ANSWER
The resulting parabola in vertex form is:
[tex](x - 4) = 4( {y + 3)}^{2}[/tex]
EXPLANATION
The original equation of the parabola is given as
[tex]x = 4 {y}^{2} [/tex]
This parabola has its vertex at the origin.
If the graph of this parabola is shifted four units right and three units down, then the new equation is:
[tex](x - 4) = 4( {y + 3)}^{2}[/tex]
This the equation of the transformed parabola.
Its vertex is now at (4,-3).
Answer:
(x-4)=4(y+3)^2
Step-by-step explanation:
As Jupiter revolves around the sun, it travels at a rate of approximately 8 miles per second. Convert this rate to miles per minute. At this rate how many miles will Jupiter travel in 2 minutes? Do not round your answers
Answer:
60 * 8 = 480 miles per minute *2 = 960 miles
Step-by-step explanation:
Writing a quadratic equation given the roots and the leading coefficient
roots 6, 4, and coefficient 5
[tex]\bf x= \begin{cases} 6\\ 4 \end{cases}\implies \begin{cases} x=6\implies &x-6=0\\ x=4\implies &x-4=0 \end{cases} \\\\\\ (x-6)(x-4)=\stackrel{y}{0}\implies \stackrel{\mathbb{F~O~I~L}}{x^2-10x+24}=0\implies \stackrel{\textit{adding a common factor of 5}}{5(x^2-10x+24)=0} \\\\\\ 5x^2-50x+120=0\implies 5x^2-50x+120=y[/tex]
now, the common factor of 5 simply makes the parabola steeper, but the roots are the same, whilst the vertex of it changes
Final answer:
To write a quadratic equation given the roots and the leading coefficient, use the formula ax² + bx + c = 0, where the roots are the values of x when the equation equals zero, and the leading coefficient determines the value of a.
Explanation:
To write a quadratic equation given the roots and the leading coefficient, you can use the formula ax² + bx + c = 0. The roots of the quadratic equation are the values of x when the equation equals zero. The leading coefficient determines the value of a in the equation. In this case, the roots are 6 and 4, and the leading coefficient is 5.
Using the formula, we get: 5x² - (6+4)x + (6)(4) = 0.
Simplifying, we have 5x² - 10x + 24 = 0. This is the quadratic equation with the given roots and leading coefficient.
Rewrite the following linear equation in slope intercept form.
Y-5=3(x+1)
Y=3x+8
Step-by-step explanation:
The slope is 3
Slope Intercept form is Y=Mx=b
We want to write the given equation in the form y = mx + b.
y-5 = 3(x+1)
y - 5 = 3x + 3
y = 3x + 3 + 5
y = 3x + 8
Done!
Which graph represents the inequality x ≤ –2 or x ≥ 0?
For this case we have the following expressions:
[tex]x \leq-2\\x \geq0[/tex]
So:
[tex]x \leq-2[/tex] Indicates all values less than or equal to -2.
That is, from -∞ to -2.
[tex]x \geq0[/tex] Indicates all values greater than or equal to 0.
That is, from 0 to ∞.
The "or" means that they do not intersect. So, the correct graph is option A.
Answer:
Option A
Answer:
Option A
Step-by-step explanation:
Edg 2020
What is the value of y in the solution to the system of equations?
x + y = 1
2x – 3y = –30
a. –8
b. –3
c. 3
d. 8
Answer:
-8
Step-by-step explanation: I worked it out and I got -8 on a graphing calculator.
in the figure below line segment mn is parallel to line op. Which of these best describes the measures of angle c?
The Measure of angle c is 144 because line segment mn is a transversal and angles a and b are corresponding angles. option B) is correct choice.
Corresponding angles are angles that are in the same position relative to the transversal and on opposite sides of it. In this case, angles a and b are both alternate interior angles, so they are corresponding angles.
Alternate interior angles are angles that are on opposite sides of the transversal and inside the parallel lines.
Since corresponding angles are congruent, we know that the measure of angle a is equal to the measure of angle b. We are also given that the measure of angle a is 100 degrees. Therefore, the measure of angle b is also 100 degrees.
