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helpppppppppppppppp mathhhhhhhhhhhh
evaluate this piecewise function at x=-4 and x=4
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Plug this into the function
f(x) = x^2
f(-4) = (-4)^2
f(-4) = 16
So when x = -4 is the input, the output is f(x) = 16
-----------------------------------------------------------------------------
For the second part, when x = 4, we will use the third piece. This is because f(x) = sqrt(x) when x > 1
f(x) = sqrt(x)
f(4) = sqrt(4)
f(4) = 2
When the input is x = 4, the output is f(x) = 2
Answer:
When x = –5, y =
3.
When x = –1, y =
-2.
When x = 3, y =
-4
The functions f(x) and g(x) are shown below: f(x) = 5x g(x) = 5x Which statement best describes the graph of f(x) and g(x)?
The graph of f(x) will eventually exceed the graph of g(x).
The graph of g(x) will eventually exceed the graph of f(x).
The graphs will both have their y-intercept equal to 1.
The graphs will both have their y-intercept equal to 5.
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Next, we can graph f(x)=5x and g(x) to quickly find the y-intercept.
The y-intercept of both of these functions is "0".
This means that the second two statements are also incorrect.
While none of these statements are correct, I would imagine that the third statement would best describe f(x) and g(x).
Perhaps there is an error in the question? Is the question copied down correctly?
Either way, none of the statements accurately describe f(x) and g(x).
The given functions f(x) and g(x) are not exceeding each other at any point as they are same function.
Both the graphs of these functions have same y-intercept of 0.
What is a function?A function is the relation between two sets. A function relates the domain to the range.
Here, f(x) = 5x and g(x) = 5x.
Therefore, both functions are equal and their graph will be same.
Hence, none of them exceeding the other one.
If we compare both functions with standard form: y = mx + c, it is clear that both functions have same y-intercept of 0.
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State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.
Part1. 10,15,20,25,30.. Step 1.State whether this sequence is arithmetic or geometric and find the explicit formula. show your work. Step 2. find the recursive formula. Show your work.
Part 2. 2,6,18,54,162.. Step 1. State whether this sequence is arithmetic or geometric and find the explicit formula. show your work. Step 2.find the recursive formula. Show your work
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Part 1: 10, 15, 20, 25, 30, ... Look at the difference between the first term and the second term: it's increased by 5. Now look at the difference between all following terms and you'll notice that this pattern is repeated. Then our recursive formula would be:
[tex] a_{n}=a_{n-1}+5 [/tex]
Now a geometric sequence, on the other hand, will have a common ratio between terms. This means that the second term divided by the first term will give you the same number as the fifth term divided by the fourth term. Let's look at Part 2:
Dividing the second term by the first term, we see that the ratio is 6/2=3. Now dividing any other two terms similarly, we can see that the ratio is still 3. Then our recursive formula is:
[tex]a_n=3a_{n-1}[/tex]
Final answer:
The first sequence is arithmetic with an explicit formula of a_n = 10 + (n - 1) × 5 and recursive formula a_n = a_(n-1) + 5, a_1 = 10. The second sequence is geometric with an explicit formula of a_n = 2 × 3^(n-1) and recursive formula a_n = a_(n-1) × 3, a_1 = 2.
Explanation:
Analysis of Sequences
The first sequence: 10, 15, 20, 25, 30... increases by a constant amount of 5 which is an indication of an arithmetic sequence. The explicit formula for an arithmetic sequence is a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference between the terms. In this case, a_1 = 10 and d = 5. Hence, the explicit formula is a_n = 10 + (n - 1) × 5. The recursive formula for an arithmetic sequence is a_n = a_(n-1) + d, which would translate to a_n = a_(n-1) + 5 with a_1 = 10.
The second sequence: 2, 6, 18, 54, 162... multiplies by a common ratio of 3 which classifies it as a geometric sequence. The explicit formula for a geometric sequence is a_n = a_1 × r^(n-1), where a_1 is the first term and r is the common ratio. For this sequence, a_1 = 2 and r = 3, so the explicit formula is a_n = 2 × 3^(n-1). The recursive formula for a geometric sequence is a_n = a_(n-1) × r, which for this sequence is a_n = a_(n-1) × 3 with a_1 = 2.
irrational numbers can never be precisely represented in decimal form . why is this?
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The sum of 5 consecutive integers is 310 What is the third number in this sequence?
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310/5 = 62
60 +61 +62 +63 +64 = 310
3rd number is 62
There are 14 boys and 6 girls in Emily’s class. One student in Emily’s class is chosen each day to hand out calculators to all the students. Also, one student in Emily’s class is chosen each day to collect calculators at the end of class. The same student can be chosen for each job. Each student is equally likely to be chosen. What is the probability a girl is selected to do both jobs on Monday?
