Answer:
f(-k)=0Step-by-step explanation:
(x + k) is a factor of f(x)
x+k=0 => x= -k; -k is a root of f(x)
=> f(-k)=0
[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]
So the correct option is B.fl-k)=0.
What is a root function example?
The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .
What is the root function?
The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.
Learn more about root function here: https://brainly.com/question/13136492
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A rectangle with an area of 25 square centimetres is rotated and reflected in the coordinate plane. What will be the area of the resulting image? Explain.
In planning a restaurant, it is estimated that a profit of $8 per seat will be made if the number of seats is no more than 50 inclusive. On the other hand, the profit on each seat will decrease 10 cents for each seat above 50.
a) Find the number of seats that will produce the maximum profit.
b) What is the maximum profit?
Answer:
a. 65 seats
b. $422.50
Step-by-step explanation:
We have the following two functions:
8 * x, {0 <= x <= 50}
x * (8 - 0.1 * (x - 50)), {x> 50}, solving we have:
-0.1 * x ^ 2 + 13 * x, {x> 50}
Now we derive both functions and we are left with:
8, {0 <= x <= 50}
-0.2 * x + 13 {x> 50}
we cannot equal to 0 the first function that is equal to 0, because it would be inconsistent, therefore we equal the second function to 0:
-0.2 * x + 13 = 0
0.2 * x = - 13
x = -13 / -0.2
x = 65
Now, test for increasing and decreasing on the intervals (0.65) and (65, infinity)
p '(60) = -0.2 * (60) + 13 = 1
since this value is positive the profit is increasing on (0.65)
p '(70) = -0.2 * (70) + 13 = -1
becuase this value is negative the profit is decreasing on (65, infinity)
Therefore 65 seats are needed to maximize profit
The maximum value would be:
P (65) = 0.1 * (65 ^ 2) + 13 * 65 = 422.5
That is, the maximum value is $ 422.50
So, the question is below, please help me find the answer. :)
Answer:
£2.70 fig rolls and £5.72 crisps
Step-by-step explanation:
£1.08+0.54+£1.08= £2.70 fig rolls
£1.43+£1.43+£1.43-£1.43= £2.86 x 2= £5.72 for 6 packets of crisps
£2.70+ £5.72= £8.42
which law would you use to simply the expression 3^10/3^4 quotient power power of a quotient product of powers power of a product
A computer has a price tag of $300. The store is giving you a 15% discount for the computer. Find the discount AND final price of the computer.
Answer:
Discount = $45
Final = $255
Step-by-step explanation:
First you would multiply $300 by .85. (You do this because your only paying for 85% of the computer) to get the final price
$255
In order to get the discount amount you would subtract 300 by 255 to get
$45
Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 60 minutes for each machine. During the 60 minutes, machine 1 filled an average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine 2 filled an avaerage of 76.1 cans per minute with a standard deviation of 4.1 cans per minute.
Required:
a. If the counts are made each minute for 60 consecutiveminutes, what assumption necessary to the validity of a hypothesistest may be violated?
b. Assuming that all necessary assumptions are met, perform a hypothesis test. Can you conclude that machine 2 is faster than machine 1?
Answer:
The calculated value |t| = | - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance
Alternative hypothesis is accepted
The average of machine two is faster than machine one
Step-by-step explanation:
Step(i):-
Given sample size n₁ = n₂ = 60 minutes
The average of first sample 'x⁻₁ = 73.8
The standard deviation of the first sample 'S₁ ' = 5.2 cans per minute
The average of second sample 'x⁻₂ = 76.1
The standard deviation of the second sample 'S₂ ' = 4.1 cans per minute
step(ii):-
Null Hypothesis : H₀: 'x⁻₁ = 'x⁻₂
Alternative Hypothesis : H₁ : 'x⁻₁ > 'x⁻₂
Test statistic
[tex]t = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S^{2} _{1} }{n_{1} } +\frac{S^{2} _{2} }{n_{2} } } }[/tex]
[tex]t = \frac{73.8 - 76.1 }{\sqrt{\frac{(5.2)^{2} }{60 } +\frac{(4.1)^{2} }{60 } } }[/tex]
t = - 2.6932
|t| = | - 2.6932 | = 2.6932
Step(iii):-
Degrees of freedom
ν = n₁ + n₂ -2 = 60 +60 -2 = 118
t₀.₀₅ = 1.9803
The calculated value |t| = | - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance
Final answer:-
Null hypothesis is rejected at 0.05 level of significance
Alternative hypothesis is accepted
The average of machine two is faster than the average of machine one
7. Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first
three terms is 26.
Answer:
Step-by-step explanation:
Let the first term is n, then the second term must be an where a is a common ratio, and the third term is a^2 n
so, n + an = 24
n + an + a^2 n = 26
solve for a, then solve for n
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below. Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4. StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4. StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4. When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ? –1 –negative StartFraction one-half EndFraction 0 StartFraction one-half EndFraction.
Answer:
x = 0
Step-by-step explanation:
Given
Karissa begins to solve the equation ...
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)[/tex]
Her work is correct and is shown below. Three lines of math.
