[tex]16r^2s^2[/tex] as the product of power is written as [tex](4rs)^2[/tex]
How would you characterize a product's strength?The power of a product rule states that [tex](a^m)(a^n) = a^(m+n)[/tex], where "a" is the base, "m" is the exponent of the first term, and "n" is the exponent of the second term. This rule allows us to simplify expressions where multiple variables are being raised to a power and multiplied together by adding the exponents.
For example, [tex](a^2)(a^3) = a^(2+3) = a^5[/tex].
It is also important to remember that when we are using the power of a product rule, the bases must be the same. If we have different bases, we cannot use this rule.
For example, [tex](a^2)(b^3) = a^2 * b^3, not a^(2+3) = a^5[/tex].
Rewritten as power of product:
[tex]16r^2 s^2= 4*4*r*r*s*s\\16r^2s^2= 4^2*r^2*s^2\\16r^2s^2=(4rs)^2[/tex]
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 8
and AD 4, what is the length of AC ? (Note: the figure is not drawn to scale. )
The required length of the side AC of the given right triangle is 32 units.
What is the right triangle?A right triangle is a triangle with one right angle or two perpendicular sides.
It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle.
The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.
A triangle is referred to be a right triangle when one of the interior angles is 90 degrees or a right angle.
So, using the hypotenuse AC as the point of convergence for the right triangle ABC,
AB is 8 and AD is 2.
Verify whether the triangle ΔABD resembles ΔACB.
∠ BCA = ∠ DBA (90 - ∠ DBC)
∠ A = ∠ A
As a result, ΔABD and ΔACB share an AAS resemblance.
Utilize the similarity property to determine the length of AC.
AC/AB = AB/AD
x / 8 = 8 / 2
x = 32
Therefore, the required length of the side AC of the given right triangle is 32 units.
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Correct question:
Given a right triangle, ABC with altitude BD drawn to hypotenuse AC. If AB = 8 and AD = 2, what is the length of AC?
−8≤2−10
Can you please help me find it?
Answer:
-8 [tex]\leq[/tex] -8
Step-by-step explanation:
-8[tex]\leq[/tex]2-10
-8[tex]\leq[/tex]-8
Answer:
-8
Step-by-step explanation:
-8≤2-10
2-10 = -8
-8≤-8
2
The scores of seven people playing a card game are listed below.
56, 103, 114, 80, 141, 68, 150
What is the interquartile range of the scores?
OA. 35
OB. 73
O C. 102
OD. 94
Answer:
B. 73
Step-by-step explanation:
An explanation is in the picture if you need it.
Contradiction Club holds a yearly proof competition, with special unique prizes for first, second, third, and fourth place. If 16 students enter the competition this year, how many ways can these prizes be distributed among the students
A proof competition is held annually by Contradiction Club, with special prizes awarded for first, second, third, and fourth place. If 16 students participate in the competition this year, the awards can be allocated among the students in 120 different ways.
How many ways can five different prizes be distributed among five people?120 ways, The first person has a choice from 5 prizes, the second has a choice from 4 prizes, and so on. The awards can be awarded in 5 different ways, or 5 × 4 × 3 × 2 × 1 = 120 different ways. When each student is qualified for each reward, the number of ways that 5 prizes can be distributed to 8 students is. [tex]5^(8)``8^(5)``8xx5!``5 xx 8!`[/tex] You may clear your doubts and achieve good exam results with the help of step-by-step solutions provided by specialists.For the first reward, there are 8 options. There are then 7 options for the second prize. Furthermore, there are 6 options for the third prize. As a result, there are 336 ways: 8 × 7 × 6. ∴ Total ways = 4× 3 ×2 = 24 ways = 4!To learn more about Contradiction Club refer to :
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Can anyone help please
The graph of the following equation will be a Parabola. The y=1 will be the line of symmetry.
Which four types of parabolas are there?Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.
What distinguishes a hyperbola from a parabola?A set of points in a plane that are equally spaced apart from a directrix or focus are known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.
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28. Anael cut several boards to build a deck.
The boards must be 100 in. ± 0.25 in. Her
measurements of the boards after cutting
them are shown in the graph. Which boards,
if any, can she not use?
