i need help simplifying this problem
Find the solution of the system of equations.
– 2 – 8y = -30
2x + 8y = 36
Answer:
x= 1.5
y= 4.125
Step-by-step explanation:
Step one:
given the two equations
[tex]-2x - 8y = -30-------1\\\\2x + 8y = 36--------2[/tex]
Step two:
let us subtract the equations
[tex]-2x - 8y = -30-------1\\\\ -(2x + 8y = 36)--------2\\\\0x-16y=-66[/tex]
[tex]-16y=-66\\\\16y=66[/tex]
divide both sides by 16
[tex]y=66/16\\\\y=4.125[/tex]
put y= 4.125 in equation 2
[tex]2x + 8(4.125)= 36\\\\2x+33=36\\\\2x=36-33\\\\2x=3\\\\x= 3/2\\\\x= 1.5[/tex]
2(i + 3) > 4(1 - i)
[tex]2(i+3)>4(1-i)[/tex]
Distribute 2 in (i+3) and 4 in (1-i)
[tex]2i+6>4-4i[/tex]
Move -4i to another side and 6 to another side. When moving to another side, you'll have to change the sign/operator to opposite (Plus -> Minus, Multiply -> Divide)
[tex]2i+4i>4-6\\6i>-2\\[/tex]
For this part, move 6 to divide -2.
[tex]i>\frac{-2}{6} \\i>\frac{-1}{3}\\i>-\frac{1}{3}[/tex]
Whenever either a numerator or a denominator is in negative, we can pull out the negative in the middle of fraction.
Note that i is the symbol of imaginary number - as defined - i = √-1 But for this one, It's just a variable if I assume.
Thus, the answer is i > -1/3
the two shorter sides in a right triangle have the same length . the area of the right triangle is 7.36 square meters. what is the length of the hypotenuse
The length of the hypotenuse is 5.426 meter
Let the two shorter sides of the right angles triangle be denoted as x meters.
The formula for the area of right triangle is given as,
A = ab/2
Where, a and b are the length of the shorter sides of the triangle
Also we have been given the area of the triangle which is 7.36 sq. meter
Thus , A = 7.36
x^2/2 = 7.36
x^2 = 14.72
x = 3.84
Now according to the Pythagoras theorem,
H = √P^2 + B^2
Where, H = hypotenuse
P = perpendicular
B = base
Now putting the required values we get
H = √x^2 + x^2
= √2x^2
= x√2
= 5.426 meter
Hence the length of the hypotenuse is 5.426 meter
Learn more about area here : https://brainly.com/question/17335144
#SPJ4
A bag contains 4 red marbles and 6 blue marbles. Brandon selects one marble from the bag. Without replacing the marble he then
selects a second marble. What is the probability he selects a red marble given that he first selects a blue marble?
A)1/5
B)2/5
C3/5
D)4/15
HELP ASAP ILL GIVE BRAINLIEST
help fast 15 points Which value of n makes this equation true? 57 – 1 9 5. A. n = -16 n = -2 n = 16
Answer:A) -16
Step-by-step explanation:
4 - 1 1/4
A. 3 1/4
B. 3 3/4
C. 2 3/4
D. 2 1/4
HELPPPPP
Which of the following are roots of the polynomial function below?
Check all that apply.
F(x) = x^3 -3x²+2
The roots of the polynomial function f(x) = x³ - 3x² + 2 are [tex]\frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, \ and \ 1[/tex].
What are the roots of the polynomial function?Given the polynomial function in the question:
f(x) = x³ - 3x² + 2
To find the roots of the polynomial function f(x) = x³ - 3x² + 2, we need to solve for values of x that make the function equal to zero.
f(x) = x³ - 3x² + 2
x³ - 3x² + 2 = 0
Factor the equation using the rational root test:
( x - 1 )( x² - 2x - 2 ) = 0
Equate each factor zero and solve for x:
( x - 1 ) = 0
x - 1 = 0
x = 1
( x² - 2x - 2 ) = 0
x² - 2x - 2 = 0
Using the quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a} \\\\x = \frac{-(-2)\±\sqrt{(-2)^2 - 4(1*-2)} }{2*1} \\\\x = \frac{2\±\sqrt{4 + 8} }{2} \\\\x = \frac{2\±\sqrt{12} }{2}\\\\Hence:\\\\x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}[/tex]
Therefore, the roots are [tex]x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, 1[/tex].
