Given:
The vertices of a quadrilateral ABCD are A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).
To find:
The perimeter of quadrilateral ABCD.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the distance formula, we get
[tex]AB=\sqrt{(4-0)^2+(1-4)^2}[/tex]
[tex]AB=\sqrt{(4)^2+(-3)^2}[/tex]
[tex]AB=\sqrt{16+9}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5[/tex]
Similarly,
[tex]BC=\sqrt{(1-4)^2+(-3-1)^2}[/tex]
[tex]BC=5[/tex]
[tex]CD=\sqrt{(-3-1)^2+(0-(-3))^2}[/tex]
[tex]CD=5[/tex]
And,
[tex]AD=\sqrt{(-3-0)^2+(0-4)^2}[/tex]
[tex]AD=5[/tex]
Now, the perimeter of the quadrilateral ABCD is:
[tex]P=AB+BC+CD+AD[/tex]
[tex]P=5+5+5+5[/tex]
[tex]P=20[/tex]
Therefore, the perimeter of the quadrilateral ABCD is 20 units.
The formula for the circumference of a circle is R = c/2(pi)
Find the radius of a circle that has a circumference of 16(pi)
A) r = 4
B) r = 8
C) r = 12
D) r = 16
Evaluate 2y when y = 6y
0.2(x + 20) – 3 > –7 – 6.2x
Answer:
x > - 1.25
Step-by-step explanation:
0.2(x + 20) – 3 > –7 – 6.2x
0.2x + 4 - 3 > - 7 - 6.2x
0.2x + 1 > - 7 - 6.2x
Collect like terms
0.2x + 6.2x > -7 - 1
6.4x > -8
x > - 8/6.4
x > - 1.25
Note:
The > didn't change because you didn't divide by a negative value
Inequality signs changes when divided by a negative value
Answer:
Step-by-step explanation:
-1.25
Select the expression that represents the following statement: add 24 to the quotient of 16 and 8.
Answer:
16/8 + 24
Step-by-step explanation:
The area of the rectangular sandbox at Dave's school is 117 square feet. The sandbox has a width of 9 feet as shown in the diagram. What is the perimeter of the sandbox?
Answer:
ay bru ima tell yu dhis rn is c
Step-by-step explanation:
Hello, Brainly community!
This question is for all of those Calculus people out there.
The volume of a swimming pool is changing with respect to time, such that the volume is given by W(t), where W(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for W(t) at t = 3 seconds. Determine the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
(I've narrowed down the answer choices to 2, and just really need to find the right way of thinking to find the answer)
(A) W(lim t) as t goes to 3.
(B) [W(3.1) - W(2.9)] / 0.2.
Thank you in advance!
Answer:
(B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Derivatives
The definition of a derivative is the slope of the tangent line.Derivative Notation
Instantaneous Rates
Tangent Line: [tex]\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}[/tex]Step-by-step explanation:
Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.
We are given 2 close answer choices that would have the same numerical answer but different meanings:
(A) [tex]\displaystyle \lim_{t \to 3} W(t)[/tex](B) [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
If a bus travel for 120 minutes at a speed of 75 kilometers per hour how far has the bus traveled?
Answer:
150 km
Step-by-step explanation:
Put the minutes into hours 120min is 2 hours.
Distance = speed * time
Distance = 75 * 2
Distance = 150
Answer:
150 kilometers
Step-by-step explanation:
if the bus is going 75 kilometers an hour and they traveled for 120 minutes (exactly 2 hours) then you would just multiply 75 by 2 to get 150 kilometers total.
There are 35 times as many students at Wow University as teachers. When all the students and
teachers are seated in the 8544 seat auditorium, 12 seats are empty. How many students attend
Wow University?
Given:
There are 35 times as many students at Wow University as teachers.
When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.
To find:
The total number of students.
Solution:
Let x be the number of teachers at Wow University. So, the number of student is :
[tex]35\times x=35x[/tex]
When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.
[tex]x+35x=8544-12[/tex]
[tex]36x=8532[/tex]
[tex]x=\dfrac{8532}{36}[/tex]
[tex]x=237[/tex]
The number of total students is:
[tex]35x=35(237)[/tex]
[tex]35x=8295[/tex]
Therefore, the total number of students is 8295.
Find ∠MPN
Help me please
Answer:
[tex]22^{\circ}[/tex]
Step-by-step explanation:
Line [tex]\overline{PM}[/tex] is a diameter of the circle because it passes through the circle's center O. Therefore, arc [tex]\widehat{PLM}[/tex] must be 180 degrees, as these are 360 degree in a circle.
