Answer:
6(7 - 3y) + 6(y + 1) = 42 - 18y + 6y + 6 =
-12y + 48 = 12(4 - y)
The expression 6(7-3y)+6(y+1) simplifies to 48-12y by distributing the 6 and combining like terms.
Explanation:To simplify the expression 6(7-3y)+6(y+1), we need to apply the distributive property and then combine like terms.
First, distribute the 6 into the parentheses: 6×7 - 6×3y + 6×y + 6×1.This simplifies to: 42 - 18y + 6y + 6.Then combine like terms (-18y and 6y): 42 - 12y + 6.Finally, add the constants (42 and 6): 48 - 12y.The simplified equivalent expression is 48 - 12y.
To check that the expression is reasonable, you can substitute values for y and see if the original and the simplified expressions yield the same result.
Thus, for the given equation, the result is obtained as: 48 - 12y.
Solve the two-step equation.
part : a
-9x + 0.4 = 4
Which operation must be performed to move all the constants to the right side of the equation?
part: b
Then, which operation must be performed to isolate the variable?
part: c
The solution to the equation is x =
a)
Subtract 0.4 from both side.
-9x +0.4 = 4
-9x + 0.4 - 0.4 = 4 - 0.4
-9x = 3.6
b)
divide by -9 both side
-9x/-9 = 3.6/-9
x = -0.4
c) x = - 0.4
The steps needed to solve the given equation is required.
Adding the opposite value of the constant to both sides.
Divide both sides by the coefficient of the variable.
The solution to the equation is [tex]x=-0.4[/tex]
The given equation is
[tex]-9x+0.4=4[/tex]
In order to solve this we first move constants to the side opposite of the variable.
This is done by adding the opposite value of the constant to both sides.
[tex]-9x+0.4-0.4=4-0.4[/tex]
Here [tex]0.4[/tex] is the constant so we add [tex]-0.4[/tex] to both sides.
[tex]\Rightarrow -9x=3.6[/tex]
Now, we divide both sides by the coefficient of the variable.
[tex]\Rightarrow \dfrac{-9x}{-9}=\dfrac{3.6}{-9}\\\Rightarrow x=-0.4[/tex]
The solution to the equation is [tex]x=-0.4[/tex]
Learn more:
https://brainly.com/question/16135223
https://brainly.com/question/8449665
PLEASE HELP ME!!! I WILL AWARD BRAINLIEST!! SOLVE EACH!!
Rewrite without absolute value for the given conditions:
1) y=|x−3|+|x+2|−|x−5| , IF -2 < X < 3
2) y=|x−3|+|x+2|−|x−5| , 3 < X < 5
Answer:
1. x
2. 3x-6
Step-by-step explanation:
1) y=|x−3|+|x+2|−|x−5| , IF -2 < X < 3
|x−3| will be less than zero if -2 < X < 3 so rewrite it as 3-x
|x+2| will be greater than zero if -2 < X < 3 so we can leave it as x+2
|x−5| will be less than zero if -2 < X < 3 so we rewrite it as 5-x
1. 3-x + x+2 - (5-x)
Combine like terms
5 - (5-x)
Distribute
5 - 5+x
x
1) y=|x−3|+|x+2|−|x−5| , IF 3 < X < 5
|x−3| will be greater than zero if 3 < X < 5 so leave it as x-3
|x+2| will be greater than zero if 3 < X < 5 so we can leave it as x+2
|x−5| will be less than zero if -2 < X < 3 so we rewrite it as 5-x
x-3 + x+2 - (5-x)
Combine like terms
2x-1 - (5-x)
Distribute
2x-1 - 5+x
3x-6
The equation of a line is given by 4x-3y=12.How do you solve for x
Simplifying
4x + -3y = 12
Solving
4x + -3y = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '3y' to each side of the equation.
4x + -3y + 3y = 12 + 3y
Combine like terms: -3y + 3y = 0
4x + 0 = 12 + 3y
4x = 12 + 3y
Divide each side by '4'.
x = 3 + 0.75y
Simplifying
x = 3 + 0.75y
Which of the following is the solution to the following system of inequalities? Let the green region represent the solution set. X+2y<=4 3x-y>2
Answer:
See picture attached.
Step-by-step explanation:
To find the solution, graph each equation using the y = mx + b form.
Start by converting to this form.
x + 2y < 4 becomes y < -1/2x +2
3x - y > 2 becomes y < 3x - 2
Then mark each y-intercept. These points are (0,2) and (0,-2).
