Step-by-step explanation:
arithmetic operations with functions just means to do these operations with the function expressions. and the result is the resulting function.
so,
(f - g)(x) = f(x) - g(x) = (2x² + 3) - (x² - 7) =
= 2x² + 3 - x² + 7 = x² + 10
Mila plants 820 hectares of potatoes and corn. To maximise his profit he plants 140 hectares more of potatoes than of corn. How many hectares of each does he plant?
Answer:
480 Hectares potatoes, 340 Hectares corn
Step-by-step explanation:
Let x be the land used to plant potatoes in hectares.
Let y be the land used to plant corn in hectares.
Given the information from the question, we know that:
x + y = 820 - Equation 1
and
x - y = 140 - Equation 2
as you can see here we have 2 equations, means we can solve them simulteanously to solve for both. We will use elimination method.
We will use Equation 1 - Equation 2.
x-x+y-(-y)=820-140
2y = 680
y = 680 ÷ 2 = 340 hectares
We substiture y into equation 1 to find x
x + 340 = 820
x = 820 - 340
= 480 hectares
Therefore, 480 hectares of potatoes and 340 hectares of corn were planted.
Answer:
p=x+140whilec=x x+140+x=820ans=340 Answer=corn 340. while potatoes 4801 pts
The Dingles have some friends drop in. They wish to serve sherry but do nor have enough to serve
all the same kind. So they mix some which is 20% alcohol with some which is 14% alcohol and have
5 quarts which is 16% alcohol. How much of each kind of sherry did they have to mix?
Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
Distance formula: √(x₂-x₁)² + (V2 - V₁)²
O(x-4)² + y² = 100
O(x-4)2 + y² = 10
O x² + (y-4)² = 10
O x² + (y-4)² = 100
Answer:
(x-4)² + y² = 100
Step-by-step explanation:
The only circles that have a center at (4 , 0) are :
(x-4)² + y² = 100
(x-4)² + y² = 10
……………………
• (-2 - 4)² + 8² = (-6)² + 64 = 36 + 64 = 100 ≠ 10
Then
The circle (x-4)² + y² = 10 doesn’t contain the point (-2, 8)
• (-2 - 4)² + 8² = 100
Then
The circle (x-4)² + y² = 100 contains the point (-2, 8)
A bank loaned out $11,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled $1500, how much was loaned at
The amount loaned at 8% is $4800.
The amount loaned at 18% is $6,200.
What are the linear equations that represent the question?a + b - 11,000 equation 1
0.08a + 0.18b = 1500 equation 2
Where:
a = amount loaned at 8%
b = amount loaned at 18%
How much was loaned at 8 and 18%?Multiply equation 1 by 0.08
0.08a + 0.08b = 880 equation 3
Subtract equation 3 from equation 2
0.10b = 620
b = 620 / .10
b = $6200
a = 11,000 - 6200 = $4800
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Mr. Zuro finds the mean height of all 15 students in his statistics class to be 67.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 63.8 inches tall. What is the mean height of the 16 students in the class?
Answer: 66.8
Step-by-step explanation:
Let the mean height of 16 students in the class = X
Therefore,
[tex]\frac{15*67+63.8}{16} =X[/tex]
[tex]X=\frac{334}{5}[/tex]
X = 66.8
Please help me answer this question in khan academy
The interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].
Option D) is the correct answer.
Over which interval does f have a positive rate of change?To determine whether the average rate of change is positive, f(max) - f(min) must be greater than zero.
Given the function; f(x) = x³ - 9x
We determine f(max) - f(min)
At interval [ -2, 1 ]
(x³ - 9x) - ( x³ - 9x )
( (1)³ - 9(1) ) - ((-2)³ - 9(-2))= -8 - 10 = -18 NOT POSITIVE
At interval [ -2, 3 ]
(x³ - 9x) - ( x³ - 9x )
( (3)³ - 9(3) ) - ((-3)³ - 9(-3))= 0 - 0 = 0 NOT POSITIVE
At interval [ -1, 2 ]
(x³ - 9x) - ( x³ - 9x )
( (2)³ - 9(2) ) - ((-1)³ - 9(-1))= -10 - 8 = -18 NOT POSITIVE
At interval [ -4, -1 ]
(x³ - 9x) - ( x³ - 9x )
( (-1)³ - 9(-1) ) - ((-4)³ - 9(-4))= 8 - (-28) = 36 POSITIVE
Therefore, the interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].
Option D) is the correct answer.
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The distance between two towns on a
map is 6.25 cm.
The scale on the map is 1 cm = 30 miles.
What is the actual distance between the
two towns?
Answer:
Actual distance=187.5miles
Step-by-step explanation:
1cm=30miles
6.25cm=6.25*30miles
=187.5miles
The distance between the two towns using the map scale is 187.5 miles.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The distance between the towns on map is 1 cm.
And, the scale of map is 1 cm = 30 miles.
As per the problem the actual distance can be found by using the scale of the map as follows,
The distance between two towns is 6.25 × 30 = 187.5 miles.
