6. when y = |x| is translated 6 units down, 6 is subtracted from the y-value: .. y = |x| -6
10. In point-slope form, the line through point (h, k) with slope m is .. y -k = m(x -h) For (h, k) = (10, -9) and m = -2, you have .. y +9 = -2(x -10)
The solution to this exercise has been attached below. The problem has been solved in this way:
1. Different forms of linear equations. Point slope-intercept equation of the line that passes through two points.2. Inverse Function. 3. Average Rate of Change.4. Comparison of linear equations and inequalities5. Real-life problems6. Imaginary Number7. Radicals8. Rational exponent and radical form9. Radical expressions10. Quadratic equation11. Trinomial12. Factoring expressions13. Quadratic and linear graph14. A problem of height
Shifting left or right is addition and subtraction respectfully inside the function.Shifting up and down is addition and subtraction respectfully outside the function.
5. A translation of 6.5 units up is +6.5 outside the function y=|x| so equation y=|x|+6.5 is the translation.
6. A translation of 5.5 units to the right is - 5.5 inside the function y=|x| so equation y=|x-5.5| is the translation.
7. A translation of 8 units to the left is +8 inside the function y=|x| so equation y=|x+8| is the translation.
3. tan(α) = height/distance
distance = height/tan(α)
distance = (648 m)/tan(13°) ≈ 1399.5 m
6. when y = |x| is translated 6 units down, 6 is subtracted from the y-value:
.. y = |x| -6
10. In point-slope form, the line through point (h, k) with slope m is
.. y -k = m(x -h)
For (h, k) = (10, -9) and m = -2, you have
.. y +9 = -2(x -10)
The solution to this exercise has been attached below. The problem has been solved in this way:
1. Different forms of linear equations. Point slope-intercept equation of the line that passes through two points.2. Inverse Function. 3. Average Rate of Change.4. Comparison of linear equations and inequalities5. Real-life problems6. Imaginary Number7. Radicals8. Rational exponent and radical form9. Radical expressions10. Quadratic equation11. Trinomial12. Factoring expressions13. Quadratic and linear graph14. A problem of height
1. y=2x-9
5. y = | x | + 6.5
6. y = | x – 5.5 |
7. y = | x + 8|
Step-by-step explanation:
There is not enough given information for some of the problems. Here are the solutions and reasons for those that area solvable:
Write a perpendicular line to the equation -3x-6y=17 by finding its slope and then flipping it to the negative reciprocal:
So -3x-6y=17 becomes y=-1/2x-17/6 where m = -1/2. The perpendicular slope is 2.
Using the point given, write the equation in point slope form and simplify to the slope intercept form:
[tex]y-y_1=m(x-x_1)\\y-3=2(x-6)\\y-3=2x-12\\y=2x-9[/tex]
When translating functions, remember:
Shifting left or right is addition and subtraction respectfully inside the function.Shifting up and down is addition and subtraction respectfully outside the function.
5. A translation of 6.5 units up is +6.5 outside the function y=|x| so equation y=|x|+6.5 is the translation.
6. A translation of 5.5 units to the right is - 5.5 inside the function y=|x| so equation y=|x-5.5| is the translation.
7. A translation of 8 units to the left is +8 inside the function y=|x| so equation y=|x+8| is the translation.
[tex]y=\cos x + 6[/tex]
Step-by-step explanation:
We are given a cos x function. We need to find the function shift 6 units up.
Graph will shift 6 units up. So, all y value of function shift vertically up.
y=f(x)
If shift h and k horizontally and vertically respectively then y=f(x+h)+k
y=cos x
Shift h and k unit then new function
y=cos(x+h)+k <=> cos x + 6
Thus, C is correct option.
