Answer:
2(5m-n)
Step-by-step explanation:
Answer:
10m-2n
Step-by-step explanation:
hope this helps :)
2. Solve the following equation for b. 6b + 2a - 4 = 2b + 3a
$b = a + 1
b= 5a+1/2
b= a+4/4
b= 5a+4/8
[tex]\bigstar\boxed{\bf\purple{\leadsto b=\dfrac{a+4}{4}}}[/tex]
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
➠ On solving the given equation for b :
[tex]\rm{\longrightarrow 6b+2a-4=2b+3a}[/tex]
[tex]\rm{\longrightarrow 6b-2b=3a-2a+4}[/tex]
[tex]\rm{\longrightarrow 4b=a+4}[/tex]
[tex]\rm{\longrightarrow b=\dfrac{a+4}{4}}[/tex]
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
Given that :
6b + 2a - 4 = 2b + 3aTo Find :
The value of bSolution :
[tex]\qquad \sf \: { \dashrightarrow 6b + 2a - 4 = 2b + 3a }[/tex]
[tex]\qquad \sf \: { \dashrightarrow 6b - 2b - 4 = 3a - 2a }[/tex]
[tex]\qquad \sf \: { \dashrightarrow 4b - 4 = a }[/tex]
[tex]\qquad \sf \: { \dashrightarrow 4b = a + 4}[/tex]
[tex]\qquad \bf \: { \dashrightarrow b = \dfrac{a + 4}{4} }[/tex]
Hence option 3 is correct!Solve (x – 3)2 = 49. Select the values of x.
–46
-4
10
52
Answer:
x=10
x=-4
Step-by-step explanation:
Quadratic Equation: (x – 3)^2 = 4
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-3)^2-(49)=0
Step 1:
valuate : (x-3)² = x²-6x+9
Factoring x²-6x-40
The first term is, x²its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 1 • -40 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -6 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 4
x²- 10x + 4x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-10)
Add up the last 2 terms, pulling out common factors :
4 • (x-10)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-10)
Which is the desired factorization
Equation at the end of step
1
:
(x + 4) • (x - 10) = 0
STEP
2 :
Theory - Roots of a product
A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
Solve : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation:
Solve : x-10 = 0
Add 10 to both sides of the equation :
x = 10
Supplement : Solving Quadratic Equation Directly
Solving x²-6x-40 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
Find the Vertex of y =x²-6x-40
For any parabola,Ax²+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000
Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 - 40.0
or y = -49.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x²-6x-40
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-49.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-4.00, 0.00}
Root 2 at {x,y} = {10.00, 0.00}
Solve Quadratic Equation by Completing The Square
Solving x²-6x-40 = 0 by Completing The Square .
Add 40 to both side of the equation :
x2-6x = 40
Now the clever bit: Take the coefficient of x , which is 6 , divide by two, giving 3 , and finally square it giving 9
Add 9 to both sides of the equation :
On the right hand side we have :
40 + 9 or, (40/1)+(9/1)
The common denominator of the two fractions is 1 Adding (40/1)+(9/1) gives 49/1
So adding to both sides we finally get :
x2-6x+9 = 49
Adding 9 has completed the left hand side into a perfect square :
x2-6x+9 =
(x-3) • (x-3) =
(x-3)2
Things which are equal to the same thing are also equal to one another. Since
x2-6x+9 = 49 and
x2-6x+9 = (x-3)2
then, according to the law of transitivity,
(x-3)2 = 49
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-3)2 is
(x-3)2/2 =
(x-3)1 =
x-3
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-3 = √ 49
Add 3 to both sides to obtain:
x = 3 + √ 49
Since a square root has two values, one positive and the other negative
x2 - 6x - 40 = 0
has two solutions:
x = 3 + √ 49
or
x = 3 - √ 49
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2-6x-40 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -6
C = -40
Accordingly, B2 - 4AC =
36 - (-160) =
196
Applying the quadratic formula :
6 ± √ 196
x = —————
2
Can √ 196 be simplified ?
Yes! The prime factorization of 196 is
2•2•7•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 196 = √ 2•2•7•7 =2•7•√ 1 =
± 14 • √ 1 =
± 14
So now we are looking at:
x = ( 6 ± 14) / 2
Two real solutions:
x =(6+√196)/2=3+7= 10.000
or:
x =(6-√196)/2=3-7= -4.000
Two solutions were found :
x = 10
x= -4
Which digit makes this statement true?
?0,003 rounded to the nearest ten thousand is 90,000.
Answer:
9
Step-by-step explanation:
4 or lower means the number stays the same
what can be multiplyed with 10.75 to make 100
Answer:
9.30232558
Step-by-step explanation:
Set up an equation to solve for it. For instance, the following:
[tex]10.75*x=100[/tex]
[tex]x=9.30232558[/tex]
if a >b, then ac> bc true or false?
