Answer:x^1/2 • 1/3 x^1/2 + 1/3
Step-by-step explanation:
The equivalent expressions are,
C) x⁻² = 1/x²
E) (2x²y⁵)³ = 8x⁶y¹⁵
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We can all the expression as,
A) (x²)⁵ = x⁷
LHS, (x²)⁵ = x¹⁰
≠ x⁷
B) x⁹ ÷ x⁴ = x¹³
LHS, x⁹ ÷ x⁴ = x ⁹⁻⁴
= x⁵
≠ x¹³
C) x⁻² = 1/x²
LHS, x⁻² = 1/x²
= 1/x²
D) (2x²y⁵)³ = 2x⁵y⁸
LHS, (2x²y⁵)³ = 8x⁶y¹⁵
≠ 2x⁵y⁸
E) (2x²y⁵)³ = 8x⁶y¹⁵
LHS, 2x²y⁵)³ = 8x⁶y¹⁵
Thus, The equivalent expressions are,
C) x⁻² = 1/x²
E) (2x²y⁵)³ = 8x⁶y¹⁵
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What is the greatest common factor of 25 and 45?
Answer:
5
Step-by-step explanation:
Factors of 25: 1, 5, 25Factors of 45: 1, 3, 5, 9, 15, 45The greatest factor that's in both lists is 5.I hope this helps!
The greatest common factor of 25 and 45 is 5.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given numbers are 25 and 45.
To find the greatest common factor, factorize the numbers,
Factor of 25 = 5 × 5
Factor of 45 = 3×3×5
The common term in 5 × 5 and 3×3×5 is 5.
Therefore, the greatest common factor is 5.
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This circle graph shows the results of a survey on favorite sandwiches.
What percentage of people chose turkey as their favorite sandwich? Round to the nearest percentage if necessary.
9%
23%
25%
40%
favorite sandwich circle graph. sectors labeled ham 4, 15 peanut butter, 9 turkey, 12 tuna
Answer:
b i think..
Step-by-step explanation:
plz dont get your hopes up it just a hunch but if you think about it 1st add ti all then u can see ig i will update if needed sorry if wrong :(
Each small square in the graph paper represents 1 square unit.
Find the area of the given figure in square units.
Do not include units (square units) in your answer.
Pls help in a pre-test thank you!
A pet store has 32 dogs. The owner gives 2 treats to each dog until she has no treats left over. How many treats did she have?
Answer:
64
Step-by-step explanation:
because 32 x 2 = 64
Answer:
32*2=64 She had 64 treats
What is the result of factoring out the GCF from the expression (24 + 36)?
please i need help!
it is on PLATO
Answer:
I gues answer is 4( factor)
if HBN ~ LYR, find the value of x.
Answer: x= 13
Step-by-step explanation:
What is the slope of the line in the graph below? Show your work. PLEASE HELP PLEASE
Answer:
5/2
Step-by-step explanation:
The line crosses two points: (0,1) and (5,3)
You can then use the slope-point formula to find the slope:
(x1 - x2)/(y1 - y2) =
(0 - 5)/(1 - 3) =
-5/-2 =
5/2
Answer:
The slope of the line is 2/5
Step-by-step explanation:
Start counting where the y-intercept is. The y-intercept is at (0,1). The line is positive since it is increasing from left to right, so you need to count up and then to the right in order to find the slope. You need to find a point where the line intercepts a coordinate point directly on the line. If you look at the point (5,3) it is directly on the intersection that runs up and down. Start at 1 and count 2 up and 5 to the right. You will end up on the point (5,3). Hope this helps. Ask more questions if you need to
Evaluate -3x 3y 2, if x = -2 and y = -1.
Answer:
6 + -3 + 2 =
5
6 * -3 * 2 =
-36
Step-by-step explanation:
I'm assuming they have plus sings in between, if not I'll evaluate with adding and multiplying.
Plug in the values for x and y.
-3(-2) + 3(-1) + 2
Then solve.
6 + -3 + 2 =
5
6 * -3 * 2 =
-36
MULTIPLE CHOICE CALCULUS
1) An object moves along a line so that its position at time t is s(t) = t^4 - 6t^3 - 2t - 1.
At what time t is the acceleration of the object zero?
A. at 3 only
B. at 0 and 3 only
C. at 0 only
D. at 1 only
2) If f(x) = e^x (sin x + cos x), then f'(x) =
A. 2e^x (cos x + sin x)
B. e^x cos x
C. e^x (cos^2x - sin^2x)
D. 2e^x cos x
Answer:
1) B. at 0 and 3 only
2) D. 2eˣcosx
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringQuadraticsCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[sinu] = u'cosu[/tex]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[cosu] = -u'sinu[/tex]
eˣ Derivative: [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]
Step-by-step explanation:
*Note:
Velocity is the derivative of position.
