Determine whether the figure is a right triangle. a right triangle contains one 90 degree angle. Justify your answer with slopes. ( question 16)

Answers

Answer 1

Answer: If the slopes of two lines are opposite reciprocals of each other, then the lines are perpendicular. This means the angles formed are 90°. To prove this triangle is a right triangle, the opposite and adjacent side must have opposite reciprocal slopes.

Opposite Side:
$m= (y2-y1)/(x2-x1) \n \n m= (-3-1)/(-2+5) \n \n m=- (4)/(3)$

Adjacent Side:
$m= (y2-y1)/(x2-x1) \n \n m= (-3-2)/(-2-4) \n \n m= -(5)/(6)$

Since their slopes are not opposite reciprocals, we know that this is not a right triangle.

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−8x+3≥27 AND−13x+5≥57

Answers

Answer:

$x \leq -4$

Step-by-step explanation:

$-8x+3\geq 27 and -13x+5\geq 57$

LEts solve each inequality separately. then we find the intersection of both solutions.

$-8x+3\geq 27$

Subtract 3 on both sides

$-8x\geq 24$

Divide both sides by $-8$ , change the inequality symbol when we divide by negative number

$x \leq -3$

Now solve the other inequality

$-13x+5\geq 57$

Subtract 5 on both sides

$-13x\geq 52$

Now divide both sides by $-13$

$x \leq -4$

Now we take the intersection of $x \leq -3$ and $x \leq -4$

for $x \leq -3$ , we shade the number line to the left

$x \leq -4$ , shade the number line to the left

Intersection of both graph is $x \leq -4$

Answer:

Step-by-step explanation:

Which table is related to the graph at the right?

Answers

The graph that best relates is F because it starts from lowest to highest which is what the graph is showing

Graph F.............

Why are the flat surfaces on a rectangular prism called faces

Answers

The flat surfaceson a rectangular prism are called faces because they form the exterior of the rectangularprism, and they are the only parts of the prism.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A rectangularprism is a polyhedron with two congruent and parallel bases.

Rectangular prism is also called a cuboid

The flat surfaces on a rectangular prism are called faces because they form the exterior of the rectangular prism, and they are the only parts of the prism that can be seen from the outside.

Each face has two dimensions (length and width) and all six faces together form the rectangular prism's shape.

Hence, the flat surfaces on a rectangularprism are called faces because they form the exterior of the rectangular prism, and they are the only parts of the prism.

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Because they act like a face that provides recognition to the shape.

Write 333 ones 444 tenths and 222 hundredths as a decimal.

Answers

333.
44.4
2.22
lol it confused me first

A 500 g model train car traveling at 0.8 m/s collides with a 300 g stationary car. The cars hook up and move off down the track together. How fast are they going? ( also how do I do it )

Answers

Answer:

$0.5ms^(-1)$

Step-by-step explanation:

Let v be the speed after the collision of both the cars.

Now, momentum is given by: mass × velocity, then by equating the total momentum before and after the collision of the two cars, we get

$500{*}0.8+300{*}0=(500+300)v$

⇒ $400+0=800v$

⇒ $400=800v$

⇒ $v=0.5ms^(-1)$

Thus, they are moving at the velocity of $0.5ms^(-1)$

Answer:

0.5 m/s

Step-by-step explanation:

A 500 g model train car traveling at 0.8 m/s collides with a 300 g stationary car.

Initial velocity of train, $v_T=0.8\ m/s$

Initial velocity of car, $v_C=0\ m/s$

Mass of train, $m_T=500\ g$

Mass of car, $m_C=300\ g$

The cars hook up and move off down the track together.

Let the final velocity of car and train, $v_T=v_C=v$

Using conservation of momentum,

Momentum before collision = Momentum after collision

$m_T* v_T+m_C* v_C=(m_T+m_C)* v$

$500* 0.8+300* 0=(500+300)* v$

$v=(400)/(800)$

$v=0.5\ m/s$

Hence, After collision they will going with 0.5 m/s

What is the value of the expression?

(–2)5

Answers

The answer of -10

what is expression?

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given:

(–2)5

Using integer (-)*(+)= (-)

=-2*5

=-10

Hence, the expression is -10.

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$(-2)5 = (-1 *2)5 = -1(2* 5) = -1(10) = \boxed{-10}$

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