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nata0808 [166]
3 years ago
13

Lines x and y intersect to make two pairs of vertical angles, q, s and r, t. Fill in the blank space in the given proof to prove

∠q ≅ ∠s. A) Transitive property B) Addition property of equality C) Subtraction property of equality D) Substitution property

Mathematics
1 answer:
bonufazy [111]3 years ago
5 0

Answer:

C) Subtraction property of equality.

Step-by-step explanation:

Given that, two lines x and y intersect to make pairs of vertical angles:

\angle q, \angle s and \angle r, \angle t.

Kindly refer to the attached image for details of the given angles and lines.

Proof that \angle q\cong \angle s :

\begin{center}\begin{tabular}{ c c}Statements & Reasons \\ m\angle q+m\angle r=180^\circ & \angle q\ and\ \angle r\ are\ supplementary  \\  m\angle r+m\angle s=180^\circ & \angle r\ and\ \angle s\ are\ supplementary  \\  \angle q+\angle r=\angle q+\angle r & Algebraic substitution  \\ m\angle q = m\angle s & Subtraction property of equality\end{tabular}\end{center}

Here, subtraction property of equality is used in the last step shown in the above.

As per the <em>Subtraction property </em>of equality, when some value is subtracted from both the sides of the equality, equality remains the same.

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adelina 88 [10]
The path is the hypotenuse of a right triangle with legs 30 and 120.

30² + 120² = c²

900 + 14400 = c²

15300 = c²

c=√15300 ≈123.7'

instead of walking 30+120=150 feet they save 26.3 feet by taking the shortcut
8 0
3 years ago
What is the equation of the line that passes through the point (-3, -1) and has a slope of -4 ?
AnnZ [28]

Answer:

y = - 4x - 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4, thus

y = - 4x ++ c ← is the partial equation

To find c substitute (- 3, - 1) into the partial equation

- 1 = 12 + c ⇒ c = - 1 - 12 = - 13

y = - 4x - 13 ← equation of line

8 0
3 years ago
The graph below shows a line of best fit for the relationship between the number of tickets that Brittany has and the number of
g100num [7]

Answer:

C.  

The slope means that for every three rides, Brittany uses about 14 tickets.

Step-by-step explanation:

The given line of best-fit is

y = -4.64x + 47.6

Y-intercept is the point where x is zero. For the given equation y-intercept will be 47.6 or 48 rounded to nearest dollar. In other words, y-intercept is also a point where the line cross the y-axis.

From the given graph we can see that the y-axis shows the number of tickets purchased. The point where the line cross y-axis is about 48.

This tells us that Brittany had 48 tickets when she did not take any ride.

In this case, the slope of the line tells us that how many tickets were used for one ride, as x represents the number of rides. For one ride 4.64 tickets were, for 2 rides 2 x 4.64 = 9.28 tickets were used, for 3 rides 13.92 or around 14 tickets were used.

Now if we look at the given options we can easily say the option C is the correct answer.

Option A is not correct as it gives the opposite information than the actual one. Option B is also wrong, as x-intercept will tell us after how many rides the tickets will expire. Option D is wrong as y-intercept gives the number of tickets not the amount of money.

8 0
3 years ago
Read 2 more answers
20 yards 8 inches is divided into 26 equal sections, how long is each section
hoa [83]
In the given question, there are several information's of immense importance and worth taking a look. based on these information's, the answer to the question can be easily determined.The length that has to be divided into 26 equal parts is 20 yards and 8 inches.Firstly we have to change the yard into inches and then we can divide the total inches into 26 equal parts.
We know
1 yard = 36 inches
20 yards = 720 inches
Then the total length that has to be divided = (720 + 8) inches
                                                                     = 728 inches
Now we have to divide the 728 inches into 26 equal parts.
Length of each section = (728/26) inches
                                      = 28 inches.
So each of the 26 parts will have a length of 28 inches.

5 0
3 years ago
Mrs. Bhatia's closet consists of two sections, each shaped like a rectangular prism. She plans to buy mothballs to keep the moth
AveGali [126]

Answer:

6.5 boxes

Step-by-step explanation:

Given

See attachment for closet

Required

Determine the number of boxes needed to fill the closet

First, we calculate the volume of the two section.

According to the attachment

The first section has the following dimension:

Width = 5ft

Length = 4ft

Height = 8ft

The second has the following dimension:

Width = 3ft ---- see the last label at the top

Length = 2ft --- This is calculated by subtracting the length of the first section (4ft) from the total length of the closet (6ft) i.e. 6ft - 4ft

Height = 8ft

So: The volume of the closet is:

Volume = W_1 * L_1 * H_1 + W_2 * L_2 * H_2

Volume = 5ft * 4ft * 8ft + 3ft * 2ft * 8ft

Volume = 160ft^3 + 48ft^3

Volume = 208ft^3

The number of box needed is then calculated by dividing the volume of the closet (208ft^3) by the volume of each box (32ft^3)

Boxes = \frac{208ft^3}{32ft^3}

Boxes= \frac{208}{32}

Boxes = 6.5

7 0
3 years ago
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