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3 years ago

Perimeter, Area And Volume

Mathematics

1 answer:

Maslowich3 years ago

6 0

$\large\huge\green{\sf{Answer:-}}$

<h3>area of shaded figure= </h3>

<h2>area of whole rectangle</h2>

= lengthx breadth=15x30= 450 cm²

<h3>area of unshaded region= lengthx breadth= (30-8)x 15cm²= 22x 15cm²= 330cm²</h3>

<h3>are of shaded region</h3>

= area of whole rectangle -area of unshaded region= 450cm²-330cm²= 120cm²

therefore 120 is correct answer

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add the term that makes the given expression into a perfect square. write the result as the square of a bracketed expression c s

Molodets [167]

<h2>Perfect Squares</h2>

Perfect square formula/rules:

$a^2+2ab+b^2=(a+b)^2$
$a^2-2ab+b^2=(a-b)^2$

Trinomials are often organized like $ax^2+bx+c$ .

The <em>b</em> value in this case is <em>c</em>, and it will always equal the square of half of the <em>b</em> value.

Perfect square trinomial: $ax^2+bx+(\dfrac{b}{2})^2$
or $ax^2-bx+(\dfrac{b}{2})^2$

<h2>Solving the Question</h2>

We're given:

$c^2-4c$

In a trinomial, we're given the $ax^2$ and $bx$ values. <em>a</em> in this case is 1 and <em>b</em> in this case is 4. To find the third value by dividing 4 by 2 and squaring the quotient:

4 ÷ 2 = 2
2² = 4

Therefore, the term that we can add is + 4.

$c^2-4c+4$

To write this as the square of a bracketed expression, we can follow the rule $a^2-2ab+b^2=(a-b)^2$ :

$(c-2)^2$

<h2>Answer</h2>

$c^2-4c+4$

$(c-2)^2$

4 0

2 years ago

The jars of peanut butter that I buy cost $7.20 each and normally contain 500 grams. At present, however, each jar contains an e

Alex_Xolod [135]

Answer:

$0.54

Step-by-step explanation:

Given:

The jars of peanut butter that I buy cost $7.20 each and normally contain 500 grams.

At present, however, each jar contains an extra 20% free.

And additionally, the supermarket has a "buy 3 jars get another one free''.

Question asked:

By how much is the cost per 100 grams of peanut butter less than it normally is if I take full advantage of the supermarket's offer today?

Solution:

Cost of a jars of peanut = $7.20

Normally, weight of peanut butter in one packet = 500 gram

At supermarket offer, each jar contains an extra 20% free, means a packet of peanut butter contains = 500 + 20% of 500 $=500+500\times \frac{20}{100} =500+100=600\ gram$

And extra benefit = buy 3 jars get another one free, means we will get 4 jars by just giving price of only 3 jars.

That means, total weight of peanut butter you are getting by giving 3 packet's price = Each jar weigh $\times$ number of jars

= 600 $\times$ 4 = 2400 gram

<u>Cost of each packet will be same as previously as during the offer;</u> $7.20

Cost of 3 packet's peanut (2400 gram) = $7.20\times3=\$21.6$

Now, we will calculate cost per 100 grams of peanut butter :

<u>During offer:</u>

Cost of 2400 grams of peanut butter = $21.6

Cost of 1 gram of peanut butter = $\frac{21.6}{2400}$

Cost of 100 gram of peanut butter = $\frac{21.6}{2400}\times100=\frac{2160}{2400} =\$0.9$

<u>Normal day:</u>

Cost of 500 grams of peanut butter = $7.20

Cost of 1 gram of peanut butter = $\frac{7.20}{500}$

Cost of 100 gram of peanut butter = $\frac{7.20}{500}\times100=\frac{720}{500} =\$1.44$

We found that cost of 100 gram of peanut butter in normal day is $1.44 while cost of 100 gram of peanut butter during offer is $0.9 means cost per 100 gram during offer is ($1.44 - $0.9 = )$0.54 less than cost during normal day.

<u>Conclusion:</u>

Therefore, cost per 100 grams of peanut butter is $0.54 less than it is normally if you take full advantage of the supermarket's offer today.

7 0

3 years ago

Solve the system of linear equations below. 4x - 3y = 17 5x + 4y = 60

LenaWriter [7]

4x-3y=17......(1)
5x+4y=60......(2)

Multiply equation (1) by 4 and equation (2) by 3:-

16x - 12y = 68
15x + 12y = 180

Adding these 2 equations:_

31x = 248
x = 248/31 = 8

Now substitute x = 8 in equation (1):-

4(8) - 3y = 17
32-3y = 17
-3y = -15
y = -15/-3 = 5

So solution is x=8,y=5

5 0

3 years ago

I could use some help w/ explanation please

Vsevolod [243]

9514 1404 393

Answer:

$2400

Step-by-step explanation:

The question is asking the amount invested in fund B. We can let 'b' represent that amount. Then the amount invested in fund A is (6000-b). The total profit from the investments is ...

0.02(6000 -b) +0.07(b) = 0.04(6000)

120 +0.05b = 240 . . . . . simplify

0.05b = 120 . . . . . . . . . subtract 120

b = 2400 . . . . . . . . . . .divide by 0.05

Alonzo invested $2400 in fund B.

7 0

3 years ago

△ABC∼△DEF , △ABC has a height of 14 centimeters, and △DEF has a height of 6 centimeters. What is the ratio of the area of △ABC t

Kamila [148]

Since triangle ABC is similar to triangle DEF then the ratio of the corresponding sides is constant.
The ratio of the corresponding lengths is referred to as the linear scale factor.
Considering the heights of the two triangles;
L.S.F = 14/6
= 7/3
The ratio in area (A.S.F) is given by (L.S.F)²
Therefore, A.S.F = (7/3)² = 49/9
Thus te ratio of the area of triangle ABC to DEF is 49:9

8 0

4 years ago

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