Ask question

Ask question

All categories

3 years ago

8

Write the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) in slope-intercept form.

1 answer:

m_a_m_a [10]3 years ago

4 0

Answer:

$y=-\frac{5}{2}x-24$

Step-by-step explanation:

$2x-5y=-12\\5y=2x+12\\y=\frac{2}{5}x+\frac{12}{5}\\$

if two lines perpendicular,

$m_{1} .m_{2}=-1\\ \frac{2}{5} .m_{2}=-1\\m_{2}=-\frac{5}{2}$

the line perpendicular to this line is

$y=-\frac{5}{2}x+k$ ; k ∈ R

the line passes through the point (10,-1)

so,

$-1=-\frac{5}{2} (10)+k\\-1=-25+k\\k=-24$

∴the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) is

$y=-\frac{5}{2}x-24$

You might be interested in

Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

3 years ago

The ratio of chaperones to students on a field trip is2:7 there are 14 chaperones on the field trip in all how many chaperones a

Luden [163]

Answer:

14 chaperones, 49 students

Step-by-step explanation:

6 0

3 years ago

The number of kilograms of water in a human body varies directly as the mass of the body. An 87-kg person contains 58 kg of wat

katen-ka-za [31]

Answer:

50 kg water.

Step-by-step explanation:

We have been given that the number of kilograms of water in a human body varies directly as the mass of the body.

We know that two directly proportional quantities are in form $y=kx$ , where y varies directly with x and k is constant of variation.

We are told that an 87-kg person contains 58 kg of water. We can represent this information in an equation as:

$58=k\cdot 87$

Let us find the constant of variation as:

$\frac{58}{87}=\frac{k\cdot 87}{87}$

$\frac{29*2}{29*3}=k$

$\frac{2}{3}=k$

The equation $y=\frac{2}{3}x$ represents the relation between water (y) in a human body with respect to mass of the body (x).

To find the amount of water in a 75-kg person, we will substitute $x=75$ in our given equation and solve for y.

$y=\frac{2}{3}(75)$

$y=2(25)$

$y=50$

Therefore, there are 50 kg of water in a 75-kg person.

3 0

3 years ago

What Is the value of x

SCORPION-xisa [38]

Answer:

15

Step-by-step explanation:

5 0

3 years ago

A water company charges a connection fee each month of $22 and an additional $2.30 per cubic foot of water used. Which function

EastWind [94]

Answer

Find out the total monthly charges for x cubic feet of water used .

To prove

As given

A water company charges a connection fee each month of $22 and an additional $2.30 per cubic foot of water used.

Than the equation become

Total monthly charges for x cubic feet of water used = Monthly connection fee + charges for x cubic feet of water

thus

f(x) = 22 + 2.30x

where x is the x cubic feet of water used .

Therefore Option (B) is correct i.e f(x) = 22 + 2.30x .

4 0

2 years ago

Read 2 more answers