We can then find the measure of arc [tex]\widehat{LM}[/tex]:
[tex]\widehat{LP}+\widehat{LM}=180^{\circ},\\92^{\circ}+\widehat{LM}=180^{\circ},\\\widehat{LM}=88^{\circ}[/tex]
Arc [tex]\widehat{LM}[/tex] is formed by angle [tex]\angle LPM[/tex]. Define an inscribed angle by an angle with a point on the circle creating an arc on the circumference of the circle. The measure of an inscribed angle is exactly half of the measure of the arc it forms.
Therefore, the measure of [tex]\angle LPM[/tex] must be:
[tex]m\angle LPM=\frac{88}{2}=44^{\circ}[/tex]
Similarly, the measure of [tex]\angle LNP[/tex] must be:
[tex]m\angle LNP=\frac{92}{2}=46^{\circ}[/tex]
Angles [tex]\angle LPM[/tex] and [tex]\angle MPN[/tex] form angle [tex]\angle LPN[/tex], which is one of the three angles in [tex]\triangle LPN[/tex]. Since the sum of the interior angles of a triangle add up to 180 degrees, we have:
[tex](\angle MPN+\angle LPM)+\angl+ PLN+\angle LNP=180^{\circ},\\\angle MPN+44+46+68=180,\\\angle MPN=180-44-46-68,\\\angle MPN=\boxed{22^{\circ}}[/tex]
Find value of x.
A. 110
B. 47
C. 68
D. 112
Answer:
B
Step-by-step explanation:
The sum of the inner angles of a quadrilateral is 360 degrees
135 + 110 + 68 + x = 360
313 + x = 360
x = 47 degrees
Answer:
47
Step-by-step explanation:
whole thing is 360 degrees
68 + 110 + 135 = 313
360 - 313 = 47
x looks small too (if you had to guess in a multiple choice question)
Arturo is building a flower bed in the shape of a right triangle. The hypotenuse of the right triangle is 13 feet. One of the legs needs to be 7 feet longer than the other leg.
Which equation can be used to find x, the length of the shorter leg?
x(x + 7) = 13
x(x + 7) = 169
x2 + (x + 7)2 = 13
x2 + (x + 7)2 = 169
Answer:
x(x + 7) = 169
Step-by-step explanation:
We are given that
Let length of shorter leg of right triangle = x ft
Length of other leg = x+7 ft
Hypotenuse of right triangle = 13 ft
We have to find the equation which can be used to find x, the length of shorter leg.
By pythagorous theorem
(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2
Substitute the values then, we get
(13)^2=x^2+(x+7)^2
x^2+(x+7)^2=169
This is required equation which can used to find x.
Answer:
d. x2 + (x + 7)2 = 169
Step-by-step explanation:
use Pythagorean theorem, substitute in the given values, and you get this
pls help me don't know what to do
Answer:
x=15
Step-by-step explanation:
The 60 degree angle and the (x+45) degree angle are both the same degree because they are vertical angles.
So to solve, just subtract 45 from 60
60-45=15
That's your answer!
Hope this helps!
Greg buys 60 garden plants at a cost price of $2.00 each to sell in his shop. He sells 25 of them at the profit of 75% and 18 of them at the profit of 35%. He sells the rest of the plants for 4/5 of the cost price calculate the profit or loss he makes from selling 60 plants stating if it is a profit or loss
Answer:
$43.30 profitStep-by-step explanation:
Total cost of plant:
60*2 = 120Greg makes total of:
25*(2 + 0.75*2) + 18*(2 + 0.35*2) + (60 - 25 - 18)*2*4/5 = 163.3Since Greg mare than cost, he has a profit and the amount is:
163.3 - 120 = 43.3Choose the smallest number 3 1/8 or 10/3
Answer:
10/3
Step-by-step explanation:
31/8= 3.8
10/3= 3.3
2 1/4 x 3 1/5 brainliest
Answer:
36/5
Step-by-step explanation:
9/4×16/5
144/20
36/5
hope this is helpful
Answer:
[tex]7\frac{1}{5}[/tex]
Step-by-step explanation:
1. start by turning the fractions improper fractions:
[tex]2\frac{1}{4} =\frac{9}{4}[/tex]
[tex]3\frac{1}{5} =\frac{16}{5}[/tex]
2. then multiply them together:
[tex]\frac{9}{4}[/tex] x [tex]\frac{16}{5}[/tex] = [tex]\frac{144}{20}[/tex]
3. then simplify the fraction:
[tex]\frac{144}{20}[/tex][tex]=\frac{36}{5}[/tex]
4. turn it into a proper fraction:
[tex]\frac{36}{5} =7\frac{1}{5}[/tex]
A cinema is doing a promotion to celebrate their 50th anniversary for 1 week. They give
away a free drink to every 98th customer, a free bag of popcorn to every 112th customer and
a free cinema ticket to every 224th customer. Which lucky customer will be the first to
receive all 3 items?
