Answer:
[tex]g(x) = x - 11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 5[/tex]
Required
Translate to the right by 6 units
When a function is translated to the right, the resulting function becomes
[tex]g(x) = f(x - h)[/tex]
Where h is the number of units moved;
Since; h = 6
[tex]g(x) = f(x - h)[/tex]
becomes
[tex]g(x) = f(x - 6)[/tex]
Solving for f(x - 6);
[tex]f(x) = x - 5[/tex]
Substitute x - 6 for x
[tex]f(x - 6) = x - 6 - 5[/tex]
[tex]f(x - 6) = x - 11[/tex]
This implies that [tex]g(x) = x - 11[/tex] is the result of the translation
Which equation represents the line that passes
through the point (1,5) and has a slope of -2?
1) y = -2x + 7
2) y = -2x + 11
3) y = 2x-9
4) y = 2x + 3
Answer:
Step-by-step explanation:
y - 5 = -2(x - 1)
y - 5 = -2x + 2
y = -2x + 7
Option 1 is the answer
Find all x-intercepts and y-intercepts of the graph of the function . f(x) = - x ^ 3 + x ^ 2 + 12x If there is more than one answer, separate them with commas. Click on "None" if applicable.
Answer:
The y-intercept is (0,0)
The x-intercepts are (-3,0), (0,0), and (4,0)
Step-by-step explanation:
So we have the function:
[tex]f(x)=-x^3+x^2+12x[/tex]
And we want to solve for the x- and y-intercepts.
Y)
To solve for the y-intercept, recall that the y-intercept is when the graph touches the y-axis. At that point, the x values is 0. Thus, to find the x-intercept, substitute 0 for x:
[tex]f(x)=-(0)^3+(0)^2+12(0)[/tex]
Simplify:
[tex]f(x)=0[/tex]
So, the y-intercept is (0,0)
X)
To solve for the x-intercept(s), set the function equal to 0 and solve for x:
[tex]0=-x^3+x^2+12x[/tex]
First, factor out a negative x:
[tex]0=-x(x^2-x-12)[/tex]
Factor within the parentheses:
[tex]0=-x(x-4)(x+3)[/tex]
Zero Product Property:
[tex]-x=0\text{ or } x-4=0\text{ or } x+3=0[/tex]
Divide by -1 on the first one. Add 4 on the second one. And subtract 3 on the right:
[tex]x=0\text{ or } x=4\text{ or } x=-3[/tex]
So, our x-intercepts are:
[tex](-3,0), (0,0), (4,0)[/tex]
And we're done :)
Are the functions inverses? Why or why not?
Answer:
The answer is not an inverse function.
Step-by-step explanation:
The inverse function does not reverse. In other words, f(x) = x-5/10 and h(x) =10x+5 does not mirror.
Sam is 4 times as old as Allie. Write an equation to model this situation. a) s=4A b) A=4S c) S= 4+A d) A= 4+S
Answer:
a) s=4A
Step-by-step explanation:
If you read the equation out loud it may help!
Sam=4 times Allie
Sams age Equals 4 times the age of Allie
In division, does the big or small letter go first?
Answer: Big number
Step-by-step explanation:
In division, does the big or small letter go first?
Answer:
In division, the big one go first.
Step-by-step explanation:
So, when you do division, you can put the big or small ones first but, preferably the big ones because it will be easier to solve the equation.
The sum of three numbers is 49. The second number is five less than three times the third number. If the first number is twice the amount of the third number, what is the value of the second number?
Answer:
(x, y, z) → (18, 22, 9)
Step-by-step explanation:
sum of three numbers is 49
x + y + z = 49
second number is 5 less than three times the third number
y = 3z - 5
first number is twice amount of third number
x = 2z
set of equations
x + y + z = 49
y = 3z - 5
x = 2z
plug in 2nd and 3rd equation into first
(2z) + (3z - 5) + z = 49
combine like terms
2z + 3z - 5 + z = 49
6z - 5 = 49
add 5 to both sides
6z = 54
divide by 6
z = 9
plug z into 2nd and 3rd equations
y = 3(9) - 5
y = 27 - 5
y = 22
x = 2(9)
x = 18
check:
18 + 22 + 9 = 49
(x, y, z) → (18, 22, 9)
4/5, √9, -0.95, √32/8, 2.9, - √6 PLEASE order from least to greatest
Answer:
-√6 -0.95 √32/8 4/5 2.9 √9
Step-by-step explanation:
4/5, √9, -0.95, √32/8, 2.9, - √6
4/5 = 0.8
√9 = 3
√32/8 = 4√2 / 8 = √2/2 = 0.707
-√6 = -2.449
-√6 -0.95 √32/8 4/5 2.9 √9
Solve the following system of equations using substitution:
2x - 2y + z = 8
-y+z=4
2z=4
Answer:
Step-by-step explanation:
2z = 4
z = 2
-y + 2 = 4
-y = 2
y = -2
2x + 4 + 2 = 8
2x + 6 = 8
2x = 2
x = 1
(1, -2, 2)
Which sets of numbers does -3/4 belong to
Answer:
It belongs to the... RATIONAL number set
Given: <1 and <2 are supplementary, and <2 and <3 are supplementary. Prove: <1 is congruent to <3
Step-by-step explanation:
If ∠1 and ∠2 are supplementary, then m∠1 + m∠2 = 180° (1).
