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kotegsom [21]
3 years ago
12

What is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)

Mathematics
2 answers:
Licemer1 [7]3 years ago
8 0
3\sqrt2\cdot(5\sqrt6-7\sqrt3)=3\cdot5\cdot\sqrt{2\cdot6}-3\cdot7\cdot\sqrt{2\cdot3}\\\\=15\sqrt{12}-21\sqrt6=15\sqrt{4\cdot3}-21\sqrt6=15\cdot\sqrt4\cdot\sqrt3-21\sqrt6\\\\=15\cdot2\cdot\sqrt3-21\sqrt6=\boxed{30\sqrt3-21\sqrt6}
Used:\\\sqrt{a}\cdot\sqrt{b}=\sqrt{a\cdot b}

liraira [26]3 years ago
8 0

The answer is C. !!!!

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Theorem: A line parallel to one side of a triangle divides the other two proportionately.
Kisachek [45]

Answer:

Segment BF = 16

Step-by-step explanation:

The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately

The given theorem is the Triangle Proportionality Theorem

According to the theorem, given that segment DE is parallel to segment BC, we have;

\dfrac{AD}{BD} = \dfrac{AE}{EC}

Therefore;

BD = \dfrac{AD}{\left(\dfrac{AE}{EC} \right) }  = AD \times \dfrac{EC}{AE}

Which gives;

BD = 6 \times \dfrac{18}{12}= 9

Similarly, given that EF is parallel to AB, we get;

\dfrac{AE}{EC} = \dfrac{BF}{FC}

Therefore;

BF = FC \times \dfrac{AE}{EC}

Which gives;

BF = 24 \times \dfrac{12}{18} = 16

Therefore, the statement that can be proved using the given theorem is segment BF = 16.

8 0
3 years ago
A total of 300 trees will be planted in a park. there will be 2 pine trees planted for every 3 maple trees planted. how many pin
quester [9]
The problem is stating that there is a a ratio of 2:3 of pine to maples trees. Thus the total number of pine trees planted will be given by:
total ratio=2+3=5
thus the  number of pines will be:
2/5×300
=120 pines

Answer: 120 pines
8 0
3 years ago
Read 2 more answers
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kipiarov [429]

Answer:

(3/4)/5=.15, or in fractions, 3/20

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
1. It is three-digit whole number.
sergiy2304 [10]

Answer:

375

Step-by-step explanation:

thre digit odd multiples of 25 >200  and <700 are 225,275,325,375,425,475,525,575,625,675

if all the digits are odd and different ,then 375,475

4+7+5=16 so not divisible by  3.

3+7+5=15 divisible by 3

375 satisfies all the conditions.

5 0
3 years ago
The Pentagon is planning to build a new, spherical satellite. As is typical in these cases, the specifications keep changing, so
MaRussiya [10]

Answer:

$553300

Step-by-step explanation:

Let the rate of increase of radius with respect to time be dr / dt. Hence:

dr / dt = 0.4  ft/week

The cost of increasing the radius is  $1,100 per cubic foot. We can calculate how fast the cost is growing by determining the rate at which the volume increases with time (dV / dt).

The volume (V) of a spherical object is given by:

V=\frac{4}{3} \pi r^3\\\\differentiating\ with\ respect\ to\ t:\\\\\frac{dV}{dt}= \frac{d}{dt}(\frac{4}{3} \pi r^3)\\\\ \frac{dV}{dt}= \frac{4}{3} \pi\frac{d}{dt}(r^3)\\\\ \frac{dV}{dt}= \frac{4}{3} \pi*3r^2\frac{dr}{dt} \\\\ \frac{dV}{dt}= 4\pi r^2\frac{dr}{dt} \\\\Substituting:\\\\ \frac{dV}{dt}= 4\pi (10 \ feet)^2(0.4\ feet/week)\\\\ \frac{dV}{dt}=503\ feet^3/week

Therefore, the cost of increasing volume = 503 feet³/week * $1100 / feet³ = $553300

3 0
3 years ago
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