Answer: \(30x^5y^5\)
\(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\)
\(x^4x=\:x^{4+1}\)
\(=10y^2\cdot \:3x^{4+1}y^3\)
\(\mathrm{Add\:the\:numbers:}\:4+1=5\)
\(=10y^2\cdot \:3x^5y^3\)
\(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\ y^2y^3=\:y^{2+3}\\ =10\cdot \:3x^5y^{2+3}\\ \mathrm{Add\:the\:numbers:}\:2+3=5\\ =10\cdot \:3x^5y^5\\ \mathrm{Multiply\:the\:numbers:}\:10\cdot \:3=30\\ =30x^5y^5\\ \)
Final Answer: \(30x^5y^5\)
The perimeter of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle. Ravi says he can find the width using the equation 2(x + 14) = 40. Fran says she can find the width using the equation 2x + 28 = 40. Answer the questions to solve the equations and to compare the steps and solutions. 1. Which of these is the most helpful first step for solving Ravi's equation, 2(x + 14) = 40? Circle the best answer. Add 14 to both sides Subtract 14 from both sides Divide both sides by 2 Multiply both sides by 2
Answer:
Divide both sides by 2
Step-by-step explanation:
We have the equation
2(x + 14) = 40
We divide both sides by 2
2(x + 14) = 40/2
x + 14 = 20
x = 20 - 14
x = 6
Therefore, the most helpful first step for solving Ravi's equation is: Divide both sides by 2
Answer:
Divide both sides by 2 Step-by-step explanation:We have the equation 2(x + 14) = 40We divide both sides by 22(x + 14) = 40/2x + 14 = 20x = 20 - 14x = 6
Step-by-step explanation:
Are the equations 3x = −9 and 4x = −12 equivalent? Explain
Answer:
yes
Step-by-step explanation:
3x=-9
3x/3 -9/3
x=-3
4x=-12
4x/4 -12/4
x=-3
ps i need brainliest so... plzzz
HELPPPPP !!!!!!!! PLSSSS AWNSERRR!! i'm not looking for "X"! Unit 7: Polygons & Quadrilaterals Homework 3: Rectangles i'm looking for the answers of 11, 12, 13, 14.
Answer:
11) 5x + 8 = 7x - 16
24 = 2x
x = 12
7(12) - 16 = 68
90 - 68
m<GJK = 22
12) 4x + 15 + 13x + 7 = 90
17x + 22 = 90
17x = 68
x = 4
4(4) + 15 = 31
90 + 31 + ADE = 180
m<ADE = 59
13) 5x - 12 + 2x - 3 = 90
7x - 15 = 90
7x = 105
x = 15
5(15) - 12 = 63
VWZ + 63 = 90
m<VWZ = 27
14) 9x + 3 = 14x - 27
30 = 5x
x = 6
9(6) + 3 = 57
14(6) - 27 =57
90 - 57 = 33
33 + 33 + DHG = 180
m<DHG = 114
Measure of angles of polygons and quadrilaterals:
1) ∠GJK = 22°
2) ∠ADE = 59°
3) ∠VWZ = 27°
4) ∠DHG = 114°
11)
5x + 8 = 7x - 16
24 = 2x
x = 12
Now substitute the value of x,
7(12) - 16 = 68
90 - 68
∠GJK = 22°
12)
4x + 15 + 13x + 7 = 90
17x + 22 = 90
17x = 68
x = 4
Now substitute the value of x,
4(4) + 15 = 31
90 + 31 + ADE = 180
∠ADE = 59°
13)
5x - 12 + 2x - 3 = 90
7x - 15 = 90
7x = 105
x = 15
Now substitute the value of x,
5(15) - 12 = 63
∠VWZ + 63 = 90
∠VWZ = 27°
14)
9x + 3 = 14x - 27
30 = 5x
x = 6
Now substitute the value of x,
9(6) + 3 = 57
14(6) - 27 =57
90 - 57 = 33
33 + 33 + DHG = 180
∠DHG = 114°
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Question 1: 18 Marks (1.1) Suppose that the population of South Africa was approximately 60, 04 million at the beginning of year 2021, and that it follows the Malthusian model approximately, with a growth rate of 1.24 percentper year.
