Find the perimeter of quadrilateral ABCD with vertices A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).
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.
6h=2k+9. 3h+4k=12 use elimination please help me
Answer:
h = 2 and k = 1.5
Step-by-step explanation:
The solution is, Solve of the system of equations. using elimination,
6h=2k+9 & 3h+4k=12 is, h = 2 & k=3/2.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
given that, the system of equations.
6h-2k=9.......(1)
3h+4k=12 ...........(2)
now, for solving, multiply (1) by 2 & add with (2),
we get,
12h - 4k = 18
3h + 4k = 12
---------------------
15h = 30
i.e. h = 2
from (1), we get, k = 3/2
Hence, The solution is, Solve of the system of equations. using elimination,
6h=2k+9 & 3h+4k=12 is, h = 2 & k=3/2.
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Quadratic equation with root 1 is :-(A) 2x ^ 2 + x - 1 = 0 (B) 2x ^ 2 - x - 1 = 0 (C) 2x ^ 2 + x + 1 = 0 (D) 2x ^ 2 - x + 1 = 0
Answer:
option b is correct
tag me as brilliaiest
PLEASE HELP ME <3!!!
Answer:
Wasim has enough money.
Step-by-step explanation:
1. find the area of the garden path:
600 cm x 120 cm = 72,000 sq. cm
2. find the area of each stone:
it is a square of 30 cm by 30 cm, so:
30 cm x 30 cm = 900 sq. cm
3. find how many stones can fit in the path:
72,000 / 900 = 80 stones
4. multiply that by the price of each stone:
80 stones x $2.50 = $200
Wasim's budget is $220 and the stones will only cost $200, so it is within the budget
Isabell drove 819 miles in 13 hours. at the same rate how many miles would she drive in 7 hours
Answer:
441 miles
Step-by-step explanation:
Rate of the Car: 819/13 = 63mph
Miles Driven in 7 Hours: 63*7 = 441 miles
Answer:
441 miles
Step-by-step explanation:
* means multiply
819/13 = x/7
13 * x = 819 * 7
13x = 5733
x = 5733 ÷ 13
x = 441
Someone to help me with these math problems please !!!
Answer:
square tables
round tables
12
Step-by-step explanation:
is this really that difficult ?
just think logically.
a square table sits 8 people. that means every square table "stands" for 8 people present.
a round table sits 6 people. so, every round table "stands" for 6 people present.
now, the whole party has 150 people.
that means the sum of all people on all tables is 150.
so, if we count all square tables, we know how many people are sitting at square tables, as each table "stands" for 8 people (we multiply the number of square tables by 8).
similar for the round tables.
so, we say we have x square tables and y round tables.
therefore the equation is
150 = 8×x + 6×y
the variable with the factor 8 must be describing the square tables (due to the reasons above).
that is x.
and the variable with the factor 6 must describe the round tables.
that is y.
now we are told that there are 9 round tables (y=9).
using the equation from above
150 = 8×x + 6×9 = 8×x + 54
96 = 8×x
x = 12
so, we must have 12 square tables to satisfy the condition that we have in total 150 people present.
Hello please help ASAP!
find the area of the triangle
Answer:
Formula for area of a triangle= L*H/2
Step-by-step explanation:
Let's say your triangle has an A length of 15 and your B height is 12. You then multiply your length and height to get 180. Then you divide your answer by 2 and get 90.
Hope this helps!! :)
A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without
looking, how many ways can you get 5 apples?
Answer:
6 I think
Step-by-step explanation:
Charity and her family are going on vacation to visit family over the summer. Their flight will last 6.94 hours. Charity says, "If we round this number, it is a seven-hour flight." Her sister says, "I think you're wrong. If we round it, it is 6.9-hour flight." Who is correct? Explain your reasoning.
Answer:
Charity is more correct
Step-by-step explanation:
Flight time = 6.94 hours
Charity estimation = 7 hours
Her sister's estimation = 6.9 hours
Charity is more correct if we are to round to the nearest whole hour
6.94 hours is approximately 7 hours
Her sister is only correct if we are to round up to 1 decimal place
6.94 hours is approximately 6.9 hours to 1 decimal place
Which expression can be used to find the difference of the polynomials?