If ∠2 and ∠3 are supplementary, then m∠2 + m∠3 = 180° (2).
From (1) we have
m∠1 + m∠2 = 180° /subtract m∠1 from both sides
m∠2 = 180° - m∠1
substitute it to (2)
(180° - m∠1) + m∠3 = 180°
180° - m∠1 + m∠3 = 180° /subtract 180° from both sides
- m∠1 + m∠3 = 0 /add m∠1 to both sides
m∠3 = m∠1 ⇒ m∠1 = m∠3 ⇒ ∠1 ≅ ∠3
On a number line, point A is at coordinate 1. Point B is at coordinate-5. Find the
coordinate that is the midpoint from A to B.
Answer:
-2
Step-by-step explanation:
Midpoint is the half of the sum of endpointsPoint A = 1
Point B = - 5
Midpoint :
(1 + (-5))/2 = -4/2 = -2What is the base of a triangle with an area of 207 in.² and a height of 18 inches
We just need to divide so we can find the base length of the triangle:
207 / 18 = 11.5
Therefore, the base length of the triangle is 11.5 inches.
Best of Luck!
Answer:
23 inches
Step-by-step explanation:
A = [tex]\frac{1}{2}[/tex] bh
207 = [tex]\frac{1}{2}[/tex] b x 18
[tex]\frac{207}{9}[/tex] = b
b = 23
Jonas is planning out his route for an upcoming race. He uses negative numbers to represent points before the finish line and positive numbers to represent points after the finish line.
On Jonas's map, there is a bridge at -91 3/4 meters, and his wife is watching him at 14 1/2 meters.
What do 0 meters represent?
Answer:
The finish line
Step-by-step explanation:
This is because, since negative numbers are used to represent points before the finish line, and positive numbers are used to represent points after the finish line, the finish line can only be represented by the number zero. Since on Jonas' map, there is a bridge at -91 3/4 metres, therefore, the bridge is 91 3/4 metres before the finish line. And, since his wife is watching at 14 1/2 metres, since this number is positive, she is 14 1/2 metres after the finish line. So, the finish line itself, will be represented by 0 metres since this is indicated a change from negative to positive.
(10 pts) Light bulbs of a certain type are advertised as having an average lifetime of 800 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised.
Answer:
We conclude that the true average lifetime is smaller than what is advertised.
Step-by-step explanation:
The complete question is: Light bulbs of a certain type are advertised as having an average lifetime of 800 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 21 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using SPSS, resulting in the accompanying output.
Sample Mean Sample Standard Deviation
Lifetime 738.44 38.30
Test the appropriate hypothesis for this study (i.e., state the hypotheses, compute the test statistics, compute the p-value, and make a conclusion). What conclusion would be appropriate for a significance level of 0.05?
We are given that Light bulbs of a certain type are advertised as having an average lifetime of 800 hours.
A potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised.
Let [tex]\mu[/tex] = true average lifetime of the light bulbs.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 800 hours {means that the true average lifetime is greater than or equal to what is advertised}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 800 hours {means that the true average lifetime is smaller than what is advertised}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean lifetime = 738.44 hours
s = sample standard deviation = 38.30 hours
n = sample of bulbs = 21
So, the test statistics = [tex]\frac{738.44-800}{\frac{38.30}{\sqrt{21} } }[/tex] ~ [tex]t_2_0[/tex]
= -7.36
The value of t-test statistics is -7.36.
Also, the P-value of test-statistics is given by;
P-value = P([tex]t_2_0[/tex] < -7.36) = Less than 0.05% {from t-table}
Since the P-value of our test statistics is less than the level of significance of 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average lifetime is smaller than what is advertised.
A survey was given to 277 people asking whether people like dogs and/or cats. 126 said they like dogs 112 said they like cats 90 said they don't like cats or dogs. How many said they liked both cats and dogs?
