Answer:
Option 4- Graph of g(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
Given : Graph of [tex]g(x)=\frac{1}{x+4}-6[/tex]
To find : How does the graph of g(x) compare to the graph of the parent function [tex]f(x)=\frac{1}{x}[/tex]
Solution :
The graph f(x) is being translated to form the graph g(x).
In graph [tex]g(x)=\frac{1}{x+4}-6[/tex] there is
Translation of 4 unit left and 6 unit downward.
In graph f(x) if we shift the graph with 4 unit left it form
f(x)→f(x+b) , the function is shifted towards left with b unit.
So, [tex]f(x)=\frac{1}{x+4}[/tex]
In graph f(x) if we shift the graph with 6 unit downward it form
f(x)→f(x)-a , the function is shifted downward with a unit.
So, [tex]f(x)=\frac{1}{x+4}-6[/tex]
Therefore, Option 4 is correct.
Graph of g(x) is shifted 4 units left and 6 units down from f(x).
Which function has the greatest y-intercept? (2 points)
f(x)
g(x)
h(x)
All three functions have the same y-intercept.
The function h(x) has the greatest y-intercept of 8, as it crosses the y-axis at the highest point.
Explanation:The function that has the greatest y-intercept is the one that crosses the y-axis at the highest value. The y-intercept is the point where the graph of a function intersects the y-axis, which is when x = 0. So, to find the function with the greatest y-intercept, we need to evaluate the y-value when x = 0 for each function.
Let's consider the functions f(x), g(x), and h(x). If f(x) has an equation of y = 3x + 5, g(x) has an equation of y = x - 2, and h(x) has an equation of y = -2x + 8, we can plug in x = 0 and see which function gives us the greatest y-value.
For f(x), when x = 0, y = 3(0) + 5 = 5. For g(x), when x = 0, y = 0 - 2 = -2. And for h(x), when x = 0, y = -2(0) + 8 = 8. Thus, h(x) has the greatest y-intercept because it crosses the y-axis at the highest point, which is 8.
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2n^2+3n-9 factoring trinomials
The trinomial [tex]2n^2[/tex]+3n-9 cannot be factored using integers as no two numbers exist that multiply to give -18 (the product of the leading coefficient and the constant term) and add up to 3 (the middle coefficient).
To factor the quadratic trinomial [tex]2n^2[/tex]+3n-9, one must find two binomials that, when multiplied together, give the original trinomial. Factoring complex trinomials can sometimes be achieved by finding two numbers that multiply to give the product of the leading coefficient (2 in this case) and the constant term (-9 in this case), and add to give the middle coefficient (3 in this case). However, for this particular trinomial, such numbers do not exist, and it cannot be factored using integers. This means that either the trinomial is prime (cannot be factored), or it would require the quadratic formula to solve for factors involving irrational or complex numbers.
What is the missing part of the equation below?
²³⁸U₉₂→²³⁴Th₉₀ + ?
A. ⁴He₂
B. ⁴³⁸He₂
C. ⁴He₄
D. ²He₄
Why is a larger down payment beneficial to a home investor?
a.
A larger down payment would only be beneficial to an investor if they intended on renting out the house.
b.
A larger down payment would enable an investor to get a loan with a higher interest rate and lower monthly payments.
c.
A larger down payment would enable an investor to get a loan with a lower interest rate and lower monthly payments.
d.
A larger down payment is essentially a larger bribe to the lending institution and gets the investor in their good favor.
The larger down payment beneficial to a home investor is because of option C.
The following information should be considered:
The large down payment could enables the investor for getting out the loan that have the less interest payment and less monthly payment. So that it is easy for the investor to pay off.Learn more: https://brainly.com/question/537797?referrer=searchResults
A triangle has side length of 14 cm 48 cm and 50 cm classify it as acute obtuse or right
The triangle with side lengths of 14 cm, 48 cm, and 50 cm is a right triangle.
Explanation:The lengths of the sides of the triangle are 14 cm, 48 cm, and 50 cm. To classify the triangle, we need to determine if it is acute, obtuse, or right.
Using the Pythagorean theorem, we can check if it satisfies the condition for a right triangle. If the square of the length of the longest side (50 cm) is equal to the sum of the squares of the other two sides (14 cm and 48 cm), then it is a right triangle.
In this case, (50)^2 = (14)^2 + (48)^2, which is true. Therefore, the triangle is a right triangle.
Final answer:
A triangle with side lengths of 14 cm, 48 cm, and 50 cm is classified as an acute triangle.
Explanation:
A triangle with side lengths of 14 cm, 48 cm, and 50 cm can be classified as an acute triangle.
To determine this, we need to check if the square of the longest side (50 cm) is less than the sum of the squares of the other two sides (14 cm and 48 cm).
