4) 4x + 3y = 56
2x + y = 24
Solve using elimination please show work

Answer:

B. (0, 5)

Step-by-step explanation:

All points on the blue shaded area are solutions. Points on the dashed line and on the white area are not solutions.

(-3, -6) and (3, 2) are on the dashed line and are not solutions.

(5, 0) is in the white area and is not a solution.

(0, 5) is in the shaded area and is a solution.

Answer: B. (0, 5)

Answer:

see explanation

Step-by-step explanation:

The orthocentre is

• Inside all acute triangles

• Outside all obtuse triangles

• On all right triangles

To determine if the triangle is any of the above, we require the lengths of the 3 sides of the triangle.

Calculate the lengths using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

L(0, 5) and M(3, 1)

LM = [tex]\sqrt{(3-0)^2+(1-5)^2}[/tex] = [tex]\sqrt{3^2+(-4)^2}[/tex] = [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5

L(0, 5) and (N(8, 1)

LN = [tex]\sqrt{(8-0)^2+(1-5)^2}[/tex] = [tex]\sqrt{8^2+(-4)^2}[/tex] = [tex]\sqrt{64+16}[/tex] = [tex]\sqrt{80}[/tex] = 4[tex]\sqrt{5}[/tex]

M(3, 1) and (N(8, 1)

MN = [tex]\sqrt{(8-3)^2+(1-1)^2}[/tex] = [tex]\sqrt{5^2+0^2}[/tex] = [tex]\sqrt{25}[/tex] = 5

Given 3 sides of a triangle a, b, c where c is the longest side, then

• a² + b² = c² ⇒ right triangle

• a² + b² < c² ⇒ acute triangle

• a² + b² > c² ⇒ obtuse triangle

Here a = 5, b = 5, c = 4[tex]\sqrt{5}[/tex]

a² + b² = 5² + 5² = 25 + 25 = 50

c² = (4[tex]\sqrt{5}[/tex] )² = 80

Since a² + b² < c² then triangle is obtuse and the orthocentre is outside the triangle.

The orthocentre is the point of intersection of the 3 Altitudes of the triangle.

We only require to find the equation of 2 of the altitudes and solve them simultaneously to obtain the coordinates of the orthocentre.

An Altitude is a line from a vertex at right angles to the opposite side

Altitude from M to LN

Calculate the slope of LN using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{1-5}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex] ⇒ [tex]m_{perpendicular}[/tex] = 2

Equation of altitude

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y = 2x - 5 → (1)

Altitude from N to LM

m = [tex]\frac{1-5}{3-0}[/tex] = - [tex]\frac{4}{3}[/tex] ⇒ [tex]m_{perpendicular }[/tex] = [tex]\frac{3}{4}[/tex]

Equation of altitude

y - 1 = [tex]\frac{3}{4}[/tex](x - 8)

y - 1 = [tex]\frac{3}{4}[/tex] x - 6

y = [tex]\frac{3}{4}[/tex] x - 5 → (2)

Equating (1) and (2)

2x - 5 = [tex]\frac{3}{4}[/tex] x - 5 ( multiply through by 4 )

8x - 20 = 3x - 20

5x - 20 = - 20 ( add 20 to both sides )

5x = 0 ⇒ x = 0

Substitute x = 0 into (1)

y = 0 - 5 = - 5

The orthocentre is (0, - 5 )

Answer:

The orthocenter is outside the triangle, at (0, -5)

Step-by-step explanation:

The orthocenter is the intersection of the altitudes. So let's find the slope-intercept equation of "LM" "MN" and "LN"  then determine it's  perpendicular:

LM: slope = m = 1-5/3-0 = -4/3, equation => y = -4/3x + 5, perpendicular => y = 3/4x + b

this line passes through the opposite point, (8, 1)...therefore we can find b:

y = 3/4x + b

1 = 3/4(8) + b, b = -5, equation => y = 3/4x - 5

______________________________________

MN: slope = m = 1-1/8-5 = 0, equation => y = 1, perpendicular => x = ?

the line passes through the opposite point (0, 5)...so we can find ? or b:

x = ?, equation => x = 0

______________________________________

LN: slope = m = 1-5/8-0  = -4/8 = -1/2, equation => y = -1/2x + 5, perpendicular => y = 2x + b

the line passes through the opposite point (3, 1)...so we can find b:

1 = 2(3) + b, b = 1-6 = -5, equation => y = 2x - 5

______________________________________

System of Equations:

[tex]\begin{bmatrix}y=\frac{3}{4}x-5\\ y=2x-5\\ x=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=\frac{3}{4}x-5: \begin{bmatrix}x=0\\ \frac{3}{4}x-5=2x-5\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=0: \begin{bmatrix}\frac{3}{4}\cdot \:0-5=2\cdot \:0-5\end{bmatrix}[/tex]