Answer:
False
Step-by-step explanation:
a>b
Let c> 0 then ac>bc because we are multiplying by a positive number
if c<0 then ac < bc because we are multiplying by a negative number we have to flip the inequality symbol
Since we do not know the value of c, we have to go with false
(ILL MARK BRAINLIEST) For Alexandra's lemonade recipe, 8 lemons are required to make 4 cups of lemonade.
Fill out a table of equivalent ratios and plot the points on the coordinate axes
provided.
Answer:
Check explanation
Step-by-step explanation:
2 lemons, 1 cup8 lemons, 4 cups10 lemons, 5 cupsNoreen can walk 1/3 of a mile in 12 minutes what is her average speed in miles per hour. (this is multiple choice)
A. 36 miles per hour
B. 12 miles per hour
C. 1/4 a mile per hour
D. 1 2/3 miles and hour
ANSWER FAST PLEEEEASE
the rule f(x)=50x - 8.5 represents the amount of a drug in milligrams, f(x), which remains in te blood stream after x hours. evaluate f(1.5)
Answer:
66.5
Step-by-step explanation:
Someone help me please
Answer: jo mama medicine
Step-by-step explanation: 1st one 2nd two!
At a mall, random people are asked what their favorite movie genre is. The results are shown in the table below.
Comedy
40
Sports
36
Animation
25
Romance
18
Drama
32
Horror
15
Documentary
22
Adventure
22
Answer:
what is the question?
210 people were asked.
Find the square root of "-2.5"
Answer:
1.58113883 i
Step-by-step explanation:
√-2.5 is error
1.58113883 i
i the square root of negative one.
Any number times itself is a positive number (or zero), so you can't ever get to a negative number by squaring. Since square roots undo squaring, negative numbers can't have square roots.
Answer:
[tex]1.58\ i[/tex]
Step-by-step explanation:
Step 1: Determine the square root of -2.5
The [tex]\sqrt{-1}[/tex] is equal to i so we can say that [tex]\sqrt{(-1)^2}[/tex] is equal to [tex]\sqrt{i^2}[/tex] which is then equal to [tex]i[/tex]. This means that we have [tex]i\sqrt{2.5}[/tex].
We can then take the square root of 2.5 which is rounded to [tex]1.58\ i[/tex]
Answer: [tex]1.58\ i[/tex]
Help please
3. A line passes through the points -6,-8 and -3,-7. What is the equation of the line in slope intercept form?
A. Y = 3x - 6
B. Y = 1/3x + 6
C. Y = 1/3x - 6
D. Y = 3x + 6
Answer:
the answer is C
Step-by-step explanation:
yeah-ya.... right?
Find the value of (2^2)^3. Then find the value of (2^3)^2. what is true about the results? Explain why.
Answer:
(2^2)3 = 2^6
(2^3)2 = 2^6
Step-by-step explanation:
There are various exponent rules. The problems that you were assigned must follow the power of a power rule:
(x^a)^b = x^a*b
Exponents must be multiplied according to this rule. Hope this helps.
The marks scored by a group of students in English examination are as follows: 30,32, 33, 31, 32, 33, 34, 35, 33, 34 . Find the mode of their marks.
Answer:
33
Step-by-step explanation:
33 appears most.
a. What is the length of the bedroom on the scale drawing?
b.
What is the width of the bedroom on the scale drawing?
PLEASE HELP ME
Given the coordinates below, what is AB and what is the midpoint of AB
A (-6, -10), B (2, 5)
Answer:
A. 17
Step-by-step explanation:
At a bookstore used hardcover books sell for $8 each and used softcover books sell for $2 each. You purchase 36 used books and spend $144. How many softcover books do you buy?
Answer:
Step-by-step explanation:
Let H be the number of harcover, and S the number of softcover books.
We know that:
H+S=36
and $8*(H) + $2*(S) = $144
Rearrange the first: H = 36 - S
Use this definition of H in the second equestion:
$8*(H) + $2*(S) = $144
$8*(36-S) + $2*(S) = $144
$288 - 8S + 2S = $144
-6S = -144
S = 24
This means H = 36 - S is:
H = 36 - 24
H = 12
"You" purchased 24 softcover and 12 hardcover books.
Check the results: 24*2 + 12*8 = 48 + 96 = $144 It
works.
simply the following
Answer:
6x^6..........................
help help help help help help help
Answer:
9. A: 3:00 A.M.
10. C: 6.535 kg
11. D: Php 1,600.00
12. D: 217,500
13. A: P450.00
14. A: 7
15. D: 5.48 x 10^4
Determina si los pares de líneas son paralelos, perpendiculares o ninguno de los dos.
