Answer:
1st & 4th answers are correct.
Step-by-step explanation:
-6 ( 2x + 5 )
Solve the brackets.
- 12x - 30
We can also write the answer like this.
Take -2 out of the brackets.
- 12x - 30 → -2 ( 6x + 15 )
Therefore, 1st & 4th answers are correct.
Which choice is equivalent to the quotient shown here when x > 0?
98x³+√72x²
O A. TV₂
OB. √26x
7x
O C. 7
6
OD. √98x3 - 72x²
Answer:
A.[tex] \frac{7}{6} \sqrt{x} [/tex]
Step-by-step explanation:
Solution Given:
[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]
Bye using indices formula
[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]
we get
[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]
[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]
[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]
[tex] \frac{7}{6} \sqrt{x} [/tex]
Which funtion has the same zeros as
==========================================================
The given graph have four zeros at x = -3 , 0 , 2 , 7
==========================================================
f(x) = x³ + x² -6x
The function f(x) is polynomial has degree = 3
so, it has only 3 zeros
==========================================================
g(x) = (x²+x-6)(x²-7x) ⇒ By factoring
⇒ By factoring
∴ g(x) = x(x-7)(x+3)(x-2)
∴ g(x) has zeros at x = -3 , 0 , 2 , 7
==========================================================
h(x) = x(x-7)(x+3)(x-2)
h(x) has zeros at x = -3 , 0 , 2 , 7
==========================================================
m(x) = (x³-4x²-21x)(x-2)
⇒ By factoring
∴ m(x) = x(x-7)(x+3)(x-2)
∴ m(x) has zeros at x = -3 , 0 , 2 , 7
==========================================================
n(x) = x²-9x+14
The function f(x) is polynomial has degree = 3
so, it has only 3 zeros
==========================================================
p(x) = x(x+2)(x-3)(x+7)
∴ p(x) has zeros at x = 3 , 0 , -2 , -7
==========================================================
By comparing zeros of the given graph to zeros of the functions
The result will be:
The functions that have the same zeros as the graph are
g(x) , h(x) and m(x)
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 414 gram setting. Based on a 8 bag sample where the mean is 407 grams and the standard deviation is 18, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
Question #2:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 26 samples is 4.6 ppm with a standard deviation of 1.2. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
A)
A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.
So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414
It is believed that the machine is underfilling the bags.
So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414
Given,
n= 8
Population standard deviation (б) = 18
x= 407
We will use the t-test since n > 8 and we are given the population standard deviation.
t=x-μ / (б/[tex]\sqrt{n-1}[/tex])
t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]
t= -1.028
Use the t table to find p value
p-value = 12.706
Level of significance α = 0.025
p-value>α
It is a two-tailed test.
So, we fail to reject the null hypothesis.
So, its bag-filling machine works correctly at the 414-gram setting.
B)
Let μ be the population mean amount of ozone in the upper atmosphere.
As per the given, we have
[tex]H_{0}[/tex] : μ = 4.8
[tex]H_{1}[/tex] : μ ≠ 4.8
Sample size: n= 26
Sample mean = 4.6
Standard deviation = 1.2
Since population standard deviation is now given, so we use a t-test.
t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]
t= -0.2/0.24
t= -0.833
It is a two-tailed test.
We are accepting the null hypothesis.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=630(1.06)^x
percentage rate increase by 206%
What is exponential growth?
An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.
Consider a population of mice that increases exponentially every year by a factor of two, starting with 2 in the first year and increasing to 4 in the second, 8 in the third, 16 in the fourth, and so on. The population is rising by a factor of 2 per year in this example. If mice gave birth to four pups instead, you would then have 4, 16, 64, and 256.
Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (which is raised to a power).
This equation represents exponential growth because the base is greater than 1, the function represents growth and Whenever the base is less than 1, the function represents decay.
The base 1.06 is greater than 1, hence The equation represents exponential growth.