(10m – 6) – (7m – 4)
Answer:
3m -2
Step-by-step explanation:
(10m – 6) – (7m – 4)
Distribute the minus sign
(10m – 6) – 7m + 4
Combine like terms
3m -2
Find the coordinates of the other endpoint when given midpoint (point M) and one of the endpoints (point P). P=(3,5) and M=(-2,0)
Answer:
About Points
S = (x,y) searched point (it will be in the third quadrant )
M = (-2,0) Midpoint | SP |
P = (3,5) one end of the segment | SP |
You have to draw Cartesian.
we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .
We use the information that | SM | = | MP |
Answer : S = (-7,-5)
Step-by-step explanation:
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad \underline{Q}(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+3}{2}~~,~~\cfrac{y+3}{2} \right)=\stackrel{M}{(-2,0)}\implies \begin{cases} \cfrac{x+3}{2}=-2\\[1em] x+3=-4\\ \boxed{x = -7}\\[-0.5em] \hrulefill\\ \cfrac{y+3}{2}=0\\[1em] y+3=0\\ \boxed{y=-3} \end{cases}[/tex]
PLEASE HELP TIMED. Verify which of the following are identities.
SOMEONE HELP ME QUICK!!!
Answer:
75% probability
Step-by-step explanation:
calculating the total ratio and percentage
Question 3 of 5
Select the correct answer.
Which of these tables represents a function?
Х
х
у
Х
у
Х
у
১| u
0
2
2.
-3
1
1
3
-3
9
0
3
2.
1
1
0
3
0
2
3
0
1
1
-3
2.
-3
1
3
1
1
2
-3
w.
X.
Y.
z.
w
Х
Answer:
only Y
Step-by-step explanation:
all the others have for at least 1 value of x more than one different y values defined.
but a function must be clear about the association between an x unit value and the corresponding result.
many different input values can have the same functional result. but there can be only one defined result per input value. otherwise it is not a function.
you cannot say 1+1 = 2 or 3. it is either 2 or 3, but you need to define what. you can't leave it open.
The function is given by the table Y
x = { -3 , 2 , 0 , 3 } and y = { 1 , 1 , 1 , 1 }
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
Let the x values of the function be represented as
x = { -3 , 2 , 0 , 3 }
Now , the y values of the function is
y = { 1 , 1 , 1 , 1 }
From the table , we can see that for every different values of x there are range of values of y
No two same values of ranges have the same domain
Therefore , it is a function
Hence , the function is table Y
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3. Find the volume of the figure. Simplify.
Cube
x + 4
Answer:
[see below]
Step-by-step explanation:
V = s^3
V = (x+4)^3
V = x^3 + 3x^2 * 4 + 3x * 4^2 + 4^3
V = x^3 + 12x^2 + 48x + 64
Hope this helps.
A triangle has vertices on a coordinate grid at D(6,-1)D(6,−1), E(-4,-1)E(−4,−1), and F(-4,-6).F(−4,−6). What is the length, in units, of DE ?
Answer:
2units
Step-by-step explanation:
Given the coordinates D(6,−1), E(-4,-1), using the distance formula
DE = √(x2-x1)²+(y2-y1)²
DE = √(-1-(-1))²+(4-6)²
DE = √(-1+1)²+(-2)²
DE = √0+4
DE = √4
DE = 2units
Hence the length od DE in units is 2units
39. Boat ride
A boat travels 50 miles
due west before adjusting
its course 25 degrees north of west and traveling an
additional 35 miles. How far is the boat from its point of departure?
How far as the boat from
its point of departure?
Answer:
64.0655322 miles is maybe the answer
A fish tank in a pet store has 23 fish in it. 10 are orange and 13 are white. Determine the probability that if we select 4 fish from the tank, at least 2 will be white.
Answer:
ok so the probility of gettting one white fish is
13/23
and if we take out one white fish the problity is
12/22
so we just multiply
12/22*13/23=0.30830039525
so the problity is 0.30 if you choose two fish you will get white for both
I WILL GIVE BRAINLIEST I NEED HELP NOW!!! I PROMISEThe table shows the relationship “Kevin read 35 pages per hour.”
Hours (h)
Pages (p)
1
35
2
70
3
105
4
140
5
175
Which statements are correct? Check all that apply.
The variable h is the independent variable.
The variable p is the independent variable.
The number of pages read increases as the amount of time decreases.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
The variable h is the dependent variable.
The more pages that are read, the less time it takes.
