The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.
On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 5) and (2, 25). g (x) approaches y = negative 10 in quadrant 2 and increases into quadrant 1. It goes through (0, negative 9), (1, negative 5), (2, 15).
What is the equation of g(x)?
g(x) = 5x – 9
g(x) = 5x – 10
g(x) = 5x – 9
g(x) = 5x – 10
According to the function transformations, the equation of function g(x) is [tex]g(x) = 5^x - 10[/tex]
How to determine the equation of g(x)?The complete question is in the attachment
The function f(x) is given as:
[tex]f(x) = 5^x[/tex]
From the attached graph, we can see that the function f(x) is 10 units down to get g(x).
This is so because the y values of g(x) are 10 less than the corresponding y values of f(x)
This transformation is represented by:
(x, y) => (x, y - 10)
So, we have:
g(x) = f(x) - 10
Substitute [tex]f(x) = 5^x[/tex]
[tex]g(x) = 5^x - 10[/tex]
Hence, the equation of function g(x) is [tex]g(x) = 5^x - 10[/tex]
Read more about function transformations at:
https://brainly.com/question/3381225
#SPJ1
Please help! Will give the brainliest :)
Answer: J. A translation of △XYZ to the right.
Step-by-step explanation:
I'll explain each bullet point one by one. A good hint is to pay attention to where the letters are.
-J is correct because the figure was shifted to the right.
-K is incorrect because if it was a reflection across the x-axis, the figure would be in Quadrant 3, or the bottom left.
-L is incorrect because if you pay attention to the letters, they are in the exact same place. If it was a reflection across the y-axis, the X' and Y' would switch places if you know what I mean.
-M is incorrect because if the figure was rotated 90°, point Z' would be furthest from the x-axis. In other words, the triangle would have been pointing up and not down.
-N is incorrect because if the figure was rotated 180° clockwise, the figure would have been in Quadrant 4, or the bottom right.
Given this information, the most appropriate answer is J.
I hope this helps! Pls give brainliest!! :)
Catalina and Morgan are finding the length of the third side of the right triangle. Who is correct? Explain your reasoning.
Answer:
Morgan
Step-by-step explanation:
because the pythagoras theorem is
H
[tex] {h1}^{2} = {b}^{2} + {h2}^{2} [/tex]
where h1=hypotenuse
h2=height
b=base
A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50. Required: How many of each animal should he raise to maximize profit? What is the maximum profit?
Answer:
1050 max profit
Step-by-step explanation:
cow 5brr 30br 600 × 6 cows 570
sheep 2brr 20br 500 ×10 sheeps 480
sheep&cows = 1050 max profit
what is the decimal value that represents
the total percent markdown for the following scenario, after being rounded to the nearest percent:50%, 31%,and 9%
The decimal value that express the total percent markdown for the given scenerio are 0.5,0.31,0.09.
Given the total percent markdown for the following scenario, after being rounded to the nearest percent:50%, 31%,and 9%
Percentage is a ratio of the numbers expressed as a fraction of 100.
We have to just convert the percentages into decimal number which will be done as under:
To convert percentages into decimals we need to divide the number by 100. In this way the percentages will become:
50%=50/100
=0.5
31%=31/100
=0.31
9%=9/100
=0.09
Hence the decimal value of 50% ,31 % and 9% in percentages are 0.5,0.31,0.09.
Learn more about percentages at https://brainly.com/question/24304697
#SPJ10
Answer:0.69
Step-by-step explanation:
Point P has coordinates P(-4, 3).
What are the coordinates of the image P" after I translate point P: 1
unit to the right 7 units down and then I reflect its image across the
y-axis?
The x-coordinate of P" is:
The y-coordinate of P" is:
What happened in this situation?
........................................................................................................
(Maya raises her hand)
Ms. Teacher: Yes, Maya?
Maya: Someone passed gas.
(Another student, Nylo, begins silently laughing)
(Another student, Lia, notices Nylo laughing)
Lia: it was Nylo.
(the entire class begins laughing, except for Maya)
...............................................................................................
Why did Lia think it was Nylo and expose them? And why didn't Maya laugh?
Answer:
It's because Maya friend did not pass gas
Will mark brainliest if you can help!
