Answer:
statement 1 is the true answer
The correct statements about function h(x) are:
1) As x approaches ∞, h(x) approaches ∞
2) The y-intercept is (0, 5)
3) The domain of a function h(x) is [tex](-\infty, \infty)[/tex]
4) As x approaches -∞, h(x) approaches -∞
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."What is exponential function?"A function of the form [tex]f(x)=a^x[/tex], where “x” is a variable and “a” is a constant."
What is domain?"It is a set of all possible input values for which a function is well defined."
What is range?"It is a set of all possible output values."
What is intercept?"It is a point at which the graph of the function intersects the X-axis or Y-axis."
For given question,
A function [tex]f(x)=x^{\frac{1}{3} }[/tex] is transformed to function [tex]h(x)=(2x)^{\frac{1}{3} }+5[/tex]
The domain of function h(x) is all real values.
To find the y-intercept, substitute x = 0
[tex]\Rightarrow h(0)=(2\times 0)^{\frac{1}{3} }+5\\\\ \Rightarrow h(0)=5[/tex]
So, the y-intercept of function h(x) is (0, 5)
To find the x-intercept, substitute y = 0 i.e., h(x) = 0
[tex]\Rightarrow 0=(2x)^{\frac{1}{3} }+5\\\\\Rightarrow (2x)^{\frac{1}{3} }=-5\\\\\Rightarrow 2x=-125\\\\\Rightarrow x=-62.5[/tex]
This means, the x-intercept of h(x) is (-62.5, 0)
From the graph of the function h(x), we can observe that as x approaches -∞ then h(x) approaches -∞ and as x approaches ∞ then h(x) approaches ∞
Therefore, the correct statements about function h(x) are:
1) As x approaches ∞, h(x) approaches ∞
2) The y-intercept is (0, 5)
3) The domain of a function h(x) is [tex](-\infty, \infty)[/tex]
4) As x approaches -∞, h(x) approaches -∞
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Please can someone help me with this question?
9514 1404 393
Answer:
C. f^-1(x) = (x +4)^2; x ≥ -4
Step-by-step explanation:
The range of the given function f(x) is -4 ≤ f(x). This will be the domain of the inverse function.
We find the inverse function by solving ...
x = f(y)
x = √y -4
x +4 = √y
(x +4)^2 = y
The inverse function is ...
f^-1(x) = (x +4)^2 . . . for x ≥ -4
1 point (1) Three times a number minus two times a number* Your answer
Answer:
Three times a number minus two times a number
3x-2x
=x
Graph the following inequality 6x-2y>8
Please help me and show me how to graph it.
Answer:
6x - 2y > 8
First, solve the inequality (Isolate the y-variable & put it in function format):
[tex]6x - 2y > 8\\-2y > 8 - 6x\\(-1)(-2y) > (-1)(8-6x)\\2y < 6x-8\\y < \frac{6x-8}{2} \\y < 3x - 4[/tex]
Second, graph the function y = 3x - 4 on the graph.
It should be linear.Because the inequality is < and not ≤, the values on the line aren't included in the solution, so your line should be dotted, not solid.Third, shade in the area below the line(where y-values are smaller).
Since the inequality is <, that means the solutions are smaller than the solutions of the function 3x - 4.f(x) = x2 What is g(x)?
O A. g(x) = 25x2
O B. g(x) =1/5x2
O C. g(x) = 5x2
O D. g(x) = (5x)2
Answer:
C
Step-by-step explanation:
The graph is 5x^2. Hence the option C is correct
The required function g(x) is 5x² for the given graph, which is the correct option (C).
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The given function is as follows:
f(x) = x²
Substitute the value of x = 1 in the above equation,
f(1) = 1
As per the given graph, we have
g(1) = 5
Now, we can write the proportion as:
f(x)/g(x) = f(1)/g(1)
Substitute the known values in the above proportion, and solve for g(x):
x²/g(x) = 1/5
Cross-multiplying and we get:
g(x) = 5x²
Therefore, the required function g(x) is 5x².
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Triangle SKY with vertices S(-7, 2), K(-1,8), and Y(-2,1) undegoes a reflection with new corrdinates S'(-7,-2), K'(-1, -8), and Y'(-2,-1). Name the line of reflection.
Step-by-step explanation:
reflection under
x-axis
hope this will help you
The line of reflection is given as x-axis.
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
For left shifting it is f(x + a).
The coordinates of the triangle SKY before and after reflection are given as below,
S(-7, 2) → S'(-7, -2)
K(-1, 8) → K'(-1, -8)
Y(-2, 1) → Y'(-2, -1)
It is clear from the transformed coordinates that the x coordinates are the same but y-coordinate changes.