The estimated population of South Africa at the end of the year 2025, based on the Malthusian model and the given growth rate, is approximately 63.089 million.
To answer this question, we can use the Malthusian model to estimate the population of South Africa at a future year, given the initial population and the growth rate. The Malthusian model assumes exponential growth, where the population P(t) at time t is given by:
P(t) = P₀ * e^(rt)
Where:
P(t) = population at time t
P₀ = initial population
r = growth rate
e = base of the natural logarithm (approximately 2.71828)
Given that the initial population in 2021 is 60.04 million and the growth rate is 1.24% per year, we can calculate the population at a future year by substituting the values into the equation.
Let's say we want to find the population at the end of the year 2025 (t = 2025 - 2021 = 4):
P(2025) = 60.04 million * e^(0.0124 * 4)
Calculating this expression gives us:
P(2025) ≈ 60.04 million * e^(0.0496)
≈ 60.04 million * 1.050862
P(2025) ≈ 63.089 million
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Colin knows his book is 1 foot long. He uses his book to help him estimate the length of his bike.
I want to help you but ... What's the question?
Define the nonprobability sampling methods and give examples of each.
Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.
In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.
due last weeeekk help!!!!
A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:
Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).
In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;
(x, y) → (y, -x)
Ordered pair B' (-2, 1) → E (1, 2)
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Guys please can someone solve this problem I’ve been trying for the last 50 minutes.
Answer: 110/290
Step-by-step explanation:
USE A PROTRACTOR
Answer:
\(5y - 23 + 7y + 5 = 90 \\ 12y - 18 = 90 \\ 12y = 108 \\ y = 9\)
If the volume of a cube is 64units3, what is the area of one of the face of the cube?
Answer:
16 units²
Step-by-step explanation:
Volume:
v = s³
64 = s³
Take the cube root of both sides
4 = s
Area:
a = s²
a = 4²
a = 16 units²
The following data represents the age of 30 lottery winners Complete the frequency distribution for the data
EXPLANATION
We can complete the frequency table by arranging each given value with its corresponding age class, as shown as follows:
Age class Frequency
20-29 1
30-39 4
40-49 2
50-59 7
60-69 11
70-79 4
80-89 1
The complete frequency distribution for the data is,
Age Frequency
20-29 1
30-39 4
40-49 2
50-59 7
60-69 11
70-79 4
80-89 1
We have to given that;
The following data represents the age of 30 lottery winners.
Now, We can formulate;
By given table,
Age Frequency
20-29 1
30-39 4
40-49 2
50-59 7
60-69 11
70-79 4
80-89 1
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please help me!!
write an equation in standard form
(0, 2) and (8,0)
Which group of three side lengths will form a triangle?
A. 11, 5, 4
B. 22, 17, 14
C. 28, 15, 10
D. 30, 15, 14
Answer:
when in doubt choose c
Step-by-step explanation:
Answer:
its C
Step-by-step explanation:
A triangle with side lengths 7, 6, 4 is
Acute
Right
Obtuse
Right
so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.
(a)²+(b)²=c²
(6)²+(4)²=c²
36+16=c²
(square root) 52=c²
the square root of 52 is 7
so therefore it is a right triangle.
A video game is in high demand and the store can't keep them in stock. Instead of selling it for $60 they markup the price 17%. What is the new price after the markup?
Answer:
$70.20
Step-by-step explanation:
60 x 1.17 = 70.20
The expression 8x + 2(3y) represents the total amount, in dollars, that Davellyn spent on tank tops and scarves, where x represents the number of tank tops she bought and y represents the number of scarves she bought. Which statement must be true about the amount Davellyn spent?
She spent 8x dollars on scarves.
She spent 8 dollars for each scarf.
She spent 6y dollars on scarves.
She spent a total of 14 dollars.
Answer:
She spend 6y dollars on scarves.
