 16 (6 - 2 = 4 and 4^2 is 16)
10 -> 64 (10 - 2 = 8 and 8^2 is 64)
In a raffle, there are winners drawn of the first, second, and third prizes. Three sisters are participating along with 9 other people. What is the exact probability that the first sister wins the first prize, the second sister wins the second prize, and the third sister wins the third prize?
The probability that the first sister wins the first prize, the second sister wins the second prize, and the third sister wins the third prize is given as follows:
1/1320.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The probabilities for each sister are given as follows:
First sister wins the first prize: 1/12 -> there are 12 people.Second sister wins the second prize: 1/11 -> there are 11 people.Third sister wins the third prize: 1/10 -> there are 10 people.Hence the probability is given as follows:
1/12 x 1/11 x 1/10 = 1/(12 x 11 x 10) = 1/1320.
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1. A plane flies due east for 500 km and then on a heading of 120" for 150 km. What are its distance and bearing from its starting point?
2. A ship leaves port and sails due west for 120 km, then due south for 40 km. What are the distance and bearing of the port from the ship?
(1) The distance from the starting point to the final point is 589.5 km and the bearing from the starting point to the final point is 16.7° north of east
(2) The distance from the ship to the port is 126.49 km and the bearing of the port from the ship is 18.4° south of west.
What is the distance and bearing of the plane?
To solve this problem, we can use the law of cosines to find the distance from the starting point to the final point. We can also use trigonometry to find the bearing (angle) between the starting point and final point.
See the diagram attached:
We want to find the distance and bearing from the starting point (x) to the final point.
Using the law of cosines, we have:
c² = a² + b² - 2abcos(C)
c² = 500² + 150² - 2x500x150xcos(120°)
c² = 250,000 + 22,500 + 75,000
c² = 347,500
c = √347,500
c = 589.5 km
To find the bearing, we can use trigonometry. Let θ be the angle between the line from the starting point to the final point and due east.
tan(θ) = (150 km) / (500 km)
θ = tan⁻¹(0.3)
θ = 16.7°
2. To solve this problem, we can use the Pythagorean theorem to find the distance from the ship to the port. We can also use trigonometry to find the bearing (angle) between the ship and the port.
We want to find the distance and bearing of the port (P) from the ship (S).
Using the Pythagorean theorem, we have:
d² = 120² + 40²
d² = 14400 + 1600
d² = 16000
d = √(16000)
d = 126.49 km
To find the bearing, we can use trigonometry. Let θ be the angle between the line from the ship to the port and due west.
tan(θ) = (40 km) / (120 km)
θ = tan⁻¹ (1/3)
θ = 18.4°
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Felix and his friends attended the opening of the new community center at Forest Ridge Park. The mayor unveiled a parallelogram-shaped decorative plaque at the entrance to the park with the date of the special event. Its bottom edge is 9 inches long, and its area is 126 square inches.
Which equation can you use to find how tall the plaque is, h?
How tall is the plaque?
Write your answer as a whole number or decimal. Do not round.
inches
The answer to this question is as follows The plaque measures 14 inches equation tall as a result.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Because we are aware that the plaque has a parallelogram shape, we may determine its height using the formula for a parallelogram's area. The formula for a parallelogram's area is:
Base area x height
In this instance, we are aware that the area is 126 square inches, and the base (the bottom border) is 9 inches. Thus, we can enter those values into the formula to find the height:
126 = 9h
h = 126/9
h = 14
The plaque measures 14 inches tall as a result.
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1
Destiny combines 8.27 liters of red paint with 6.65 liters of blue paint to make purple paint. She
pours the paint equally into 2 containers, and has 1.56 liters of paint left over. How many liters
of paint are in each container? >
Container
?
2
There are
Solve on paper. Then check your work on Zearn.
Total paint = 8.27 + 6.65
M1|L16
3
4
Decimal Problem Solving
5 6
Container
liters of paint in each container.
7 8 90
Paint left
1.56
Enter ✔
The number of liters in each container is 8.24 liters.
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Destiny combined a total of 8.27 + 6.65 = 14.92 liters of paint to make purple paint.
She poured this paint equally into 2 containers, which means each container has half of the total amount of paint:
= 14.92 / 2
= 7.46 liters
However, Destiny also had 1.56 liters of paint left over that she didn't use.
To divide the remaining paint equally between the two containers, each container gets half of the remaining paint:
= 1.56 / 2
= 0.78 liters
Therefore, each container has 7.46 + 0.78 = 8.24 liters of paint.
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HELP ASAPP!
The parallel lines are marked with "feathers". Find the measures of the angles located at positions a, b, c, d, e, & f.