Thus, the reflection is about x-axis.
Hence, the line of reflection is x-axis.
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Can someone help me with this math homework please!
Answer:
2+4/6=1
y-2/x-6=1
y-2=x-6
y=x-4
or y+4=x
Answer:
3rd option
y + 4 = x
Step-by-step explanation:
look,
point A (0, -4) forms the y intercept
(remember the condition for y intercept? the coordinates for which value of x is 0)
so in the equation
[tex]\boxed{ y= mx+c}[/tex]
c being the y intercept is equal to (-4)
finding the slope :-
[tex]m = \frac{ 2 + 4 }{6 - 0} \\ = \frac{6}{6} = 1[/tex]
plugging all these values into the equation
y = 1x - 4
y= x - 4
taking 4 to the other side
y+ 4 = x
Solve log6 + log6 (x-1) = 1
Answer:
[tex]\boxed{\sf x = 7 }[/tex]
Step-by-step explanation:
We are here given a logarithmic equation and we need to solve it out and then find the value of x. The given equation is ,
[tex]\sf\longrightarrow log_6 + log_6 ( x -1) = 1 [/tex]
Here I am assuming that the base of the logarithm is 6 . The equation can be written as ,
[tex]\sf\longrightarrow log_6 1+ log_6 ( x -1) = 1 [/tex]
Recall the property of log as , [tex]\sf log_x a + log_x b = log_x(ab) [/tex] , on using this property we have ,
[tex]\sf\longrightarrow log_6 \{ 1 ( x -1)\} = 1 [/tex]
Simplify ,
[tex]\sf\longrightarrow log_6 ( x -1) = 1 [/tex]
We know that , if [tex]\sf log_a b = c [/tex] then in expotential form it can be expressed as [tex]\sf a^c = b [/tex] . Using this we have ,
[tex]\sf\longrightarrow 6^1 = x - 1[/tex]
Simplify ,
[tex]\sf\longrightarrow 6 = x - 1[/tex]
Add 1 both sides ,
[tex]\sf\longrightarrow x = 6 + 1[/tex]
Therefore ,
[tex]\sf\longrightarrow \boxed{\blue{\sf \quad x = 7\quad }} [/tex]
Hence the value of x is 7 .
Answer:
x=7
Step-by-step explanation:
log6(1) + log6 (x-1) = 1
We know that log (a) * log (b) = log (ab)
log6 (1*(x-1)) = 1
log6 (x-1) = 1
Raising each side to the base of 6
6 ^log6 (x-1) = 6^1
x-1 = 6
Add 1 to each sdie
x-1+1 = 6+1
x=7
If you car was going 60mph and you increased your speed by 5mph every minute for seven consecutive minutes how fast would you be going at the end
Solve for b. Round your answer to the nearest whole degree.
5.1
bº
3.6
100
Answer:
b =44
Step-by-step explanation:
We need to use the law of sines to determine b
sin b sin 100
---------------- = ----------------
3.6 5.1
Using cross products
5.1 sin b = 3.6 sin 100
sin b = 3.6 sin 100 / 5.1
Taking the inverse sin of each side
b = arcsin ( 3.6 sin 100 / 5.1)
b = 44.03984209
To the nearest degree
n = 44
Find the width of a rectangular strip of land with length 25 m and area 12 square meters?
Answer:
5/4
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
1/2 = 2/5 * w
Multiply each side by 5/2
5/2 * 1/2 = 2/5 *w * 5/2
5/4 = w
Formula we use,
→ A = l × w
Then the width of the rectangle,
→ A = I × w
→ 1/2 = 2/5 × w
Now multiply each side by 5/2,
→ 1/2 × 5/2 = 2/5 × w × 5/2
→ w = 5/4
Hence, the width is 5/4.
PLs help T^T im to dum.b to understand this equation
are
equivalent to 192 ounces?
How many pounds
24
pounds.
192 ounces is equivalent to
Answer:
12 lbs
Step-by-step explanation:
There are 16 ounces in a pound
192 ounces * 1 pound / 16 ounces = 12 pounds
Step-by-step explanation:
1 pound = 16 ounces
24 pound = 16 x 24 ounces = 384 ounces
1 ounce = 1/16 pounds
192 ounces = 192/16 pounds = 12 pounds
Daniel and Saquon are each saving money. Daniel starts with $50 in his savings account and adds $8 per week. Saquon starts with $65 in his savings account and adds $5 each week.
After four weeks, who has more money in their savings account? Explain how you know.
After how many weeks will Daniel and Saquon have the same amount of money in their savings accounts?
