To get x * 1 point, the product of X and 2 should have x added to it.
let us assume unknown value = y
2x+y=x
y=x-2x
y=-x
so if we add "-x" in the product of x and 2 we get x
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign.
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Please help me !!
this the last question !!
Answer:
2 ≥ p
Step-by-step explanation:
-14 ≤ -7p
Divided both sides by -7. Because divided by a negative number, the < will turn to >
So, the equation is
2 ≥ p
Because there is an equal, the circle will be close and to the left of 2.
Answer:
2 ≥ p
Step-by-step explanation:
Have a great day :) <3
Write a possible explicit rule, then find a 10-
(0, 7, 26, 63, 124, ...)
n³ - 1
Explicit rule: an = n³
a10 =
Here the 10th term of this arithmetic sequence is 999.
What is an arithmetic sequence in math?An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.A series of integers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.Using the method for locating the nth term, we may locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the numbers a = 2 and d = 3 into the formula to determine the nth term.Given data :
an = n³ - 1
a1 = 1³ - 1 = 1 - 1 = 0
a2 = 2³ - 1 = 8 - 1 = 7
a3 = 3³ - 1 = 27 - 1 = 26
a4 = 4³ - 1 = 64 - 1 = 63
a5 = 5³ - 1 = 125 - 1 = 124
a10 = 10³ - 1 = 1000 - 1 = 999
I saw that these numbers were one less than the cubes. So the answer is
a_n = n^3 - 1
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Blair has a box of candy to sell. She has 4 chocolate bars, 4 fruit chews, 1 pack of bubble gum and 3 sour candies. If she chooses a piece of candy at random, how many possible outcome are there?
Answer:
12 possible outcomes
Step-by-step explanation:
The equation to find the possible outcomes is:
possible outcomes x total
We know she picks 1, so we have
1 x 12 = 12 possible outcomes
So, there are 12 possible outcomes
Find value of c
[tex]48c+ 6 = 408 \div 4[/tex]
Answer:
2
Step-by-step explanation:
408 / 4 = 102
48c + 6 = 102
48c = 102 - 6
48c = 96
c = 96/48
c = 2
Hence, the value of c is 2.
Answer:
[tex] \sf \: c = 2[/tex]
Step-by-step explanation:
Given equation,
→ 48c + 6 = 408 ÷ 4
Now the value of c will be,
→ 48c + 6 = 408 ÷ 4
→ 48c + 6 = 102
→ 48c = 102 - 6
→ c = 96 ÷ 48
→ [ c = 2 ]
Hence, the value of c is 2.
Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation. (4 points)
Part B: Logan made a profit of $210. 00 as a mobile groomer. He charged $75. 00 per appointment and received $35. 00 in tips, but also had to pay a rental fee for the truck at $10. 00 per appointment. Write an equation to represent this situation. (4 points)
Part C: Explain how the equations from Part A and Part B differ. (2 points)
The equations for parts A and B are 170 = 60x + 50 and 210 = 75x + 35 - 10x, respectively.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
A) It is stated that Maci once earned $170 by grooming dogs.
For each appointment, she charges $60, and she received $50 in tips. Consequently, the equation to illustrate this is;
170 = 60x + 50
the number of appointments is x.
B) Logan earned $210.00 in profit. He charged $75.00 for each session and got $35.00 in gratuities. In addition, he had a $10.00 truck rental fee per appointment. In order to represent this, the equation is;
210 = 75x + 35 - 10x
the number of appointments is x.
C) The quantity of tips they will receive even without an appointment varies between the formulae.
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A(3,-1); y= 1/3x +10
write an equation of the line passing through the given point that is parallel to the given line
the equation of the desired line is x = 3y + 6.
To find the equation of a line that is parallel to the given line
y = 1\3x + 10
and passes through the point (3,-1), since parallel lines have the same slope.
Therefore, the slope of the desired line is also 1\3.
Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:
y - (-1) = 1\{3}(x - 3)
Simplifying, we get
y + 1 = 1\ 3x - 1
Multiplying both sides by 3, we get
3y + 3 = x - 3
Adding 3 to both sides, we get
3y + 6 = x
Therefore, the equation of the desired line is x = 3y + 6.