Using the slope mark the next points at (-1,4) and (1, -1) respectively.
Connect using dash lines since this is not equal to in either inequality.
Test a point no on either line like (-1,-1).
If the inequality holds true, shade the area.
Where the areas overlap is the solution. See picture.
Inequalities are used to represent unequal expressions.
The solution to the inequality is [tex]x \le \frac 87[/tex] and [tex]y < \frac{10}7[/tex]
The inequalities are given as:
[tex]x + 2y \le 4[/tex]
[tex]3x - y > 2[/tex]
Express both inequalities as equations'
[tex]x + 2y = 4[/tex]
[tex]3x -y = 2[/tex]
Make y the subject in [tex]3x -y = 2[/tex]
[tex]y = 3x - 2[/tex]
Substitute [tex]y = 3x - 2[/tex] in [tex]x + 2y \le 4[/tex]
[tex]x + 2(3x - 2) \le 4[/tex]
Open brackets
[tex]x + 6x - 4 \le 4[/tex]
[tex]7x - 4 \le 4[/tex]
Collect like terms
[tex]7x \le 4+4[/tex]
[tex]7x \le 8[/tex]
Divide both sides by 7
[tex]x \le \frac 87[/tex]
Substitute 8/7 for x in [tex]3x - y > 2[/tex]
[tex]3 \times \frac 87 - y > 2[/tex]
[tex]\frac{24}7 - y > 2[/tex]
Collect like terms
[tex]- y > 2 -\frac{24}7[/tex]
Take LCM
[tex]- y > \frac{14 -24}7[/tex]
[tex]- y > \frac{-10}7[/tex]
Divide both sides by -1
[tex]y < \frac{10}7[/tex]
Read more about inequalities at:
https://brainly.com/question/15137133
a baseball field is in the shape of a square that is 90 feet on a side as shown. A player catches a ball at point x, which is three-quarters of the way between 2nd base & 3rd base, and throws the ball to 1st base.
What is the distance the player throws the call?
Answer:
The distance the player throws the ball is [tex]112.5\ ft[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
In the right triangle ABX
[tex]AB=90\ ft[/tex]
[tex]BX=(3/4)90=67.5\ ft[/tex]
XA --------> is the distance the player throws the ball (hypotenuse of the right triangle)
Applying the Pythagoras Theorem
[tex]XA^{2}=AB^{2}+BX^{2}[/tex]
substitute the values
[tex]XA^{2}=90^{2}+67.5^{2}[/tex]
[tex]XA^{2}=12,656.25[/tex]
[tex]XA=112.5\ ft[/tex]
The distance player throws the call was calculated using Pythagoras theorem and it is 112.5 feet.
It is given that
Side of the square = 90 feet
Distance of point x from the second base = 3/4 * 90 = 67.5
The distance the player throws the call let us say D will be the shortest distance between x and 1st base.
Distance D can be calculated by Pythagoras theorem
What is Pythagoras theorem?
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the perpendicular and the base.
[tex]D = \sqrt{90^{2} +67.5^{2} }[/tex]
[tex]D = \sqrt{8100+4556.25} \\\\D = \sqrt{12656.25\\}\\[/tex]
[tex]D=\sqrt{12656.25} = 112.5[/tex]
Therefore, the distance the player throws the call is 112.5 feet.
To get more about Pythagoras theorem, visit:
https://brainly.com/question/343682
If b2 + 2b − 24 = 0, and b < 0, what is the value of b?
A) −6
B) −4
C) −2
D) 0
The value of b is -6.
Explanation:To find the value of b, we need to solve the quadratic equation b2 + 2b - 24 = 0.
Since b < 0, we can eliminate the positive solution.
We can factor the equation by finding two numbers whose product is -24 and sum is 2.
The numbers are -4 and 6.
So, the factored form of the equation is (b - 4)(b + 6) = 0.
Setting each factor equal to zero, we find that b = -6 or b = 4.
Since b < 0, the value of b is -6.
Learn more about Quadratic equation here:https://brainly.com/question/30098550
#SPJ12
Final answer:
Using the quadratic formula, we find that b = -6 (option A), considering the requirement that b < 0 for the equation b² + 2b - 24 = 0.
Explanation:
To find the value of b given the quadratic equation b² + 2b − 24 = 0 and knowing that b is less than zero, we can use the quadratic formula:
The quadratic formula is −b ± √(b² − 4ac /2a), where a, b, and c are coefficients from the quadratic equation in the form ax2 + bx + c = 0.