The sum of the measures of the angles in a triangle is 180 degrees. Therefore, the measure of angle c is equal to 180 degrees - 100 degrees - 100 degrees = 144 degrees.
The other options are incorrect:
Option A: The measure of angle c cannot be 36 degrees because angle b and angle c are vertical angles, and vertical angles are always congruent.
Option B: The measure of angle c cannot be 144 degrees because of the properties of the exterior angles of a triangle. The exterior angle of a triangle is equal to the sum of the two remote interior angles, and the two remote interior angles in this case are angles a and b, which have a combined measure of 200 degrees. Therefore, the measure of angle c must be less than 144 degrees.
Option C: The measure of angle c cannot be 44 degrees because line segment MO is not a transversal. A transversal is a line that intersects two parallel lines. In this case, line segment NO is the transversal.
Option D: The measure of angle c cannot be 100 degrees because angles m and c are not alternate interior angles. Alternate interior angles are angles that are on opposite sides of the transversal and inside the parallel lines. In this case, angle m is an alternate interior angle, but angle c is an exterior angle.
Therefore, the best answer is The measure of angle c is 144 because line segment mn is a transversal and angles a and b are corresponding angles. option B) is correct choice.
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Plz I can’t do this
Answer: f(g(x))=x and g(f(x)) = x
f⁻¹(x) = g(x) YES ARE INVERSES
f⁻¹(x) ≠ g(x) NOT INVERSES
Step-by-step explanation:
Inverse is when you swap the x's and y's and then solve for y.
If f⁻¹(x) = g(x), then they are inverses of each other.
Similarly, if g⁻¹(x) = f(x), they are inverses of each other.
NOTE: You can also use composition to determine if they are inverses --> If (fog)(x) = x, then they are inverses of each other.
[tex]f(x) = \dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's. NOTE: f(x) is y}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Add 9 to both sides}\\x+9=\dfrac{1}{y+4}\\\\\\\text{Flip the fractions}\\\dfrac{1}{x+9}=y+4\\\\\\\text{Subtract 4 from both sides}\\\dfrac{1}{x+9}-4=y\\\\\\\boxed{f^{-1}(x)=g(x)\text{ so f(x) and g(x) are inverses of each other}}[/tex]
[tex]f(x) = 3x+27\\\\\\\text{Swap the x's and y's NOTE f(x) is y}\\x=3y+27\\\\\\\text{Subtract 27 from both sides}\\x-27=3y\\\\\\\text{Divide everything by 3}\\\dfrac{1}{3}x-\dfrac{27}{3}=y\\\\\\\text{Simplify}\\\dfrac{1}{3}x-9=y\\\\\\\boxed{f^{-1}(x)\neq g(x)\text{ so f(x) and g(x) are NOT inverses of each other}}[/tex]
URGENT HELP)
Shari rolls a pair of dice, numbered 1 to 6, 64 times. How many times can she expect to roll an odd number!
Answer:
32
Step-by-step explanation:
Possible outcomes in a fair sided die 1,2,3,4,5,6 = 6 possible outcomes
Odd numbers = 1,3,5 = 3 odd numbers
Probability of rolling an odd number = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Total number of rolls = 64
expected number of odd number rolls in 64 roll,
= [tex]\frac{1}{2}[/tex] x 64 = 32
What is the volume of a sphere with a radius of 2.7 in? Round your answer to the nearest tenth of a cubic inch.
82.4 cubic inches
164.8 cubic inches
261.8 cubic inches
92.1 cubic inches
it is 82.4
i hope you have a good day now
Final answer:
The volume of a sphere with a radius of 2.7 inches is calculated using the formula V = (4/3)πr³. After substituting the radius into the formula and calculating, the volume is approximately 82.5 cubic inches when rounded to the nearest tenth. None of the options provided match this value exactly.
Explanation:
To calculate the volume of a sphere with a radius of 2.7 inches, we use the formula for the volume of a sphere, which is V = (4/3)πr³. Plugging the radius into the formula gives:
V = (4/3)π(2.7 in)³
To find the volume, we perform the following calculations:
Calculate the radius cubed (2.7 in)³ = 19.683 in³.
