Answer:
Option D.
Step-by-step explanation:
The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{0^2+(2)^2}=\sqrt{4}=2[/tex]
Similarly,
[tex]BC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2}=3[/tex]
[tex]CD=\sqrt{\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=2[/tex]
[tex]AD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=3[/tex]
[tex]AB = CD[/tex]
[tex]BC = AD[/tex]
Measure of diagonals:
[tex]AC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{13}[/tex]
[tex]BD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=\sqrt{13}[/tex]
[tex]AC = BD[/tex]
Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.
Hence, the correct option is D.
A surveyor, standing 100 ft. from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
Wendy wants $15,000 saved in 6 years to make a down payment on a house. How much money should she invest now at 4.65% compounded annually in order to meet her goal?
What is the best approximation of the sine of 50°?
A. 0.2624
B. 0.6428
C. 0.7660
D. 1.1918
the function f is defined by f(x)=x2+3x-10
if f(x+5)=x2+kx+30, k=____________(<<
If arc CE= 40°, and m∠CDE = 30°, what is arc AB ?
A) 70°
B) 100°
C) 140°
D) 20°
Answer:
B is the right answer [tex]100^{o}[/tex]
Step-by-step explanation: Hope This Helps ;)
Oscar Montez’s savings account has a principal of $7,201. It earns 6% interest compounded quarterly. What is the amount of interest he earned by the end of the second quarter?
Simplify (8j3 + 5j2 – 3) – (5j3 + 7j2 – 12j + 7) ...?
Answer:
3j^3 - 2j^2 + 12j - 10
Step-by-step explanation:
I took the test and got a 100%
Help With Number 8 Please?
PLEASE HELP!!
Oscar entered y=−0.4^x+3y=−0.4^x+3 into an online graphing tool.
What function did he graph?
y=(−0.4)x+3y=(−0.4)x+3
y=(−0.4)x+3y=(−0.4)x+3
y=−(0.4)x+3y=−(0.4)x+3
y=−(0.4)x+3
What times what equals 80.73
A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?
To maximize profit, the candy manufacturer should use mathematical linear programming. The decision variables are the amounts of Candy A (x) and Candy B (y). The profit function P = 285x + 260y is to be maximized subject to constraints arising from available stock of dark chocolate, caramel, and walnuts, leading to a typical linear programming problem.
Explanation:To solve this problem, we need to use Linear Programming, a mathematical model that helps in making optimal decisions. The candies are what we call decision variables. Our decision variables here are Candy A and Candy B.
Candy A: x kilograms (dark chocolate and caramel in equal parts).
Candy B: y kilograms (two parts of dark chocolate and one part of walnut).
We want to maximize the profit function P = 285x + 260y subject to constraints arising from the available stock of dark chocolate (DC), caramel (C), and walnuts (W).
DC constraint: A uses DC in equal parts, and B uses two parts DC. Therefore, x + 2y ≤ 360.C constraint: A uses equal parts C, x ≤ 430 (as B doesn't use C).W constraint: B uses one part W, y ≤ 210 (as A doesn't use W).
The next step is to solve these inequalities graphically or using mathematical methods to get values of x and y that maximize P while respecting constraints. This case, where we want to optimize a certain function with respect to constraints, is a typical linear programming problem in mathematics.
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If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful
launches? ...?
Answer: The required probability of three consecutive successful launches is 91.27%.
Step-by-step explanation: Given that a satellite launch has a 97% chance of success.
We are to find the probability of three consecutive successful launches.
Let P(A) denotes the probability of the event of the success of the satellite launch.
Then, according to the given information, we have
[tex]P(A)=97\%=\dfrac{97}{100}=0.97.[/tex]
Therefore, the probability of three consecutive successful launches will be
[tex]p\\\\=P(A)\times P(A)\times P(A)\\\\=0.97\times0.97\times0.97\\\\=0.912673\\\\=0.912673\times100\%\\\\=91.2673\%\\\\=91.27\%.[/tex]
Thus, the required probability of three consecutive successful launches is 91.27%.
solve for X. y=1/4 (x)+3
A furniture company misprinted a sales ad for a living room set but honors the advertised price. For each customer who purchases the living room set, the company suffers a loss of $125. Write a function to represent the company's total loss. What is the value of the function for an input of 50, and what does it represent? ...?
find all the zeros of the function y=x^3+6x^2+x+6
The zeros of a function are the values of x for which the function equals zero. The function given here is a cubic function, and finding its zeros can be complex, often requiring numerical methods or advanced mathematical approaches like the cubic formula.