In this case, a = 1, b = 2, and c = −24. Applying these values to the quadratic formula, we have:
−(2) ± √((2)² − 4(1)(−24) /2(1))
The discriminant part of the formula, b² − 4ac, equals (2)² − 4(1)(−24) = 4 + 96 = 100. Therefore, the square root of the discriminant is 10.
Simplifying further, we have:
(−2 ± 10) / 2 = −6 or +8
Since b < 0, we disregard the positive solution and consider b = −6, which is option A.
Leila and joe are two partners in a business. Leila makes $8 in profit for every $9 that joe makes. if joe makes $54 profit on the first item they sell, how mutch profit does leila make?
Answer: $48
Step-by-step explanation: The amount of money Joe made can be divided by 9. 54/9 = 6. Joe made 9 dollars six times so Leila made 8 dollars 6 times. 6 x 8 = 48.
A line contains the points (a,b) and (a+3,b+3). Find the equation of the line in terms of a and b in point slope form and then convert it to slope intercept form?
Answer:
y - b = 1(x - a) - point-slope formy = x + b - a - slope-intercept formStep-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (a, b) and (a + 3, b + 3). Substitute:
[tex]m=\dfrac{b+3-b}{a+3-a}=\dfrac{3}{3}=1[/tex]
[tex]y-b=1(x-a)[/tex] - point-slope form
Convert to the slope-intercept form: y = mx + b:
[tex]y-b=x-a[/tex] add b to both sides
[tex]y=x+b-a[/tex] - slope-intercept form
Answer:
Step-by-step explanation:
answer for edmentum
Find all polar coordinates of point P where P = ordered pair 5 comma negative pi divided by 6 .
A.(5, negative pi divided by 6 + 2nπ) or (-5, negative pi divided by 6 + 2nπ)
B.(5, negative pi divided by 6 + 2nπ) or (-5, negative pi divided by 6 + (2n + 1)π)
C.(5, negative pi divided by 6 + 2nπ) or (5, pi divided by 6 + (2n + 1)π)
D.(5, negative pi divided by 6 + (2n + 1)π) or (-5, negative pi divided by 6 + 2nπ)
Answer:
The correct option is B.
Step-by-step explanation:
If polar coordinates of point P are
[tex]P=(r,\theta)[/tex]
Where, r is real number and θ is in radian, then all polar coordinates of point P are defined as
[tex]P=(r,\theta+2n\pi)[/tex]
[tex]P=(-r,\theta+(2n+1)\pi)[/tex]
The given coordinates are [tex]P(5,-\frac{\pi}{6})[/tex]. So, all polar coordinates of point P are
[tex]P=(5,-\frac{\pi}{6}+2n\pi)[/tex]
[tex]P=(-5,-\frac{\pi}{6}+(2n+1)\pi)[/tex]
Therefore correct option is B.
what is the area of this parallelogram? A 10.35 cm2 B 12.5 cm2 C 20.25 cm2 D 30.6 cm2
A test consists of 20 true/false questions. If a student guesses on each question, what Is the probability of getting exactly 15 correct
Answer:
50%
Step-by-step explanation:
due to the fact that its true/false questions, so that means when you answer you have 2 choices. a 50/50 chance of getting them right or wrong
convert 84 inches to yards
Answer:
The answer is 2.333 yards
Step-by-step explanation:
In every one yard there's thirty-six inches.
84/36= 2.333
Hope this helps :)
To convert 84 inches to yards, first convert inches to feet by dividing by 12, resulting in 7 feet. Then, convert feet to yards by dividing by 3, resulting in approximately 2.33 yards.
To convert 84 inches to yards, we need to use the relationships between inches, feet, and yards.
Start by converting inches to feet, and then convert feet to yards.
1. Convert inches to feet:
There are 12 inches in a foot, so divide the number of inches by 12.
84 ÷ 12
= 7 feet
2. Convert feet to yards:
There are 3 feet in a yard, so divide the number of feet by 3.
7 ÷ 3
= 2.33 yards
Thus, 84 inches is equal to approximately 2.33 yards.
9. What’s the answer to this please
What is 3 8/9 - 1 5/8
Answer:
2 19/72
Step-by-step explanation:
Overall without stating all the steps, it'd be 2.