Anael can not use the fourth board measurement. This can be solved by using the concept of inch scale.
What is inch scale?A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.
Since the international yard was adopted in the 1950's and 1960's, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.
The question given here,
the first board measurement: [tex]99\frac{3}{4} =[/tex] 99 inch ± 0.75 inch
the second board measurement: [tex]99\frac{7}{8} =[/tex] 99 inch ± 0.875 inch
the third board measurement: [tex]100\frac{1}{6} =[/tex] 100 inch ± 0.16 inch
the fourth board measurement: [tex]100\frac{5}{16} =[/tex] 100 inch ± 0.3125 inch
the fifth board measurement: [tex]99\frac{13}{16} =[/tex] 99 inch ± 0.8125 inch
Thus, Anael can not use the fourth board measurement.
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Word Problems
1) Sandy has 22 books in her library. She bought several books at a yard
over the weekend. She now has 61 books in her library. How many be
did she buy at the yard sale?
) How many ink cartridges can you buy with 143 dollars if
one cartridge costs 11 dollars ?
) Melanie is baking a cake. The recipe calls for 6 cups of flour. She alre
4 cups. How many more cups does she need to add ?
Answer:
1) 39
2) 13
3) 2
Step-by-step explanation:
1) She had 22 books, she now has 61 books, so she bought 61-22 = 39 books at the yard sale.
2) 143/11 = 13
3) 6-4 = 2
how do i anser this question
The graph that is not a straight line does not represent a direct variation.
What is direct variation?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor.
Given are the graphs representing direct variation.
Direct variation is represented by the equation -
y = kx
The graphs representing the direct variation are straight lines. Since all the graphs are not given, any graph that is not a straight line does not represent a direct variation.
Therefore, the graph that is not a straight line does not represent a direct variation.
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Don’t know need help
I think that the answer would be 14
What are the values of sin cos and tan?
Step-by-step explanation:
bhshshssf just use some time and fouries and fouries and I don't have a car but who wants the French
The point (14, –3) and (–10, –3) fall on a particular line. What i it equation in lope-intercept form?
Its equation in the slope-intercept form will be y = -3 because the y coordinates of both points are equal.
Given points in terms of coordinates so let's try to understand what are coordinates.
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis(vertical) are the two axes that make up a coordinate plane. (Telling children that the x-axis crosses because "x" is a cross helps them remember which of these is which.)
We have total 4 coordinates
First Coordinate both x and y are positive.
Second Coordinate x is negative and y is positive.
Third Coordinate both x and y are negative.
Fourth Coordinate x is positive and y is negative.
Point A is (14, -3)
Point B is (-10, -3) both have the same y coordinate.
So line AB is parallel to the x-axis.
The formula for the equation in the slope-intercept formula is
y = mx + c.
m is the slope of the line and c is the intercept on the y-axis.
Line AB is parallel to the x-axis the equation is y = -3.
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12. Find T in the diagram, if R = 110° and S = 60°.
Answer:
∠T = 130°
Step-by-step explanation:
The figure we are given is a quadrilateral, a 4 sided shape.
There are many different types of quadrilaterals, such as a rhombus, rectangle, etc.
How will we know which quadrilateral the given figure is?
We will have to look at the given properties of the figure to find out.
We are given that there are two adjacent pairs of congruent sides.
RS = RU, and ST = UT.
Thus, the given quadrilateral is a kite.
Now that we know that the given figure is a kite, we can utilize a kite's angle properties to find out ∠T.
In a kite, the non-vertex angles (∠S and ∠U) are congruent.
If ∠S = 60°, then ∠U = 60°.
In a kite, the sum of the interior angles is 360°.
Hence:
∠R + ∠S + ∠T + ∠U = 360°
Therefore, we can substitute the angles we know into the equation and solve for ∠T.
∠R + ∠S + ∠T + ∠U = 360°
110 + 60 + ∠T + 60 = 360
110 + 120 + ∠T = 360
230 + ∠T = 360
∴ ∠T = 130°
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28.2, 27.22, 27.62 , 27.54 , 27.5 in Greatest to Least
Answer:
28.2, 27.63, 27.54, 27.5, 27.22
Answer: 28.2, 27.62,27.5,27.22
Step-by-step explanation:
What is represented by P ∨ Q?
