Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
\(\begin{gathered} a) \\ (10^2)\text{ }^{-3\text{ }}=\text{ 10}^{(\text{ 2 x -3 \rparen }}=\text{ 10}^{-6} \\ Hence\text{, \lparen10}^2)^{-3}=\text{ 10}^{-6} \end{gathered}\)\(\begin{gathered} b)\text{ } \\ (\text{ 3}^{-3})^2=\text{ 3}^{(-3\text{ x 2\rparen}}=3^{-6} \\ Hence,\text{ \lparen3}^{-3})^2=\text{ 3}^{-6} \end{gathered}\)\(\begin{gathered} \text{ c\rparen }3^{-5\text{ }}\times\text{ 4}^{-5}=\text{ \lparen3}\times\text{4 \rparen}^{-5}=\text{ \lparen12\rparen}^{-5} \\ Hence,\text{ 3}^{-5}\times\text{ 4}^{-5}=\text{ \lparen12\rparen}^{-5} \end{gathered}\)\(\begin{gathered} d) \\ 2^5\times\text{ 3}^{-5}=\text{ 2}^5\text{ x }\frac{1}{3^5}=\frac{2^5}{3^5}=\text{ \lparen}\frac{2}{3})^5 \\ Hence,\text{ 2}^5\text{ x 3}^{-5}=\text{ \lparen }\frac{2}{3})^5 \end{gathered}\)
Related Questions
how many solution does 5x - 1 = 10x -4 - 5 x + 3 have?
Answers
5x - 1 = 10x - 4 - 5x + 3
Combining like terms, we have:
5x - 1 = 5x - 1
Notice that the variables and coefficients on both sides of the equation are the same. This means that the equation is an identity, and any value of x will satisfy the equation. In other words, this equation has infinitely many solutions.
The volume of a tree stump can be modeled by considering it as a right cylinder. Lauren measures it’s height as 0.7ft and it’s radius as 20in find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary
Answers
The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.
To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:
Volume = π * r^2 * h
Given:
Radius (r) = 20 inches
Height (h) = 0.7 feet
First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:
Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches
Now, we can substitute the values into the volume formula:
Volume = π * (20 inches)^2 * 8.4 inches
Calculating the volume:
Volume = 3.14159 * (20 inches)^2 * 8.4 inches
≈ 3.14159 * 400 inches^2 * 8.4 inches
≈ 1005.3096 cubic inches
Rounding the volume to the nearest tenth:
Volume ≈ 1005.3 cubic inches
Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.
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PLEASE HELP ASAP 20 POINTS
Answers
The simplified form of the algebraic expressions 1, 2, 3, 4 and 5 are -2m-10, 3x + 11, 3²xy + 2z - 16, -7x - 11 and -m + 8 respectively
How to simplify algebraic expressions?An algebraic expression is defined as an expression that is made up of variables and numbers, along with algebraic operations such as addition, subtraction, etc.
Given:
1. -3+ 4m + (-7) -6m = -3 + 4m - 7 - 6m = -2m-10
2. 6x + (-1) - 3x + 12 = 6x - 1 - 3x + 12 = 3x + 11
3. 3xy + 2z - 16 + 6xy = 9xy + 2z - 16 = 3²xy + 2z - 16
4. 4x - 8+ 2x + (-3) - 5x = -4x - 8+ 2x -3 - 5x = -7x - 11
5. 3m² - m + 7 - 3m² + 1 = -m + 8
Therefore, the expressions 1,2,3,4 and 5 simplifies to -2m-10, 3x + 11, 3²xy + 2z - 16, -7x - 11 and -m + 8 respectively
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I don’t get this one but the question was something about finding the equation.
Answers
9514 1404 393
Answer:
y = -(x -3)^2 +2
Step-by-step explanation:
The vertex form of the equation for a parabola is ...
y = a(x -h)^2 +k
where the vertex is (h, k) and the value 'a' is a vertical scale factor.
