Answer:
a) An input of 5 gives an output of 14. An input of -1 gives an output of -4.
An input of x gives an output of 3x - 1
b) y = 3x - 1
Step-by-step explanation:
The pattern is that you multiply the number by 3 then subtract 1.
3*3 - 1 = 9 - 1 = 8
10 * 3 - 1 = 30 - 1 = 29
20 * 3 - 1 = 60 - 1 = 59
So:
a)
For an input of 5,
5 * 3 - 1 = 15 - 1 = 14
For an input of -1:
-1 * 3 - 1 = -3 - 1 = -4
For an input of x:
x * 3 - 1 = 3x - 1
So the equation is
b) y = 3x - 1
where x is the input value.
What is the equation of the line that passes through the point (-2,5) and has a
slope of -4?
Answer:
[tex]\boxed {\boxed {\sf y= -4x -3}}[/tex]
Step-by-step explanation:
We are asked to find the equation of a line given a point and the slope. We will use the point-slope formula.
[tex]y-y_1= m(x-x_1)[/tex]
In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of this line is -4 and the line passes through (-2,5).
m= -4 x₁= -2 y₁ = 5Substitute the values into the formula.
[tex]y-5 = -4 (x--2)[/tex]
[tex]y-5 = -4 (x+2)[/tex]
We are finding the equation of the line, so we should find the slope-intercept form or y=mx+b ( where m is the slope and b is the y-intercept).We must isolate the variable y on one side of the equation.
First, distribute the -4 on the right side of the equation. Multiply each term inside the parentheses by -4.
[tex]y-5=( -4 *x ) + (-4* 2 )[/tex]
[tex]y-5 =(-4x)+ (-8)\\y-5= -4x -8[/tex]
5 is being subtracted from y. The inverse operation of subtraction is addition, so we will add 5 to both sides of the equation.
[tex]y-5 =-4x -8 + 5[/tex]
[tex]y= -4x -3[/tex]
The equation of the line is y= -4x -3. The slope of the line is -4 and the y-intercept is -3.
If I started at 7:20 and ended at 8:07 how much times is that?
Answer:
47 minutes
Step-by-step explanation:
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A solution to a system of equations are where the two lines cross over each other.
System A the graph shows one line which means the two lines are on top of each other. This means any point on the lines are a solution so there are infinite number of solutions.
System B, the lines cross at one point is there is only one solution which is at (-3,2)
System C the two lines are parallel to each other and never cross so there are no solutions.
Step-by-step explanation:
(i) Infinite solution
If there is only one line then it is a infinite solution.
(ii) One solution
Both are intersecting each other.
Solving
-x - 1 = x + 5
-x - x = 5 + 1
-2x = 6
x = 6/-2
x = -3
y = -x + 5
y = -3 + 5
y = 2
(iii) No solution
Because they are parallel to each other
|2x+9|>10=5 Please help ASAP
Simplifying
2x + 9 + -10 = -5
Reorder the terms:
9 + -10 + 2x = -5
Combine like terms: 9 + -10 = -1
-1 + 2x = -5
Solving
-1 + 2x = -5
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + 2x = -5 + 1
Combine like terms: -1 + 1 = 0
0 + 2x = -5 + 1
2x = -5 + 1
Combine like terms: -5 + 1 = -4
2x = -4
Divide each side by '2'.
x = -2
Simplifying
x = -2
I hope it helps you
simplify 2 root 3 + 3 root 3 - 4 root 3
Answer:
√ 3
Step-by-step explanation:
2√3 + 3√ 3 - 4√ 3
5√3 - 4√ 3
1√3
=> √ 3
Answer:
→ 2√3 + 3√3 - 4√3
= (2+3-4)√3
= (5-4)√3
= √3
Therefore, √3 is the right answer.
Explain how to do order of operations. Use an example
Answer:
First, solve what is in the parentheses of the function. Next, solve the exponents. This includes normal exponents, negative exponents, square roots, cube roots, etc. After that, multiply and divide, and finally, add and subtract the remaining equation.
