A banner contains 21 colorful equilateral triangles. In the middle of the banner is the biggest triangle, whose base is 300 mm long. On the left and the right of the middle triangle, there is a series of triangles working outward such that the next triangle’s base is 25 mm shorter than the one before it. How long is the banner

Q: The height of a triangle is 4 m more than twice the length of the base. The area of the triangle is…

A: The height of a triangle is 4 m more than twice the length of the base.Base=bHeight =2b+4The area of…

Q: 2. Use this function to answer questions a- d. Please show your work f(x) = 3x³-7x²-14x +24 a. Using…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Determine if the given value of x is a solution to the logarithmic equation. log4 (x-63)=3-log.x…

A: given equation

Q: Find the eigenvalues of the matrix [0-3] 2 5 A =

A:

Q: 1. In the following problems, find the equation of the line: 5 a. m =- and point (8,3) 8

A:

Q: Use the specified row transformation to change the matrix. - 3 times row 1 added to row 2 What is…

A:

Q: Find the missing coordinates such that the three vectors form an orthonormal basis for R³: GOE -1…

A:

Q: 15. The row of Pascal's triangle containing the binomial coefficients is: 1 10 45 120 210 252 210…

A: The of Pascal's triangle containing the binomial coeffcient is

Q: Analyze the polynomial function f(x) = x³ + x²-20x using parts (a) through (h) below. (a) Determine…

A: Note: This question has 6 subparts. According to Bartleby guidelines I'll solve first three…

Q: Given = 2 1 A 6 34 9 8 -7 5 " find the closest point to in the subspace W spanned by 2 -6 1₂ 1 and

A:

Q: A new hybrid car sold in the United States reports a fuel usage of 32mpg. Write the equivalent rate…

A: The objective of this question is to convert the fuel efficiency of a car from miles per gallon…

Q: system Find the least-squares solution of the 1 1 1 1 1 -1 18 || ** 2 - 10

A:

Q: Solve the following equation using the quadratic formula. 3x²-x=2 The solution set is (Simplify your…

A: .

Q: Write the function shown in each graph.

A:

Q: - 11 4 -12 -8 1 -12 . Find an 4 -2 3 nvertible matrix P and a diagonal matrix D such hat D = P-¹AP.…

A:

Q: Write the ratio 870:960 in lowest terms.

A: The objective of this question is to simplify the given ratio 870:960 to its lowest terms. This…

Q: Rewrite as sums or differences of logarithms.   logb (x8 y2 z)

A: The objective of the question is to rewrite the given logarithmic expression as a sum or difference…

Q: Solve the equation by the square root property. (x + 2)² = 81 The solution set is {}. (Simplify your…

A:

Q: The fastest 50-yard dash was completed in 5.11 seconds. To the nearest hundredth, how many hours was…

A: The objective of this question is to convert the time taken to complete a 50-yard dash from seconds…

Q: Two cars started from the same point at the same time. One is headed at a bearing of E42S and is…

A: One car is headed to the E 42 S with 10.2 miles per hourOther car is headed to the W 46 S with 13…

Q: (a) Find the rational zeros and then the other zeros of the polynomial function ​f(x)=x3−43x+42​;…

A: The objective of this question is to find the rational zeros of the polynomial function f(x)=x^3 -…

Q: Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then…

A: x2−8x+16=64

Q: Let W be the set of all vectors X y x + y with x and y real. Find a basis of W¹.

A: The given set  is the set of all vectors of the form .The aim is to find the basis of .

Q: Let W be the set of all vectors [5] x + y ㅗ with x and y real. Find a basis of W

A: The given set  is the set of all vectors of the form .The aim is to find the basis of .

Q: Solve. please

A: The objective of the question is to find the value of x that satisfies the equation (x - 9)^2 + 4 =…

Q: Thank you! Does this mean that the plate is 0.35 units from the bottom of the bowl, as the question…

A: Yes, the distance of the plate from the top of the bowl is 12.65 units.Since the radius of bowl is…

Q: 2. Find the inverse of D if it exists where 1 0 D= = 0 0 0 00 -1 1 0 0 11 001

A:

Q: P = Let D= If possible, find an invertible matrix P so that D = P-¹ AP is a diagonal matrix. If it…

A: The objective of the question is to determine if the given matrix A is diagonalizable over the real…

Q: Given functions f and g, find (a) (fog)(x) and its domain, and (b) (gof)(x) and its domain.…

A:

Q: The cross product of two vectors in R³ is defined by a1 b₁ BHBH a2 b3 Let v = 3 2 2 -2 Find the…

A:

Q: Which of the following mappings is NOT a function? 1 B 4 ABCO А D 23 1 A 2 3 4 C VA 2 46 8 8 4 0 2 2…

A:

Q: Change the exponential statement to an equivalent statement involving a logarithm. 2.3=3x is 0.…

A: The given equation is

Q: The given image is rotated about it's center. What is the order of rotational symmetry and the angle…

A: The given image is rotated about it's center. What is the order of rotational symmetry and the angle…

Q: Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility…

A:

Q: A water storage tank is shaped like a cone. The diameter of the circular base of the tank is 4.5…

A:

Q: Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility…

A:

Q: Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint…

A: xy=-x+30y=-0+3=32(Hole point)y=-2+3=1

Q: 1. For which values of a and b is the following system of equations inconsistent. x + 2y3z=4 3x - y…

A: The given system of equations are,The aim is to find the value of  and  for which the system is…

Q: The length of a rectangle is three times its width. If the width were increased by 2 meters while…

A:

Q: If $6000 is invested for six years and seven months at 6% compounded semi-annually, what is the…

A: I have appended the formula used in the solution procedure

Q: The function s(t) = 16t models the distance, s(t), in feet, that an object falls in t seconds. Use…

A:

Q: YOU PICK Directions Solve the equation x² - 12x +23=0 by completing the square. You may choose to…

A:

Q: It takes an ant habitat 4 days to consume % of a banana. At that rate, in how many days will the ant…

A: It takes an ant habitat 4 days to consume  of a banana.At that rate, to determine the number of days…

Q: Solve the polynomial inequality x3 + x² - 7x-3 ≤0 by using the rational zeros theorem and synthetic…

A:

Q: What type of comic is the equation 3x^2-12xy+5y^2+2x-3y-5=0

A: The General equation of a conic section is , where A,B,C,D,E,F are constants.Then the following are…

Q: 7. Let T: R³ R³ be defined by (a) (b) (1) - = Find the matrix of linear transformation T x1+x₂ + x3…

A:

Q: 3. For what value of k, if any, will the system have (a) no solution, (b) a unique solution, (e)…

A:

Q: Solve the following inequality. xử +5x <0 The solution is (Type your answer in interval notation.…

A:

Q: 1. Solve the following system of linear equations using the substitution method. Verify that your…

A: We are authorized to answer one question at a time , so we are answering the first one, please…

Q: Solve the​ triangle, if possible.   a=13 ​m, b=24 ​m, c=32 m

A: The objective of the question is to solve the triangle given the lengths of its sides. In this case,…