Multiply by π (approximately 3.14159): 19.683 in³ × 3.14159 ≈ 61.8982 in³.
Multiply by 4/3: ≈ (4/3) × 61.8982 in³ ≈ 82.5309 in³.
Finally, round the volume to the nearest tenth: 82.5309 in³ rounds to 82.5 in³, which is not one of the options given. However, if we round to the nearest whole number, then 82.5 in³ would be rounded to 83 in³, which is also not one of the options. This indicates there may have been a mistake in the calculations or options provided.
None of the options given precisely match the calculated volume when rounded to the nearest tenth. However, the calculation we did indicates that the volume is approximately 82.5 cubic inches when we round to one decimal place. There may be an issue with the provided options or expected precision, so it's advisable to double-check the calculations and verify the choices provided for the answer.
Find the area of a regular pentagon with an apothem of 3.1ft and a side length of 4.5ft. Round your answer to the nearest whole number
Answer:
≈ 35 ft²
Step-by-step explanation:
The area (A) of a regular pentagon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 5 × 4.5 = 22.5 ft, thus
A = 0.5 × 22.5 × 3.1 = 34.875 ≈ 35 ft²
The area of a regular pentagon with an apothem of 3.1ft and a side length of 4.5ft is 35 ft².
What is an irregular pentagon shape?A pentagon is considered to be irregular when all five sides are not equal in length. However, sometimes two or three sides of a pentagon might have equal sides but it is still considered as irregular.
The area (A) of a regular pentagon is
A = perimeter × apothem
perimeter = 5 × 4.5 = 22.5 ft, thus
A = 0.5 × 22.5 × 3.1 = 34.875 ≈ 35 ft²
A regular pentagon has all equal sides and angles. In a regular pentagon, its interior angles are 108 degrees and its exterior angles are 72 degrees.
The angles of a pentagon add up to 540 degrees. In an irregular pentagon, pentagon sides and angles can be different sizes.
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Latitude and longitude describe locations on the Earth with respect to the equator and prime meridian. The table shows the
Latitude and daily high temperatures on the first day of spring for different locations with the same longitude.
Temperature vs. Latitude
Latitude
("N)
High Temp
12
53
16
41
30
67
36
63
32
70
11
58
10
61
33
67
30
72
Which statement describes the slope of the line of best fit for the data?
The temperature decreases by about 0.9" for each 1 degree increase north in latitude.
The temperature decreases by about 1.7" for each 1 degree increase north in latitude,
The temperature increases by about 0.8" for each 1 degree increase north in latitude,
The temperature increases by about 1.3" for each 1 degree increase north in latitude.
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Mark this and refum
choice A ("decreases by about 0.9°") is more likely the correct description of the slope.
Step 1: Look for the trend between temperature and latitude
Generally, as we move north in latitude (higher latitude values), temperatures tend to decrease. Analyze the high temperatures in the table. Warmer temperatures are at lower latitudes and cooler temperatures are at higher latitudes.
Step 2: Interpret the slope
The slope of the best fit line tells you how much the temperature changes (on the y-axis) on average with every one-degree increase in latitude (on the x-axis). Since temperature decreases as latitude increases, the slope will be negative.
The temperature decreases by a certain value for each 1-degree increase north in latitude. The answer choices with a positive slope (increase in temperature) can be eliminated (choices C and D). Looking at the remaining choices (A and B), a lower negative value indicates a smaller decrease in temperature with increasing latitude.
We know that generally, temperatures get cooler as we move north (higher latitudes). This means as the latitude values increase (on the x-axis), the temperature values (on the y-axis) should decrease.
Slope and Interpretation: The slope of the best fit line through the temperature data tells us how much temperature changes (goes up or down) on average with every one-degree increase in latitude. Since temperature goes down (decreases) with increasing latitude, the slope will be negative.