502 < 142 + 482
2500 < 196 + 2304
2500 < 2500
This inequality is not true, so the triangle is not obtuse or right. Thus, it is classified as an acute triangle.
find the nonpermissible replacement for the variable y in this expression (y^2)/(-3y+9) find the nonpermissible replacement for the variable y in this expression (y^2)/(-3y+9)
cell phone company A charges $20 per month plus $0.05 per text message. Cell phone company B charges $10 per month plus $0.07 per text message. Is there any number of text messages that will result in the exact same charge from both companies?
Answer : The number of text messages that will result in the exact same charge from both companies is, 500
Step-by-step explanation :
Let the number of text messages be, 'x'
Cell phone company A charges $20 per month plus $0.05 per text message. Thus, the equation will be:
[tex]20+0.05x=0[/tex] ............(1)
Cell phone company B charges $10 per month plus $0.07 per text message. Thus, the equation will be:
[tex]10+0.07x=0[/tex] ............(2)
Now equating equation 1 and 2, we get:
[tex]20+0.05x=10+0.07x[/tex]
[tex]20-10=0.07x-0.05x[/tex]
[tex]10=0.02x[/tex]
[tex]x=\frac{10}{0.02}[/tex]
[tex]x=500[/tex]
Thus, the number of text messages that will result in the exact same charge from both companies is, 500
A painting measures 15 cm long by 24 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 45 cm long by 72 cm high. The second poster measures 97.5 cm long by 156 cm high. Which of the following is true? (Hint: To be an accuarate representation of the painting, would the the poster be similar to the painting?)
I had the same thing. Please mark as Brainiest Answer.
Answer:
Both posters ARE accurate representations of the painting
Step-by-step explanation:
Gradpoint
What is the coefficient of the term 43yz ? A. 1/3 B.4 C.4/3 D.4yz
If x =4 calculate the value of 2x squared - 5
can someone please explain?
Show that the point (7/25, 24/25) is on the unit circle
To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.
Explanation:To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.
The distance between two points, (x1, y1) and (x2, y2), is given by the formula: √((x2-x1)² + (y2-y1)²).
In this case, the distance between the point (7/25, 24/25) and the origin (0, 0) can be calculated as: √((7/25-0)² + (24/25-0)²) = √((49/625) + (576/625)) = √(625/625) = 1.
Since the distance between the given point and the origin is indeed equal to 1, we can conclude that the point is on the unit circle.
Definition of a line segment?
Simplify by combining like terms step by step
- (3x - 4y) + x
Solve each formula for the indicated variable. step by step
h = vt -5t^2 , for v
Find the area of the region. Use a graphing utility to verify your result.
y = 6 sin(x) + sin(6x)
the graph goes from x=0 to x=pi ...?
To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval. Using a graphing utility, we can plot the function and verify the result.
Explanation:To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval.
Using a graphing utility, we can plot the function and verify the result. The integral will give us the area under the curve.
A graphing utility like Desmos or Wolfram Alpha can be used to plot the function and find the area under the curve.
find the zero of the function. state the multiple zero . y=9x^3 -9x
The zeros of the function y = 9x³ - 9x are x = 0, x = 1, and x = -1. There are no multiple zeros for this function.
The question seeks to identify the zeros of the function y = 9x^3 - 9x. To find the zeros, we set the function equal to zero and solve for x.
Step 1: Set the function equal to 0: 0 = 9x³ - 9x.Step 2: Factor out a common term: 0 = 9x(x² - 1).Step 3: Factor further using difference of squares: 0 = 9x(x - 1)(x + 1).Step 4: Set each factor equal to zero: x = 0, x = 1, x = -1.Step 5: Identify the multiple zero, if any. In this case, there are no multiple zeros.The zeros of the function are x = 0, x = 1, and x = -1.
Therefore, as per the above explaination, the correct answer is x = 0, x = 1, and x = -1.
Find the area of a regular hexagon with the given measurement.
2 sqrt3 apothem
A =
...?
Answer:
41.57 unit²
Step-by-step explanation:
We know,
Area of a regular hexagon = [tex]3\times (sidelength)\times (apothem)[/tex].
The length of the apothem = [tex]2\sqrt{3}[/tex] units.
Since, we know, 'a regular hexagon splits into 6 identical equilateral triangles'.
As, the apothem of the regular hexagon = height of the equilateral triangle
So, height of the equilateral triangle = [tex]2\sqrt{3}[/tex] units.
As, in the equilateral triangle, 'One of the side length is the S, other will be [tex]\frac{S}{2}[/tex] and height is [tex]2\sqrt{3}[/tex] units'.
So, using Pythagoras Theorem, we have,
[tex]hypotenuse^{2}=perpendicular^{2}+base^{2}[/tex]
i.e. [tex]S^{2}=(\frac{S}{2})^{2}+(2\sqrt{3})^{2}[/tex]
i.e. [tex]S^{2}=\frac{S^2}{4}+12[/tex]
i.e. [tex]S^{2}-\frac{S^2}{4}=12[/tex]
i.e. [tex]\frac{3S^2}{4}=12[/tex]
i.e. [tex3S^2=48[/tex]
i.e. [texS^2=16[/tex]
i.e. S= 4 units
That is, the side length of the hexagon = 4 units.
