Given (x − h)2 = 4p(y − k), the ordered pairs representing the vertex and focus are __________ and __________, respectively. The directrix is the line defined by the equation __________.

Q: Suppose that two microphones 1500 m apart at points A and B detect the sound of a rifle shot. The ti...

A: Frist draw a diagram with given information as shown in below figure.

Q: For Exercise, solve the equation. 50e2x+1 = 2000

A: Given: The equation

Q: For Exercise, graph the solution set. −30x ≥ 20y + 600

A:

Q: Find the dimensions of a rectangle whose perimeter is 36 m and whose area is 80 m2

A: First of all, consider the formula of perimeter for rectangle.Then put the given value of the perime...

Q: Devon invested $8000 in three different mutual funds. A fund containing large cap stocks made 6.2% r...

A: Let he invested $x in the large cap stock fund.$y in real estate fund$z in  bond fundTotal x+y+z=800...

Q: For Exercise, find the number of terms of the finite arithmetic sequence. 8, 14, 20, 26, … , 320

A: Let there are n terms in the sequence.a_1= 8 and a_n=320common difference = d= second term - first t...

Q: Solve the following logarithmic equation. log (4x + 9) = 1 + log (x - 5) %3D Select the correct choi...

A: Given,

Q: For Exercise, solve the system of equations. 3(x-y)=y-3 -2x+y/2=-11

A: Given the system of equations

Q: Perform the row operation(s) on the given augmented matrix. R2 = - 2r1 +r2 - 5 3 - 4 - 3 4 - 2 - 1 -...

A:

Q: For Exercise, graph the equation. (x + 4)2 + ( y − 1)2 = 4

A: Given,

Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 6,...

A: Given:

Q: For Exercise, write the standard form of the equation of the hyperbola subject to the given conditio...

A: To determine the standard equation of the hyperbola.

Q: For Exercise, an equation of a parabola is given. a. Write the equation of the parabola in standard ...

A: Consider the given equation.(a) 

Q: Write as the sum and/or difference of logarithms. Express powers as factors. х+6 log 4 X' O A. log 4...

A: Given,

Q: A solution to a nonlinear system of equations in two variables is an __________ pair with real-value...

A: A solution to a nonlinear system of equations in two variables is an ordered pair with real-valued c...

Q: Use the horizontal line test to determine whether the function is one-to-one. One-to-one Ay 20- Not ...

A: The horizontal line test is used to determine whether a function is one-to-one or not.According to i...

Q: Stuart pays back two student loans over a 4-yr period. One loan charges the equivalent of 3% simple ...

A: Given: -

Q: For Exercise, determine the center and radius of the circle. (x − 4)2 + (y + 3)2 = 81

A: Given:

Q: Find the sum. 8+7.2+6.4+5.6+.............+(-45.6)

A: It is required to calculate the sum of:

Q: For Exercise, solve the system if possible by using Cramer’s rule. If Cramer’s rule does not apply, ...

A: Given: solve the system of equations using Cramer’s rule

Q: Solve the following exponential equation. Express irrational solutions in exact form and as a decima...

A: From the given information it is required to solve the exponential equation:

Q: For Exercise, fill in the blank. Let |p| represent the focal length (distance between the vertex and...

A:

Q: For Exercise, find three ordered triples that are solutions to the linear equation in three variable...

A: Given,

Q: For Exercise, write the standard form of an equation of an ellipse subject to the given conditions. ...

A: Since major axis parallel to the x-axis so:

Q: A matrix with the same number of rows and columns is called a __________ matrix.

A: A matrix with the same number of rows and columns is called a square matrix.

Q: A theater charges $50 per ticket for seats in Section A, $30 per ticket for seats in Section B, and ...

A: A theater charges $50 per ticket for seats in Section A, $30 per ticket for seats in Section B, and ...

Q: For f(x) = 8x + 4 and g(x) = 5x, find the following composite functions and state the domain of each...

A:

Q: For Exercise, a. Write the equation of the hyperbola in standard form. b. Identify the center, verti...

A: (a) Write the equation of the hyperbola in the standard form as follows.

Q: For Exercise, solve the system of equations using a. The substitution method or the addition method ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: José must choose between two job offers. The first job pays $50,000 the first year. Each year therea...

A: Given: -

Q: A sedan gets 12 mpg in the city and 18 mpg on the highway. If a driver drives a total of 420 mi on 2...

A: Let x represent the miles sedan drove in the city and y represent the miles sedan drove on the highw...

Q: For Exercise, determine the center and radius of the circle. x2 + y2 = 25

A: The given equation of circle is,

Q: For Exercise, write the standard form of an equation of a hyperbola subject to the given conditions....

A:

Q: For Exercise, find the value of n so that the expression is a perfect square trinomial. Then factor ...

A: If a trinomial is in the form px 2 + qx + r is said to be perfect square, if only it satisfies the c...

Q: For Exercise, determine whether the sequence is arithmetic. If so, find the common difference.  15, ...

A: To determine whether the sequence is arithmetic or not and find the common difference.

Q: An aquarium is 16 in. high with volume of 4608 in.3(approximately 20 gal). If the amount of glass us...

A:

Q: What is the difference between the minor of an element aij and the cofactor of the element?

A:

Q: For Exercise, identify each equation as representing a circle, an ellipse, a hyperbola, or a parabol...

A:

Q: Graph the solution set to the inequality. a. 3x + 4y≤ 8 b. 3x + 4y>8

A: a)To graph the inequality

Q: Given A= [aij], the __________ of the element aij is the determinant obtained by deleting the ith ro...

A: Given A= [aij], the __________ of the element aij is the determinant obtained by deleting the ith ro...

Q: For Exercise, write an inequality to represent the statement. The sum of x and y does not exceed 18.

A: The sum of x and y is represented by x + y. The sum of x + y is does not exceed by 18 means: 

Q: Given an arithmetic sequence with a14 = 148 and a35 = 316, find a1 and d

A: Use the term formula to get two equations of a_1 and d 

Q: What is an objective function?

A: An objective function can be defined as a real-valued function in the mathematical optimization prob...

Q: Write the standard form of an equation of a hyperbola with vertices (−1, −3) and (5, −3) and slope o...

A:

Q: Find the inverse of the function and state its domain and range. {(- 3,4),(- 1,5),(0,2),(2,6).(5,7)}...

A: The set of ordered pairs of the function is given below. {(- 3,4),(- 1,5),(0,2),(2,6).(5,7)}

Q: Write a system of inequalities that represents the points inside the triangle with vertices (−3, −4)...

A: First draw the triangle with given vertices. 

Q: A courier company makes deliveries with two different trucks. Truck A costs $0.62/mi to operate and ...

A: Let x be the number of miles that the truck A traveled and y be the number of miles that the truck B...

Q: What can you conclude about a system of equations if the corresponding reduced row-echelon form cons...

A: Given:

Q: Use the given zero to find the remaining zeros of the function. 3 h(x) = x* – 9x° + 21x + 21x - 130 ...

A: Since 3-2i is a zero of h(x)So the conjugate of 3-2i , that is 3+2i is also a zero of h(x). 

Q: For Exercise, solve the equation. log2(x − 4) = log2(x + 1) + 3

A: To solve the given equation.