How do I Graph h(x)=8|x+1|-1
Answers
Answer:
Step-by-step explanation:
To graph the function h(x) = 8|x+1| - 1, plot key points at (-3, 15), (-1, -1), and (1, 15). The graph exhibits vertical stretching due to the coefficient 8 and symmetry around the line x = -1.
To graph the function (h(x) = 8|x+1| - 1), follow these steps:
1. Identify Key Points:
Determine critical points where the expression inside the absolute value becomes zero. Here, when (x = -1), (h(x) = -1). Additionally, consider points on either side of -1.
2. Plot Points:
Plot these points on the coordinate plane: (-3, 15), (-1, -1), and (1, 15).
3. Determine Behavior:
Understand that the absolute value function |x+1| ensures symmetry around the vertical line x = -1. The coefficient 8 stretches the graph vertically, and the constant -1 shifts it downward.
4. Connect Points:
Draw a smooth curve connecting the points, considering the shape of the absolute value function.
5. Label Axes:
Label the x-axis and y-axis appropriately.
The resulting graph represents the function [tex]\(h(x) = 8|x+1| - 1\)[/tex].
Related Questions
Indicate the equation of the given line in standard form. The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
Answers
Answer:
3x-4y=2
Step-by-step explanation:
step 1
Plot the figure
we have
A (2, 2), B(-2, -2), C(1, -1), and D(6, 4)
using a graphing tool
The longer diagonal is BD
see the attached figure
step 2
Find the slope of the diagonal BD
we have
B(-2, -2) and D(6, 4)
m=(4+2)/(6+2)
m=3/4
step 3
Find the equation of the diagonal BD into point slope form
y-y1=m(x-x1)
we have
m=3/4
D(6,4)
substitute
y-4=(3/4)(x-6)
step 4
Convert the equation in standard form
The equation of the line in standard form is equal to
Ax+By=C
y-4=(3/4)(x-6)
y=(3/4)x-(18/4)+4
Multiply by 4 both sides
4y=3x-18+16
3x-4y=18-16
3x-4y=2 -----> equation of the diagonal in standard form
Solve the system of equations
x + 3y = −1
2x + 2y = 6
Answers
y = -2
x = 5
*Step By Step Explanation*
To find y:
You’ll need to remove the x from the TOP equation, to do so,
You’ll need to find what is x + y, like so
2x + 2y = 6
x + y = 3
After you get this from division, subtract x + y from x + 3y and you’ll get this:
x + 3y - (x + y)
= x + 3y - x - y
= 2y
To find what 2y is, you have to subtract the value of x + y which is 3 from the value of x + 3y which is -1.
-1 - 3 = -4
Hence,
2y = -4
y = -2
To find x:
You would need to substitute the expression given with y. Like so:
x + 3y = -1
x + 3(-2) = -1
x - 6 = -1
x = 5
Hope it helps!
(There are also other ways to solve this system)
Which graph represents an inverse variation
Answers
Answer:
The second graph.
Step-by-step explanation:
In inverse variation, an increase in one variable leads to a decrease in the other value in the relationship.
xα1/y
x=k/y
meaning
xy= constant
Such a graph slants with a negative gradient from left to right of the Cartesian plane. (the second graph).
Answer:
it's B
Step-by-step explanation:
QUICK!!
The x-intercepts of a quadratic function are −3 and 5. What is the equation of its axis of symmetry?
A. x=-3
B. x=1
C. x=5
D. x=-15
Answers
Answer:
B. x=1
Step-by-step explanation:
Let us define axis of symmetry first.
The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.
We have x-intercepts of -3 and 5
In ordered to find the axis of symmetry we have to find their middle intercept
To find the axis of symmetry:
[tex]= \frac{-3+5}{2}\\=\frac{2}{2}\\ =1[/tex]
So the axis of symmetry is x = 1 ..
Answer:
B x=1
Step-by-step explanation:
edge 2020 2021
Which of these statements describe properties of parallelograms? Check
that apply.
