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1 year ago

Determine the point of intersection between the lines with equations x+3y=5 and 3x−2y=26.

Mathematics

2 answers:

Marianna [84]1 year ago

7 0

Answer:

(8,-1)

Step-by-step explanation:

The point of intersection can be found out by solving the system of equations.

x + 3y = 5
3x - 2y = 26

Multiply (1) by 3 :-

→ 3 ( x + 3y ) = 5 × 3

→ 3x + 9y = 15

Subtracting 3(1) and 2 :-

→ 3x + 9y - 3x +2y = 15 - 26

→ 11y = -11

→ y = (-1)

Put it in 1 :-

→ x -3 = 5

→ x = 3 + 5

→ x = 8

<h3>Hence the point of intersection is (8,-1)</h3>

Zolol [24]1 year ago

4 0

Answer:

the ans is :

Step-by-step explanation:

First, it would be helpful to draw a quick sketch of the lines. It helps to visualize the problem.

To find the intersection point, we need to find the point where x and y are the same value in both equations.

The line equations:

6x+2y=26 ................... 1

2x+3y=18 ................... 2

Can be rearranged to the common line equation form: y = mx + c

y = 13 - 3x ................... 3

y = 6 - 2/3 x ................. 4

At the intersection point, y will be equal for both equations. So, we can set 3 equal to 4 and solve for x.

13- 3x = 6 - 2/3 x

13 = 6 + 3x - 2/3x ....... add 3x to both sides

13 = 6 + 2 1/3x ........ simplify

7 = 2 1/3 x ........ subtract 13 from both sides

7 = 7/3 x ......... multiply both sides by 3/7

3 = x

To calculate the y-coordinate substitute x = 3 into 3.

y = 13 - 3x

y = 13 - 3(3)

y = 4

To check your answer, substitute the values for x and y into the other equation, 4.

The point of intersection is (3,4).

If you drew a sketch of the problem, you should be able to see that this point of intersection makes sense.

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In equilateral ∆ABC with side a, the perpendicular to side AB at point B intersects extension of median AM in point P. What is t

Sergeeva-Olga [200]

Answer:

Perimeter = (2 + √3)·a

Step-by-step explanation:

Given: ΔABC is equilateral and AB = a

The diagram is given below :

AM is a median , PB ⊥ AB , PM = b

Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°

Since, AM is perpendicular bisector of BC. So,

$MB = \frac{a}{2}$

Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

Now, in ΔBMP :

$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

3 0

1 year ago

When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected

jasenka [17]

Answer:

A. Initially, there were 12 deer.

B. N(10) corresponds to the amount of deer after 10 years since the herd was introducted on the reserve.

C. After 15 years, there will be 410 deer.

D. The deer population incresed by 30 specimens.

Step-by-step explanation:

$N=\frac{12.36}{0.03+0.55^t}$

The amount of deer that were initally in the reserve corresponds to the value of N when t=0

$N=\frac{12.36}{0.33+0.55^0}$

$N=\frac{12.36}{0.03+1} =\frac{12.36}{1.03} = 12$

A. Initially, there were 12 deer.

B. $N(10)=\frac{12.36}{0.03 + 0.55^t} =\frac{12.36}{0.03 + 0.0025}=\frac{12.36}{y}=380$

B. N(10) corresponds to the amount of deer after 10 years since the herd was introducted on the reserve.

C. $N(15)=\frac{12.36}{0.03+0.55^15}=\frac{12.36}{0.03 + 0.00013}=\frac{12.36}{0.03013}= 410$

C. After 15 years, there will be 410 deer.

D. The variation on the amount of deer from the 10th year to the 15th year is given by the next expression:

ΔN=N(15)-N(10)

ΔN=410 deer - 380 deer

ΔN= 30 deer.

D. The deer population incresed by 30 specimens.

8 0

1 year ago

Justify each step of the solution by stating the property that was used to get to each step.

Olenka [21]

I hope this helps you

4 0

1 year ago

The label on a ceiling lighting fixture warns you to use a lightbulb of 60 watts or less. The voltage to the lightbulb is 120 vo

patriot [66]

Answer:

0.5 A

Step-by-step explanation:

Hi,

I believe the question is incomplete. However, as per the information provided:

The simplest way to calculate the Current (unit is Amperage), is understanding the relationship between the three: Power, Voltage and Current.

(Quick Tip: W=AV; where W -> Watts (Power), A -> Ampere (Current), V -> Volts (Voltage))

Using the formula we calculate the Ampere:

W = A x V

60 = A x 120

60/120 = A (We divide the equation be 120)

0.5 = A (Simply reduce the fraction 60/120 = 1/2 = 0.5)

Tip:

8 0

1 year ago

The number of people that can be safely carried in a lift depends on their mass. A lift will safely

vitfil [10]

Answer:

Step-by-step explanation:

If a lift will carry 8 people safely with an average mass of 75kg each we multiply to find the weight the lift can safely carry.

8 x 75kg = 600kg

If the average mass of the people is 100kg each, we divide to find the number of people it can carry. We know the lift can carry 600kg.

600kg/100kg = 6

So the lift can carry 6 people if their average mass is 100kg.

8 0

1 year ago