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We have been given that PQ bisects [tex]\angle RPS[/tex]. In the second statement of the given two-column proof, the statement is [tex]\angle RPQ\cong\angle QPS[/tex].

This implies that the two angles formed by bisection of angle [tex]\angle RPS[/tex] by the line PQ are equal. We know that the reason for this is simple. It is the definition of bisection of an angle that the two smaller angles formed will be equal to each other.

Therefore, the reason for statement 2 of the given two column proof is c) Definition of bisect

Answer:

1

Step-by-step explanation:

Given: A polynomial [tex]8x^{2} +4x-3[/tex] is divided by another polynomial [tex]2x-1[/tex]

To find: Remainder when [tex]8x^{2} +4x-3[/tex]  is divided by [tex]2x-1[/tex]

Solution:

To find the remainder when [tex]8x^{2} +4x-3[/tex]  is divided by [tex]2x-1[/tex]

First, equate [tex]2x-1[/tex] with 0.

Now, [tex]2x-1=0[/tex]

[tex]\implies2x=1[/tex]

[tex]\implies x=\frac{1}{2}[/tex]

Now, to find the remainder put [tex]x=\frac{1}{2}[/tex] in [tex]8x^{2} +4x-3[/tex]

So, we have

[tex]8\times(\frac{1}{2})^{2}+4(\frac{1}{2} )-3[/tex]

[tex]=8\times\frac{1}{4} +2-3[/tex]

[tex]=2+2-3[/tex]

[tex]=4-3[/tex]

[tex]=1[/tex]

Hence, the remainder is 1.

David can cycle [tex]\( \frac{xy}{15} \)[/tex] kilometers in 12y minutes if he maintains the same average speed.

To find out how far David can cycle in 12y minutes, we first need to convert the time from minutes to hours, since David's speed is given in kilometers per hour.

Since there are 60 minutes in an hour, we can convert 12y minutes to hours by dividing by 60:

[tex]\[ \text{12y minutes} = \frac{12y}{60} = \frac{y}{5} \text{ hours} \][/tex]

Now, we know that David cycles x kilometers in 3 hours, so we can find his average speed:

[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} \]\[ \text{Average speed} = \frac{x \text{ km}}{3 \text{ hours}} \][/tex]

Now, using the average speed, we can find the distance David can cycle in [tex]\( \frac{y}{5} \)[/tex] hours:

[tex]\[ \text{Distance} = \text{Average speed} \times \text{Time} \]\[ \text{Distance} = \left( \frac{x}{3} \right) \times \left( \frac{y}{5} \right) \]\[ \text{Distance} = \frac{xy}{15} \][/tex]

To solve this problem, we need to find for the LCM of each number. That is:

12: 12, 24, 36, 48, 60

16: 16, 32, 48, 64, 80

So we can see that the LCM is 48.

Therefore the least number of each color of marble must be 48.

Answer:48

Step-by-step explanation:love ya thank me later

Answer:

Option B is correct.

Step-by-step explanation:

Given Function is,

y = x² + 4x - 32

X-intercepts of the graph of given function is the solution of the equation when y is equal to 0 is substituted.

y = 0

x² + 4x - 32 = 0

x² + 8x - 4x - 32 = 0

x ( x + 8 ) - 4 ( x + 8 ) = 0

( x + 8 ) ( x - 4 ) = 0

x + 8 = 0   and x - 4 = 0

x = -8 and x = 4

So x-intercept are ( -8 , 0 ) and  ( 4 , 0 )

Therefore, Option B is correct.

Answer:

[tex]BT=6.3[/tex]

Step-by-step explanation:

We have been given that triangle VAT is congruent to triangle BDT. We are asked to find the length of segment BT.

Since both triangles are congruent, therefore, their corresponding sides will be equal by the definition of congruence.

[tex]\Delta VAT\cong \Delta BDT[/tex]

By the definition of congruence:

[tex]VA=BD[/tex]

[tex]AT=DT[/tex]

[tex]VT=BT[/tex]

Since the length of side VT is 6.3 units, therefore the length of BT is 6.3 units as well.

Answer:

Look at pic...

The points were (-3,-6) and (2,-2)

Step-by-step explanation:

You could just use desmos graphing calculator

The equation of a line is a form of representing the set of points, which form a line in a coordinate system. 

The two points on the line are (0, -3) and (1, -11/5).

The equation of a line is a form of representing the set of points, which form a line in a coordinate system. 

The general equation of a straight line is given as:

y = mx + c,

where m = slope of the line and c = y-intercept.

We have,

y + 6 = 4/5 ( x + 3 )

Subtract 6 on both sides.

y = 4/5 ( x + 3 ) - 6

y = (4/5)x + 4/5 x 3 - 6

y = (4/5)x + 12/5 - 6

y = (4/5)x + (12 - 30)/6

y = (4/5)x - 3

The y-intercept is at -3.

We have a point as (0, -3).

For x = 1,

y = (4/5) x 1 - 3

y = 4/5 - 3

y = (4 - 15) / 5 = -11/5

The other point is (1, -11/5)

Thus,

The two points on the line are (0, -3) and (1, -11/5).

Learn more about equation of a line here:

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Ian could have his website on site B for less than 10 months for it to be cheaper than hosting on site A.

To solve this question, we need to find when the costs between site a and site b equal each other. Since site a charges $4.95 per month plus a $49.99 startup fee, the cost of site a can be modelled by the equation: 4.95x + 49.99. Site b charges $9.95 per month with no startup fee, so its cost can be modelled by the equation 9.95x. We can now set up the inequality as follows:

4.95x + 49.99 > 9.95x

To solve for x, we will subtract 4.95x from both sides of the inequality, getting 49.99 > 5x. Finally, we divide each side by 5 to solve for x, resulting in x < 10. So Ian could have his website on site b for less than 10 months and still keep his total cost less than site a.

https://brainly.com/question/15086723

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the equation is - tan2 x + sec2 x = 1.

Left hand side identity : - tan2 x + sec2 x.

Trigonometric function : tan x = sin x / cos x,

Reciprocal identity : sec x = 1/cos x.

- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2

= - sin2 x/cos2 x + 1/cos2 x

= (1 - sin2 x)/cos2 x

Pythagorean identity : sin2 x + cos2 x = 1 .

= cos2 x / cos2 x

= 1

Final answer:

To find the price per dozen, divide the sale price of $2.55 by 4 to get the price per muffin, then multiply by 12. The price per dozen muffins is $7.65.

Explanation:

To calculate the price per dozen muffins at the bakery when the sale price is $2.55 for 4 muffins, you first need to determine the price of one muffin. You can do this by dividing the sale price by the number of muffins in the offer:

$2.55 ÷ 4 = $0.6375 per muffin.

Next, because a dozen consists of 12 items, you would find the price per dozen by multiplying the price per muffin by 12:

$0.6375 × 12 = $7.65

Therefore, the price per dozen muffins is $7.65.

Answer:

The system of the equations is: j+s=63 and j-s=33

The Jackets price is j=48

The slacks prices is s=15

Step-by-step explanation:

You know for the problem that:

j+s=65

And

j= s+33; from this equation you get j-s=33

Then you replace j "j=s+33" in the first equation:

(s+33)+s=63

2s+33=63

2s=63-33

s=(63-33)/2

s=15

and you know that: j=s+33

Then, j=15+33=48

and j+s=63

48+15=63

1 foot = 12 inches

135 / 12 = 11.25 feet 0.25 feet = 0.25 * 12 = 3 inches

answer is: 11 feet 3 inches