Answer:
Step-by-step explanation:
a=70
b=45
c=65
d=45
e=70
f=110
make sure to add degree symbol
Enjoy :)
Our local movie theater polls its customers about their favorite candy to eat during the movie. Name each sampling method described.
a. Employees ask every 45th customer that purchases a movie ticket:
b. An employee divides the theater into sections: left, right, front, back. He/she randomly chooses a section and polls every customer within that section:
The sampling method of (a) is systematic sampling, and (b) is cluster sampling.
What is the sampling method?It is an advanced form of simple random sampling. In this form, from the population of members, sample members are selected randomly. In this random selection, a starting point is fixed. The sample is created when the members are selected from the fixed intervals.
a. The sampling method described is systematic sampling, where every 45th customer that purchases a movie ticket is selected for the survey.
b. The sampling method described is cluster sampling, where the theater is divided into sections (clusters) and one cluster is randomly selected for the survey. Then, every customer within that cluster is polled.
Therefore, the sampling method of (a) is systematic sampling, and (b) is cluster sampling.
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1. Mr. Bryan’s pet turtle walks 280 feet at a speed of 4ft/min. How long does his walk take?
2. Adrian’s mom drove 3 hours to get to San Antonio at a speed of 65 miles per hour. How far away is San Antonio?
Answer:
1. 1hour 10minutes = 70 minutes
2. 190 miles
Step-by-step explanation:
1.
*Fraction*
Feet/minutes
- Divide
4/1 - 4feet over 1minute
4/1 = 280/x
4x70=280
1x70= 70
70 minutes = 1 hour 10 minutes
2.
1 hour = 65 miles
65x2hours=130miles
2hours= 130 miles
65x3hours= 195miles
3hours = 195miles
what is the measure of a
Answer:
∠ A = 19.8°
Step-by-step explanation:
the 3 angles of the triangle sum to 180°
sum the 3 angles and equate to 180
5x - 18 + 4x + x = 180
10x - 18 = 180 ( add 18 to both sides )
10x = 198 ( divide both sides by 10 )
x = 19.8
Then
∠ A = x = 19.8°
equals zero, which expression is equ (25-4x^(2))/(6x^(2)+9x-15)*(6x^(2)-2x-4)/(2x^(2)-x-10)
The solver for this expression is x = -5/2, 5/2, 2, -1/3, 1, 2.
To solve this expression, we will first need to factor the numerator and denominator of each fraction.
For the first fraction, we can factor the numerator as follows:
[tex]25 - 4x^2 = (5 + 2x)(5 - 2x)[/tex]
The denominator can be factored as follows:
[tex]6x^2 + 9x - 15 = (2x + 5)(3x - 3)[/tex]
For the second fraction, the numerator can be factored as follows:
[tex]6x^2 - 2x - 4 = (2x - 4)(3x + 1)[/tex]
The denominator can be factored as follows:
[tex]2x^2 - x - 10 = (2x + 5)(x - 2)[/tex]
Now we can simplify the expression by canceling out any common factors:
[tex](5 + 2x)(5 - 2x)/(2x + 5)(3x - 3) * (2x - 4)(3x + 1)/(2x + 5)(x - 2)[/tex]
[tex]= (5 + 2x)(5 - 2x)(2x - 4)(3x + 1)/(2x + 5)(3x - 3)(2x + 5)(x - 2)[/tex]
[tex]= (5 + 2x)(5 - 2x)(2x - 4)(3x + 1)/(3x - 3)(x - 2)[/tex]
Since the expression is equal to 0, we can set each factor equal to 0 and solve for [tex]x[/tex]:
[tex]5 + 2x = 0 \\5 - 2x = 0 \\2x - 4 = 0 \\3x + 1 = 0 \\3x - 3 = 0 \\x - 2 = 0 \\[/tex]
Solving for x, we get the following solutions:
[tex]x = -5/2 \\x = 5/2 \\x = 2 \\x = -1/3\\ x = 1 \\x = 2 \\[/tex]
Therefore, the solver for this expression is [tex]x = -5/2, 5/2, 2, -1/3, 1, 2[/tex].
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Danny attends baseball games throughout the summer all of the tickets that Danny buys cost the same amount the amount of money in dollars why spent on X Games is shown on the graph below Point c means that Danny spent blank dollars on tickets for blank games the unit rate can be represented by the point blank, blank on the graph
Point c means that Danny spent $80 dollars on tickets for 5 games . then the unit rate can be represented by the point (5, 80) on the graph.
Explain about the rate of change?The term "rate of change" (ROC) describes the rate at which something evolves over an extended period.
So, it is not the amount of specific features themselves but rather the deceleration or acceleration of changes (— in other words, the rate).Technically speaking, the Price Rate of Change marker calculates the percentage difference in price between the present price and the price from a predetermined number of periods ago.Since it enables investors to identify trends and other trends, rate of change is a crucial financial term.Danny purchases the same number of tickets for every baseball game he attends during the summer, and the graph below shows how much was spent on the X Games in dollars.
