MATH QUESTIONS!!!
Geometry Questions? (20 PTS)

Answers

Answer 1

Answer: Questions 1-3
A triangle is:
either scalene, isoceles, or equilateral, and
either acute, right, or obtuse.

Question 1: The triangle is right b/c it has a right angle.
The triangle is isoceles because it has two congruent sides.
Right isoceles triangle

Question 2: The triangle is obtuse b/c it has an obtuse angle. (>90°)
The triangle is isoceles b/c it has two congruent sides.
Obtuse isoceles triangle

Question 3: All angles in a triangle add up to 180°. Let's find the 3rd angle.
180 - (80 + 60) = 180 - 140 = 40°
Congruent angles $\doublearrow$ congruent sides, so...
If the angles are all different, the sides are all different and the triangle is scalene. It is also acute because all angles are <90°.
Acute scalene triangle

Question 4
An exterior angle of a triangle = the sum of its remote interior angles.
what does this mean? In this case, it means that
4x + 10 = 50 + x + 5
The reason this works: <ACD is supplementary to <ACB, so they must both add up to 180. Likewise, the angles of the triangle <ACB, <BAC, and <ABC all add up to 180. Since both = 180, we can set them equal (substitution prop)
m<ACD + m<ACB = m<ACB + m<BAC + m<ABC
subtract m<ACB from each side
m<ACD = m<BAC + m<ABC
now let's solve our equation.
4x + 10 = 50 + x + 5
4x + 10 = 55 + x
subtract x from each side
3x + 10 = 55
subtract 10 from each side
3x = 45
divide by 3
x = 15
the measure of the interior angle = (x+5)° = (15+5)° = 20°
the measure of the exterior angle = (4x+10)° = (4(15)+10)° = (60+10)° = 70°

Question 5
As we can see from the diagram...
AB = CD, AD = BC
<ABD = <BDC, <ADB = <CBD
Also obvious from the reflexive prop...
BD = BD
And because the three angles add up to 180° and we know that two of them are the same, the third must be the same as well.
<A = <C
(three points don't need specified because only one angle is possible with this vertex)

Question 6
Because the angles in a triangle add up to 180°...
m<A + m<ADB + m<ABD = 180°
We know that m<A = 60°...
60 + m<ADB + m<ABD = 180°
We know that m<DBC = 70°, and from the diagram, <ADB is cong. to <DBC.
Therefore m<ADB = 70°.
60 + 70 m<ABD = 180°
130 + m<ABD = 180°
m<ABD = 50°

Answer 2

Answer:

Answer:

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Step-by-step explanation:

Answer:

Hence, the property:

A ∩ B = A ∪ B never hold .

Step-by-step explanation:

We are given that set A⊂B .

This means that set A is properly contained in set B.

i.e. A≠B

This means that there are some elements in set B which are not in set A.

Now we have to show whether the following property A∩B=A∪B

always, sometimes or never hold.

As A is a proper set of B.

This means that: A∩B=A ( Since A is a smaller set)

Also, A∪B=B (Since B is a bigger set)

Hence, A∩B ≠ A∪B (Since A≠ B)

The answer is never.

Urgent!!!!! Which equation describes the graphed line

Answers

Answer: Hello, this is Bing. I can help you with your math problem.

To find the equation of the graphed line, we need to identify its slope and y-intercept. The slope is the ratio of the vertical change to the horizontal change between any two points on the line. The y-intercept is the point where the line crosses the y-axis.

Looking at the image, we can see that the line passes through the points (-3, 4) and (3, -2). We can use these points to calculate the slope:

slope = (y2 - y1) / (x2 - x1) slope = (-2 - 4) / (3 - (-3)) slope = -6 / 6 slope = -1

The slope of the line is -1. This means that for every unit increase in x, the y value decreases by 1 unit.

To find the y-intercept, we can use either of the points and plug them into the equation y = mx + b, where m is the slope and b is the y-intercept. For example, using the point (-3, 4), we have:

4 = -1 * (-3) + b 4 = 3 + b b = 1

The y-intercept of the line is 1. This means that the line crosses the y-axis at (0, 1).

Therefore, the equation of the graphed line is:

y = -x + 1

This equation matches with one of the options given below the graph: y = -1/2x + 4. This is because we can multiply both sides of the equation by 2 and get:

2y = -2x + 2 y = -1/2x + 4

Answer: The equation that describes the graphed line is y = -1/2x + 4.

The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?

Answers

The ground floor: 52 windows.
We will use the arithmetic sequence:
a 1 = 52
d = - 6
a n = a 1 + ( n - 1 ) d
a 8 = a 1 + 7 d
a 8 = 52 + 7 * ( - 6 ) = 52 - 42 = 10
S n = n/2 * ( a 1 + a n )
S 8 = 8/2 * ( 52 + 10 ) = 4 * 62 = 248
Answer:
There are 248 windows on the first eight floors.

(A) this relation is a function

(B) this relation is not a function