Step-by-step explanation:
The question states that y represents the number of scarves she bought, so the first and second statements would be incorrect. You don't know how much she spent in total, so the fourth statement would also be wrong. So it's the third statement.
Also, you can just do 2*(3y), which is 6y.
Answer:
The answer is C
Step-by-step explanation:
2021edge
find the derivative (or jacobian) matrix, DF(x), of the nonlinear system x′=f(x) given by. x'1=ax, x'2=bx2+c(x2)^3, where a,b, and c are constants.
The derivative (or jacobian) matrix, DF(x), of the nonlinear system x′=f(x) given by x'1=ax, x'2=bx2+c(x2)^3, where a,b, and c are constants, is [a 0; 0 2bx+3cx^2].
To find the derivative (or jacobian) matrix, DF(x), of the nonlinear system x′=f(x):
We first need to find the partial derivatives of each equation with respect to each variable.
For the first equation, x'1=ax,
the partial derivative with respect to x1 is a, and the partial derivative with respect to x2 is 0.
For the second equation, x'2=bx2+c(x2)^3,
the partial derivative with respect to x1 is 0, and the partial derivative with respect to x2 is 2bx + 3cx^2.
Putting these partial derivatives into a matrix, we get:
DF(x) =
[a 0]
[0 2bx+3cx^2]
Therefore, the derivative (or jacobian) matrix, DF(x), of the nonlinear system x′=f(x) given by x'1=ax, x'2=bx2+c(x2)^3, where a,b, and c are constants, is [a 0; 0 2bx+3cx^2].
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the shopkeeper sold a camera for 2570 and made a loss of rs180 at what price did he/she purchasr the camera
purchase they sold it for: $2570
loss= $180
They purchased it for= loss + selling cost
=2570+180
=$2750
8 added to the product of 7 and x cubed
Answer:
7x³+8
Step-by-step explanation:
I'm guessing that you are looking for the equation
if we increase the objective function coefficient of both x and y, by $1, would the optimal solution change? explain your answer using the sensitivity report.
Yes, increasing the objective function coefficient of both x and y by 1 would change the optimal solution.
In a sensitivity report, the objective function coefficients are represented by the "Objective Coefficients" row in the "Variable Cells" section. When you increase the objective function coefficient of a variable, it means that you place more importance or weight on that variable in the optimization problem. This can affect the optimal solution because it changes the relative importance of the variables and the trade-offs that the optimization algorithm needs to make in order to find the optimal solution.
For example, if you increase the objective function coefficient of both x and y, the optimization algorithm may prioritize increasing the values of x and y more in order to maximize or minimize the objective function. This could result in a different optimal solution compared to the original problem where the objective function coefficients were lower.
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A block of ice contains 40 three-ounce portions of shaved ice. A food truck owner wants to use the block of ice to make as many spheres of ice as possible, each weighing 18 lb. How many spheres can she make?
The maximum number of spheres that can be made through ice will be 135.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
As per the given,
Number of ice portions = 40
Weight of one ice portion = 3 ounce
Since, 1 lb = 16 ounce
3 ounce = 3/16 lb
Weight of 40 portion = 120/16 lb
The weight of one sphere of ice = 18 lb
Number of possible spheres = (120/16)/18
⇒ 120/16 x 18
⇒ 135 sphere
Hence "135 spheres are the most that can be produced by ice".
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A small gasoline shop engine develops 60 hp at 2000 rpm. At 2300 rpm its power output is increased by 15%. What actual horsepower does it produce at 2300 rpm? The engine produces___hp at 2300 rpm
Answer:
\(69\text{ hp}\)Explanation:
Here, we want to get the amount of horsepower produced by the engine at 2300 rpm
From the question, we have :
60 hp produced at 2000 rpm
At 2,300 rpm, there would be 15% increase in hp
Thus, at 2300 rpm, the hp would be:
\(\begin{gathered} 60\text{ + 15\% of 60} \\ 60\text{ + }\frac{15}{100}\times60 \\ \text{ = 60 + 9 = 69 hp} \end{gathered}\)Thus, this means that the engine produces 69 hp at 2300 rpm
An airline tracks the time an airplane is parked unloading and loading passengers. The line plot displays the amount of time a number of airplanes were parked on one day. If the total amount of time were divided equally among all the airplanes, how long would each airplane have been parked? Amount of Time Planes are Parked A. B. C. D.