Answer:
Sequon has more money after 4 weeks. It would take 5 weeks for their savings accounts to be equal.Step-by-step explanation:
Daniel
Daniel starts with $50 and each week he adds $8. To find out the amount he has in any given week, the following formula would work:
= 50 + 8x
The x is the number of weeks and is multiplied by 8 because the amount of money he has increase by 8 every week.
After 4 weeks he would have:
= 50 + (8 * 4)
= 50 + 32
= $82
Saquon
Applying the same formula:
= 65 + 5x
After 4 weeks:
= 65 + (5 * 4)
= 65 + 20
= $85
Saquon has more money after 4 weeks.
Number of weeks it would take for both of them to have the same amount.
To find this out, equate both formulas and solve for x.
50 + 8x = 65 + 5x
8x - 5x = 65 - 50
3x = 15
x = 15/3
x = 5 weeks
At 5 weeks they will both have:
50 + 8 * 5 = $90
65 + 5 * 5 = $90
Ferrero Rocher chocolates are manufactured in the shape of spherical balls, which are
wrapped in foil. The Ferrero Rocher Company introduced the Ferrero collection, which
is a package of 15 chocolates, one layer deep in a 3 chocolate x 5 chocolate orientation.
A single chocolate has a diameter of 3.2 cm.
Answer:
N/A
Step-by-step explanation:
What's the question to the question?
If {3,4,5} is the domain of function f:x --> 2x-1, find the range.
Answer:
Range = {5, 7, 9}
Step-by-step explanation:
Range is the set of values that are the results of respective values of x when placed in the function f(x).
[tex] \mathfrak{\blue {\underline{\implies If\: x = 3 }}} [/tex]
f(3) = 2 × 3 - 1
f(3) = 6 - 1
f(3) = 5
[tex] \mathfrak{\blue{\underline{\implies If \:x = 4 }}} [/tex]
f(4) = 2 × 4- 1
f(4) = 8 - 1
f(4) = 7
[tex] \mathfrak{\blue{\underline{\implies If\: x = 5 }}} [/tex]
f(5) = 2× 5 - 1
f(5) = 10 - 1
f(5) = 9
Therefore, the range is the set of all these values :-
Range = {5, 7, 9}
Need help on this!!!
Answer:
7.8391
Step-by-step explanation:
Answer:
Step-by-step explanation:
The key to solving this equation is knowing how to "undo" a natural log. Just like square roots are "undone" by squaring, and cubing "undoes" a cubed root, raising a natural log to the base of e, Euler's number, undoes a natural log. Because this is an equation you have to raise both sides of it to the base of e:
[tex]e^{ln(x+3)}=e^5[/tex]
That leaves us on the left with simply
x + 3
On the right we have a constant. e is not a variable, it is a number. You can find its value on your calculator. Solving for x:
[tex]x=e^5-3[/tex] and
[tex]e^5=148.4131591[/tex], so
x = 148.4131591 - 3 and
x = 145.4132, the first choice listed.
is this righ or not please say me
Answer:
Step-by-step explanation:
It's right
Two numbers have a difference of 28. If the sum of the squares of the numbers is
392, what are the two numbers?
Answer:
The two numbers are 182 and 210. I hope this will help you.
The snack bar at your school has added sushi to its menu. The ingredients for one roll include sushi rice, seaweed sheets, cucumbers, cream cheese, and 2 oz of smoked salmon. One roll can be cut into 9 servings. Write an expression for the amount of salmon needed to make s servings of sushi. How much salmon is needed to make 18 servings? 36 servings? 90 servings? 100 servings?
Answer:
The answer si:
- 16 servings - 6 oz of salmon
- 24 servings - 9 oz of salmon
- 80 servings - 30 oz of salmon
- 100 servings - 37.5 oz of salmon
1 roll is 8 servings and it is also made of 3oz of smoked salmon. That means that 3oz of smoked salmon is needed fo 8 servings.
Now, let's made some proportions:
16 servings:
3 oz is for 8 servings, how much oz is for 16 servings:
3 : 8 = x : 16
x = 3 · 16 ÷ 8 = 6 oz
24 servings:
3 oz is for 8 servings, how much oz is for 24 servings:
3 : 8 = x : 24
x = 3 · 24 ÷ 8 = 9 oz
80 servings:
3 oz is for 8 servings, how much oz is for 80 servings:
3 : 8 = x : 80
x = 3 · 80 ÷ 8 = 30 oz
100 servings:
3 oz is for 8 servings, how much oz is for 100 servings:
3 : 8 = x : 100
x = 3 · 100 ÷ 8 = 37.5 oz
how u do the sum pls
Answer:
[tex]{ \tt{x + 36 \degree + 48 \degree = 360 \degree}} \\ { \tt{x = (360 - 48 - 36) \degree}} \\ { \tt{x = 276 \degree}}[/tex]
PLSSS HELP I NEED IT REALLY BAD
1.