Eliminate positive slopes (choices C and D) because they indicate a temperature increase with latitude, which contradicts the trend.Focus on the remaining choices (A and B) with negative slopes.A lower negative value (like -0.9° in choice A) means a smaller decrease in temperature for each degree of latitude increase. This suggests a more gradual decrease in temperature compared to a larger negative value.Therefore, considering the trend and how the slope reflects temperature change, choice A ("decreases by about 0.9°") is the most likely description of the slope. It suggests a gradual decrease in temperature with increasing latitude.what is 22% of 60?
Answer: 13.2
Step-by-step explanation: First, turn the percent into a decimal by dividing it by 100.
22/100 = 0.22
Multiply the decimal by 60.
0.22 x 60 = 13.2
Pleaseee helpppp!!!!!!!!!!!
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=\cfrac{3}{5}(x-2)\implies y+4=\cfrac{3}{5}(x-2) \\\\\\ y+4=\cfrac{3}{5}x-\cfrac{6}{5}\implies y=\cfrac{3}{5}x-\cfrac{6}{5}-4\implies y=\cfrac{3}{5}x-\cfrac{26}{5}[/tex]
What are the zeros of f(x)=x^2+3x-10
You must remember that a polynomial is written like so...
ax^2 + bx + c
In this case...
a = 1
b = 3
c = -10
To factor you must find two numbers who both add up to b (3) AND multiply to c (-10)
-2 + 5 = 3
-2 * 5 = -10
so...
(x - 2)(x + 5)
To find the zero you must set each factor equal to zero and solve for for x like so...
x - 2 = 0
x = 2
x + 5 = 0
x = -5
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
x= -5 and x= 2
Step-by-step explanation:
What is the product of 3a + 5 and 2a2 + 4a - 2?
Answer:
6a^3 + 22a^2 - 6a - 10
Step-by-step explanation:
(3a + 5)(2a^2 + 4a - 2)
distribute 3a
6a^3 + 12a^2 - 6a
distribute 5
10a^2 + 20a - 10
combine like terms/simpify
6a^3 + 22a^2 - 6a - 10
Answer:
6a^3 + 22a^2 +14a-10
Step-by-step explanation:
Hi, to solve this you have to apply the distributive porperty:
So:
[tex](3a +5)x ( 2a^{2} +4a -2)\\6a ^{3} +12a^{2} -6a + 10a^{2} +20a^{2} -10\\\\[/tex]
Then, combine like terms and solve using addition or subtraction:
[tex]6a^{3} +12a^{2} +10a^{2} +20a-6a-10\\6a^{3} +22a^{2} +12a-10[/tex]
In conclusion the product is 6a^3 + 22a^2 +14a-10.
Feel free to ask for more if it´s necessary or if you did not understand something.
Is the graph increasing, decreasing, or constant where -3 < X <-1?
Answer:
decreasing
Step-by-step explanation:
since its negative it will slope down
The graph is increasing.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.
Given: range: -3 < X <-1
The graph related to this question is attached below
as, seen from the graph the graph slope will rise up from -3 to -1.
Hence, the graph is increasing.
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The table below shows the details of three different river rafting adventures. Adventure Duration (in hours) Distance (\text{km})(km)left parenthesis, k, m, right parenthesis High Tide 111 333 Monsoon 222 555 Tsunami 4 Which river rafting adventure offers the lowest average speed? Choose 1 answer: Choose 1 answer: (Choice A) A High Tide (Choice B) B Monsoon (Choice C) C Tsunami
Answer:
Monsoon
Step-by-step explanation:
in High tide every 1 hour, you move 3 km that is faster then Monsoon which every 2 hours you move 5 km because if you multiply 1 by 2 you get 2 (hours) but if you multipy 3 by 2 yuo get 6 and 6 is more than 5. if you use this method one more time then to you will find that the answer is Monsoon.
The river rafting adventure that offers the lowest average speed would be the option Monsoon.
Explain Multiplication no sign?We don't write symbols like currency generally and understand it from context.
Also, a sign of multiplication is often hidden if there are non-numeric symbols and numbers being multiplied are written together.
The table below shows the details of three different river rafting adventures.