A. 9/100
b. 107/190
C. 3/5
d. 3/38
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Same girl can be chosen for both jobs, is the probability with replacement. Multiply the individual probabilities.
(6/20) * (6/20) = 9/100
The probability of a girl being selected to do both jobs on Monday will be 3 / 38. Then the correct option is D.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
There are 14 boys and 6 girls in Emily’s class.
One student in Emily’s class is chosen each day to hand out calculators to all the students.
Also, one student in Emily’s class is chosen each day to collect calculators at the end of class.
The same student can be chosen for each job.
Each student is equally likely to be chosen.
Then the total number of the students will be
Total students = 14 + 6
Total students = 20
Then the probability a girl is selected to do both jobs on Monday will be
P = ⁶C₂ / ²⁰C₂
P = 15 / 190
P = 3 / 38
Then the correct option is D.
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What is the decay rate?
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Hope this helps!
a square reflecting pool has an area of 183.84 square meters. What is the approximate perimeter of the reflecting pool?
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The perimeter of a square reflecting pool with an area of 183.84 square meters is approximately 54.24 meters.
Explanation:The area of a square is calculated by squaring the length of one of its sides. So, to find the side length of the square reflecting pool, we need to take the square root of the area. The square root of 183.84 is approximately 13.56 meters.
Now considering that a square has four equal sides, the perimeter is calculated by multiplying the side length by 4. So, the perimeter of the pool is 13.56 multiplied by 4, which gives us approximately 54.24 meters. Therefore, the approximate perimeter of the reflecting pool is 54.24 meters.
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f(x)=(x^3+6) inverse
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The inverse of this function is f(x) = [tex] \sqrt[3]{x - 6} [/tex]
You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.
f(x) = x^3 + 6 ----> Switch f(x) and x
x = f(x)^3 + 6 ----> Subtract 6 from both sides
x - 6 = f(x)^3 ----> Take the cube root of both sides
[tex] \sqrt[3]{x - 6} [/tex] = f(x) ----> Switch the order for formatting purposes
f(x) = [tex] \sqrt[3]{x - 6} [/tex]
And that would be your new inverse function.
What is 8 21/40 I don't understand how to do it
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If you want to know it as a "improper fraction" , you can
Multiply the denominator from the front number
Whatever the denominator and front number is , you add it to the numerator
So, for this problem we first have the multiply the front number from the denominator
Like: 8 (40)
That gives us the answer of: 320
Now we have to add 320 to 21
Like: 320 + 21
That gives us the answer of:341
We keep our denominator (which is "40" )
Your improper fraction would be:
341 / 40
Good luck on your assignment and enjoy your day!
~MeIsKaitlyn:)
You can either solve this by dividing 21/40 and then adding 8 to it.
21/40 = 0.525
0.525 + 8 = 8.525
Another way is to change it into an improper fraction. This is done by multiplying the denominator (40) by the whole number (8) then adding that to the numerator (21). That number then becomes the numerator, but make to keep the denominator the same (40).
40 × 8 = 320
320 + 21 = 341
8 21/40 = 341/40
Then input 341/40 into a calculator or do long/short division.
341/40 = 8.525
Either way, the answer will be 8.525.
The Environmental Protection Agency (EPA) estimates that the average passenger vehicle emits about 5 1/2 (5.5) metric tons of CO2 each year. How much is this in pounds?
(A) about 12000 pounds
(B) about 120 pounds
(C) about 5500 pounds
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So answer is A.
Answer:
its A about 12,000 pounds.
Step-by-step explanation:
What's the unit rate for 4 shirts for $32:00
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32/4 = 8
The unit rate (price per t-shirt) is $8
What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months
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Pv=pmt [(1-(1+r/k)^(-n))÷(r/k)]
PV the amount of the loan 4250
PMT monthly payment?
R interest rate 0.1325
K compounded monthly 12
N time 24 months
Solve the formula for PMT to get
PMT=pv÷ [(1-(1+r/k)^(-n))÷(r/k)]
PMT=4,250÷((1−(1+0.1325÷12)^(−24))÷(0.1325÷12))=202.55
Now to find the total finance charge use the formula of
Total finance charge=monthly payment×number of months-the amount of the loan
Total finance charge=
202.55×24−4,250=611.2
So the answer is 611.2
Hope it helps!
The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months can be calculated using the formula: Total Finance Charge = Total Amount Repaid - Principal Amount.