A curve with equation
[tex]y = a {x}^{2} + bx + c[/tex]
crosses the x-axis at (-4,0) and (9,0) and it also passes through the point (1,120).
where does the curve cross the Y axis
[tex]y = a(x)^(2) + bx + c [/tex]
Write 10 2 /19 as an improper fraction.
Answer:192/19
Step-by-step explanation:
10/1 +2/19=190/19+2/19=192/19
Answer: 192/19
Step-by-step explanation:
find all numbers whose absolute value is 6
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is 6 and -6.
Since absolute value is to figure the distance from 0, it is regardless of positive or negative.
6, -6 are the only numbers.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
1/2 + 1/6 is simplest form
Answer:
[tex]\frac{2}{3}[/tex]Step-by-step explanation:
[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{6}[/tex]
⇒ [tex]\frac{3}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex]
⇒[tex]\frac{2}{3}[/tex]
What is the capacity of the cube in liters 7 cm
Answer:
0.343 L
Step-by-step explanation:
A liter has 1000 mL which is 1000 cm^3
The volume of the cube = s^3
s = 7
Volume = 7^3
V = 343 cc
The number of liters = 343 / 1000 = 0.343 L
Given that the radius of the circle is 5 cm , calculate the area of the shaded sector. (Take pie = 3.142). Someone please help me out.
THE AREA OF A CIRCLE = πr^2
Here π = 3.142
r = 7.5
now A = πr^2
A = 3.142× 7.5×7.5
A = 176.7375cm^2
Hope it helped you.
Answer:
The area of shaded = 13.09 cm^2
Step-by-step explanation:
360 /6 = 60
So the shaded area is 1/6 of the circle
Area of circle = pie r^2
So area of shaded = 1/6(pie r^2)
= 1/6 * 3.142 * 5^2
= 13.09 cm^2
Which expression is equivalent to m^2-13m-30?
(m – 15) (m + 2)
(m – 10) (m – 3)
(m + 15) ( m – 2)
(m + 10) (m + 3)
Answer: First option
Step-by-step explanation:
You have the quadratic equation given in the problem:
[tex]m^2-13m-30[/tex]
To find an equivalent expression you cacn factorize. Find two numbers whose sum is -13 and whose product is -30.
These numbers would be -15 and 2.
Therfore, you obtain the following equivalent expression:
[tex](m-15)(m+2)[/tex]
If you don't want to apply the method above, you can use the quadratic formula:
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
Where:
[tex]a=1\\b=-13\\c=-30[/tex]
When you susbstitute values you obtain that:
[tex]x=15\\x=-2[/tex]
Then you can rewrite the equation as [tex](m-15)(m+2)[/tex]
Answer:
[tex](m-15)(m+2)[/tex]
Step-by-step explanation:
The given expression is
[tex]m^2-13m-30[/tex]
Split the middle term
[tex]m^2-15m+2m-30[/tex]
Factor
[tex]m(m-15)+2(m-15)[/tex]
Factor further to obtain;
[tex](m-15)(m+2)[/tex]
The correct answer is A.
If b+3/7 = 2/5 then which of the following is true?5b + 15 = 14 b + 3 = 14 5b + 3 = 14 b + 15 = 14
Answer:
The first one is true. 5b+15=14
Step-by-step explanation:
(b+3)/7= 2/5
After cross-multiplication:
5(b+3)=2*7
5b+15=14
need help before 6:00am tomorrow morning
Answer:
1) true
2)False
3) False
4)true
Step-by-step explanation:
1) I doubled 50 to make a hundred girls = 100% and theni had to double 18 to get 36= 36%
2) because it is 8.4%
3) Because the total number of girls is the highest for 1 fruit
Suppose ABCD is a rhombus with AB = 12 inches. The midpoints of its sides are joined to form a quadrilateral. b What is the length of a diagonal of this quadrilateral?
Answer:
12 inches.
Step-by-step explanation:
The quadrilateral will be rectangle and the diagonals will be parallel and equal to the sides of the rhombus.
If the midpoints of the rhombus with sides of 12 inches are joined to form a quadrilateral. The quadrilateral formed would be a square with diagonal of 12 inches.
What is a rhombus?A rhombus is a quadrilateral (has four sides and four angles) in which the opposite sides are equal and parallel. All the sides of a rhombus are equal.
If the midpoints of the rhombus with sides of 12 inches are joined to form a quadrilateral. The quadrilateral formed would be a square with diagonal of 12 inches.
find out more on rhombus at: https://brainly.com/question/20627264
find each unit price and decide which is a better buy (cheaper) Treated lumber $3.79 for an 8 foot board. or $6.18 for a 12 foot board?