Selecciona la respuesta correcta para las partes identificadas con letras.
a. x - 5y = 10; y = x + 4
(select)
b.
x+y =
+ y = 8; y = -7x
(select)
c. 5x – 3y = -1; 5y = -3x + 2 ||(select)
(select)
d. y = 4x - 1; 12x – 3y = 12
e. 5y = 3x + 1; 10x + 6y = 12 | (select)
Answer:
256
Step-by-step explanation:
Find the slope of the line that passes through (-1, -1) and (98, 87).
The question gives us two points, (-1, -1) and (98, 87), from which we can find the slope and later the equation of the line.
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (87 - (-1)) ÷ (98 - (-1))
= (88) ÷ (99)
= ⁸/₉
Checking my answer visually:
Finding the Equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. Once we have that equation, we can graph it to see if it passes through the two points. If it does, then we calculated the slope correctly.
⇒ y - (-1) = ⁸/₉ (x - (-1) [using the point (-1, -1)]
y + 1 = ⁸/₉ (x + 1)
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
help, i need 3x+2y=-3 in slope intercept form and ive never been taught how to do it :/
Answer: y = -1.5x - 1.5 or y = -3x/2 -3/2
Step-by-step explanation:
Basically you need to know first what slope intercept form is:
y = mx + b
b is the y intercept and m is the slope
so first you have the equation 3x + 2y = -3
you will first subtract 3x from both sides because if you do something to one side of the equal sign, you have to do it to the other side:
3x + 2y - 3x = -3 - 3x
now you have 2y = -3x -3
Then you are going to divide both sides by 2:
2y/2 = -3x/2 -3/2
That gets you to
y = -3x/2 -3/2
or in fraction form, it is
y = -1.5x - 1.5
Answer:
Step-by-step explanation:
The slope intercept form uses y=mx +b where m is the slope. To convert the equation into slope intercept form you just need to isolate y.
3x+2y=-3
subtract 3x from both sides
2y= -3x-3
divide everything by 2 to isolate y
[tex]y=-\frac{3}{2} x-\frac{3}{2}[/tex]
Which is an equation of the line through (0,0) and (2, -3)?
A. y = 3/2x
B. y = 2/3x
C. y = - 2/3x
D. y = -3/2x
The equation of the line passing through the points (0,0) and (2, -3) is y = (-3/2)x. Option D.
To find the equation of the line passing through the points (0,0) and (2, -3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.
Given the points (0,0) and (2, -3), we can calculate the slope as follows:
slope (m) = (change in y) / (change in x)
= (-3 - 0) / (2 - 0)
= -3/2
Now that we have the slope, we can substitute one of the given points and the slope into the point-slope form to find the equation of the line. Let's use the point (0,0):
y - y1 = m(x - x1)
y - 0 = (-3/2)(x - 0)
y = (-3/2)x Option D is correct.
For more such question on equation. visit :
https://brainly.com/question/22688504
#SPJ8
20 students are standing in a line to buy food at football game the first three students spend 24$ on food how much do thr first three stundents spend on food per person
Answer:
The first 3 student spend $8 per person
Step-by-step explanation:
1. $24=3x (divide both sides by 3)
2. $8=x
Hopefully I understood the question correctly
Simplify the expression
-1 - 2/3 (6/7 - 3/7 n)
please help me.... duogqfhefbjehfyugihkbjnfjkhdsg
Answer:
B. 12w + 62 = 242 is the answer Happy to Help :)
Step-by-step explanation:
(m+3)square - (m-5) square
Answer:
16m-16
Step-by-step explanation:
Im not sure that’s the correct answer
Solve for x.
(8x -23)
Answer:
x = 12
Step-by-step explanation:
want is385 rond to ten
Answer:
390
Step-by-step explanation:
5 or more, means round up.
So 385 ( 5 or above ) - round to the nearest tenths place...
= 390
Answer:
390
Step-by-step explanation:
The number in the tenth place is 80 so you look on the right, the number is 5. If the number is 5 or above, that means you go up. SO it's 390
Which of the following could be the number shown on the number line?
O A. 35
B. 738
C. 30
O D. 37
Pllllzzzzz help
Answer: A) √35
Step-by-step explanation:
You can notice that the point is in the interval (5 ; 6 )That is , we can write in this form:[tex]5<x<6[/tex] ; where x is our point that lies on the segment (5 ; 6 )Let 's write down 5 and 6 in this form[tex]5=\sqrt{25} \ \ ; \ \ 6=\sqrt{36 }[/tex] [tex]\sqrt{25} <x<\sqrt{36} \Longrightarrow x \ can \ be \ equal \ to \ \sqrt{35} \ and \ \sqrt{30 } \\\\ But \ since \ the \ point \ is \ closer \ to \ point \ 6, \ then \ \boxed{x=\sqrt{35} }[/tex]