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Sunny_sXe [5.5K]

2 years ago

12

(08.01)Consider the following system of equations:

2 answers:

eduard2 years ago

8 0

Answer:

The correct option is 1.

Step-by-step explanation:

If a system of equation have two equation, then the intersection points of both equation are the solutions of the system of equation.

The given system of equations is

$y=5x+6$

$y=-x-7$

Both equations represent lines because both have degree 1.

The solution to the system of equations is the intersection of both the lines. It means the statement "Line y = 5x + 6 intersects line y = −x − 7" describes the solution to the system of equations.

Therefore the correct option is 1.

amid [387]2 years ago

3 0

The first one is correct.

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n △ABC, point P∈ AB is so that AP:BP=1:3 and point M is the midpoint of segment CP. Find the area of △ABC if the area of △BMP is

monitta

Answer: The area of ABC is 56 m².

Explanation:

It is given that in △ABC, point P∈ AB is so that AP:BP=1:3 and point M is the midpoint of segment CP.

Since point P divides the line AB in 1:3, therefore the area of triangle APC and BPC is also in ratio 1:3. To prove this draw a perpendicular h on AB from C.

$\frac{\text{Area of } \triangle BCP}{\text{Area of } \triangle ABC} =\frac{\frac{1}{2}\times BP\times CH}{\frac{1}{2}\times AB\times CH} =\frac{BP}{AB}= \frac{3}{4}$

Since the area of BPC is $\frac{3}{4}$ th part of total area, therefore area of APC is $\frac{1}{4}$ th part of total area.

The point M is the midpoint of CP, therefore the area of BMP and BMC is equal by midpoint theorem.

$\text{Area of } \triangle BMP=\text{Area of } \triangle BMC$

$21=\text{Area of } \triangle BMC$

Area of BPC is,

$\text{Area of } \triangle BPC=\text{Area of } \triangle BMP+\text{Area of } \triangle BMC$

$\text{Area of } \triangle BPC=21+21$

$\text{Area of } \triangle BPC=42$

Area of APC is,

$\text{Area of } \triangle APC=\frac{1}{3}\times \text{Area of } \triangle BPC$

$\text{Area of } \triangle APC=\frac{1}{3}\times 42$

$\text{Area of } \triangle APC=14$

Area of ABC is,

$\text{Area of } \triangle ABC=\text{Area of } \triangle APC+\text{Area of } \triangle BPC$

$\text{Area of } \triangle ABC=14+42=56$

Therefore, the area of ABC is 56 m².

5 0

3 years ago

What is 615 rounded to the nearest hundred?

Svetlanka [38]

615 ≈ 600 (nearest hundred)

6 0

3 years ago

How many acute/obtuse/right angles does a pentagon have

KengaRu [80]

5 obtuse no acute and no right

4 0

2 years ago

A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is an hourly wage of $20. Opt

sdas [7]

Answer:

40$

Step-by-step explanation:

they have

20$

5%

40hours

i=prt

multiplication of both

=40×20×5/100

=40$

the amount required at the week is 40$

7 0

2 years ago

What is the result of adding these two equations?

timofeeve [1]

Answer:

the result of adding these two equations is

3x = 14

Step-by-step explanation:

We are given two equations

5x − y = 6 eq. 1

−2x + y = 8 eq. 2

Add the like terms together

5x - 2x = 3x

− y + y = 0

6 + 8 = 14

So the result of adding these equations is

3x + 0 = 14

3x = 14

Bonus:

The value of x is

3x = 14

x = 14/3

6 0

2 years ago