The formula for exponential growth:
[tex]y=a(1+r)^{x}[/tex]
where,
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
In this case, [tex]r=1.06+1 = 2.06[/tex]
which represents percentage rate increase by 206%
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use the mean value theorem to verify that at some time during the first 3 seconds of fall the instataneous velocity equals the average velocity
Verified that during the first 3 seconds of fall the instantaneous velocity equals the average velocity, the time is 1.5 seconds
The height of an object t seconds after it is dropped from a height of 300 meters is
s(t) = -4.9t^2 + 300
The average velocity of object during first 3 seconds
= s(3) - s(0) / 3 - 0
s(3) = -4.9 × (3)^2 + 300
= -44.1 + 300
= 255.9 meters
s(0) = -4.9(0)^2 + 300
s(0) = 300
The average velocity = (255.9 - 300) / 3 - 0
= -44.1 / 3
= -14.7 meter per second
To find instantaneous velocity differentiate the function
= -9.8t
The instantaneous velocity = The average velocity
-9.8t = -14.7
t = -14.7/-9.8
t = 1.5 seconds
Therefore, time is 1.5 seconds
I have answered the question in general, as the given question is incomplete
The complete question is :
The height of an object t seconds after it is dropped from a height of 300 meters is s(t) = -4.9t^2 + 300.
(b) Use the Mean Value Theorem to verify that at some time during the first 3 seconds of fall, the instantaneous velocity equals the average velocity. Find that time.
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use proof by contraposition to show that for intergers m and n that if mn is even then m is even and n is even
In order for m n to be even, m must be even or n must be an even number.
Let's understood what is integers.
In mathematics, a collection of both positive and negative integers is referred to as an integer. Like whole numbers, integers do not contain a fractional portion. The definition of an integer is that a number that can be either positive, negative, or zero but is not a fraction. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Examples of integers include 1, 2, 5, 8, -9, and -12. "Z" stands for an integer.
Proof by contraposition:
Suppose that the statement m“ is even or is even n” is not true. Consequently, m and n should both be odd. Let's check to determine if the sum of two odd numbers is even or odd: Let m and n be equal to 2a+1 and 2b+1 respectively, then their product is:
(2a+1) (2b+1) = 4ab+2a+2b+1 =2(2ab+a+b) +1
This shows that the expression 2(2ab+a+b) +1 is of the form 2n+1, thus the product is odd. If the product of odd numbers is odd, then m n is not true to be even. Therefore, in order for m n to be even, m must be even, or n must be an even number.
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A group consisting of 28 aggressive zombies triples in size every hour. Which
equation matches the number of zombies after 7 hours?
Answer:196
Step-by-step explanation:
1 hour 15 minutes. is what in minutes
Answer:
75
Step-by-step explanation:
I hour and 15 minutes in minutes is 75 minutes
1 hour = 60 minutes
you add 15 and you get
60+15=75
The answer would be 75 Minutes.
1 Hour = 60 Minutes
[tex]60 + 15 = 75[/tex] Minutes.
let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
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Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie
Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) =
8100p
100 − p
(a) Is C(p) undefined at any p-value? If so, what value? (If an answer does not exist, enter DNE.)
p =
(b) What is the domain of C(p) as given by the equation? (Enter your answer using interval notation.)
(c) What is the domain of C(p) in the context of the application? (Enter your answer using interval notation.)
(d) What happens to the cost as the percent of pollution removed approaches 100%?
The cost increases (bounded by 8100) as p increases.
The cost decreases (bounded by 0) as p increases.
The cost decreases without bound as p increases.
The cost increases without bound as p increases.
The cost remains constant a
(a) C(p) is not defined since we can't divide by 0.
(b) The domain of C(p) as given by the equation is (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is [0, 100)
(d) The percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100
Here we have given that Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) = 8100p / (100 − p)
And we need to find the following.
(a) In general ma the we know that dividing by zero is not possible one.
Therefore, C(p) is undefined when we try to divide it by 0.
(b) The domain of C(p) is the function is not defined at p =100 the domain would be written as,
=> D = (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is calculated as,
=> D = [0, 100)
Therefore, the percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100.
