MATHEMATICS HIGH SCHOOL

Emil's backpack weighs six and three eights pounds. He removes a book that weighs three fourth pound. Then he removes a book that weighs one half pound .How much does Emil's back pack weigh now

Answers

Answer 1

Answer:

Answer:

Emil's back pack weigh now $5(1)/(8)\ pounds$ .

Step-by-step explanation:

Given:

Total Weight of backpack = $6(3)/(8)\ pounds$

$6(3)/(8)\ pounds$ can be Rewritten as $(51)/(8)\ pounds$

Weight of backpack = $(51)/(8)\ pounds$

Weight of Book 1 = $(3)/(4)\ pound$

Weight of Book 2 = $(1)/(2)\ pound$

We need to find weight of back pack after removing books.

Solution:

Now we can say that;

weight of back pack after removing books can be calculated by Subtracting Weight of Book 1 and Weight of Book 2 from Total Weight of backpack.

framing in equation form we get;

weight of back pack after removing books = $(51)/(8)-(3)/(4)-(1)/(2)$

Now to solve the equation we will first make the denominator common using LCM.

weight of back pack after removing books = $(51*1)/(8*1)-(3*2)/(4*2)-(1*4)/(2*4)=(51)/(8)-(6)/(8)-(4)/(8)$

Now the denominators are common so we will solve the numerator.

weight of back pack after removing books = $(51-6-4)/(8)=(41)/(8)\ pounds \ \ OR \ \ 5(1)/(8)\ pounds$

Hence Emil's back pack weigh now $5(1)/(8)\ pounds$ .

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Solve for x. 3x+1/14=2x/8

Answers

it depends if it is
1. 3x+(1/14)=(2x)/8 or
2. (3x+1)/14=(2x)/8

if it is 1

1.
3x+(1/14)=2x/8
simplify 2x/8
2x/8=x/4
3x+(1/14)=x/4
find least common multiple of 14 and 4
factors of 14=2 and 7
factors of 4 are 2 and 2 so LCM=2 times 2 times 7=28
multiply both sides by 28
84x+2=7x
subtract 7x from both sides
77x+2=0
subtract 2 from both sides
77x=-2
divide both sides by 77
x=-2/77

2.
(3x+1)/14=2x/8
simpify 2x/8
2x/8=x/4
(3x+1)/14=x/4
find least common multiple of 14 and 4
factors of 14=2 and 7
factors of 4 are 2 and 2 so LCM=2 times 2 times 7=28
multiply both sides by 28
(2)(3x+1)=7x
distribute
6x+2=7x
subtract 6x from both sides
2=x

There were 15 cars and 25 trucks in the parking garage. what is the ratio of cars to total vehicles

Answers

15:25 = 3:5
simply divide 15 and 25 both by 5 to get 3:5.

Andy has two rectangular gardens. His smaller garden is 8 feet long and 4 feet wide. The larger garden is 12 feet long and six feet wide. Which statement correctly describes Andy gardens?a/The gardens are only congruent.
b. The gardens are similar and congruent.
c. The gardens are congruent, but not similar.
d. The gardens are similar, but not congruent.

Answers

The garden are similar, but not congruent option (D) is correct after applying the concept of similarity.

What is the congruent triangle?

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

It is given that:

Andy has two rectangular gardens. His smaller garden is 8 feet long and 4 feet wide.

The larger garden is 12 feet long and six feet wide.

As the corresponding dimensions are not same but have in equal ratio or proportions.

Thus, the garden are similar, but not congruent option (D) is correct after applying the concept of the similarity.

Learn more about the congruent triangle here:

brainly.com/question/12413243

#SPJ2

The garden are similar, but not congruent.

If f(x) = 4x − 6 and g(x) = 6x − 4, what is f · g?

Answers

Answer:

f · g = 24x² - 52x + 24

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Expand by FOIL
Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4x - 6

g(x) = 6x - 4

Step 2: Find f · g

Substitute in function values: f · g = (4x - 6)(6x - 4)
Expand [FOIL]: f · g = 24x² - 16x - 36x + 24
[Subtraction] Combine like terms: f · g = 24x² - 52x + 24

2, 10, 50, 250, ...
Write a recursive formula for

Answers

Answer:

$a_(n)$ = 5 $a_(n-1)$

Step-by-step explanation:

The sequence has a common ratio r between consecutive terms, that is

r = 10 ÷ 2 = 50 ÷ 10 = 250 ÷ 50 = 5

Thus the sequence is geometric with recursive formula

$a_(n)$ = 5 $a_(n-1)$

Write a numerical example of how multiplication and division by the same number undo each otherPlease help

Answers

Answer:

2 x 4 = 8 / 4 =2

Step-by-step explanation:

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