Answer:
y= ¼x +1
Step-by-step explanation:
Rewriting the equation into the slope-intercept form (y= mx +c, where m is the gradient and c is the y- intercept):
4y -x= -20
4y= x -20 (+x on both sides)
y= ¼x -5 (÷4 throughout)
Thus, slope of given line is ¼.
Parallel lines have the same gradient.
Gradient of line= ¼
y= ¼x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= 3,
3= ¼(8) +c
3= 2 +c
c= 3 -2
c= 1
Hence the equation of the line is y= ¼x +1.
If 4x + 2y = 14 and x - 2y = 6, what is the value of y?
Answer:
y is -1
Step-by-step explanation:
[tex]4x + 2y = 14 - - - (a) \\ x - 2y = 6 - - - (b)[/tex]
(a) + (b):
[tex]5x = 20 \\ x = 4[/tex]
therefore:
[tex]x - 2y = 6 \\ 4 - 2y = 6 \\ 2y = - 2 \\ y = - 1[/tex]
Answer:
y must be -1
Step-by-step explanation:
We are given the system of linear equations
4x + 2y = 14
x - 2y = 6
and need to find the value of y. Combining the two equations yields
5x = 20, and so we know that x must be 4.
If x is 4, then the second equation becomes 4 - 2y = 6, or -2y = 2.
Then y must be -1.
Help with this question please!!!!
Answer:
I think that the answer is 5
Solve for x. Leave your answer in simplest radical form. *Giving brainliest*
Answer:
x= 10.630145
I hope it's helps you
Can anyone help me with this?
8.6
Answer:
Solution given:
[tex]\bold{\sqrt{74}=8.60232526704≈8.6}[/tex]
Answer:
[tex]8.6[/tex]
Step-by-step explanation:
Step 1: Find the approximate value of [tex]\sqrt{74}[/tex]
[tex]\sqrt{74}[/tex]
[tex]\sqrt{74}[/tex] ≈ [tex]8.6[/tex]
Answer: [tex]8.6[/tex]
Can someone find this for me please?
Answer:
the larger one is 183
Step-by-step explanation:
[tex]x + y = 262 \\ x - y = 104 \\ y = 262 - x \\ x - (262 - x) = 104 \\ x - 262 + x = 104 \\ 2x = 104 + 262 \\ 2x = 366 \\ x = 183 \\ y = 262 - 183 \\ y = 79[/tex]
.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
What is the constant of variation?
What is the equation representing the direct variation?
Answer:
The constant of variation is 1/9
The equation representing the direct variation is y/x= 1/9
Step-by-step explanation:
In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get
y/x = k
3 / 27 = k
(3/27) / (3/3) = 1/9* = k
Therefore, the constant of variation is 1/9
Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation
* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both
The constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation of direct variation is given by,
y = kx ....(i) where "k" is a constant.
Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
Given that y varies directly with x, and x = 27, then y = 3.
Substitute the values of y = 3 and x = 27 in the direct variation equation and solve for k:
⇒ 3 = 27k
⇒ k = 3/27
⇒ k = 1/9
Substitute the values of k = 1/9 in the direct variation equation :
⇒ y = (1/9)x
Thus, the constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.
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Ross took a survey of his classmates' preferred food as well as recording their genders. The results are in the table below:
Answer:
30 people took part in the survey
Step-by-step explanation:
5+7+6+5+4+3= 30
Look at this graph:
100
90
80
70
60
50
40
30
20
10
х
0
10 20 30 40 50 60 70 80 90 100
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
See pic below.
slope = 2/3
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
2x+3y=19 // 6x+2y=22
Answer:
(2, 5 )
Step-by-step explanation:
Given the 2 equations
2x + 3y = 19 → (1)
6x + 2y = 22 → (2)
Multiplying (1) by - 3 and adding to (2) will eliminate the x- term
- 6x - 9y = - 57 → (3)
Add (2) and (3) term by term to eliminate x
0 - 7y = - 35
- 7y = - 35 ( divide both sides by - 7 )
y = 5
Substitute y = 5 into either of the 2 equations and solve for x
Substituting into (1)
2x + 3(5) = 19
2x + 15 = 19 ( subtract 15 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
solution is (2, 5 )
Complete the steps to solve the equation. 9 – 4x = 2x 1. Addition property of equality: 9 = 6x 2. Division property of equality: = x
Answer:
x = 3/2
Step-by-step explanation:
Given:
9 - 4x = 2x
Step 1: Addition property of equality
9 - 4x + 4x = 2x + 4x
9 = 6x
Step 2: Division property of equality:
9 = 6x
9/6 = 6x/6
9/6 = x
x = 9/6
= 3/2
x = 3/2
Check:
9 - 4x = 2x
9 - 4(3/2) = 2(3/2)
9 - 12/2 = 6/2
9 - 6 = 3
3 = 3
what is value of y and x if 3x+2y=2 and 2x+3y=4
We need to form a system of equations:
3x + 2y = 2
2x + 3y = 4
Now, we can multiply the first equation by 2, and the second equation by 3, to even out the coefficients by the variables (to make them the same thing).