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Which of the following gives the correct matrix for this system of equations in reduced row echelon form? x1-3x2-x3 + 3x4 = 2 -xi-2x2-x3 +4x4 = 2 -2x1+4x2 +4x3 +4x4 =-3 12 5 14 100 17 5 18 001 14 1 -3 -1 32 0 -5 -2 74 00ー36-3 b) 1 0 0 -36 9 1 22 010 001_ -_ 1 22 -1 -3 1 3 2 d 0 1 0 0 0 22 -12 -7 1 0 0 0 e) 25 010 -5 0 0 6 -16 f O None of the above
The correct matrix for this system of equations in row reduced echelon form amongst the given options is none of the above.
The given system of equations to get the reduced row echelon form is:
x1 - 3x2 - x3 +3x4 = 2
-x1 - 2x2 - x3 +4x4 = 2
-2x1 + 4x2 + 4x3 +4x4 = -3
To get the reduced row echelon form we need to form the matrix:
[tex]\left[\begin{array}{ccccc}1&-3&-1&3&2\\-1&-2&-1&4&2\\-2&4&4&4&-3\end{array}\right][/tex]
Row reduced echelon form of a matrix is one in which the pivot points equal 1, go from top left to bottom right, there are 0's above and below each pivot point.
R2-R1:
[tex]\left[\begin{array}{ccccc}1&-3&-1&3&2\\-2&1&0&1&0\\-2&4&4&4&-3\end{array}\right][/tex]
R3-R2 then R2+2R1 then R1+R3 then R2+2R3 then R3-3R2
[tex]\left[\begin{array}{ccccc}1&0&3&6&-1\\0&1&6&13&-2\\0&0&-14&-36&3\\\end{array}\right]\\[/tex]
(-1/14)R3 then R2-6R3 then R1-3R3
[tex]\left[\begin{array}{ccccc}1&0&0&-12/7&-5/14\\0&1&0&-17/7&-5/7\\0&0&1&18/7&-3/14\\\end{array}\right]\\[/tex]
which is the reduced row echelon form of the given system of equations.
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Given h(x)=-5x-4 find h(3)
The value of the equation h(x) = -5x-4 is - 19 when h = (3).
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, the equation we have is:
h(x) = -5x-4
Now, solve the equation when h = (3)
h(x) = -5x-4
h(3) = -5(3) -4
h(3) = -15 - 4
h(3) = - 19
Therefore, the value of the equation h(x) = -5x-4 is - 19 when h = (3).
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What is it? I swear I have no idea
By using matrix, it can be calculated that:
[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
What is a matrix?The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.
In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.
Here,
[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]
[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
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A side of the triangle below has been extended to form an exterior angle of
132°. Find the value of x
Answer:
x = 15°
Step-by-step explanation:
⭐the exterior angle of a triangle is equal to the sum of the angles that is opposite of said exterior angle
Thus, to solve for x, we have to make an equation in regards of the exterior angle.
132° = x° + 117°
∴ 15 = x° . . . . subtract 117 from LHS and RHS
⭐if this response helped you, please mark it the "brainliest"!⭐
NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]
Apply the factorial rule to the numerator and denominator of the given rational factorial expression:
[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]
[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]
Answer:
[tex]\cfrac{1}{6n(6n+1)}[/tex]--------------------------------
We know that:
n! = 1·2·3·4·...·nTherefore:
(6n + 1)! = (6n - 1)!·6n·(6n + 1)Therefore:
[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex]-x+y≤-1
x + 2y ≥ 4
Graph the system of inequalities.
Answer:
Step-by-step explanation:
[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]
dark blue is the required region.
Can anyone solve I need help urgent thank you
Answer:
Step-by-step explanation:
3.14 x 3=9.42
The volume of a rectangular prism is 6,618.375 cm3. If the height is 13.25 cm and the length is 27 cm, what is the value of the width?
A: 18.125 cm
B: 18.5 cm
C: 18.75 cm
D: 18.86 cm
The value of width will be;
⇒ 18.5 cm
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.