The value of 'a' can be found by looking at the y-value of points ±1 either side of the vertex relative to the vertex. Here, the vertex y-value is +2 at x=3, and either side goes down 1 unit (to y=1) for 1 unit to the right or left. So, a = -1.
Using the values we've read from the graph for the vertex (h, k) = (3, 2) and the scale factor a = -1, we can write the equation as ...
y = -(x -3)^2 +2
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
What is the solution set of this inequality?
Answers
Answer:
(-3,1) U (3,8) is the right answer.
Wally wants to determine the height of a statue that casts a 94-inch shadow by comparing it to his own height and shadow length. If Wally, who is 69 inches tall, casts a shadow that is 47 inches in length, what is the height of the statue?
A.
159 inches
B.
117 inches
C.
138 inches
D.
64 inches
Answers
Answer: 138 inches
Step-by-step explanation:
We can use proportions here, let h = height of the statue
height/height = shadow/shadow
\(\frac{h}{69} = \frac{94}{47}\)
h/69 = 2
*69 (h/69 = 2) *69
h = 138 inches
What number is 24% of 100
Answers
The number, n which is 24% of 100 as required in the task content is; n = 0.24 × 100.
What number is 24% of 100 as in the task content?It follows that the required number is to be 24% of 100, hence, the number can be represented as follows;
24% of 100
= (24/100) × 100
= 0.24 × 100
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Determine whether each function is linear or nonlinear. Function Linear Nonlinear {(–1, 2), (0, 3), (1, 4), (2, 5)} Linear – {(–1, 2), (0, 3), (1, 4), (2, 5)} Nonlinear – {(–1, 2), (0, 3), (1, 4), (2, 5)} {(–3, 9), (–2, 4), (3, 9), (4, 16)} Linear – {(–3, 9), (–2, 4), (3, 9), (4, 16)} Nonlinear – {(–3, 9), (–2, 4), (3, 9), (4, 16)} y = –14x + 9 Linear – y = –14 x + 9 Nonlinear – y = –14 x + 9 y = x Linear – y = x Nonlinear – y = x
Answers
A. {(–1, 2), (0, 3), (1, 4), (2, 5)} → Non-linear function.
B. {(–3, 9), (–2, 4), (3, 9), (4, 16)} → Non-linear function.
C. y = –14x + 9 → Linear function
D. y = x → Linear function
What is a linear function?A linear function has a straight line as its graph. A linear function has the form shown below.
a + bx = y = f (x).
A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.
When the absolute value of the input value of the function is connected to more than 1 output value, then the function is linear else it is a non-linear function.
From the given choices;
A. {(–1, 2), (0, 3), (1, 4), (2, 5)}
Here, the absolute value of 1 is connected to more than one point, so non-linear function.
B. {(–3, 9), (–2, 4), (3, 9), (4, 16)}
Here, the absolute value of 3 is connected to more than one point, so non-linear function.
C. y = –14x + 9 is equivalent to the slope-intercept form of linear function y = ax + b.
D. y = x is a linear function.
Therefore, B and D are linear functions.
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giving brainliest for correct answer
Answers
Answer:
Option A 64/27 cm³
Step-by-step explanation:
Side of each cube=1/3 cm
Volume of a cube=side³=(1/3)³=1/27 cm³
Total no. of cubes in the prism=4*4*4=64 cubes
Volume of prism=Volume of 1 cube*Total no. of cubes
=(1/27)*64
=64/27 cm³
Hope this helps
Find the midpoint of the longest side of a triangle withvertices at W(0,0), X(5,0), and Y(0,-4).
