The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]
Here we have to determine the sign for exponential or radical expression
(-3m[tex]n^{5}[/tex])^4
Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]
Similarly
(-3m[tex]n^{5}[/tex])^4
= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]
Now using the exponent power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get
= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]
Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].
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The fraction n/12 is between 1/4 and 2/3. Write down all the possible values of n.
When the fraction n/12 is between 1/4 and 2/3, the possible values of n will be 4, 5, 6, and 7.
How to calculate the fraction?It should be noted that a fraction simply means a number that isn't whole. It can be illustrated as a/b where a is the numerator and b is the denominator.
It should be noted that 1/4 is equivalent to 3/12.
It should be noted that 2/3 is equivalent to 8/12.
Therefore, the values of n will be numbers between 3 and 8. They are 4, 5, 6, and 7.
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HELP!!
Write the slope-intercept form of the equation for each line.
The equation of the line in slope intercept form is y = -5 / 9x + 2 / 9
How to find the equation of a line in slope intercept form?The slope intercept form of the equation of a line can be represented as follows:
y = mx + b
where
m = slope of the lineb = y-interceptLet's find the slope using the points (4, -2)(-5, 3)
Hence,
m = y₂ - y₁ / x₂ - x₁
x₁ = 4
x₂ = -5
y₁ = - 2
y₂ = 3
m = 3 + 2 / -5 - 4
m = 5 / -9
m = - 5 / 9
Therefore, let's find the y-intercept using (4, -2).
-2 = - 5 / 9 (4) + b
-2 = - 20 / 9 + b
b = -2 + 20 / 9
b = -18 + 20/ 9
b = 2 / 9
Therefore, the equation is y = -5 / 9x + 2 / 9
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Fats, sugars, and proteins are important food molecules. What do these types of molecules have in common?
The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.
What are macronutrients?The many categories of macronutrients include proteins, lipids—also known as fats—carbohydrates, or sugars. These are the three primary nutrients that the body uses to function. This indicates that they are chemical substances that your cells use as a source of chemical energy and that you require in quite significant quantities. These nutrients also produce energy or calories. They are broken down into smaller components during digestion. Energy is derived from carbohydrates (glucose). After being broken down into fatty acids, fats are used for energy. Although it can be used as fuel, protein's primary function is in the synthesis of hormones, muscle, and other proteins.To know more about macronutrients visit:
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Answer:
They all have carbon atoms.
Step-by-step explanation:
what is 30/cos40° rounded to 1 d.p.
The value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.
How to round off any decimal number to one decimal place?
When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.
We have 30/cos40°
Value of 30/cos40° = 30/0.766044 = 39.162241 (cos40° = 0.766044)
Since the number in the hundredths place is 6, which is between 5 and 9, we would round the tenth decimal point up to 2.
Therefore, the value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.
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How can I solve this question
Answer:
x = 10
The interior angles measure 93°, 126°, 60°, and 81°.
Step-by-step explanation:
[tex]9x + 3 + 12x + 6 + 6x + 8x + 1 = 360[/tex]
[tex]35x + 10 = 360[/tex]
[tex]35x = 350[/tex]
[tex]x = 10[/tex]
9(10) + 3 = 90 + 3 = 93°
12(10) + 6 = 120 + 6 = 126°
6(10) = 60°
8(10) + 1 = 80 + 1 = 81°
Increase 270 by 20%
please help asap
Answer:
324
Step-by-step explanation:
20%-> 0.2
0.2(270)= 54
270+54=324
Answer:The answer is 324
Step-by-step explanation:20% of 270 is 54 so add 54 and 270 because you increase by 20 to get the answer
[tex]\rm\int_0^1 \frac{( {x}^ \varphi - 1 {)}^{2} }{ log {}^{2} (x) } dx\\[/tex]
I assume the natural logarithm, and not the base-10 log. Parameterize the integral as
[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]
Differentiate twice with respect to [tex]a[/tex].
[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]
[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]
Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].
[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]
[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]
[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]
Let [tex]a=\phi[/tex] to recover the original integral.