Lauren bought snacks for her team's practice. She bought a bag of popcorn for $2.37 and a 6-pack of juice bottles. The total cost before tax was $15.45. How much was each bottle of juice?
Answer:
$2.18
$15.45-$2.37=$13.08
$13.08/6
$2.18
Find the value of k. please help
Answer:
k=57
Step-by-step explanation:
-k+15=k-99(vertically opposite angles)
k=57
Opposite angles are equal
[tex]\\ \rm\longmapsto -k+15=k-99[/tex]
[tex]\\ \rm\longmapsto -k-k=-99-15[/tex]
[tex]\\ \rm\longmapsto -2k=-114[/tex]
[tex]\\ \rm\longmapsto 2k=114[/tex]
[tex]\\ \rm\longmapsto k=\dfrac{114}{2}[/tex]
[tex]\\ \rm\longmapsto k=57[/tex]
There are 8 cupcakes on a plate. Five children will share them equally. How many cupcakes will each child receive? Represent the scenario three ways:
With math vocabulary, as an expression, and as a fraction.
Answer:
Each child will receive eight fifths of the cupcakes.
5x=8 ; x represents how many cupcakes each child receives.
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
There are 8 cupcakes in total.
5 children.
Divide 8 by 5. [tex]\frac{8}{5}[/tex]
I hope this helps!
pls ❤ and mark brainliest pls!
Solve for x: 4x + 1/2 (2x + 4) > 12
( 9th grade Algebra 1)
Answer:
x > 2
Step-by-step explanation:
Distribute and cross-simplify 1/2 with parenthesis
4x + x + 2 > 12
Solve left side
5x + 2 > 12
Subtract 2 from both sides
5x > 10
Divide both sides by 5
x > 2
if there are two containers of sugar solution, the first is 4% concentration and second is 8% concentration. how much of each should we combine to get 40 gallons of 5% concentrate solution
Answer:
30 gallons solution 4% and 10 gallons solution 8%
Step-by-step explanation:
x•4%+y•8%=40•5%4x+8y=40•5 and x+y=40
x=40-y
4(40-y)+8y=200
160-4y+8y=200
4y=200-160
4y=40 => y=10 (gallons solution 8%)
=> x=40-10=30 (gallons solution 4%)
30 gallons solution 4% and 10 gallons solution 8%
10. The triangle has a perimeter of 23 feet. Find the value of x.
x ft
(x + 3) ft
3x ft.
How many solutions does the system have?
5y = 152 – 40
y = 3r – 8
Find the are of the shaded region
Answer:
16 units squared
Step-by-step explanation:
shape: square (ALL equal sides)
length: 4
width: 4
4 X 4 = 16
if x=1+3i ,y=x-i find the value of x^2-y^2
Answer:
Step-by-step explanation:
x = 1 + 3i
x^2 = (1 + 3i)(1 + 3i)
f: 1 * 1 = 1o: 1 * 3i = 3ii: 3i * 1 = 31L: = 3i * 3i = 9i^2 = - 9x^2 = 1 + 6i - 9 = -8 + 6i
By a similar method
y = (x - i)
y^2 = x^2 - 2i*x + i^2
y^2 = x^2 - 2ix - 1
y^2 = -8+6i - 2i(1 + 3i) -1
y^2 = -8+6i -2i - 6i - 1
y^2 = -8 - 2i - 1
y^2 = - 9 - 2i
x^2 - y^2 = -8 + 6i - (9 - 2i)
x^2 - y^2 = -8 + 6i - 9 + 2i
x^2 - y^2 = -17 + 8i
12 bars of chocolate costs $3.00 . What is the cost of each chocolate bar?
Answer:
$0.25
Step-by-step explanation:
Divide the cost by the amount.
[tex]\frac{3}{12}=0.25[/tex]
Therefore, the cost of each chocolate bar is $0.25.
