Two sides of a triangle have lengths 10 and 15 what must be true about length of the third side

Answers

Answer 1

Answer: x - length of the 3rd side
$10+15>x \wedge 10+x>15 \wedge 15+x>10\n x<25 \wedge x>5 \wedge x>-5\n x\in(5,25)$

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HELP ); Match each function formula with the corresponding transformation of the parent function y = - (x + 2)2.

1. y = - (x + 4)2
2. y = - (x + 2)2 - 2
3. y = (x - 2)2
4. y = 2 - (x + 2)2
5. y = -x2
6. y = (x + 2)2

A. Reflected across the x-axis and the y-axis

B. Translated right by 2 units

C. Translated up by 2 units

D. Reflected across the x-axis

E. Translated left by 2 units

F. Translated down by 2 units

Answers

Always remember general rules of transformation.

1) Vertical Shift:

y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.

2) Horizontal Shift:

y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.

3) Reflection across x-axis

y= - f(x) ; reflect the graph of f across the x-axis.

Now,

The parent function is y= -(x+2)²

1. y= -(x+4)²

In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²

So, according to rule 2 it will shift the parent function to the left by 2 units.

E is the correct option.

2. y = - (x + 2)² - 2

In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2

So, according to rule 1, it will shift the graph down by 2 units.

F is the correct option.

3. y=(x - 2)²

In this question, two operations are performed on the parent function.

First one, -4 is added with x+2 so we get x+2-4= x-2

Second one, -1 is multiplied with parent function.

By performing the two operations at a time we get a new function which is

y=-(-(x+2-4)²)=(x-2)²

The first operation will translate the parent function 4 units right (according to rule 2).

The second operation will reflect the graph across x-axis(according to rule 3).

D and translation 4 units to right is correct option.

4. y= 2 -(x+2)²

In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.

C is the correct option.

5. y= -x²

In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²

So, according to rule 2 it will shift the graph right by 2 units.

B is the correct option.

6. y= (x+2)²

In this question, -1 is multiplied with parent function and we get

y= -(-(x+2)²)= (x+2)²

So, according to rule 3 , graph is reflected across x-axis.

D is the correct answer.

The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).

Write standard form of the equation of the line described.Through (2,0) parallel to y =2/3x

Answers

$y=(2)/(3)x , \ \ (2,0)\n \n m=(2)/(3) \n \n The \ slope \ of \ lines \ parallel \ is \ the \ same \n \n use \ y = mx + b \ and \ the \ point \ (2,0) \ to \ find \ b \n \n 0= -(2)/(3)\cdot 2+b$

$0=-(4)/(3) +b \n \nb=-(4)/(3) \n \ny=-(2)/(3)x+(4)/(3)$

L onUURS allu ueposits in transit in the are added to the bank statement balancedeposits to 75. l of the following are reasons touse an estimated method of costing inventory excepta. Interim financial statements are required but physicalimventory is only taken at the end of the financialaccounting period.b. A disaster has destroyed the inventory records and the inventory.c. Perpetual inventory records are not maintained.d. Purchase records are not maintained.

Answers

The right answer for the question that is being asked and shown above is that: ".b. A disaster has destroyed the inventory records and the inventory."L onUURS allu ueposits in transit in the are added to the bank statement balancedeposits to 75.

Use long division to divide x3 + x2 - 2x + 14 by x + 3.

Answers

To solve the problem we must know about Expressions.

What is Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The solution to the problem is $x^2-2x+4 + (2)/(x + 3)$ .

To find

divide x3 + x2 - 2x + 14 by x + 3

Solution

$(x^3 + x^2 - 2x + 14)/(x + 3)$

$= x^2+( -2 x^2 - 2x + 14)/(x + 3)$

$= x^2-2x+(4x + 14)/(x + 3)$

$= x^2-2x+4 + (2)/(x + 3)$

Hence, the solution to the problem is $x^2-2x+4 + (2)/(x + 3)$ .

Learn more about Division:

brainly.com/question/12978781

Answer:

x^2 - 2x + 4 + 2/x+3

Hope this helps.

2^1-x=3^2x-3 solve for X

Answers

Hello,

if the exact equation is

$2^(1-x)=3^(2x-3)$

==>(1-x)ln 2=(2x-3) ln 3

==>2x ln 3+x ln 2=ln 2 +3 ln 3

==>x=ln (2*3^3) / ln (2*3²)

==> x= ln(54)/ ln (18)

==>x ≈1,3800937....

if the equation is 2^1 -x =3^2 *x -3 then

2-x=9x-3
==>10x=5
==>x=1/2

Solve 4(x - 3) - 2x - 1) > 0

Answers

Answer:

x > 5.5

Step-by-step explanation:

4(x - 3) - (2x - 1) > 0

4x - 12 - 2x + 1 > 0

4x - 2x - 11 > 0

2x - 11 > 0

2x - 11 + 11 > 0 + 11

2x > 11

2x ÷ 2 > 11 ÷ 2

x > 5.5

Answer:

x>13/2

Step-by-step explanation:

4x-12-2x-1>0

2x-13>0

2x>13

X>13/2

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