Explanation:The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months can be calculated using the formula:
Total Finance Charge = Total Amount Repaid - Principal Amount
First, calculate the total amount repaid:
Convert the annual interest rate to the monthly interest rate by dividing it by 12: 13.25% / 12 = 1.1042%Convert the loan term from months to years: 24 months / 12 = 2 yearsCalculate the total amount repaid using the formula: Total Amount Repaid = Principal Amount + InterestNow, calculate the principal amount:
Principal Amount = Loan Amount = $4,250
Finally, substitute the values into the formula and calculate the total finance charge:
Total Finance Charge = Total Amount Repaid - Principal Amount
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A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
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Answer with explanation:
[tex]S_{n}= 1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + n\times(n + 1) = \frac{n(n + 1)(n + 2)}{3}\\\\S_{k}= 1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + k\times(k + 1) = \frac{k \times(k + 1)(k + 2)}{3}\\\\S_{k+1}= 1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + k\times(k + 1)+(k+1) \times (k+2)=\frac{(k+1) \times(k +1+ 1)(k +1+ 2)}{3}\\\\=\frac{(k+1) \times(k +2)\times(k +3)}{3}[/tex]
Suppose a railroad rail is 3 kilometers and it expands on a hot day by 12 centimeters in length. Approximately how many meters would the center of the rail rise above the ground
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The center of the rail would rise approximately 0.06 meters above the ground.
The expansion of the railroad rail is given as 12 centimeters. To convert centimeters to meters, you divide by 100 since there are 100 centimeters in a meter.
So, the expansion in meters is 12/100 meters.
Now, the center of the rail would rise approximately half of this expansion because the rail expands equally on both sides. Therefore, the rise in the center of the rail above the ground would be
=1/2 × 12/ 100.
Let's calculate that:
Rise in the center= 1/2 × 12/100
Rise in the center=6/100
Now, to express this fraction in decimal form, you divide the numerator by the denominator:
Rise in the center= 0.06
So, the center of the rail would rise approximately 0.06 meters above the ground.
Describe the shape of the data for German male adults, and explain how you came to that conclusion. Are there any outliers in the data?
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Answer:
the answer is
Step-by-step explanation:
skewed left and 220
Which equation can be used to find the answer? an aquarium worker removed 78 fish from a tank. there were still 186 fish left in the tank. how many fish were in the tank before any were removed?
a. f ÷ 2 =78 f = 156 156 fish
b. f ÷ 2 =186 f = 372 372 fish
c. f – 78 = 186 f = 264 264 fish
d. f + 78 = 186 f = 108 108 fish?
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Answer:
f/2=186 fish
186 x 2 = 372
372 fish left in the tank
Step-by-step explanation:
What is the standard form equation of the line shown below? Graph of a line going through negative 3, negative 1 and 3, 2 y + 1 = one half(x + 3) y = one halfx + five halves −x + 2y = 1 x − 2y = −1
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slope = (2 - (-1) / (3 - (-3) = (2 + 1) / (3 + 3) = 3/6 = 1/2
y = mx + b
slope(m) = 1/2
use either of ur points...(3,2)...x = 3 and y = 2
now sub and find b, the y int
2 = 1/2(3) + b
2 = 3/2 + b
2 - 3/2 = b
4/2 - 3/2 = b
1/2 = b
so ur equation is : y = 1/2x + 1/2...but we need it in standard form of Ax + By = C
y = 1/2x + 1/2....subtract 1/2x from both sides
-1/2x + y = 1/2 ...multiply both sides by -2
x - 2y = -1 <== standard form
Answer:
The correct answer is D, "x − 2y = −1."
Step-by-step explanation:
I just completed the test.
How many numbers are evenly divisible by four between 39 and 59?
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39/4=9.
59/4=14.
add 14.+9.=23
now divide 23/4=5
40 is the first number evenly divided by 4 and is the 10th multiple of 4 (4*10=40)
56 is the last number evenly divisible by 4 and is the 14th multiple of 4 ( 4*14 =56)
14-10 = 4 +1 = 5
there are 5 numbers evenly divisible by 4
Use compatible numbers to solve the problem 326 divided by 44.
A 340 divided by 32 = 10
B 320 divided by 40 = 8
C 330 divided by 30 = 11
D 352 divided by 44 = 8
PLEASE ONLY ANSWER IF YOU KNOW THE ANSWER FOR SURE
Please explain the answer and why the answer is correct
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So instead of: 326 : 44,
we will do: 320 : 40 = 8
And we know that the real result is:
326 : 44 = 7.4
Answer:
B ) 320 divided by 40 is 8.