Answer:
ln(20) = 2.9957
Here given:
ln(4) = 1.3863
ln(5) = 1.6094
Evaluating with that:
[tex]\rm \Rightarrow ln\left(20\right)=ln\left(5\right)+ln\left(4\right)\\[/tex]
[tex]\rm \Rightarrow ln\left(20\right)=1.3863 \ + \ 1.6094[/tex]
[tex]\rm \Rightarrow ln\left(20\right)=2.9957[/tex]
Competitive firms that earn a loss in the short run should
Competitive business firms that earn a loss in the short-run should shutdown if price (P) is lesser than average variable cost (AVC).
What is an average variable cost?An average variable cost (AVC) can be defined as the cost of production per unit item incurred by a business firm and divided by total output of production. Thus, it's calculated by dividing total variable cost (TVC) by total output of production.
As a general rule in Economics, competitive business firms that earn a loss in the short-run are advised to shutdown their production when price (P) is lesser than average variable cost (AVC).
Read more on average variable cost here: https://brainly.com/question/17010492
#SPJ1
a) Construct a 95% confidence interval for the average test score for Delhi students. (1 Mark)
(b) Is there statistically significant evidence that Delhi students per form differently than other students in India? (1 Mark)
(c) Another 503 students are selected at random from Delhi. They are given a 3-hour preparation course before the test is administered. Their average test score is 1019, with a standard deviation of 95. Construct a 95% confidence interval for the change in average test score associated with the preparation course. (2 Marks)
(d) Is there statistically significant evidence that the preparation course helped? (1 Mark)
The solution to all the answers are given below.
The complete question includes
Grades on a standardized test are known to have a mean of 1,000 for students in the Delhi. 453
randomly selected Delhi students take the test, yielding sample mean of 1,013 and sample standard
deviation (s) of 108.
What is Confidence Interval ?It is given by
Confidence Interval for 95% confidence Interval is given by
[tex]\rm Z = X \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]
(a) Construct a 95% confidence interval for the mean test score for Delhi students.
The confidence interval is given by
[tex]\rm 1,013 \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\rm 1,013 \pm 1.96 \dfrac{108}{\sqrt{453}}[/tex]
1013 ± 5.07
so the interval is [1003.06,1022.94]
(b)Yes, since the null of no difference is rejected at the 5% significance level (interval excludes Delhi sample mean of 1,013)
(c) Another 503 Delhi students are randomly selected to take a 3-hour prep course and then give the test. Their average score is 1,019 with a standard deviation of 95.
The standard deviation now is
[tex]\rm \sqrt{\dfrac{95^2}{453} + \dfrac{108^2}{503}}[/tex]
= 6.61
The interval is given by
[tex](1,019-1,013) \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]
= [-7,+19]
(d) No, the interval includes 0, the null difference between the two populations
To know more about Confidence Interval
https://brainly.com/question/24131141
#SPJ1
THE PROBLEM:
Kip had to renew his license and while sitting at the DMV he surveyed everyone else there, asking them their age. The data turned out to have normal distribution, the mean age was 41, and the standard deviation was 5.
1. On paper, make a bell curve with the appropriate values listed on the axis below. Show your teacher.
2. What % of people were below 31 years old?
3. What % of people were above 31 years old?
4. What % of people were between 41 and 46?
5. About what % of people were older than Kip (he's 38 years old)?
y=2x+40 and y=4x+20 when will these be equal
Answer:
When x = 10, they will both be y = 60
(10, 60)
Step-by-step explanation:
2(10) + 40 = 60
4(10) + 20 = 60
Answer:
x = 10
Step-by-step explanation:
2 (10) +40 = 60
4(10) +20 = 60
Question 2(Multiple Choice Worth 4 points)
If (89)P=818, what is the value of p?