Answers
Let's begin by identifying key information given to us:
\(\begin{gathered} W\mleft(0,0\mright),X\mleft(5,0\mright),Y(0,-4) \\ \\ \end{gathered}\)We will find the longest side as shown below:
\(\begin{gathered} WX=(5-0,0-0)=(5,0) \\ XY=(5-0,0--4)=(5,4) \\ WY=(0-0,0--4)=(0,4) \\ We\text{ will calculate using the formula:} \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_{wx}=\sqrt[]{(5-0)^2+(0-0)^2}=\sqrt[]{5^2+0^2}=\sqrt[]{25+0}=\sqrt[]{25} \\ d_{wx}=5 \\ \\ d_{xy}=\sqrt[]{(5-0)^2+(0--4)^2}=\sqrt[]{5^2+4^2}=\sqrt[]{25+16}=\sqrt[]{41} \\ d_{xy}=\sqrt[]{41} \\ \\ d_{wy}=\sqrt[]{(0-0)^2+(0--4)^2}=\sqrt[]{0^2+4^2}=\sqrt[]{0+16}=\sqrt[]{16} \\ d_{wy}=4 \end{gathered}\)Therefore, the longest side is XY. The midpoint of XY is given by:
\(\begin{gathered} Midpoint(XY)=(\frac{5+0}{2},\frac{0+4}{2}) \\ Midpoint(XY)=(\frac{5}{2},\frac{4}{2}) \\ Midpoint(XY)=(\frac{5}{2},2) \\ Midpoint(XY)=(2.5,2) \end{gathered}\)The midpoint is (2.5, 2)
which of the following angle measure combinations will form a triangle?
A. 47° degrees, 63 degrees, and 70 degrees
B. 160 degrees, 50 degrees, and 150 degrees
C. 90 degrees, 1 degrees, and 88 degrees
D. 182 degrees, 1 degrees, and 2 degrees
Answers
Emily is entering a bicycle race for charity. Her mother pledges $0.20 for every 0.5 mile she bikes. If Emily bikes 10 miles, how much will her mother donate?Emily is entering a bicycle race for charity. Her mother pledges $0.20 for every 0.5 mile she bikes. If Emily bikes 10 miles, how much will her mother donate?
Answers
Answer: $4
Step-by-step explanation:
In this situation let's set up a proportional relationship .
\(\frac{0.20}{x } = \frac{0.5}{10}\) Now solve by cross multiply
0.5x = 2 Divide both sides by 0.5
x = 4
This means that if Emily bikes 10 miles, her mother will donate $4.
Answer:
\(\$4\)
Step-by-step explanation:
Number of \(0.5\) miles in \(10\) miles = \(10\)÷\(0.5\)
= \(20\)
Amount of money donated = \(0.20\) × \(20\)
= 4
\(\therefore\) Emily's mother donated a total of \(\$4\) given that Emily biked for 10 miles.
Hope this helps :)
A triangle has a base length of 3ac2 and a height 2 centimeters more than the base length. Find the area of the triangle if a = 2 and c = 3.
Answers
The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.
We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.
(1/2) * Base * Height = Area
We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.
Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters
Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).
Using these values as a substitute in the formula, we obtain:
Area =\((1/2) * 54 * 56 = 1512\) square centimeters
centimetres square
It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.
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Sumita buys a set of earphones for £7.23. She pays with £10. How much change does she get?
Answers
Sumita get £2.77 amount in change for buys a set of earphones.
Since, We know that;
Subtraction in mathematics means that is taking something away from a group or number of objects.
And, When you subtract, what is left in the group becomes less.
We have to given that;
Sumita buys a set of earphones for £7.23.
And, She pays with the amount £10.
Since, When you subtract, what is left in the group becomes less.
Here, To find the amount to get amount of change.
Hence, We can formulate;
To find the change amount we can subtract cost of earphone from pay amount which she pay.
Thus, WE get;
The Change Amount getting by her is,
⇒ Amount = £10 - £7.23
⇒ Amount = £2.77
Therefore, We get;
⇒ Amount = £2.77
That is,
£2.77 amount in change for buys a set of earphones.