Answers
Answer:
A, B, C and D.
Step-by-step explanation:
Opposite sides are congruent (B) as well as the 3 that are marked.
Answer:
Options A, B, C and D are correct choices.
Step-by-step explanation:
We are asked to choose the properties of parallelograms from our given choices.
By the definition of parallelogram:
The opposite sides of a parallelogram are parallel and congruent.The two consecutive angles of parallelogram are supplementary.Opposite angles of parallelogram are congruent.Diagonals of parallelogram bisect each other.Upon looking at our given choices, we can see that options A, B, C and D are correct choices.
What is the initial value of the sequence?
The points shown on the graph represent the numbers in a
geometric sequence.
Answers
Answer:
The initial value of the given geometric sequence is 2.
Step-by-step explanation:
The given points are (1,2), (2,4) and (3,8).
It means the first term is 2, second term is 4 and third term is 8. So, the common ratio is
[tex]r=\frac{a_2}{a_1}=\frac{4}{2}=2[/tex]
A geometric sequence is defined as
[tex]f(n)=ar^{n-1}[/tex]
Where, a is first term of the sequence, r is common ratio and n is number of term. In other words f(1) is the initial value of the geometric sequence.
The given geometric sequence is
[tex]f(n)=2(2)^{n-1}[/tex]
The value of f(1) is 2.
Therefore the initial value of the given geometric sequence is 2.
Answer:Just took the test, it is 2 on edg
Step-by-step explanation:
:)
If (17, 4) is an ordered pair of the inverse of F(x), which of the following is an
ordered pair of the function F(x)?
A. (17,4)
B. (4.17)
C. (4,0)
D. 0,17)
Answers
Answer:
B
Step-by-step explanation:
Given a point (x, y) on f(x) then the corresponding point on the inverse is (y, x)
Given (17, 4 ) is a point on the inverse then the corresponding point on f(x) is
(4, 17 ) → B
In the triangle below, x=?. Round to the nearest tenth.
Please help!!
Answers
Answer:
58 deg
Step-by-step explanation:
Look at x and then look at the sides that are given... 9 is adjacent and 17 is the hypotenuse so use cosine.
cos(x)=9/17
To solve for x just use arccos( ) or cos^(-1)
Type cos^(-1)(9/17) into calc to receive answer (make sure mode is in degrees)
The answer should come to be roughly 58 deg.
Answer:
x ≈ 58.0°
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for x
cosx° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{17}[/tex], thus
x = [tex]cos^{-1}[/tex] ([tex]\frac{9}{17}[/tex] ) ≈ 58.0°
Which number line represents the solution set for the inequality -4(x + 3) 5-2-2x?
O
+
-7
+
-6
+
-4
-5
-3
-2
-1
0
1
2
3
4
5
6
7
-7
+
-6
+
-5
+
-4
+
-3
+
-2
+
-1
+
0
+
1
+
2
+
3
+
4
5
6
7
-7 -6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
7
+
+
+
+
+
-7
-6
-5
-4
+ +
-3 -2
+
-1
0
1
2
3
4
5
6
7
Answers
Answer:
A
Step-by-step explanation:
Consider the smaller than sign as smaller or equal to sign as I couldn,t type the sign
-4(x+3)<-2-2x
Expand the bracket
-4x-12<-2-2x
Add 2x to both sides
-2x-12<-2
Add 12 to both sides
-2x<10
add 2x to both sides
0<10+2x
minus 10 on both sides
-10<2x
SImplify
-5<x
X is larger or equal to -5 which means the option A
Using the triangle pictured, find the measure of side AB. Round your answer to the nearest tenth. A) 1.6 B) 2.2 C) 2.7 D) 3.3
Answers
Answer:
Option B (AB = 2.2 units).
Step-by-step explanation:
The diagram shows that there are two sides given and one angle is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin ABC / AC = sin BAC / BC.
Plugging ABC=72 degrees, AC=2.5, and BC=2.1 in the sine rule gives:
sin 72 / 2.5 = sin BAC / 2.1.