Answer:
The correct answers are:
The variable p is the independent variable.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
Step-by-step explanation: Hope this helps :)))
These two statements are correct and applicable
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
What is a variable?"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."
What is a dependent variable?"A dependent variable is the variable that changes as a result of the independent variable manipulation."
What is a linear graph?"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"
We have,
Kelvin read 35 pages per hour
According to the question,
Number of hours increasing, number of pages also increasing
∵ The table data shows linear graph
We can clearly say that from a line graph definition,
These two are correct and applicable to Kelvin's situation
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
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There is the photo and the question
please show the working.
The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2000 there were about
1,150 fish. Write an exponential decay function to model this situation. Then find the population in
2006.
Answer:
Number of fish in 2006 = 845 fishes (Approx.)
Step-by-step explanation:
Given;
Number of fish in 2000 = 1,150 fishes
Decreasing rate = 5% per year
Find:
Number of fish in 2006
Computation:
Exponential decay function:
F = P[1-r]ⁿ
Number of year = 2006 - 2000
Number of year = 6 year
Number of fish in 2006 = 1,150[1-5%]⁶
Number of fish in 2006 = 1,150[1-0.05]⁶
Number of fish in 2006 = 1,150[0.95]⁶
Number of fish in 2006 = 1,150[0.735]
Number of fish in 2006 = 845.25
Number of fish in 2006 = 845 fishes (Approx.)
B) T is due north of C, calculate the bearing of B from C
Answer:
(a) 52°
(b) 322°
Step-by-step explanation:
(a) The details of the circle are;
The diameter of the circle = AOC
The center of the circle = Point O
The point the line AT cuts the circle = Point B
The point the tangent PT touches the circle = Point C
Angle ∠COB = 76°
We have that angle AOB and angle COB are supplementary angles, therefore;
∠AOB + ∠COB = 180°
∠AOB = 180° - ∠COB
∴ ∠AOB = 180° - 76° = 104°
∠AOB = 104°
OA = OB = The radius of the circle
Therefore, ΔAOB = An isosceles triangle
∠OAB = ∠OBA by base angles of an isosceles triangle are equal
∠AOB + ∠OAB + ∠OBA = 180° by angle summation property
∴ ∠AOB + ∠OAB + ∠OBA = ∠AOB + ∠OAB + ∠OAB = ∠AOB + 2×∠OAB = 180°
∠OAB = (180° - ∠AOB)/2
∴ ∠OAB = (180° - 104°)/2 = 38°
∠TAC = ∠OAB = 38° by reflexive property
AOC is perpendicular to tangent PT at point C, by tangent to a circle property, therefore;
∠TCA = 90° and ΔTCA = A right triangle
∠TAC + ∠ATC + ∠TCA = 180° by angle sum property
∠ATC = 180° - (∠TAC + ∠TCA)
∴ ∠ATC = 180° - (38° + 90°) = 52°
Angle ATC = 52°
(b) In ΔABC, ∠ABC = Angle subtended by the diameter = 90°
∴ ΔABC = A right triangle
∠ABC and ∠TBC are supplementary angles, therefore;
∠ABC + ∠TBC = 180°
∠TBC = 180° - ∠ABC
∴ ∠TBC = 180° - 90° = 90°
∠TCB = 180° - (∠TBC + ∠ATC)
∴ ∠TCB = 180° - (90° + 52°) = 38°
The bearing of B from C = (360° - 38°) = 322°.
An arithmetic sequence follows a specific pattern where a number is _____________ to get from one term to the next.
Answer:
Added
Step-by-step explanation:
For example, take the arithmetic sequence of 3, 5, 7, 9...
Here, the number that gets us from the first number to the second (from 3 to 5), is 2. Meaning, we need to add 2 to 3 in order to get 5. I believe that makes "addition" or "added" the answer. Please let me know if I misunderstood and I will change my answer! Thank you!
Answer:
added or subtracted
Step-by-step explanation:
A student can walk to school in 3/4 of an hour. She can ride to school in 1/6 of that time. What fraction of an hour does it take the student to bike to school?
Answer:
1/8 of an hour
Step-by-step explanation:
3/4 x 1/6 = 3/24 = 1/8
Hope this helps!
Is the following shape a rectangle? How do you know?
