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2 years ago

Simplify the linear expression

Mathematics

1 answer:

vekshin12 years ago

5 0

Answer:

$\huge\boxed{-\frac{7}{8}a - \frac{1}{6}}$

Step-by-step explanation:

This question utilizes combining like terms and common denominators. First you have to convert both terms including "a" to have a denominator of 8. You would do this by multiplying both the numerator, and the denominator by the same value. This value in the case of $-\frac{1}{4} a$ would be 2, and in the case of $\frac{2}{3}$ the value would be 2. This would result in the equation: $-\frac{5}{8}a+\frac{4}{6}-\frac{2}{8}a-\frac{5}{6}$ . Then simply combine like terms to get your final answer.

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Find the intersection points using substitution or elimination for each system of equations:

natka813 [3]

Answer:

Step-by-step explanation:

Okay, so I think I know what the equations are, but I might have misinterpreted them because of the syntax- I think when you ask a question you can use the symbols tool to input it in a more clear way, otherwise you can use parentheses and such.

Problem 1:

(x²)/4 +y²= 1

y= x+1

*substitute for y*

Now we have a one-variable equation we can solve-

x²/4 + (x+1)² = 1

x²/4 + (x+1)(x+1)= 1

x²/4 + x²+2x+1= 1

*subtract 1 from both sides to set equal to 0*

x²/4 +x^2+2x=0

x²/4 can also be 1/4 * x²

1/4 * x² +1*x² +2x = 0

*combine like terms*

5/4 * x^2+2x+ 0 =0

now, you can use the quadratic equation to solve for x

a= 5/4

b= 2

c=0

the syntax on this will be rough, but I'll do my best...

x= (-b ± √(b²-4ac))/(2a)

x= (-2 ±√(2²-4*(5/4)*(0))/(2*(5/4))

x= (-2 ±√(4-0))/(2.5)

x= (-2±2)/2.5

x will have 2 answers because of ±

x= 0 or x= 1.6

now plug that back into one of the equations and solve.

y= 0+1 = 1

y= 1.6+1= 2.6

Hopefully this explanation was enough to help you solve problem 2.

Problem 2:

x² + y² -16y +39= 0

y²- x² -9= 0

6 0

3 years ago

Go step by step to reduce the radical.

zysi [14]

2x16 is 32 so you would take square root of 16 out which is 4 and leave the 2 inside. So the answer is 4sqrt(2)

4 0

2 years ago

Can anyone help me solve 23, 24?

zimovet [89]

Answer:

Problem 23) $y=3x+6$

Problem 24) $y=-\frac{1}{3}x-5$

Step-by-step explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(0,2)\ B(3,1)$

Substitute the values

$m=\frac{1-2}{3-0}$

$m=-\frac{1}{3}$

step 2

Problem 23

we know that

If two lines are perpendicular then the product of its slopes is equal to minus 1

$m1*m2=-1$

Find the slope of the line

we have

$m1=-\frac{1}{3}$

substitute in the equation and solve for m2

$(-\frac{1}{3})*m2=-1$

$m2=3$

with the slope m2 and the point $(0,6)$ find the equation of the line

Remember that

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=3$

$b=6$ -----> the given point is the y-intercept

substitute

$y=3x+6$

step 3

Problem 24

we know that

If two lines are parallel, then its slopes are the same

with the slope m1 and the point $(0,-5)$ find the equation of the line

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{3}$

$b=-5$ -----> the given point is the y-intercept

substitute

$y=-\frac{1}{3}x-5$

8 0

3 years ago

Find the product of (3^6)(3)(3^5) Express your answer using exponents

VikaD [51]

Answer:

3^12

Step-by-step explanation:

When multiplying the same number with different exponents you have to add the the exponents. For example:

$a^x + a^y = a ^{x+y}$

So (3^6)(3)(3^5) or (3^6)(3^1)(3^5) = 3^(6+1+5) = 3^12

6 0

3 years ago

Read 2 more answers

7.22 (10b-3) =7b-14

faust18 [17]

Multiply 7.22 onto 10b and -3
new equation - 72.2b-21.66=7b-14

add 21.66 onto -14
new equation - 72.2b=7b+7.66

subtract 7b from 72.2
new equation: 65.2b=7.66

divide 65.2 from b
new equation: b=7.66/65.2

final answer: b=0.117

3 0

3 years ago