Cross multiplying gives:
sin BAC = (2.1*sin 72)/2.5.
sin BAC = 0.79888747368.
Taking sin inverse on both sides gives:
BAC = arcsin (0.79888747368) = 53.0239949 degrees.
To find AB, first, the angle ACB is required. To find that angle, use the triangular law of angles. All the three angles sum up to 180 degrees. Therefore ACB = 180 - 72 - 53.0239949 = 54.9760051 degrees.
Now applying the Sine Rule to find AB:
sin ACB / AB = sin ABC / AC.
sin (54.9760051) / AB = sin 72 / 2.5.
AB = (2.5*sin (54.9760051))/sin (72) = 2.2 (to the nearest tenth).
Therefore, AB = 2.2 units, i.e. Option B!!!
Answer please. If you answer, you get 44 points. I don't use the points here. So answer please. I want full work.
Answers
Answer: you simplfy the two equations already there then plug them in to find factors
Step-by-step explanation:
Answer:
65
Step-by-step explanation:
These are called vertical angles. Vertical angles are equal.
145 = 2x + 15
130 = 2x
x = 65
What is the scale factor? ( the answer must be a fraction).
Answers
Use the bottom side. Going from the first triangle to the second the scale factor is:
15/9 = 5/3
15. SHORT ANSWER Define a variable and
write an expression to represent the
following phrase.
seven years younger than Lisa
Answers
Answer:
see below
Step-by-step explanation:
Let L = lisa's age
seven years younger than Lisa
L-7
Shown below is a right angle triangle. Find the exact length of the side labeled y.
Answers
Answer:
sine 30=y/(8+10√2)
(8+10√2)sin 30=y
Check the picture below.
The triangles shown below may not be congruent.
Answers
let's take a peek at the triangles.
they have a 30° angle and a 80° each, and a side that is not in between in common.
[A]ngle [A]ngle [S]ide, AAS congruence.
Answer:
Option B, False.
Step-by-step explanation:
In the given figure two triangles have been given. In these triangles two angles and corresponding side has been given as equal in measure.
Therefore, by AAS theorem for congruence, the given triangles are congruent.
The given statement that the triangle shown may not be congruent is False.
Option B is the answer.
Find the common difference of the sequence shown.
1/2, 1/4 , 0, ...
Answers
Answer:
-1/4
Step-by-step explanation:
Given sequence is:
1/2, 1/4 , 0, ...
In order to find the common difference in the terms of a sequence, the preceding term is subtracted from the next term.
For example in the given sequence:
first term will be subtracted from second term and second term will be subtracted from third term
So,
[tex]\frac{1}{4}-\frac{1}{2} \\=\frac{1-2}{4}\\ =-\frac{1}{4}\\ Similarly,\\=0-\frac{1}{4} \\=-\frac{1}{4}[/tex]
The common difference is - 1/4 ..
Answer:
-1/4
Step-by-step explanation:
What is the simplified form of the rational expression below 6x^2-54 / 5x^2+15x
Answers
Answer:
[tex]\large\boxed{\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}}[/tex]
Step-by-step explanation:
[tex]6x^2-54\qquad\text{distributive}\\\\=6(x^2-9)=6(x^2-3^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=6(x-3)(x+3)\\\\5x^2+15x\qquad\text{distributive}\\\\=5x(x+3)\\-----------------\\\\\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)(x+3)}{5x(x+3)}\qquad\text{cancel}\ (x+3)\\\\=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}[/tex]
Edna says that when (x - 2)^2 = 9, that x - 2 = 3. Use
complete sentences to explain whether Edna is correct.
Use specific details in your explanation.
Answers
Answer:
She is partially correct. There are 2 possible answers to this problem, and x - 2 = 3 is one of the answers. When applying the square root to both sides, the resulting answer could be either negative or positive. Therefore, applying the square root to both sides leads to the two following equations: x - 2 = 3 or x - 2 = -3.
