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zlopas [31]
3 years ago
11

The sum od the squares of two consecutive even integers is 164. Find the integers.

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
7 0
Let x be the smaller integer, then x+2 is the larger integer.
We're given 
x^2+(x+2)^2=164
Expand and simplify
2x^2+4x+4=164
x^2+2x-80=0
(x-8)(x+10)=0
=> x=-10 or x=8.

Therefore the integers are{8,10} or {-10,-8}.
Note: question asks for integers, so negative integers count.
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Carla is baking brownies for the school bake sale. The batter fills a pan that is 20 cm long by 16 cm wide by 4.4 cm deep.Then,
barxatty [35]

The volume of the first pan is (length x width x depth) =

                                               (20cm x 16cm x 4.4cm) = 1408 cm³ .

The batter fills it, so we know there is 1408 cm³ of batter.

Somehow, Carla manages to transfer every drop and smidgen of batter to
the new pan, leaving not a single drip of it in the first pan.  So we know that
there is 1408 cm³ of batter in the new pan.  It will spread out to fill the whole
length and width of the new pan, and we're to calculate how deep it will be.

                         (length x width x depth)  =  1408 cm³

                       (20cm x 20cm) x (depth)  =  1408 cm³

                                (400 cm²) x (depth)  =  1408 cm³

Divide each side by  400cm² :      depth  =  1408 cm³ / 400cm²

                                                               =  3.52 cm

Since the new pan is 5 cm deep, this works.  The batter doesn't
overfill it and glurb out over the top and all over the counter.

The question asked how far the batter is <em>from the top of the pan</em>.

The pan is        5 cm deep.
The batter is 3.52cm deep.

The batter comes up to (5 - 3.52) = 1.48 cm from the top of the pan.

Rounded to the nearest tenth of a cm, that's  <em>1.5 cm  </em>from the top.

5 0
3 years ago
Give the boundaries of 9 pounds
AleksandrR [38]

Answer: The boundaries of 9 pounds are;

               8.5 – 9.5 pounds

Step-by-step explanation: Method used to find the boundaries.

The boundaries of an indicated value are the upper and lower bounds of

the value, which are the possible minimum or maximum values the

number may be before being rounded to the current value.

The given boundaries is = 9 pounds

The lowest possible value, 9 pounds can be before rounding up is 8.5 pounds.

Therefore; 8.5 pounds is the lower bound of 9 pounds.

The highest possible value of 9 pounds is 9.44999... pounds which is approximately 9.5 pounds

Therefore; The upper bound of 9 pounds is 9.5 pounds

Which gives;

The boundaries of 9 pounds are;

8.5 – 9.5 pounds

7 0
2 years ago
Ariel is filling a giant beach ball with air. The radius of the beach ball is 30 cm. What is the volume of air that the beach ba
boyakko [2]
The answer is v=113040
5 0
3 years ago
Read 2 more answers
2. angle ABE = angle MNP <br><br> Write another valid congruency statement:​
Free_Kalibri [48]

Given:

\Delta ABE\cong \Delta MNP

To find:

The congruent angles and sides, then find the another valid congruency statement.

Solution:

We have,

\Delta ABE\cong \Delta MNP

We know that, corresponding parts of congruent triangles are congruent (CPCTC).

Using CPCTC, we get

Angles:

\angle A\cong \angle M

\angle B\cong \angle N

\angle E\cong \angle P

Sides:

AB\cong MN

BE\cong NP

AE\cong MP

The another congruent statement is \Delta BEA\cong \Delta NPM.

Therefore, the required table is

Angles                                              Sides

\angle A\cong \angle M                                        AB\cong MN

\angle B\cong \angle N                                        BE\cong NP

\angle E\cong \angle P                                        AE\cong MP

The another congruent statement is \Delta BEA\cong \Delta NPM.

4 0
3 years ago
A number tripled and tripled again is 729 what is the number
MatroZZZ [7]
Its 81 because 729 divided by 3 and divided by 3 again is 81
8 0
4 years ago
Read 2 more answers
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