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Write the equation of the horizontal line that goes through the point (2, 4)
Answers
Answer:
y=2
Step-by-step explanation:
Help PLEASE PLEASE IMBEGGING
Answers
Answer:
last statement is correct.
Answer:
D is correct
Step-by-step explanation:
Brainliest would be appreciated
The function g is defined by the following rule.
g(x)=(1/5)^x
Find g(x) for each x-value in the table.
Answers
Answer:
\(g(-2) = 25\)
\(g(-1) = 5\)
\(g(0) = 1\)
\(g(1) = \frac{1}{5}\)
Step-by-step explanation:
Given
\(g(x) = \frac{1}{5}^x\)
Solving (a): When x = -2
This gives:
\(g(x) = \frac{1}{5}^{(-2)\)
\(g(x) = \frac{1}{5}^{-2\)
\(g(x) = 5^2\)
\(g(-2) = 25\)
Solving (b) When x = -1
This gives:
\(g(x) = \frac{1}{5}^{-1}\)
\(g(-1) = 5\)
When x = 0
This gives:
\(g(x) = \frac{1}{5}^0\)
\(g(0) = 1\)
When x = 1
This gives:
\(g(x) = \frac{1}{5}^1\)
\(g(1) = \frac{1}{5}\)
Which expressions are completely factored?
Select each correct answer.
Responses
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
Answers
The expressions that are completely factored are:
16a5−20a3=4a3(4a2−5) is correct.12a3+8a=4(3a3+2a) is correct.24a4+18=6(4a4+3) is correct.Why are they considered to be correct?The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.
For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.
Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).
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Answer:
16a^5−20a^3=4a^3(4a^2−5)
and
24a^4+18=6(4a^4+3)
Step-by-step explanation:
graph the line with the equation
Answers
Answer:
See graph below
Explanation:
Give the equation y = x+1
We are to graph the equation of the line
Get the x and y intercept of the line.
The x intercept occurs at where y = 0
Substitute and get the x intercept
0 = x+ 1
-x = 1
x= -1
Hence the x intercept is (-1, 0)
Get the y intercept.
When x = 0
y = 0+1
y = 1
Hence the y intercept is (0, 1)
The line therefore will pass through the coordinate (-1, 0) and (0, 1). This is as shown below;
Note that the line passes through point -1 and 1
Needing help
Giving points asap
Answers
Step-by-step explanation:
I just answered this. please look at your copy post.
PLEASE HELP AS SOON AS POSSIBLE
Find the quotient and explain the process and reasoning. 0 . 27 ÷ 0 . 03 =
Answers
Good luck
Solve -4(x + 1) - 3 = -3(x - 4).
1.-19
2.19
3.2
4.0
Answers
Answer:
(1) x=-19
Step-by-step explanation:
Let's solve your equation step-by-step.
−4(x+1)−3=−3(x−4)
what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
Suppose sam deposited 1000$ every month in the beginning for his retirement fund for 20 years at 5% compounded monthly. What is value of N
Answers
To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.
To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.
Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.
The formula to calculate the future value of a series of monthly deposits is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the investment,
P is the monthly deposit amount,
r is the monthly interest rate, and
n is the number of deposits.
In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.
By rearranging the formula, we can solve for n:
n = log((FV * r) / (P * r + FV)) / log(1 + r)
Plugging in the values, we get:
n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)
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consider the continuous random variable x, which has a uniform distribution over the interval from 40 to 44. the variance of x is approximately . a. 46 b. 1.333 c. 1.155 d. 0.333
Answers
Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.
The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:
Var(x) = (b-a)^2 / 12
For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:
Var(x) = (44 - 40)^2 / 12 = 1.155
Therefore, the variance of 'x' is approximately 1.155
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Help 20 points (show ur work)
There are 2 questions
Answers
The length of the trail is equal to 3mi and the selling price of the item is equal to $120.
RatioIn mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
In this question, we have to use the ratio given to determine the length of the trail.
Given that the ratio is 5in : 2mi, we have to convert the values to uniform units.