SQ bisects TSR. Find the value of x.
Answers
Answer: The answer is 10
Answer:
10
Step-by-step explanation:
math
Each angle measure of a regular polygon is 60°. What is the polygon?
Answers
Answer:
Triangle
Step-by-step explanation:
A regular polygon of n sides has interior angles of:
a = 180 (n-2) / n
Given a = 60:
60 = 180 (n-2) / n
n = 3 (n-2)
n = 3n - 6
6 = 2n
n = 3
The polygon has three sides, so it's a triangle.
A regular polygon with each angle measuring 60° is an equilateral triangle.
A regular polygon is a polygon with all sides and angles equal. To find the type of polygon where each angle measures 60°, we use the formula for the measure of each interior angle of a regular polygon, which is (n-2) x 180° / n, where n is the number of sides.
Let's solve for n:
Set the angle measure formula to 60°: (n-2) x 180° / n = 60°
Multiply both sides by n to clear the fraction: (n-2) x 180° = 60n
Distribute 180°: 180n - 360° = 60n
Move the terms involving n to one side: 180n - 60n = 360°
Simplify: 120n = 360°
Divide both sides by 120: n = 3
Therefore, a regular polygon with each angle measuring 60° is an equilateral triangle.
A rectangle's length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find
its width, w?
Answers
Answer:
I think the answer would be 5 divided by 50 times two to find the width.
Step-by-step explanation:
I think my answer above explains it well enough.
Answer: w(2w + 5) = 50
Step-by-step explanation:
Given the system of inequalities below: -3x - y < 12 2x + 3y ≥ 9 Give the coordinates of three points that are members of the solution set. () () () (-3, 7) (-3, -7) (3,-7) (-4,-0) (0,-4) (0,4) (2,3) (-2,3) (2,-3)
Answers
Answer:
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Step-by-step explanation:
we have
[tex]-3x-y< 12[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dashed line
[tex]2x+3y\geq 9[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the solid line
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
Remember that,
If a ordered pair is a solution of the system of inequalities, then the ordered pair must be in the shaded area of the solution
Plot the points
(-3, 7), (-3, -7), (3,-7), (-4,-0), (0,-4), (0,4), (2,3), (-2,3), (2,-3)
therefore
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Answer:Answer:
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Step-by-step explanation:
we have
----> inequality A
The solution of the inequality A is the shaded area above the dashed line
----> inequality B
The solution of the inequality B is the shaded area above the solid line
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
Remember that,
If a ordered pair is a solution of the system of inequalities, then the ordered pair must be in the shaded area of the solution
Plot the points
(-3, 7), (-3, -7), (3,-7), (-4,-0), (0,-4), (0,4), (2,3), (-2,3), (2,-3)
therefore
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Step-by-step explanation:
How will the solution of the system change if the inequality sign on both inequalities
Answers
Shown below
Step-by-step explanation:The first system of inequality is the following:
[tex]\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y<2x+\frac{1}{3}\end{array}\right.[/tex]
To find the solution here, let's take one point, say, [tex](0,0)[/tex] and let's taste this point into both inequalities, so:
FIRST CASE:First inequality:
[tex]y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False![/tex]
The region is not the one where the point [tex](0,0)[/tex] lies
Second inequality:
[tex]y<2x+\frac{1}{3} \\ \\ 0<2(0)+\frac{1}{3} \\ \\ 0<\frac{1}{3} \ True![/tex]
The region is the one where the point [tex](0,0)[/tex] lies
So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there
SECOND CASE:First inequality:
[tex]y<2x+\frac{2}{3} \\ \\ 0<2(0)+\frac{2}{3} \\ \\ 0<\frac{2}{3} \ True![/tex]
The region is the one where the point [tex](0,0)[/tex] lies
Second inequality:
[tex]y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True![/tex]
The region is not the one where the point [tex](0,0)[/tex] lies
So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.
CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.