Adventure Duration (in hours)
Distance (\text{km})(km)left parenthesis, k, m, right parenthesis
High Tide 111 333 Monsoon 222 555 Tsunami 4
In High tide every 1 hour, you move 3 km which is faster than Monsoon
Every 2 hours you move 5 km because 1 x 2 gives 2 (hours)
But 3 x 2 = 6 and 6 is more than 5.
Therefore, The answer is Monsoon.
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Who knows what the middle part is asking
Answer
I assume you're talking about 6-7, so on the left lines, you already did it, you just regularly subtract the numbers, and then on the right lines, you round the first problem to the nearest ten, remember five and up, round up, so for question 6 the new number model would be 90-40=50. since 93 rounds down to 90 and 38 rounds up to 40. continue to do that and write the entire model AND answer on the line to the right. hope this helps
Step-by-step explanation:
Answer:
Step-by-step explanation:
Estimate means put your calculator in a drawer or under a pillow. You are not going to use it.
The question means round to the nearest 10 (as it says)
One
93 rounds to 90 (93 is only 3 away from 90)
38 rounds to 40 (38 is very close to 40. You are only 2 away).
90 - 40 = 50
If you answer 55, you should get it wrong. That's not estimating.
Two
67 rounds to 70
49 rounds to 50
70 - 50 = 20 18 is just too exact.
Three
75 is very nasty. My call would be that you can call it 70 or 80. It all depends on what you have been told about 5s. On Brainly, I think you round up. So 75 become 80
27 rounds to 30
80 - 30 = 50
The last one is all yours.
What is the product of (3x+5) and (x+4)
For this case we must find the product of [tex](3x + 5) (x + 4)[/tex]
By definition, the distributive property states that:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
Then, according to the expression we have:
[tex]3x ^ 2 + 12x + 5x + 20 =\\3x ^ 2 + 17x + 20[/tex]
Answer:
[tex]3x ^ 2 + 17x + 20[/tex]
Option C
Answer:
C
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
3x(x + 4) + 5(x + 4) ← distribute both parenthesis
= 3x² + 12x + 5x + 20 ← collect like terms
= 3x² + 17x + 20
f as a function of x is equal to the square root of quantity 5 x plus 7, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).
Answer:
(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]
Step-by-step explanation:
f(x) = [tex]\sqrt{5x+7}[/tex]
and g(x) = [tex]\sqrt{5x-7}[/tex]
We need to find (f+g)(x)
(f+g)(x) = f(x) + g(x)
(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]
It can't be further solved so,
(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]
x 2 + y 2 = 36
x + y = 6
Solve the system of equations.
Answer:
x = 6 and y = 0 or x = 0 and y = 6 → (6, 0) or (0, 6)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x^2+y^2=36\\x+y=6&\text{subtract y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x^2+y^2=36&(1)\\x=6-y&(2)\end{array}\right\qquad\text{substitute (2) to (1):}\\\\(6-y)^2+y^2=36\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\6^2-(2)(6)(y)+y^2+y^2=36\\36-12y+2y^2=36\qquad\text{subtract 36 from both sides}\\2y^2-12y=0\qquad\text{distributive}\\2y(y-6)=0\iff2y=0\ \vee\ y-6=0\\\\2y=0\qquad\text{divide both sides by 2}\\y=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6[/tex]
[tex]\text{put the values of y to (2):}\\\\for\ y=0:\\x=6-0=6\\\\for\ y=6\\x=6-6=0[/tex]
Subtract the problem below.
Answer:
C. 3x^2 -13x + 7
Step-by-step explanation:
Lets start in the ones place:
+3
- (-4)
_______
+7
Now go to the tens place:
-5x
-(8x)
________
-13x
Lastly, go to the hundreds place:
6x^2
-(3x^2)
_________
3x^2
So, the correct answer is "3x^2 -13x + 7", which is C.
I hope this helps! :)
Answer:
C) 3x squared - 13x + 7
Step-by-step explanation:
To subtract this problem you need to combine like terms
6x squared - 3x squared = 3x squared
-5x - 8x = -13
3 - -4 = 7
Since you combined the like terms put it back into an expression
3x squared - 13x + 7
Since the 13 is negative it becomes a subtraction sign in this expression.