The statement [tex]P\land Q[/tex] in Tautology is represented as P and Q , and the symbol "[tex]\land[/tex]" is called as AND operator .
What is Tautology ?
Tautology can be defined as a compound statement which always results in Truth value. It does not matter what individual part consists of, the result in tautology is always true.
AND Operator : The AND is represented by the symbol "[tex]\land[/tex]". When the 2 simple statements are used in forming the compound statement by using AND operator , then it is called as a conjunction of two statements .
The AND operator returns TRUE value only when both the statements P and Q are TRUE , if any one of the statement is FALSE , then it returns FALSE value .
The given question is incomplete , the complete question is
What is represented by [tex]P\land Q[/tex] in Tautology ?
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How do you call 2 angles with the sum of 90?
The two angles that have the sum of angles as 90° are called as Complementary Angles .
What are Complementary Angles ?
The two angles are said to be complimentary Angles when the sum of two angles is 90° .
In other words, we can say that if the measure of two angles add up to form a right angle, then these angles are called as Complementary Angles. We can also say that the two angles complement each other.
For Example : the angles having the measure of 30 degree and 60 degree can be called as Complimentary as their sum adds up to 90 degree .
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In 2017 the Hindu festival of Diwali occurred on Thursday, 19 October. What fraction of the year was this
The Diwali occurred on 0.408 or 40.8% of the year in 2017.
To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.
Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.
There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.
So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408
So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.
Therefore, Diwali occurred on 0.408 or 40.8%
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David invested $220 in an account paying an interest rate of 1. 7% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest ten dollars, would be in the account after 10 years?
David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.
Here we have been given that David invested $220.
The interest rate was 1.7%
Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.
There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula
Amount = Principal X eᵃˣ
where a = rate of interest/100
x = time
Therefore, we can say that
Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷
= $260.76707
rounding off to the nearest 10 dollars we get
= $260
Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.
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if you are traveling at 60 mph you will travel almost the length of a football field in how many seconds
Time taken to cross the field will be 3.36 seconds.
What does physics mean by speed?Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. There are four different types of speed. constant speed, varying speed, an average rate, instantaneous speed.
Solution,
Given,
speed=60 mph
length of football field=0.056 miles
time taken to cross it = distance/speed
time=0.056/60=0.00093 hour = 3.36 seconds.
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What is an example of ordered pair function?
An ordered pair function is a type of mathematical function that associates certain pairs of elements (called ordered pairs) with a single output. For example, the function f(x,y) = x+y associates the ordered pair (2,3) with the output 5.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions such as print(), etc. but you can also create your own functions. These functions are called user-defined functions.
This is because 2+3 = 5. Another example is the function f(x,y) = x×y,
which associates the ordered pair (3,4) with the output 12, since 3×4 = 12.
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In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 13 of all the ninth graders are paired with 25 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy
Answer:
13/25
I hope this is the correct answer.
Kourtney and Kayla are sisters who are taking the same classes this semester: MAT 003, CHM 131/3131A, and ACA 122. If kourtney earns a pee a P in MAT 003, a B in CHM 131A, and an A in ACA, then what will her GPA be?
A. 3. 5
B. 3. 2
C. 2. 58
D. 3. 8
the GPA for the current semester will be 3.5.
What is GPA?
A metric used to assess your performance throughout the course of your complete degree program is your grade point average.
The average grade point average (GPA) is a figure that represents your typical performance in classes over the course of a semester, term, or year. In line with how much you raise your overall grade point average over your time at the university, your typical GPA score will fluctuate (or, in some cases, how much you fall behind).
A pass grade is a P, an A is a grade of excellent performance worth 4 points per credit, and a B is a grade of good performance worth 3 points per credit. The grade averages do not take P grade into account.
MAT 003, CHM 131a, and ACA 122 each have three, one, and two credits. Thus, the final score is 3 + 1 + 1 = 5. P in MAT 003, B in CHM 131a, and A in ACA 122 are the grades she receives.
