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3 years ago

Find the value of x, which makes the area of this triangle equal 72.

Mathematics

2 answers:

Ghella [55]3 years ago

5 0

Area of a triangle=1/2(base x height)
Area=72, Base=8, Height=2x-3
Plug it in.
72=1/2(8 x (2x-3))
72=1/2(16x-24)
72=8x-12
84=8x
x=10.5

sveticcg [70]3 years ago

5 0

Area=1/2 times base times height
height=2x-3
base=8

area=72
72=1/2 times (2x-3) times 8
72=(2x-3) times 4
divide both sides by 4
18=2x-3
add 3 to both sides
21=2x
divide both sides by 2
21/2=x
x=21/2=10.5

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Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees a

Ivenika [448]

Answer:

<h2>70 possible groups</h2>

Step-by-step explanation:

Given the total number of employee to be equal to 12 temporary employee.

Number of women employee = 5 women

Number of men employee = 12 - 5 = 7 men

If 4 will be hired as permanent employees, the possible ways they can be grouped so that the 4 temporary employees consists of 3 women and 1 man can be done by applying the combination formula.

Combination has to do with selection. For example, if r objects are to be selected from n pool of similar objects, this can be done in nCr different ways.

$nCr = \frac{n!}{(n-r)!r!}$

According to question, we are to select 3 women from 5 women and 1 man from 7 men. Based on similarity in sex, this can be done in (5C3* 7C1) different ways .

$5C3 * 7C1\\= \frac{5!}{(5-3)!3!} * \frac{7!}{(7-1)!1!}\\\\= \frac{5!}{2!3!} * \frac{7!}{6!1!}\\\\= \frac{5*4*3!}{3!*2} * \frac{7*6!}{6!*1}\\\\= \frac{20}{2} * \frac{7}{1}\\ \\= 10*7\\\\= 70\ possible\ groups$

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Clarge%5Cfrak%7B%20%5Corange%7B%20Question%7D%7D" id="TexFormula1" title=" \large\frak{ \

SVEN [57.7K]

Answer:

$\boxed{\sf distance \: between \: the \: objects \: \: is \: 2.5 \: cm}$

Step-by-step explanation:

According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to

the product of their masses, given by standard formula.

$A = G \cdot \frac{m_1.m_2}{ {d}^{2} }$

where A,d & G are force of attraction, distance of separation & proportionality constant respectively.

Given:

A1 = 2 units

d1= 5 cm

A2 = 8 units

To find:

Distance of separation when the force of attraction is 8 units d2 = ?

Solution:

Substituting the given values in above at each point,

$A_1 = G \cdot \frac{m_1.m_2}{ {d_1}^{2} } \\ 2 = G \cdot \frac{m_1.m_2}{ {5}^{2} } \\ \sf similarly \: at \: second \: point \: of \: attraction \\ A_2 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ 8 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ \sf \: \: dividing \: both \: of \: the \: equation \\ \frac{2}{8} = \frac{G \cdot \frac{m_1.m_2}{ {5}^{2} }}{G \cdot \frac{m_1.m_2}{ {d_2}^{2} } } \\ \sf \: G \: m_1 and \: m_2 \: are \: \: constant \: hence \\ \sf they \: can \: be \: cancelled \: out \\ \frac{2}{8} = \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } } \\ \sf rearranging \: above \: equation \\ \frac{1}{4} = \frac{{d_2}^{2} }{ {5}^{2} } \\ {d_2}^{2} = \frac{ {5}^{2} }{4 } \\ {d_2}^{2} = \frac{25}{4} \\ {d_2}^{2} = 6.25 \\ \sqrt{{d_2}^{2} } = \sqrt{6.25} \\ \boxed{ \sf{d_2} = 2.5 \: cm}$

Answer: the distance between the two objects is 2.5 cm, if the attraction between them is 8 units.

Learn more about universal law of gravitation here brainly.com/question/27244479

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7 0

2 years ago

Shanti has just joined a DVD rental club. She pays a monthly membership fee of $4.95, and each DVD rental is $1.95. If Shanti's

DerKrebs [107]

X = number of DVDs

1 DVD costs $1.95 to rent
x DVDs cost 1.95x dollars to rent

tack on the membership fee of 4.95 and the total cost is 1.95x+4.95

set this equal to 42 and solve for x

1.95x+4.95 = 42
1.95x+4.95-4.95 = 42-4.95
1.95x = 37.05
1.95x/1.95 = 37.05/1.95
x = 19

So Shanti can rent 19 DVDs

6 0

3 years ago

Need help with ratios quick plss

dalvyx [7]

X/3=y this is what I got hopes this helps

3 0

2 years ago

3.3 Factorise fully: 3.3.1 x²-x-6

Tom [10]

Answer:

(x-3)(x+2)

Step-by-step explanation:

¹ you open brackets.

² you put the "x" in both brackets

³ you then check for factors, that will give you a "6" when you multiply them and give you the "x" when you add or subtract them.

3 0

2 years ago