The 7 is positive so it becomes an addition sign.
simplify (3x^2+4x-3)-(4x^2-3x+2)
Answer:
−x^2+7x−5
Step-by-step explanation:
---- times this by 1 (3x^2+4x−3) −(4x^2-3x+2) ---- times this by - 1
3x^2+4x−3−4x^2+3x−2
3x^2+4x−3−4x^2+3x−2 - collect like terms
(3x^2+−4x^2)+(4x+3x)+(−3+−2) - solve it
(3x^2+−4x^2)= −x^2
(4x+3x) = 7x
(−3+−2) = −5
−x^2 + 7x−5
On simplifying the given equation [tex](3x^2+4x-3)-(4x^2-3x+2)[/tex] we get [tex]-x^2+7x-5[/tex]
Given: [tex](3x^2+4x-3)-(4x^2-3x+2)[/tex]
To find: simplify
We have been given an equation and for solving it we first need to open the parenthesis
[tex]3x^2+4x-3-4x^2+3x-2[/tex]
Now we will group terms on which addition or subtraction can be performed
[tex]3x^2-4x^2 +4x+3x-3-2\\= -x^2+7x-5[/tex]
Which expression is equivalent 5÷7
a.7/5
b.7×1/5
c.35
d.5×1/7
Final answer:
The expression 5÷7a is equivalent to 5a/7 when rewritten in simplest algebraic form. It represents multiplying 5 by the reciprocal of 7a. None of the provided answer options match this expression. Option. A
Explanation:
The expression 5÷7a can be rewritten as 5÷7 × a or 5/7a. This is because division by a number is the same as multiplying by its reciprocal. Thus, we take the reciprocal of 7a to be (1/7)a or a/7, multiply it by 5, giving us 5a/7. This is how we denote division within algebraic expressions and simplifies the equation.
If the question is looking for an equivalent single-term expression, none of the given options (5×7b, 7÷5b, 7×1/5c, 35d, 5×1/7) are correct, as they are all different in terms of algebraic structure and value. However, if you're looking for an equivalent expression in the simplest algebraic form, the equivalent expression for 5÷7a is simply 5a/7.
Consider the exponential function f(x)
its
graph.
Answer:
# The growth value of the function is 1/3 ⇒ 2nd
# f(x) shows exponential decay ⇒ 3rd
# The function is a stretched of the function [tex]f(x)=(\frac{1}{3}) ^{x}[/tex] ⇒ 4th
Step-by-step explanation:
* Lets explain the exponential function
- The form of the exponential function is f(x) = a b^x, where a ≠ 0,
b > 0 , b ≠ 1, and x is any real number
- a is the initial value of f(x) ⇒ (when x = 0)
- b is the growth factor
- The exponent is x
- If the growth factor (b) is in between 1 and 0 then it is exponential
decay
* Lets solve the problem
∵ [tex]f(x)=3(\frac{1}{3})^{x}[/tex]
- Lets find the initial value
∵ At the initial position x = 0
∴ [tex]f(0)=3(\frac{1}{3})^{0}=3(1)=3[/tex]
* The initial of f(x) is 3
∵ b = 1/3
∵ b is the growth factor of the function
* The growth value of the function is 1/3
∵ b = 1/3
∵ 0 < b < 1
∴ The function is exponential decay
* f(x) shows exponential decay
- A vertical stretching is the stretching of the graph away from the x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
∵ [tex]f(x)=(\frac{1}{3})^{x}[/tex]
∵ Its parent function is [tex]f(x)=3(\frac{1}{3})^{x}[/tex]
∴ k = 3
∵ k > 1
∴ the function is stretched vertically
* The function is a stretched of the function [tex]f(x)=(\frac{1}{3})^{x}[/tex]
∴ The true statements are:
# The growth value of the function is 1/3
# f(x) shows exponential decay
# The function is a stretched of the function [tex]f(x)=(\frac{1}{3})^{x}[/tex]
For f(x)=4x+1 and g(x)=x^-5, find (f+g)(x)
Answer:
x^(-5)+4x+1
given f(x)=4x+1 and g(x)=x^(-5)
Step-by-step explanation:
f(x)=4x+1
g(x)=x^(-5)
(f+g)(x) means you are just going to do f(x)+g(x)
or (4x+1)+(x^(-5))
There are absolutely no like terms so it can't be simplified. We can use commutative and associative property to rearrange the expression.