Answer:
B
Step-by-step explanation:
b is the closest answer to th actual aswer ad the most reasonable
The pair of points is on the graph of an inverse variation. Find the missing value. (2.4, 3) and (5, y) 1.44 6.25 0.69 1
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So we have y = 7.2 / 5 = 1.44
Answer is 1.44.
Answer:
Hence, the value of y is:
1.44
Step-by-step explanation:
It is given that:
The pair of points is on the graph of an inverse variation.
(2.4, 3) and (5, y)
We have to find the missing value y in the point.
As we know that in the inverse variation the value of y is the inverse value of x by some k.
i.e. in first point (2.4,3) let 'k' be a number such that:
[tex]3=\dfrac{k}{2.4}\\\\k=7.2[/tex]
Hence, the inverse is k=7.2
Now in the second point (5,y) we find the value of y as:
[tex]y=\dfrac{7.2}{5}\\\\y=1.44[/tex]
Hence, the value of y is:
1.44
is this in standard form ? if it isn't then what would it be in standard form ?
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To answer your first question, no, that isn't in standard form.
For something to be in standard form, x can't be negative, both x and y need to be on the left side, and there can't be fractions.
Taking the three rules, let's make that equation have no fractions. In order to remove the fractions, you multiply everything by 3.
2/3x - 1/3y = 2
2x - y = 6
Let's go over the rules again to make sure:
X isn't negative - correct.
x and y is on the left side - correct
No fractions - correct.
Now that it passed all the rules, 2x - y = 6 would be your correct standard form equation.
Hope I helped (:
A 12 foot ladder is placed 4 feet away from a house as shown. What is the value of x, rounded to the nearest degree ?
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Answer: The value of x is 70.52°.
Step-by-step explanation:
Since we have given that
Length of ladder = 12 foot
Length of base = 4 feet
We need to find the value of 'x'.
We will use "Cosine of triangle":
[tex]\cos x=\dfrac{4}{12}\\\\x=\cos^{-1}(\dfrac{1}{3})\\\\x=70.52^\circ[/tex]
Hence, the value of x is 70.52°.
Sydney has 972$ to spend on tickets. if each ticket costs 27$ how many tickets can she purchase
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divide total cost by ticket price
972/27 = 36 tickets
What is the formula to find the midpoint on a coordinate plane?
Answers
Add.
(6x^3+3x^2−2)+(x^3−5x^2−3)
Express the answer in standard form.
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is your answer
hope this helps
Which graph below shows a system of equations with infinitely many solutions?
A)coordinate plane with two parallel lines
B)coordinate plane with two intersecting lines
C)coordinate plane with two coinciding lines
D)coordinate plane with two intersecting lines
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Answer: C)coordinate plane with two coinciding lines has infinitely many solution.
Step-by-step explanation:
Since, By option A) If there is a coordinate plane with two parallel lines.
Then, It has no solution ( because, we get the solution at the the intersection point of the two lines but parallel lines do not intersect each other).So, it does not have infinite many solution.
By Option B) If there are two intersecting lines then we can get only one solution. So, it does not have infinite many solution.
By Option C) If there are two coinciding lines then we can get infinite number of intersection points therefore the system must have infinite number of solution.
Note: here, Option D) is same as Option B)
Therefore Only option C) is correct.
You are planning a party to the local pizza arcade for your child's birthday. The cost of a birthday party is $8.95 per person, and you plan to have 12 people at the party.
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The total cost would be $107.40
If the ratio of soccer balls to footballs is 7:6 and the ratio of footballs to basketballs is 2:1, what is the ratio of soccer balls to basketballs?
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s:f is 7:6
f:b is 2:1
f:b can also then be written as 6:3 (multiply by 3)
therefore s:f:b is 7:6:3
therefore ratio of s:b is 7:3
Find the distance between the points t(13, 1.6)t(13, 1.6) and v(5.4, 3.7)v(5.4, 3.7).
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7.88 units is the distance between points T(13, 1.6) and V(5.4, 3.7).
To find the distance between the points T(13, 1.6) and V(5.4, 3.7), we can use the distance formula:
Distance formula:
For two points [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex], the distance between them is [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.[/tex]
Let's plug in the coordinates of points T and V:
Distance = [tex]\sqrt{(5.4 - 13)^2 + (3.7 - 1.6)^2}[/tex]
= [tex]\sqrt{(-7.6)^2 + (2.1)^2}[/tex]
= √(57.76 + 4.41)
= √62.17
= 7.88.
So, the distance between points T(13, 1.6) and V(5.4, 3.7) is approximately 7.88 units.
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