Thus, point c means that Danny spent $80 dollars on tickets for 5 games . then the unit rate can be represented by the point (5, 80) on the graph.
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the complete question is attached.
Need help asap! Step by step please, greatly appreciated!
The value of x from the given exponential function is -8.159.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given equation is [tex]9^{3x}=4^{5x+2}[/tex].
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Here, [tex]ln(9^{3x})=ln(4^{5x+2})[/tex]
x=2ln(4)/3ln(9)-5ln(4)
x= -8.159
Therefore, the value of x is -8.159.
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Translate the following to an algebraic expression: r squared minus the product of 6 and d plus 5
The algebraic expression for "r squared minus the product of 6 and d plus 5" is r2 - 6d + 5.
What is algebraic expression?An algebraic expression is an expression that contains at least one variable and uses mathematical operations such as addition, subtraction, multiplication, and division. It can also include exponents and/or roots. Algebraic expressions are used to represent mathematical relationships between different variables or constants. They can be used to represent real-world problems, such as finding the area of a rectangle.
In this expression, r2 represents "r squared", - 6d represents "minus the product of 6 and d", and + 5 represents "plus 5".
So, the final algebraic expression is r2 - 6d + 5.
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Fill in each blank with a number or expression such that each row and column adds up to the same total.
The blanks are filled by the following
8-3x 3x-6 4x-5 -2x+5
2x-3 3 2-x x
1-2x 4x-1 3x-2 -3x+4
5x-4 6-5x -4x+7 6x-7
How to fill the blanksThe blanks are filled by adding the complete row, this will be used for comparison and solve for other missing spaces.
let the missing value in each case be y
Adding the complete row gives
2x - 3 + 3 + 2 - x + x = 2x + 2
Column 1
8 - 3x + 2x - 3 + 1 - 2x + y = 2x + 2
6 - 3x + y = 2x + 2
y = 5x - 4
Column 2
y + 3 + 4x - 1 + 6 - 5x = 2x + 2
y + 8 - x = 2x + 2
y = 3x - 6
Row 4
5x - 4 + 6 - 5x + y + 6x - 7 = 2x + 2
6x - 5 + y = 2x + 2
y = -4x + 7
Column 3
y + 2 - x + 3x - 2 - 4x + 7 = 2x + 2
y + 7 - 2x = 2x + 2
y = 4x - 5
Row 1
8 - 3x + 3x - 6 + 4x - 5 + y = 2x + 2
-3 + 4x + y = 2x + 2
y = -2x + 5
Row 3
1 - 2x + 4x - 1 + 3x - 2 + y = 2x + 2
5x - 2 + y = 2x + 2
y = -3x + 4
check
This should be equal to Row 1 which is y = -2x + 5
Column 4
y + x - 3x + 4 + 6x - 7 = 2x + 2
y + 4x - 3 = 2x + 2
y = -2x + 5
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The area of a rectangle is 228 square feet. If the length of the rectangle is 12 feet what is the width of the rectangle
Answer: 19
Step-by-step explanation: The formula for the area of a quadrilateral is length x width.
Here, we have the width missing. So our equation would be,
12x=228.
dividing both sides by 12 gives us x=228/12.
solving this, we get x=19.
So, your answer will be 19.
Answer:
The width of the rectangle is 19 feet
Step-by-step explanation:
The formula for the area of a rectangle is length times width which can be expressed as
[tex]A=lw[/tex]
We can rearrange the equation and solve for the width.
Divide both sides of the equation by [tex]l[/tex].
[tex]\frac{A}{l}=w[/tex]
Now we have an equation to evaluate the width.
Numerical Evaluation
Substituting our values into the equation yields
[tex]\frac{228}{12}=w[/tex]
[tex]w=19[/tex]
What is the answer to this problem
The required equation of the line in slope-intercept form is y = 2x + 24.
What is the slope-intercept form of a line?To find the slope-intercept form of a line, we need to use the formula: y = mx + b
Where "m" is the slope and "b" is the y-intercept.
Here,
To find the slope of the line passing through the two given points (-2,20) and (-1,22), we can use the slope formula:
m = (y₂ - y₁) / (x₁ - x₁)
where (x₁, y₂) = (-2,20) and (x₁, y₂) = (-1,22).
m = (22 - 20) / (-1 - (-2))
m = 2 / 1
m = 2
Now that we have the slope, we can use one of the given points and the slope to find the y-intercept. Let's use the point (-2,20):
y = mx + b
20 = 2(-2) + b
20 = -4 + b
b = 24
Therefore, the equation of the line in slope-intercept form is y = 2x + 24.