Acceleration is the derivative of velocity.
Question 1
Step 1: Define
s(t) = t⁴ - 6t³ - 2t - 1
Step 2: Differentiate
[Velocity] Basic Power Rule: s'(t) = 4 · t⁴⁻¹ - 3 · 6t³⁻¹ - 1 · 2t¹⁻¹[Velocity] Simplify: v(t) = 4t³ - 18t² - 2[Acceleration] Basic Power Rule: v'(t) = 3 · 4t³⁻¹ - 2 · 18t²⁻¹[Acceleration] Simplify: a(t) = 12t² - 36tStep 3: Solve
[Acceleration] Set up: 12t² - 36t = 0[Time] Factor: 12t(t - 3) = 0[Time] Identify: t = 0, 3Question 2
Step 1: Define
f(x) = eˣ(sinx + cosx)
Step 2: Differentiate
[Derivative] Product Rule: [tex]\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x\frac{d}{dx}[sinx + cosx][/tex][Derivative] Rewrite [Derivative Property - Addition]: [tex]\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])[/tex][Derivative] eˣ Derivative: [tex]\displaystyle f'(x) = e^x(sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])[/tex][Derivative] Trig Derivatives: [tex]\displaystyle f'(x) = e^x(sinx + cosx) + e^x(cosx - sinx)[/tex][Derivative] Factor: [tex]\displaystyle f'(x) = e^x[(sinx + cosx) + (cosx - sinx)][/tex][Derivative] Combine like terms: [tex]\displaystyle f'(x) = e^x[2cosx][/tex][Derivative] Multiply: [tex]\displaystyle f'(x) = 2e^xcosx[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Graph the function f(x)=-3/5X +4
What is f(5)?
Answer:
f(x)= -3x+4
Step-by-step explanation:
so plug in 5 for x then +4 is your y-intercept and then your slope is -3/1 so you go down 3 over 1 from there and so on
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Consider points A(3, 6) and B(8, 4). Find point C on the x-axis so AC +BC is a minimum.
I need help
Answer:
(6,0)
Step-by-step explanation:
Which of the following is the word expression for this numerical expression? 32÷4⋅3
A glacier in Alaska moves about 29.3 meters a day. About how much farther will it move in 1000 days then it will move in 100 days?
A glacier will move about ______ meters farther in 1000 days then it will move in 100 days.
Fill in the blank
Your answer has to be in decimal form.
BIG THANKS!
Answer:
If it moves 29.3 meters a day, then we need to find the total amount of days:
1000 days + 100 days = 1100 days
Since it moves 29.3m per day, we can write:
29.3m x 1100 which equals 32230m
So it moved 32230 meters
Step-by-step explanation:
Which is the "better buy"? A 12 ounce can of corn for $1.92 of a 20 ounce can of corn for $3.00?
John has $255 in his bank account. His bank charges a $10.50 administration fee each month. If he makes no other deposits or withdrawals, how much money is in John’s account at the end of 5 months?
Answer:
10.50×5=52.50 255-52.50=202.50
Step-by-step explanation:
well if 10.50 is taken for 5 months he will have 202.50 because 255-52.50=202.50
A car is traveling at a constant speed. It travels 34 miles in 5 minutes.
How many minutes will it take the car to travel 70 miles?
helppppp
Answer:
10.30 or 10 1/6 if this answer is not on the answer choices round to the nearest answer close to this.
Step-by-step explanation:
how to solve.
34/5=6.8 - this is how many miles the car is traveling per minuet.
6.8/70=10.30 - this should be the answer because this is how many minutes it takes the car to travel 70 miles
A classroom of children has 17 boys and 19 girls in which five students are chosen to do presentations. In how many ways can the five students be chosen so that more boys than girls are selected
Answer:
167688 ways
Step-by-step explanation:
Given that:
Number of boys = 17 &;
Number of girls = 19
The number of ways that five students can be chosen such that more boys than girls are selected are:
The ways of choosing = 5 boys 0 girls + 4 boys 1 girl + 3 boys 2 girls
The ways of choosing = [tex]^{17}C_5 +( ^{17}C_4 \times ^{19}C_1} )+( ^{17}C_3 + ^{19}C_2})[/tex]
The ways of choosing = [tex]\dfrac{17!}{5!(17-5)!} + \begin {pmatrix} \dfrac{17!}{4!(17-4)!} \times \dfrac{19!}{1!(19-1)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(17-3)!} \times \dfrac{19!}{2!(19-2)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17!}{5!(12)!} + \begin {pmatrix} \dfrac{17!}{4!(13)!} \times \dfrac{19!}{1!(18)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(14)!} \times \dfrac{19!}{2!(17)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17*16*15*14*13*12!}{5!(12)!} + ( \dfrac{17*16*15*14*13!}{4!(13)!} \times \dfrac{19*18!}{1!(18)!} ) + ( \dfrac{17*16*15*14!}{3!(14)!} \times \dfrac{19*18*17!}{2!(17)!} )[/tex][tex]=6188 + ( 2380\times19 ) + (680 \times171)[/tex]
= 167688 ways
Using the combination principle, the number of ways of selecting 5 students such that the number of boys is greater the number of girls selected ls 167688 ways.
