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1 year ago

HELP!!! 31) Find the measure of line segment DF. A) 12 B) 13 C) 14 D) 15

Mathematics

1 answer:

oksian1 [2.3K]1 year ago

6 0

Step-by-step explanation:

for the relationship of lengths of internal chords the product of both segments of a chord is equal for all intersecting chords.

in our case

(x+8)×8 = 7×16 = 112

8x + 64 = 112

8x = 48

x = 6

so, D-F = x + 8 = 6 + 8 = 14

so, C is correct

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Given the following equation, at what point will the graph intersect? f(x) =5x+1 g(x)= -2x+15

Andru [333]

Answer: (2,11)

Step-by-step explanation:

To find the point where the functions will intersect, we want to find the place that they are equal to each other. We do this by setting the equations equal to each other.

5x+1=-2x+15 [add both sides by 2x]

7x+1=15 [subtract both sides by 1]

7x=14 [divide both sides by 7]

x=2

Now, we know that the functions intersect at x=2. To find the point, we would plug x back into both equations to ensure that the points are the same.

f(2)=5(2)+1 [multiply]

f(2)=10+1 [add]

f(2)=11

The point on f(x) is (2,11).

g(2)=-2(2)+15 [multiply]

g(2)=-4+15 [add]

g(2)=11

The point on g(x) is (2,11).

Since the point at x=2 is the same for f(x) and g(x), we know that the graph intersects at (2,11).

8 0

3 years ago

You are creating identical coupon booklets to sell for a fundraiser. You have 32 dry cleaning coupons 80 coupons for a local res

marishachu [46]

No. It means that you should find a integer to divide 32 47 80 , and the equals must be integer also. But the 3 numbers have no common factor

3 0

3 years ago

There are 158 students registered for American History classes. There are twice as many students registered in second period as

Margarita [4]

There are 28 students in first period and 56 students in sceond period and 74 students in third period

Solution:

Let the number of students in first period be "x"

Let the number of students in second period be "y"

Let the number of students in third period be "z"

There are 158 students registered for American History classes.

Therefore,

x + y + z = 158 ---------- eqn 1

There are twice as many students registered in second period as first period

number of students in second period = twice of number of students in first period

y = 2x ------- eqn 2

There are 10 less than three times as many students in third period as in first period

number of students in third period = 3 times number of students in first period - 10

z = 3x - 10 ------ eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

x + 2x + 3x - 10 = 158

6x = 168

Substitute x = 28 in eqn 2

y = 2(28)

Substitute x = 28 in eqn 3

z = 3(28) - 10

z = 84 - 10

Thus there are 28 students in first period and 56 students in sceond period and 74 students in third period

5 0

2 years ago

The question has been posted below:

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Answer:

Step-by-step explanation:

b:)

4 0

2 years ago

19. Describe the sequence of transformations from quadrilateral WXYZ to W"X"Y"Z"

Tpy6a [65]

Answer:

The sequence is as following:

1. Reflection 180°

2. Reflection over the line x=5

3. Translation 2 units down.

Step-by-step explanation:

The question is as following:

Describe the sequence of transformations from Quadrilateral WXYZ to W”X”Y”Z”.

The picture is a coordinate plane with

W= (-8,8)

X= (-2,8)

Y= (-2,4)

Z= (-8,4)

W”= (2,-10)

X”= (8,-10)

Y”= (8,-6)

Z”= (2,-6)

=================================

See the attached figure

The sequence is:

Reflection 180° ⇒ Reflection over the line x=5 ⇒ translation 2 units down.

Rule of reflection 180° is (x, y) → (–x, –y)

Rule of reflection over the line x=5 is (x, y) → (–x+10 , y)

Rule of translation 2 units down is (x, y) → (x , y–2)

The way of thinking:

1. The rectangle at the second quadrant, we need make it at the fourth quadrant, so, the suitable is Reflection 180°

2. After reflection 180°, it is noticed that we need reverse the vertices so we need to make a reflection over its vertical axis which is at x = 5

3. We need to translate it 2 units down to overlap with the required coordinates.

Check the points:

W(-8,8) ⇒ (8,-8) ⇒ (2,-8) ⇒ (2,-10)⇒W"

X(-2,8) ⇒ (2,-8) ⇒ (8,-8) ⇒ (8,-10)⇒X"

Y(-2,4) ⇒ (2,-4) ⇒ (8,-4) ⇒ (8,-6)⇒Y"

Z(-8,4) ⇒ (8,-4) ⇒ (2,-4) ⇒ (2,-6)⇒Z"

5 0

3 years ago