A pillow that usually costs $18 is marked down 25%. Use the table to find the pillow’s new price.
It would be 13.50 because 50% off of 18$ is 9$ but it’s not 50% off itS 25% off so If you take the 50% Off price of 9$ and add 4.50 (One more 1/4th) you get $13.50
what's 198.040 divided by 98.100 and plus 100.000 times 4.300.
Answer:
868.065
Step-by-step explanation:
198.040 ÷ 98.1 + 100 x 4.3
= 2.0188 + 100 x 4.3
= 201.8756 x 4.3
= 868.065
Steps to solve:
198.040 ÷ 98.1
~Divide
2.0187563... or 2.02
Steps to solve:
100 * 4.3
~Multiply
430
Best of Luck!
Square root !!!!!!!!
Answer:
hope this helped
Step-by-step explanation:
Step 1: Calculate. We calculate the square root of 50 to be: √50 = 7.07106781186548.
Step 2: Reduce. 7.07.
Step 3: Round. Round 7.07 so you only have one digit after the decimal point to get the answer: 7.1.
PLEASE HELP RIGHT AWAY: Set the left side of this equation equal to f(x) and the right side equal to g(x) . Then graph y=f(x) and y=g(x) on the same coordinate grid. (x+1)^2-2=2/x
Answer:
Step-by-step explanation:
heres the answer
Find the slope of a line parallel to the line:
5 x plus y equals 15
Answer:
the answer is y=-5
Two consecutive EVEN numbers have a sum of 30. What are the numbers?
Answer:
14 and 16
Step-by-step explanation:
Consecutive even numbers are even numbers that follow each other from smallest to biggest for example 2,4,6,8 are consecutive even numbers. So the consecutive even numbers that have a sum of 30 are 14 and 16 (14+16=30).
HOPE IT HELPED
This angle has all of the following names, except:
Answer:
its c. <vwx
Step-by-step explanation:
i got it right
help please! Will mark you as Brainliest!
Answer:
21
Step-by-step explanation:
which ratio is less then 15/24 a.1/2 b.7/8 c. 19/24 d. 6/8
Answer:
A. 1/2
Step-by-step explanation:
So 15/24 = 0.625
therefore you need to convert all the fractions into decimals and determine which decimal is less than 0.625
a) 0.5 ------ding ding ding correct answer :)
b) 0.875
c) 0.79
d) 0.75
If this helped, please don't forget to give me brainliest!
The Key Club is selling personalized valentines to raise money. The print shop charges $2 for each valentine, plus a flat rate of $10 for printing. Write an equation to represent how many valentines the club can print with a budget of $125.
Answer:
2x + 10 = 125 is the answer
did it on edge
Step-by-step explanation:
297,060 + 0.0004839 =
Answer in Scientific Notation
Answer:
2.970600004839 × 10^5
Step-by-step explanation:
First, we add up these 2 numbers.
297,060 + 0.0004839 = 297060.0004839
Then, we convert that into scientific notation.
297060.0004839 = 2.970600004839 × 10^5
Finally, we check if it's right.
10^5 = 100000
2.970600004839 * 100000 = 297060.0004839
Hope this helps.
Which of the following could be a rational number? A. the sum of two irrational numbers B. the product of two irrational numbers C. the sum of a rational number and an irrational number D. the product of a rational number and an irrational number
Answer:
B. the product of two irrational numbers
Step-by-step explanation:
To be a rational number, we need to multiply two irrational numbers
An example would be
sqrt(2) * sqrt(2) = sqrt(4) = 2
Answer:
The product of two irrational numbers
Step-by-step explanation:
whats the difference between a variable and a numeral
Answer:
a numerical variable is a variable where the measurement or number has an empirical meaning.
a variable is a category or a type
Answer:
A numerical variable is a variable where measurement or a number has a numerical meaning.
3(2x-4)=4(4x-1) can someone please help ?
Answer:
x=-4/5
Step-by-step explanation:
3(2x-4)=4(4x-1)
6x-12=16x-4
-10x=8
x=-8/10
x=-4/5
A point on a pre-image is G(5, -2). If its image has coordinates G'(2, 1), what was the translation? (x - 3, y - 3) (x + 3, y - 3) (x - 3, y + 3) (x + 3, y + 3)
Answer:
(x - 3, y + 3 )
Step-by-step explanation:
Note G(5, - 2 ) → G'(2, 1 )
Requires 3 to be subtracted from 5 to obtain 2 and 3 to be added to - 2 to obtain 1, thus
(x, y ) → (x - 3, y + 3 ) is the translation rule
Answer:
the answer is (x - 3, y + 3 )
Step-by-step explanation:
hope this helps