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)\qquad\text{given}\\\\\dfrac{1}{2}x-7+11=\dfrac{1}{2}x-x+4\qquad\text{eliminate parentheses}\\\\\dfrac{1}{2}x+4=-\dfrac{1}{2}x+4\qquad\text{collect terms}[/tex]
When she subtracts 4 from both sides, the result is ...
[tex]\dfrac{1}{2}x=-\dfrac{1}{2}x[/tex]
Find
What is the value of x?
Solution
Karissa can determine the value of x by adding 1/2x to both sides:
[tex]x=0[/tex]
Answer:
Option C (0)
Step-by-step explanation:
Based on the measures shown, could the figure be a
parallelogram?
Answer:
its A
Step-by-step explanation:
ed 2020
Can someone please please help me
Answer:
The answer is None
Step-by-step explanation:
Multiply 6 2 and 1 and also multiply 12 4 and 2 separately now divide 96 with 12 and you get 8 which is none of the answer choices
Does this graph represent a function? Why or why not?
A
B
C
D
Answer:
B
Step-by-step explanation:
As said in B, use the vertical line test. For any vertical line, does it hit the graph in two points? No. Therefore, the answer is B.
This particular function is f(x)=x^2.
Hope that helped,
-sirswagger21
Answer:
Yes is passes the vertical line test
Step-by-step explanation:
This parabola is a function. it has a one to one correspondence and passes the vertical line test
Simplify -|-5 + 2|. this is all of the question
Answer:
-3
Step-by-step explanation:
-(absolute value of -3)
-(3)
-3
Find the area of the circle. Use pialmost equals 3.14. Radius equals19 yd
What weighs more a pound of feathers or a pound of pennies
A.
B.
C.
D.
Does this table represent a function? Why or why not?
Answer:
Yes, Because every x-value corresponds to exactly one y-value.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Express this number in scientific notation. 5.3×104+4.7×104
Answer:
for [tex]5.3 * 10^4 + 4.7 * 10^4[/tex] the answer would be [tex]1 * 10^5[/tex]
Step-by-step explanation:
After adding like terms we would get [tex]10^4 *10[/tex]
Then we use the exponent rule and get [tex]10^1^+^4[/tex]
Which after adding would result in [tex]10^5[/tex]
Over which interval is the graph of fx =-x2 + 3x + 8 increasing
Answer:
Step-by-step explanation:
it is increasing in [tex]]-\infty;3/2][/tex]
because this is like
[tex]f(x)=ax^2+bx+c[/tex]
where a > 0
and -b/a=3/2
Benjamin has 3 gallon of punch he adds another 1/2 gallon of juice to the punch . How many gallons of punch does he have now ? How many cups? Explain
Answer:
3 1/2 gallons or 56 cups
Step-by-step explanation:
1. Analyze the questions.
We have 3 gallons, and we add another 1/2 gallon. This means that our equation must be 3 + 1/2.
2. Solve.
3 + 1/2 = 3 1/2 gallons
3. Convert.
1 gallon = 16 cups
1 * 3 1/2 gallons = 16 * 3 1/2 cups
3 1/2 gallons = 56 cups
Answer: 3 1/2
Hope this helped! :D
What is the approximate value for the modal daily sales?
Answer:
Step-by-step explanation:
Hello!
The table shows the daily sales (in $1000) of shopping mall for some randomly selected days
Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5
Days 18 27 31 40 56 55 23
Use it to answer questions 13 and 14.
13. What is the approximate value for the modal daily sales?
To determine the Mode of a data set arranged in a frequency table you have to identify the modal interval first, this is, the class interval in which the Mode is included. Remember, the Mode is the value with most observed frequency, so logically, the modal interval will be the one that has more absolute frequency. (in this example it will be the sales values that were observed for most days)
The modal interval is [3.1-3.5]
Now using the following formula you can calculate the Mode:
[tex]Md= Li + c[\frac{(f_{max}-f_{prev})}{(f_{max}-f_{prev})(f_{max}-f_{post})} ][/tex]
Li= Lower limit of the modal interval.
c= amplitude of modal interval.
fmax: absolute frequency of modal interval.
fprev: absolute frequency of the previous interval to the modal interval.
fpost: absolute frequency of the posterior interval to the modal interval.
[tex]Md= 3,100 + 400[\frac{(56-40)}{(56-40)+(56-55)} ]= 3,476.47[/tex]
A. $3,129.41 B. $2,629.41 C. $3,079.41 D. $3,123.53
Of all options the closest one to the estimated mode is A.
14. The approximate median daily sales is …
To calculate the median you have to identify its position first:
For even samples: PosMe= n/2= 250/2= 125
Now, by looking at the cumulative absolute frequencies of the intervals you identify which one contains the observation 125.
F(1)= 18
F(2)= 18+27= 45
F(3)= 45 + 31= 76
F(4)= 76 + 40= 116
F(5)= 116 + 56= 172 ⇒ The 125th observation is in the fifth interval [3.1-3.5]
[tex]Me= Li + c[\frac{PosMe-F_{i-1}}{f_i} ][/tex]
Li: Lower limit of the median interval.
c: Amplitude of the interval
PosMe: position of the median
F(i-1)= accumulated absolute frequency until the previous interval
fi= simple absolute frequency of the median interval.