(05.01 LC)
A square is shown below. Which expression can be used to find the area, in square units, of the shaded triangle in the square?
A square with a side length of 4 units is shown. A diagonal is drawn with one section shaded inside the figure.
(5 points)
fraction 1 over 4 ⋅ 4 ⋅ 4
fraction 1 over 2 ⋅ 4 ⋅ 4
fraction 1 over 2 ⋅ 2 ⋅ 2
fraction 1 over 4 ⋅ 2 ⋅ 2
Answer:
If a square has a side length of 4, then the area is 16.
A = [tex]s^{2}[/tex] where s = side length.
If a diagonal is drawn to create 2 halves, then the area of each half is 8.
So most likely the answer you are seeking is: [tex]\frac{1}{2}[/tex] ( 4 · 4 )
Without actual division prove that x4 +2x3 -2x2 +2x -3 is exactly divisible by
x2 +2x-3
Answer:
Step-by-step explanation:
[tex]\displaystyle\Large\boldsymbol{} x^4+2x^3-2x^2+2x-3= \\\\\\x^4+2x^2(x-1)+2x-\underbrace{2-1}_{-3}= \\\\\\x^4-1+2x^2(x-1)+2x-2 = \\\\\\(x^2-1)(x^2+1)+2x^2(x-1)+2(x-1) = \\\\\\\underline{(x-1)}(x+1)(x^2+1)+2x^2\underline{(x-1)} +2\underline{(x-1)} =\\\\\\(x-1)((x+1)(x^2+1)+2x^2+2)=\\\\\\(x-1)(x^3+x^2+2x^2+x+2+1)=\\\\\\(x-1)(x^3+3x^2+x+3) =\\\\\\(x-1)( \underline{(x+3)}x^2+\underline{(x+3)})=(x^2+1)\underbrace{(x-1)(x+3)}_{x^2+2x-3}= \\\\\\(x^2+1)(x^2+2x-3) : (x^2+2x-3)=x^2+1[/tex]
The product of two algebraic expression is 4x²-9.If one of the expression is (2x+3),find the other expression
Answer:
Solution given:
we have formula
a²+b²=(a+b)(a-b)
now
4x²-9
(2x)²-3²
using formula
(2x+3)(2x-3)
other expression is 2x-3.
Answer:
( 2x - 3 )
Step-by-step explanation:
4x² - 9 is a perfect square meaning it can be factored into 2 expressions,
( 2x + 3 ) ( 2x - 3 )
Can someone help me with this math homework please!
Answer:
8/5
Step-by-step explanation:
[8-(-8)]/[2-(-6)] = 16/10 = 8/5
Which of the following functions is graphed below?
(picture included)
Answer:
B
Step-by-step explanation:
the graph has been shifted 4 units to left, and 2 units down.
Answer:
Graph shifted down by 2 ... -2
graph slid 4 to the left ... + 4
B is the answer y = |x+4| -2
Step-by-step explanation:
at the school festival , raffle tickets were sold at $1 each, or 3 for $2. At the end of the day, 15 books of tickets, each containing 20 tickets, were sold. the money collected from the sale was $236. How many tickets were sold at 3 for $2?
Answer:
you have to take away you word they said how many
A pie chart is to be drawn for Cathy’s spending.
Cathy spent a total of $800 last month.
She spent $120on entertainment last month.
Calculate the size of the angle for entertainment in the pie chart.
Answer:
54°
Step-by-step explanation:
$800 is 360° of a pie chart
$120 is ?° of the pie chart
?° = (360*120)/800 = 54°
*if you need the answer to be in radiants
(54*π) /180 = 0.942478 rad
Step-by-step explanation
Help me ASAP with this problem
Answer:
114cm
Step-by-step explanation:
3×8×4=96
3×3×2=18
96+18=114
28a-4a^2
Helpp it’s simplifying
Answer:
[tex]{ \tt{ = 28a - {4a}^{2} }} \\ = 4a(7 - a)[/tex]
Abigail picked 72 pears. Sandeep picked p fewer pears than Abigail. Choose the expression that shows how many pears Sandeep picked.
Answer:
72-p=(the number of pears sandeep picked)
Step-by-step explanation:
Answer:
72 - p
Step-by-step explanation:
When it says a number fewer, that means to put it behind rather than in the front.