02
09
10
18
Answer:
p = 2
Step-by-step explanation:
using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](8^{9}) ^{2}[/tex] = [tex]8^{9(2)}[/tex] = [tex]8^{18}[/tex]
so value of p = 2
A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
Answer:
[tex]\boxed {f(x) = x^{2} - 6x + 1}[/tex]
Step-by-step explanation:
Substituting each x value and checking it corresponds to the table :
x = -6
⇒ f(-6) = (-6)² - 6(-6) + 1
⇒ f(-6) = 36 + 36 + 1
⇒ f(-6) = 73
x = -2
⇒ f(-2) = (-2)² - 6(-2) + 1
⇒ f(-2) = 4 + 12 + 1
⇒ f(-2) = 17
x = 2
⇒ f(2) = (2)² - 6(2) + 1
⇒ f(2) = 4 - 12 + 1
⇒ f(2) = -7
x = 6
⇒ f(6) = (6)² - 6(6) + 1
⇒ f(6) = 36 - 36 + 1
⇒ f(6) = 1
x = 10
⇒ f(10) = (10)² - 6(10) + 1
⇒ f(10) = 100 - 60 + 1
⇒ f(10) = 41
In the expansion of (3a + 4b)^8, which of the following are possible variable terms?
a2b3; a7b; ab8; b8; a4b4; a6b2; a3b4; a8
i don’t get this can someone please explain
A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. The various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.
What is a binomial expression?A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. x² + 4x is an example of a binomial polynomial.
The variable terms that are possible in the expansion of (3a + 4b)⁸ are terms whose sum of powers is equal to 8.
a²b³ → 3 + 2 = 5 ⇒ Not possiblea⁷b → 7 + 1 = 8 ⇒ Possibleab⁸ → 1 + 8 = 9 ⇒ Not possibleb⁸ → 8 ⇒ Possiblea⁴b⁴ → 4 + 4 = 8 ⇒ Not possiblea⁶b² → 6 +2 = 8 ⇒ Possiblea³b⁴ → 3 + 4 = 7 ⇒ Not possiblea⁸ → 8 ⇒ PossibleHence, the various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.
Learn more about Binomial Expression:
https://brainly.com/question/2165968
#SPJ1
The quotient of (x5 – 3x3 – 3x2 – 10x + 15) and (x2 – 5) is a polynomial. What is the quotient?
The quotient [tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex] is [tex]x^3 + 2x - 3[/tex]
How to determine the quotient?The quotient can be represented as:
[tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex]
Start by expanding the dividend
[tex]x^5 + 2x^3 - 5x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex]
Rewrite as:
[tex]x^5 + 2x^3 - 3x^2 - 5x^3 - 10x + 15 \div x^2 - 5[/tex]
Factorize the dividend
[tex]x^2(x^3 + 2x - 3) - 5(x^3 + 2x - 3) \div x^2 - 5[/tex]
Factor out x^3 + 2x - 3
[tex](x^2- 5)(x^3 + 2x - 3) \div x^2 - 5[/tex]
Cancel out the common factor
[tex]x^3 + 2x - 3[/tex]
Hence, the quotient [tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex] is [tex]x^3 + 2x - 3[/tex]
Read more about polynomials at:
https://brainly.com/question/1498111
#SPJ1
Answer: x3 + 2x – 3
Step-by-step explanation:
help
Divide.
22.7 ÷ 0.04
Answer:
567.5
Step-by-step explanation:
it's 567.5. please add me to your followers
What is the a-value of the graph?
elect the correct answer.
which direction must the graph of f(x) = 2* be shifted to produce the graph of g(x) = 2(x+8)
OA. left
OB. right
O C.
down
OD.
The answer to this question is (A) left.
A shop is opened at 7.45 am and closed at 6.30 pm on each day from Monday to Friday. Calculate the total time the shop is opened from Monday to Friday.
Answer:
53 hours and 45 minutes
Step-by-step explanation:
since they open for 10 hours and 45 minutes a day.
10*5=50 hours, 45*5=225 minutes
add the minutes and hours together and it is 53 hours and 45 minutes
if 200÷10=4×u then u=?
Answer:
The answer is 5
Because 200÷10 =20.
So I'm this case, 4x=20. Divide both sides by 4 and the answer is 5. So X=5
5
Answer:
u = 5Step-by-step explanation:
if 200÷10=4×u then u=?
200 : 10 = 4u
20 = 4u
u = 20 : 4
u = 5
---------------------------
check
200 : 10 = 4 * 5
20 = 20
the answer is good
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Answer:
4x + 3y = - 6
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 )
• Parallel lines have equal slopes
calculate the slope of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-3}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex] = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 3, 2 ) into the partial equation
2 = 4 + c ⇒ c = 2 - 4 = - 2
y = - [tex]\frac{4}{3}[/tex] x - 2 ← equation in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 4x - 6 ( add 4x to both sides )
4x + 3y = - 6 ← in standard form
what is the value of n in the equation -1/2(2n +4) + 6 = -9 + 4 (2n +1)
Answer:
n=1
Step-by-step explanation:
-n+4=8n-5
9=9n
n=1
hope that helps
find the lenght of (a) using the pytoagorean theorem.
