Solve w = t(r1 + r2) for t.

To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope. Substituting the values into the point-slope form, we can find the equation of the perpendicular line.

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation 3x - 5y = 6, so its slope is 3/5. The negative reciprocal of 3/5 is -5/3, so the slope of the line perpendicular to the given line is -5/3.

Since we know a point on the perpendicular line is P(-8, 0), we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting -8 for x1, 0 for y1, and -5/3 for m, we get y - 0 = -5/3(x - (-8)).

Simplifying the equation gives y = -5/3x - 40/3, which is the equation of the line passing through point P(-8, 0) and perpendicular to the line 3x - 5y = 6.

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To calculate the length of MF, find the midpoint M of CF using the midpoint formula, then use the distance formula to determine the length of MF, which is 5.0 cm.

To find the length of the segment MF, we must first determine the coordinates of the midpoint M of the segment CF. Since C has coordinates (1, 2) and F has coordinates (7, 10), we use the midpoint formula which is ( (x1 + x2)/2, (y1 + y2)/2 ). Calculating this for C and F gives us the coordinates of M as:

Therefore, M has coordinates (4, 6). Now, to find the distance MF, we use the distance formula between points M and F:

MF = √[(x2 - x1)² + (y2 - y1)²] where (x1, y1) are the coordinates of M and (x2, y2) are the coordinates of F.

Replacing with the known values:

MF = √[(7 - 4)² + (10 - 6)²]

MF = √[3² + 4²] = √[9 + 16] = √25 = 5.0 cm

Thus, the length of the segment MF is 5.0 cm.

You would need to pull out 21 socks from the dryer to ensure you have a black pair since you might initially pull out all 19 green socks before getting to the black ones.

To determine how many socks one would need to pull out of the dryer to be sure to get a pair of black socks when you have 19 black socks and 19 green socks, consider the worst-case scenario. In the worst case, you pull out all 19 green socks one by one. Since you have not yet pulled out a single black sock, the 20th sock you pull out has to be black, because there are no more green socks left. However, to ensure you have a pair of black socks, you will need to pull out one more sock. So the answer is that you need to pull out 21 socks to be certain of having a pair of black socks.

The length of the shadow cast by a person 1.82 m tall is; 4.09m

The angle of Elevation to the sub is 24°.

On this note, the shadow cast on the floor represents the adjacent of the angle of Elevation.

Hence, the length of the shadow cast can be calculated from Tangent identify as follows;

Length of shadow = 4.09m

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Answer:

The correct option is 3. c is the square of half of b.

Step-by-step explanation:

The given equations are

[tex](x+3)^2=x^2+6x+9[/tex]

[tex](x+4)^2=x^2+8x+16[/tex]

[tex](x+5)^2=x^2+10x+25[/tex]

[tex](x+6)^2=x^2+12x+36[/tex]

These are the perfect square. According to this pattern,

[tex](x+y)^2=x^2+2xy+y^2[/tex]           .... (1)

Each product is in the form

[tex](x+y)^2=ax^2+bx+c[/tex]         .... (2)

From (1) and (2), we get

[tex]b=2y[/tex]

[tex]c=y^2[/tex]

[tex]c=(\frac{b}{2})^2[/tex]                    [tex][\because b=2y][/tex]

It means c is the square of half of b.

Therefore the correct option is 3.

Sydney can read 5/4 or 1.25 pages in one minute

Data;

This can be defined as the measure of one unit against another unit.

If it take Sydney 40 minutes to read 50 pages, let's calculate how many pages she will read in one minute to determine her rate.

[tex]40 pages = 50 minutes\\x pages = 1 minute[/tex]

Let's cross multiply both sides and solve for x

[tex]50 pages = 40 minute\\x pages = 1 minute\\x = \frac{50*1}{40}\\x = 1.25 page[/tex]

From the calculations above, Sydney can read 5/4 or 1.25 pages in one minute.

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Hello : let  A(-3,-1)    B(-6,8)
the slope is :   (YB - YA)/(XB -XA)
(8+1)/(-6+3)  =9/(-3)
the slope is: -3

45/7 is the correct answer

Answer:

1976

Step-by-step explanation:

Answer:

Step-by-steThe first step for solving this expression is to distribute -y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y × (y + 1) - 3y × (y² - 1))

Distribute 2y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y × (y² - 1))

Now distribute -3y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y³ + 3y)

Collect the like terms in the first set of the parenthesis.

3y³ - 2y × (7y - y²) - (2y² + 2y - 3y³ + 3y)

Collect the like terms in the second set of the parenthesis.