6x + 4y = 4
6x + 9y = 12
Next, we can subtract the second equation from the first. We get:
0x - 5y = -8
Then this becomes:
-5y = -8
÷-1 ÷-1
5y = 8
÷5 ÷5
y = 1.6
Substitute 1.6 for y in one of the equations:
2x + 3(1.6) = 4
2x + 4.6 = 4
2x = -0.6
÷2 ÷2
x = -0.3
Answer: [tex]\Large \boldsymbol{(-0,4 \ \ ; \ \ 1,6)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} - \left \{ {{3x+2y=2} \ \ |\times3\atop {2x+3y=4}\ \ |\times2} \right. => \\\\\\\ 9x-4x+6y\!\!\!\!\!\!\diagup-6y\!\!\!\!\!\!\diagup=6-8 \\\\5x=-2 \\\\x=-0,4 \ \ ; \ \ y=(2+1,2):2 =1,6[/tex]
if 1/a=1/b+1/c+1/d find c when a=2, b=3 and d=5
guys help me with this question please
Answer:
c is -30
Step-by-step explanation:
I. 1/a - 1/b - 1/d = 1/c
II. 1/2 - 1/3 - 1/5 = 1/c
III. (15-10-6)/30 = 1/c
IV. -1/30 = 1/c
V. so c.value is -30
write 3/2 4/5 8/5 in decimal notation
Answer:
hope it will help you Mark me as a brilliant
help please I'll give brainliest
Answer:
35
Step-by-step explanation:
6:5
We need to get the first number to 43
6*7 = 42
Multiply each term by 7
6*7 : 5*7
42 : 35
If x^2-ax+b and x^2-cx+d both have a factor x-m prove that m=d-b/c-a
Answer:
see explanation
Step-by-step explanation:
Given (x - m) is a factor of both then x = m make both expressions equal to zero.
m² - am + b = 0
m² - cm + d = 0
Then
m² - am + b = m² - cm + d ( subtract m² - cm from both sides )
cm - am + b = d ( subtract b from both sides )
cm - am = d - b ← factor out m from each term on the left side
m(c - a) = d - b ← divide both sides by (c - a)
m = [tex]\frac{d-b}{c-a}[/tex] ← as required
answer + explanation would be appreciated
Answer:
-2 + 2i
Step-by-step explanation:
[tex](1 + i)^{3}[/tex]
i = [tex]\sqrt{-1}[/tex]
[tex](1 + \sqrt{-1})^3[/tex]
[tex][(1 + \sqrt{-1})(1 + \sqrt{-1})] (1 + \sqrt{-1})[/tex]
distribute the first 2 expressions
(1 + 2[tex]\sqrt{-1}[/tex] - 1 ) [tex](1 + \sqrt{-1})[/tex]
distribute
1 + 2[tex]\sqrt{-1}[/tex] - 1 +
combine like terms
-2 + 2 [tex]\sqrt{-1}[/tex]
which is -2 + 2i
How many times more ?
Answer:
1.3
Step-by-step explanation:
bc for each time x increases by 1, it multiplies by 1.3
i cant think of any other way to explain it
but i hope this helped :D
Answer:
1.3 times
Step-by-step explanation:
f(x)= 68 (1.3) ^x
it, means each year, the expected number of squirrels is 1.3 times, the number the year before.
x=0 so, f(0)=68
New x=1, so f(1)= 68(1.3)¹
= 68 × 1.3
f (1)= f(0) × 1.3
So, 1.3 times
OAmalOHopeO
If $a$ and $b$ are positive integers such that $\gcd(a,b)=210$, $\mathop{\text{lcm}}[a,b]=210^3$, and $a
Answer:
[tex]a * b = 210^4[/tex]
Step-by-step explanation:
Given
[tex]a,b>0[/tex]
[tex]gcd(a,b) = 210[/tex]
[tex]lcm(a,b) = 210^3[/tex]
Required
The product of a and b --- missing from the question
To do this, we make use of the following formula:
[tex]a * b = gcd(a, b) * lcm(a, b)[/tex]
So, we have:
[tex]a * b = 210 * 210^3[/tex]
Using the product law of indices, we have:
[tex]a * b = 210^4[/tex]
This means that the product of a and b gives [tex]210^4[/tex]
please help me T-T.......