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How do you know which inequality represents a graph?
In order to determine which inequality represents a graph, you need to look at the inequality and identify if the equation is an open or closed interval. If it is an open interval, it will be represented by a dashed line on the graph. If it is a closed interval, it will be represented by a solid line on the graph.
1. Look at the inequality and identify if the equation is an open or closed interval.
2. If it is an open interval, it will be represented by a dashed line on the graph.
3. If it is a closed interval, it will be represented by a solid line on the graph.
4. Determine the starting and ending points of the inequality, and plot them on the graph.
5. Draw the line that connects the two points, either dashed or solid, depending on whether the interval is open or closed.
6. Shade the area of the graph that is represented by the inequality.
7. Label the graph with the inequality, the points, and the shading.
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What is the answer to inequality?
The direction of inequality is reversed when you multiply or divide both sides by a negative value.
When expressions are compared using the operators "less than" (), "less than or equal to" (=), "greater than" (>), or "greater than or equal to" (>=), an inequality is created.
Example- x + 3 <= 10
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not.
The solution set of an inequality is the set of all solutions.
The solution set of example 1 is the set of all x <= 7. In interval notation, this set is (-inf, 7], where we use inf to stand for infinity.
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Write an equation of the line that passes through (3,-4) and is perpendicular to y=1/2x+7.
An octagonal prism (shown) has __________ faces and ___________ vertices. Question 20 options: A) 16, 10 B) 10, 16 C) 8, 10 D) 6, 8
With 10 faces and 16 vertices, an octagonal prism is depicted.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.
Do octagonal prisms have eight vertices?An octagonal prism therefore has 10 faces, 24 vertices, and 16 vertices.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape. 16 vertices, 10 faces, and 24 edges make up its surface.Eight of the nine vertices of an octagonal pyramid are found where the triangle faces of the base meet, while the ninth vertex is found where the triangular faces of the pyramid's top meet.There are 8 faces on an octahedron, which is a polyhedron. The octahedron shape of a hexagonal prism is defined by its 8 faces, which include its 2 bases and 6 sides.With 10 faces and 16 vertices, an octagonal prism is depicted. Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.To learn more about octagonal prism refer to:
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Can you make a triangle with 3 different length sides?
Yes, you can make a triangle with three different length sides.
1. Draw three lines of different lengths on a piece of paper.
2. Connect the ends of the lines to form a triangle.
3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.
4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.
5. Measure each side of the triangle with a ruler and add them together.
6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.
7. Once the triangle is valid, it will be a triangle with three different length sides.
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What number multiple by 7/9 has the product of 1?
Answer: In mathematics, the reciprocal of a number is 1 divided by that number. So the reciprocal of 7/9 is 1/(7/9) which can be simplified to 9/7.
Therefore, 9/7 is the number that when multiplied by 7/9 will result in the product of 1.
Another way of arriving at the same solution is to remember that the product of a number and its reciprocal is always 1. In this case, the number is 7/9, and its reciprocal is 9/7.
Step-by-step explanation:
The side of a square is 2.5 find its perimeter and area
Answer:
perimeter = 10
area = 6.25
Step-by-step explanation:
Every square has four equal sides. If we know one side is 2.5, then all sides are 2.5.
2.5*4 = 10
To find the area of a square you multiply the height and length. Since all sides of a square are the same, you just multiply 2.5 with itself.
2.5*2.5=6.25
Simplify the expression below:
20-10y-7y + 9
A) Зу — 29
B) 3y + 11
C) 3y + 29
D) -17y + 11
E) -17y + 29
To simplify the expression 20-10y-7y + 9, we can combine like terms.
Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.