\(1mi = 63360in\\2mi = x\\x = 126720\)
The ratio is now 5in : 126720in
Given that on the map, the length is 7.5in
\(5 = 126720\\7.5 = x\\x = 190080in\)
Let's convert this into mi.
\(190080in = 3mi\)
The actual length of the trail is 3in.
b)
To find the selling price of the item, let's use the percentage given to do that.
discount = 40%actual price = $200We can find 40% of 200 and then subtract the value from 200.
\(40\% of 200 = 0.4 * 200 = 80\)
The discount price is $80 and we can find the selling price here.
\(selling price = actual price - discount price\\selling price = 200 - 80\\selling price = 120\)
The selling price of the item is $120
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Penny is the manager of a nursery for pre-school children.
She knows that the ratio of the number of adults to the number of children
must be 1:8
Penny has 56 children at the nursery.
Answers
Answer:
7 adults
Step-by-step explanation:
I'm assuming you need to know how many adults are needed for 56 children.
Use a ration to find your answer.
1 adult X adults
---------------- = ---------------
8 children 56 children
Cross multiply then solve for X.
8X = 56
X = 7
Which statement about the linear equation 3a + 1 over 3(6a −9) = 1 over 2(10a − 6) is true?
A
The equation has exactly one solution at a = 0.
B
The equation has an infinite number of solutions.
C
The equation has exactly one solution at a = 1.
D
The equation has no solutions.
Answers
The statement about the linear equation 3a + 1/3(6a −9) = 1/2(10a − 6) that is true is: "The equation has an infinite number of solutions." (Option B)
What is a linear equation?A linear equation is defined as an equation with a maximum of one degree. A nonlinear equation is one with a degree greater than or equal to two.
On the graph, a linear equation looks like a straight line. On the graph, a nonlinear equation creates a curve.
To justify the above answer, we state the linear equation above:
3a + 1/3(6a −9) = 1/2(10a − 6) ; Simplified by opening the brackets, we have
3a + 2a − 3 = 5a − 3; collecting like terms on the left side, we have
5a -3 = 5a -3
Because 5a -3 = 5a -3, the expression holds true regardless of what integer or value a represents. Hence, it has an infinite number of solutions.
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Using the present value approach, solve the following:
Tom has $100 in a bank account that pays a guaranteed 5% interest rate each year. How much would Tom have at the end of Year 3?
Answers
Answer:
Step-by-step explanation:
$100x0.5x1=$5
If x-3 is a factor of x4−3x3+kx+3, what is the value of k?
Answers
k = -1
ExplanationIf x-3 is a factor of x4−3x3+kx+3, what is the value of k?
1. The remainder theorem tells us that you get the same thing when you
substitute 3 into a polynomial as you get when you divide the polynomial
by x-3 and take only the remainder.
2. The factor theorem thell us that since x-3 is a factor of the polynomial
then if we divided the polynomial by x-3, the remainder would be 0.
Putting these two facts together we can see that if we substituted 3 into
the polynomial, we will get the same result as the remainder would be if we
divided the polynomial by x-3. And furthermore due to 2, that remainder must
be 0. So all we have to do is substitute 3 for x in the polynomial and set
it equal to 0.
So substituting 3 for x in x^4-3x^3+kx+3 gives
3^4-3(3)^3+k(3)+3
81-3(27)+3k+3
81-81+3k+3
3k+3
Setting 3k+3 = 0
3k = -3
k = -1
Now let's check to see if we are right. If we are then the polynomial
x4-3x3^+kx+3 becomes x4-3x3^-x+3. We will divide that
synthetically by x-3 to see if we get a 0 remainder. First we must
insert a +0x2^ term, and write it as x4^--3x3^+0x2^-x+3
3 | 1 -3 0 -1 3
| 3 0 0 -3
1 0 0 -1 0
Sure enough, we do get 0 for a remainder.
So k = -1 is correct.