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erma4kov [3.2K]
3 years ago
9

Simplify.

itle="m\sqrt{p} + n\sqrt{p} - \sqrt{p}" alt="m\sqrt{p} + n\sqrt{p} - \sqrt{p}" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
madreJ [45]3 years ago
8 0

Answer:

First option is the correct answer.

(m + n - 1) \sqrt{p}

Step-by-step explanation:

m\sqrt{p} + n\sqrt{p} - \sqrt{p} \\  \\  = (m + n - 1) \sqrt{p}

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Vector v has magnitude5 units, w has magnitude 3, and the acute angle between them is 45°.
givi [52]

Answer:

25 units

Step-by-step explanation:

No matter the direction of the vector, if we multiply the vector v by -5v, the magnitude can be calculated as follows:

|-5*V|

Due to properties of absolute value:

|-5*V|=5*|V|=5*(5units) = 25 units

8 0
3 years ago
- 5x+6=-12x+62<br> Simplify your answer as much as possible.
S_A_V [24]

Answer:

x=8

Step-by-step explanation:

-5x+6=-12x+62

-5x+12x=62-6

7x=56

x=8

7 0
3 years ago
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Which of the following is not a rational number?<br><br><br> Help please
Pavlova-9 [17]
A, because negative is not rational
3 0
3 years ago
What does the 75th term look like of 6,9,12
leva [86]

Answer:

228

Step-by-step explanation:

We are adding 3 each time so general rule is

Tn= 3n + 3

Therefore

T= 3(75)+3

= 228

3 0
3 years ago
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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T
Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180                      ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}

105^{\circ}+ m\angle B=180^{\circ}

Simplify:

m\angle B=75^{\circ}

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle  to the sines of its angles.

\frac{\sin A}{BC} = \frac{\sin C}{AB}

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}

then,

BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}

BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798 unit

Similarly for  AC:

\frac{\sin B}{AC} = \frac{\sin C}{AB}

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}

then,

AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}

AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283 unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

A = \frac{1}{2} \times AB \times AC \times \sin A

Substitute the values in above formula to get area;

A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}

A = 4 \times 10.9283 \times 0.86602540378

Simplify:

Area of triangle ABC = 37.856 (approx) square unit





4 0
3 years ago
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