Hi
1) f(x)= 0.9 x
2) g(x) = x-100
3) f °g. is first apply g then f. so :
f°g = 0.9 ( x-100) = 0.9x-90
4) g°f. is first apply f then g
so g°f = (0.9x) -100 = 0.9x-100
I let you conclude which is the best deal :)
2. For all real numbers x and y, (2x + 3y)² = ?
Answer:
Step-by-step explanation:
(a + b)² = a² + 2ab + b²
a = 2x ; b = 3y
(2x)²= 2x * 2x = 4x²
(3y)² =3y * 3y = 9y²
(2x + 3y)² = (2x)² + 2 *2x*3y + (3y)²
= 4x² + 12xy + 9y²
How many significant digits are there in the number 1.00250? OA) 7 OB) 6 OC) 5 OD) 4
Answer:
OB
Step-by-step explanation:
start counting from 1
Then your significant digit is 6
Find the slope of the line that passes through (-26, 9) and (32, 71).
Answer:
[tex]Slope = \frac{31}{29}[/tex]
Step-by-step explanation:
Step 1: Define the slope formula
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Step 2: Find the slope
[tex]Slope = \frac{71-9}{32-(-26)}[/tex]
[tex]Slope = \frac{62}{58}[/tex]
[tex]Slope = \frac{31}{29}[/tex]
Answer: [tex]Slope = \frac{31}{29}[/tex]
6. Solve for x!! please help!
x/2 = -7
=> x = -7 × 2
=> x = -14
Answer:
x=-14
Step-by-step explanation:
[tex]\frac{x}{2} =-7\\\\x=-14\\[/tex]
is there any responsible way to use student loans why or why not
Answer:just use your student loans that you need as a student don’t waste it on games or unnecessary things.
Step-by-step explanation:
Write an inequality and show on a number line all numbers:
less than 4 but greater than or equal to 0
Answer:
the inequality is 0<x<4
Step-by-step explanation:
(0,4)
Find the value of -3x + 5,
if –3 + 4x = -19
Answer:
17
Step-by-step explanation:
Solve the equation for x then plug that into the 1st expression.
-3 + 4x = -19
4x = -19 + 3
4x = -16
x = -4
then
-3x + 5
-3(-4) + 5 = 12 + 5 = 17
I NEED HELP ASAPPP!!!! It’s urgentttttt!!!!
Answer: (x - 2)² + (y - 14)² = 1
Step-by-step explanation:
Concept:
Here, we need to know the idea of the circle formula.
Circle formula: (x - h)² + (y - k)² = r²
Center = (h, k)
Radius = r
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
Center = (2, 14)
Radius = 1
Given formula
(x - h)² + (y - k)² = r²
Substitute the value into the formula
(x - 2)² + (y - 14)² = (1)²
Simplify
(x - 2)² + (y - 14)² = 1
Hope this helps!! :)
Please let me know if you have any questions
For the polynomial, (((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)
a. Determine the coefficient of x^3.
b. Determine the coefficient of x^6.
c. Determine the constant of the term
polynomial.
d. Determine the degree of the polynomial.
Answer:
Hello,
Step-by-step explanation:
[tex](((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)\\\\=\dfrac{x^3}{5} +\dfrac{3*x}{5} +\dfrac{2}{5} +\dfrac{5*x^2}{2} -x^6\\\\\\=-x^6+0x^5+0x^4+\dfrac{x^3}{5} +\dfrac{5*x^2}{2} +\dfrac{3*x}{5}+\dfrac{2}{5} \\\\\\a)\ \dfrac{3}{5} \\\\b)\ -1\\\\c)\\degree=6\\[/tex]
PLEASE HELP ASAPP :(
Find the area of triangle ABC.
Answer Options:
A. 18.52 units²
B. 12.16 units²
C. 15.14 units²
D. 31.27 units²
Answer:
Option C, 15.14 units²
Step-by-step explanation:
area of the triangle,
6.82×5.04×sin(61.73)/2
= 15.1365001284..
= 15.14 units² (rounded to the nearest tenth)
The required area of the irregular triangle is 15.14 unit². Option C is correct.
Given that,
A figure of the triangle is shown,
Side AB = a =6.82
Side BC = b = 5.04
Angles, ∠A = 45.03°, ∠B = 61.73°.
The triangle is a geometric shape which includes 3 sides and the sum of the interior angle should not be greater than 180°.
Altitude is perpendicular bisector to the side of the triangle from the opposite vertex of the triangle.
The area of the given triangle can be given as,
Area = 1/2 * a * b sinB
= 1/2 * 6.82 * 5.04 * sin61.73°
= 1/2 * 6.82 * 5.04 * 0.88
= 15.14 unit²
Thus, the required area of the irregular triangle is 15.14 units². Option c is correct.
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BRAINLEST IF CORRECT
Answer:
422.39
Step-by-step explanation:
[tex]A = \pi r^2\\A = 144\pi \\\\144\pi -30 = 422.39[/tex]
use a calculator for the above and round