Number of boys = 17Number of girls = 19Number of selections to be made = 5
In other to choose more boys than girls :
5 boys and 0 girls4 boys and 1 girl3 boys and 2 girlsUsing the combination relation :
(17C5 × 19C0) + (17C4 × 19C1) + (17C3 × 19C2)
(6188 × 1) + (2380 × 19) + (680 × 171)
(6188 + 45220 + 116280)
= 167688 ways
Therefore, the Number of ways of making the selection is 167688 ways
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Write each percent as a decimal and as a mixed number or fraction in simplest form
1. 120%
2. 0.08%
3. 0.35%
i need help
The perimeter of quadrilateral ABCD is 85. Find the value of x.
The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.
What is meant by Quadrilateral?A quadrilateral is a four-sided polygon with four angles and four vertices. The term "quadrilateral" comes from the Latin words "quadri," which means "four," and "latus," which means "side." A quadrilateral is depicted in the image above. The outcome of an image The perimeter of the quadrilateral ABCD is 85 feet. Find out what the value of x is.The perimeter of a quadrilateral is the entire length of its boundary. Perimeter = AB + BC + CD + DA, for example, can be used to define the perimeter of the quadrilateral ABCD.The perimeter is 85. (the total of all sides). X = 5.5, and 4x + 3x + 4 + 5x-7 + 6x-11 = 85 (18x - 14 = 85). 18 x = 85 + 14 = 99.Therefore,
The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.
When we substitute the provided values, we get: ABCD perimeter = 9 units plus 5 units plus 9 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units As a result, the perimeter of ABCD is 28 units.
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find the product of 1.6 and 3.4
Choices:
3.24
5.04
5.44
3.1
Answer:
5.44
Step-by-step explanation:
1.6*3.4=5.44
Slove the equation for x, and enter your answer in the box below.
x - 9 = 5
x=-14
move x to the right side and move 5 to the left side and 5 turns to a negative
x-9=5
-5-9=x
x=14
Marta walked at 4.7 miles per hour for 0.71 hours. How far did she walk?
Answer:
3.337 miles
Step-by-step explanation:
D = Distance
S = Speed
T = Time
D = S x T
D = 4.4 x 0.17
D = 3.337
this is a kind weird number so this might be wrong tho
Least common multiples are most helpful for
A
adding and subtracting fractions
B
B
reducing fractions
с
multiplying and dividing fractions
D
finding the greatest common factor
Answer:
A
Step-by-step explanation:
Least common multiples are most helpful for adding and subtracting fractions because in order to add and subtract fractions you need to find a common denominator. If you want to do that you have to use least common multiples.
Suppose you roll a special 4-sided die. What is the probability that the number rolled is a "1" OR a "2"?
awnser:25%
because 4/100=25
The probability of the number rolled is a "1" OR a "2" is,
⇒ 1/2
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
You roll a special 4-sided die.
Now, After roll a special 4-sided die, the probability to get 1 is,
⇒ 1/4
And, After roll a special 4-sided die, the probability to get 1 is,
⇒ 1/4
Hence, The probability of the number rolled is a "1" OR a "2" is,
⇒ 1/4 + 1/4
⇒ 2/4
⇒ 1/2
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I need help plz ASP
Answer:
b. 20 songs
Step-by-step explanation:
when you look at (0,0), the y-intercept is 20, so that is the initial starting point.
The vegetable display automatically sprays a mist over the vegetables according to a repeating timer you set. How many minutes should you set the timer for in order to spray the vegetables 5 times each hour
Answer:
✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️
You need a 45% alcohol solution. On hand, you have a 105 mL of a 40% alcohol mixture. You also have 80%
alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired solution?
You will need
mL of the 80% solution
Submit Question
You have 105 mL of a 40% alcohol solution, which contains 0.4 • 105 mL = 42 mL of alcohol.