Answer:
$3.79 for an 8 foot board
Step-by-step explanation:
The way to find the answer is calculating the price per foot.
Part 1
$3.79 for an 8 foot board.
one foot would cost:
$3.79 ÷ 8 = 0.47375
Part 2
$6.18 for a 12 foot board?
Price of one foot would be:
$6.18 ÷ 12 = 0.515
$0.47375 is less than $0.515. So, the cheaper treated lumber is the one costing $3.79 for an 8 foot board.
A polynomial function has a zeros at -1,2,7 and all are multiplicity of 1 write a function in standard form that could represent this function
Final answer:
To create a polynomial with zeros at -1, 2, and 7, each with a multiplicity of 1, you start with the factored form (x + 1)(x - 2)(x - 7) and expand it to get the standard form x^3 - 8x^2 + 15x + 14.
Explanation:
The question involves finding a polynomial function with given zeros. When a polynomial has zeros of -1, 2, and 7, all with a multiplicity of 1, the function can be expressed as product of linear factors associated with each zero. Starting from the factored form f(x) = (x - (-1))(x - 2)(x - 7), which encapsulates the given zeros, you can then expand this expression to get the polynomial in its standard form.
The expanded form of the polynomial is then f(x) = (x + 1)(x - 2)(x - 7), which, when expanded, yields f(x) = x^3 - 8x^2 + 15x + 14. This is a polynomial function in standard form that has the required zeros, each with a multiplicity of 1.
Cindy had 13 stickers. She bought 18 stickers from a store in the mall and got 5 stickers for her birthday. Then Cindy gave 8 of the stickers to her sister and used 10 to decorate a greeting card. How many stickers does Cindy have left?
Answer:
18 stickers.
Step-by-step explanation:
Cindy buys 18 more stickers in the start. This results in 13+18= 31 stickers. She then gets five for her birthday. 31+5=36 so she now has 36 stickers but she then gives eight away which means she has 36-8=28 stickers. She uses ten stickers to decorate so Cindy has 28-10=18 stickers left
Answer:
si esta bien
Step-by-step explanation:
What is the Slope and y intercept
Answer:
The slope is .075 and the y intercept is -.125
Step-by-step explanation:
8y = .2(3x -5)
Distribute the .2
8y = .6x - 1
Divide by 8
8y/8 = .6x/8 -1/8
y = .075x -.125
This is in slope intercept form y= mx+b where m is the slope and b is the y intercept.
The slope is .075 and the y intercept is -.125
what is the area of the space that Nadia has shown for scrapbooking
Answer:
52
Step-by-step explanation:
Answer:
The answer is,52
Step-by-step explanation:
Definition of area:The area of a 2D form is the amount of space within its perimeter. It's measured in square units like [tex]cm^{2}[/tex],[tex]m^{2}[/tex] , and so on. You must multiply the length by the width to find the area of a square formula or other quadrilateral.
According, to the question:
[tex]Area=l[/tex]×[tex]b[/tex]
area=13×4
area= 52
Hence, The scrapping area is 52 square feet.
To know more about area here, https://brainly.com/question/1297098
#SPJ2
Indicate the formula for the following conditions. P(n,r)=
Hence , Formula for permutation and combination is
[tex]P(n,r)=\frac{n!}{n-r!}[/tex]
What is Permutation?No of ways in which we can obtain possible no. of ways in which particular arrangement can be made.
what is combination?The way in which we can select item as per given situation
what Is Formula for P(n,r)?[tex]P(n,r)=\frac{n!}{n-r!}[/tex]
earn more about Permutation and Combination https://brainly.com/question/11732255
#SPJ2
The formula for [tex]P(n,r)[/tex], which represents the number of permutations of r objects from a set of n distinct objects, is given by: [tex]\[ P(n,r) = \frac{n!}{(n-r)!} \][/tex]
To understand this formula, let's break it down:
1. [tex]\( n! \)[/tex] gives the number of ways to arrange n distinct objects in a sequence.
2. [tex]\( (n-r)! \)[/tex] gives the number of ways to arrange the remaining [tex]\( n-r \)[/tex] objects that are not chosen for the permutation.
3. Dividing [tex]\( n! \)[/tex] by [tex]\( (n-r)! \)[/tex] effectively cancels out the arrangements of the [tex]\( n-r \)[/tex] objects that we are not interested in, leaving us with the number of ways to arrange just the r objects.