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4 years ago

Please help with these

Mathematics

1 answer:

MatroZZZ [7]4 years ago

8 0

Set up a proportion.

$\frac{3~minutes}{2~questions}$ = $\frac{x~minutes}{12~questions}$

Cross multiply.

2x=36
x=12

It would take her 12 minutes.

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Formula for surface area of a cube: 6a² where a=20.

6 x (20)²
6 x 400
= 2400

Surface area: 2400 cm

----------------------------------------------

Mean absolute deviation: The average distance from each number in the set to the mean of the set.

Mean of the set: $\frac{(3+8+10+12+15)}{5} = \frac{48}{5} = 9.6$

9.6-3=6.6
9.6-8=1.6
10-9.6=0.4
12-9.6=11.4
15-9.6=5.4

Mean of 6.6, 1.6, 0.4, 11.4, and 5.4: $\frac{(6.6+1.6+0.4+11.4+5.4)}{5} = \frac{25.4}{5} = 5.08$

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√(11 - 6 √(2)) (not decimal form)

bogdanovich [222]

Answer:

$\huge\boxed{\sqrt{11-6\sqrt2}=3-\sqrt2}$

Step-by-step explanation:

$\sqrt{11-6\sqrt2}=(*)\\\\11=9+2=3^2+(\sqrt2)^2\\6\sqrt2=(2)(3)(\sqrt2)\\\\(*)=\sqrt{3^2-(2)(3)(\sqrt2)+(\sqrt2)^2}\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=\sqrt{(3-\sqrt2)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|3-\sqrt2|=3-\sqrt2\\\\^{\text{because}\ 3>\sqrt2\to3-\sqrt2>0}$

6 0

3 years ago

For a science experiment Marcia dissolved 1.0 kilogram of salt in 3.0 liters of water. For a different experiment, Bobby dissolv

nekit [7.7K]

Marcia dissolved 1 kg of salt in 3 litres of water.
Bobby dissolves 2 pounds of salt in 7 pints of water
2.11 pints = 1 litre
7 pints = 7/2.11
= 3.32 litre
1 pound =0.45 kg
2 pound = o.45*2 kg
= 0.9 kg
So we find that Bobby is dissolving 0.9kg of salt in 3.32 litre of water
Marcia is dissolving 1 kg of salt in 3 litres of water.

5 0

3 years ago

Find all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm

miskamm [114]

Answer:

15cm by 20cm by 25cm

Step-by-step explanation:

Let the sides of the right angle be x, y and h

x is the breadth

y is the height

h is the hypotenuse

Perimeter = x + y + h

x + y +h = 60

x+y = 60-h .... 1

If its area is equal to 150 square cm, then;

Area = 1/2 * base * height

Area = 1/2 *x * y

xy/2 = 150

xy = 300 ....2

According to pythagoras theorem;

x² + y² = h²

On expanding x² + y²

x² + y² = (x+y)² - 2xy

The equation becomes

(x+y)² - 2xy = h² ... 3

Substitute equation 1 and 2 into 3;

From 3;

(x+y)² - 2xy = h² ... 3

(60-h)² - 2(300) = h²

3600-120h + h² - 600 = h²

3600-120h - 600 = 0

-120h = 600-3600

-120h = -3000

h = 3000/120

h = 25cm

Recall that x+y+h = 60

x+y+25 = 60

x+y = 60 - 25

x+y = 35 ... 4

From equation 2;

xy = 300

x = 300/y ..... 5

Substitute 5 into 4;

300/y + y = 35

(300+y²)/y = 35

300+y² = 35y

y²-35y + 300 = 0

y²-20y-15y + 300 = 0

y(y-20)-15(y-20) = 0

y-20 = 0 and y - 15 =0

y = 20 and 15

since x+y = 35

x + 20 = 35

x = 35 - 20

x = 15

Hence the sides of the triangle are 15cm by 20cm by 25cm

8 0

3 years ago

Show that if u+v and u-v are orthognal, then the vectors u and v must have the same length.

pashok25 [27]

Answer with Step-by-step explanation:

We are given that

u+ v and u-v are orthogonal

We have to prove that u and v must have the same length.

When two vector a and b are orthogonal then

$a\cdot b=0$

By using the property

$(u+v)\cdot (u-v)=0$

We know that

$(a+b)\cdot (a-b)=\mid a\mid^2-\mid b\mid^2$

$\mid u\mid ^2-\mid v\mid^2=0$

$\mid u\mid^2=\mid v\mid^2$

Magnitude is always positive

When power of base on both sides are equal then base will be equal

Therefore,

$\mid u\mid=\mid v\mid$

Hence, the length of vectors u and v must have the same length.

5 0

4 years ago

Which expression is equivalent to (xy)z? A (x+y)+z B 2z(xy) C x(yz) D x(y+z)

qwelly [4]

Answer:

Step-by-step explanation:

5 0

3 years ago

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