Options A, B and D are the correct answers.
Learn more about quadratic equations here: brainly.com/question/1863222
#SPJ1
Find the volume of the shape
Answer:
The volume of cylinder is 58.2 cm³.
Step-by-step explanation:
The formula of volume of cylinder is :
[tex]v = \pi \times {r}^{2} \times h[/tex]
So, you have to substitute the values into the expressions :
[tex]let \: r = 2.1,h = 4.2[/tex]
[tex]v = \pi \times {2.1}^{2} \times 4.2[/tex]
[tex]v = 58.2 \: {cm}^{3} \: (3sf)[/tex]
If EF = x + 3, FG = 3x, and EG = 7, what is FG?
Answer:
FG = 3
Step-by-step explanation:
let me know if you are still confused!
r = -5 + 19. r = ?
Please help me with this
Answer:
r = 14
Step-by-step explanation:
r = -5 + 19
Simplify the right side by subtracting 5 from 19
r = 14
A special 8-sided die is marked with the numbers 1 to 8. It is rolled 15 times with the results shown in the table. Results 3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 The experimental probability of rolling an odd number is %, which is % more than the theoretical probability.
Let us consider,
A special [tex]8-[/tex]sided die is marked with the numbers [tex]1[/tex] to [tex]8[/tex].
The odd numbers on the die are [tex]1,3,5,7.[/tex]
The even numbers are [tex]2,4,6.[/tex]
For the experimental sequence of [tex]15[/tex] rolls.
There are [tex]9[/tex] odd number out of 15, which is [tex](3,5,7,1)[/tex].
So the experimental probability is,
[tex]\frac{9}{15} =\frac{3}{5} \\\\=0.60\\[/tex]
[tex]\implies0.60=60[/tex] %
The theoretical probability given that there are odd numbers [tex](1,3,5,7)[/tex] out of [tex]8[/tex] on the dice should be [tex]50[/tex] % because [tex]\frac{1}{2}[/tex] of the numbers are prime.
Thus,
The theoretical probability is [tex]50[/tex] % .
Then,
[tex]60[/tex]%[tex]-50[/tex]%[tex]=10[/tex]%
Hence, the experimental probability of rolling an odd number is [tex]60[/tex]%, which is [tex]10[/tex] % more than the theoretical probability [tex]50[/tex]%.
For more information,
https://brainly.com/question/537526
Answer:
60%, 10%
Step-by-step explanation:
Plato/Edmentum
Find the slope of the line.
copy and paste the link in the download in a new tab
Answer:
lol ok
Step-by-step explanation:
Answer:
ok Y?
Step-by-step explanation:
20-34+ 8/2 =? PLS HELP ME I GIVE ALL MY POINTS.
Answer:
-10
Step-by-step explanation:
20-34=-14, 8/2 is just 4, so add 4 to -14 which = -10
please help me............
Answer:
38.24
Step-by-step explanation:
You need to do 45.3-7.06 and you get x
Fabulous fitness charges a one time fee of $90 and an additional $25 per month wonder weights charges a one time fee of only $ 27 dollars but charges an additional $32 each month for how many months is fabulous fitness less expensive than wonder weights? Set up and solve an equality to determine your answer
Answer:
9 months
Step-by-step explanation:
Given
Fabulous fitness charges a one-time fee of $90 and an additional $25 per month
let the number of months be x
and the total charges be y
y= 25x+90---------1
Wonder weights charges a one-time fee of only $ 27 dollars but charge an additional $32 each month
let the number of months be x
and the total charges be y
y= 32x+27------------2
Required
The value of x, that is the number of months
Step two:
Equating both equations we have
25x+90=32x+27
collect like terms
25x-32x=27-90
-7x=-63
7x=63
divide both sides by 7
x= 63/7
x= 9 months
What is the value of the absolute value expression |−152| + |5| − |−24|?