Given that;
The volume of a rectangular prism = 6,618.375 cm³
The height is 13.25 cm and the length is 27 cm.
Now,
We know that,
The volume of rectangular prism = Length x Width x Height
Substitute all the values, we get;
⇒ 6,618.375 = 27 × x × 13.25
⇒ 6,618.375 / 357.75 = x
⇒ x = 18.5 cm
Thus, The value of width = 18.5 cm
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write an equation of a circle with a radius of 8 and a center of (3,-4)
Answer: [tex](x-3)^2+(y+4)^2=64[/tex]
Step-by-step explanation:
The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. h and k are the points of the center corresponding with x and y respectively. r is radius. All we have to do is plug the values in.
[tex](x-3)^2+(y-(-4))^2=8^2[/tex]
With our values plugged in, we can now simplify.
[tex](x-3)^2+(y+4)^2=64[/tex]
Therefore, our final equation is [tex](x-3)^2+(y+4)^2=64[/tex].
One hundred elk, each 1 year old, are introduced into a game preserve. The number N(t) alive after t years is predicted to be N(t)=100(0.9)^t
(a) Estimate the number alive after 7 years. (Round your answer to the nearest whole number.)
(b) What percentage of the herd dies each year?
a) The number alive after 7 years is given as follows: 48.
b) The percentage of herd that dies each year is of 10%.
What is the exponential function?The exponential function in the context of this problem is defined as follows:
N(t)=100(0.9)^t.
The parameters of the function are defined as follows:
The amount of herd alive after 7 years is found with the numeric value at t = 7, replacing the lone instance of t in the function by 7, hence:
N(7) = 100 x (0.9)^7 = 48.
(rounding to the nearest whole number).
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find the probability of rolling a five or six on six sided number cube
Answer:
non-violence and kindness with animals
Step-by-step explanation:
1. Using the stopping distance calculator and your internet browser complete the following table to compare stopping distances at various speeds.
2. You overhear your friend say “It is OK to go 10 mph over the speed limit.” Explain why your friend is wrong using your evidence from the table above to support your answer.
The stopping distance table and the analysis of the stopping distance are presented as follows;
1. The stopping distance calculator, an online tool, provides the stopping distance at a specified speed as presented in the table on the following sections.
2. Increasing the vehicle speed by 10 mph, increases the required stopping distance exponentially, which reduces the safety of driving
What is the stopping distance?The stopping distance is the distance traveled by a vehicle, which is the sum of the distance traveled during the reaction time and the distance traveled during braking (the braking distance)
The table in the question using a perception–reaction time of 2.5 seconds, and the online stopping distance calculator is completed as follows;
Speed (mph) [tex]{}[/tex] Speed (m/s) Stopping Distance (m)
60 mph [tex]{}[/tex] 26.82 m/s 119.55 m
50 mph [tex]{}[/tex] 22.35 m/s 92.34 m
40 mph [tex]{}[/tex] 17.88 m/s 68.05 m
30 mph [tex]{}[/tex] 13.41 m/s 46.665 m
20 mph [tex]{}[/tex] 8.94 m/s 28.197 m
10 mph [tex]{}[/tex] 4.47 m/s 12.642 m
2. The details from the above table indicates that as the speed increases, the stopping distance increases exponentially, such that increasing the speed by 10 mph increases the required stopping distance when the vehicle is moving at an already high speed, thereby reducing safety by increasing the speed by 10 mph.
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Karla is saving money to visit her relatives in Florida. It costs $1,000 for the plane ticket and $250 per night for the hotel. Using the function that represents the cost c based on the number of nights n Karla spends in Florida, how many nights can Karla stay in Florida if she saves $3,000?
Answer: 8 Nights
Step-by-step explanation:
Cost of a plane ticket to Florida(c) = $1000
cost at the hotel per night (n)
Amount left with Karla after spending on the flight ticket =
$3000-$1000= $2000
To find out how many nights she can stay we should divide the remaining amount she has with (n) = $2000/$250 = 8
Hence Karla can stay for 8 nights
Select all of the lines of reflection that will carry the rectangle back onto itself.