We can start by combining the like terms:
20 - 10y - 7y + 9
= 20 + (-10y - 7y) + 9
= 20 + (-17y) + 9
Next, we can combine the constants:
20 + (-17y) + 9
= (20 + 9) + (-17y)
= 29 + (-17y)
The simplified expression is: 29 + (-17y)
[tex]20-10y-7y + 9[/tex]
Combine Like Terms:
[tex](-10y+-7y)+(20+9)[/tex]
[tex]-17y+29[/tex]
[tex]\fbox{Option E}[/tex]
Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes
1.3584655000
2.85760000
3.146737000
4.5555627000
5.7777000
1) Number of 200 notes = 17,923,275
Number of 100 notes = 35,846,550
Number of 50 notes = 71,693,100
Number of 20 notes = 179,232,750
2) Number of 200 notes = 428,800
Number of 100 notes = 857,600
Number of 50 notes = 1,715,200
Number of 20 notes = 4,288,000
3) Number of 200 notes = 733,685
Number of 100 notes = 1,467,370
Number of 50 notes = 2,934,740
Number of 20 notes = 7,336,850
4) Number of 200 notes = 27,778,135
Number of 100 notes = 55,556,270
Number of 50 notes = 111,112,540
Number of 20 notes = 277,781,350
5) Number of 200 notes = 38,885
Number of 100 notes = 77,770
Number of 50 notes = 155,540
Number of 20 notes = 388,850
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Ghana credits 200,100,50 and 20 notes.
Now,
Since, Ghana credits 200,100,50 and 20 notes.
1) Hence, To credit the amount 3584655000,
Number of 200 notes = 3584655000/200 = 17,923,275
Number of 100 notes =3584655000/100 = 35,846,550
Number of 50 notes =3584655000/50 = 71,693,100
Number of 20 notes = 3584655000/20 = 179,232,750
2) To credit the amount 85760000;
Number of 200 notes = 85760000/200 = 428,800
Number of 100 notes = 85760000/100 = 857,600
Number of 50 notes = 85760000/50 = 1,715,200
Number of 20 notes = 85760000/20 = 4,288,000
3) To credit the amount 146737000;
Number of 200 notes = 733,685
Number of 100 notes = 1,467,370
Number of 50 notes = 2,934,740
Number of 20 notes = 7,336,850
4) To credit the amount 5555627000;
Number of 200 notes = 27,778,135
Number of 100 notes = 55,556,270
Number of 50 notes = 111,112,540
Number of 20 notes = 277,781,350
5) To credit the amount 7777000;
Number of 200 notes = 38,885
Number of 100 notes = 77,770
Number of 50 notes = 155,540
Number of 20 notes = 388,850
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I really need help on this question
Step-by-step explanation:
2×4=8
8×2/3
8×2=16
16×3=48
ans = 48
Find the length of the third side. If necessary round to the nearest tenth
The side lengths of a right-angle triangle can be calculated using the Pythagorean Theorem. Which states that the square of the hypotenuse is equal to the sum of squares of the other sides in the triangle.
[tex]a^2+b^2=c^2[/tex]
the hypotenuse is always the longest side of a triangle and is always the opposite side length to the right anglerearranging the equation can help calculate the third side:
[tex]c^2-a^2=b^2[/tex]
[tex](5)^2-(4)^2=b^2[/tex]
[tex]25-16=b^2[/tex]
[tex]9=b^2[/tex]
[tex]\sqrt{9}=\sqrt{b^2}[/tex]
[tex]{ {{b_1=+3} \atop {b_2=-3}} \right.[/tex]
note: a length can never be negative so never take into account a negative answer
b = 3
For each equation determine whether it has no solutions, exactly one solution, or is true
for all values of x (and has infinitely many solutions). If an equation has one solution, solve
to find the value of x that makes the statement true.
a. 6r+8 = 7x + 13
b6r + 8 = 2(3x + 4)
c. 6r+8 = 6r+ 13
For the given equations , the solutions are as follows :
(a) the equation [tex]6x + 8 = 7x + 13[/tex] has exactly one solution , and the solution is .
(b) the equation [tex]6x + 8 = 2(3x + 4)[/tex] has Infinitely Many Solutions .
(c) the equation [tex]6x + 8 = 6x + 13[/tex] has No Solution .
Equation (a) ;
the equation is given as [tex]6x + 8 = 7x + 13[/tex] , we solve the equation further ,
we get ;
[tex]7x - 6x = 13 - 8[/tex] ;
[tex]x = 5[/tex] ;
So , the equation has exactly one solution and the solution is [tex]x = 5[/tex] .
