We will have the following:
A. The function is compressed in the y-axis by a factor of 0.5 and then it is inverted in its direction; since it is a line the line is then decreasing instead of increasing.
B. The function is increased by a factor of 2 in the y-axis and then it is moved 3 units up:
C. The function is increased by a factor of 5/3 (Approximately 1.67) in the y-axis and then it is made so it is no longer increasing, but decreasing:
D. The function is increased in the y-axis by a factor of 9 and then it is moved 9 units down:
<h3><u>The equation in slope-intercept form for the line that passes through the point (-8, 3) and is parallel to the line -5x + 4y = 8 is:</u></h3>
<em><u>Solution:</u></em>
Given that,
We have to find the equation in slope-intercept form for the line that passes through the point (-8, 3) and is parallel to the line -5x + 4y = 8
<em><u>The equation of line in slope intercept form is given as:</u></em>
y = mx + c
Where "m" is the slope of line
From given,
-5x + 4y = 8
Rearrange to slope intercept form
4y = 5x + 8
On comparing the above equation with slope intercept form,
We know that, slopes of parallel lines are equal
Therefore, slope of line parallel to the line -5x + 4y = 8 is:
Substitute c = 13 and m = 5/4 in eqn 1
Thus the equation of line in slope intercept form is found
Answer:
5
Step-by-step explanation:
to cancel out the bottom part of the fraction, we multiply by 3. so now we have y+1= 6. we subtract 1, and get y=5
Answer: The required length of the golden thread needed is 30 cm.
Step-by-step explanation: Given that a triangular colorful scenery is made in a wall with sides 50 cm, 50 cm and 80 cm. A golden thread is to hang from the vertex so as to just reach the side 80 cm.
We are to find the length of the golden thread required.
As shown in the attached figure below, ABC is the triangular scenery with sides
AB = AC = 50 cm and BC = 80 cm.
AD is drawn perpendicular to BC, so that AD is the length of the golden thread required to reach side BC with length 80 cm from the vertex A.
Now, since AD ⊥ BC and ΔABC is isosceles (AB = AC), so we must have
D is the midpoint of BC.
That is,
Now, from the right-angled triangle ABD, we have
Thus, the required length of the golden thread needed is 30 cm.
Answer:
Step-by-step explanation:
Let the age of of Mrs brook be x
Age of her son be y
If Mrs.Brooks lacks 7 years from being five times as old as her son, this means;
x = 5y - 7 ..... 1
six years from now;
Mrs brooks age = x + 6
sons age = y + 6
If Six years from now she will lack 3 years from being three times as old as her son, this means;
x+ 6 = 3(y+6) - 3
x+6 = 3y + 18 - 3
x+6 = 3y + 15 .... 2
substitute 1 into 2;
(5y - 7)+6 = 3y + 15
5y - 1 = 3y + 15
5y-3y = 15 + 1
2y = 16
y = 8
substitute y = 8 into equation 1;
x = 5y - 7
x = 5(8)-7
x = 40-7
x = 33
Hence the mrs brook is 33 years old
her son is 8 years old