Solve the following inequality algebraically: 1<3x-2<4
A. 1
B. 0
C. 1>x>2
D. 0>x>3
Answers
Answer:
1 < x < 2
Step-by-step explanation:
Given
1 < 3x - 2 < 4 ( add 2 to each of the 3 intervals )
3 < 3x < 6 ( divide each interval by 3 )
1 < x < 2
Answer:
A
Step-by-step explanation:
Edge 2021
If A and B are dependent events, which of these conditions must be true?
Answers
Answer:
i would think A
Answer:P(B|A)is not equal P(B)
Step-by-step explanation:
Which equation represents the graphed function?
Answers
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0+3}{2-0}[/tex] = [tex]\frac{3}{2}[/tex]
note the line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = [tex]\frac{3}{2}[/tex] x - 3 → C
Choose the possible descriptions of cross sections formed by the intersection of a plane and a cylinder choose all that apply
-circle
-rectangle
-triangle
-line segment
-point
Answers
Answer:
circle and rectangle
Step-by-step explanation:
we know that
A cross section that is perpendicular to the base of cylinder is a rectangle
A cross section that is parallel to the base of cylinder is a circle
A cross section that is angled to the base of cylinder is an oval
Final answer:
A plane intersecting a cylinder can create a circle if perpendicular to the cylinder's axis, or a rectangle if cut parallel to the side of the cylinder. Ellipses are also possible when the cutting angle is oblique, and may look circular from certain perspectives. Triangles, line segments, and points are not typical cross sections for a cylinder.
Explanation:
When a plane intersects a cylinder, several different cross sections can result, depending on the angle and position of the plane relative to the cylinder. If the plane is perpendicular to the axis of the cylinder, the cross section will be a circle. If the plane intersects the cylinder at an angle to the axis, the cross section can be an ellipse, which in some cases may appear to be a circle depending on the perspective. A plane intersecting parallel to the side of the cylinder will produce a rectangle. It is not possible for a cylinder to have a triangular, line segment, or point as a cross section through normal slicing, as these do not represent the way planes intersect with the smooth curved surface of a cylinder.
Ben climbed 15 feet up a hill,8 feet down a hill, and 11 feet up another hill. What is his overall change in elevation?
Answers
Answer:
18 feet
Step-by-step explanation:
15-8+11=18
What are the solutions of x2=-7x-8
Answers
Answer:
x^2 = -7x -8
x^2 +7x +8 = 0
D = 49 -32 = 17
x_1,2 = (-7+/-sqrt17)/2 = (-7-sqrt17)/2 and (-7+sqrt17)/2
Step-by-step explanation:
Answer:
x = [tex]\frac{1}{2}[/tex] (-7±√17)
Step-by-step explanation:
x² = -7x - 8
x² + 7x + 8 = 0
Using the quadratic formula, with a=1, b = 7 and c=8,
you will get x = [tex]\frac{1}{2}[/tex] (-7±√17)
24 people go to joe's birthday party.half walk and a quarter travel by bus all the others go by taxi. How many guests walk? How many travel by bus? How many use taxis? What fraction use taxis? What fraction don't use taxis?
Answers
Answer:
How many guests walk? 12How many travel by bus? 8How many use taxis?4What fraction use taxis? [tex]\frac{1}{6}[/tex]What fraction don't use taxis?[tex]\frac{5}{6}[/tex]Step-by-step explanation:
Number of people that attended the party= 24.....let this be x
Number of people that walked= 1/2 x
[tex]=\frac{1}{2} *24 =12[/tex]
Number of people that travel by bus= 1/4 x
[tex]=\frac{1}{4} *24= 8[/tex]
Number of people that go by taxi= the rest
[tex]=24-(12+8)=24-20=4[/tex]
The fraction that used taxis= those that used tax/total number of people
Those that used taxi=4
Total number of people=24
Fraction = [tex]\frac{4}{24} =\frac{1}{6}[/tex]
Fraction that did not use taxi = whole-fraction that used taxi
[tex]\frac{6}{6} -\frac{1}{6} =\frac{5}{6}[/tex]