[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]
Using various properties of the golden ratio [tex]\phi[/tex], namely
[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]
[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]
[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]
we can simplify the result to
[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]
Estimate quotients. Convert decimal division expressions to fractional division expressions to create whole number
divisors. Compute the quotient using the division algorithm. Check your work with a calculator and your estimate.
1. Lisa purchased almonds for $3.50 per pound. She spent a total of $24.50. How many pounds of almonds did she
purchase?
After conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.
What are mathematical operations?A mathematical function known as an operation is one that converts zero or more discrete input values into discrete output values.Depending on how many operands there are, the operation's complexity changes.The four mathematical operations are transformational functions that change numerical inputs into numerical outputs (i.e., another number).These are addition, subtraction, division, and multiplication.So, pounds of Almonds Lisa purchased:
Almonds per pound costs: $3.50Lisa spends the total amount: $24.50Now, calculate the pounds of almonds Lisa purchased as follows:
24.50/3.50 = 7(Refer to the image attached below for calculation)
Therefore, after conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.
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The correct question is given below:
Lisa purchased almonds for $3.50 per pound. She spent a total of $24.50. How many pounds of almonds did she purchase?
2. Complete the table for the equation, and graph the equation. (4pts)
2x - y = - 3
If this trapezoid is
translation
moved through the
(x+3, y-2), what will the
coordinates of D' be?
D' = ([?], [ ])
The coordinates of D' are (4,0)
A Trapezoid is regarded as a quadrilateral that has only one pair of opposite sides that are said to be parallel.
The coordinates of the given trapezoid are:
A = (-6,2)
B = (-5,4)
C = (-2,4)
D = (1,2)
It is given that the trapezoid is moved to the points of (x+3, y-2) on the graph.
Now, consider A = (-6,2)
A' = (-6+3, 2-2)
A' = (-3,0)
Consider B = (-5,4)
B' = (-5+3, 4-2)
B' = (-2,2)
Consider C = (-2,4)
C' = (-2+3, 4-2)
C' = (1,2)
Consider D = (1,2)
D' = (1+3, 2-2)
D' = (4,0)
Therefore, D' has the coordinates (4,0)
Refer to the full question given in the following image.
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Charles meets with customers on a daily basis. He uses the function f(x) = 5| x - 8| + 20 to calculate how many dollars he charges, per hour, for his time. How much does Charles charge per hour if a customer hires him for 3 hours
Answer:
$45
Step-by-step explanation:
Charles meets with customers on a daily basis. He uses the function f(x) = 5| x - 8| + 20 to calculate how many dollars he charges, per hour, for his time. How much does Charles charge per hour if a customer hires him for 3 hours?
f(x) = 5| x - 8| + 20
solve for when x = 3
f(3) = 5| 3 - 8| + 20
f(3) = 5| -5| + 20
f(3) = 25 + 20
f(3) = 45
Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 55mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.
The rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other is 101.54 km per hour.
How to calculate the rate?Let l = distance further away at which they'll meet. This will be illustrated as:
l = ✓13² - ✓5²
= ✓169 - 25
= ✓144
= 13m
Assuming that each bus drives a constant 55mph. The passes towards each other will be:
= -(55 + 55)
= -110m/h
Therefore, h² + l² = b².
Differentiate
2hdh/dt + 2ldl/dt = 2bdb/dt
= 2 × 5 × 0+ 2 × 12 (-110)
= 3 × 13db/dt
= -101.54 m/h
The rate is 101.54 m/h.
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Solve the proportion. 7 42 = 1 w w=
When the given proportion is solved the value of w is calculated to be 6.
What is proportion?
A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.
When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.
for example 5/10 = 1/2, 5:10 = 1: 2
7:42 = 1 : w
[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]
[tex]\frac{1}6{} = \frac{1}{w}[/tex]w = 1 x 6
w = 6
When the given proportion is solved the value of w is calculated to be 6
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Which shows the integers in order from least to greatest?
a.20, 6, -2, -13
b. -2, 6, -13, 20
c..-13, -2, 6, 20
d.20, -13, 6, - 2
The integers that are in order from least to greatest will be C. -13, -2, 6, 20.
What is an integer?It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.
In this case, the numbers will be illustrated as thus:
The smallest number is -13.
The biggest number is 20.