Hence, the actual distance between the two towns is 187.5 miles.
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What is the value of f(4) in the function below? f(x) = -1/1·2x A. 16 OB. 8 C. 2 OD. 4
Answer: 4
Step-by-step explanation:
[tex]f(4)=\frac{1}{4} \cdot 2^{4}=\frac{1}{4} \cdot 16=4[/tex]
Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f.
The function that is a tangent to the graph of f is [tex]f(x) = (5/4)x^4+60[/tex]
What is the concept of integral?The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.
Knowing that :
40x + y = 0 is tangent of f(x)slope of the line = -40therefore, f'(x)|x=a = -40, so only look for a we have:
[tex]5a^3 = -40\\a^3 = -8\\a = -2[/tex]
if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:
[tex]f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60[/tex]
Therefore,
[tex]f(x) = (5/4)x^4+60[/tex]
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Im trying to figure out the answer
Step-by-step explanation:
[tex]\sqrt{35} =\sqrt{5} *\sqrt{7};[/tex]
all the details are in the attachment.
Find the first three terms of the sequence, Classify the sequence as arithmetic ( give d value ), geometric ( give r value ), both, or neither..... Sn = 10n
The first three terms of the sequence are 10, 20, and 30.
How to depict the sequence?The function given is 10n. In this case, the terms will be:
First term = 10n = 10 × 1 = 10
Second term = 10 × 2 = 40
Third term = 10 × 3 = 30
In this case, the first three terms of the sequence are 10, 20, and 30.
It an arithmetic sequence as there is a common difference of 10.
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Given a normally distributed data set with the mean = 88 and the standard deviation = 6, according to the empirical rule, what percent of the data points are above 76?
According to the empirical rule, the percent of the data points that are above 76 is; 2.28%
How to use Empirical Rule in Statistics?We are given;
Mean; μ = 88
Standard deviation; σ = 6
Sample mean; x' = 76
Formula for z-score is;
z = (x' - μ)/σ
z = (76 - 88)/6
z = -2
Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%
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a²-b when a = 8 and b = 7
Answer:
[tex]57[/tex]
Step-by-step explanation:
You just plug in 8 as a, and 7 as b. This gives you the following equation: [tex](8)^2-7[/tex] which becomes [tex]64-7[/tex] by squaring the 8, Then subtract 7 and you get [tex]57[/tex]
Answer:
57
Step-by-step explanation:
a = 8
b = 7
a² - b
= 8² - 7
= (8*8) - 7
= 64 - 7
= 57
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
The transformation was a 180° rotation about the origin.
We can solve this question by plotting the points R (1, 1)
S (3, 1) T (1, 6) and R' (–1, –1) S' (–3, –1) T' (–1, –6) on the graph as shown below.
As we can see from the graph, the original triangle RST which was in quadrant 1, now becomes triangle R’S’T’ in quadrant 3. Thus, when triangle RST was transformed using the rule (x, y) → (–x, –y), from quadrant 1 to quadrant 3 it is a 180° rotation about the origin.
Hence, the transformation was a 180° rotation about the origin.
Your question was incomplete. Please check below for full content.
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6)
Which best describes the transformation?
The transformation was a 90° rotation about the origin.
The transformation was a 180° rotation about the origin.
The transformation was a 270° rotation about the origin.
The transformation was a 360° rotation about the origin.
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enter your answer in scientific notation
It takes 1.7 x 10 ^4 for light from the sun to reach the comet.
How do scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
Scientific notations have some of the profits as:
Better readability due to compact representation
Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.
A comet is about [tex]5.1 \times 10 ^9[/tex] km from the sun.
Light travels at about [tex]3.0 \times 10 ^5[/tex] km per second.
[tex]\dfrac{5.1 \times 10 ^9}{3.0 \times 10 ^5}[/tex]
= [tex]1.7 \times 10 ^4[/tex]
Hence, It takes 1.7 x 10 ^4 for light from the sun to reach the comet.
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How to get T. I have gotten this question wrong multiple times already. It is not simplified it wants it in the complete decimal form.
Answer:
t = 4.0
Step-by-step explanation:
1.) P(t) = 1578
2.) Divide both sides by 1400
3.) Take the natural log of both sides (to remove the "e")
4.) Divide both sides by 0.03
5.) Properly round to the 1st decimal place
Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points) graph of 2 x plus 4, with discontinuity at negative 2, 0 graph of 2 x plus 4, with discontinuity at 2, 8 graph of 2 x minus 4, with discontinuity at negative 2, negative 8 graph of 2 x minus 4, with discontinuity at 2, 0
We can simplify the given rational function into a linear one, the graph is below.
Which graph represents the function?
Here we have the rational function:
[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]
Factorization the numerator, we get:
4x² - 16 = 0
4x² = 16
x² = 16/4 = 4
x = ±√4 = ±2
Then the numerator can be written as:
4*(x - 2)*(x + 2)
And the denominator can be rewritten as:
2x - 4 = 2*(x - 2)
Then the function becomes:
[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]
So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.