Answer:
1,568 customer
Step-by-step explanation:
Find the lowest common multiple of 98, 112, and 224
98 = 98, 196, 294, 392, 490, 588, 686, 784, 882, 980, 1078, 1176, 1274, 1372, 1470, 1568, 1666
112 = 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120, 1232, 1344, 1456, 1568, 1680, 1792, 1904
224 = 224, 448, 672, 896, 1120, 1344, 1568, 1792, 2016, 2240
The lowest common multiple of 98, 112, and 224 is 1568
Therefore, the 1,568th customer will be the first to receive all 3 iitem
The center of the circle is at the point
, and its radius is
units. The equation of this circle in standard form is
.
D=22/7×d-90 Solve the equation
Find D
Fast!
Answer:
D=22-90+22d/7
Step-by-step explanation:
D=22/7×d-90
D=-90+22d/7
What is the quotient of (x^3 - 3x^2 + 3x - 2) ÷ (x^2 - x + 1)?
O x - 2
O x + 2
O x- 4
O x + 1
Answer:
x-2
The choose (1)
Step-by-step explanation:
(x³-3x²+3x-2)÷(x²-x+1)
(x-2)(x²-x+1) ÷ (x²-x+1)
Delete (x²-x+1)
so = (x-2)
On the unit circle, which of the following angles has the terminal point
coordinates.
A. 45
B. 135
C. 225
D. 315
Answer: C. 225
Step-by-step explanation:
jordan wants to save to buy a car and decides to open a banking account that is offering an interest rate of 4.5% compounded annually how much will jordan have in the account after 5 years it he deposits $7,000 today?
Answer:
8,723.27$
Step-by-step explanation:
Which operation will solve the following word problem? Jeff earns $14.00 per hour, Tom earns half as much as Jeff. How much does Tom earn per hour?
Multiplication
Subtraction
Addition
Division
Answer:
The correct option is (d).
Step-by-step explanation:
Given that,
Jeff earns $14.00 per hour.
Tom earns half as much as Jeff.
We need to find the amount earn by Tom per hour.
Tom's amount = Jeff's amount/2
So,
[tex]T=\dfrac{14}{2}\\\\T=\$7[/tex]
So, Tom earn $7 per hour. Hence, division operation is used. Jeff's amount is divided by 2.
According to the number line, what is the distance between points A and B?
0 6 units
7 units
O 12 units
O 14 units
Answer:
14 units
Step-by-step explanation:
A = - 2, B = 12
Therefore,
d(A, B) = 12 - (-2) = 12 + 2 = 14 units
What’s the equation of the line that passes through the point (-4,4) and has a slope of 3/4
Answer:
y-y1=m(x-x1)
y-4=3/4(x+4)
y=3/4x+7
lidentify the domain of the function shown in the graph
O A 15257
O B. 19334
O C. 221
O D. All real numbers
Answer:
B.
Step-by-step explanation:
the visible line is the defined function.
this line goes from x=1 to x=4, and has the functional results from y=1 to y=7.
the domain is the valid interval of the input variable (typically x), while the range is the valid inescapable of the result variable (typically y).
so, B is the right answer.
Can someone help me with this math homework please!
Answer:
1: the number of years since 2008 2. t is greater than or equal to 0 3. negative values 4. continuous
Step-by-step explanation:
1. t usually represents time
2. t must be greater than 0 as you can not go backward in time
3. the range must be positive as you can not have negative bobcats
4. its continuous because its a quadratic equation
1. no. of bobcats since 2008
2. greater than equal to 0
3 negative values
4. discrete because no. of bobcats cannot be broken into fraction.
find the domain of f(x)=sec(2x)
Answer:
*Refer the image attached
Step-by-step explanation:
*Refer the image attached
What is the scale of the y-axis in this coordinate graph?
A. 1 tick mark represents 1 unit
B. 1 tick mark represents 8 units
C. 1 tick mark represents 12 units
D. 1 tick mark represents 16 units
Answer:
Obviously B
Step-by-step explanation:
A statistics professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 24 years. This is an example of
Answer:
propbability ???
Step-bp explanation:
Answer:
Step-by-step explanation:
This is an example of a statistical mean.
PLS HELP SOON WILL MARK BRAINLYEST
A railroad tunnel is shaped like a semi-ellipse, as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.
According to the question
b= 35 and (8,21) lies on the ellipse
After calculation we get a= 10
equation for the ellipse.
[tex] \frac{ {x}^{2} }{100} + \frac{ {y}^{2} }{1225} = 1[/tex]