Therefore, the arrangement is -13, -2, 6, 20.
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I need help......................................................................
Answer: The answer is D.
Step-by-step explanation: Because I use a graphing calculator
There are 8 students in the class in art club. If 40%of the class is in art club, how many students are in class in all?
Answer: 20 is the answer
Step-by-step explanation:
Answer: 20 students
Step-by-step explanation
40% of 20 can be written as 40% × 20.
= 40/100 × 20
= 8
For the rhombus below, solve for y
Notice that this set of angles is congruent
herefore,
[tex]y-60=56[/tex]Solving for y ,
[tex]\begin{gathered} y=56+60 \\ \rightarrow y=116 \end{gathered}[/tex]nswer: 116
The graph shows your distance from home while out on a walk. The next day, you jog the same route twice at a constant speed. The entire jog takes 1 hour. Compare your walk to your jog
Using proportions, it is found that your walk and jogging rates are given as follows:
Walking: 3.75 miles per hour.Jogging: 5 miles per hour.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations.
One example of application, in the context of this problem, is for the relation between velocity, distance and time, as velocity is distance divided by time, that is:
v = d/t.
From the graph, the walk takes 40 minutes = 2/3 of an hour, and you walk 1.25 x 2 = 2.50 miles, as you walk 1.25 miles and then you come back home, hence the rate is given as follows:
v = 2.50/(2/3) = 3 x 2.50/2 = 3.75 miles per hour.
For the jog, you jog the same distance twice in one hour, hence you jog 5 miles in one hour, and the rate is given as follows:
v = 5/1 = 5 miles per hour.
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Please help I’ll mark you as brainliest if correct!
Triangle MNP is dilated by a factor of 2 with a center of dilation at (0,0).
What are the new coordinates of point N?
A
(1, -1)
B
(-4, 4)
C
(4, 0)
D
(4, -4)
The new coordinates of the point N after the given dilation transformation is; (-2, 6)
What is the Dilation of the triangle?
From the attached image, we see the given triangle MNP. We see that it's coordinates are;
M(-1, -2)
N(0, 2)
O(2, -2)
Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.
Thus, triangle MNP will be dilated according to the rule (x,y), where point P is the center of dilation.
Given the coordinate N = (0, 2)
The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:
(x, y) = (2x - 2), (2x + 2)
Thus;
N = (0, 2) → N'(2(0) - 2), (2(2) + 2)
= N'(-2, 6)
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Find the value of x.
Answer:
x = 8
Step-by-step explanation:
You want to know the value of x in an expression for an angle measure at parallel lines.
Angles at a transversalWhere at transversal crosses parallel lines, all acute angles created are congruent, all obtuse angles created are congruent, and the acute angles are supplementary to the obtuse angles.
The angle marked 83° is acute. The angle marked (12x+1)° is obtuse, so these angles are supplementary:
83° +(12x +1)° = 180°
12x +84 = 180 . . . . . . . divide by ° and simplify
12x = 96 . . . . . . . . . . subtract 84
x = 8 . . . . . . . . . . . . divide by 12
The value of x is 8.
B ВaAbСLet c=12, and a=4.020. What is tan(A) in radians? Round to 3 decimal places.
Answer
Tan (A) = 0.109 radians
Explanation:
The figure given is a right angles triangle
Given that AB = c is the hypotenus
AC = b = adjacent
BC = a = opposite
Tan A can be calculated using SOH CAH TOA
Tan A = opposite / adjacent
Tan A = BC / AC
BC = a = 4.020
We need to find b uisng pythagoras theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 12^2=4.020^2+b^2 \\ 144=16.1604+b^2 \\ \text{Collect the like terms} \\ b^2\text{ = 144 - 16.1604} \\ b^2\text{ = 127.8396} \\ b\text{ = }\sqrt[]{127.8396} \\ b\text{ = 11.307} \end{gathered}[/tex]b = 11.307
Tan A = 4.020 / 11.307
Tan A = 0.3555
A = tan ^-1 (0.3555)
A = 19.570 degrees
Convert degrees to radian
since 1 pi = 180 degrees
x pi = 19.570
Cross multiply
19.570 * 1 = x * 180
x = 19.570 / 180
x = 0.109
Therefore, tan (A) is 0.109 radians
i need help with the 2 problems in this picture.