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Find the real numbers x and y.
27+yi= 11-x + 4i
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -16 [/tex]
[tex]\qquad \tt \rightarrow \: y =4 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 27 + yi = 11 - x + 4i[/tex]
[tex]\qquad \tt \rightarrow \: yi + x = 11 + 4i - 27[/tex]
[tex]\qquad \tt \rightarrow \: x + yi = - 16 + 4i[/tex]
By equating both equations we get :
[tex]\qquad \tt \rightarrow \: x = - 16[/tex]
[tex]\qquad \tt \rightarrow \: y = 4[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
What is the next whole number after 3355 in the base six system
Answer:
Ordinal, 3,355th. This number as US currency, three thousand three hundred fifty-five dollars ... 3355 is NOT a triangle number ... Base 6
Cindy has decided to lease a car. the lease includes a money factor of 0.00354. what interest rate is cindy being charged in her lease? a. 0.85% b. 8.5% c. 1.475% d. 14.75% please select the best answer from the choices provided a b c d
The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.
Given The factor included in lease is 0.00354.
Interest is the amount that a bank or person who gives loan charges from loan taker.
Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.
Money factor=0.00354.
So the interest rate that Cindy will charge is equal to 2400*0.00354
The interest rate Cindy will be charged =8.496%
=8.5%
Hence the interest rate charged is approximately 8.5%.
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The common _____ of two rays that make an angle is called the vertex.
your answer goes here
if there are 24 sushi pieces in 6 packages of sushi how many pieces of sushi are in 2 packages of sushi HURRY!!!!
Answer: 8 pieces
Step-by-step explanation:
- if there are 24 pieces of sushi in 6 packages then 24/6 = 4 so there’s 4 pieces of sushi in each package
- since there’s 4 pieces of sushi in each pack just do 4 x 2 = 8
- so there’s 8 pieces of sushi in 2 packages
hope this helps :)
Will is 30% taller than Wanda, so Will's height is ____% of Wanda's height.
Will's height is % of Wanda's height.
Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.
Will is 34% taller than Wanda, so Will's height is 134% of Wanda's height.
If Will is 34% of Wanda's height, we can conclude that he has all of Wanda's height plus 34% of that height.
All the height of Wanda represents 100% as it is referring to a complete system.
What is the height?
Height is a way to measure someone or something from base to top or head to toe.
From this, we can conclude that Will is 100% more than 34% of Wanda's height.
Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
What does point H represent in this context?
CORRECT (SELECTED)
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Explanation: Point HHH is on line aaa, so it represents Josiah's distance at a certain time. Point HHH is also on line bbb, so it represents the same distance and time for Chana.
The point that is labeled H on this graph is the point where Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah.
How to solve for the point H.At the point H, there is an intersection between the distance covered by both of these individuals.
This point is the point where we are shown that Chana has caught up with Josiah as they are skating.
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Write
2660
1000
as a decimal.
Solve this system using the substitution method. -3x + 4y = 1 -4x + 5y = -2
Answer:
the x value is 13 and the y value is 10. x=13 and y=10
I need help with this question I got 1 as an answer but it’s saying it’s wrong
log 4 (x³ +255) = 4
Answer:
see image
Step-by-step explanation:
I did two different problems depending on whether the 4 beside the log is a base or not.
If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.
For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.
0.2 was divided into a particular number. this quotient was the multiplied by 7, and 2.8 was taken from that product. if the previous operation resulted in -499.8 find the initial number
Answer:
(x/0.2)(7)-2.8=-499.8
x=-14.2
Step-by-step explanation:
(x/0.2)(7)-2.8=-499.8
7x/0.2 -2.8 = -499.8
35x -2.8 = -499.8
35x = -499.8 +2.8
35x = -497
35x/35 = -497/35
x = -14.2
you probably already got it solved, but at least this can help anyone else!
Please help!
If a student (represented by initials) was chosen at random, find P(HH|C).
P(HH|C)=2/5
P(HH|C)= 13/16
P(HH|C)=9/16
P(HH|C)=3/5
Answer:
a.) P(HH|C)=2/5
Explanation:
Given following:
P(HH) = 7P(C) = 10P(HH ∩ C) = 4P(HH ∪ C) = 13Solving steps:
[tex]\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}[/tex]
[tex]\sf P(HH|C) = \dfrac{4 }{10}[/tex]
[tex]\sf P(HH|C) = \dfrac{2 }{5}[/tex]
(1 point) The matrix
6 4
-7 k
is invertible if and only if k is not equal to
Answer:
k ≠ -14/3
Step-by-step explanation:
A square matrix is invertible if and only if its determinant is not zero.
DeterminantThe determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:
det = (6)(k) -(-7)(4) = 6k +28
Restriction on kThe requirement that the determinant is not zero places a restriction on k.
6k +28 ≠ 0
k +14/3 ≠ 0 . . . . . . divide by 6
k ≠ -14/3 . . . . . . . . subtract 14/3
For the matrix to be invertible, the value of k must not be -14/3.