Which best explains whether or not all isosceles triangles are similar?a.All isosceles triangles are similar. Two angles within each triangle are always congruent.
b.All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined.
c.All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
d.All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

Answers

Answer 1

Answer:

The correct answer is:

C) All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Explanation:

Imagine we have an isosceles triangle in which the base angles are each 45°. This would make the vertex angle 90°.

Now imagine we have an isosceles triangle in which the base angles are each 30°. This would make the vertex angle 120°.

Since the angles of the first triangle are not congruent to the angles in the second triangle, the triangles are not similar.

This shows that not all isosceles triangles are similar.

Answer 2

Answer:

Answer: c. All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Step-by-step explanation:

An isosceles triangle is a triangle that has two sides of equal length.

Also, the isosceles theorem says that "If two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Consider a triangle with equal angles measure as 30°( which means the third angles will be 120°) measure and another triangle with equal angles measure as 60 ° °( which means the third angles will be 60°).

⇒ It contradicts the similarity criteria for triangle which says that in similar triangles all corresponding angles are congruent .

∴ All isosceles triangles are not similar .The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

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Answers

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(5+2yi)(4-3i) - (5-2yi)(4-3i) in a + bi form, where y is a real number.

Answers

(5+2yi)(4-3i) - (5-2yi)(4-3i)

Factorize out (4 - 3i)

(4 -3i)( (5 + 2yi) - (5 -2yi) )

(4 -3i)(5 + 2yi - 5 + 2yi)

(4 -3i)(5 - 5 + 2yi + 2yi)

(4 -3i)4yi

4*4yi - 4yi*3i

= 16yi - 12yi². i² = -1

= 16yi - 12y(-1)

= 16yi + 12y

= 12y + 16yi in the form a + bi.

$(5+2yi)(4-3i) - (5-2yi)(4-3i)=\n(4-3i)(5+2yi-5+2yi)=\n(4-3i)\cdot4yi=\n16yi+12y=\n12y+16yi$

What is the collection of numbers that includes the natural numbers, together with their negatives and zero?

Answers

we know that
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
so
the answer is
the collection of numbers that includes the natural numbers, together with their negatives and zero are the integers

A kite string is attached to a peg in the ground. If 100 meters of kite string are played out on the kite and the string makes an angle of 49° with the ground, what is the distance, in meters, from the kite to the ground? (Assume that the string is taut and the ground is level.)A. 133
B. 115
C. 75
D. 66
E. 52

Answers

The answer would be C) 75 meters between the kite and ground.

An open box will be made from a rectangular piece of cardboard that is 8 in. by 10 in. The box will be cut on the dashed red lines, removing the corners, and then folded up on the dotted lines. What is the MAXIMUM possible volume for the box?A) 1.5 in3
B) 5.8 in3
C) 52 in3
D) 64 in3

Answers

The correct answer is this one: "C) 52 in3."

Given the illustration, we can be able to know the dimensions of the formed box.

The dimensions are
Length: 10 - 2x
Width: 8 - 2x
Height: x

So the volume is
Volume = (10-2x) * (8-2x) * (x)
Let x = 2.5
Volume = (5) * (3) * (2.5) = 37.5
Let x = 2
Volume = (6) * (4) * (2) = 48
Let x = 1.5
Volume = (7) * (5) * (1.5) = 52.5
Let x = 1
Volume = (8) * (6) * (1) = 48
Let x = 0.5
Volume = (9) * (7) * (.5) = 31.5

Answer:

Step-by-step explanation:

The height, width, and length of the box will be (x)(8 - 2x)(10 - 2x). The volume of the box will be 4x3 - 36x2 + 80x = 0 Use a graphing calculator to graph the polynomial. Use the maximum feature to see the greatest volume the box can have. Be sure to set your window accordingly and think about what constraints are on the box. The maximum volume for the box is 52 in3. The cut would be 1.5 inches long. This is where the graph crosses the x-axis.

How many solutions does the nonlinear system of equations graphed below have? A. Zero B. One C. Two D. Four

Answers

Answer:

D, 4

Step-by-step explanation:

The graph crosses the x-axis 4 different times

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