For a craft project, four students each chose three pieces of wire from a box.Don’s wires measure 3 inches, 5 inches, and 12 inches.
Margo’s wires measure 6 inches, 8 inches, and 14 inches.
Sonji’s wires measure 12 inches, 8 inches, and 17 inches.
Liam’s wires measure 16 inches, 8 inches, and 27 inches.

Which student chose pieces that can be used to construct a triangle?

Don
Margo
Sonji
Liam

Answers

Answer 1

Answer:

Answer:

Sonji

Step-by-step explanation:

Given :

We will use the third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

So, applying this property in each case:

Case 1. Don’s wires measure 3 inches, 5 inches, and 12 inches.

Now using property

since sum of two sides = 3+5 =8

But third side 12 is not less than 8

So, Don’s wire cannot be used .

Case 2. Margo’s wires measure 6 inches, 8 inches, and 14 inches.

Now using property

since sum of two side :8+6=14

But third side 14 is not less than 14

So, Margo’s wire cannot be used .

Case 3. Sonji’s wires measure 12 inches, 8 inches, and 17 inches.

Now using property

since sum of two side :12+8=20

third side 17 is less than 20

Now , difference of two sides : 12-8=4

third side 17 is greater than 4

So, Sonji’s wire can be used .

Case 4. Liam’s wires measure 16 inches, 8 inches, and 27 inches.

Now using property

since sum of two side :16+8 =24

But third side 27 is not less than 24

So, Liam’s wire cannot be used .

Hence sonji's wire can be used to construct a triangle

Answer 2

Answer: Sonji's.

The third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other twosides and greater than the difference of the lengths of the other two sides.

Answer:

Hence, we have:

a= 3 and b= 4

Step-by-step explanation:

It is given that:

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).

i.e.

$(a+ib)(2+3i)-i=(-11+5i)(1-i)\n\ni.e.\n\na(2+3i)+ib(2+3i)-i=-11(1-i)+5i(1-i)\n\ni.e.\n\n2a+3ai+2bi+3bi^2-i=-11+11i+5i-5i^2$

Since, we know that :

$i^2=-1$

Hence, we have:

$2a+3ai+2bi-3b-i=-11+11i+5i+5\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-11+5+11i+5i\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-6+16i$

i.e. we have:

$2a-3b=-6---------(1)$

and

$3a+2b-1=16\n\ni.e.\n\n3a+2b=16+1\n\ni.e.\n\n3a+2b=17------------(2)$

On multiplying equation (1) by 2 and equation (2) by 3 we get:

$13a=39\n\ni.e.\n\na=3$

on putting the value of a into equation (1) we get:

$2* 3-3b=-6\n\ni.e.\n\n6-3b=-6\n\ni.e.\n\n-3b=-6-6\n\ni.e.\n\n-3b=-12\n\ni.e.\n\nb=4$

(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16

Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
2(2a-3b=-6)
3(3a+2b=17)
----------------------
   13a=39 ⇒a=39/13=3

3(2a-3b=-6)
-2(3a+2b=17)
----------------------
   -13b=-52 ⇒ b=52/13=4

Answer: a=3;    b=4

Helpppppppppp aasapppp

Answers

Answer:

Step-by-step explanation:

Convert mixed fraction to improper fraction

$-2(2)/(3)=-(8)/(3)\n\n\n-1(1)/(3)=-(4)/(3)$

$-2(2)/(3)$ ÷ $-1(1)/(3) =$ $(-8)/(3)$ ÷ $-(4)/(3)$

$=-(8)/(3)*-(3)/(4)\n\n\n=2 *1 \n\n= 2$

Answer:

Step-by-step explanation:

Simplify the following:

(-(2 + 2/3))/(-(1 + 1/3))

(-(2 + 2/3))/(-(1 + 1/3)) = (-1)/(-1)×(2 + 2/3)/(1 + 1/3) = (2 + 2/3)/(1 + 1/3):

(2 + 2/3)/(1 + 1/3)

Put 1 + 1/3 over the common denominator 3. 1 + 1/3 = 3/3 + 1/3:

(2 + 2/3)/(3/3 + 1/3)

3/3 + 1/3 = (3 + 1)/3:

(2 + 2/3)/((3 + 1)/3)

3 + 1 = 4:

(2 + 2/3)/(4/3)

Put 2 + 2/3 over the common denominator 3. 2 + 2/3 = (3×2)/3 + 2/3:

((3×2)/3 + 2/3)/(4/3)

3×2 = 6:

(6/3 + 2/3)/(4/3)

6/3 + 2/3 = (6 + 2)/3:

((6 + 2)/3)/(4/3)

6 + 2 = 8:

(8/3)/(4/3)

Multiply the numerator by the reciprocal of the denominator, (8/3)/(4/3) = 8/3×3/4:

(8×3)/(3×4)

(8×3)/(3×4) = 3/3×8/4 = 8/4:

8/4

The gcd of 8 and 4 is 4, so 8/4 = (4×2)/(4×1) = 4/4×2 = 2:

Answer: 2

Sam determines the zeros of the function f(x) to be 8 and 7. What could be Sam’s function?1.

f(x) = (x − 8)(x + 7)
2.

f(x) = (x − 8)(x − 7)
3.

f(x) = (x + 8)(x + 7)
4.

f(x) = (x + 8)(x − 7)

Answers

Answer:

2. $f (x) = (x - 8)\cdot (x-7)$

Step-by-step explanation:

Given that function is polynomial, each zero is contained in binomials of the form (x - a), where a is the value of the zero. The number of roots means the number of binomial and the grade of the polynomial. Then, the function has the following form:

$f (x) = (x - 8)\cdot (x-7)$

In cosequence, the right answer is 2.

Option 2: f(x) = (x-8)(x-7)

x-8 = 0 ⇒ x = 8

x-7 = 0 ⇒ x = 7

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude. True or false?

Answers

Answer:

The statement is false.

Step-by-step explanation:

For any vector 'r' we have

$\overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k}$

The magnitude is given by

$|r|=\sqrt{x^(2)+y^(2)+z^(2)}..........(i)$

As we know that the upon squaring a term the result is always positive thus the term in right side of equation i is always positive no matter weather the terms (x,y,z) are positive or negative hence we conclude that magnitude of any vectorial quantity is always positive irrespective of it's direction.

Write 2 + 3x + 4x2 + 3x3 in
standard form.

Answers

2+3x+4x2+3x3 is 2+3+8+9

Step-by-step explanation:

you have to result the multiple firt and then to add the rest operation.

the result of the operation is 57

What happened to the cat who swallowed a ball of yarn?

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