Thus, the area of the hexagon is given by,
Area of a regular hexagon = [tex]3\times (4)\times (2sqrt{3})[/tex]
i.e. Area of a regular hexagon = [tex]12\times (2sqrt{3})[/tex]
i.e. Area of a regular hexagon = [tex]24sqrt{3}[/tex]
i.e. Area of a regular hexagon = 41.57 unit²
Hence, the area of the regular hexagon is 41.57 unit².
An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Find the exact dimensions of the box.
For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 9, then x2 = 81.
a)If x2 = 81, then x = 9.
b)If x2 = 81, then x = 9.
x2 = 81 if and only if x = 9.
c)If x2 = 9, then x = 81.
d)If x2 = 81, then x = 9.
x = 9 if and only if x2 = 81
The converse statement interchange the hypothesis and the conclusion.
The converse of x=9 then [tex]x^{2} =81.[/tex] is [tex]x^{2} = 81 then x=9.[/tex] is true.
A biconditional statement is defined to be true whenever both parts have the same truth value . combining the statements as a biconditional we have
If [tex]x^{2}[/tex]. = 81, then x = 9.
x = 9 if and only if [tex]x^{2} .[/tex] = 81
Option D is the right answer.
A sweater that originally cost $40 is on sale for 10 percent off. What is the amount of the discount?
$2
$4
$30
$36
Answer:
B) $4
Step-by-step explanation:
In 2000 Michigan had a population of 9,938,444. The number of people living in Michigan decreased by 0.6% in 2010. What was Michigan’s approximate population in 2010?
Answer:
9,878,813
Step-by-step explanation:
First, make 0.6% into a decimal
0.6 / 100 = 0.006
Then, multiply the number of people living in Michigan in 2000 by the number of people decreased (the percentage decrease) in 2010
9,938,444 x 0.006 = 59630.664
Last, subtract the percentage decrease by the original population in 2000
9,938,444 – 59630.664 = 9,878,813
In 2010 the approximate population in Michigan was about 9,878,813 (to the nearest whole person)
Which of the following is the best estimate for the capacity of a bottle of salad dressing?
1 fl oz
1 gal
1 pt
I'm just having trouble picturing a bottle of salad dressing... I don't use it that often. ...?
Answer:
1 gal
Step-by-step explanation:
a1,a2,a3....a30-each of these 30 sets has 5 elements.b1,b2,....bn-each of these n sets has 3 elements.union of a1,a2...a30=union of b1,b2....bn=S.
if each elements of S is in 10 a sets and 9 bsets.then n=?
The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card
(State wether the graph of the linear relationship is a solid line or a set of unconnected points.
If 3x-1=11, then 2x=?
To find 2x, we first need to solve for x in the equation 3x - 1 = 11. We isolate x by adding 1 to both sides and divide by 3 to obtain x = 4. Finally, multiplying x by 2 gives us 2x = 8.
Explanation:To solve the equation 3x - 1 = 11 for 2x, we need to isolate x first. Adding 1 to both sides, we get 3x = 12. Dividing both sides by 3, we find that x = 4. Now, to find 2x, we simply multiply x by 2, which gives us 2(4) = 8.
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3. Brinn’s rectangular kitchen has an area of 81 square feet. The kitchen is 9 times as many square feet as Brinn’s pantry. If the rectangular pantry is 3 feet wide, what is the length of the pantry?
The length of the pantry is 3 feet.
To find the length of the pantry, we need to determine its area first. According to the question, the kitchen is 9 times the size of the pantry. With the kitchen's area being 81 square feet, the pantry's area would be 81 square feet divided by 9, which equals 9 square feet. Since we are given that the width of the pantry is 3 feet, we divide the total area of the pantry by its width to find the length.
The calculation is as follows:
Area of kitchen: 81 sq ft
Area of pantry: 81 sq ft / 9 = 9 sq ft
Width of pantry: 3 ft
Length of pantry: Area of pantry / Width of pantry = 9 sq ft / 3 ft = 3 feet long.
how do you graph this function rule: y = |X| - 7
Solve the system by substitution.
2x - y + z = -4
z = 5
-2x + 3y - z = -10
Answer: a
Step-by-step explanation: that person coulda said that
What is the circumference of a circle whose area is 121 pi square meters?
If Anton can carry 3 boxes per trip, how many trips will it take him to move 51 boxes? 17 27 30 37
Answer:
17 trips will it take him to move 51 boxes
Step-by-step explanation:
Given: Anton can carry 3 boxes per trip.
That's mean for 1 trip he carry 3 boxes .
To carry 51 boxes he make , [tex]\frac{51}{3}=17[/tex] trip
Therefore, 17 trips will it take him to move 51 boxes.
Angle ABD and angle BDE are supplementary. Find the measures of both angles.
m angle ABD =5x degrees, m angle BDE = (17x-18)degrees