x^(-5)+4x+1
ANSWER
[tex](f + g)(x) = \frac{4{x}^{6} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 4x + 1[/tex]
and
[tex]g(x) = {x}^{ - 5} [/tex]
We now want to find
[tex](f + g)(x)[/tex]
We use this property of Algebraic functions.
[tex](f + g)(x) = f(x) + g(x)[/tex]
We substitute the functions to get:
[tex](f + g)(x) = 4x + 1 + {x}^{ - 5} [/tex]
Writing as a positive index, we get:
[tex](f + g)(x) = 4x + 1 + \frac{1}{ {x}^{5} } [/tex]
The property we used to obtain the positive index is
[tex] {a}^{ - n} = \frac{1}{ {a}^{n}} [/tex]
We now collect LCD to get:
[tex](f + g)(x) = \frac{4x \cdot {x}^{5} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]
This simplifies to:
[tex](f + g)(x) = \frac{4{x}^{6} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]
A tV set was bought for $3900 and $200 was spent on
transportation and $900 on repair. It was sold at a loss of 10%
the selling price of the television
Answer:
$4,500
Step-by-step explanation:
Given:
Price Bought: $3,900
Transportation: $200
Repair: 900
Total amount spent = 3,900 + 200 + 900 = $5,000
10% of amount spent = 10% x 5,000 = 0.1 x 5000 = $500 (= amount loss)
TV was sold at a 10% loss,
selling price = $5,000 - $500 = $4,500
Answer:
Rs.4500
Step-by-step explanation:
1.total cost of TV=3900+200+900
=5000
2. loss=10/100*5000
=500
selling price of TV=5000-500
=Rs.4500
Solve the system of equations by substitution.
x + y =
x + 7y = 8
Answer:
Lol I just took this text couple weeks ago. The answer is (1,1) Solve the system of equations by substitution.
3/8x + 1/3y = 17/24
x + 7y = 8
x = -7y + 8 and substituting it to the first equation
3/8x + 1/3y = 17/24
3/8(-7y + 8 )+ 1/3y = 17/24
Solving for the value of y = 1
And substituting y =1 to the second equation
X= 1
(1, 1)
Answer:
1,1
Step-by-step explanation:
if f(x) =5x-6 what is the inverse of f(x)
Replace f(x) with y:
y = 5x-6
Swith the variables:
x = 5y -6
Now solve for y:
add 6 to each side:
x +6 = 5y
Divide both sides by 5:
y = (x+6)/5
Now replace y with the inverse function f^-1 (x):
f^-1(x) = (x+6)/5
Answer:
See below attachment
Step-by-step explanation:
A p E x
For the data set 7,5,10,11,12 the mean is x, is 9. What is the standard deviation?
Answer:
SD(σ)=2.91548
Step-by-step explanation:
Definition:
Standard deviation (SD) measures the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ)
To find out SD you must know the value of Mean and Variance.
Mean=sum of values / N (number of values in set)
Mean=7+5+10+11+12/5
Mean=45/5
Mean=9
Variance=((n1- Mean)2 + ... nn- Mean)2) / N-1 (number of values in set - 1)
Variance=((7-9)^2 +(5-9)^2+(10-9)^2+(11-9)^2+(12-9)^2))/5-1
Variance=((-2)^2+(-4)^2+(1)^2+(2)^2+(3)^2)/4
Variance=(4+16+1+4+9)/4
Variance=34/4
Variance=8.5
Standard Deviation(σ)=√Variance
σ = √8.5
By taking the square root of √8.5 we get;
σ = 2.91548
Thus the value of Standard Deviation(σ)=2.91548....