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.
help me solve the simultaneous linear inequalities
Answer:
The inequality form is -4<x<-2
The Interval Notation is (-4, -2]
I hope this helps!
CAN SOMEONE PLEASE HELP ME!!
Answer:
29.8
Step-by-step explanation:
a^2+b^2=c^2
a^2+7^2=11^2
a = h = 8.5
A= 1/2*b*h
A= 1/2*8.5*7
A=29.8
The probability distribution for a
random variable x is given in the table.
-5
-3
-2
0
2
3
Probability
.17
.113
.133
.16
.11
.10
Find the probability that -2
Note: The values in the table are not correct because the sum of the probability of all events is not equal to one. The should be 0.13 and 0.33 instead of 0.113 and 0.133 respectively.
Given:
The probability distribution for a random variable x is given in the table.
x : -5 -3 -2 0 2 3
P(x) : 0.17 0.13 0.33 0.16 0.11 0.10
To find:
The probability of -2.
Solution:
From the given probability distribution for a random variable x, it is clear that the value of the probability is 0.33 corresponding to -2.
[tex]P(-2)=0.33[/tex]
Therefore, the probability of -2 is 0.33.
What is the equation of the following line?
(-4, 8)
(0,0)
Answer
Step-by-step explanation:
y = -2x + 0
Therefore; y = -2x
Can someone help me with this math homework please!
Answer:
See step by Step
Step-by-step explanation:
Both are correct. As long as we undo the operations that was given from the original term to both sides until we get the variable by itself., any way can be applied.
Both, Spencer and Jeremiah are correct. We can verify this by testing their methods.
Spencer's method:
[tex]6x - 2 = - 4x + 2[/tex]
[tex]6x - 2 + 4x= - 4x + 2 + 4x[/tex]
[tex]10x - 2 = 2[/tex]
[tex]10x = 2 + 2[/tex]
[tex]10x = 4[/tex]
[tex]x = \frac{4}{10} [/tex]
[tex]x = 0.4[/tex]
Jeremiah's method:
[tex]6x - 2 = - 4x + 2[/tex]
[tex]6x - 2 - 6x = - 4x + 2 - 6x[/tex]
[tex] - 2 = - 10x + 2[/tex]
[tex] - 2 - 2 = - 10x[/tex]
[tex] - 4 = - 10x[/tex]
[tex] \frac{ - 4}{ - 10} = x[/tex]
[tex]0.4 = x[/tex]
As seen, we get the correct answer by using Spencer's and Jeremiah's method. So, we can say that they both are correct.
Find the missing side. Round to the nearest tenth.
A) 38.4
C) 33.9
B) 5.0
D) 27.6
Answer:
C)33.9. I hope it's help
3(y+6)=30 solve equation
Answer:
3(y+6)=30
3y + 18 = 30
18 - 30 = 3y
12 = 3y
12/3 = y
4 = y
or
y = 4
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answer:
Inside
Step-by-step explanation:
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of poiñt from centre is less than the radius.
Hence the point lies within the circle
Find the measure of each numbered angle for each figure
Answer:
Angle 1 is 58. Angle 2 is 32.
Step-by-step explanation:
The measure of Angle ACB is 90 because C is on the circle and A and B connect to form a diameter of the circle. So, Angle 1 and Angle 2 add up to 90 (total degrees in triangle - 90). Now you can add the expressions the question gave for Angle 1 and Angle 2, and you get 7x + 6. So you have the equation 7x + 6 = 90. Solve the equation and you get x = 12. Now you can plug in that value for x into the expressions for Angles 1 and 2 to find their measures.
You invest $4.000 in a savings account. The account pays 3% annual interest. How much money will be in the savings account after 9 years?
A) $4,938.29
B) $5,219.20
C) $5,124.33
D) $6,003.45
Answer:
4000*0.03*9=1080
4000+1080=5080
umm but like thats not one of the answers sorry
Hope This Helps!!!
Step-by-step explanation:
4000*3% = 120
120*9= 1080
1080+4000=5080
What is the mode of the set of numbers {55, 57, 59, 61, 62, 63, 64, 64, 65, 68, 69)
Answer:
64
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. So, just look for the number that appears the most.
I hope this helps!
The difference between two numbers is 12 and their sum is 26. Find the smallest number. A)9 B)7 C)-7 D)-9
Answer:
Step-by-step explanation:
We need a system of equations to solve for this. The first equation comes from "The difference between 2 numbers is 12". Difference means subtraction, the 2 numbers will be x and y, and the word "is" means equals:
x - y = 12
The second equation comes from "...their sum is 26". The numbers are still x and y but this time we have their sum, which is what they equal when they are added together. The word "is" means equals:
x + y = 26. So we will go back up to the first equation. If y taken away from x leaves a positive number, that means that y is smaller than x. We are looking for the value of the smaller number so we will find y. Solve the first equation for x to get it in terms of y:
x = 12 + y and we sub that into the second equation:
(12 + y) + y = 26 and
12 + 2y = 26 and
2y = 14 so
y = 7. Choice B is the one you want.
Find the domain of the following piecewise function.
Answer:
[tex](2,8][/tex]
Step-by-step explanation:
Given
The attached piece wise function
Required
The domain
To do this, we simply consider the inequalities that bound the values of x.
The inequalities are:
[tex]2 < x < 4[/tex] [tex]4 < x < 8[/tex] and [tex]x \ge 8[/tex]
Combine the first two inequalities:
[tex]2 < x < 8[/tex] and [tex]x \ge 8[/tex]
For the inequality to be true, we must have:
[tex]2 < x \le 8[/tex]
In interval notation, the inequality is:
[tex](2,8][/tex]
Evaluate x^-2 for x = -3 plsss i really need help on this thank you
Answer: -1/9
Step-by-step explanation:
Answer:
- 1/9 OR -0.111....