Equation (b) ;
the equation is given as [tex]6x + 8 = 2(3x + 4)[/tex] , we solve equation further ,
we get ;
[tex]6x + 8 = 6x + 8[/tex] ;
On solving further ,
we have ;
[tex]8 = 8[/tex] ;
So , the equation has infinitely many solutions .
Equation (c) ;
the equation is given as [tex]6x + 8 = 6x + 13[/tex] , we solve equation further ,
we get ;
[tex]8 = 13[/tex] ;
and we know that [tex]8\neq 3[/tex] ,
So , the equation have No Solution .
The given question is incomplete , the complete question is
For each equation determine whether it has no solutions, exactly one solution, or is true . for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.
(a) 6x + 8 = 7x + 13
(b) 6x + 8 = 2(3x + 4)
(c) 6x + 8 = 6x + 13
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Solve the system of equation using the elimination multiplication method 3c+6d=18
6c-2d=22
show your work
So the solution to the system of equations is:
c = 4, d = 1
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.
Define quadratic equation.x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given equation I is [tex]3c+6d=18[/tex] and equation II is [tex]6c-2d=22[/tex]
We can start by multiplying the first equation by -2 and adding it to the second equation. This will eliminate the d variable:
[tex]-6c - 12d = -36[/tex]
[tex]6c - 2d = 22[/tex]
[tex]0c - 14d = -14[/tex]
solving this we know value of [tex]d=1[/tex]
So we know that d = 1, and we can substitute that into the first equation to find the value of c:
[tex]3c + 6d = 18[/tex]
[tex]3c + 6(1) = 18[/tex]
[tex]3c = 12[/tex]
[tex]c = 4[/tex]
So the solution to the system of equations is:
[tex]c = 4, d = 1[/tex]
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we the following mixed operations word problems
During a normal day, there are 782 passengers in average that
are late for their plane each day. However, during the
Christmas holidays, there are 1,835 passengers that are late for
their planes each day which caused delays of 14 planes. How
many more passengers are late for their planes in each day
during the Christmas holidays?
An average of 782 travelers miss their flight each day during a typical day. In contrast, 1,835 passengers are late for their flights every day over the Christmas holiday, which results in 14 planes being delayed.
1,053 travelers (2,835-782 = 1,053)
During the Christmas holidays, there are 1,053 extra passengers who are late for their flights.
How do you figure out the average number of days late?In order to compute WADO, we multiply the total amount of each overdue invoice by the number of days past due, then divide that total by the number of days past due. You may figure out your average daily sales by dividing your total sales over a certain period of time by the number of days in that same period.
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How do you find the terminal point of a line segment?
To find the terminal point of a line segment, identify the starting point, measure the length and direction, and use these parameters to calculate the coordinates of the terminal point.
To find the terminal point of a line segment, first identify the starting point of the line. Then, measure the length of the line segment and the direction in which it is going. Finally, use a combination of the starting point coordinates, the length, and the direction to calculate the coordinates for the terminal point of the line.
1. Identify the starting point of the line.
2. Measure the length of the line segment and the direction in which it is going.
3. Use the starting point coordinates, the length, and the direction to calculate the coordinates of the terminal point.
4. The coordinates of the terminal point are the location of the line segment’s endpoint.
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What is the area of right triangle with base 10 cm and height 5 cm?
Answer:25cm
Step-by-step explanation:area of triangle=1/2 × base× height
=1/2×10×5
= 25cm^2
2. Write a factored form function, f(x) for a cubic function that has zeros (- 7, 0) and (3, 0)
The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).
How to derive a cubic equation in factor form
Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:
y = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Real zeros.Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)
f(x) = (x + 7) · (x - 3) · (x - r)
Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.
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What is 6 divided by 9.51
Answer:
The result of 6 divided by 9.51 is approximately 0.63.
Answer:
0.63091482649
Step-by-step explanation:
Can u please help?.........................
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(2(9) + 3(-1))/(2 + 3)], [(2(6) + 3(-4))/(2 + 3)]
P(x, y) = [(18 - 3)/(5)], [(12 - 12)/5]
P(x, y) = [15/5], [0/5]
P(x, y) = [3, 0]
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Complete Question:
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?