If you mix it with x mL of 80% solution, you end up with a (105 + x) mL solution that contains (42 + 0.8x) mL of alcohol.
In this solution, you want to have a concentration of 45%, so
((42 + 0.8x) mL) / ((105 + x) mL) = 0.45
Solve for x :
(42 + 0.8x) / (105 + x) = 0.45
(42 + 0.8x) / 0.45 = 105 + x
280/3 + 16/9 x = 105 + x
7/9 x = 35/3
x = 15
So you need 15 mL of the 80% solution.
Evaluate the line integral, where C is the given curve. (x 6y) dx x2 dy, C C consists of line segments from (0, 0) to (6, 1) and from (6, 1) to (7, 0)
Answer:
[tex]\mathbf{\int _c (x+6y)\ dx + x^2 \ dy = \dfrac{91}{6}}[/tex]
Step-by-step explanation:
The integral of the curve is given as:
[tex]\int (x +6y) \ dx +x^2 \ dy[/tex]
Where the line segment from (0,0) to (6,1) is:
0 < x < 6 and [tex]y = \dfrac{x}{6} \implies dy = \dfrac{dx}{6}[/tex]
Thus;
[tex]\int ^{6,1}_{0,0} (x+ 6 * \dfrac{x}{6}) \ dx + \dfrac{x^2*dx}{6 } = \int^6_0 (x+x+\dfrac{x^2}{6}) \ dx[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \int^6_0 (2x +\dfrac{x^2}{6}) \ dx[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} \dfrac{2x^2}{2}+\dfrac{x^3}{18} \end {bmatrix}^6_0[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} x^2+\dfrac{x^3}{18} \end {bmatrix}^6_0[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} (6)^2+\dfrac{(6)^3}{18} \end {bmatrix}[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} 36+12 \end {bmatrix}[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx =48 --- (1)[/tex]
Similarly; at (6,1) to (7,0)
[tex]\implies 6 \leq x \leq 7 \ and \ y = -x +7[/tex]
Thus; the integral can be computed as :
[tex]\int ^{(7,0)}_{(6,1)} \ (x+6(-x+7)) \ dx + x^2 (-dx) = \int^7_6 (-5x +42 -x^2) \ dx[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5x^2}{2}+ 42x -\dfrac{x^3}{3} \end {bmatrix}^7_6[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(7^2-6^2)}{2}+ 42(7-6) -\dfrac{(7^3-6^3)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(49-36)}{2}+ 42(1) -\dfrac{(343-216)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(13)}{2}+ 42 -\dfrac{(127)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{-195+252-254}{6}\end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= - \dfrac{-197}{6} --- (2)[/tex]
By adding (1) and (2) ; we have:
[tex]\int _c (x+6y)\ dx + x^2 \ dy = 48 + (-\dfrac{197}{6})[/tex]
[tex]\int _c (x+6y)\ dx + x^2 \ dy = (\dfrac{288-197}{6})[/tex]
[tex]\mathbf{\int _c (x+6y)\ dx + x^2 \ dy = \dfrac{91}{6}}[/tex]
The sum of two positive numbers is 28. When the smaller integer is subtracted from four times the larger, the result is 47. Find the two integers
Answer:
15 & 13
Step-by-step explanation:
15 x 4 = 60 - 13 = 47
10. While catching fireflies, you and a friend decide to have a competition. After m minutes, you have (4m +11) fireflies and your friend has (5m +6) fireflies
A. Write an expression in simplest form that represents the number of fireflies you and your friend caught together.
B. The competition ends after 5 minutes(m). Who has more fireflies. Explain how you know.
Answer:
Lets look at the expressions with respect to the competition parameters:
Expressions:
You(Y) =4m+11
Friend(F)=5m+6
1. The competition begins AFTER you and friend already caught some flies. This would be represented by the CONSTANT terms in each expression (in this case, 13 for you, 6 for friend).
So the number of flies caught BEFORE THE COMPETITION would be...
11+6=17 flies total
2. The competition length was "m" minutes long when flies are caught and counted. This would be represented by the VARIABLE terms in each expression (in this case, 4m for you, 5m for friend). We are not given a numeric value for the variable "m" to evaluate.
So the number of flies caught DURING THE COMPETITION (timed "m" minutes long) would be....
4m+5m=9m flies total
...and the number of flies per minute would be calculated as......
9m÷m=9 flies per min....total #flies divided by total minutes
3. If the problem asked for the total number of flies caught by you and friend, before and after the competition....
9m+17 flies total.....add like terms in each expression.
Answer:
a. 9m+17
b. You caught more fireflies
Step-by-step explanation:
