MATHEMATICS HIGH SCHOOL

What is the difference in simplest form? (n^2+10n+21/n^2+3n-28)-(3n/n-4)

Answers

Answer 1

Answer:

Answer:

$(3-2n)/(n-4)$

Step-by-step explanation:

We have been given the expression

$(n^2+10n+21)/(n^2+3n-28)-(3n)/(n-4)$

Let us write the numerator and denominator of first expression in factored form using AC method.

$n^2+10n+21\n=n^2+7n+3n+21\nn(n+7)+3(n+7)\n(n+7)(n+3)$

And the factors of denominator is

$n^2+3n-28\n=n^2+7n-4n-28\nn(n+7)-4(n+7)\n(n+7)(n-4)$

Therefore, the expression becomes

$((n+7)(n+3))/((n+7)(n-4))-(3n)/(n-4)\n\n\text{Cancel the common terms}\n\n(n+3)/(n-4)-(3n)/(n-4)\n\n\text{Denominator of both rational expression is same}\n\text{hence, we can directly add the numerators}\n\n(n+3-3n)/(n-4)\n\n(3-2n)/(n-4)$

Thus, the simplified form is $(3-2n)/(n-4)$

Answer 2

Answer:

The answer is $(-2n+3)/(n-4)$

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Solve the equation. Check for extraneous solutions.
What is the inequality of 0.3(0.3x+0.8)<-0.3
What is the solution to the equation?5(8 + 7) = 5 • x + 5 • 7 A. x = 1 B. x = 5 C. x = 7 D. x = 8

What is the inverse of the logarithmic function f(x)= log2x.

Answers

Answer:

the inverse is :10^x/2

Step-by-step explanation:

f(x)= log2x.

f^-1(x)=10^x/2

find the lateral area and surface area of a right cone with radius 6 in. and height 8 in. give your answers in terms of pie

Answers

$r=6in\n\nH=8in\n\nA=\pi rl\n\nPythagoras\ theorem:\n\nr^2+H^2=l^2\n\nl^2=6^2+8^2\n\nl^2=36+64\n\nl^2=100\n\nl=√(100)\n\nl=10\ (in)$

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PLEQAEEEE HELPPP MEEE

Answers

Answer:

Box 2 : ( 1,5,3,10,9)

[(5-3)×1]-(10-9)

(2*1)-1 =1

Box 3 : {1,6,2,8,7,4}

(1+6+3 -7)- (8÷4) =

10-7-2 = 1

Answer:

2) 1 · 5 + 9 - 3 - 10 = 1

3) 1 · 8 + 6 - 2 - 4 - 7 = 1

Solve - 2x - 8> 3x + 12.
Please help!

Answers

Answer:

B. X < -4

Step-by-step explanation:

-2x - 8 > 3x + 12

Subtract 3x from both sides

-5x -8 > 12

Add 8 both sides

-5x > 20

Divide -5 both sides

X < -4

Answer: x < -4

Step-by-step explanation:

Subtract 3x from both sides

-5x - 8 > 12

Add 8 to both sides

-5x > 20

Divide both sides by -5

x < -4

How many solutions are there to the following system of equations? 2x+5y=-11
10x+25y=-55

A. 0
B. 2
C. 1
D. Infinitely many.

Answers

If you would like to know how many solutions are there to the following system of equations, you can calculate this using the following steps:

2x + 5y = -11 /*(-5)
10x + 25y = -55
_______________
-10x - 25y = 55
10x + 25y = -55
_______________
0 = 0

The correct result would be D. Infinitely many.

Answer:

D. There are infinitely many solutions to the system.

Step-by-step explanation:

Got it correct on edge 2020

Consider the following system of equations: y = −x + 2
y = 3x + 1

Which description best describes the solution to the system of equations?

Line y = −x + 2 intersects line y = 3x + 1.
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
Line y = −x + 2 intersects the origin.

Answers

Answer:

The correct option is A. Line y = −x + 2 intersects line y = 3x + 1.

Step-by-step explanation:

The first equation is given to be :

y = -x + 2

x 0 2

y 2 0

The second equation is :

y = 3x + 1

x 0 -1/3

y 1 0

Now, The graphs of both the equation are attached below :

So, By seeing the graph, We can observe :

Line y = −x + 2 intersects line y = 3x + 1.

Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.

Lines y = −x + 2 and y = 3x + 1 intersect the y-axis

But the description that best describes the solution to the system of equations is : Line y = −x + 2 intersects line y = 3x + 1.

Hence, The correct option is A. Line y = −x + 2 intersects line y = 3x + 1.

y = -x + 2
y = 3x + 1

-x + 2 = 3x + 1
+ x + x
2 = 4x + 1
- 1 - 1
1 = 4x
4 4
¹/₄ = x

y = 3x + 1
y = 3(¹/₄) + 1
y = ³/₄ + 1
y = 1³/₄
(x, y) = (¹/₄, 1³/₄)

The answer is A.

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Complete the table for the equation of the line y = 3x - 1 X f(x) -1 0 2

Can someone please help