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3 years ago

Given that Ray B A bisects ∠DBC, which statement must be true? m∠ABD = m∠ABC AB ≅ BC B is the midpoint of DC. m∠DBC = 90°

Mathematics

2 answers:

Sloan [31]3 years ago

8 0

Answer:

Step-by-step explanation:

Because I said this was the answer. I know all.

nadya68 [22]3 years ago

4 0

Answer:

A. $m\angle ABD=m\angle ABC$

Step-by-step explanation:

We are given that a ray BA bisects angle DBC.

We have to find true statement .

Angle bisector property:When a ray bisect any angle then the angles made by bisection of angle are equal.

When ray BA bisects angle DBC

Then, $m\angle ABD=m\angle ABC$

By angle bisector property.

Therefore, option A is true.

Answer:A. $m\angle ABD=m\angle ABC$

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The resultant of two forces acting on a body has a magnitude of 60 pounds. The angle between the 28-pound force and the resultan

Leto [7]

1. We will use the Cosine Law:
x² = 60² + 28² - 2 · 60 · 28 · cos 50°
x² = 3,600 + 784 - 3360 · 0.6428
x² = 2,224.234
x = √2,224.234
x = 47.16 pounds ≈ 47.2
Answer: B ) 47.2 pounds
2. By the Cosine Law ( angle of 135° is opposite the forces resultant ):
R² = 150² + 50² - 2 · 150 · 50 · cos 135°
R² = 22,500+2,500 -15,000 · ( -0.71 )
R² = 35,650
R = √35,650 = 188.812 mph
After that we will use the Sine Law:
50 / sin α = 188.812 / sin 135°
50 / sin α = 188.812 / 0.71
sin α = 50 · 0.71 / 188.812
sin α = 0.188
α = sin^(-1) 0.188
α = 10.83° ≈ 10.8°
Answer: C ) 10.8°

4 0

3 years ago

Write the following expression

Rashid [163]

Answer:

2x^2 - 18x + 45

Step-by-step explanation:

Standard form is ax^2 + bx + c

Expand the (x-5)^2 = (x-5)(x-5) --

x^2 - 5x - 5x + 25

x^2 - 10x + 25

So we now have

2(x^2 - 10x + 25) + 2(x-5) + 5

From here, distribute the 2 to each term in x^2 - 10x + 25, and distribute the 2 to each term in x - 5.

2x^2 - 20x + 50 + 2x - 10 + 5

Combine like terms

2x^2 - 20x + 2x + 50 - 10 + 5

2x^2 - 18x + 40 + 5

2x^2 - 18x + 45

6 0

3 years ago

Without sketching the graph, find the x intercepts and y-intercepts of the graph of the equation 2x+3y=12 What isjare the x-inte

den301095 [7]

Answer:

x-intercept: (6,0)

y-intercept: (0,4)

Step-by-step explanation:

The x-intercepts lay on the x-axis and therefore their y-coordinate is 0.

To find the x-intercept, you set y to 0 and solve for x.

2x+3y=12

Set y=0.

2x+3(0)=12

2x+0 =12

2x =12

Divide both sides by 2:

x =12/2

x =6

The x-intercept is (x,y)=(6,0).

The y-intercepts lay on the y-axis and therefore their x-coordinate is 0.

To find the y-intercept, you set x to 0 solve for y.

2x+3y=12

2(0)+3y=12

0+3y =12

3y =12

Divide both sides by 3:

y =12/3

y =4

The y-intercept is (0,4).

8 0

3 years ago

On a certain airline, customers are assigned a row number when they purchase their ticket, but the four seats within the row are

maksim [4K]

Answer:

The probability that they sit next to each other is 50%.

Step-by-step explanation:

Consider the provided information.

It is given that there are four seats within the row are first come, first served during boarding.

There are 4 seats and 2 customers (Karen and Georgia)

The total number of ways in which Karen and Georgia can sit is: $^4C_2$

Now if they will sit together, then consider Karen and Georgia as a single unit.

Thus, the number of ways in which they can sit together is: $^3C_1$

The required probability is:

$P=\frac{^3C_1}{^4C_2} \\\\P=\frac{3}{6}\\\\P=\frac{1}{2}$

Hence, the probability that they sit next to each other is 50%.

6 0

3 years ago

What effect would doubling all the dimensions of a triangular pyramid have on the volume of the pyramid?

lana66690 [7]

Answer:

The effect of doubling all the dimensions of a triangular pyramid will have on the volume of the pyramid is to increase it by 8 times.

Step-by-step explanation:

i) volume of triangular pyramid = $\frac{1}{3}$ $\times$ Area $\times$ height

= $\frac{1}{3}$ $\times$ (Base of triangle $\times$ perpendicular height of triangle) $\times$ height

ii) if we double all the dimensions then the three variables((Base of triangle, perpendicular height of triangle, height of pyramid) will be doubled

and the volume of the new pyramid will be 8 times that of the original one.

3 0

3 years ago