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Anastasy [175]
3 years ago
13

If r is five less than three times l, then r = A)3l - 5 B)5 - 3l C)5l - 3 D)3(l - 5)

Mathematics
2 answers:
marshall27 [118]3 years ago
8 0

Answer:  The correct option is

(A) r=3l-5.

Step-by-step explanation:  Given that r is five less than three times l.

We are to write the expression for r.

We have

5 less than three times l can be written as follows :

3\times l-5=3l-5.

Since this is equal to r, so the expression can be written as

r=3l-5.

Thus, the required answer is r=3l-5.

Option (A) is CORRECT.

masha68 [24]3 years ago
3 0
The answer is A) 3I-5
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What angle is this and explain
REY [17]

The measures of the angles are 59 degrees

<h3>How to determine the value of the angles?</h3>

The angles are given as:

Angle 1 = 2x + 17

Angle 2 = 3x - 4

By the interior angle theorem, the angles are congruent

So, we have

Angle 1 = Angle 2

Substitute the known values in the above equation

2x + 17= 3x - 4

Collect the like terms

3x - 2x = 17 + 4

Evaluate the like terms

x = 21

Substitute x = 21 in Angle 1 = 2x + 17

Angle 1 = 2 * 21 + 17

Evaluate

Angle 1 = 59

This means that

Angle 1 = Angle 2 = 59

Hence, the measures of the angles are 59 degrees

Read more about angles at:

brainly.com/question/25716982

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8 0
1 year ago
(a) If G is a finite group of even order, show that there must be an element a = e, such that a−1 = a (b) Give an example to sho
Dahasolnce [82]

Answer:

See proof below

Step-by-step explanation:

First, notice that if a≠e and a^-1=a, then a²=e (this is an equivalent way of formulating the problem).

a) Since G has even order, |G|=2n for some positive number n. Let e be the identity element of G. Then A=G\{e} is a set with 2n-1 elements.

Now reason inductively with A by "pairing elements with its inverses":

List A as A={a1,a2,a3,...,a_(2n-1)}. If a1²=e, then we have proved the theorem.

If not, then a1^(-1)≠a1, hence a1^(-1)=aj for some j>1 (it is impossible that a^(-1)=e, since e is the only element in G such that e^(-1)=e). Reorder the elements of A in such a way that a2=a^(-1), therefore a2^(-1)=a1.

Now consider the set A\{a1,a2}={a3,a4,...,a_(2n-1)}. If a3²=e, then we have proved the theorem.

If not, then a3^(-1)≠a1, hence we can reorder this set to get a3^(-1)=a4 (it is impossible that a^(-1)∈{e,a1,a2} because inverses are unique and e^(-1)=e, a1^(-1)=a2, a2^(-1)=a1 and a3∉{e,a1,a2}.

Again, consider A\{a1,a2,a3,a4}={a5,a6,...,a_(2n-1)} and repeat this reasoning. In the k-th step, either we proved the theorem, or obtained that a_(2k-1)^(-1)=a_(2k)

After n-1 steps, if the theorem has not been proven, we end up with the set A\{a1,a2,a3,a4,...,a_(2n-3), a_(2n-2)}={a_(2n-1)}. By process of elimination, we must have that a_(2n-1)^(-1)=a_(2n-1), since this last element was not chosen from any of the previous inverses. Additionally, a_(2n1)≠e by construction. Hence, in any case, the statement holds true.

b) Consider the group (Z3,+), the integers modulo 3 with addition modulo 3. (Z3={0,1,2}). Z3 has odd order, namely |Z3|=3.

Here, e=0. Note that 1²=1+1=2≠e, and 2²=2+2=4mod3=1≠e. Therefore the conclusion of part a) does not hold

7 0
3 years ago
Write and equivalent expression to 8(4x+3)<br><br><br> Write an equivalent expression to 0.5(2x+4)
Serhud [2]

Answer:

8(4x + 3) = 32x + 24

0.5(2x + 4) = x + 2

4 0
2 years ago
Jose bought 1.5 pounds of apples for $3.60.<br><br> How much would 3/4 of a pound of apples cost?
Vladimir [108]

Answer:

$1.80 is the cost for 3/4 of a pound of apples. If you divide 1.5 over 2, it would be 3/4, which means you will divide the price too, 3.60/2 = $1.80

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The combined area of a pair of congruent rectangles can be represented, in square units, by the expression 18y^2-818y 2 −8. The
sveta [45]

Answer:

Perimeter = 12y

Step-by-step explanation:

Given

Area = 18y^2 - 8 -- two rectangles

Required

Determine the perimeter of one of the rectangles

First, calculate the area (A) of 1 rectangle

A =\frac{1}{2}Area

A =\frac{1}{2}(18y^2 - 8)

A =9y^2 - 4

Express as difference of two squares

A =(3y - 2)(3y+2)

Area is calculated as:

A = Length * Width

So, by comparison:

Length = 3y - 2

Width = 3y + 2

The perimeter is:

Perimeter = 2 *(Length + Width)

Perimeter = 2 *(3y-2+3y+2)

Collect Like Terms

Perimeter = 2 *(3y+3y-2+2)

Perimeter = 2 *(6y)

Perimeter = 12y

8 0
2 years ago
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