Answer:
It was A 4/7
Step-by-step explanation:
i wish math would fly away into outer space and never return
The base of the window is 9 1/2 feet.
An equation to find the length of the base of the triangle is 34 = 17b/4.
The length of the base of the triangle is 8 inches.
How to calculate the area of a parallelogram?Mathematically, the area of a parallelogram can be calculated by using this formula:
Area of a parallelogram = b × h
Where:
b represents the base area of a parallelogram.h represents the height of a parallelogram.Substituting the given parameters into the area of a parallelogram formula, we have the following;
26 3/5 = b × 2 4/5
133/5 = 14b/5
70b = 665
b = 665/70
b = 9 1/2 feet.
Mathematically, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle = 1/2 × b × h
Where:
b represents the base area of a triangle.h represents the height of a triangle.34 = 1/2 × b × 17/2
34 = 17b/4
b = 8 inches.
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What is the area, in square feet, of the isosceles trapezoid below?
Answer:
A≈78.54
Step-by-step explanation:
A¹=7.7×6.6=50.82(area of rectangle inside)
16.1-7.7=8.4/2=4.2
A²=6.6×4.2=27.72(area of triangles)
A=50.82+27.72=78.54
a newsletter publisher believes that more than 51% of their readers own a personal computer. is there sufficient evidence at the 0.05 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
Answer: The null hypothesis for this scenario is that the proportion of readers who own a personal computer is 0.51 or less:
H0: p <= 0.51
The alternative hypothesis is that the proportion of readers who own a personal computer is greater than 0.51:
Ha: p > 0.51
To test this hypothesis, we would need to collect a random sample of readers and determine the proportion of readers who own a personal computer in the sample. We could then use a one-sample proportion test to determine whether the proportion in the sample is significantly different from the null hypothesis value of 0.51. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is sufficient evidence to substantiate the publisher's claim that more than 51% of their readers own a personal computer. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not sufficient evidence to substantiate the publisher's claim.
Step-by-step explanation:
anyone else’s brainly heating up their phone like crazy
Mine is not heating up I don't know about others
Quadrants on the coordinate plane Select the quadrant or axis where each ordered pair is located on a coordinate plane. Quadrant Quadrant II Quadrant III Quadrant IV I-axis y-axis (-9.-8) (1.0) (7.5.2 Stuck? Watch a video or use a hint. Report a problem
Answer:
lll
Step-by-step explanation:
What is the value of the expression below when x=5x=5?
8x+9
The value of the expression below when x=5x=5?
8x+9 is equal to \(7^{2}\) (or) 49.
Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)
The expression,
y = 8x + 9
If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:
So, we can substitute x = 5,
Then, y = 8 * 5 + 9
Calculate the product or quotient,
y = 40 + 9
Calculate the sum or difference,
y = 49
We can write alternative form,
y = \(7^{2}\)
Therefore,
Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.
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Solve by using the elimination method.
Sally spent $14.85 to buy 13 flowers. She bought lilies, which cost $1.25 each, and tulips, which cost $0.90 each. How many of each flower did Sally buy?
CAN SOMEONE HELP ME WITH THIS ONE PLEASE!!!!!!!
a = lilies
13 - a = tulips
We have: 1.25a + 0.90(13 - a) = 14.85
=> 1.25a + 11.7 -0.90a = 14.85
=> 0.35a = 14.85 - 11.7 = 3.15
=> a = 3.15 ÷ 0.35 = 9
=> She bought 9 lilies and 4 tulips
Is this proportional or not proportional?
Answer: it is proportional
Step-by-step explanation: Because the y and the x numbers equal are the same
Answer:
It is proportional
Step-by-step explanation:
Both x and y increases at a constant rate