[tex]Me= 3,100+400[\frac{125-116}{56} ]= 3164.29[/tex]
A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $2,664
Of all options the closest one to the estimated mode is C.
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
It's a football ....=> So ... A sphere !!
George is given two circles 0 and circles X as shown if he wants to prove that two circles are similar what would be the correct second step in his proof
Answer: Option A.
Step-by-step explanation:
Here we have two equations for the circumference, one for each circle:
C = 2*pi*r
C' = 2*pi*r'
now, if we take the quotient of those two equations, the left side must still be equal to the left side, this means that:
C/C' = 2*pi*r/(2*pi*r') = r/r'
So we have the relation:
C/C' = r/r'
And this is obtained for the division property of equality.
IF A = B, then as both numbers are equal, if we divide both sides by the same thing, then the equality must remain true.
Then the correct option is A.
If 20 drops fall in 76 seconds, how long will 8 drops take?
Answer:
x =30.4 seconds
Step-by-step explanation:
We can use ratios to solve
20 drops 8 drops
--------------- = ----------------
76 seconds x seconds
Using cross products
20x = 8*76
20x =608
Divide each side by 20
20x/20 = 608/20
x =30.4 seconds
Answer:
30.4 secs = 30secs
Step-by-step explanation:
20 drops fall in 76s
Hence 1 drop is 76/20
Therefore 8 drops would be ;
76/20 × 8 = 30.4 secs
The product of two integers
is 270. If one of the integers
is-18, find the other.
Step-by-step explanation:
To find it we will simply divide 270 by - 18
270 ÷ - 18 = - 15
Answer:
- 15
Step-by-step explanation:
ab=270
-18b=270
b=270/(-18)
b= - 15
Which undefined term is used to define an angle
Answer:
The undefined term which is used to define an angle is line i.e., . Further explanation: In geometry the three terms which are considered to be undefined are line, point and plane.
Answer:
Line
Step-by-step explanation:
A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect
3. Write 52/6
as a mixed number.
Give your answer in its simplest form.
Answer:
26/3 as an improper fraction in simplest form. :)
Step-by-step explanation:
What is the vertex of f(x) = |x+ 8|– 3?
(-8, -3)
(-8,3)
(8, -3)
(8,3)
Answer:
The vertex is at (-8,-3)
Step-by-step explanation:
The function is of the form
y = a|x-h| + k where (h,k) is the vertex
f(x) = |x+ 8|– 3
f(x) = |x - - 8|– 3
The vertex is (-8,-3)
Sally earns $12.50 an hour cleaning houses. If she works from 8:00am to 6:00pm, how much money will she make?
Answer:
She will make 125 dollars
Step-by-step explanation:
First figure out how many hours are in between 8 AM and 6PM
Second multiply that number by the salary she makes per hour. In this case its 12.50*10
Lastly Get the answer and add a dollar sign :D
Please answer this correctly
Answer:
153 square feet is the area
Answer:
153 ft^2
Step-by-step explanation:
If the top side were 24 ft long and the right side 10 ft long, you'd have a yellow rectangle with area 10 ft * 24 ft = 240 ft^2.
Now we subtract the parts that are missing.
3 ft * 13 ft = 39 ft^2
3 ft * 16 ft = 48 ft^2
240 ft^2 - 39 ft^2 - 48 ft^2 = 153 ft^2
In the expression what is the numerical coefficient in this question ?
Answer:
-7
Step-by-step explanation:
The numerical coefficient of [tex] - 7yz^2 [/tex] is - 7.
The coefficient of -7yz² is -7
In the given equation,
5x⁶÷3xy-7yz²+2y÷z
the coefficient is -7 , because the coefficient is the constant term of an expression.
A numerical coefficient is a constant multiplier of the variable in a term. And here, -7 is preceded by -7yz²
Hence it is the numerical coefficient.
learn more about numerical coefficients:
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When Sunita weighed herself on Monday, she found that she had gained 1 1/4 kg. Earlier her weight was 46 3/8 kg. What was her weight on Monday? Please give me Statements! Please Do it fast(Its ok if you dont do it fast ok its not like that much of an urgent) #GoAwayCoronaVirus
Answer:
[tex]47\frac{5}{8}[/tex]
Step-by-step explanation:
Weight from before + Weight gained
[tex]46\frac{3}{8} +1\frac{1}{4}[/tex]
Convert to improper fractions.
[tex]371/8 + 5/4[/tex]
Find the common denominator.
[tex]371/8 + 10/8[/tex]
Add.
[tex]381/8[/tex]
Convert to a mixed fraction.
[tex]47\frac{5}{8}[/tex]
Answer:
47 5/8 kg
Step-by-step explanation:
Ealier weight + gained weight = Monday's weight
46 3/8 + 1 1/4
= 371/8 + 5/4
= 371/8 + 10/8
= 381/8
= 47 5/8 kg