(x-3)/(-3) = 27 /3 - x
Answer:
X= 12
Step-by-step explanation:
Divide 27/3= 9
Multiply 3 from both sides: x-3/-3 * 3 = 9 *3- x * 3
Simplify: -(x-3) =27-x*3
2x=24
Divide 2 from both sides: 2x/2= 24/2
x=12
Complete the pattern 13, 14, 16, 19, 23, ______.
Answer:
28
Step-by-step explanation:
it is increasing by 5 then 6,7,8,9...
Answer:
28
Step-by-step explanation:
Two cars leave towns 760 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 4 hours, what is the rate of the slower car?
Answer:
Let speed of slower car be xkm/h
Therefore rate of other car=x+20 km/h
After 4 hrs ,
Distance covered by Car A=4x
Distance covered by Car B=4x+80
4x+4x+80=760km
8x=680
x=45
The rate of the slower car=45km/h
Solve for x please will mark brainliest
Answer:
[tex]4y + 6y = 90 \\ 10y = 90 \\ y = 9 \\ thank \: you[/tex]
Pls I need help! Multiple choice question
Answer:
D is right answer
Chen rode his skateboard 3 3/4 miles in of 3/4 an hour. What was his average speed in miles per hour?
Answer:
5
Step-by-step explanation:
Dont ask why i think its 5 mph
Name the figure below in two different ways.
Answer:
Line segment. (That's what I know)
Step-by-step explanation:
There are two points on the ends, so its a line segment. I think thats it
Quadrilateral ABCD is a rectangle. What is the length of AC?
Select the best answer from the choices provided.
A.14
B.17
C.25
D.31
Answer:
option c is correct answer
A patient is to take 4 2/3 tablespoons of medicine per day in 4 equally divided doses. How much medicine is to be taken in each dose?
Answer:
1 1/6
Step-by-step explanation:
4 2/3 ÷ 4
Convert the mixed number into an improper fraction:
4 2/3 = 14/3
14/3 ÷ 4
14/3 ÷ 4/1
Use cdf (copy dot flip)
14/3 × 1/4
14 × 1 / 3 × 4
14/12
Convert improper fraction into a mixed number:
14/12 = 1 2/12
1 1/6
why is this simplified by combining like terms
3(4x+5) +2
You have one box that is 1 4/11
feet tall and a second box that is 1.36 feet tall. Write the decimal expansion for
. If you stack the boxes, about how tall will the stack be?
The stacked boxes would be 2.72 feet tall
The height of the stacked box is the sum of the lengths of the two boxes
1 4/11 is a mixed number and it has to be converted to a decimal
A mixed number is a number that has a whole number and a proper fraction.
A proper fraction is a fraction is which the numerator is less than the denominator.
The whole number is 1 and the proper fraction is 4/11
To convert to a decimal, divide the numerator by the denominator. Add this number to the whole number
4/11 = 0.36
1 + 0.36 = 1.36 feet
Height of the stacked boxes = 1.36 + 1.36 = 2.72 feet
To learn more about decimals, please check:
https://brainly.com/question/18657762?referrer=searchResults
help me please????????
Answer:
c
Step-by-step explanation:
Option c is correct. All points are equally spaced from the line x=1 as their images do. They are symmetric about the line x=1. For instance, point A and A' are both 3 units from the line x=1.
Option a and B are wrong as we cannot see and swapping of x and y coordinates to a point.
For option d, only point A is shifted 6 units to the left to A', but point B shifted 8 units to B'. Incorrect.
what is the commutative property in x+3y
PLEASE ANSWER QUICKLY
Answer:
3y+x
Step-by-step explanation:
commutative property :
a+b=b+a
Similarly:
x+3y=3y+x
Answer:
[tex]we \: know \: that \: commutative \: \\ prop \: is \: x + y = y + x \\ so \: x + 3y = 3y + x \\ \\ thank \: you[/tex]