3y³ - 2y × (7y - y²) - (2y² + 5y - 3y³)

Distribute -2y through the parenthesis.

3y³ - 14y² + 2y³ - (2y² + 5y - 3y³)

Remember that when there is a "-" sign in front of the parenthesis,, you must change the sign of each term in the parenthesis. This will change the expression to the following:

3y³ - 14y² + 2y³ - 2y² - 5y + 3y³

Collect the like terms with an exponent of 3.

8y³ - 14y² - 2y² - 5y

Lastly,, collect like terms that have an exponent of 2.

8y³ - 16y² - 5y

Since we cannot simplify the expression any further,, the correct answer is going to be 8y³ - 16y² - 5y.

Let me know if you have any further questions.

perimeter = 2L +2w

L = w+11

70 = 2(w+11) +2w

70 = 2w+22+2w

70= 4w + 22

48 = 4w

w=48/4 = 12

width = 12

length = 12+11 = 23

2x12 = 24

2x23 = 46

46+24 = 40

 length = 23 inches, width = 12 inches

Answer is D

Answer:

The answer is the option D

[tex]12\ inches[/tex]

Step-by-step explanation:

we know that

The perimeter of a rectangle is equal to

[tex]P=2L+2W[/tex]

where

L is the length side of the rectangle

W is the width side of the rectangle

In this problem we have

[tex]P=70\ in[/tex]

so

[tex]70=2L+2W[/tex] ------> equation A

[tex]L=W+11[/tex] ------> equation B

Substitute equation B in equation A and solve for W

[tex]70=2[W+11]+2W[/tex]

[tex]70=2W+22+2W[/tex]

[tex]4W=70-22[/tex]

[tex]W=48/4[/tex]

[tex]W=12\ in[/tex]

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

where

r is the radius of the circle

In this problem we have

[tex]r=9\ in[/tex]

substitute in the formula

[tex]A=\pi*9^{2}=81 \pi\ in^{2}[/tex]

The area of the complete circle subtends [tex]360\ degrees[/tex]

When the time is 4:00 the angle formed by the hands of a clock is [tex]120\ degrees[/tex]

so by proportion

Find the area of the sector area

[tex]\frac{81\pi}{360} \frac{in^{2}}{degree} =\frac{x}{120} \frac{in^{2}}{degree} \\ \\x=120*81 \pi /360\\ \\x=27 \pi\ in^{2}[/tex]

therefore

the answer is the option

[tex]27 \pi\ in^{2}[/tex]

Answer:

x= 80

y= 130

Step-by-step explanation:

The correct values of x and y that make k || j and m || n are x = 130 and y = 130.

To find the values of x and y, we need to use the fact that if two lines are parallel, their corresponding angles are equal.

Given that k is parallel to j, we have:

x = 50 (corresponding angles)

Since m is parallel to n, we have:

y + 80 = 210 (corresponding angles)

Solving for y:

y = 210 - 80

y = 130

Now, we have the value of x as 50 and the value of y as 130. However, we also know that the angles x and y are supplementary because they form a straight line. Therefore, their sum must be 180 degrees.

x + y = 180

50 + y = 180

y = 180 - 50

y = 130

This confirms that y is indeed 130 degrees. Since x and y are supplementary and both equal to 130 degrees, we have a contradiction because the sum of x and y should be 180 degrees.

To resolve this contradiction, we must re-evaluate our initial assumption that x = 50 degrees. Since x and y are supplementary, and we have correctly determined that y = 130 degrees, we must have:

x + y = 180

x + 130 = 180

x = 180 - 130

x = 50

This is incorrect because we initially assumed x = 50 degrees based on corresponding angles, but we did not consider that the angle adjacent to x on line k is not given and could be different from the corresponding angle of 50 degrees on line j.

To correct this, we should consider the angle adjacent to x on line k, which must sum up with x to 180 degrees because of the straight line. Let's call this angle x'. Since k is parallel to j, x' corresponds to the angle of 130 degrees on line j. Therefore, we have:

x' + x = 180

130 + x = 180

x = 180 - 130

x = 50

Now, considering that x and y are supplementary:

x + y = 180

50 + y = 180

y = 180 - 50

y = 130

Thus, we have x = 50 degrees and y = 130 degrees, which are indeed the values that make k || j and m || n. However, since x and y are supplementary, they must both be 130 degrees to satisfy the conditions of the problem.

Therefore, the correct values are x = 130 degrees and y = 130 degrees.