Explanation:This problem deals with finding the zeros of the cubic function y=x^3+6x^2+x+6. A zero of a function is a value of x for which the function equals zero. You can find the zeros of this function by setting the equation equal to zero and solving for x.
Unfortunately, this particular cubic equation does not have an easy solution using basic algebraic methods. We can't factor it in an easy and straightforward manner. However, you can use numerical methods, or online calculator tools, to get an approximate value for the zeros. Alternatively, you can use the cubic formula (somewhat similar to the quadratic formula), but this requires knowledge of more advanced mathematics.
Please consult your teacher or textbook for more detailed instructions on how to use higher level methods to solve cubic equations. Remember that each method has its own level of accuracy and complexity, so choose the method that best suits your abilities and the requirements of your task.
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What is another way to write 250,000 ml?
A percent is the result of a number being expressed as a fraction of 100. True or False? ...?
Answer:
True
Step-by-step explanation:
Percentage is expressed as the part from 100.
Thus, Percentage sign means divide by 100.
Also, it is the resultant number when divided by 100.
Thus, the given statement is absolutely true.
How are mc091-2.jpg and mc091-3.jpg related?
Which of the following statements is true?
A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
Please help
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B′. What is the scale factor of the dilation?
1
2
0.5
-0.5
Answer:
The diameter of B is from -2 to 2, which = 4 units.
The diameter of B' is from -1 to 1, which equals 2 units.
2/4 = 1/2 = 0.5 scale factor.
The answer is C. 0.5
Step-by-step explanation:
The mean number of hours that Raphael worked over the past four weeks is 37.75. If he works 40 hours this week, what will the mean number of hours be that he will have worked over the five-week period?
What is the five-week mean?
What is the solution to the equation?
5(8 + 7) = 5 • x + 5 • 7
A.
x = 1
B.
x = 5
C.
x = 7
D.
x = 8
Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?
a.) y – 12 = –5(x + 2)
b.) y – 12 = 2(x + 2)
c.) y + 12 = 2(x – 2)
d.) y + 12 = –5(x – 2)
A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?
Answer:
Step-by-step explanation:
A vehicle travels at a rate of 65 m/h, How long does it take the vehicle to travel at 25 miles?
Apply the "distance formula":
d = rt
25 = 65t
25/65 = t
5/13 hour = t
or
0.385 hour = t
or
23.08 minutes = t
What is d if p equals 15 in d=-3p^2+168p-315
Which of the following is not a way to prove a quadrilateral is a parallelogram?
The way to not prove a quadrilateral is a parallelogram is; Show one set of opposite sides of the quadrilateral is congruent.
Parallelogram and CongruenceA parallelogram is a quadrilateral which has opposite sides to be congruent and parallel as the name implies and hence, opposite angles of the parallelogram are congruent.
However, showing one set of opposite sides of the quadrilateral is congruent is not a confirmatory test for a parallelogram, as it evades the parallel law of opposite sides of the Parallelogram.
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Kurt johnson delivers packages for a delivery company. he receives $7.50 for every package delivered. what does kurt earn in a week if he delivers 48 packages? 360.00 405.00 555.00 640.00
Answer:
He earned $ 360.00.
Step-by-step explanation:
Given,
The amount he gets for a package of delivery = $ 7.50
The number of packages he delivered in a week = 48,
Hence, the amount he earned in the week = The amount he gets for a package of delivery × The number of packages he delivered
= 7.50 × 48
= $ 360.00
An Antique vase is projected to be worth $1000 in 2 years and $1,300 after 5 years. If the value continues to appreciate at the same rate, what will it be worth in 8 years?
The value of the antique vase after 8 years with a consistent appreciation rate, it would amount to $1,600.
An antique vase:
Value after 2 years: $1,000
Value after 5 years: $1,300
To find the value after 8 years, we can assume a constant rate of appreciation:
In 8 years, the value will be: $1,000 + ($1,300 - $1,000) = $1,300 + ($1,300 - $1,000) = $1,600
Find the missing length. The triangle in each pair are similar.
Answer:
39 UNIT
Step-by-step explanation:
According to similar triangle.
Let's call NG "X"
45/27 = 65/x
X=( 65*27)/45
X= 1755/45
X = 39
Six times the sum of a number and twelve is forty.
Which equation represents this?
6N + 12N = 40
6N + 12 = 40
6(N + 12) = 40