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3 years ago

How many triangles exist with the given angle measures? 32°, 51°, 97°

1 answer:

6 0

For each triangle sum of it's angles must add to 180°.
We need to check if these angles satisfy that condition:
32°+51°+97°=180°

They do satisfy. Now we check if any angle has value that is not possible.
32° and 51° angles are OK.
97° angle is also OK. It is obtuse angle.

For each angle measures exactly one triangle exists. In this example we have an obtuse-angle triangle.

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How many solutions does the following system of equations have?<br> 2y= 5x + 4<br> 1 = 3x + 2

Elden [556K]

Looks like a pretty regular system, no parallel lines. In fact the second equation is a vertical line as written; not sure if that's a typo. Either way,

Answer: EXACTLY ONE SOLUTION

4 0

3 years ago

The distance between the points (12,9) and (0,4) is A) 14 units B) 13 units C) 15 units D) 16 units

Juliette [100K]

Answer:

Option B 13 units is correct.

Step-by-step explanation:

The formula used to find distance between 2 points is:

$d(P1,P2)=\sqrt{(x_{2} -x_{1})^2 + (y_{2} -y_{1})^2 }$

x₁ = 12 x₂ = 0 y₁= 9 and y₂=4

Putting values in the formula:

$=\sqrt{(0-12)^2+(4-9)^2}\\=\sqrt{(-12)^2+(-5)^2}\\=\sqrt{144+25} \\=\sqrt{169} \\=13$

So, Option B 13 units is correct.

6 0

3 years ago

Read 2 more answers

Can someone help with this question

Zielflug [23.3K]

Answer:

<1= 60

<2=120

<3=60

<4=60

<5=120

<6=120

<7=60

Step-by-step explanation:

6 0

3 years ago

WILL GIVE BRAINLIEST THANKS!!!

scoray [572]

Answer: B

Step-by-step explanation:

7 0

3 years ago

The given line passes through the points and (-4, -3) and (4, 1).

Debora [2.8K]

Answer:

The equation of the line is y - 3 = -2(x + 4)

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line which passes through the points (x1 , y1) and

(x2 , y2) is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The product of the slopes of the perpendicular lines = -1

- That means if the slope of a line is m then the slope of the

perpendicular line to this line is -1/m

- The point-slope of the equation is $y - y_{1}=m(x - x_{1})$

* lets solve the problem

∵ A given line passes through points (-4 , -3) and (4 , 1)

∴ x1 = -4 , x2 = 4 and y1 = -3 , y2 = 1

∴ The slope of the line $m=\frac{1-(-3)}{4-(-4)}=\frac{1+3}{4+4}=\frac{4}{8}=\frac{1}{2}$

- The slope of the line perpendicular to this line is -1/m

∵ m = 1/2

∴ The slope of the perpendicular line is -2

- Lets find the equation of the line whose slope is -2 and passes

through point (-4 , 3)

∵ x1 = -4 , y1 = 3

∵ m = -2

∵ y - y1 = m(x - x1)

∴ y - 3 = -2(x - (-4))

∴ y - 3 = -2(x + 4)

* The equation of the line is y - 3 = -2(x + 4)

4 0

3 years ago