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3 years ago

Find the value of k so that the line through the given points has slope m.

1 answer:

6 0

$(2k,3) \\
x_1=2k \\ y_1=3 \\ \\
(1,k) \\ x_2=1 \\ y_2=k \\ \\
\hbox{the slope: } m=\frac{y_2-y_1}{x_2-x_1}=\frac{k-3}{1-2k}$

The slope is equal to 2.
$\frac{k-3}{1-2k}=2 \\
k-3=2(1-2k) \\
k-3=2-4k \\
k+4k=2+3 \\
5k=5 \\
k=\frac{5}{5} \\
\boxed{k=1}$

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The area of a bulletin board is 52 square feet. The length is 3 feet less than4 times the width. Find the length and width

Brilliant_brown [7]

Answer:

The length of the bulletin board is $13\ ft$

The width of the bulletin board is $4\ ft$

Step-by-step explanation:

Let

x-----> the length of the bulletin board

y-----> the width of the bulletin board

we know that

The area of the rectangle (bulletin board) is equal to

$A=xy$

we have

$A=52\ ft^{2}$

$52=xy$ ------> equation A

$x=4y-3$ ------> equation B

substitute equation B in equation A and solve for y

$52=(4y-3)y$

$4y^{2}-3y-52=0$

Using a graphing calculator------> solve the quadratic equation

The solution is

$y=4\ ft$

see the attached figure

Find the value of x

$x=4(4)-3=13\ ft$

6 0

4 years ago

A builder was building a fence. In the moring he worked 2/5 of an hour. In the afternoon he wirked for 9/10 of an hour how many

Burka [1]

Answer:

2 1/4 times

Step-by-step explanation:

A builder was building a fence. In the moring he worked 2/5 of an hour. In the afternoon he wirked for 9/10 of an hour. how many times as long in the morning did he work in the afternoon

Note that:

1 hour = 60 minutes

In the moring he worked 2/5 of an hour.

= 2/5 × 60 minutes

= 24 minutes

In the afternoon he worked for 9/10 of an hour

Hence:

9/10 × 60 minutes

= 54 minutes

How many times as long in the morning did he work in the afternoon?

This is calculated as number of minutes worked in the afternoon ÷ Number of minutes worked in the morning

= 54 minutes/24 minutes

= 2 6/24

= 2 1/4 times

4 0

3 years ago

What is 3 + -5= and is it a positive or negative number and how?

Natalka [10]

It is -2. This is negative. For instance, if you had 3 candies and your mother took away 5, you would not only have 0 candies, but you would owe your mother 2. This is expressed as a negative number. Please mark Brainliest!!!

7 0

3 years ago

Read 2 more answers

If there are 13 people in club a and 20 people in club b and 25 students in total, how many people are in both clubs?

Svetradugi [14.3K]

Answer:

2 students are in both clubs

Step-by-step explanation:

x = 1 student (this number may be more than the total because one student can be in 2 clubs)

Club a = 13

Club b = 20

13 + 20 = 27x

Total members of clubs - total number of students = 27x - 25 = 2

2 students are in both clubs

Hope this was useful to you!

8 0

3 years ago

Find the area of an equilateral triangle with a side of 10cm

r-ruslan [8.4K]

Answer:

Since it is an equilateral triangle, all sides are 10cm

Step-by-step explanation:

8 0

3 years ago