Answer:
5 degree Celsius
Explanation:
Using the formula for conversion included in the image attached, we have:
[tex]\begin{gathered} \frac{5(F-32)}{9}=C \\ F^{\circ}=41 \\ \frac{5(41-32)}{9}=C \\ \frac{5(9)}{9}=C \\ 5^=C^{\circ} \\ \\ \therefore41^{\circ}F=5^{\circ}C \end{gathered}[/tex]Therefore, 41 degrees Fahrenheit is equivalent to 5 degrees Celsius
1) Multiply. Write your answer in scientific notation.
60. (5 x 102)
Find the missing side. Round answer to the nearest tenth.46°X145.910.10 0 0 013.219.5
Given the rigth triangle, you have to determine the length of the missing side marked with an x.
To do so you have to apply the trigonometric functions, these are calculated as:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{\text{hypotenuse}} \\ \cos \theta=\frac{adjacent}{hypotenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]Where
θ is one of the inner angles of the triangle.
"opposite" indicates the opposite side to than angle
"adjacent" is the side in contact or next to the angle
and "hypotenuse" is the longest side of the triangle.
In this exercise we know the measure of the angle and the hypotenuse, the trigonometric function you have to use to determine the length of "x" is the Sine:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \text{opposite}=\sin \theta\cdot hypotenuse \end{gathered}[/tex]Replace with:=46º
hypotenuse=14
opposite=x
[tex]\begin{gathered} x=\sin 46\cdot14 \\ x=10.07\cong10.1 \end{gathered}[/tex]Correct option is b. 10.1
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In order to make a specific shade of green paint, a painter mixes 1/2 of a gallon of blue paint with 4/5 of a gallon of yellow paint. How many gallons of yellow paint are needed to mix with 3 gallons of blue paint?
To make a specific shade of green paint, 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
In the question ,
it is given that
to make a specific shade of green paint , the painter mixes 1/2 gallon of blue paint and 4/5 gallon of yellow paint .
so , the ratio of yellow paint to blue paint [tex]=\frac{\frac{4}{5} }{\frac{1}{2} }[/tex]
writing in the simplified form , we get
= 4/5 × 2/1
= 8/5
So, for the given specific shade of green , the ratio of yellow : blue paint will remain same ,
let the amount of yellow paint used to mix with 3 gallons of blue paint be x gallons .
[tex]\frac{8}{5} =\frac{x}{3}[/tex]
On simplifying
x = 24/5
x = 4.8
so yellow paint required is 4.8 gallons
Therefore , to make a specific shade of green paint , 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
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Which of the following is an equivalent expression of 15x2 +12x + 8?
27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)
The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.
If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.
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Solve ×^2-4×-5=?
Your Genius If You Answered This Correctly
Answer:
(x+1)(x-5)
Step-by-step explanation:
what are the account titles needed for statement of cash flows
A cash flow statement is divided into three sections: operating activities, investments, and financial activities.
What is cash flow?The net balance of money coming into and going out of a business at a particular period is referred to as cash flow. A firm constantly receives and expends cash. For instance, when a retailer buys merchandise, money leaves the company and goes to its suppliers.
According to question:
A cash flow statement is divided into three sections: operating activities, investments, and financial activities.
Operating activities: Cash flow activities that either produce income or keep track of the funds used to produce a good or service are referred to as operating activities. Inventory transactions, interest and tax payments, employee paychecks, and rent payments are all examples of operational business activity. This section does not cover any additional sources of cash flow, such as investments, debts, or dividends.
Investment activities: The cash flow statement's second column lists profits and losses resulting from investments in assets like property, plant, or equipment (PPE), demonstrating how the company's overall cash position has changed. Analysts look for changes on a cash flow statement when they want to determine the company's investment in PPE.
Financial activities: The cash flow between the company's owners and creditors is tracked in the third section of the cash flow statement. Transactions involving debt, stock, and dividends are all considered financial operations. In these transactions, the receipt of capital (from lenders or investors, for example) triggers the recording of incoming cash, and the payment of dividends triggers the recording of outgoing cash.
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