179
133
−125
−173
The value of absolute value expression is equal to 133. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The absolute value or modulus of a real number x abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.
The absolute value of the function will be calculated as,
E = |−152| + |5| − |−24|
E = 152 + 5 - 24
E = 133
To know more about expression follow
https://brainly.com/question/28505282
#SPJ1
4) What is the equation of the line that passes through the points (3,0) and 2 points
(5,4)?
Your answer
If there are 180 grams of radioactive material with a half-life (decrease by half or 50%) of 1 hour, how much of the radioactive material will be left after 3 hours?
Answer:
After 3 hours there is left 22.5 grams of radioactive material.
Step-by-step explanation:
We can calculate the mass of radioactive material remaining after 3 hours, by using the decay equation:
[tex]N_{t} = N_{0}*e^{-\lambda t}[/tex] (1)
Where:
[tex]N_{0}[/tex]: is the initial mass = 180 g
[tex]N_{t}[/tex]: is the remaining mass after time t
λ: is the decay constant
The decay constant is given by:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]
Where [tex]t_{1/2}[/tex] = 1 h.
By entering λ into equation (1) we hve:
[tex] N_{t} = N_{0}*e^{-\frac{ln(2)}{t_{1/2}} t} [/tex]
[tex] N_{t} = 180 g*e^{-\frac{ln(2)}{1 h} 3 h} = 22.5 g [/tex]
Therefore, after 3 hours there is left 22.5 grams of radioactive material.
I hope it helps you!
What is the equation is y=Mx+b form?
Answer: y=5x+ 10
Step-by-step explanation:
40-30/6-4=10/2=5
each time x moves 1 it moves 5 vertically so
4, 30
3, 25
2, 20
1, 15
0, 10
Raymond can paint 5/8 of a wall in 16 minutes. How long would it take to for him to paint 1/3 of a wall
Answer: 128/15 min or 8.5 min
i
am
right
so
trust
me
i
swear
on
my
mama
this
is
correct
my
g
Which statement is true about the two lines whose equations are given below?
A. The lines are parallel.
B. The lines are perpendicular.
C. The lines intersect but are not perpendicular.
D. The lines coincide.
Answer: C. The lines intersect but are not perpendicular.
Step-by-step explanation:
The correct option is C, the lines intersect but are not perpendicular.
How to determine the equation of the line?To determine which statement is true about the two lines whose equations are given below:
y = 3x + 2
y = -4x + 9
We can compare the slopes of the two lines. The slopes of these lines are 3 and -4 respectively.
Two lines are parallel if and only if their slopes are equal. Since the slopes of these lines are not equal, we can eliminate options A.
Two lines are perpendicular if and only if the product of their slopes is -1. The product of the slopes of these lines is -12, which is not equal to -1. Hence, we can eliminate options B.
Since the lines are neither parallel nor perpendicular, they intersect. To determine whether they intersect perpendicularly, we can compute the angle between them using the slopes.
The angle between two lines is given by the formula:
[tex]tan \theta = \dfrac{(m_2 - m_1)}{ (1 + m_1m+_2)}[/tex]
where m₁ and m₂ are the slopes of the two lines.
Substituting the slopes of the given lines, we get:
[tex]tan \theta = \dfrac{|(-4 - 3)} { (1 + (3 \times -4))|} \\[/tex]
tanθ = 7 / 11
Therefore, the correct option is C: the lines intersect but are not perpendicular.