[tex]\mathrm{Simplify\:}: \begin{bmatrix}-5=-5\end{bmatrix}[/tex]

[tex]\mathrm{For\:}y=\frac{3}{4}x-5,\\\mathrm{Substitute\:}x=0,\\y=\frac{3}{4}\cdot \:0-5 = -5[/tex]

[tex]y=-5,\:x=0[/tex]

_____________________________________

The orthocenter is outside the triangle, at (0, -5)

Answer:

48/5 or in simplified version its 9 3/5

Step-by-step explanation:

Answer:

9 3/5

Step-by-step explanation:

Answer:

3/4 x 24 = 3/4 x 24/1 = 72/4 = 18

Let me know if this helps!

Answer:

1. medium

2. 20%

3. 12.48

4. Noah

Answer: Multiply n299 by n by adding the exponents

Step-by-step explanation:

8n230+15=0

Answer:

Step-by-step explanation:

16>-2x

-2x<16

x>-8

Answer:

a. Doors = 31 doors

b. Windows =155 windows

Step-by-step explanation:

Given the following data;

Ratio D:W = 1:5 = 1 + 5 = 6

Total number of doors and windows = 186

Ratio of doors to windows = 1/6

Ratio of windows to doors = 5/6

To find the ratio of the doors;

Doors = 1/6 * 186

Doors = 186/6

Doors =31 doors

To find the ratio of windows;

Windows = 5/6 * 186

Windows = 930/6

Windows =155 windows

Answer:

D

Step-by-step explanation:

It's D

Answer:

Answer D

Step-by-step explanation:

Its right I just took the test.

Answer:

7/8

Step-by-step explanation:

I think but im 60% im right

Answer:

in 10 hours you will travel 800 km which is like 500 miles if you're driving

Step-by-step explanation:

Answer:

multiplying by a fraction

Step-by-step explanation:

rational answers can be a fraction.

hope this helps :)

x=2

y=6  

x and yt are different variables

Answer:

999

Step-by-step explanation:

[tex]log(x)=y\\x=10^y\\log(x+1)=3\\x+1=10^3\\x=999[/tex]

Answer:

I really don't know, but you submitted this like 23 hours ago, so I don't think it will help if I answer!!!

Step-by-step explanation:

Can I be Brainliest!!!

Answer:

the asswer is 1 2 4

Step-by-step explanation:

1×20=30

2×10=20

4×5=2

A ) I am just guessing

isbslw

Answer:

I think 2/8 + 1/8 = 3/8

8/8 - 3/8 = 5/8

Answer:

1.52

Step-by-step explanation:

Answer:

No it is not a function for sure.

Answer:

I wrote the answers below

Step-by-step explanation:

x+3<70------>0,60

-5x<2--------->3,5

5x<2---------->-3,-1

-3x>18-------->-10,-20

Answer:

6.8

Step-by-step explanation:

(2/5)*17

=6.8

Answer:

the answer is 6.8

Step-by-step explanation:

2                  17

---     x          -------- =      34

5                      1               ------  

                                            5

34 divided by 5 = 6.8

hope this helped have a great day.

Answer:

7,14,21,28,35

Step-by-step explanation:

Answer:

14.90 to 16.70 tons

Step-by-step explanation:

We are given;

Sample size; n = 49

Mean; x¯ = 15.8

Sample standard deviation; s = 3.85

At 90% Confidence interval, z = 1.645

Formula for confidence interval is;

CI = x¯ ± z(s/√n)

Thus;

CI = 15.8 ± 1.645(3.85/√49)

CI = 15.8 ± 0.90

CI = 14.90 to 16.70 tons

Answer:

2 Blocks

Step-by-step explanation:

Answer:2/3

Step-by-step explanation: 2 blocks apart so just 1/3 times 2=2/3

Answer:

2)

[tex]2x + 6x + 8 = 32[/tex]

collect like terms

[tex]8x + 8 = 32[/tex]

move the constant to the right hand side and change its sign.

[tex]8x = 32 - 8[/tex]

Subtract the numbers

[tex]8x = 24[/tex]

Divide both sides of the equation by 8

[tex]x = 3[/tex]

Answer:

Step-by-step explanation:

Given expression:

Answer options for equivalent expression:

A. (2x - 1)(x + 4)= 2x² + 8x - x - 4 = 2x² + 7x - 4

B. (2x + 1)(x - 4) = 2x² - 8x + x - 4 = 2x² - 7x - 4

C. (2x + 1)(x + 4) = 2x² + 8x + x + 4 = 2x² + 9x + 4

D. None of these​

Answer:

35.5 kilograms

Step-by-step explanation:

An average human's brain is 1.5 kilograms.

1.5 + 34 = 35.5

Answer:

Lol what do I do?

Step-by-step explanation:

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