The lines that carry the rectangle onto itself are x = 0 and y = 1
How to determine the lines that carry the rectangle onto itself?The graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangular graph
The coordinates of one end of the graph are
(-3, 3) and (-3, -1)
Next, we calculate the midpoint of these ends
So, we have
Midpoint = 1/2(x₁ + x₂, y₁ + y₂)
Substitute the known values in the above equation, so, we have the following representation
Midpoint = 1/2(-3 + 3, -1 + 3)
Evaluate the like terms
Midpoint = 1/2(0, 2)
So, we have
Midpoint = (0, 1)
So, we have
x = 0 and y = 1
Hence, the reflection lines are x = 0 and y = 1
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and drop each item into the correct column. Order does not matter:
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
Line of transversal:
Any line that crosses two straight lines at different locations is known as a transversal.
Corresponding Angles:
When two parallel lines cross the third one, the angles that are in the same relative position at each junction are referred to as corresponding angles to one another
Alternate Interior Angles:
The alternative interior angles are those that are on the inner side of the parallel lines but on the opposing sides of the transversal.
Alternate Exterior Angles:
Alternate external angles are positioned on the opposing sides of the transversal and are always outside the two lines where the transversal intersects.
Consecutive Interior Angles:
The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles.
Here we have
Two parallel lines intersected and formed the angles, ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
By the given information,
∠1 and ∠ 5 are corresponding angles
∠4 and ∠ 7 are corresponding angles
∠3 and ∠5 are Alternate Interior Angles
∠2, and ∠7 are Alternate Exterior angles
∠1 and ∠ 8 are Alternative Exterior angles
∠3 and ∠ 6 are Consecutive Interior Angles
Therefore,
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) C 540 a 3.0, 4.0, LA = C = Solve triangle ABC. (If an answer does not exist,, enter DNE. Round your answers to one decimal place.) b 69 35, LA 72° C = C = a = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a 28, b = 39, c 29 LA = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) = 17, 13, c 22 a = LA= o Sketch the triangle 500 LA B 770 C = 270 c 270 50° 77 50° 770 270 A A A 770 50° 270 270 50° 77 C A Solve the triangle using the Law of Sines. (Round side lengths to the nearest integer.) a = b Sketch the triangle. 100° LA = 270, C=60 C 100° 60 100° 27 27° C 60 C C 270 60 100° 27 100° A 60 A Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.) a = b =
The measures of the lengths of the sides and angles of the triangles found using the law of cosines and the law of sines are presented as follows;
Question 1
∠A = 47.35°
∠B = 78.65°
c = 3.3
Question 2
∠B = 78.24°
∠C = 29.76°
a = 67.03
Question 3
∠A = 45.77°
∠B = 86.417°
∠C = 47.813°
Question 4
∠A = 36.15°
∠B = 60.48°
∠C = 93.37°
Question 5
a = 258.98
b = 327.41
∠C = 53°
Question 6
a = 34.11
b = 73.987
∠C = 53°
What is the law of cosines?The law of cosines is a relationship between two sides (b and c) and the included angle, (∠A) and the third side (a) of the triangle.