Step-by-step explanation:
Make x= -3
-3^-2= -1/9
solve it please please
Answer:
D. 5 and 14
Explanation:
5,8,11,14
How many solutions does the nonlinear system of equations graphed below
have?
• A. One
• B. Two
• C. Four
O D. Zero
SUBMIT
Evaluate: 4x3 - 7x2 for x = 3
Answer:
45
Step-by-step explanation:
4[tex]x^{3}[/tex] - 7[tex]x^{2}[/tex] for x = 3
Substitute 3 in for x
4([tex]3^{3}[/tex]) - 7([tex]3^{2}[/tex])
4(3·3·3) - 7(3·3)
4(27) - 7(9)
108 - 63
45
Answer:
45
Step-by-step explanation:
Hi there!
We are given 4x³-7x² and we need to evaluate the expression if x=3.
To do this, substitute 3 as x into the expression, and then use the order of operations to solve
so substitute 3 as x into the expression (remember: x² is x*x, or (x)²)
4(3)³-7(3)²
now using the order of operations, start by evaluating the exponents
(3)³=3*3*3=9*3=27
(3)²=3*3=9
the expression then becomes:
4*27-7*9
multiply
108-63
subtract
45
Hope this helps! :)
Someone please help me ASAP please
Answer:
hey mate
plz mark it as brainliest
Pls help, I will give 50 points
Someone to give me the answer on the number line please
Answer:
Step-by-step explanation:
Equation for the total volume of the bucket has been given as,
V = 4 + 2t
Here V = Total volume
t = elapsed time
Table for the input-output values,
t 0 1 2 3 4
V 4 6 8 10 12
Therefore, line passing through the given points in the table will be the graph for the equation.
Select the two values of x that are roots of this equation.
x² + 3x-6=0
A. X=
-3+ /33
2
B. x=-3-83
c. x. -3-15
D. x. -3*4/15
please help
Answer:
[tex]x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 + - \sqrt{9 + 24} }{2} \\ x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]
What is the domain of the square root function graphed below
Answer:
Dominio de una Raíz cuadrada
Cuando tenemos una raíz, para estudiar su existencia debemos saber que una raíz existe si y solo sí el radicando (lo que está dentro de la raíz) sea mayor o igual a cero.
Por lo tanto deberemos estudiar el signo de lo que se encuentra dentro de la raíz; y determinar las zonas positivas y las raíces que son las zona de existencia de la función raíz o dominio de esta función.
Step-by-step explanation:
qsy
What is the interval of increase f(x)=3x^2-6x
Answer:
F(g(×)1=3(6+2)-5=18×+6-5=18×+1
Step-by-step explanation:
so correct answer is the last one pa brainliest plss
FG has a midpoint at M(5, 7). Point G is at (9,5). Find the coordinates of point F. Write the coordinates as decimals or integers.
The distance traveled (in meters) by a frog is modeled by the equation d=2t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 25 minutes.
Given,
d = 2t
here, t = 25
Therefore,
d = 2*25
= 50m
I need help with this, Im never good with these
Answer:
(a) basketball
(b) hat
(c) stuffed animal
explanation:
I'm not sure if got right but from what i see;
Chances from 1-23 you get a stuffed boi
Chances from 24-54 you get a hat (why)
Chances from 55-100 you get a basketball
Winner 5 got 90, which is between 55-100
Winner 6 got 35, which is between 24-54
winner 8 got a 7, which is between 1-23
Hope I didn't read it wrong
. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. population mean math score parents college grads. population mean math score parents high school grads. _____ _____ b. What is the point estimate of the difference between the means for the two populations
Answer:
Following are the responses to the given question:
Step-by-step explanation:
For point a:
Following are the null and alternative hypotheses:
[tex]H_0 : \mu_1 \leq \mu_2\\\\H_1 : \mu_1 > \mu_2[/tex]
For point b:
By using the Excel we obtained the output of the 2 sample t-test that is defined in the attached file.
These point estimately are the difference among the mean for the two populations:
[tex]\to \mu_{\bar{x_1}-\bar{x_2}} = \mu_{\bar{x_1}}-\mu{\bar{x_2}} ={\bar{x_1}-\bar{x_2}}=573-491=82[/tex]
y = 2x + 3
y=2x-1
The system has how many solutions?
one solution
two solutions
no solution
an infinite number of solutions
Is the product of two prime numbers a prime number or a composite
number?
Step-by-step explanation:
No, the product of two (or more) prime numbers cannot result in another prime number. By definition, a prime number is a number that is divisible by 1 or itself - the act of multiplying two or more primes together will always yield a number divisible by 1, itself and the prime numbers multiplied together to achieve it.
Answer:
a composite one
Step-by-step explanation:
Why?
It is easy-peasy.
First, it is impossible to have a prime number. Because primes are only divisible by 1 and themselves.
For example, 3 is a prime. 7 is a prime. Multiply them and get 21.
I hope it helped:)
A man is twice as old as his son. Five years ago, the ratio of their ages was 9:4. Find the son's present age
Answer:
Son's age is 25.
Step-by-step explanation:
Let the Father's age be 2x.
Let the son's age be x.
Five years ago:
Man's age will be = 2x - 5
Son's age will be = x - 5
If the ratio of their ages five years ago was 9:4, then:
2x - 5/x-5 = 9/4
⇒ 4(2x - 5) = 9(x - 5)
⇒ 8x - 20 = 9x - 45
⇒ -20 + 45 = 9x - 8x
⇒ 25 = x
∴ x = 25
Hence, the son's age = 25 years
If x = 25, the father's age (2x) will be 2 × 25 = 50 years