Longest line is 8
shortest line is 6
Answer:
5.29
Step-by-step explanation:
8
[tex] \sqrt{8 { = }^{2} { - 6 {?}^{2} }^{2} } [/tex]
Answer: Missing side length (b) = 5.3 units
Step-by-step explanation:
Hii, I'd love to help you out! (:
We are provided with two sides, which are:
Longest side = 8Shortest side = 6Luckily, there's a formula to find the third side!
The Pythagorean TheoremThe Pythagorean Theorem ([tex]\pmb{a^2+b^2=c^2}[/tex]) is the formula that we will use to find the missing side. In this formula "a" and "b" denote the "legs" of the triangle (the two shorter sides) and "c" denotes the hypotenuse (the longest side which is opposite the right angle (the 90 degree angle)
NB: a and b are interchangeable, because a+b is the exact same thing as b+a; c is always the hypotenuse.
Now it's time for us to stick in the values.
[tex]\bigstar\underbrace{\boxed{\sf a=6;\;c=8}}[/tex]
This is what we obtain upon sticking in the values:
[tex]\tt 6^2+b^2=8^2[/tex]
Now we can solve for b.
[tex]\tt 36+b^2=64}\\b^2=64-36\\b^2=28\\b\approx5.3[/tex]
Thus, the value of "b" is 5.3. (Rounded to the nearest tenth, or one decimal place - one digit after the decimal point)
_____________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_____________
[tex]\underbrace[/tex]
Please help !!! I will give 20 points to the correct answer !!! Thanks so much
Answer:
x=-4,8
Step-by-step explanation:
To solve this, we can take the absolute value sign off -4x+8 and make the right side ±24. This makes the equation -4x+8=±24.
Simplifying, we have
[tex]-4x=\pm24-8\\x=\frac{\pm24-8}{-4} \\x=\frac{+24-8}{-4}, \frac{-24-8}{-4} \\x=-4, 8[/tex]
The sum of the digits of a two-digit number is 14. When the digits are
reversed, the new number is 36 less than the original number. Find the
original number. Check your answer.
O The original number is 59.
O The original number is 68.
O The original number is 86.
O The original number is 95
First, lets figure out which ones add up to 14
5+9=14
6+8=14
8+6=14
9+5=14
They all add up to 14.
Next, reverse the digits and see if it is 36 less than the original number
95 is not 36 less than 59
86 is not 36 less than 68
68 is only 18 less than 86
59 is 36 less than 95
So, the answer would be 95.
Will give brainliest or whatever it’s called
C is the right answer.
hope it helps...
Answer:
C.
Step-by-step explanation:
Calculating this in Desmos, the closest equation to the points on the graph will have to be c
Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents.
Rational exponents are beneficial in removing the root over or radicals
Let's check the rule
n√a=a^{1/n}Take an example
⁵√3²(3²)⅕3⅖Which of the following is the graph of y= e^x + 1?
Answer + Step-by-step explanation:
y= e^x + 1
+ 1 will shift the graph up 1In the natural exponential function, eˣ = e power x, we employ e. In the eˣ function, the tangent line's slope to any point on the graph is equal to that point's y-coordinate. The sequence we employ to calculate the value of e is (1 + 1/n)Learn more about Natural Exponential Functions here: https://brainly.com/question/1979778
Which of the following statements best describes the relationship between the point (3, 0) and the system
of inequalities below?
3x +2y ≤4
(-x+ 5y > 6
A. The point does not satisfy either the top or the bottom inequalities. Therefore, it is not a
solution to the system.
B. The point satisfies the top inequality but not the bottom. Therefore, it is not a solution to the
system.
C. The point satisfies the bottom inequality but not the top. Therefore, it is not a solution to the
system.
D. The point satisfies both the top and the bottom inequalities. Therefore, it is a solution to the
system
Answer:
d because the point satisfied both
Answer:
D
Step-by-step explanation:
