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3 years ago

What is the ratio of the corresponding side lengths? 4:9 4:2 26:26 4.5:2

Mathematics

2 answers:

Evgen [1.6K]3 years ago

8 0

Answer:

4:2

Step-by-step explanation:

Tcecarenko [31]3 years ago

4 0

Answer:

4 : 2

Step-by-step explanation:

We are given ΔABC ≅ ΔA'B'C'.

When two triangles are congruent, their corresponding sides and angles are congruent.

Since, the sides of the triangles are in relation,

AB = 2 × A'B' and side BC = 2 × B'C' i.e. 4 = 2 × 2 and 9 = 2 × 4.5.

Therefore, the ratio of the corresponding sides are given by 4 : 2 and 9 : 4.5 i.e. 2 : 1.

Since, the ratio of the corresponding sides comes out to be 2 : 1 = 4 : 2.

Hence, the ratio of the corresponding sides is 4 : 2.

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1) Find the 128th term for the sequence 9, 4, -1, -6, 11,...

Nikitich [7]

To determine an nth term of an arithmetic sequence, we use the expression an = a1 + (n-1)d where a1 is the first term in the sequence, n is the number of the term in the sequence and d is the common difference. For a geometric sequence, it is expressed an = a1r^(n-1). We calculate as follows:

1. a128 = 9 + (128-1)(-5)
a128 = -626

2. a97 = (-3)(-2)^(97-1)
a97 = -2.377x10^29

5 0

3 years ago

The nature of the roots of 3x^2+4x-5=0

Alexxandr [17]

Answer:

Imaginary Roots

Step-by-step explanation:

The quadratic equation ax^2 + bx + c = 0 is written in standard form, and the formula is

x = [-b ± √(b^2 - 4ac)]/ 2a

Given:

3x2 - 4x + 5 = 0'

Here a = 3, b = -4 and c = 5

Substituting:

x = [-(-4) ± √((-4)2 - 4 × 3 × 5)]/ (2 × 3)

Further Simplification:
x = [4 ± √(16 - 60)]/6 ----> Discriminant: b^2 - 4ac = -44 < 0.

x = [4 ± √-44]/ 6

Now, we get:

x = [4 ± 2√-11]/ 6

x = [2 ± i √11]/ 3

Therefore, The best description of the roots of the equation 3x2 - 4x + 5 = 0 is imaginary roots.

7 0

2 years ago

The bookstore sells packages of 15 pens

AlexFokin [52]

Considering the definition of least common multiple, this means that smallest number of packages of each they can buy is 60.

<h3>Least common multiple</h3>

A number is a multiple of another when it contains it exactly n times. In other words, the multiples of a number are the ones you get when you multiply one number by another.

The least common multiple allows us to know what is the smallest number that is a multiple of a certain set of numbers.

One procedure for calculating the least common multiple is to break each number into prime factors. Then the common and uncommon factors are raised to the highest exponent, which must be multiplied.

<h3 /><h3>Smallest number of packages</h3>

To calculate the smallest number of packages of each they can buy, you calculate the least common multiple.

First, the decomposition of the numbers into prime factors is carried out:

15= 3×5

12= 2×2×3= 2²×3

Then, the least common multiple is calculated as 2²×3×5

Solving, the least common multiple between 12 and 15 is 60.

Finally, this means that smallest number of packages of each they can buy is 60.

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8 0

2 years ago

3x+2(x+4)=5(x+1)+3. Show work please

Nesterboy [21]

First, we distribute the 2 through the parenthesis.

3x+2x+8=5(x+1)+3

Then we distribute the 5 through the parenthesis

3x+2x+8=5x+5+3

Collect the like terms

5x+8=5x+5+3

Add the numbers

5x+8=5x+8

The statement is true for any value of x, because both sides are identical

6 0

3 years ago

Find the value of x. Please

Studentka2010 [4]

Answer:

113

Step-by-step explanation:

96+17=113

180-113=67

67+x=180

x=180-67

x=113

7 0

3 years ago