Answer: The Answer is A
Step-by-step explanation:
How do I find the area for this shape
Answer:
you do length times width then add them
Given y = f(u) and u=g(x), find =f(g(x))g'(x) for the following functions.
dx
y = cos u, u = 4x - 3
dy
dx = f'(g(x))g'(x) = 0
Answer:
-4sin(4x-3)
Step-by-step explanation:
Given y = cos u, u = 4x - 3
dy/dx = dy/du * du/dx
dy/du = -sinu
du/dx = 4
dy/dx = -4sinu
since u = 4x - 3
dy/dx = -4sin(4x-3)
help pls!!
2xy + 3xt - 7yt = 0
In the equation above, x and y are positive and
x< y. What is t in terms of x and y?
A) t= 1/2
B) t= 2xy / 3x - 7y
C) t= 2xy / 7y - 3x
D) t= xy / 2(y-x)
Answer:
B
Step-by-step explanation:
[tex]2xy + 3xt - 7yt = 0[/tex]
[tex]3xt - 7yt = - 2xy[/tex]
Factor out t
[tex]t(3x - 7y) = - 2xy[/tex]
Divide by 3x-7y
[tex]t = - \frac{2xy}{3x - 7y} [/tex]
But since x and y are positive, the answer is positive
[tex]t = \frac{2xy}{3x - 7y} [/tex]
find m to cos²x-(m²-3)sinx+2m²-3=0 have root
Answer:
[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex] would ensure that at least one real root exists for this equation when solving for [tex]x[/tex].
Step-by-step explanation:
Apply the Pythagorean identity [tex]1 - \sin^{2}(x) = \cos^{2}(x)[/tex] to replace the cosine this equation with sine:
[tex](1 - \sin^{2}(x)) - (m^2 - 3)\, \sin(x) + 2\, m^2 - 3 = 0[/tex].
Multiply both sides by [tex](-1)[/tex] to obtain:
[tex]-1 + \sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 3 = 0[/tex].
[tex]\sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 2 = 0[/tex].
If [tex]y = \sin(x)[/tex], then this equation would become a quadratic equation about [tex]y[/tex]:
[tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex].
[tex]a = 1[/tex].[tex]b = m^{2} - 3[/tex].[tex]c = -2\, m^{2} + 2[/tex].However, [tex]-1 \le \sin(x) \le 1[/tex] for all real [tex]x[/tex].
Hence, the value of [tex]y[/tex] must be between [tex](-1)[/tex] and [tex]1[/tex] (inclusive) for the original equation to have a real root when solving for [tex]x[/tex].
Determinant of this quadratic equation about [tex]y[/tex]:
[tex]\begin{aligned} & b^{2} - 4\, a\, c \\ =\; & (m^{2} - 3)^{2} - 4 \cdot (-2\, m^{2} + 2) \\ =\; & m^{4} - 6\, m^{2} + 9 - (-8\, m^{2} + 8) \\ =\; & m^{4} - 6\, m^{2} + 9 + 8\, m^{2} - 8 \\ =\; & m^{4} + 2\, m^{2} + 1 \\ =\; &(m^2 + 1)^{2} \end{aligned}[/tex].
Hence, when solving for [tex]y[/tex], the roots of [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] in terms of [tex]m[/tex] would be:
[tex]\begin{aligned}y_1 &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) + \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) + (m^{2} + 1)}{2} = 2\end{aligned}[/tex].
[tex]\begin{aligned}y_2 &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) - \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) - (m^{2} + 1)}{2} \\ &= \frac{-2\, m^{2} + 2}{2} = -m^{2} + 1\end{aligned}[/tex].
Since [tex]y = \sin(x)[/tex], it is necessary that [tex]-1 \le y \le 1[/tex] for the original solution to have a real root when solved for [tex]x[/tex].
The first solution, [tex]y_1[/tex], does not meet the requirements. On the other hand, simplifying [tex]-1 \le y_2 \le 1[/tex], [tex]-1 \le -m^{2} + 1 \le 1[/tex] gives:
[tex]-2 \le -m^{2} \le 0[/tex].
[tex]0 \le m^{2} \le 2[/tex].
[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
In other words, solving [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] for [tex]y[/tex] would give a real root between [tex]-1 \le y \le 1[/tex] if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].
On the other hand, given that [tex]y = \sin(x)[/tex] for the [tex]x[/tex] in the original equation, solving that equation for [tex]x\![/tex] would give a real root if and only if [tex]-1 \le y \le 1[/tex].
Therefore, the original equation with [tex]x[/tex] as the unknown has a real root if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].