GPA can be calculated by
GPA = ( 3 × 1 + 4 × 1)/ 5
GPA = ( 3 + 4)/ 5
GPA = 3.5
Hence the GPA for the current semester will be 3.5.
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If a_1=7a
1
=7 and a_n=a_{n-1}+5a
n
=a
n−1
+5 then find the value of a_5a
5
The final value of a_5 is 27a.
The equation a_n=a_{n-1}+5a is a recursive formula that gives the value of a_n in terms of the value of a_{n-1}. To find the value of a_5, we need to apply this formula repeatedly, starting with the given initial value of a_1=7a.
Using the recursive formula:
a_2 = a_1 + 5a = 7a + 5a = 12a
a_3 = a_2 + 5a = 12a + 5a = 17a
a_4 = a_3 + 5a = 17a + 5a = 22a
a_5 = a_4 + 5a = 22a + 5a = 27a
so a_5 = 27a
This is the final result and no need to calculate more.
Thus the final value of a_5 is 27a.
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Chris put $5,500 into a savings account that pays 5% interest compounded monthly. How much would be in his account after one month?
Answer:
$5,775
Step-by-step explanation:
The equation is:
A = P( 1 + rt)
We know
P = $5,500
r = 5% = 0.05
t = 1 month
Let's solve
A = 5,500( 1 + 0.05 x 1)
A = 5,500( 1.05)
A = $5,775
So, his account will be at $5,775 after one month.
What is the largest positive multiple of $12$ that is less than $350?$
Answer: 348
Step-by-step explanation: 12*29 = 348, which is the largest multiple less than 350.
Please hurry its timed
The correct option regarding the high tide and the low tide is given as follows:
B. high tide at 6 a.m. and 6 p.m., depth of 28 ft.
low tide at 12 midnight and 12 noon, depth of 20 ft.
What is the definition of the cosine function?The cosine function is defined as follows:
g(x) = acos(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.The amplitude for this problem is of 4, with a vertical shift of 24, hence the low and high tides are given as follows:
Low: -4 + 24 = 20 ft.High: 4 + 24 = 28 ft.The function is reflected over the x-axis, due to the multiplication by the negative number, hence the low tide is at midnight.
The period of the function is given as follows:
2π/(π/6) = 12 hours.
Thus the low tide also happens at noon, meaning that option B is correct.
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(m² - 7m - 11) ÷ (m-8)
By diving polynomials
Step 4: Calculating the right recipe for Jerome
Twenty-two people are running in tomorrow’s road race and Jerome thinks they will each want two cups of energy drink.
How many cups of energy drink does Jerome need to make?
Answer:
44
Step-by-step explanation:
If there are 22 people running and they each want two energy drinks, then Jerome needs to make 44 cups. 22 times 2 is 44
(2x+6y) exponent 2 with solution po thanks
Answer: (2x+6y)^2 = (2x+6y)(2x+6y) = 4x^2 +12xy + 12yx + 36y^2 = 4x^2 + 24xy + 36y^2
So the result of (2x+6y)^2 is 4x^2 + 24xy + 36y^2
At a coffee shop, the first 100
customers' orders were as follows.
Small
Medium
Large
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered a
hot drink given that he or she ordered a large?
P( Hot Large ) = [?]
Round to the nearest hundredth
Answer:
0.07
Step-by-step explanation:
lets make a chart first
small | medium | large
hot | 5 | 48 | 22
cold | 8 | 1 | 5
1. add all the hot drinks
5+48+22=75
2. find 5/75,
5/75=0.0666666
The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.
The total surface area of the hemisphere is 108 pi cm^2.
Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.
The surface area of a sphere with the radius r is 4 pi r^2
The surface area of a hemisphere with the radius r = 2 pi r^2 + pi r^2
where pi r^2 represents the area of the circular base of the hemisphere of radius r.
The surface area of a hemisphere sphere with the radius r is 3 pi r^2
For radius r=6cm
TSA of the hemisphere is 3 pi (6x6) cm^2
TSA = 108 pi cm^2
108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.
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