To know more about the equation of line follow
https://brainly.com/question/19015497
#SPJ3
The missing equation of lines are:
y = 3x + 2
y = -4x + 9
the multiplicative property of
-1 1/4
Answer:
Step-by-step explanation:
1 is the answer
Express 80% as a fraction or mixed number in simplest form
Answer: 4/5
Step-by-step explanation:
80%=
100% * 80/100 =
1 * 80/100=
80/100=
8/10=4/5
Consider the line y=8x-9
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
compare the line y=8x-9 to y=mx+b where m is a slope and b is y-intercept
so, the line y=8x-9 has a slope m=8
by definition, the slope of a line parallel to this line will be same, m=8
by definition, the slopes of perpendicular lines are negative reciprocals to each other; so, m = -1/8
What is the rate of change or slope?
Question 1 options:
m= 1/2
m=-2/1
m=-1/2 or m=-2/4
m=-2/1 or m=-4/2
Answer:
m=-1/2 or m=-2/4
Step-by-step explanation:
The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]
Given :
The graph of a line . To find out the slope or rate of change , we pick two points on the line.
Two points are (-8,2) and (4,-4)
Lets apply slope formula
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
(-8,2) is (x1,y1)
(4,-4) is (x2,y2)
Substitute all the values inside the formula
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}\\slope =\frac{-4-2}{4+8} =\frac{-6}{12} =-\frac{-2}{4} =-\frac{1}{2}[/tex]
The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]
Learn more : brainly.com/question/17572076
WRITE THE NEXT 2 TERMS OF EACH SEQUENCE
1) 2, 6, 18, 54, __, __
2) 2, - 4, 8, - 16, __, __
3) 1, 3, 5, 7, __, __
4) 1, 2/3, 4/6, 8/9, ___, ___
Answer:
1) 2,6,18,54,162,468 (multiply by 3 each time)
2) 2, -4, 8, -16, 32, -64 (i'm not sure what this is but i'm pretty confident i'm right lol)
3) 1,3,5,7,9,11 (add 2 each time)
4) 1, 2/3 , 4/6 , 8/9 , _ _ (i'm sorry i tried my hardest but i don't know this one)
Step-by-step explanation:
hope this helped! so sorry about 4...
1 The distance on the number line from a to 7 is 0.5. Which of the following could be the value of a ? A) 7.5 B) -3.5 C 0.5 D 6.5
Answer:
6.5
Step-by-step explanation:
Answer:
6.5
Step-by-step explanation:
cual de las siguientes compraraciones es correcta? a)1\8>1\2 b) 1/3<1\5 c)1\12>1\100 d)1\4>1\6
Las comparaciones correctas son (c) ( 1/12 ) > ( 1/100 ) y (d) ( 1/4 ) > ( 1/6 ).
Considere las comparaciones,
Para la opción (a),
( 1/8 ) > ( 1/2 )
Ahora, encuentre el valor de cada término en forma decimal.
( 1/8 ) = 0.125 y;
( 1/2 ) = 0.5
Por lo tanto, ( 1/2 ) > ( 1/8 )
Por lo tanto, esta opción es incorrecta.
Para la opción (b),
( 1/3 ) < ( 1/5 )
Ahora, encuentre el valor de cada término en forma decimal.
( 1/3 ) = 0.333 y;
( 1/5 ) = 0.2
Por lo tanto, ( 1/3 ) > ( 1/5 )
Por lo tanto, testa opción es incorrecta.
Para la opción (c),
( 1/12 ) > ( 1/100)
Ahora, encuentre el valor de cada término en forma decimal.
( 1/12 ) = 0.0833 y;
( 1/100 ) = 0.01
Por lo tanto, ( 1/12 ) > ( 1/100 )
Por lo tanto, esta opción es incorrecta.
Para la opción (d),
( 1/4 ) > ( 1/6 )
Ahora, encuentre el valor de cada término en forma decimal.
( 1/4 ) = 0.25 y;
( 1/6 ) = 0.1666
Por lo tanto, ( 1/4 ) > ( 1/6 )
Por lo tanto, esta opción es correcta.
Obtenga más información sobre las comparaciones aquí:
https://brainly.com/question/1404938
#SPJ9