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Order the numbers from least to greatest
Step-by-step explanation:
-10, -8, 0, 7 is the answer
The answer should be:
-10, -8, 0, 7
Which city should you live in if you want to live in a city with greater variability of temperature?
Answer: If you want to live in a city with greater variability of temperature, you should look for cities with a continental climate. Continental climates are characterized by hot summers and cold winters, with large temperature fluctuations between day and night and between seasons.
Cities located in the interior of large landmasses, far from large bodies of water, are more likely to have a continental climate. Examples of cities with a continental climate include Moscow (Russia), Calgary (Canada), and Chicago (USA). These cities experience wide temperature swings throughout the year, with hot summers and cold winters.
On the other hand, cities located near large bodies of water tend to have a more moderate climate, with smaller temperature fluctuations. Examples of such cities include San Francisco (USA), Sydney (Australia), and London (UK). These cities experience mild summers and winters, with relatively constant temperatures throughout the year.
Step-by-step explanation:
Calculate the determinant: \( \left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| \)
The determinant of the given matrix is 12.
Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)
The determinant of a 4x4 matrix can be calculated using the formula: \( \left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right| = a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right| - b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right| + c\left|\begin{array}{ccc}e & f & h \\ i & j & l \\ m & n & p\end{array}\right| - d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ m & n & o\end{array}\right|\)
Plugging in the values from the given matrix, we get: \(-3\left|\begin{array}{ccc}4 & 2 & 1 \\ 3 & -1 & -2 \\ -1 & 1 & 0\end{array}\right| - 0\left|\begin{array}{ccc}-1 & 2 & 1 \\ 0 & -1 & -2 \\ 5 & 1 & 0\end{array}\right| + 1\left|\begin{array}{ccc}-1 & 4 & 1 \\ 0 & 3 & -2 \\ 5 & -1 & 0\end{array}\right| - 2\left|\begin{array}{ccc}-1 & 4 & 2 \\ 0 & 3 & -1 \\ 5 & -1 & 1\end{array}\right|\)
Calculating the determinants of the 3x3 matrices, we get: \(-3(-4) - 0(0) + 1(-8) - 2(-4) = 12 - 8 + 8 = 12\)
Therefore, the determinant of the given matrix is 12.
Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)
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Given f (x)=7x-9, (a) Find f (x+h) and simplify. f(x+h)-f(x) (b) Find and simplify. h Part: 0/2 Part 1 of 2 (a) f(x+h)=
From equation f (x)=7x-9, f (x+h)= 7h and we can simplify it as 7.
For part (a), we can start by substituting x+h for x in the equation for f(x):
f(x+h) = 7(x+h) - 9
f(x+h) = 7x + 7h - 9
We can then simplify the expression to:
f(x+h) = 7x + 7h - 9
Now, to find f(x+h) - f(x), we can subtract f(x) from both sides of the equation:
f(x+h) - f(x) = 7x + 7h - 9 - (7x - 9)
f(x+h) - f(x) = 7h
Therefore, for part (a) we can conclude that f(x+h) - f(x) = 7h.
Now, we can simplify the difference quotient using f(x+h) and f(x):
f(x+h) - f(x) = [7(x+h) - 9] - [7x - 9]
= 7h
f(x+h) - f(x) / h = 7h / h = 7
We have already simplified the difference quotient to 7.
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Quadratic worded question
The owner of a fish shop bought x kilograms of salmon for $400 from the wholesale market. At the end of the day, all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. From the sale of the fish, a total of $540 was made. Calculate how many kilograms of salmon the fish-shop owner bought at the market.
Answer: 23 kg
Step-by-step explanation:
Let's begin by using algebra to solve the problem.
Let x be the number of kilograms of salmon the fish-shop owner bought at the market.
We know that the total cost of the salmon was $400, so we can write:
400 = x * c
where c is the cost per kilogram of salmon.
We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.
The total revenue from the sale of the fish was $540, so we can write:
540 = (x - 2) * (c + 10)
Now we can use these two equations to solve for x.
First, we can use the first equation to solve for c:
c = 400 / x
Then we can substitute this expression for c into the second equation:
540 = (x - 2) * (400/x + 10)
Simplifying this equation:
540 = 4000/x + 10x - 20 - 80/x
Multiplying both sides by x:
540x = 4000 + 10x^2 - 20x - 80
10x^2 - 20x - 4600 = 0
Dividing both sides by 10:
x^2 - 2x - 460 = 0
We can solve for x using the quadratic formula:
x = [2 ± sqrt(4 + 4*460)] / 2
x = [2 ± 44] / 2
Discarding the negative solution, we get:
x = (2 + 44) / 2
x = 23
Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.