Mathematically; a² = b² + c² - 2·b·c·cos(A)
Question 1
The dimensions of the triangle ΔABC are;
a = 3.0, b = 4.0, ∠C = 54°
The law of cosines indicates that we get;
c² = b² + a² - 2·b·a·cos(∠C)
Therefore;
c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893
c ≈ √(10.893) ≈ 3.3The law of sines indicates that we get;
sin(54°)/3.3 = sin(∠A)/3.0
∠A = arcsine(3 × sin(54°)/3.3) ≈ 47.35°∠B = 180° - 54° - 47.35° ≈ 78.65°Question 2
b = 69, c = 35, ∠A = 72°
a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45
a ≈ √(4493.45) ≈ 67.03The law of sines indicates that we get;
sin(72°)/67.03 = sin(∠B)/69
∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°
∠B ≈ 78.24°∠C = 180° - 72° - 78.24° ≈ 29.76°
∠C ≈ 29.76°Question 3
a = 28, b = 39, c = 29
a² = b² + c² - 2·b·c·cos(A)
cos(A) = (a² - (b² + c²)) ÷ (2·b·c)
Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976
∠A = arccos(0.6976) ≈ 45.77°sin(45.77)/28 = sin(B)/39
sin(B) = 39 × sin(45.77)/28 ≈ 0.998
∠B = arcsine(0.998) ≈ 86.417°∠C = 180° - 45.77° - 86.417° = 47.813°Question 4
a = 13, b = 17, c = 22
cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807
∠A ≈ arccos(0.807) ≈ 36.15°sin(36.15)°/13 = sin(∠B)/17
sin(∠B) = 17 × sin(36.15)°/13
∠B =50.48° ∠C = 180° - 36.15° - 50.48° ≈ 93.37°Question 5
The parameters of the triangle are; ∠A = 50°, ∠B = 77°, c = 270
Please find attached the sketch of the triangle in the correct option created with MS Word
∠C = 180° - 50° - 77° = 53°a/sin(50°) = 270/sin(53°)
a = sin(50°) × 270/sin(53°) ≈ 258.98
a = 258.98b = sin(77°) × 270/sin(53°) ≈ 329.41
b ≈ 329.41Question 6
The parameters of the triangle are;
∠A = 27°, ∠B = 100°, c = 60
Please find attached the drawing of the correct triangle
∠C = 180° - 27° - 100° = 53°
∠C = 53°
60/sin(53°) = a/sin(27°)
a = sin(27°) × 60/sin(53°) ≈ 34.11
b = sin(100°) × 60/sin(53°) ≈ 73.987
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A function is shown in the table below:
What is the average rate of change of the function from X equals -7 to X equals 2?
A. -90/101
B. 101/90
C. -101/90
D. 90/101
The average rate of change of the given function from x equals -7 to x equals 2 is calculated as: B. 101/90.
How to Find the Average Rate of a Function for a Given Interval?If we are given a function, f(x), to find the average rate of change of the function within the interval from a to b, the formula to use is:
Average rate of change = f(b) - f(a) / b - a.
Given the table that represents function, we have the following:
a = -7
b = 2
f(a) = f(-7) = -2.7
f(b) = f(2) = 7.4
Plug in the values into the formula:
Average rate of change = (7.4 - (-2.7)) / (2 - (-7))
= (7.4 + 2.7) / 2 + 7)
= 10.1 / 9
= 101/90
Therefore, the average rate of change is: B. 101/90.
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10 -8 -6 -4
| 10+
8
67
-2
4.2
-2
-4-
-6
-8
-10
2
4 6 8 10
Write an equation for the graph, where y depends on x.
The equation of given graph is y = 2x + 6.
What is equation of line?
The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.
Given:
The graph of the line is given.
From graph we have to find the equation of line.
Let the graph passes through the points (0, 6) and (2, 10).
From these two points to find the slope.
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, [tex](x_1, y_1) = (0, 6), (x_2, y_2) = (2, 10)[/tex]
⇒ Slope = m = [tex]\frac{10-6}{2-0}= \frac{4}{2} = 2[/tex]
So, the slope is 2.
Now to find the equation of line.
Consider, the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 2, (x_1, y_1) = (0, 6)[/tex]
⇒
[tex]y-6=2(x-0)\\y-6=2x\\y=2x+6[/tex]
Hence, the equation of given graph is y = 2x + 6.
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If 24000 bricks of the same shape and size are required to build a wall of dimension 15m*6m*20m find the volume of each brick
The volume of each brick is 0.75m³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object. It is measured in cubic units.
A brick has a cuboidal shape. This means the volume of a cuboid is given as:
V = l×b×h
This means volume = area × height
The volume of the whole wall is calculated as:
15× 6× 20 = 18000m³
Since there are 24000 bricks needed for the wall. The volume of each brick is therefore calculated as:
V =18000/24000
= 0.75m³
Therefore the volume of each brick is 0.75m³
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