What is an angle with 3 acute angles?
Three straight sides and three angles make up the shape of a triangle. The angles of a triangle can either be acute, right, or obtuse. An angle with three acute angles is a triangle where all three angles measure less than 90 degrees.
A triangle is a three-sided shape with three angles. The sum of the internal angles of a triangle is always 180 degrees. An angle is the amount of turn or change in direction between two lines. There are three types of angles, acute, right and obtuse. An acute angle is an angle which measures less than 90 degrees. A right angle is an angle which measures exactly 90 degrees, and an obtuse angle is an angle which measures more than 90 degrees. Therefore, an angle with three acute angles is a triangle where all three angles measure less than 90 degrees. A triangle with three acute angles is also known as an acute triangle. All three angles must add up to 180 degrees, so the measure of each angle must be less than 60 degrees.
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In a single experiment, a die is tossed and a spinner with the letters A, B, and C is spun. Each letter is equally likely.Draw your sample space and then find the probability of getting a 2 or a B.a.The sample space is 9. The probability of getting a B is StartFraction 1 Over 9 EndFraction.b.The sample space is 18. The probability of getting a 2 or a B is StartFraction 18 Over 8 EndFraction
The required probability as calculated from the data given above is found to be as 1 / 9.
Given,
The spinner is having the letters as A, B and C.
The possibility of getting any of these letters when the spinner is rolled is same.
Therefore , the sample space will be as follows ,
6 + 3 = 9
This is due to the fact a die has 6 sides.
Then the probability of getting a B will be , 1/9
Sample space is known as the collection of all values which are used in an experiments. The total number of favorable outcomes are taken from this sample space only.
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A lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for 24. 00 each and slices of cheesecake for 3. 50 each. If they want to raise at least 700 how many of each could they sell
the total of 29 cheesecake and 2 slices of cheesecake will be making $703.
What is the arithmetic operation?
The four basic arithmetic operations are addition, subtraction, multiplication, and division of two or more quantities. They all fall under the umbrella of mathematics, and among them is the study of numbers, particularly the order of operations, which is crucial for all other branches of the subject, such as algebra, data organisation, and geometry. To solve the problem, you must be familiar with the fundamentals of mathematical operations.
A lacrosse team is raising money by selling cheesecakes.
The players plan to sell an entire cheesecake for 24. 00 each and slices of cheesecake for 3. 50 each.
A multiplier of 24 close to 700 is 29
So 29 cheesecake will cost 696.
Now they need more 4 dollars to raise so they have to sell 2 slices, which will be 7$.
So the total of 29 cheesecakes and 2 slices of cheesecake will be making $703.
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Use synthetic division to find all the real zeros of the polynomial.
f(x) = x³ + x² - 8x - 6
so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.
well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.
so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]
now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.
A pole that is 3.2 m tall casts a shadow that is 1.32 m long. At the same , a nearby tower casts a shadow that is 46.75 m long. How tall is the tower? Round your answer to the nearest meter.
Answer:
The tower is 113 meters.
Step-by-step explanation:
We are given a pole and a tower that both create a shadow.
Hence, the figures made are triangles.
If you draw the figure (attached to this response), you can see the two triangles are similar triangles.
⭐What are similar triangles?
two triangles whose corresponding side lengths are proportional and have the same shapeStrategycreate a proportion of the ratios of the corresponding side lengthssolve for the length of the towerCreate a ratio for the corresponding side lengthsThe length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).
The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).
Therefore, our two ratios are:
[tex]\frac{3.2}{x}[/tex] and [tex]\frac{1.32}{46.75}[/tex]
Create a proportion for the corresponding side lengthsA proportion is when you set two ratios equal to each other:
[tex]\frac{3.2}{x} = \frac{1.32}{46.75}[/tex]
Solve for the length of the tower (x)To solve for x, cross multiply by multiplying the opposite parts of the fraction together.
[tex]\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x[/tex]
∴ The tower is 113 meters tall!
if this response helped you, please mark it the "brainliest" :)