5. When the dome is 50 feet high, the distance from the center is 5 feet
6. The equation that model the price y of an x-mile long ride is given as follows;
y = 0.1×x + $3.00
7. The discriminant is < 0; The equation has no real root
8. f(3) = 68
9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7
Step-by-step explanation:
5. The given equation for the shape of the dome is presented as follows;
h = -2·d² + 100
Where;
h = The height of the dome (in feet)
d = The distance from the center
Therefore, we have;
When h = 50, d is found as follows;
h = -2·d² + 100
50 = -2·d² + 100
50 - 100 = -2·d²
-50 = -2·d²
∴ 2·d² = 50
d² = 50/2 = 25
d = √25 = 5 feet
Therefore when the dome is 50 feet high, the distance from the center is 5 feet
6. The given rate the cab charges per mile, x = $0.10
The rate the cab charges as flat fee = $3.00
Therefore, the price, y a person traveling by cab for x miles is given by the straight lie equation as y = m·x + c,
Where;
m = the slope or rate which in this case = $0.1/hour
c = A constant term which in this case = $3.00
Therefore
y = 0.1×x + $3.00
The equation that model the price y of an x-mile long ride is y = 0.1×x + $3.00
7. The discriminant, b² - 4·a·c of the quadratic equation is (-4)² - 4×3×6 = -56
which is < 0, the equation has no real root
8. Given f(x) = 7·x² + 5
f(3) = 7 × (3)² + 5 = 68
f(3) = 68
9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is given as follows;
Down 4 units is equivalent to subtracting 4 from the y-coordinate value, therefore, we have;
f(x) - 4= 7·x + 3
f(x) = 7·x + 3 + 4
f(x) = 7·x + 7
The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7
B: y=cos(x-5). I'm sorry I can't really explain.
1.
[tex]y = m(x - 4) + 7[/tex]
Explanation:
as we know that equation of straight line passing through a fixed point and having undefined slope is given as
[tex]y - y_1 = m(x - x_1)[/tex]
here we have
[tex](x_1, y_1) = (4, 7)[/tex]
so we will have
[tex]y - 7 = m(x - 4)[/tex]
[tex]y = m(x - 4) + 7[/tex]
2.
slope = ZERO
Explanation:
Slope of the straight line is defined as the tangent of the angle made by the line with respect to x axis
here we need to find the slope of a straight line parallel to x axis so the angle is ZERO degree
hence the slope will be given as
[tex]m = tan 0[/tex]
[tex]m = 0[/tex]
3.
[tex]m = 0.5[/tex]
Explanation:
Slope of a straight line passing through two different points is given as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
here we will have
[tex]m = \frac{7 - 5}{1 + 3}[/tex]
[tex]m = \frac{2}{4}[/tex]
[tex]m = 0.5[/tex]
4.
[tex]y = |x - x'|[/tex]
here x' = any positive number
Explanation:
If we translate the graph 2 units left of the given position so we can say that we have shifted the graph above from its given position.
So we will have
[tex]y = |x - x'|[/tex]
here x' = any positive number
D.y-4=f(x+3)
Step-by-step explanation:
The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.
Hope this helps
1.
[tex]y = m(x - 4) + 7[/tex]
Explanation:
as we know that equation of straight line passing through a fixed point and having undefined slope is given as
[tex]y - y_1 = m(x - x_1)[/tex]
here we have
[tex](x_1, y_1) = (4, 7)[/tex]
so we will have
[tex]y - 7 = m(x - 4)[/tex]
[tex]y = m(x - 4) + 7[/tex]
2.
slope = ZERO
Explanation:
Slope of the straight line is defined as the tangent of the angle made by the line with respect to x axis
here we need to find the slope of a straight line parallel to x axis so the angle is ZERO degree
hence the slope will be given as
[tex]m = tan 0[/tex]
[tex]m = 0[/tex]
3.
[tex]m = 0.5[/tex]
Explanation:
Slope of a straight line passing through two different points is given as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
here we will have
[tex]m = \frac{7 - 5}{1 + 3}[/tex]
[tex]m = \frac{2}{4}[/tex]
[tex]m = 0.5[/tex]
4.
[tex]y = |x - x'|[/tex]
here x' = any positive number
Explanation:
If we translate the graph 2 units left of the given position so we can say that we have shifted the graph above from its given position.
So we will have
[tex]y = |x - x'|[/tex]
here x' = any positive number
Everything he said was correct!
Step-by-step explanation:
I hope this helps!
- sincerelynini